a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.454 received september 10, 2019; revised november 12, 2019; accepted december 4, 2019. *corresponding author: hel_ca@petrochina.com 1 a new method for estimating the peak gas rate lei he*, yilin he, liangrong you, feng li, and fang zhang, research institute of exploration and development, changqing oilfield company, petrochina, beijing, china abstract every winter from november of the first year to march of the next year, gas consumption would roar. as a result, all gas fields will increase gas rate to meet the needs. traditionally, peak rate and rational rate are usually determined by methods such as pressure drop rate, rate transient analysis (rta), and numerical simulation. these approaches have been verified in the production, but they show flaws like heavy workload and poor time effectiveness. theoretical research indicates that a plot of the increment of gas rate and the pressure drop rate should be linear, when pseudo-steady state is reached. in consequence, based on numerical simulation, correlations of the increment of gas rate and pressure drop rate were developed respectively for a series of reservoir pressure and well types. field applications show that this method can not only process a huge batch of data in one time, but quickly estimate the rational and peak gas rate in real time. introduction changqing oilfield company provides fuel for more than 13 provinces and so it enjoys the reputation of the natural gas base in china. as a major block in changqing, it is vital to predict the rate during the peak gas supply period. however, after ten years of production since 1997, ever-decreasing pressure has caused great difficulties in maintaining plateau and meeting the needs of consumption in winter. conventional gas rate predicting methods include pressure drop rate (luo et al. 2008), rate transient analysis (blasingame et al. 1991; oghena 2012) and numerical simulation (li et al. 2004). but they show flaws like heavy workload and poor time effectiveness. therefore, this study aimed at establishing a quick and accurate way to predict peak gas rate. peak gas rate evaluation flow performance in pseudo steady state. theoretical research indicates that if a surrounded well produced at a constant flow rate, every cell pressure will decline with a constant rate when the effect of the outer boundary has been felt (figure 1). and this period of time is called the pseudo steady state (pss) which develops with a linear relationship of gas rate and reservoir pressure. field applications show that type i wells in jingbian gas field need 0.5 year to reach the sss, type ii wells 1 year and type ii wells 2.5 years. with ten years of producing history, most wells in the study area has reached the sss and so the relationship of gas rate and reservoir pressure can be widely established. mailto:hel_ca@petrochina.com 2 figure 1—pressure distribution under pseudo steady state. correlation of casing pressure and reservoir pressure. reservoir pressure is hard to get, but the casing pressure can be monitored with real time. as a result, this article developed a quick way to estimate reservoir pressure by casing pressure. first as shown in eq. 1, applying cullender-smith method (wang et al. 2011), bottom-hole-pressure can be obtained ∫ 𝑝 𝑍𝑇 ( 𝑝 𝑍𝑇 ) 2 + 1.324×10−18𝑓𝑞𝑠𝑐 2 𝑑5 𝑝𝑤𝑓 𝑝𝑡𝑓 𝑑𝑝 = ∫ 0.03415𝛾𝑔𝑑ℎ ℎ 0 ...……………….……………………..…………….(1) then with the bottom-hole-pressure, reservoir pressure could be abstained by solving the gas well inflow eq. 2 (wang et al. 2014) 𝑃𝑅 2 − 𝑃𝑤𝑓 2 = 𝐴𝑞 + 𝐵𝑞2.…….…………………………………………………………………………..(2) based on the above methods, reservoir pressures were calculated as shown in figure 2, which indicates the reservoir pressure and casing pressure yield a linear relationship. compared with real reservoir pressure, the average errors of this method is only about 3% (figure 3). figure 2—relationship of casing pressure reservoir pressure. 15 20 25 30 35 40 0 5 10 15 20 25 30 p e（ m p a ） pwh（mpa） pe linear 3 figure 3—errors of the calculating method. graphical correlation of pressure drop rate and increment of gas rate. base on the theoretical research and numerical simulation analysis, correlations of pressure drop rate as a function of increment of gas rate and reservoir pressure were established for three types of wells, respectively (figures 4 through 6). figure 4—correlation of pressure drop rate and increment of gas rate of type i well. figure 5—correlation of pressure drop rate and increment of gas rate of type ii well. 0 1 2 3 4 5 6 0 5 10 15 20 25 30 e r r o r s（ % ） pwh（mpa） 0.010 0.015 0.020 0.025 0.030 0.035 1 1.2 1.4 1.6 1.8 2 p re ss u re d ro p r at e (m p a/ d ) magnification of gas rate 27 mpa 24 mpa 21 mpa 18 mpa 15 mpa 12 mpa 0.005 0.010 0.015 0.020 0.025 0.030 1 1.2 1.4 1.6 1.8 2 p re ss u re d ro p r at e (m p a/ d ) magnification of gas rate 27 mpa 24 mpa 21 mpa 18 mpa 15 mpa 12 mpa 4 figure 6—correlation of pressure drop rate and increment of gas rate of type iii well. after determining the reservoir pressure, these graphic correlations can be used for peak gas rate evaluation quickly and massively. but fig. 6 shows that when reservoir pressure is less than 21 mpa, even tiny rate increase will cause huge casing pressure drop, then these wells are not qualified for peak gas production. field application in order to verify the graphic correlations, 22 wells in jingbian gas field were put into calculations and results show that errors of this method is only about 10%. well x-1 was selected for peak gas production on oct 12th, 2016. as shown in figure 7, with the reservoir pressure of 17.2 mpa, when gas rate increase 1.3 times, from 12×104m3/d to 15.3×104m3/d, casing pressure drop rate increases to 0.0188 mpa/d. and the graphic correlation (figure 8) indicates the rate increase corresponds to a pressure drop rate of 0.0179 mpa/d, which yield errors of 4.8%. well x-2 was selected for peak gas production on oct 6th, 2016. as shown in figure 9, with the reservoir pressure of 15.1 mpa, when gas rate increase 1.3 times, from 2.2×104m3/d to 2.8×104m3/d, casing pressure drop rate increase to 0.0113 mpa/d. the graphic correlation (figure 10) indicates the rate increase corresponds to a pressure drop rate of 0.0120 mpa/d, which yield errors of 5.8%. figure 7—well x-1 production history (i). 0.000 0.003 0.006 0.009 0.012 0.015 1 1.2 1.4 1.6 1.8 p re ss u re d ro p r at e (m p a/ d ) magnification of gas rate 30 mpa 27 mpa 24 mpa 21 mpa 0 4 8 12 16 20 2015/12/1 2016/3/1 2016/6/1 2016/9/1 2016/12/1 g a s ra te (1 0 4 m 3 ) 0 3 6 9 12 15 18 p re ss u re （ m p a） gas rate tubing pressure casing pressure 0.0188mpa/d magnification of ×1.3 5 figure 8—well x-1 gas rate evaluation chart (i). figure 9—well x-2 production history (ii). figure 10—well x-2 gas rate evaluation chart (ii). conclusions theoretical research shows that when pseudo steady state is reached, gas rate and pressure drop rate yield a linear relationship. base on the theoretical research and numerical simulation analysis, correlations of pressure drop rate as a function of increment of gas rate and reservoir pressure were established for three 0.010 0.015 0.020 0.025 0.030 0.035 1 1.2 1.4 1.6 1.8 2 p re ss u re d ro p r at e (m p a/ d ) magnification of gas rate 27 mpa 24 mpa 21 mpa 18 mpa 15 mpa 12 mpa 0.0179 mpa/d errors of 4.8% 0 1 2 3 4 2015/1/1 2015/6/1 2015/11/1 2016/4/1 2016/9/1 g a s ra te (1 0 4 m 3 ) 0 5 10 15 20 25 p re ss u re (m p a ) gas rate casing pressure tubing pressure 0.0113mpa/d magnification of ×1.25 0.005 0.010 0.015 0.020 0.025 0.030 1 1.2 1.4 1.6 1.8 2 p re ss u re d ro p r at e (m p a/ d ) magnification of gas rate 27 mpa 24 mpa 21 mpa 18 mpa 15 mpa 12 mpa 0.012 mpa/d errors of 5.8% 6 types of wells, respectively. these graphic correlations not only can process a huge batch of data in one time, but quickly estimate the peak gas rate in real time. field applications show that the errors of this method are less than 10%. conflicts of interest the author(s) declare that they have no conflicting interests. references blasingame, t. a., mccray, t. l., and lee, w. j. 1991. decline curve analysis for variable pressure drop/variable flow rate systems. paper spe-21513-ms presented at spe gas technology symposium, houston, usa, 22-24 january. li, y., chen, j., zhang, l., et al. 2004. new model of numeral simulation for development of gas reservoirs with low permeability. natural gas industry 24(8):65-68. luo, w., tang, h., wang, x., et al. 2008. application of pressure-drop method to sebei-1 gas field. oil & gas geology 29(1):84-87. oghena, a. 2012. pressure drawdown decline curve analysis. paper spe-150906-ms presented at north africa technical conference and exhibition, cairo, egypt, 20-22 february. wang, l., peng, c., ni, x., et al. 2011. optimal for calculating method about bottom-hole pressure of gas well. well testing 20(4):25-26. wang, c., li, z., and lai, f. 2014. a novel binomial deliverability equation for fractured gas well considering non-darcy effects. journal of natural gas science and engineering 20(9):27-37. he lei is a senior engineer engaged in research institute of exploration and development, changqing oilfield company, petrochina. he mainly focuses on dynamic monitoring of gas filed and numerical simulation. yilin he is a senior engineer engaged in research institute of exploration and development, changqing oilfield company, petrochina. yilin he specializes in production analysis and numerical simulation of unconventional gas reservoirs. liangrong you is a senior engineer of research institute of exploration and development, changqing oilfield company, petrochina. liangrong you specializes in dynamic monitoring of unconventional gas reservoirs. feng li is a senior engineer engaged in research institute of exploration and development, changqing oilfield company, petrochina. feng li mainly focuses on dynamic monitoring of gas filed and numerical simulation. fang zhang is a senior engineer engaged in research institute of exploration and development, changqing oilfield company, petrochina. fang zhang mainly focuses on dynamic monitoring of gas filed and production analysis of tight gas reservoirs. a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.457 received september 5, 2019; revised november 2, 2019; accepted january 13, 2020. *corresponding author: 278142801@qq.com 1 application of numerical well testing in strong anisotropic sandstone gas field yanyan sun*, jiwu fan, zhenpingxu, and zhichao li, changqing oilfield, petrochina, xi’an, china abstract sulige gas field in the ordos basin, a typical tight sandstone gas field with great heterogeneity, has difficulties in its development because its reservoirs are featured by small-scale effective sandbodies, rapid changes, strong horizontal heterogeneity, and poor connectivity. analytical well testing widely used in sulige gas field has limitations. numerical well testing, which provides a way of tuning a static model with dynamic well testing information, can more accurately estimate reservoir parameters and wellbore effects, and improve the understanding of different types of gas seepage theory. this study compared the difference between numerical well testing and analytical well testing, and summarized the key points of numerical well testing analysis technology, formed technical ideas of numerical well testing, proposed an interpretation workflow on the typical numerical well testing, and estimated the distribution of the main parameters, such as effective permeability reservoir, fracture halflength, and fracture conductivity, and so on. the interpretation results from various vertical and horizontal wells can deepen the understanding of reservoir and provide valuable technical support for stable gas production. introduction sulige gas field in the ordos basin, a typical tight sandstone gas field with great heterogeneity, has difficulties in its development because its reservoirs are featured by small-scale effective sand bodies, rapid changes, strong plane heterogeneity, and poor connectivity. it plays a crucial role on stabilizing gas production. well testing can deepen the understanding of reservoir and reduce the uncertainty of estimates. currently, analytical well testing widely applied in sulige gas field has limitations, mainly manifested in three aspects: (1) analytical well testing of reservoir heterogeneity is simplified to the radial composite or linear composite, which is difficult to effectively depict gas field in a complex geological condition and the characteristic of the strong heterogeneity of the reservoir; (2) analytical well testing is derived by solving a second order partial deferential diffusivity equation. uncertainty is resulted from the inverse nature of the problem. in general, ideal assumptions are made in order to solve a mathematical model. this results in the limit of its practical application. analytical solution usually can be derived when a mathematical model is ideal. non-ideal case (real case) is analysed using solutions derived from ideal model. engineers use analytical model and solutions (type curves) for well test analysis. the final results are verified by matching analytical solution with measured pressure data. assumptions made are ignored while perusing “perfect match” during the analysis. results derived by such an approach are misleading. well testing-a very useful engineering dynamic measurement itself is flawed due to this practice (zheng 2006). numerical well testing has significant advantages over analytical well testing that assume constant reservoir and fluid properties. by contrast, numerical well testing can handle multiphase flow and stress2 dependant reservoir properties, and relative permeability functions to handle complex problems (deng et al. 2011). thus, numerical well testing can more accurately estimate reservoir properties and wellbore effects, and provide valuable technical support for stable gas production. the difference between numerical well testing and analytical well testing the difference between numerical well testing and analytical well testing is that fluid seepage equation in the porous media are solved by different methods. seepage equation of analytical well testing is solved by means of analytic expression. however, for numerical well testing, seepage equation is solved by numerical methods and various parameters are calculated in each grid node. therefore, numerical well testing can be more widely adapted to detailed requirements of actual field applications. in other words, numerical well testing can overcome almost all the actual problems in analytical well testing, including different permeability, porosity, formation thickness, and fluid saturation at an arbitrary point of the formation, the influence of the reservoir rock stress, the special problems of unconventional reservoirs and multiple well productions, and the effect of interference and irregular internal and external boundary problems, et al. numerical well testing technical ideas interpretation of numerical well testing is a technology based on unstructured mesh technology on the complex seepage area. it applies numerical discrete methods to solve the fluid seepage equation, and then determines reservoir parameters, reservoir limits, and wellbore effects (skin and storage) by fitting the measured bottom-hole-pressure and production (li 2000; zhuang 2004; liu 2008). figure 1 illustrates the key steps of a numerical well test. first, reservoir numerical model is established by referring the effective thickness, porosity and permeability of geological information. then, the initial value of the fitting parameters is got by analytic method for numerical well testing interpretation model. the fitting parameters and reservoir numerical parameters are adjusted by validation of production dynamic data to establish numerical well testing model. figure 1—numerical well testing technology. establishing the numerical well testing model not only can accurately characterize heterogeneity of the reservoir, including reservoir thickness, porosity, permeability, boundaries, skin factor, and wellbore storage, but also visually display pressure distribution dynamically. key technical points of numerical well testing feature recognition of different types of well testing models is the key. sulige gas field is a typical tight gas reservoir. it needs horizontal drilling and hydraulic fracturing to improve well performance. thus, it is critical to establish typical curves of unsteady well test based on theoretical study on fractured vertical 3 wells and horizontal wells (wang et al. 2013; qi et al. 2007; yang et al. 2010; wu et al. 2010), as shown in figure 2 and 3. figure 2—typical curves of fractured vertical well. figure 3—typical curves of fractured horizontal well. permeability heterogeneity has strong effect on the shape of pressure drop curve and pressure derivative curve at the end of the effect of wellbore storage and skin, as shown in figure 4 and 5. 4 figure 4—reservoir permeability distribution. figure 5—influence of heterogeneity of permeability on well test curve. typical wells numerical well test analysis workflow take sua-b-ch2 well as an example. first, we obtained the average reservoir parameters with analytical well testing technique. interpretation results are shown in table 1 and figure 6. then, we drew the effective sandbodies isopach map (figure 7). 5 table 1—analytical well test interpretation results of sua-b-ch2 well. parameters value well model 5 stage fractured horizontal well reservoir model homogeneous reservoir + infinite boundary c (cm3/mpa) 5.39 s -7.11 kh(md.m) 3.8 k (md) 0.38 pi (mpa) 23.25 hw (m) 331 xf (m) 30.5 fc (md.m) 274 1e-3 0.01 0.1 1 10 time [day] 100 1000 10000 g as p ot en tia l [ m m pa 2/ cp ] figure 6—log-log curves of analytical well test of sua-b-ch2 well. figure 7—distribution of effective thickness around sua-b-ch2 well. next, porosity logging data from adjacent wells was used to determine the porosity distribution around sua-b-ch2 well which is shown in table 2 and figure 8. 6 table 2—porosity statistics of sua-b-ch2 adjacent wells. well name porosity (%) well name porosity (%) sua-b-13a 7.2 sua-d-9 6.6 sua-c-9 6.9 sua-d-10 9.0 sua-c-10 9.5 sua-d-10h1 8.4 sua-c-12 9.3 sua-d-11 9.3 sua-c-13 7.1 sua-d-12 10.8 sua-d-13 10.9 figure 8—porosity distribution of sua-b-ch2 wells. based on the analytical solution and geological information constraints, permeability distribution of formation was obtained by fitting the well test data (figure 9). figure 9—numerical model of permeability distribution of sua-b-ch2 well. interpretation and fitting results by numerical well test are shown in table 3 and figure 10, respectively. 7 table 3—numerical well test interpretation results of sua-b-ch2 well. parameters value well model numerical model c (cm3/mpa) 4.39 s 0.11 k (md) 0.511 pi (mpa) 24.5 hw (m) 331 xf (m) 30.5 1e-3 0.01 0.1 1 10 time [day] 100 1000 10000 g as p ot en tia l [ m m pa 2/ cp ] figure 10—log-log curves of numerical well test of sua-b-ch2 well. the results of numerical well test interpretation interpretation results of statistics vertical numerical well testing. statistics of parameters estimates from 19 vertical wells are shown in figure 11 through 13. effective permeability of reservoir is 0.03-0.74 md, with a mean of 0.22 md. fracture half-length is between 11.6 m and 228.4 m, with a mean of 71.1 m. fracture conductivity is from 101 to 301 md.m, mean is 167 md.m. figure 11—cumulative frequency distribution of vertical wells permeability. 8 figure 12—cumulative frequency distribution of fracture half-length of vertical well. figure 13—cumulative frequency distribution of fracture conductivity of vertical wells. the horizontal well numerical well test interpretation results of statistics. statistics of parameters estimates from 18 horizontal wells are shown in figure 14 through 16. effective permeability reservoir is 0.02-0.94 md, with a mean of 0.295 md. fracture half-length ranges from 22 to 197 m, with a mean of 65.8 m. fracture diverting capacity is 26.5-498 md, with a mean of 179 md. figure 14—cumulative frequency distribution of horizontal wells permeability. 9 figure 15—cumulative frequency distribution of horizontal well fracture half length. figure 16—cumulative frequency distribution of horizontal well fracture conductivity range. conclusions compared with the analytical well test, the numerical well test can obtain the reservoir and wellbore information more accurately, and the application effect of the numerical well test is better in the tight and strong heterogeneous sandstone gas field. conflicts of interest the author(s) declare that they have no conflicting interests. references deng, h., bao, x., chen, z., et al. 2011. numerical well testing using unstructured pebi grids. paper presented at spe middle east unconventional gas conference and exhibition, muscat, oman. 31 january-2 february. spe-142258-ms. li, s. 2000. gas engineering. beijing, china: petroleum industry press. liu, n. 2008. practical modern well testing interpretation method. beijing, china: petroleum industry press. qi, e., hong, h., tian, w., et al. 2007. application of numerical well test analysis in complex gas wells. natural gas industry 27(5): 97-99. 10 wang, b., jia, y., li, y. et al. 2013. a new solution of well test model for multistage fractured wells. acta petrlolei sinica 34(6): 1150-1156. wu, m., yao, j., jia, w., et al. 2010. streamline numerical well-testing interpretation model for horizontal wells and its application. xinjiang petroleum geology 31(4):408-412. yang, l., chang, z., zhu, z., et al. 2010. application of numerical well test in development of kela 2 gas field. natural gas geoscience 21(1):163-167. zheng, s. 2006. fighting against non-unique solution problems in heterogeneous reservoir through numerical well testing. paper presented at spe asia pacific oil & gas conference and exhibition, adelaide, australia. 11-13 september. spe-100951-ms. zhuang, h. 2004. gas reservoir dynamic description and well testing. beijing, china: petroleum industry press. yanyan sun has worked as a reservoir engineer at research institution of petroleum exploration and development, changqing oilfield, petrochina, for the last 12 years. his research interests are in dynamic analysis for low permeability gas reservoir. he holds a bachelor degree in resources exploration from chengdu university of technology. jiwu fan is a senior reservoir engineer at research institution of petroleum exploration and development, changqing oilfield, petrochina. his research interests are in dynamic analysis for low permeability gas reservoir. he holds a bachelor degree in mathematics from jilin university. zhenping xu is a reservoir engineer at research institution of petroleum exploration and development, changqing oilfield, petrochina, where she has worked for the last 7 years. her research interests are in well testing for low permeability gas reservoir. she holds a master degree in field development from southwest petroleum university. zhichao li is a reservoir engineer research institution of petroleum exploration and development, changqing oilfield, petrochina, where he has worked for the last 9 years. his research interests are in development geology for low permeability gas reservoir. he holds a bachelor degree in resources exploration from xi'an shiyou university. abstract introduction the difference between numerical well testing and numerical well testing technical ideas key technical points of numerical well testing typical wells numerical well test analysis workflo the results of numerical well test interpretation conclusions conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1190 received april 15, 2021; revised july 12, 2021; accepted august 12, 2021. *corresponding author: minh.vo@chevron.com 1 using machine learning techniques for enhancing production forecast in north malay basin truc (trevor) doan, bear and brook consulting, brisbane, australia; and minh van vo*, chevron unocal east china sea ltd., chengdu, china abstract the geological environment in the gulf of thailand (got) is very complicated, with thousands of small discontinuous reservoirs, in part due to a high density of faults. with this geological characteristic, hundreds of required slim-hole wells will be planned and drilled annually to ensure enough capacity to meet gas demand in gas sale agreement. hence, production forecast plays key role to deal with drilling schedule and operations planning and installing surface facilities. an accuracy degree of production forecast is required highly based on production data from existing produced wells and future produced wells. in recent years, machine learning techniques have been widely applied to the oil and gas industry, in this case, the gulf of thailand. machine learning methods of support vector regression (svr) and kmeans clustering have been applied effectively for removing outliers or noisy data. by using a huge dataset of production data from thousands of wells in this area, a solution can be rapidly made to automatically eliminate unreliable data in given historical data from existing produced wells. in brief, this study provides an automated approach to apply machine learning algorithms to assist technical teams in improving the quality of data in production data analysis, with the aim of enhancing reliable production forecast, optimizing drilling schedule and saving operating costs. introduction a several thousands of wells have been drilled with slim-hole well technologies and the commingle production strategy has been used in north malay basin since the early 1980s. for a typical well in this area, with an average of 10 pay sands, the reservoir properties of each individual sand tend to vary by depth and by location. figure 1 is used as an excellent illustration for a drilling program with a complex subsurface picture, which includes many small and discontinuous gas reservoirs in the high density of faults (pinto et al. 2004). production forecast plays a critical role to provide production throughput information that can be used for facilities capacity design, drilling sequence/schedule, and then economic evaluation during development of a field development plan fdp. therefore, a reliable degree of production forecast is highly required, which is based on historical production data from both the existing producing wells and future producing wells. figure 2 explains how importance of the production forecast in scheduling drilling projects (doan and vo 2019a). 2 figure 1—reservoir structure and complexity in the north malay basin. figure 2—an illustration of drilling project timeline and number of rig allocation schedule. in recent years, machine learning techniques have been widely applied in the oil and gas industry, and in this case, the north malay basin in the gulf of thailand got. machine learning methods of support vector regression (svr) and k-means clustering have effectively been applied for removing outliers or noisy data. by applying the machine learning techniques, the production forecast can be enhanced with the high quality of forecasting in short term and long term. with geological characteristics in north malay basin, hundreds of wells are annually required to drill to ensure enough capability to meet the market gas demand (figure 3). time was known to be the top priority because any delay or failure to deliver gas to gas buyers would make a financial loss to the company and its partners. hence, a robust solution to improve production forecast is very necessary to develop oil and gas in this geological environment. figure 3—example with multiple wells drilled in the north malay basin. 3 methodology the methodology is developed which mainly integrates the machine learning-based techniques with the approach of decline curve analysis approach from a huge dataset of the existing produced wells. in production operation, measured data are frequently contaminated with anomalies (noise or outliers) that can be generated internally from the measurement device or come in from external sources. in particular, the solution will be built to automatically eliminate unreliable data points in given historical production data by using machine learning methods and then to estimate remaining hydrocarbon reserves and predict production performance by using the decline curve analysis. decline curve analysis the approach of decline curve analysis (dca) is used to generate production profiles and to allocate gas rate from every single well/platform to meet the gas sales contract requirements. this approach is very powerful in estimating ultimate gas recoveries and in predicting field development performance from the analysis of long-term gas production data, either from individual wells or from entire fields. it is proper when large uncertainty limits the data to justify a complex reservoir simulation. figure 4 below describes the typical production profile for a well, when the initial production is controlled at the maximum plateau rate for a period and then the production will naturally decline. figure 4—a rate model by using decline curve analysis. machine learning methods k-means clustering is an unsupervised machine learning very popular which can be applied to detect any anomalies in dataset. it is a centroid-based algorithm, or a distance-based algorithm, where the distances is calculated to assign a point to a cluster (doan and vo 2020). in this study, it is used as a first step of data preprocessing to remove any outliers in a given dataset before analysis, as shown in figure 5. figure 5—a k-means clustering method to detecte anomalies or outliers. 4 support vector regression (svr) uses the same principle as support vector machine. however, svr allows to be changed easily in defining how much error is good enough in selecting our model and will find an appropriate line (hyperplane in higher dimension) to fit the data, as shown in figure 6. it has been applied effectively to remove noise data in the analysis. in this study, the method is used to make a more reliable rate prediction for the existing produced wells. figure 6—an example of svr method for removing noisy data (doan and vo 2019b) based on the methodology, a workflow for this approach is divided into five steps as follows: step 1: data pre-processing this is the first step to identify and reduce any outliers of historical data, including reservoir pressure, water cut, wellhead pressure, choke size and rate, which are collected from a huge number of producing wells in got by using the k-means clustering method before moving to step 2. step 2: dataset this step is to categorize and arrange the data in step 1 into a standard dataset before proceeding in step 3. step 3: prediction model this step is to apply the svr method to remove any noise data before forecasting production rate at the well level at acceptable quality using decline curve analysis. step 4: production forecast the main task of this is to integrate production profile of the existing producing wells into the production forecast model (doan and vo 2019a) for generating many different development scenarios. step 5: results at the final step, many alternatives of perforated sands sequencing in the new wells are automatically made for economic evaluation. the diagram in figure 7 below illustrates the workflow on how to improve production forecast with machine learning methods. figure 7—workflow in the application of machine learning to improve production forecast. 5 application and results based on the methodology and workflow, doan and vo (2019a) have developed an application to improve production forecast by integrating python scripts (using for machine learning techniques) into excel vba scripts. figure 8 describes a user-friendly interface of the application. figure 8—an interface of production forecast modelling. key features of the model are:  user-friendly interface;  structure of a simple and small model file;  production forecast support for both modes (manual and automatic); and  rapid execution to give the forecasting results and economic evaluations. production forecast model will automatically allocate gas flow rate of each platform which contributes to meet the market demand. it also provides the installation time and the number of platforms to be installed or wells to be drilled, which could be necessary to satisfy the demand as shown in figure 9. figure 9—drilling project sequence and number of required whp/development wells. by applying machine learning approaches, the results have provided an effective sequence and drilling schedule for future drilling projects and aligned with the current production capacity of existing producing wells. the drilling project timeline and number of rigs allocation schedule have refined to be more realistic in compared with the previous scenarios (figure 10). 6 old scenarios new scenarios figure 10—drilling project timeline and number of rig allocation schedule. furthermore, the outputs provided not only the drilling schedule for future drilling projects, but also risk mitigation in project planning and management to optimize the logistic work (mobilize/demobilize, long lead items, and labor costs). conclusions this study provided an integrated solution using machine learning methods to improve the quality of production forecast and drilling schedule. the results have effectively supported engineers to make decisions for both short-term and long-term asset development and to make significant savings in operating costs. it is strongly believed that the model can be applied to solve many similar engineering challenges in the oil and gas field, especially for oil and gas fields that have many wells and a complicated dataset in the north malay basin. nomenclature dca = decline curve analysis svr = support vector regression got = gulf of thailand whp = well head platform ml = machine learning vba = visual basic application conflicts of interest the author(s) declare that they have no conflicting interests. references pinto, c.j., pendleton, l.e., dick, j.l., et al. 2004. ultrafast drilling in the gulf of thailand: putting science into the design process. paper presented at the iadc/spe drilling conference, dallas, texas, 2-4 march. spe87173-ms. doan, t.t. and vo, m.v. 2019a. a rapid modelling approach to optimize drilling and production for a complex field development in north malay basin. paper presented at international petroleum and petrochemical technology conference, xi'an, china, 3-5 july. doan, t.t. and vo, m.v. 2019b. using machine learning techniques to evaluate performance for existing waterflood projects in the gulf of thailand. paper presented at spe workshop: water injection excellence, kuala lumpur malaysia, 3-5 march. doan, t.t. and vo, m.v. 2020. application of machine learning for initial completion plan of multiple zone gas wells in north malay basin. proceedings of the international petroleum and petrochemical technology conference & exhibition, beijing, china, 11-13 september. 7 truc (trevor) doan, spe, is a senior petroleum engineer at bear and brook consulting. before that, he had worked as petroleum engineering lecturer for 2+ years at ho chi minh city university of technology hcmut and as petroleum engineer for chevron for 10+ years at various locations. he holds bachelor's in petroleum engineering from hcmut, master’s degree in petroleum engineering from ait, and currently, has been studying for phd degree at school of engineering, edith cowan university in australia. minh vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 6+ years. he has had 25+ years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. abstract introduction methodology decline curve analysis machine learning methods application and results conclusions nomenclature conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1156 received march 2, 2019; revised may 14, 2020; accepted may 20, 2020. *corresponding author: lichen1125@foxmail.com 1 sweet spots selection of low-abundance coalbed methane reservoir li chen*, china unite coalbed methane limited company, beijing, china abstract low abundance coalbed methane reservoirs are characterized by low abundance, unclear factors affecting gas well productivity, and strong heterogeneity. these characteristics make the development of gas reservoirs difficult. the study is based on well logging interpretation and the guidance of the gas well production capacity against these difficulties. using methods of the gas reservoir production characteristics analysis and numerical simulation, the relationships among the low abundance of cbm reservoir production well productivity, reserves abundance, main coal desorption pressure, interlayer interference, and continuous water drainage, were studied. studies have shown that the main controlling factors of low abundance of cbm are block construction factors, resource abundance and gas saturation. the study also confirmed that 2# coal seam is not suitable for mining with the main coal seam, and 6# coal seam in some areas is suitable for mining with the main coal seam. this method is highly targeted, has a strong production basis and high reliability based on the current production situation of the block. geological characteristics of aa block the aa coalbed methane block is located in shanxi province. the permian and triassic systems are widely distributed in gullies and mountain tops. the main structural framework is the north-northeast parallel fault. the north-south fold runs through the central and western part of the xishan coalfield, forming a syncline coal basin with a gentle slope in the east and a steep slope in the west. the coal-bearing rocks in this area include the middle carboniferous benxi formation, the upper carboniferous taiyuan formation, the lower permian shanxi formation and the lower shihezi formation. the development layers are mainly 2#, 6#, 8# and 9# coal seams. the main coal seam is 8# and 9# coal seam. the physical properties of the main coal production layers in the area are basically the same, showing black or dark brown color, the streak color is dark black or brown, glass-strong glass luster. the hardness is generally 3-4, with certain toughness, mostly block structure, and primary fissures are well developed. it is so brittle to be broken into powder, with staggered or shell-shaped fracture, bulk density 1.39-1.43 tons/cubic meter. the main characteristics of the whole area is that the thickness of the main coal seam is thin, the gas content is low, the distribution is uneven, and the development is difficult. analysis of main control factors of production block construction factors. affected by the late tectonic movement, a nasal structure was formed in the mailto:lichen1125@foxmail.com 2 middle of the block. it leads to stress concentration in the strata near the structure, and the effect of reconstruction measures is poor. it is difficult to add sand during fracturing, which is difficult for engineering reconstruction. the gas content is low and the coal structure is broken, forming a low production area. high and stable production wells are mainly distributed in non-structural areas. the structural area is characterized by low output and difficulty in stabilizing production. at present, the average gas production of a single well in a non-structural area is 5 times that of a structural area. resource abundance. resource abundance is an important factor for evaluating coalbed methane reservoirs, and it is also a key factor affecting the productivity of coalbed methane (yan et al. 2008; chen et al. 2010; wu et al. 2018; tian et al. 2018). aa block is affected by reservoir-forming factors, among which the resource abundance is low, and the distribution is uneven. there are currently few indicators to evaluate resource abundance, especially for coalbed methane. the application of well logging data can solve the problem of characterizing resource abundance of heterogeneous coalbed methane. in areas with relatively mature development, using logging data to study reserves abundance has achieved good results. the result was well verified in the later development. gas saturation. there are less experimental data on desorption and adsorption during the development of coalbed methane reservoir, so is measurement data of gas saturation, which cannot be evaluated in the whole region (liu et al. 2013; li et al. 2020). according to the desorption characteristics of coalbed methane, the desorption characteristics of the whole area can be evaluated by the critical desorption pressure of upper main layer. according to the statistics of observed gas pressure and gas production volume of no.8 coal in the whole region, the observed gas pressure is exponentially related to the average gas production volume of a single well, and the gas production effect is better when the observed gas pressure reaches 1.8mpa (figure 1). figure1—the relationship between the gas critical desorption and average gas production rate. research on different layered and combined production productivity performance law of co-production wells in the whole area. according to the perforation situation of existing wells, the production situation of wells with different perforation conditions is analyzed (qin et al. 2018; qin et al. 2010; zhang and tong 2007). the analysis results are 3 shown in figure 2. regardless of the co-production of 8# and 9# coal, or the co-production of 6#, 8# and 9# coal, after adding 2# coal, the production is significantly reduced. regardless of the co-production of 8# and 9# coal, or the co-production of 2#, 8# and 9# coal, after adding 6# coal, the production is significantly reduced. figure 2—different production rate with different layer combination. comparison of combined production capacity in the same well group. this study compared 28 wells in 10 different well groups. different production wells in the same well group have similar geological characteristics, consistent development processes and production schedule, but different co-production layers. the optimal combination of layers can be determined by comparing the production effect of different single wells in the same well group. through this comparison (table 1 and 2), 2# coal is not good for co-production with main coal seam, and well groups with good co-production effect are basically located in the area with high abundance of 6# coal reserves. table 1—the comparison of well production contains 2# coal and not contains 2# coal. well group name well number contains 2# coal well number not contains 2# coal average well production contains 2# coal(m3/d) average well production not contains 2# coal(m3/d) no.1 2 3 556 839 no.2 2 4 632 909 no.3 3 4 509 798 4 table 2—the comparison of well production contains 6# coal and not contains 6# coal. well group name well number contains 6# coal well number not contains 6# coal average well production contains 6# coal(m3/d) average well production not contains 6# coal(m3/d) no.1 2 3 446 732 no.2 2 4 773 721 no.3 3 4 711 732 no.4 4 2 899 733 no.5 2 3 936 802 no.6 4 1 831 701 no.7 3 3 956 785 therefore, 2# coal seam is not suitable for co-production with 8# coal seam and 9# coal seam, which is mainly due to the long distance between 2# coal seam and 8# coal seam and 9# coal seam. those coalbed seams are not under the same pressure system, and interlayer interference is great. the distance between 6# coal seam and 8# coal seam is shorter. those layers are under the same pressure system and interlayer interference was smaller. when the reserves abundance of 6# coal seam reaches a certain value, it can be co-produced with 8# coal seam and 9# coal seam. research on the combined production limit of non-main coal seam and main coal seam. a numerical simulation model of three-layer co-production in aa block is established to study the contribution of 6# coal gas production when 6#, 8#, 9# coal is combined. the basic parameters of the model displayed in tab. 3. the model has 1280 grids, including three formations, representing coal seam no. 6, no. 8 and no. 9 successively from top to bottom. the production well type is directional well, of which the development method is constant pressure production. the numerical model is displayed in figure 3. table 3 shows the basic parameters that were used to build the model. when the abundance of 6# coal reserves reaches 0.25 bcm/km2, the gas production of a single well increases by 610,000 cm (figure 4), the increase of production rate reaches 24%, and the contribution amount reaches 18%, which is suitable for co-production. table 3—the basic parameters of the model. parameters values average depth, m 650 6# coal thickness, m 1.5 8# coal thickness, m 4.5 9# coal thickness, m 3 permeability, md 0.05 porosity, % 4.5 original pressure, mpa 2.26 original gas content, m3/t 9.9 gas saturation, % 48 langmuir volume, m3/t 20.49 langmuir pressure, mpa 2.58 5 figure3—numerical simulation model of reservoir. figure4—contribution of 6# coal under different reserve abundance. well pattern optimization when the permeability of aa block is between 0.01md-0.1md, the diffusion of pressure drop funnel was difficult. especially, when the coal seam in the block is thin, selecting directional well development will result in low recovery factor and poor economic benefits for the entire block. according to the drilling condition in block aa in the early stage, the effective drilling catching rate of horizontal well is relatively low in some areas, and the economic benefits of using horizontal wells are poor. moreover, for the areas where geological parameters are not implemented, the horizontal well development has great risks. to sum up, the mixed pattern of directional well and horizontal well is selected for development this time, with horizontal well as the main one and directional well as the secondary one to improve the development efficiency. under the influence of the direction of hydraulic fracture extension, there is a large gap between the gas productivity in the fracture extension direction and perpendicular to fracture extension direction (figure 5). in view of this feature of strong heterogeneity, the diamond well network is used as the basic well pattern to deploy wells in the block. the long side of the diamond well pattern is consistent with the direction of fracture extension, while the short side is perpendicular to the direction of fracture extension. 6 figure 5—gas content change along fracture extension direction and perpendicular to fracture in 8# coal. conclusions in this study, we conducted geological research, production analysis, numerical simulation, and summarize the conclusions as follows, 1. the aa block is affected by the late tectonic movement, and a nosal structure formed in the middle. nosal structure is the main reason for the formation of low-yield areas. other main factors affecting the productivity of a single well are the resource abundance and gas saturation of the block. 2. since they are not under the same pressure system, the 2# coal seam in the whole area is not suitable for co-production with 8# coal seam and 9# coal seam. 6# coal can be produced together with 8# coal seam and 9# coal seam when the reserves abundance reaches 0.25 bcm/km2. 3. the aa block is currently suitable for the development by a mixed directional wells and horizontal wells, with horizontal wells as the main and directional wells as the secondary. the directional wells are better deployed with diamond pattern with the long side of the diamond pattern consistent with the fracture extension direction, while the short side perpendicular to the fracture extension direction. acknowledgement we appreciated the fund “national science and technology major project-cbm development from high-rank coals in the qinshui basin” (2017zx05064) for financial support. conflicts of interest the author(s) declare that they have no conflicting interests. references yan, b., wang, y., feng, q., et al. 2008. coalbed methane enrichment classifications of qinshui basin based on geological key controlling factors. journal of china coal society 33(10): 1102-1106. chen, z., tang, d., xu, h., et al. 2010. the pore system properties of coalbed methane reservoirs and recovery in western guizhou and eastern yunnan. journal of china coal society 35(6): 158-163. wu, c., liu, x., and zhang, s. 2018. construction of index system of “hierarchical progressive” geological selection of coalbed methane in multiple seam area of eastern yunnan and western guizhou. journal of 7 china coal society 43(6):1647-1653. tian, z., dong, y., wang, j., et al. 2018. seismic facies controlled inversion and cbm sweet spot prediction in deep coalseam of yushe wuxiang block in qinshui basin. journal of china coal society 43(6):1605-1613. liu, s., sang, s., li, m., et al. 2013. key geologic factors and control mechanisms of water production and gas production divergences between cbm wells in fanzhuang block. journal of china coal society 38(2): 277-283. li, c., yang, z., and sun, h. 2020. construction of a logging interpretation model for coal structure from multi-coal seams area. journal of china coal society 45(2): 721-730. qin, y., wu, j., shen, j., et al. 2018. frontier research of geological technology for coal measure gas joint-mining. journal of china coal society 43(6):1504-1516. qin, y., wu, j., zhang, z., et al. 2010. analysis of geological conditions for coalbed methane coproduction based on production characteristics in early stage of drainage. journal of china coal society 45(1): 241-257. zhang, x. and tong, d. 2007. the effects of pay formation combination on productivity of coalbed methane well in qinshui basin. journal of china coal society 32(3): 272-275. chen li is currently working in the research institute of china united coalbed methane co., ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. he worked as postdoc in peking university from 2016 to 2018. he holds a phd degree from research institute of petroleum exploration and development, and has a master degree from china university of geosciences, beijing, and bachelor degree from southwest petroleum university. abstract geological characteristics of aa block analysis of main control factors of production research on different layered and combined product well pattern optimization conclusions acknowledgement conflicts of interest references a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1144 received december 20, 2019; revised february 15, 2020; accepted april 10, 2020. *corresponding author: yy123@petreochina.com.cn 1 an integrated approach of uncertainty assessment for coalbed methane model yong yang*, ming zhang, aifang bie, zehong cui, zhaohui xia, research institution petroleum exploration & development (riped), beijing, china abstract this study deals with quantitative detection of parameters uncertainty in coalbed methane(cbm) modelling and a systematic and integrated workflow is developed to analyze the uncertainty of cbm model. in structure modelling, the uncertainty of measure depth (md) and coal thickness were analyzed by disturbing the structure surfaces or thickness surfaces while fixed at the well locations. in property modelling, an analysis of the residual distribution between each correlation and its measurements was used to characterize the uncertainty of each parameter. sensitivity analysis was performed for the parameters, such as gas content, structure surfaces, coal thickness, density, ash content, etc., to evaluate the uncertainty of original gas in place (ogip). the critical sensitive attributes were used to build multiple realizations to determine the p90, p50 and p10 of ogip. the low, middle and high probabilistic geological models were achieved corresponding to the probabilistic ogip, and used for the following reservoir simulation and development plan design. introduction limited amount of hard data, lack of well control and scarcity of geology studies are the great challenges in the exploration and development phase of a cbm field. most of the risks are related to the uncertainty in the static reservoir characterization, which also affects the dynamic response (shirazi et al. 2010; mohsen et al. 2007; sharma et al. 2008). the inability to properly manage subsurface uncertainty is often a key reason for the cbm projects failing to meet their objectives. thus, quantification of the significant uncertainty exiting in the geologic cbm model is critical in the field development. the uncertainties mainly come from structure modelling and property modelling procedures when building a cbm model. in the structure modelling, the uncertainties are the picking and interpretation of coalbed surface, geometry distribution of the coalbed geological heterogeneities. in the property modelling, the uncertainties are mainly from modelling the petrophysical parameters, such as gas content, density, ash content, etc. in this paper an integrated workflow was developed to quantify these uncertainties of cbm geologic modelling. 3d modelling for cbm three dimensional, geocellular static models was built to model cbm reservoirs with all the available information from wells, seismic data, outcrop, sample data, etc. a typical 3d modelling workflow for the cbm reservoir is as follows (zhang et al. 2014): 1) structure modelling. build the coal seam structural formations, including the horizons and faults, truncation, erosion, etc. 2) coalbed thickness modelling. build the top and bottom surfaces of the coal surfaces based on the high resolution coal ply picking and correlation, and depict the swelling, pinching out, merging or mailto:yy123@petreochina.com.cn 2 erosion of the coal plies. 3) property modelling. build the 3d distribution of the parameters, such as gas content, density, ash, moisture, permeability, langmuir volume, saturation, etc. a) log density (ssd) model: built with well density log using kriging or move average method. b) relative density (rd) model: built with formula from the correlation analysis between the sample density data and density log data. c) ash model: built with the correlation formula between the relative density (rd) and ash sample data. d) moisture model: usually regarded as a constant value. e) gas content dry ash free (gc_daf) model: calculated with using the correlation with the measure depth. f) permeability model: calculated with using the correlation with the measure depth. based on the above models, the original gas in place (ogip) is calculated with the formula, ogip = ∑(v𝑏𝑢𝑙𝑘 ∗ gc_daf ∗ (1 − ash − moisture) ∗ rd),…..……………………………………...(1) where vbulk is the cell volume of the model. uncertainty analysis uncertainty of structure modelling. the uncertainties in structure model generally relate to the well picks and surface interpolation, time-depth conversion, etc. (leahy and skorstad 2013; piquet et al. 2013). to assess the horizon uncertainty, an alternative surface is created by perturbing the base surface while honoring the well picks at the well locations (figure 1). the detailed procedure consists the following steps: step 1: a measure depth surface of the base horizon is calculated, and the uncertainty surface which has the value of 10% of the measure depth is created. here the value of 10% can be changed based on experience. step 2: a random surface is created by the sequential gaussian simulation (sgs) method, with a minimum value of -1 and a maximum value of +1, and mean value of zero, and zero at well locations. step 3: the uncertainty surface and the random surface are multiplied, and then the result is added to the base horizon to obtain an alternative surface. the alternative surface is considered as an uncertainty realization of the base horizon. it disturbs around the base horizon within the upper and lower boundary and match with the picks at well locations. multiple realizations of the alternative surface can be achieved by the difference random surface created with difference seed in step 2. figure 1—structure uncertainty analysis. uncertainty of coal thickness. this refers to the uncertainty of the coal ply isochore thickness interpolated in the zonation process. the procedure is as follows (figure 2): ☼ ☼ md well a well b topography upper boundary base horizon lower boundary +10%md -10%md 3 1) surfaces of 10th and 90th percentile values of the coal ply thickness are generated and named as "min" and "max" surfaces while maintaining zero thickness at well locations. 2) the “high_residual” and the “low_residual” surfaces are created by calculating the difference between the “base case” isochore thickness and the “max” and the “min” surfaces, respectively. 3) a random surface is created by the sgs method, with a minimum value of -1 and a maximum value of +1, mean value of zero, and zero at well locations. 4) a residual surface is generated by multiplying the random surface from step 3) with the “high_residual” or the “low_residual” surfaces from step 2) according to the positive or negative value of the random surface. a one third is introduced to the residual surface considering the experience. 5) the uncertainty thickness surface is then calculated by adding the “base case” isochore surface and the residual surface from step 4). multiple realizations of the thickness surface can be achieved by different random surface created with difference seed in step 3). the uncertain thickness surface disturbs around the “base case” isochore surface and match with the picks at well locations, and the uncertainty of the coal ply thickness ranges within one third of the "min" and the "max" surfaces. figure 2—procedure to quantify the uncertainty of coal thickness. property uncertainty. different uncertainty assessment methods are used for different parameters. for the log density (ssd), the assessment uses the same method as that used for the coal thickness uncertainty, in which the “base case” is the log density surface, and the “min” and the “max” surfaces are the 10th and 90th percentile values of the coal ply log density. for the rd, ash, gas content data, as can be seen from the cbm modelling workflow, several correlations are involved (figure 3). significant uncertainty exists around each fitted trend, which is shown by the scatter points observed in figure 3. the uncertainties for these parameters are considered as the result of the heterogeneity of the coal and quantifying the range related to their specific locations. max minbase case base case high_residual low_residual sgs grid uncertainty residualbase case sgs x high_res/3 sgs x low_res/3 = = = + + 0 4 figure 3—parameters uncertainty analysis. to capture these uncertainties, the residual or error is calculated between the fitted line and each measurement, then the “low” and the “high” limits are drawn by analyzing the residual distribution and choosing the 10th and 90th percentile values of the distribution as shown in figure 3. it guarantees that most of the sample data are within the high and low limits. other percentile values could be used if a smaller or bigger limit is required. for the permeability data, the uncertainty is related to the limited sample data. if more data added the fitted trend from a limited sample is liable to become steeper or shallower (figure 4). to capture this type of uncertainty a confidence interval approach is introduced as the following equation �̂�|𝑥=𝜔 ∈ [�̂� + �̂�𝜔 ± 𝑡𝑛−2 ∗ √ 1 𝑛−2 ∑𝜀�̂� 2 ( 1 𝑛 + (𝜔−�̅�)2 ∑(𝑥𝑖−�̅�) 2)]...……………………..…………………………....(2) figure 4—permeability uncertainty analysis. integrating uncertainty models to integrate the uncertainties from multiple sources, it is convenient to use the ogip that aggregates the influence of the uncertainties. therefore, an integrated workflow using the above uncertainty analysis is implemented to estimate reservoir properties. sensitivity analysis and the probability modelling are the two main steps in this workflow. sensitivity analysis. a range or distribution is estimated for each parameter, and then multiple realizations are generated to calculate the ogip by varying one parameter at a time while keeping all other parameters as its base case value. these calculations estimate the uncertainty of ogip due to the variables which are shown in horizontal bar in tornado chart (figure 5). base trend: y = 0.49x + 0.77 r² = 0.5119 1.0 1.2 1.4 1.6 1.8 2.0 1.0 1.2 1.4 1.6 1.8 2.0 2.2 r d (g /c c ) ssd(g/cc) high base low base trend: y = 75.487x 92.53 r² = 0.8446 0 20 40 60 80 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 a s h (% ) rd(g/cc) high base low base trend: y = 7.67ln(x) 32.68 r² = 0.6218 0 5 10 15 20 25 0 100 200 300 400 500 600 700 800 g c _ d a f (m 3 /t ) measure depth(m) high base low base trend: y = 497.1e-0.015x r² = 0.5789 0.001 0.010 0.100 1.000 10.000 100.000 1000.000 0 200 400 600 800 p e rm (m d ) depth(m) perm vs depth of rcm trend low high 指数 (trend) high base low 5 figure 5—sensitivity analysis. from the chart it can be seen that the most influent parameter to the ogip is gc_daf, followed by the coal thickness and structure, and density is the least sensitive parameter which has relative small impact on the ogip compared to other parameters. probability models. considering the sensitive parameters which rank on the top of the tornado chart, multiple realizations were performed with all these parameters varies simultaneously in each range. the ogip of all these models are calculated and its distribution was plotted in figure 6 from which the p90, p50 and p10 are obtained. based on these probabilistic ogips, 3d static models with ogips within +/5% of p90, p50 and p10 are chosen as low, middle and high probability models to be used for reservoir simulation and well planning in future. (kimber et al. 2016; zhao et al. 2014; philpot et al. 2013). ogip figure 6—probability distribution of ogip. conclusions a systematic and integrated approach to analyze the uncertainty of cbm model was proposed in the study. the workflow captures the uncertainties related to the structure and coal thickness surfaces in the structure modelling, and the uncertainties associated with various correlations developed during the property modelling. the procedure of sensitivity and uncertainty analysis ranks the impact of each parameter on ogip, and estimates the ogip probabilistic distribution to get the p90, p50 and p10 of ogip, and then selects the low, middle and high probabilistic cbm models for the reservoir simulation and well plan. the -30% -20% -10% 0% 10% 20% 30% 40% ssd rd ash structure thickness gc_daf 0 2 4 6 8 10 12 14 16 giip fr eq u en cy (% ) 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 p90 p50 p10 1.0 0.9 c u m u la ti ve p ro b ab ili ty 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 5 10 15 20 坐 标 轴 标 题 坐标轴标题 图表标题 系列1 6 workflow in this paper has been successfully carried out in several cbm projects in australia and been confirmed to be reliable, efficient and effective for the cbm exploration and development. acknowledgements thanks are extended to arrow beijing study center for providing the opportunity to carry out the research. thanks are also due to a number of our colleagues for their warm help. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature �̂�|𝑥=𝜔 = confidence interval at x=ω �̂� + �̂�ω = trend fitted by linear regression 𝑡𝑛−2 ∗ = t-value of the student’s t-distribution n = number of data points in sample 𝜀�̂� 2 = residual squared references kimber, r.n., curtis, m.d., boundy, f.o., et al. 2016. volumetric and dynamic uncertainty modelling in block 22, offshore trinidad and tobago. petroleum geoscience 22(1):21-36. leahy, g.m. and skorstad, a. 2013. uncertainty in subsurface interpretation: a new workflow. first break 31(9): 87-93. mohsen, a., maskeen, a.a, and sung, r.r. 2007. advanced geological modeling and uncertainty analysis in a complex clastic gas reservoir from saudi arabia. paper presented at asia pacific oil and gas conference and exhibition, jakarta, indonesia, 30 october-1 november. spe-109275-ms. philpot, j.a., mazumder, s., naicker, s., et al. 2013. coalbed methane modelling best practices. paper presented at international petroleum technology conference, beijing, china, 26-28 march. iptc-17137-ms. piquet, g., pivot, a.l., and pivot, f. 2013. geomodel geometry distorted by seismic velocity uncertainties. paper presented at spe reservoir characterization and simulation conference and exhibition, abu dhabi, uae, 1618 september. spe-165973-ms. shirazi, a.f., solonitsyn, s.v., and kuvaev, i.a. 2010. integrated geological and engineering uncertainty analysis workflow, lower permian carbonate reservoir, timan-pechora basin, russia. paper presented at spe russian oil and gas conference and exhibition, moscow, russia, 26-28 october. spe-136322-ru. sharma, a., leung, j., srinivasan, s., et al. 2008. an integrated approach to reservoir uncertainty assessment: case study of a gulf of mexico reservoir. paper presented as spe annual technical conference and exhibition, denver, colorado, usa, 21-24 september. spe-116351-ms. zhang, m., yang, y., xia, z., et al. 2014. a best practice in static modeling of a coalbed-methane field: an example from the bowen basin in australia. spe reservoir evaluation & engineering, 18(2):10-18. spe171416-pa. zhao, c., xia, z., zheng, k., et al. 2014. integrated assessment of pilot performance of surface to in-seam wells to de-risk and quantify subsurface uncertainty for a coalbed methane project: an example from the bowen basin in australia. paper presented at spe/eage european unconventional resources conference and exhibition, vienna, austria, 25-27 february. spe-167766-ms. yong yang is a senior engineer in petroleum exploration and development research institute, petrochina, beijing. dr. yang specializes in production analysis, reservoir simulation, and unconventional reservoirs. ming zhang is a senior engineer in petroleum exploration and development research institute, petrochina, beijing. dr. zhang specializes in production analysis, reservoir simulation, and unconventional reservoirs. aifang bie is a senior engineer in petroleum exploration and development research institute, petrochina, beijing. dr. bie specializes in production analysis, reservoir simulation, and unconventional reservoirs. 7 zehong cui is a senior engineer in petroleum exploration and development research institute, petrochina, beijing. dr. cui specializes in production analysis, reservoir simulation, and unconventional reservoirs. zhaohui xia is a senior engineer in petroleum exploration and development research institute, petrochina, beijing. dr. xia specializes in production analysis, reservoir simulation, and unconventional reservoirs. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.423 received april 11, 2017; revised april 30, 2017; accepted may 9, 2017. *corresponding author: caiatwang@sina.com 1 physical models for shale gas reservoir considering dissolved gas in kerogens cai wang*, gang lei, andweirong li, peking university, beijing, china abstract to figure out the complexity of the fabric and gas flow mechanism within the shale gas reservoirs shapes our preliminary study purpose. the pore structure and composition of shale are much more complicated than that of conventional and tight gas reservoirs. apart from the classic matrix and fracture media, two new triple porous medium models regarding kerogen as the third medium are proposed in this paper. furthermore, integrated gas flow mechanisms (containing darcy flow, slippage flow, transient flow, knudsen diffusion and henry diffusion) within each of the models are illustrated. overall, four types of gas flow models are presented and related gas flow patterns and flow principles are explicated. introduction shale gas resources are termed “unconventional” due to its super low permeability (10-16 m2 to 10-20 m2) and severe heterogeneity caused by various scales of connected and unconnected fractures, fissures, micro, macro, and inter-aggregate pores, and organic matters. moreover, free gas, adsorption gas and dissolved gas are widespread in shale gas reservoirs. all of these reservoir characteristics complicate the gas flow mechanisms which make shale gas extraction more difficult. thus, to uncover the secrets of gas storage and flow in shale gas reservoir is one of the hottest topics in petroleum engineering. x-ct technology is one of the most common methods to study the microscopic structure of rocks. while it could not be used to analyze the inner structure of shale due to its ultra-low pore diameters. therefore, a more advanced technology named fib-sem is used to engage in 3d digital core analyses. by making use of fib-sem, curtis et al. (2010) got 500 pieces of cross-sectional slices each of whose thickness is 10 nm (figure 1). the images from this process formed a 3d dataset which was used to reconstruct a volume of the sectioned shale material (figure 2). knudsen (1909) conducted his research on the interaction between gas molecules and pore walls and explicated phenomenon of knudsen diffusion. he proposed the concept of knudsen number and used it to differentiate gas flow patterns. in the aspect of mechanism of non-darcy gas flow in tight porous media and based on the achievements of knudt and warburg (1875), klinkenberg (1941) applied the theory of gas slippage effects occurring on the surface of solid walls into gas reservoirs and presented the corresponding first order apparent permeability expression. beskok and karniadakis (1999) studied the gas flow mechanisms in tight gas reservoir and deduced a generalized apparent permeability formula which contains continuum flow, slippage flow, transition flow and molecular diffusion flow. civan (2002) concluded that gas flow in tight porous media was subject to the integrated influence of mailto:caiatwang@sina.com 2 darcy flow, slippage flow and knudsen flow. he also proposed a triple porous media model considering fractal characters to model gas flow in tight reservoirs. javadpour (2007) found that the gas flow in nanopores of shale can be modeled with a diffusive transport regime with a constant diffusion coefficient and negligible viscous effects. they deduced a new diffusion model and proposed the diffusion coefficient for gas flow in nanopores of shale. the obtained diffusion coefficient is consistent with the knudsen flow which supports the slip boundary condition at the nanopore surfaces. this model can be used for shale gas development evaluation and production optimization. figure 1—cross-sectional slices by fib-sem. figure 2—a 3d shale reservoir model reconstructed by fib-sem. a higher-order permeability correlation for gas flow called knudsen’s permeability was deduced by ziarani and aguilera (2011). as opposed to klinkenberg’s correlation, which is a first-order equation, knudsen’s correlation is a second-order approximation. they concluded that knudsen’s permeability correlation was more accurate than klinkenberg’s model especially for extremely tight porous media with transitional and free molecular flow regimes. the results from their study indicated that klinkenberg’s model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high knudsen number. what’s more, there are a large amount of gas adsorbed on the surface of pore walls of shale which will highly affect shale gas in place evaluation, apparent permeability calculation and shale gas production prediction. 3 ambrose (2012) combined the langmuir adsorption isotherm with the volumetrics for free gas and formulate a new gas-in-place equation accounting for the pore space taken up by the sorbed phase. the calculation result showed the role of sorbed gas is more important than previous thought and a 10-25% decrease in total gas-storage capacity compared with that using the conventional approach. based on scanning electron microscope images and a drainage experiment in shale, sakhaee-pour and bryant (2012) analyze the effects of adsorbed layers of methane and of gas slippage at pore walls on the flow behavior in individual conduits of simple geometry and in networks of such conduits. at large pressures such as typical initial shale-gas-reservoir pressures, the effect of the adsorbed layer dominates the effect of slip on gas-phase permeability. slip dominates at smaller pressures typical of those after longer periods of production. consequently, the reservoir matrix permeability is predicted to increase significantly throughout the life of a well, by a factor of 4.5, as production continues and pressure declines. the models predict that the typical conditions for laboratory measurements of permeability cause those values to overestimate field permeability by as much as a factor of four. the model results are captured in simple analytical expressions that allow convenient estimation of these effects. huang et al. (2007) established a comprehensive model for multi-scale shale gas flow which considered dissolved gas diffusing in kerogen bulk, desorption gas on the pore walls, knudsen diffusion and slippage effects in nanopores, and conventional gas flow in fracture network towards the wellbore. it was found that desorption, knudsen diffusion and slippage flow in nanopores have significant influences on transient flow behavior. the desorption effect could supplement gas to the reservoir, effects of diffusion and slippage could increase the apparent permeability and ease gas flow in nanopores, all of them decrease the rate of pressure depletion in shale gas reservoir. the purpose of this paper is to figure out the relationship among matrix, natural fractures and kerogen and clarify the gas flow mechanism in these porous media. scales for shale gas flow javadpour et al. (2007) proposed the concept of transport regime which divided the gas flow in shale porous media into five scales, shown in figure 3. (a) macroscale, referring to gas flow from shale gas reservoir to wellbore (i.e., methane flow from hydraulic fractures and stimulated reservoir network to wellbore; (b) mesoscale, referring to gas flow in natural fractures; (c) microscale, referring to gas flow in nanopores; (d) nanoscale, referring to desorption of gas from nanopore walls; (e) molecular scale, referring to diffusion of dissolved gas in kerogens. shale reservoir models of triple porous media the triple porous media model, which includes vuggy pores, matrix and fractures, has already been widely used in carbonate reservoirs. the fluid flow in carbonate reservoir follow the principle of darcy law. different from carbonate reservoirs, gas flow in shale reservoirs contain both darcy flow and non-darcy flow (e.g., slippage, desorption, diffusion, et al.). it is discovered that there are substantial volumes of methane dissolved in organic matters (ross and bustin 2009). according to the gas transport regime proposed by javadpour (2007), flow of dissolved gas in kerogen adheres to henry diffusion equation (huang et al. 2007) which belongs to molecular scale. here, we regard kerogens as the third porous media. thus, the triple porous media of shale gas reservoir comprises matrix system, kerogen system and enriched natural fractures. it should be noted that 4 kerogens play the role of both matrix system the micro pores of whom provide storage spaces for sorbed and free gas and the triple porous media system in which substantial dissolved gas enrich. if there are a lot of organic matters (i.e., kerogens) and natural fractures in the shale gas reservoirs, the natural fractures existing in the form of widespread fracture network could effectively connect the pores within matrix and organic matters. figure 3—different length scales for shale gas evolution and production. we define triple porous media mentioned above as first type of triple porous media (f-tpm). the real and ideal physical models of f-tpm are shown in figure 4a and 4b, respectively. in the model of f-tpm, natural gas dissolved in the organic matters could either diffuses into fracture system directly or diffuses into matrix system and then flows from matrix system to fracture regime. at last, natural gas will flow from fracture system to the wellbore. if the content of organic matters and the density of natural fracture in the shale gas reservoir are relative low, the natural fractures exist in the form of a sparse fracture network and play the role of high conductive passageway which connect matrix system with wellbore. moreover, organic matters are embedded into matrix system and are isolated from fracture system. we definite this kind of triple porous media as the second type of triple porous media (s-tpm). the real and ideal physical models of s-tpm are shown in figure 5a and 5b, respectively. in this model, natural gas dissolved into organic matters have to diffuse into fracture system first and then flows from fracture system to the wellbore. (a) (b) figure 4—the first type of triple porous media (f-tpm). real physical model. (b) ideal physical model. 5 (a) (b) figure 5—the second type of triple porous media (s-tpm). real physical model. (b) ideal physical model. according to pathways of gas flow from reservoir systems to the wellbore, we divide shale gas reservoir models into two major categories: (1) triple porosity singular permeability model (tpsp), and (2) triple porosity dual permeability model (tpdp). if gas within wellbore is only provided by fracture system, this kind of model is defined as tpsp. if gas within wellbore is not only from fracture system but matrix system, this kind of model is defined as tpdp. the model of tpsp which is derived from f-tpm is called first type of triple porosity single permeability model (f-tpsp) (figure 6a). gas flow within f-tpsp mainly experience four steps: (a) gas flow from fracture system to wellbore, conforming to darcy flow or slippage flow and belonging to the flow scale of mesoscale; (b) under the effect of concentration difference, gas diffuse from matrix (conforming to knudsen diffusion law and belonging to the flow regime of microscale) and organic matters (conforming to henry diffusion law and belonging to the flow regime of molecular scale) to natural fractures; (c) abundant adsorbed gas is desorbed from surface of matrix or organic matters to nanopores, conforming to langmuir desorption law and belonging to the flow regime of nanoscale; (d) concentration difference will exist between surface and inside of organic matters and gas will diffuse from inside of organic matters to nanoproes within matrix blocks. the model of tpsp which is derived from s-tpm is called second type of triple porosity single permeability model (s-tpsp) (figure 6b). gas flow within s-tpsp mainly experience four steps as well: (a) gas flow from fracture system to wellbore, conforming to darcy flow or slippage flow and belonging to the flow regime of mesoscale; (b) under the effects of concentration difference, gas diffuse from matrix to natural fractures, conforming to knudsen diffusion law and belonging to the flow regime of microscale; (c) abundant adsorbed gas is desorbed from surface of matrix to nanopores, conforming to langmuir desorption law and belonging to the flow regime of nanoscale; (d) concentration difference will exist between surface and inside of organic matters and gas will diffuse from inside of organic matters to nanoproes within matrix system. the model of tpdp which is derived from f-tpm is called first type of triple porosity dual permeability model (f-tpdp) (figure 7a). gas flow within f-tpdp mainly experience four steps: (a) gas flow from fracture system (conforming to darcy flow or slippage flow and belonging to the flow regime of mesoscale) or matrix system (conforming to knudsen diffusion law and belonging 6 to the flow regime of microscale) to wellbore simultaneously; (b) under the effects of concentration difference, gas diffuse from matrix (conforming to knudsen diffusion law and belonging to the flow regime of microscale) and organic matters (conforming to henry diffusion law and belonging to the flow regime of molecular scale) to natural fractures; (c) abundant adsorbed gas is desorbed from surface of matrix or organic matters to nanopores, conforming to langmuir desorption law and belonging to the flow regime of nanoscale; (d) concentration difference will exist between surface and inside of organic matters and gas will diffuse from inside of organic matters to nanoproes within matrix blocks. (a) (b) figure 6—schematics for shale gas flow in tpsp. (a) f-tpsp. (b) s-tpsp. (a) (b) figure 7—schematics for shale gas flow in tptp. (a) f-tptp. (b) s-tptp. the model of tpdp which is derived from s-tpm is called second type of triple porosity dual permeability model (s-tpdp) (figure 7b). gas flow within s-tpdp mainly experience four steps as well: (a) gas flow from fracture system (conforming to darcy flow or slippage flow and belonging to the flow regime of mesoscale) or matrix system (conforming to knudsen diffusion law and belonging to the flow regime of microscale) to wellbore simultaneously; (b) under the effects of concentration difference, gas diffuses from matrix to natural fractures, conforming to knudsen diffusion law and belonging to the flow regime of microscale; (c) abundant adsorbed gas is desorbed from surface of matrix to nanopores, conforming to langmuir desorption law and belonging to the flow regime of nanoscale; (d) concentration difference will exist between surface and inside of organic matters and gas will diffuse from inside of organic matters to nanoproes within matrix blocks. 7 conclusions the following conclusions can be drawn, 1. natural gas in the shale gas reservoirs restored in the form of free gas in natural fractures and pores within matrix and kerogens, adsorption gas on pore walls and dissolved gas in kerogens. kerogens in shale gas reservoirs play multiple roles, it could contain not only free and desorption gas but also dissolved gas. the triple porous media model of shale gas is made up of fractures system, matrix system comprising pores within organic and non-organic matters and kerogen blocks containing dissolved gas. 2. four models for shale gas flow are proposed according to relationships of location of different flow media and permeability mode. multiple mechanisms of darcy flow, slippage flow, knudsen flow, henry law and langmuir desorption contribute to gas flow in shale reservoirs and enhance the complexity of shale gas flow. conflicts of interest the author(s) declare that they have no conflicting interests. references ambrose, r., hartman, r., diaz-campos, m., et al. 2012. shale gas-in-place calculations part i: new pore-scale considerations. spe journal 17(1): 219-229. spe-131772-pa. beskok, a. and karniadakis, g. e. 1999. a model for flows in channels, pipes, and ducts at micro and nano scales. nanoscale and microscale thermophysical engineering 3(1): 43-77. civan, f. 2002. a triple-mechanism fractal model with hydraulic dispersion for gas permeation in tight reservoirs. paper presented in spe international petroleum conference and exhibition, villahermosa, mexico, 10-12 february. spe-74368-ms. curtis, m. e., ambrose, r. j., sondergeld, c. h., et al. 2010. structural characterization of gas shales on the microand nano-scales. paper presented at canadian unconventional resources and international petroleum conference, calgary, alberta, canada, 19-21 october. spe-137693-ms. huang, t., guo, x., and chen, f. f. 2015. modeling transient flow behavior of a multiscale triple porosity model for shale gas reservoirs. journal of natural gas science and engineering 23(2):33-46. javadpour, f., fisher, d., and unsworth, m. 2007. nanoscale gas flow in shale gas sediments. j can pet technol 46(10): 55-61. jcpt-07-10-06. klinkenberg, l.j.1941. the permeability of porous media to liquid and gases. socar proceddings 2(2): 200-213. knudsen, m. 1909. the laws of molecular and viscous flow of gases through tubes. ann. phys. 333 (1): 75-130. ross, d.j.k. and bustin, r.m. 2009. the importance of shale composition and pore structure upon gas storage potential of shale gas reservoirs. mar. pet. geol. 26(6): 916-927. sakhaee-pour, a. and bryant, s. l. 2012. gas permeability of shale. spe reservoir evaluation and engineering, 15(4):401-409. spe-146944-pa. ziarani, a. s. and aguilera, r. 2011. knudsen’s permeability correction for tight porous media. transport in porous media 91(1): 239-260. 8 cai wang is now a postdoctoral fellow in peking university, beijing, china. his research interests mainly contain contamination of shale gas development on underground water, productivity analysis and numerical modeling of shale gas and tight gas reservoirs. dr. wang hold a doctoral degree and a bachelor degree in china university of geosciences (beijing). gang lei is a postdoctoral fellow at the peking university. his research interests include theory and laboratory studies of the fundamental properties and behavior of fractured reservoirs, numerical modeling of fractured horizontal wells, and enhanced oil recovery of tight sandstone reservoirs. lei holds a phd degree from the china university of petroleum, beijing. he is a member of spe. weirong li, is a postdoctoral fellow at the peking university. his research interests include enhance oil recovery, reservoir simulation, numerical modeling of fractured horizontal wells. dr. li holds a phd degree from texas a&m university, and master degree from research institute of petroleum exploration and development, petrochina, beijing, china. he is a member of spe. abstract introduction scales for shale gas flow shale reservoir models of triple porous media conclusions conflicts of interest references a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.441 received october 3, 2019; revised november 12, 2019; accepted december 2, 2019. *corresponding author: minh.vo@chevron.com 1 hydrate management with real time data visualization jianjiang lv, jianbo yuan, minh vo*, chevron unocal east china sea ltd, chengdu, china; and junliang zhang, southwest oil & gas field company, cnpc, chengdu, china abstract hydrate is a common issue in the natural gas production, which can be accelerated by the presence of h2s and co2. this paper is to present the current experience in a gas project in sichuan, including application of several surveillance technologies for the benefit of hydrate prevention and management, to support production optimization. this sour gas project has high h2s and co2 content. with the high deliverability at the wells, the project has used a two-choke configuration in the surface system to manage the surface pressure to feed the gas into the production process. given a design of the 2-choke system, the sour gas is choked, heated, and then choked again, and finally flows to the tri-ethylene glycol (teg) dehydration unit. hydrate formation risk normally exists downstream of the first choke and the second choke if the heater is not efficient, and at the filtration process upstream of the dehydration. hydrate prevention had been considered during the design phase of the surface production facilities. methyl-ethylene glycol (meg) is therefore selected and injected to the upstream of the first choke to mix with the gas flow stream. real time data surveillance (i.e., pressure and temperature) with digital gauges are installed in the areas with high probability of hydrate formation. the most important next step is the real-time data (i.e., gas rate, water rate, pressure, temperature and meg injection rate), which are updated and the hydrate formation curves are plotted to display on the central control computer. based on the displayed relation of the pressure and temperature, the integrated digital control system can be used to optimize production by controlling gas rate, heater temperature and meg injection. in brief, with this visualized monitoring system in place, hydrate prevention has been visually and effectively managed and meg consumption has been optimized to minimize the operational cost. introduction methane hydrate, a crystalline solid that consists of a methane molecule surrounded by a cage of interlocking water molecules, is very common in the natural gas industry. methane hydrate is an "ice" that only forms when temperature and pressure conditions are favourable for its formation, such as presence of “free” water, low temperature, high operating pressures, presence of h2s and co2, high velocities, or agitation, or pressure pulsations (king 2017). figure 1 shows an example of pipeline hydrate blockage. the components of hydrate is not limited to methane, but also, many other natural gas components, such as ethane, propane, isobutene, hydrogen sulphide, carbon dioxide and nitrogen. oil companies have known about methane hydrate since the 1930s, when they began using high pressure pipelines to transport natural gas in cold climates. pipelines were noted to be obstructed by icelike crystals, even though temperatures were higher than the freezing point of water. before gas enters the pipeline, water must be carefully removed, since formation of methane hydrate will impede the flow of gas. although scientists have been working to reduce formation of hydrates, the problem still exists and it affects the normal operations and increases cost (psu 2017). mailto:minh.vo@chevron.com 2 the prevention of hydrate formation is preferable to remediation to ensure operational safety and efficiency. some common hydrate prevention techniques are temperature control, water jacket heater and dehydration, inhibitors. there are several steps which may be employed to remove hydrates once formed, for instance, heating, pressure reduction and chemical injection. figure 1—hydrate. sour gas project this greenfield sour gas project is developed in sichuan, china. the full field development schematic is shown in figure 2. the project involves development of gas resources in triassic carbonate reservoirs. the unique challenges for this project are sour gas, rugged terrain, large operating area, and high population. figure 2—sour gas development project. two-choke production system. sour gas from the gas reservoir flows via the production tubing in the well to the wellhead, losing heat to the wellbore strings. the wellhead temperature, however, is still high enough to prevent hydrate formation. as illustrated in figure 3, the first choke remotely controlled by operators in the central control room reduces the gas pressure to meet the pressure design of the surface flowline, resulting in a dramatic temperature drop due to the joule thompson j/t cooling effect. meanwhile water vapor is condensed at such lower pressure and temperature conditions, and flows together with sour gas to the water jacket heater, where the sour gas is heated up to a temperature as per 3 the designed heating capacity. next, the gas is choked again to further reduce the gas pressure to meet the pressure design of the pipeline to the gathering station, resulting in a further drop in gas temperature. the second choke is operated at automated motion to maintain the gas pressure both upstream and downstream of the choke as designed. figure 3—schematics of two-choke production system. note that the sour gas reservoir has high h2s and co2 content. this, together with the pressure and temperature profiles and condensed water along the surface process, introduce risk of hydrate formation for the surface facilities. because methane hydrates consist of geometric lattices of water molecules containing cavities occupied by methane and other gaseous components, and h2s and co2 have higher solubility in water than methane, it’s easier for h2s and co2 to combine with water to form hydrate with than it is for methane at the same pressure and temperature conditions. more is shared in the next section. at the gathering station, sour gas is filtered using a filter cartridge (figure 4) to ensure clean gas to the inlet of teg dehydration unit to dry the sour gas. temperature drops as gas is flowing through the cartridge due to friction pressure loss. next, dry and clean sour gas enters the pipeline to the gas plant to remove the hydrogen sulphide. figure 4—filter cartridge. although the condensed water volume is small it raised up the risk of hydrate formation in the downstream of the two chokes and the filter separator, as the pressure and temperature (p/t) in the three positions may fit the requirement to form hydrate. hydrate inhibitor (meg) is injected upstream of the first choke to prevent hydrate formation in the surface facilities. 4 hydrate pressure temperature p/t curve. a typical hydrate formation curve (phase diagram) is illustrated in figure 5, which clearly shows that hydrate formation is favored by low temperature and high pressure. point q1 typically occurs at 32 °f which is the water freezing point. hydrocarbon gas and water form hydrate at the region above the p/t curve q3-q1-q2. in other words, the region below the curve with higher temperature and lower pressure is free of hydrate risk. the factors that affect the hydrate p/t curve are gas composition, gas rate, water-gas-ratio (wgr), inhibitor type and inhibitor volume. the sour gas is dry gas, without condensed oil or condensed gas. the produced water is condensed water vapor formed in the surface facilities, not produced from formation aquifer. condensed water has much lower salinity than the formation aquifer, resulting in a higher risk of hydrate formation, because an increase in the salinity shifts the methane-hydrogen sulfide hydrate equilibrium condition to lower equilibrium temperatures at a given pressure (ballard et al. 2011; bulbul et al. 2014; avaldsne 2014). hydrate +free waterhydrate +ice ice +hc gas water + hc gas liquid hc +water c q2 q1 q3 t p conditions at which gas and liquid water combine to form hydrates figure 5—phase diagram for water/hydrocarbon mix (psu 2017). using the srk-hv model and srk-peneloux model, the p/t curve is generated based on the sour gas composition, as in figure 6 and 7. for example, when p/t data are plotted in the area above the curve, it indicates a hydrate formation risk (e.g., point a), and no risk if the data are plotted below the curve (e.g., point b with the same pressure). figure 6—hydrate formation curve without meg injection. 5 figure 7—hydrate formation curve with meg injection. without inhibitor injection, the p/t curve is independent of water production rate. because inhibitor has the effect of preventing gas molecules from being caged by water molecules, the ratio of inhibitor to water volume affects the p/t curve. without inhibitor, water volume will not affect the hydrate formation pressure and temperature, but affect the hydrate quantity. meg injection mitigates the hydrate risk. for example, if the condensed water rate is 24 cubic meter per day, at 13 mpa pressure (megapascal), the hydrate formation temperature is around 3 oc lower than that without meg injection. additionally, with the same meg injection rate, higher condensed water rate, higher hydrate formation temperature at the same pressure, thus a higher hydrate risk. carbon dioxide, hydrogen sulfide and nitrogen are the main impurities in natural gas affecting the hydrate formation. at a specific temperature, nitrogen increases the required hydrate formation pressure while both carbon dioxide and hydrogen sulfide lower the required hydrate formation pressure (rajnauth et al. 2010). figure 8 shows the impact of gas composition on the p/t curve. with a higher h2s concentration, the hydrate formation temperature is higher at the same pressure. for instance, at the same pressure 10 mpa, the hydrate formation temperature for pure methane is 13 oc, but it is 18.5 oc for a mixture of 95 mol% of methane and 5 mol% of h2s. in another similar view, when looking at the impact of co2, h2s has a much bigger impact than co2 on the p/t curve, for instance, hydrate formation temperature differential is 5 oc at 10 mpa. figure 8—hydrate formation curve for various gas composition without meg injection. 6 hydrate forms in liquid phase. not only hydrocarbon gas and liquid water can combine to form hydrate; gas components dissolved in water can form hydrate as well at favorable pressure and temperature conditions. for instance, the water outlet of sour gas compressors, used to compress the flashed sour gas from the teg system, is operating at 3 mpa and 25 oc, and the solubility of each gas component is calculated using the internal pvt analysis software as illustrated in table 1. therefore, hydrate p/t curve can be calculated for the specific solution as per table 1, to evaluate if the risk exists. figure 9 indicates the hydrate forming temperature at 3 mpa is around 10 oc, so the compressor’s water outlet operating at 25 oc has no hydrate risk in the liquid phase. in other words, normal operations need to ensure that the water outlet temperature shall be above 10 oc. table 1—solubility of each gas component in water. solubility, mol % p at 3 mpa, t at 25 oc co2 0.104 h2s 0.446 c1 0.055 figure 9—hydrate p/t curve for sour water without meg injection. real time data visualization system. pressure and temperature transmitters and gauges are installed in all the hydrate risk areas:  downstream of the first choke and of the second choke on the well pads,  downstream of the filter separator on the gas gathering station, and  water phase of the sour gas compressor. because all the real-time data is recorded and displayed on the computer screen in the central control room, the next step is to develop a real-time monitoring system, which can be used to displace all the information available and conditions that hydrate formation risk could be obvious. furthermore, it is to help operators see a trend of a parameter or set up an alarm to catch abnormal operating conditions. at this jv gas project, the team has worked together and a hydrate monitoring module has been developed, and incorporated with the central control system to manage the real-time hydrate risk and meg consumption. 7 as illustrated in figure 10, an alarm will be triggered by real time pressure and temperature along the surface process, to notify operators by audio and red color twinkling. the operators will click the “plot” button to analyze the hydrate formation temperature curve, as figure 11. figure 10—conceptual schematic of real-time hydrate management and monitoring interface. more specifically, the systematic design of the downstream pressure of the second choke is a constant value to ensure stable gas flow from well-pads to the gathering station. table 2 shows the basic data for hydrate risk analysis at the second choke downstream, such as water production rate, meg injection rate and downstream temperature. the basic data is plotted in figure 11 to visually compare to the hydrate formation temperature curve. table 2—primary well data for hydrate management. well water production rate, m3/d temperature at second choke downstream, c meg injection rate, m3/d a 5.2 23.7 0.2 b 4.9 19.0 0.7 c 2.8 17.2 0.4 well a data point locates far above the hydrate temperature curve with 10 m3/d water rate, so there is no hydrate risk at the second choke downstream for well a. indeed, with such high temperature 23.7 oc, there is no need to inject meg, so 200 litres/d of meg can be saved. figure 11—sour gas hydrate formation temperature at the second choke downstream at fixed pressure and various meg injection rate. 8 the required 700 litres/d of meg is injected upstream of first choke of well b. with the second choke downstream temperature 19 oc, the meg injection rate can be cut to 450 litres/d as the new data point will still locate above the green curve with 5 m3/d water rate, as illustrated by the red arrow for well b. however, well c data point locates below the blue curve, with 3 m3/d water rate, indicating hydrate formation risk, so meg injection rate needs to be increased to 500 litres/d, as shown by the red arrow for well c. figure 12 shows the hydrate formation temperature at the pipeline inlet from one pad to the gas gathering station. sour gas from several wells in the same pad flows into the same pipeline, so the pipeline inlet temperature is the average temperature from all the wells. each well has the same twochoke surface system as described in figure 3. however, even the wellhead gas temperature is similar among the wells at the same gas rate, the working efficiency of the water jacket heaters equipped for each well could be different. therefore, in addition to monitoring the hydrate risk downstream of the first and/or the second chokes of each well, the hydrate formation curve needs to be monitored at several critical areas, specifically at the pipeline connection after all gas streams from the wells are combined. figure 12—sour gas hydrate formation temperature at pipeline inlet at a given pressure & various meg rates. data point a locates below the curve with 600 liters/d meg rate, indicating the meg rate is insufficient for preventing hydrate risk, and shall be increased up to 1,200 liters/d (for reliability) to ensure hydrate-free condition in the pipeline. data point b represents higher gas rate and higher pipeline inlet temperature, because the wellhead gas temperature is higher due to higher gas production rate from the reservoir. for point b, 600 liters/d meg injection rate into the pipeline is sufficient to prevent hydrate risk. care must be taken as ambient temperature variation (i.e., in winter and summer) can affect the temperature profile of the surface facilities, so normally higher meg rate is required in winter than summer. lessons learned higher gas production leads to higher gas temperature at the wellhead, resulting in a corresponding higher j/t cooling effect through the chokes. the designed constant pressure profile both upstream and downstream of the second choke, which is maintained by the automatic adjustment of the choke, prevents agitation and pressure pulsations along the surface process. that can accelerate the hydrate formation, because turbulence can serve as a catalyst. 9 when adjusting gas production from each well, care must be taken to analyze the hydrate formation curves in various locations because the p/t profiles of the surface process change simultaneously with gas rate. conclusions with the visualization system in place, operators can easily see and understand where would be potential areas for hydrate formation risk, what conditions are required for hydrate formation, presence of water and hydrate formers, and the prevention method to manage hydrate risk.  the visualized monitoring module, integrated with the central control system, makes the work easier to monitor and to analyze the hydrate risk, and to optimize the meg injection rate for cost management.  this is to support our operations team at field site to develop best practices and focus areas for an effective hydrate prevention and management. acknowledgment the authors thank uecsl and cnpc for their permission to publish this paper. the authors also thank all the personnel, particularly field operators, who involved in the data collection at the field site and providing suggestions to the design of the real-time visualization system. conflicts of interest the author(s) declare that they have no conflicting interests. references avaldsne, o.g. 2014. an analysis of co2, ch4 and mixed co2-ch4 gas hydrates: experimental phase equilibria measurements and simulations with state-of-the-art software. https://pdfs.semanticscholar.org/6d1c/3b10e3758bcd64d156060036af586ad42a2e.pdf ballard, a., shoup, g., and sloan, d. 2011. industrial operating procedures for hydrate control. natural gas hydrates in flow assurance 23(2): 145-162. bulbul, s., parlaktuan, m., mehmetoglu, t., et al. 2014. hydrate formation conditions of methane hydrogen sulfide mixtures. energy sources, part a: recovery, utilization, and environmental effects 12(3):2527-2535. king, h.m. methane hydrate. downloaded 10 november 2017. http://geology.com/articles/methane-hydrates/. rajnauth, j.j., barrufet, m.a., and falcone, g. 2010. hydrate formation: considering the effects of pressure, temperature, composition and water. paper presented at spe europec/eage annual conference and exhibition, barcelona, spain, 14-17 june. spe-131663-ms. the hydrate problem. pennsylvania state university (psu). downloaded 10 november 2017. https://www.e-education.psu.edu/png520/m21_p3.html. jianjiang lv, spe, is production engineer in unocal east china sea ltd., where he has worked for 7 years. his research interests are in production and reservoir engineering. he holds master’s degree and ph.d. from southwest petroleum university, both in petroleum engineering. jianbo yuan, spe, is drilling and completion engineer in unocal east china sea ltd., where he has worked for 7 years. his research interests are in drilling and completion engineering. he holds master’s degree from china petroleum university beijing in drilling engineering. minh vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 4+ years. he has had 25 years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. https://pdfs.semanticscholar.org/6d1c/3b10e3758bcd64d156060036af586ad42a2e.pdf https://www.sciencedirect.com/science/article/pii/b9781856179454000078 https://www.sciencedirect.com/book/9781856179454 https://www.sciencedirect.com/book/9781856179454 http://geology.com/articles/methane-hydrates/ https://www.e-education.psu.edu/png520/m21_p3.html 10 junliang zhang, spe, is a production engineer in southwest oil & gas field company, where he has worked for 13 years. his research interests are in production engineering and daily field operations. he holds master’s degree from southwest petroleum university in petroleum engineering. abstract introduction sour gas project lessons learned conclusions acknowledgment conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.426 received july 2, 2018; revised september 23, 2018; accepted october 13, 2018. *corresponding author: liuss.gwdc@cnpc.com.cn 1 comparison of fracturing treatment design with an in-house code, mfrac and fracpro shanshan liu*, great wall drilling company, beijing, china abstract hydraulic fracturing software is widely used in our industry nowadays for fracturing treatment design. some of them are fracturing simulators that can actually mimic fracture growth while some kind is solely for treatment design. although being different, they can provide reasonable ultimate fracture geometry and design procedure. this project aims to compare design results from three different fracturing software. four case scenarios are studied, which involve sensitivity of consistency index of fracturing fluid, out-ofzone fluid loss multiplier, minimum horizontal stress and reservoir permeability. each parameter is studied with individual software without interference. results from this project can help users to understand how to cope with design changes when there is dramatic input change. introduction three software are used for this study. they are m23(a self-developed program), mfrac and fracpro. mfrac and fracpro are fracturing simulator that can provide fracture properties under every time step so that users can see how the fracture grows. meanwhile, they also provide treatment design. not being a simulator for m23, it will not provide how fracture grows during the treatment, but it will give the ultimate fracture geometry and treatment design. no matter which software is used for treatment design, users must cope with different input changes. once there are input changes, the ultimate fracture geometry and pumping sequence are likely to change. so, users have to understand the physics behind the software so that these changes can be properly treated. to achieve this, this project selects four representative parameters and investigate how they influence fracture design. this paper is written in such a way that there is no interference between each software. all four parameters are studied by each individual software, as shown in figure 1. input data the layer data are shown in table 1. it is a sandstone reservoir with shale layer laminated. data for proppant and fracturing fluid are shown in table 2 and 3. table 4 shows reservoir property. study through m23 in this section, we studied the effect of consistency index, out-of-zone fluid loss multiplier, minimum horizontal stress of top layer and reservoir permeability by using m23. we first run a base case and get the results. then we run separate case by changing one of the parameters above, and compare results with the results of the base case. for this section, the results are summarized in appendix a. mailto:liuss.gwdc@cnpc.com.cn 2 table 1—reservoir layer data. top ft thickness ft stess psi kic psi in1/2 perf e 106psi v k md lith 1 9000 500 7585 1000 false 4.28 0.3 0.001 shale 2 9500 100 7831 1000 false 4.28 0.3 0.001 shale 3 9600 15 7110 1200 true 2.80 0.26 0.5 sand 4 9615 50 7905 1000 false 4.28 0.3 0.001 shale 5 9665 10 7156 1200 true 2.80 0.26 0.5 sand 6 9675 30 7946 1000 true 4.28 0.3 0.001 shale 7 9705 10 7158 1200 true 2.80 0.26 0.5 sand 8 9715 15 7972 1000 true 4.28 0.3 0.001 shale 9 9730 10 7204 1200 true 2.80 0.26 0.5 sand 10 9740 100 8028 1000 false 4.28 0.3 0.001 shale 11 9840 500 8274 1000 false 4.28 0.3 0.001 shale table 2—proppant data. proppant mass 400000 lbm proppant permeability 50000 md proppant relative gravity 2.65 stressed proppant porosity 0.3 unstressed proppant porosity 0.38 table 3—fracturing fluid data. power law fracturing fluid consistency index, k 0.1 lbf·ft-2·sn flow behavior index, n 0.6 table 4—reservoir property. reservoir area, ad 40 acre proppant mass, m2w 400000 lbm proppant permeability, kf 50000 md reservoir permeability, k 0.5 md net pay, hn 45 ft figure 1—project framework. case 1: consistency index of fracturing fluid decrease 10 times. fracturing fluid is power law fluid. based on pkn model, the fracture width of power law fluid is calculated with eq. 1. ��,0 = 9.15 1 2�+2 × 3.98 � 2�+2 1+2.14� � � 2�+2� 1 2�+2 �� �ℎ� 1−��� �' 1 2�+2 ,…………………….......………………….(1) we can see fracture width is function of fluid rheology properties, fracture height, rock plane modulus and pumping rate. if fluid consistency index decreases by 10 times, the fracture width will become approximately 2 times smaller, as shown in eq. 2. �1 �2 = �1 �2 1 2�+2 = 10 1 2∗0.6+2 = 2.05,..………………………………………………………….…..…….(2) in m23, the ultimate fracture length is pre-designed fracture length, which comes from ufd optimization. fracture height is coupled with fracture width through net pressure. with the changed parameter, m23 cannot give a treatment design. it is not feasible, so we need to focus on m10. in m10, the fracture length and height are kept the same as base case. decreasing fracture width will decrease fracture volume. if proppant mass is kept the same, the slurry concentration in some stage will be larger than movable slurry concentration. the calculation is through eq. 3. ��ℎ� = ��−1���� ����ℎ��� ，��ℎ� > ���������,…………………………………..………………………..….…….(3) 4 in order to solve this problem, we need to decrease slurry concentration. we can either increase fracture volume or decrease proppant mass. after calculation, the following two methods are suggested.  design a longer fracture with half length 670 ft  reduce mass of proppant to 245,000 lbm. however, both methods produce a lower jd. case 2: increase fluid loss multiplier outside pay zone from 0.25 to 0.45. in order to get the optimal jd, ufd method is used to get the optimum fracture length and conductivity. the fluid loss multiplier outside the pay zone does not affect the ufd optimization. so, the designed fracture half-length will not change. it is still 463 ft. due to the layer data, net pressure and fluid density remain the same, the fracture height will also not change. based on eq. 1, the fracture width will not change either. however, the fluid loss multiplier affects the slurry mass balance equation. �� ℎ��� � − 2��� � − (��� + 2��) = 0,…...…………………………………………………….…………(4) ������� = ���� ,...………….…..…………….……………………………………………………….….(5) ������� = ������� − �����,..…….…………….…………………………………………..……..………(6) � = ����� ������� ,.…………………………………….………………………………………………....…….(7) ���� = ���� ,…………………………………………………………………………………………….(8) the increase of cl and sp results in a larger pumping time. in this case, parameters that are related with pumping will change based on eqs. 4 to 8. generally, as the slurry volume, liquid volume, pumping time and pad time increase, the slurry efficiency decreases. the results can be seen in appendix a. by comparing the results between base case and this changed case, we can see m23 can help users to decrease the negative effect of changing fluid loss multiplier and give an adjusted design. case 3: increase minimum horizontal stress in layer 1 by 1000 psi. minimum horizontal stress is involved when calculating net pressure, and further this will affect the calculation of stress intensity factor, as shown in eq. 9. the equilibrium fracture height will be affected. ��+ = 1 �� −� � ��(�) �+� �−� ��� ,….……..…………………………………………………………...…….(9) if we look at the fracture height of the base case, the upper tip is at 9,510 ft. the first layer is from 9,000 ft to 9,500 ft. that means the fracture upper tip does not penetrate into layer 1, as shown in figure 2. therefore, before doing the design, we can guess that changes of minimum horizontal stress in layer 1 will not affect the fracture upper tip position. and the whole fracture geometry will remain the same. correspondingly, the treatment schedule will also be the same. this speculation is proved by running m23 with the changed parameters. the results comparison is shown in appendix a. case 4: decrease reservoir permeability by 5 times. reservoir properties determine the fracture optimization design. fracture needs to be designed to produce maximum productivity index for given amount of proppant. therefore, change of reservoir properties will need a new fracture optimization. figure 3 describes the effect of reservoir permeability. a new fracture optimization and treatment design is obtained by running m23 with changed reservoir permeability. the results are shown in appendix a. we can see the new jd is larger than the base case. the comparison between this case and base case shows that m23 can give adjusted new design if reservoir permeability changes. figure 2—fracture profile of base case. change of reservoir permeability change of proppant number change of jd, cfd-opt and xf-opt change of whole pumping schedule figure 3—effect of reservoir permeability. study through mfrac in this section, we studied the effect of consistency index, out-of-zone fluid loss multiplier, minimum horizontal stress of top layer and reservoir permeability by using mfrac. likewise, we first run a base case and get the results. then we run separate case by changing one of the parameters above, and compare results with the results of the base case. for this section, the results are summarized in appendix b. case 1: consistency index of fracturing fluid decrease 10 times. in mfrac, the final proppant concentration is set to stop the simulation process. if the proppant concentration across the fracture is larger than this value, the simulated pumping continues until this concentration is reached. in this study, we set the final proppant concentration to be 10 ppga. if we change consistency index of fracturing fluid, the fracture width during pumping becomes smaller. in order to accommodate the proppant, the fracture length has to become longer. in other words, mfrac will always produce a treatment design, with fracture geometry being very different. in this case, the fracture half-length is around 300 ft longer than base case. meanwhile, the fracture height in mfrac is obtained from an aspect ratio with fracture length. if the length increase due to pumping, the fracture height will also keep increasing correspondingly. the calculated results are shown in appendix b. we can see mfrac can provide user an adjusted design if the consistency index changes. case 2: increase fluid loss multiplier outside pay zone from 0.25 to 0.45. fluid loss data are modified layer by layer in mfrac. modification is only applied to shale zone. provided the same amount of proppant, same fracturing fluid, and same final proppant concentration, the simulation process (fracture propagation process) will keep going until the final proppant concentration reaches the pre-set value. in 6 other words, the fracture volume is the same as base case. the fracture width in mfrac is calculated through radial model (eq.10) � ∝ 1−�2 � ���� 2−� 2 2 3�+6 ,..………………………………………………..………..…………..…….(10) we can see the fracture width will not change due to fluid loss change. in the meanwhile, the fracture height and fracture length is coupled. so for the same fracture volume, if fracture width does not change, neither the fracture height nor length will change. the mass balance equation in mfrac is also described with eqs. 4 through 8. so larger fluid loss coefficient leads to a larger pumping time, volume pumped and pad time. the slurry efficiency will become smaller. we can see, mfrac can adjust another design if fliud loss parameter changes. the results are shown in appendix b. case 3: increase minimum horizontal stress in layer 1 by 1000 psi. in base case, the fracture upper tip is at 9349 ft, which is in layer 1. so if the minimum horizontal stress in layer 1 increases, the fracture height will decrease according to eq. 6. the simulation results are shown in appendix b. we can see the fracture height decreases from 503 ft to 380 ft. in order to accommodate the proppant, the product of fracture length and width should increase. we can see mfrac can adjust treatment design if minimum horizontal stress changes. case 4: decrease reservoir permeability by 5 times. mfrac is fracture treatment design software. it cannot give fracture optimization design. if we change the reservoir permeability but keep the proppant mass, fracturing fluid the same and final proppant concentration the same, the ultimate fracture geometry will not change. in the meanwhile, the fluid loss parameters are not correlated with permeability in mfrac, so the simulated pumping parameters will also be the same. this can be seen in appendix b. however, as a designed, we always want to have a maximum jd. so, the user should be knowledgeable to have a rough estimation towards the fracture geometry and dimensionless conductivity. mfrac cannot substitute users at this point. study through fracpro in this section, we studied the effect of consistency index, out-of-zone fluid loss multiplier, minimum horizontal stress of top layer and reservoir permeability by using fracpro. like previous two cases, we first run a base case and get the results. then we run separate case by changing one of the parameters above, and compare results with the results of the base case. for this section, the results are summarized in appendix c. case 1: consistency index of fracturing fluid decrease 10 times. in fracpro, the target cfd is set to stop the simulation process. if the cfd is not reached after limited number of iterations, the software will stop. compared with base case, the cfd is still 4.5 in this changed case. fracpro cannot give a treatment design because the calculated fracture width is small. in order to have a treatment, users need to decrease the target cfd. in this case, the cfd is changed to 0.2, and a treatment design is calculated, as shown in appendix c. we can see the proppant mass decrease around 20 times as compared with base case. the fracture geometry remain close. this means the fracture permeability becomes smaller. in general, fracpro cannot adjust its treatment design if fracturing fluid consistency index changes. user need to make adjustments based on own knowledge. case 2: increase fluid loss multiplier outside payzone from 0.25 to 0.45. fluid loss data are correlated with formation permeability in fracpro. so, the change of fluid loss multiplier will have formation permeability changed. in this case, i changed shale layer permeability to have the fluid loss coefficient out of payzone changed. the calculated results are shown in appendix c. we can see the results are close to the base case, expect the slurry volume, liquid volume, injection time and pad time. the slurry efficiency is a little lower. these parameters are correlated with mass balance, as we have discussed in previous sections. as can be seen, fracpro can adjust its treatment design if fluid loss parameters change. case 3: increase minimum horizontal stress in layer 1 by 1000 psi. in base case, the fracture upper tip is at 9,514 ft, which is in layer 2. therefore, if we change the minimum horizontal stress of layer 1, the results will not be changed. the results are shown in appendix c. we can see the results are the same as base case. we cannot conclude fracpro can adjust its treatment if minimum horizontal stress changes by just running this case. however, m23 give correct result for this case. case 4: decrease reservoir permeability by 5 times. a target cfd is set for this simulation. if reservoir permeability decreases, the product of fracture width and fracture permeability should also decrease. in this case, fracture width remains the same because we based on eq.1, so the fracture permeability should decrease, which cause the decrease of proppant concentration inside of fracture. also, the mass proppant concentration in injected slurry will also decrease. in the meanwhile, the fluid loss parameters will also decrease for the pay zone. thus, the parameters related with mass balance will change. in the results, the slurry volume, liquid volume, injection time and pad time decreases and slurry efficiency increases. as we can see, fracpro can help to adjust the treatment design if reservoir permeability changes. table 5—summary. m23 mfrac fracpro consistency index n y n fluid loss parameter y y y minimum horizontal stress in top layer y y y reservoir permeability y n y conclusions we can draw the following conclusions: 1) in general, different software have different ability to cope with input changes. it can be summarized in table 5 (y is the software can adjust and n is not). 2) when we analyze sensitivity of parameters, first we need to know how the fracture geometry changes. 3) based on fracture geometry, we then analyze how the pumping schedule changes. conflicts of interest the author(s) declare that they have no conflicting interests. references user manual, mfrac, meyer associates user manual, fracpro, carboceramics 8 appendix a base case k1 10 times smaller flmult from 0.25 to 0.45 1000psi increase k decrease 5 times mass of proppant injected, lbm 400000 400000 400000 400000 400000 mass proppant concentration in injected slurry (ppga) 10.2 na 10.2 10.2 5.42 slurry volume injected (gal) 159000 na 226000 159000 264000 liquid volume injected (gal) 141000 na 208000 141000 246000 injection time (min) 108 na 154 108 180 pad time (min) 44.64 na 86.8 45.1 77.8 frac slurry efficiency 0.36 na 0.253 0.36 0.348 net frac pressure (psi) 312 na 312 312 319 half length (ft) 463 na 463 463 618 upper frac height (ft) 160 na 160 159 169 lower frac height (ft) 137 na 137 137 152 total frac height (ft) 296 na 296 296 321 max frac width (in.) 0.534 na 0.534 0.534 0.591 average frac width (in.) 0.336 na 0.336 0.336 0.371 average surface concentration (lbm/ft^2) 1.46 na 1.46 1.46 1.01 upper tip location (tvd) (ft) 9510 na 9510 9510 9500 lower tip location (tvd) (ft) 9810 na 9810 9810 9820 treating pressure at reference depth (psi) 7860 na 7860 7860 7870 base pressure to calculate net pressure (psi) 7550 na 7550 7550 7550 dimensionless productivity index 0.943 na 0.943 0.943 1.47 dimensionless fracture conductivity 3.02 na 3.02 3.02 12.51 appendix b base case k1 10 times smaller flmult from 0.25 to 0.45 1000psi increase k decrease 5 times mass of proppant injected, lbm 400000 400000 400000 400000 400000 mass proppant concentration in injected slurry (ppga) 10 10 10 10 10 slurry volume injected (gal) 188080 326410 293070 178940 188080 liquid volume injected (gal) 169980 308310 274970 160840 169980 injection time (min) 127.95 222.04 199.37 121.73 127.95 pad time (min) 75.07 188.12 143.66 68.25 75.07 frac slurry efficiency 0.32 0.188 0.206 0.332 0.32 net frac pressure (psi) 297 186.85 295.26 402.13 297 half length (ft) 450 742.62 451.51 517.26 450 upper frac height (ft) 320.58 361.35 323.29 182.79 320.58 lower frac height (ft) 182.43 146.61 182.31 197.58 182.43 total frac height (ft) 503.01 507.96 505.6 380.37 503.01 max frac width (in.) 0.436 0.265 0.433 0.568 0.436 average frac width (in.) 0.268 0.162 0.267 0.3 0.268 average surface concentration (lbm/ft^2) 1.11 0.656 1.101 1.26 1.11 upper tip location (tvd) (ft) 9349.4 9308.7 9346.7 9487.2 9349.4 lower tip location (tvd) (ft) 9852.4 9816.6 9852.3 9867.6 9852.4 dimensionless fracture conductivity 2.48 0.91 2.46 2.42 2.48 10 appendix c base case k1 10 times smaller flmult from 0.25 to 0.45 1000psi increase k decrease 5 times mass of proppant injected, lbm 469400 22000 476000 467900 112400 mass proppant concentration in injected slurry (ppga) 14 10 14 14 2 slurry volume injected (gal) 150528 119070 186984 149352 127596 liquid volume injected (gal) 129301 118079 165459 128197 122514 injection time (min) 102.2 81 126.9 101.5 86.8 pad time (min) 50.3 36.6 75.5 49.6 26.5 frac slurry efficiency 0.41 0.37 0.32 0.41 0.52 net frac pressure (psi) 1131 1058 1093 1132 1147 half length (ft) 498 482 510 497 495 upper frac height (ft) 157 142 158 156 159 lower frac height (ft) 140 126 141 140 145 total frac height (ft) 297 268 299 296 304 max frac width (in.) 0.68 0.56 0.65 0.68 0.71 average frac width (in.) 0.43 0.35 0.4 0.43 0.44 average surface concentration (lbm/ft^2) 2.21 0.11 2.24 2.22 0.48 upper tip location (tvd) (ft) 9514 9528 9512 9514 9510 lower tip location (tvd) (ft) 9810 9796 9811 9810 9815 treating pressure at reference depth (psi) 8287 8214 8249 8288 8303 base pressure to calculate net pressure (psi) 7156 7156 7156 7156 7156 dimensionless fracture conductivity 4.26 0.2 4.23 4.27 4.58 shanshan liu is a petroleum engineer in the drilling fluid division of great wall drilling company, a subsidiary of china national petroleum corporation. she got both mba and bachelor’s degree from shenyang university, china. abstract introduction input data study through m23 study through mfrac study through fracpro conclusions conflicts of interest references appendix a appendix b appendix c copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1195 received october 08, 2021; revised november 12, 2021; accepted december 29, 2021. *corresponding author: zh931230j@sina.com 1 optimization study of polymer-surfactant binary flooding parameters in maling jurassic low permeability reservoir jie zhang*, yonghong wang, yangnan shanguan, guowei yuan, yongqiang zhang, weiliang xiong, jinlong yang, lili wang, and shuanlian jin, changqing oilfield company, petrochina, xi'an, china abstract the low-permeability jurassic reservoir in changqing maling has been in the middle and high water cut stage after the long-term development of water injection. in order to improve development efficiency and further explore a new way to enhance oil recovery of the reservoir, a significant development test, and a polymersurfactant flooding study were carried out in the maling beisan area in 2011. compared with other polymer-surfactant flooding reservoirs of petrochina, the jurassic reservoir in the beisan area had relatively low permeability and high salinity of formation water and injected water, which puts forward higher requirements on the injectivity and salt resistance of the binary system. at the same time, the viscosity of the formation crude oil was low, and the viscosity of the polymer required to achieve the optimum fluidity ratio was relatively low, which is an important advantage of implementing binary flooding in the reservoir. in this paper, hydrophobic associating polymers and betaine surfactants were selected through laboratory experiments. according to the experimental data, numerical simulation technology was used to analyze and optimize the influence factors, including injection speed, injection-production ratio, slug size, slug polymer, and surfactant concentration. finally, the development index of binary flooding was predicted. the results show that the optimized polymer-surface system had good injectivity and high formation compatibility. through on-site differential control measurement of injection and production, the recovery was enhanced significantly. this study had guiding significance for the production of polymer-surface flooding in similar reservoirs. introduction the development of changqing oilfield started from the jurassic reservoir. currently, most jurassic reservoirs have been in the stage of high water cut development (comprehensive water cut of 69.0%, recovery degree of reserves of 76.5%); the overall decline of the reservoir was large (13.6%/11.8%); the water cut was accelerated; the oil recovery speed was low; the distribution of remaining oil was scattered and complex, and it was difficult to stabilize production. thus, it was urgent to carry out technical research to improve oil recovery. polymer-surfactant flooding technology can effectively reduce water-oil mobility ratio, expand swept volume of water drive, and improve the efficiency of oil displacement. it was an important means to effectively reduce water cut and improve the final recovery of reservoirs during the middle and high water-cut stage. compared to other oil fields of petrochina, there were some difficulties in the development of polymermailto:zh931230j@sina.com 2 surfactant flooding in the low-permeability jurassic reservoir in changqing due to its low-permeability, strong heterogeneity, high salinity of formation water and injected water, etc. the successful experience of the medium and high-permeability reservoir was difficult to be employed, so it was necessary to study a binary system with good injectivity and high-efficiency salt resistance. combined with the corresponding adjustment technology to further improve the recovery of this reservoir. test overview the main oil reservoir in the study area is the jurassic system yan10 and the secondary yan9. the depth of the yan10 reservoir was 1,500-1,750m; the average thickness was 5.9m; the average effective porosity was 15.0%; the average effective permeability was 110×10-3μm2; the oil saturation was 65% and the formation water salinity was 23.2g/l. before the on-site test, the comprehensive water cut was 88.54%, and the recovery was 23.53%. to further improve oil recovery, 14 new wells were drilled in the test area, the well pattern was adjusted from irregular anti-seven-point well pattern to five-point well pattern, and the well spacing between injector and producer was adjusted from 250-350 m to 150m, resulting in a pattern with 9 injectors and 16 producers (figure 1). the injection mode of "polymer pre-slug + main slug + sub-slug + polymer protection slug" was selected as the injection scheme of polymer-surfactant flooding. the total injection volume was 0.65pv and the injection speed was 0.15pv/a. figure 1—well location in test area. the red dots represents producer, and the blue dots are injector. optimization of a binary system according to the characteristics of the low-permeability jurassic reservoir in changqing, the formulation of the system was studied. the selected polymer molecular weight should be suitable for low permeability reservoir. for high calcium/magnesium ion and high salinity formation, the selected polymer should have good salt resistance and viscosity enhancement ability. the core of technology research is that the system has good viscosity enhancement, good injection performance, strong ability of controlling fluidity, and it can improve swept volume, reduce oil-water interfacial tension to ultra-low, improve oil displacement efficiency. the system also should stable (salt resistance, shear resistance, small adsorption, etc.). polymer optimization. 29 samples of low molecular weight polymers were collected in the laboratory. they were hydrophobic associating polymers, star polymers, composite polymers, functional polymers, zwitterion polymers, etc. all of them had the ability to resist salt and shear, and their molecular weight ranged from 6 to 20 million. 3 by evaluating the performance of hydrophobic associating polymer, the polymer had better viscosity increasing ability, and the solution with the same concentration had higher viscosity than the solution used in the beisan area (figure 2). the performance of this polymer was relatively stable and the viscosity remained basically the same as the injection water temperature increased (figure 3). the viscosity retention rate was high after rock sand adsorption and the viscosity remained the same after shear at a medium speed of 2000rpm/min. however, the viscosity will decrease at high shear speed only. the resistance coefficient of the core displacement experiment was 12.82 and the residual resistance coefficient was 1.79 (figure 4). figure 2—comparison of viscosity enhancement between hydrophobic associating polymer and other polymers. figure 3—comparison of stability between hydrophobic associating polymer and other polymers. figure 4—injection experiment of hydrophobic associating polymer. compared to the polyacrylamide polymer and functional polymer, the hydrophobic associating polymer had better properties of increasing viscosity, salt resistance, shear resistance, and adsorption resistance. therefore, hydrophobic associating polymer (8 million) was selected as the experimental polymer. surfactant optimization. the zwitterions produced by the ionization of amphoteric surfactant in aqueous solution have a certain chelating effect on the divalent metal ions, such as calcium and magnesium, giving them strong salt resistance. based on the characteristics of oil and water in the jurassic reservoir, the betaine formulation system was optimized. hydroxypropyl-sulfo betaine surfactant was synthesized by introducing hydroxysulfonic group into straight chain alkane, which gave the system excellent salt resistance and emulsification performance (table 0 20 40 60 80 100 0 1000 2000 3000 4000 5000 v is co si ty , m p a. s concentration, mg/l hydrophobic associating polymer (8 million) poly-acrylamide polymer functional polymer (4 million) functional polymer (7 million) 0 10 20 30 40 50 0 10 20 30 40 v is co si ty , m p a. s time, day hydrophobic associating polymer (8 million) poly-acrylamide polymer functional polymer (4 million) functional polymer (7 million) 3.5 12.3 43.3 66.1 88.3 12.5 6.6 0 2 4 6 8 10 12 14 0 10 20 30 40 50 60 70 80 90 100 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 v is co si ty r et en ti o n r at e, % r es id u al r es is ta n ce c o ef fi ci en t, % injection multiple, pv viscosity retention rate water flooding polymer flooding secondary water flooding 4 1). the core experiment shows that when the concentration was greater than 0.25%, the oil displacement efficiency increased and the oil washing efficiency slowed down. the oil washing efficiency experiment shows when the concentration was greater than 0.25%, the interfacial tension increased and the oil washing efficiency decreased. therefore, the optimal concentration of betaine was determined to be 0.2-0.25% (table 2). table 1—selection and comparison of surfactant for oil displacement in test area. surfactant emulsification index oil-water interfacial tension (mn/m) betaine 82 2.3×10-3 aes 78.6 6.9×10-1 nonionic surfactant 1# 35 5.6×10-3 lh-1 23.6 8.2×10-4 petroleum sulfonate 1# 36.9 4.7×10-2 gemini surfactant 52.3 3.8×10-3 table 2—results of the oil displacement test of betaine surfactant with different concentrations. porosity (%) oil saturation (%) permeability (md) surfactant concentration (wt%) oil recovery slug and viscosity water flooding chemical flooding ultimate 1 18.4 62.2 57.9 0.1 39.94 12.06 52 0.3pv main slug +0.2pv protection slug, polymer1500ppm, viscosity 30cp 2 19.68 65.3 104.3 0.15 36.3 16.26 52.56 3 18.39 66.4 76.3 0.2 36.4 20.33 56.73 4 17.3 65.07 59.2 0.25 37.3 22.19 59.49 5 18.96 64 70.7 0.3 37.38 23.74 61.12 adaptability evaluation of binary system. through a previous study, the binary system (hydrophobic associating polymer + betaine surfactant) suitable for the jurassic oil reservoir was developed. the binary system had a synergistic viscosity increase effect (figure 5), good shear resistance, and good thermal stability. compared with water flooding and polymer flooding, binary flooding increased oil displacement efficiency by 20.5% and 14.9%, respectively (figure 6). figure 5—viscosity and concentration curve of the binary system. 0 10 20 30 0 500 1000 1500 2000 v is co si ty , m p a. s concentration, mg/l betaine binary system ldf-8a+ 5 figure 6—core displacement experiment of binary system. effect of injection-production parameters based on the evaluation experiment of the parameters of the binary system and the model of the binary flood of the jurassic reservoir in the beisan area, after injected into the binary system, the simulation stopped when the water cut reached 98% under water flooding. the single-variable method was used to study the effect of different parameters on polymer flooding. the water cut and the recovery curve under different injection and production parameters was used to evaluate the increase in recovery and the decrease in water cut. effect of injection speed. the faster the injection speed was, the higher the recovery rate was. but the faster the water cut rising speed was, the shorter the corresponding production time was. when the injection speed was greater than 0.15pv/a, the recovery rate increased slowly (figure 7). the optimal injection rate was estimated to be about 0.15pv/a. effect of injection-production ratio. the cumulative oil production under different injection-production ratio was predicted using numerical simulation. with the increase in injection production ratio, the decrease range of water cuts increased. however, the water content increased quickly. when the injection-production ratio was less than or equal to 0.8, the larger the injection-production ratio was, the greater the recovery increased; when the injection production ratio was greater than 0.8, the recovery rate decreased (figure 8). thus, the suitable injection-production ratio was about 0.8. figure 7—numerical simulation of the effect of the injection rate on oil recovery. figure 8—numerical simulation of the effect of the injection-production ratio on oil recovery. 0 0.5 1 1.5 2 2.5 3 0 10 20 30 40 50 60 70 80 0 1 2 3 4 5 6 7 8 9 10 r es is ta n ce /r es id u al r es is ta n ce co ef fi ci en t o il d is p la ce m en t ef fi ci en cy , % injection multiple, pv oil displacement efficiency resistance/residual resistance coefficient water flooding binary flooding secondary water flooding 4.0 5.5 6.3 6.7 7.1 7.4 0.0 2.0 4.0 6.0 8.0 10.0 0.05 0.08 0.1 0.12 0.15 0.2 e n h an ce d o il r ec o v er y , % injection rate, pv/a 5.0 6.1 6.7 7.0 6.6 5.9 0.0 2.0 4.0 6.0 8.0 10.0 0.2 0.4 0.6 0.8 1 1.2 e n h an ce d o il r ec o v er y , % injection-production ratio, m3/m3 6 effect of the size of the main slug. with increasing slug size, the recovery rate increased and the increasing rate of water cut slowed. when the main slug size was greater than 0.3pv, the recovery rate increased slowly (figure 9). the size of the main slug was determined to be about 0.3pv. effect of the polymer concentration of the main slug. the effect of binary flooding was studied by varying the polymer concentration of the main slug. with the increase of polymer concentration, oil recovery increased. when the concentration was greater than 2000mg/l, the oil recovery rate gradually increased (figure 10). thus, the optimal concentration was determined to be 2000mg/l. figure 9—numerical simulation of the effect of the size of the main slug on oil recovery. figure 10—numerical simulation of the effect of polymer concentration on oil recovery. effect of the surfactant concentration of the main slug. the effect of binary flooding was simulated by changing the surfactant concentration of the main slug. with an increase in surfactant concentration, the recovery rate increased. when the concentration was greater than 0.15%, the oil recovery rate increased slowly (figure 11). the optimum concentration was approximately 0.2%. figure 11—numerical simulation of the effect of surfactant concentration on oil recovery. 5.5 6.4 6.9 7.3 7.4 7.5 0 2 4 6 8 10 0.05 0.1 0.2 0.3 0.4 0.5 e n h an ce d o il r ec o v er y , % pv 3.9 5.3 6.2 6.7 6.8 0 2 4 6 8 10 750 1000 1500 2000 2500 e n h an ce d o il r ec o v er y , % concentration, mg/l 4.1 6.0 7.0 7.1 7.2 0.0 2.0 4.0 6.0 8.0 10.0 0.05 0.1 0.15 0.2 0.25 e n h an ce d o il r ec o v er y , % concentration, mg/l 7 table 3—rank of influencing factors in numerical simulation. numerical simulation parameters sensitivity coefficient on eor sensitive coefficient on water cut injection-production ratio 0.407 0.411 polymer concentration 0.224 0.255 surfactant concentration 0.194 0.132 injection speed 0.192 0.087 total amount of binary slug injection 0.133 0.000 sensitivity analysis. based on the concept of variation coefficient in statistics, sensitivity coefficient was introduced as the evaluation metrics of polymer flooding parameters (table 3). taking the decrease of water content as an example, the expression for calculating the sensitivity coefficient is as follows: 𝑆 = 1 δ𝐸𝑂𝑅 √ 1 𝑛−1 ∑ (δ𝐸𝑂𝑅𝑖 − δ𝐸𝑂𝑅) 2 𝑛 𝑖=1 ,………...………………………………………………………(1) where, δ𝐸𝑂𝑅 means the average recovery increment, %; n is the number of numerical simulations, it was set to be 5 in this study; δeori is the increasing recovery range under the value of group i, %; through the calculation and statistics of the sensitivity coefficient, the sensitivity from strong to weak is as follows (table 3): injection-production ratio, polymer concentration, surfactant concentration, injection speed, total amount of binary slug injection. parameter optimization results. based on the above studies and field test performance, it was determined that the injection rate was maintained at 0.15pv / a, the injection production ratio was 0.75, the polymer concentration was kept at 2000mg / l, the surfactant concentration was adjusted from 0.12% to 0.2%, the main slug size was adjusted from 0.2pv to 0.3pv and the overall injection volume was 0.75pv. after adjustment, the recovery rate increased by 1.8% compared to the current development scheme (figure 12). figure 12—comparison of recovery efficiency before and after optimization using numerical simulation. field test results in august 2016, the pre-slug was injected into the test area. in june 2017, the binary system was injected. currently, a binary system of 0.28pv (designed volume of 0.65pv) has been injected in total, accounting for 43.5% of the designed volume. daily oil production increased from 10.9t to 20.5t, comprehensive water cut decreased from 95.2% to 91.7% (figure 13), the cumulative oil production increased by 9400t. the benefit of binary flooding was obvious. 8 from 2017 to 2018, five wells were chosen to remove the formation plugging. after the measurements, daily liquid production increased significantly, daily oil production increased by 2.8t, and cumulative oil production increased by 628t. the parameters of four oil wells were optimized, with the daily oil production increase of 1.52t and the cumulative oil production increase of 971t. in 2019, the parameters optimization was carried out in two oil wells. at present the daily oil production increased by 1.23t and the cumulative oil production increase by 482t. figure 13—daily oil production and water cut curve of the test area. conclusions 1. for changqing low permeability and high salinity reservoir, low molecular weight and salt resistant polymer was the preferred choice. the hydrophobic associating polymer (8 million) currently selected in the laboratory is the polymer with good stability, shear resistance, small adsorption, high resistance coefficient, high viscosity retention rate of the berea core displacement fluid and high efficiency of oil displacement. 2. for a changqing’s low permeability and high salinity reservoir, the performance of the surfactant for oil displacement should be based on the ability of anti-adsorption, salt resistance, and strong oil washing to maintain the continuous injection of chemicals. at present, the optimized betaine surfactant had good adaptability. 3. in the research of chemical flooding in the jurassic reservoir of changqing, the sensitivity of injection and production parameters from strong to weak was as follows: injection production ratio, polymer concentration, surfactant concentration, injection speed, total injection amount of binary slug. 4. the development of chemical flooding technology was limited to improving oil recovery in lowpermeability reservoirs, relying only on the improvement of the chemical system performance to enhance the ultimate oil recovery, which must be combined with fine injection and production control. 5. for chemical flooding in low-permeability reservoirs, it was necessary to adjust injection-production parameters, improve the injection profile, and reduce the plugging rate near the well. the small and low molecular weight polymer should be studied and developed in the laboratory, and a reasonable injection concentration should be estimated and determined. at the same time, special measurements were taken to remove the plug around the oil wells. as a result, a series of eor supporting technologies that were suitable for changqing’s low-permeability reservoir was proposed and developed. 90 91 92 93 94 95 96 97 98 99 100 0 5 10 15 20 25 2012/4/1 2013/1/26 2013/11/22 2014/9/18 2015/7/15 2016/5/10 2017/3/6 2017/12/312018/10/27 w at er c u t, % d ai ly o il p ro d u ct io n , t date daily oil production water cut blank water flooding main sulg trial injection stage overall injection 10.9 95.2 20.5 91.7 9 conflicts of interest the author(s) declare that they have no conflicting interests. references cao, r., ding, z., liu, h., et al. 2005. experimental study of permeability limit and oil displacement effect of polymer flooding in low permeability reservoirs. daqing petroleum geology & development 24(5): 71-73. liao, g. 2018. practice and understanding of major oilfield development test. beijing: petroleum industry press. liu, w. 2017. polymer surfactant composite flooding technology. beijing: petroleum industry press. liu, y. 2006. polymer flooding eor technology. beijing: petroleum industry press. mao, s., cheng, y., and pu, x. 2011. course of probability theory and mathematical statistics. beijing: higher education press. hou, s., chang, x., and yuan, q. 2009. research on the application of numerical simulation of polymer flooding. petroleum geology and engineering 23(2): 110-112. wang, x. 1990. determination of main parameters in numerical simulation of polymer flooding. petroleum exploration and development 17(3): 69-76. wang, y., huang, y., sun, z., et al. 2017. study on sensitivity of numerical simulation parameters of polymer flooding. petroleum geology and recovery efficiency 24(1): 78-79. yang, c. 2007. eor technology by chemical flooding. beijing: petroleum industry press. yuan, f. and li, z. 2008. study on the influence degree of different factors on polymer flooding effect. journal of southwest petroleum university (science & technology edition) 30(4): 98-100. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1177 received september 23, 2020; revised november 15, 2020; accepted december 18, 2020. *corresponding author: neogi@mst.edu 1 emulsion stability of heavy oil with surfactants and nanoparticles zainab abdulmohsein, baojun bai, and parthasakha neogi*, missouri university of science and technology, rolla, usa abstract the recovered crude oil is often in form of an emulsion and the recovery is cut off when water to oil ratio exceeds a certain amount. the emulsions vary from water-in-oil to oil-in-water and the step that follows is to coalesce droplets to get two continuous liquids. difficulties arise when the oil contains emulsifiers. there are naturally occurring surfactants, or the oil recovered is by enhanced oil recovery techniques which have additives that stabilize the droplets. we have considered below a heavy oil (viscosity 650-750 mpa.s) containing one of the three surfactants: a nonionic surfactant or a cationic surfactant or an anionic surfactant. in addition, the mix can have alumina or silica nanoparticles or none. most of the results have straightforward interpretations. there is no apparent effect due to nanoparticles. cationic surfactants appear to give rise to a secondary haze. if the system contains nonionic surfactant then it can be destabilized by raising the temperature, except for one notable case. there are also cases of precipitation of nanoparticles. we observe that overall, phase separation happens best in presence of anionic surfactant, although complete phase separation rarely happens. this is attributed here to the very high viscosity of oil, which feature is independent of the additives. introduction the first step in explaining emulsion stability comes from derjaguin-verwey-overbeek (dlvo) theory which looks at the london-van der waals attraction and the electrostatic double layer repulsion between two droplets. this is the flocculation step which brings two droplets together. at the next step or at larger droplet concentrations, the dlvo theory is no longer applicable as two neighboring droplets are always close. this feature is aggravated when the droplets are larger than usual. for one to use dlvo theory to get the rates of flocculation, the droplets have to be less than 0.1 µm. for concentrated systems of large droplet size such as our system below, the key feature that prevents coalescence is the thin film of dispersion medium intervening between two adjacent droplets. film thinning is determined by the mobility of the interface, and can be retarded by the use of surfactants. effects of surfactant solubility, phase, oil/water ratio appear to be known. much of the above can found in common references (miller and neogi 2008). the problem with emulsion stability involving crude oil is well known. brine is found as water-in-oil (w/o) emulsion and has to be removed before downstream operations as it is very corrosive. with time, relatively more brine and less oil is produced, and at some point the oil recovery is stopped. the emulsion may well be oil-in-water (o/w) at that point. these emulsions can be very stable, stabilized by naturally occurring materials or in case of enhanced oil recovery (eor) by additives used. the surfactant flood is used to generate ultralow interfacial tension which is necessary for a good oil displacement. recipes for practically all feasible surfactants are available, where often surfactants need cosurfactants such as alcohol, to reach ultralow interfacial tension (shah and schechter 1977; shah 1985). a recent review looks at alcohol-less sweeps, that mailto:neogi@mst.edu 2 uses the soap formed due to alkali flood and provides a list of surfactants, all with branched chains, some are partially ethoxylated but all are sulfonates or sulfates (hirasaki et al. 2011). petroleum sulfonates are also considered. finally, surfactants are often introduced as foams to provide stable sweeps (smith 1988; li et al. 2008). in some cases, some other additive is used to break the stability. as is apparent, the range of surfactants that can be found at the production well is very high and simple ones are considered in the present work. the use of nanoparticles has not yet seen field work. one difficulty with additives, including just surfactants, is that they often degrade under field conditions. nanoparticles, defined as < 30 nm in diameter, may not degrade. in addition, they appear to fulfill all the requirements for enhanced oil recovery: higher viscosity of the displacing medium and appropriate changes in interfacial tension and wettability (bera and belhaj 2016; zhang et al. 2014; cheringhian and hendraningrat 2016; ko and huh 2019). to study emulsion stability in the laboratory, it is important to look at how they are made. of interest here are emulsions from heavy crude. in the first attempt, oil and a 1% solution of nacl in water were introduced in a large measuring cylinder and emulsified using a homogenizer till the suspension turned white. it implied that the dispersions were in a range smaller than the wavelength of light and hence they scattered light. however, the process required too much heavy oil and was not used. fine emulsions of this kind are needed to study dlvo type of flocculation, hence that approach was abandoned. the next one attempted was spontaneous emulsification. miller (1988) provides one case and we tried a variation. here, oil was layered into a measuring cylinder and then 1% nacl solution in water was added to the top. as oil was less dense, it was expected to rise and form an emulsion. however, the oil chose to cling to the glass surface as it rose upwards. the experiment was redone by rinsing the measuring cylinder with silicone oil. now, the oil rose up in the center in one or two tendrils, which did not break and kept pumping oil to the top. this method of spontaneous emulsification was hence abandoned. finally, the oil was mixed with the 1% solution of nacl, 1% each of a surfactant and nanoparticles. the mixture was hand shaken and stirred with a magnetic stirrer overnight. this process was thus used to make emulsions. it gave drops that were larger than the colloidal range and usually at larger concentrations. as a result, the studies below are confined to the results of film thinning of the dispersion medium that intervenes between two large drops. this is the coalescence step. if we let emulsions stand, the then lower density liquid collects at the top. the collection times can go up to an hour if unstable, as seen by sjöblom et al. (1990) for a 50:50 by volume model oil and water system containing a nonionic surfactant. this also the method practiced industrially. kokal (2005) presents another issue involving surfactants, namely, ethoxylated and related surfactants can be used to demulsify naturally occurring crude emulsions. this is also echoed in some of the articles in brochardt and yen (1989). in the work presented below, emulsion stability of heavy oil has been explored over many emulsifiers. although some work with heavy oils are reported, we believe that we present here the first overall view of the role of emulsifiers for a heavy oil. because of the high oil concentration and large droplet sizes, it is the emulsifier that should control emulsion stability. it is the effectiveness of the additives in phase separation, that are being considered. some general conclusions are expected which are of value. mechanisms are only suggested which although reasonable, will take further work to prove that those apply. experiments crude from a-hauser, kansas, of api gravity 19.9º/specific gravity of 0.9340 and viscosity of 650 mpa.s, all at 23℃ was used. nanoparticles were purchased from sigma aldrich and used as supplied. aluminum oxide particles were < 50 nm in diameter, and silica had a nominal diameter of 12 nm. the crude oil was a-hauser as mentioned earlier. however, when a second sample was brought in, it showed a viscosity of 3000 mpa.s. it was assumed that as the oil had been left outside in a drum through the winter, some wax may have precipitated and was not dissolving under room condition. consequently, the oil was placed in an oven at 80ºf for 30 minutes and on cooling reached a viscosity of 750 mpa.s and 23º api, very close to the previous sample of 650 mpa.s and 19.9º api. water used had 1% nacl. the surfactants were used as purchased: igepal co530 (stepan), cetyl ammonium bromide (ctab) from calbiochem and sodium dodecyl sulfate (sds) from 3 aldrich, and used as received. that is, simplest of nonionic, cationic and anionic surfactants were used. sds does have the common sulfonate group, both sds and ctab have hydrocarbon chain lengths commonly encountered. the nonionic surfactant has the ethoxy group mentioned earlier. water to crude oil volumetric ratios were taken to be 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1. hence the batches were: 1) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% igepal co-530 2) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% sds 3) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% ctab 4) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% igepal co-530, 1 wt% al2o3 nanoparticles 5) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% igepal co-530, 1 wt% sio2 nanoparticles 6) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% sds, 1 wt% al2o3 nanoparticles 7) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% ctab, 1 wt%, al2o3 nanoparticles 8) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% sds, 1wt% sio2 nanoparticles 9) water: oil 1:9, 2.5:7.5, 5:5, 7.5:2.5, 9:1 v/v, water containing 1 wt% nacl, 1wt% ctab, 1 wt% sio2 nanoparticles every batch was put on a tube rack and maintained in a water bath at 24℃. phase separation took place rapidly and if phase separation did not happen in 4 hours, the temperature was raised to 40℃. results and discussion the breaking of emulsions begins with the flocculation step with small droplets colliding with each other. this step does not happen here because the concentration of the dispersed phase is large, the repulsive electrostatic forces between droplets are weak due to high nacl concentration, and drop sizes are large. even if we had started with fine emulsions, this step would be over very soon because of the above two reasons. in the next step, when the two droplets that have approached one another the intervening thin film drains. this drainage is retarded by surface active materials and by high viscosity in the thin films. at latter times the droplets are sufficiently large to show sedimentation or creaming, but the coalescence may not may not have completed. with this short overview, we look at our systems. present samples looked homogeneous. the phase separation took place almost instantaneously. the aqueous phase was often tea colored and sometimes in the oil phase two regions were seen, one black and the other dark brown but with no marked interface. all photographs shown below were taken after 24 hours with figure 1 as the only exception. (a) (b) figure 1—(a) 1% nonionic surfactant in 1% nacl, from left to right, low water to high water. all at 25℃. (b) the two at high water contents at 40℃. one apparently remains stable and the other fully destabilizes. 4 igepal co-530 is a nonionic surfactant (nonyl phenol ethoxylate c9e6). the ethoxy groups are polar but lose that property when the temperature is raised. shown in figure 1(a) are igepol co-530 with water and oil (batch 1). it is very surprising as to how small amounts of oil is able to ingest such large amounts of water. it is being assumed that one has w/o system if the emulsion appears black. on heating to 40℃, one of the samples with a high water content (7.5:2.5) did not break but the one with a higher water content (9:1) did break as shown in figure 1(b). all others broke. consequently, we find significant cases where oil is very active in emulsifying because heavy oil contains asphaltene reaching upto 15%. it is often suggested that asphaltene adsorb on the surface droplets making them stable (el-sayed abdel-raouf 2012; tchoukov et al. 2012). thus, a total of a large amount of emulsifiers may explain why so much water can get ingested into the oil. in case of sds (batch 2), no stable emulsion is found. the water is pristine as seen in figure 2. in figure 3 no stable emulsion is formed (ctab batch 3), but the water is not clear, tea colored at high water content and becomes very dark at low water content. this coloring is probably due to a secondary haze (suzuki et al. 1984) which is made out of very small droplets. now, the heavy oil is acidic, so that the oil molecules are anionic. if a cationic surfactant and an anionic surfactant are brought into contact, liquid crystals are formed. it is possible to surmise that some association of this kind happens here in presence of cationic surfactants as they form ion pairs with the oil molecules. these adsorb on the surfaces of the very small droplets making them stable. suzuki et al. (1984) showed that the stability of the secondary haze in their case was due to small amounts of liquid crystal phase present at the interface. figure 2—1% sds in 1% nacl at 25℃, all systems are quite unstable. figure 3—1% ctab in 1% nacl at 25℃, all systems are unstable with some significant differences from sds. the water: oil ratio in this figure has been reversed. we discontinue referring to the batch numbers below as the figure numbers and batch numbers are the same. we find that only the nonionic surfactant can form stable emulsion which destabilizes at 40℃. it should be mentioned that at neutral ph, sio2 has a small negative surface charge (sahai 2002) and al2o3 has a small positive surface charge (berg et al. 2009). consequently, ctab will adsorb on sio2, with their head groups and the outward pointed tails will make them hydrophobic, thus the cluster will be insoluble in water where 5 they can precipitate but the ensemble can be oil soluble. conversely, al2o3 has a small positive charge and sds head groups will adsorb on the surface. it should be mentioned that heavy oil has a significant acidity and the acid groups will be active as discussed earlier. igepal co-530 with al2o3 showed least stability at 25℃ at water: oil ratio of 7.5:2.5. at 40℃ all cases became unstable showing full or nearly full phase separation as shown in figure 4. for igepal co-530 and sio2, the whole batch formed stable oil continuous emulsions. the emulsions could not be broken at 40º to even 60℃. this is shown in figure 5. in general, we expect a smooth change in emulsion stability as we go from low water to high water. however, for igepal co-530, we find a maximum or a minimum at some intermediate value of water to oil ratio suggesting a second mechanism at work due to asphaltene. in figure 5 emulsion stability is overwhelming and there is no apparent intermediate water to oil ratio of least stability. all the stable systems above appear black and they have been assumed to be w/o type. if oil is the continuous phase, its drainage rate will be very slow because of its very large viscosity even at 60ºc. in a model for percolation threshold of random non-overlapping distribution of spheres of same diameters, park and macelroy (1989) find that the continuous phase becomes segregated only at 96.5 volume percent of water, the dispersed phase. thus, 90 percent water could be ingested into oil and still remain oil continuous, explaining why even this case is stable in figure 5. figure 4—igepal co-530 with al2o3 at 40℃ where emulsions broke fully. figure 5—igepal co-530 with sio2 at 25℃ where the emulsion did not break at 40º, 50º and 60℃. the question arises as to why only systems with nonionics appear to be oil continuous. ionic surfactants lie at oil-water interface with their hydrocarbon tails in the oil and charged groups in water. because of the charged head repulsion the interface curves outwards with oil inside and water outside. that is such surfactants favor o/w. however, the nonionics show a more flexible interface and for instance do not need alcohols as 6 cosurfactants to form microstructures of different shapes that ionic surfactants do (miller and neogi 2008). this could help to explain why nonions have a bias towards w/o compared to ionics. figures 6 and 7 show sds and ctab respectively with al2o3. both show unstable emulsion as observed from increasing water content. ctab shows a brown haze (secondary haze) as noted earlier. similarly, the cases with sds and ctab are shown respectively in figures 8 and 9. they are unstable but both have precipitates at large water content as shown there. figure 6—sds with al2o3 where all systems are unstable at 25℃. figure7—ctab with al2o3, all unstable at 25℃. figure 8—sds with sio2 at 25℃. notice the settled precipitate on the right. 7 figure 9—ctab with sio2 at 25℃. notice the settled precipitate on the right. as mentioned earlier, the combinations of constituents are large and we have aimed at breadth rather than depth. it looks like a more important feature as the starting point. with this cautionary remark, we make a few observations below. with the needs of an oil producer in mind, we note that ctab produces secondary haze. these are very difficult to coalesce and leads to the conclusion that cationic surfactants should be avoided. sds leads to unstable emulsions with no secondary haze. hence, anionic surfactants appear to be very suitable. emulsions with nonionic surfactants break with increasing temperatures. there are exceptions, particularly, where nanoparticles are present but their presence is not necessary. we have suggested based on available literature, that asphaltene plays a role in those cases. nanoparticles themselves do not seem to be very active, accept in the nonionic systems mentioned above where the range of the anomalous behavior is increased. hydrophobic nanoparticles were not used because of their cost and that they are not commonly available. if the heavy oil is extracted under hot conditions (such as by using steam) this is the best time to separate the two phases under sedimentations. additives do not make much difference, except for cationic surfactants which give rise to secondary haze, or nonionic surfactants near hlb. conclusions we have covered a very large area of heavy oil emulsions containing additives and found that phase separation was best in presence of the anionic surfactant. even then the separation was not complete. the problem lies in the large viscosity of the oil. other additives could prevent reasonable degrees of phase separation, where the mechanisms could be explained by existing literature. acknowledgements the authors thank rpsea, doe for funding. part of the work was also presented by almohsin, abdulmohsin, bai and neogi at eor conference at oil and gas west asia in muscat, oman, 26-28 march 2018, spe190440-ms. conflicts of interest the author(s) declare that they have no conflicting interests. 8 references bera, a. and belhaj, h. 2016. application of nanotechnology by means of nanoparticles and nanodispersions in oil recovery-a comprehensive review. j. nat. gas sci. eng. 34:1284-1309. berg, j.m., rosomer, a., banerjee, n., et al. 2009. the relationship between ph and zeta potential of ~30 nm metal oxide nanoparticle suspensions relevant to in vitro toxicological evaluations. nanotoxicology 3(4):276-283. brochardt, j.k. and yen, t.f. 1989. oil field chemistry: enhanced recovery and production simulation. american chemical society, washington, d.c. cheringhian, g. and hendraningrat, l. 2016. a review on applications of nanotechnology in enhanced oil recovery part b: effects of nanoparticles on flooding. int. nano letts. 6: 1-10. el-sayed abdel-raouf, m. 2012. crude oil emulsions-composition stability and characterization. intech, croatia. hirasaki, g.j., miller, c.a., and puerto, m. 2011. recent advances in surfactant eor. spe j. 16(4): 15-23. spe115386-pa. ko, s. and huh, c. 2019. use of nanoparticles for oil production applications. j. pet. sci. eng. 172: 97-114. kokal, s. 2005. crude-oil emulsions: a state-of-the art review. spe production & facilities 20(1): 5-13. li, r., yan, w., liu, s., et al. 2008. foam mobility control for surfactant eor. paper presented at spe/doe improved oil recovery symposium, tulsa, ok, usa. 20-23 april. spe-113910-ms. miller, c.a. 1988. spontaneous emulsification produced by diffusion-a review. colloids and surfaces 29(1): 89-102. park, i.a. and macelroy, j.m.d. 1989. simulation of a hard-sphere fluid in bicontinuous random media. molecular simulation 2(1): 105-145. miller, c.a. and neogi, p. 2008. interfacial phenomena equilibrium and dynamic effects (2nd edition). crc press, taylor and francis, boca raton, fl. sahai, n. 2002. is silica really an anomalous oxide? surface acidity and aqueous hydrolysis revisited. environ. sci. technol. 36(3): 445-452. shah, d.o. 1985. macroand micro-emulsions: theory and applications. american chemical society, washington, d.c. shah, d.o. and schechter, r.s. 1977. improved oil recovery by surfactant and polymer flooding. academic press, new york. sjöblom, j., mingyuan, l., höiland, h., et al. 1990. water-in-crude oil emulsions from norwegian continental shelf. part iii. a comparative destabilization of model systems. colloids surfaces 46(2): 127-139. smith, d.h. 1988. surfactant-based mobility control progress in miscible-flood enhanced oil recovery. american chemical society, washington, d.c. suzuki, t., tsutsumi, h., and ishida, a. 1984. secondary droplet emulsion: mechanism and effect of liquid crystal formation in o/w emulsion. j. disp. sci. tech. 5(2):119-141. tchoukov, p., yang, f., xu, z., et al. 2012. role of asphaltenes in stabilizing thin liquid emulsion films. langmuir 30(11): 3024-3033. zhang, h., nikolov, a., and wasan, d. 2014. enhanced oil recovery (eor) using nanoparticle dispersions: underlying mechanism and imbibition experiments. energy fuels 28(5): 3002-3009. zainab a. abdulmohsein is from alhassa, saudi arabia. zainab received her b.s. in summer 2013 in petroleum engineering as a major study and in geology as a minor study from missouri university of science and technology (s&t), rolla, mo, usa. zainab was interested in completing her education and decided again to join s&t for her master study. she was working in the lab as a researcher and her studies were focusing on the stability of crude oil emulsion using chemical products, such as surfactants and nanoparticles. in may 2015, zainab received her master’s degree in petroleum engineering from missouri university of science and technology (s&t). baojun bai, spe, is the lester r. birbeck endowed chair professor of petroleum engineering at missouri university of science and technology. previously, bai was a reservoir engineer and head of the conformance control team at the research institute of petroleum exploration and development, petrochina. he also was a post-doctoral scholar at the california institute of technology and a graduate research assistant at the new mexico petroleum recovery research center for eor projects. bai has over 20 years of experience in the area of eor. he holds phd degrees in petroleum engineering from new mexico institute of mining and technology and in petroleum geology from china university of geoscience-beijing. bai has published more 9 than 130 papers in peer-reviewed journals and international conferences. he served on the jpt editorial committee for the feature “eor performance and modeling” during 2007-2013. he is a technical editor for spe journal and spe reservoir evaluation and engineering. parthasakha neogi, is a professor of chemical engineering at missouri university of science and technology, where he has worked as faculty for the last 36 years. his research interests are in wetting, surfactants and polymers, and in interfacial transport phenomena. he holds b.tech. (hons.) from the indian institute of technology kharagpur, m. tech. from the indian institute of technology kanpur, and ph.d. from carnegie-mellon university, all in chemical engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1147 received december 29, 2019; revised february 12, 2020; accepted april 11, 2020. *corresponding author: zxn_cq@petrochina.com.cn 1 geophysical research progress on tight sandstone reservoir in sulige gas field xinning zou*, tao lu, jinbu li, and bin fu, changqing oilfield company, petrochina, xi’an, china abstract the tight sandstone reservoir in the cooperation block of sulige gas field is characterized by thin gas-bearing sand, large variation laterally, and strong heterogeneity. due to the complex surface conditions, and particularly the thick weathered zone, the 3d seismic data presented limited frequency bandwidth. both processing and reservoir prediction did not achieve expectation. to enhance the reliability of predicted results, the reprocessing data with better quality were obtained in the pilot area by using the prestack data processing procedure with wider frequency, higher fidelity and preserved amplitude from its cores. compared to the previous results, the reprocessing data exhibits wider bandwidth, higher resolution and better consistency. the seismic forward modelling shows that the data can be used to discriminate over 10 m single sandbody or sand group, and over 5m gas-bearing sand. using cross-plot interpretation of selected sensitive parameters, the thickness of reservoir and effective sandstone can be estimated quantitatively. obvious enhancements were obtained for the well-seismic match of avo features and prestack seismic inversion. the research findings in the pilot area will have an important guidance to the development of international cooperation block in sulige gas field. introduction sulige gas field lies in the northeast of ordos basin，and its regional structure is subordinate to shanbei slope. the two major gas-bearing intervals are shanxi group and lower shihezi group, both with fluvial sedimentation. it belongs to tight sandstone gas reservoir with lower permeability, lower pressure, lower production, lower abundance, and stronger heterogeneity (ding et al 2007). the target zone in this study is he8 formation within lower shihezi group. the upper he8 formation belongs to meandering river deposition, and braided river deposition for lower he8 formation. he8 reservoir is characterized by small scale single sandbody with lenticular shape mostly, and large scale compounded sandbody with multistage stacked layers vertically and quick change horizontally. the effective reservoir shows great transverse variation with isolated or small area continuous distribution, and there is not specific correlation with sandstone thickness. in addition, the geologic structure has no control on the gas sand distribution (li et al. 2009). the joint development of sulige gas field between cnpc and total began in 2006. the cooperation block is located in the south of middle area of the gas field, in which over 1000km2 full fold 3d seismic data was available (figure 1). mailto:zxn_cq@petrochina.com.cn 2 the main geophysical problems in the cooperation block are presented as complex surface conditions with large lvl thickness (mean 104m), limited frequency bandwidth (10-33hz) and lower resolution for the previous seismic data processing, unable to estimate he8 sandstone thickness accurately due to the lower precision of prestack seismic inversion results, and poor effect of the reservoir prediction. so, it is necessary to select a typical 3d seismic pilot area in the cooperation block to conduct the data reprocessing and interpretation techniques research to improve the data quality, and finally to enhance the reliability of reservoir prediction results. this study will provide an important guidance with the development of the whole cooperation block. figure 1—sulige gas field (green rectangle: cooperation block, blue rectangle: pilot area). previous seismic data analysis in the pilot area the selected 3d seismic pilot area covers a full fold area of 86km2 with 33 drilled wells. the surface conditions are complex, which basically consist of sand, alkaline land and grass land, and with a large variation of lvl thickness (60-190m) (figure 2). the quality of 3d seismic raw data is mainly affected by lvl thickness. as a result of this affection, the noises in the data including stronger refraction, stronger energy at near shots, and so on, are developed. for the target zone, effective frequency bandwidth is 5-30hz, and primary frequency of effective reflection is 15hz. the main problems from the previous data processing as follows: 1. the surface consistency problem was failed to be effectively resolved, that resulted in stronger energy on the near offset seismic traces and weaker energy on the far offset seismic traces. the maximum amplitude analysis along horizon (figure 3a) shows that there is a bigger amplitude strength difference among the five angle stacks. 3 2. the primary frequency of target zone is about 15hz, and gradually reduces along with the increasing incidence (figure 3b). 3. the substack data failed to reserve prestack avo components from the raw data (figure 3c). through the characteristics contrast analyses of target zone in 33 wells between avo forward modelling and corresponding substack data, only 14 wells exhibit good match. figure 2—map of lvl thickness in the pilot area. 4 3-11 stack 11-19 stack 19-27 stack 27-35 stack 35-43 stack (a) (b) (c) figure 3—main problems from the previous data processing. (a) maximum amplitude analysis along horizon from the previous angle stacks. (b) frequency analysis from the previous angle stacks. (c) avo forward modeling and substack sections through the well snx-09. 5 seismic data reprocessing techniques considering the features of raw data in the pilot area, and existing problems in the previous data processing, to make the need of seismic reservoir prediction, the goal of seismic data reprocessing is to take amplitude and fidelity reserved as precondition, to remove the surface impacts on the data, and to improve s/n (signal to noise ratio) and resolution of the data. the key reprocessing techniques include 3d statics, 3d prestack signal-noise separation, high resolution processing with keeping relative amplitude, and ovt (offset vector tile) prestack time migration. 3d statics. the application of conventional elevation or refraction statics could not resolve the static correction problem in the work area. by using tomostatics, we can get more accurate near surface model, and thus to improve the accuracy of statics and get better processing effect. 3d prestack signal-noise separation. the main interferences existing in the raw data include linear noise, strong energy noise at near shots, and wide frequency refraction noise. 3d cross banding cone filter was applied to remove linear noise, and multi domain frequency decomposition was applied to remove strong energy noise at near shots and wide frequency refraction noise. high resolution processing with relative amplitude reserved. the primary frequency of target zone in the better data quality area is about 20hz, and it is about 15hz in the medium data quality area. based on the significant quality difference, to meet the need of reservoir prediction, the well control processing technique was applied to enhance seismic data resolution and keep the relative relationship of amplitude. figure 4—workflow of ovt domain processing. ovt domain processing. ovt (offset vector tile) processing is carried out in the subdividing cross spread domain. this method can keep more accurate azimuth and offset information. it is not only used to improve full azimuth imaging accuracy, but also used to extract attribute vs relating to the azimuth and 6 detect fractures. the processing workflow (figure 4) mainly includes four key steps, namely ovt partition and gathers data preparation, ovt domain data regularization, ovt prestack time migration, and migrated gather processing (schapper et al. 2009; stein et al. 2010; li 2008; duan et al. 2013). seismic data reprocessing effect analysis after reprocessing, 3d seismic data in the pilot area are characterized as follows: 1. compared with previous processing results, the data show wider frequency bandwidth, higher resolution, and better coherency (figure 5a). 2. the acquired substack data are of higher fidelity, and exhibit reasonable frequency, phase and amplitude features on the near and far offset stack sections, respectively. compared with the previous processing results, there is a better match between avo features on the seismic sections and avo forward modelling results from wells. so, the reprocessed data are able to meet the needs of avo analysis and prestack seismic inversion (figure 5b). 3. by comparing the seismic section through a well with its synthetic seismogram, we find out that the features of amplitude and phase within the marker bed and target zone are of good match with well synthetics. it illustrates that the seismic data reprocessing techniques, workflow and parameters are reasonable, and the reprocessed data are of higher fidelity (figure 5c). by reprocessing, the impact of lvl on the data was removed effectively. from figure 5d, we find out that there is no similarity between the rms amplitude distributions extracted from 150ms and 15ms time window near horizon tc2, respectively. meanwhile, there is also no similarity between rms amplitude distribution mentioned above and that of lvl thickness. (a) 7 (b) (c) 8 (d) figure 5—characterization of the pilot area from 3d seismic data. (a) comparison of the data processing results (section, frequency spectrum). (b) comparison of avo features and forward modelling on the well snx-09. (c) seismic and geology synthetic calibration on the well snx-05. (d) correlation analysis between rms amplitude near horizon tc2 and lvl thickness. seismic reservoir prediction research in the pilot area the research approach is to focus on the effective reservoir forecasting, select the sensitive seismic attributes and parameters to the reservoir, finely carry out prestack simultaneous inversion，and predict the horizontal distribution of he8 sandbody and gas-bearing sand in the pilot area. optimization of sensitive seismic attributes and parameters to the reservoir. aimed at he8 target zone, 11 amplitude attributes, 7 frequency attributes, 9 statistics attributes, 6 energy spectrum attributes, and 5 single frequency attributes are extracted. according to the information from drilled wells, we select the sensitive attributes and parameters to the reservoir by combining automatic optimization with expert evaluation. based on avo forward models, reservoir forward modelling results, and rock physics analyses, we conclude that the amplitude attribute is of good correlativity with sandstone thickness, avo attribute is of good correlativity with gas-bearing sand, and vp/vs ratio is the most sensitive parameter to he8 reservoir. meanwhile, we can predict the reservoir quantitatively via the crossplot interpretation between vp/vs ratio and prestack parameter such as p-impedance or s-impedance. rms(root-mean-square) amplitude attribute. the thickness of he8 formation is 60-80m, and that of the single sand-body is 5-15m.on the seismic sections, he8 formation mainly shows mid-strong wave peak reflections, which are synthetical seismic response to multistage stacked sandbodies. the seismic response characteristics of wedged sandstone forward modelling show (figure 6a) that the relationship between reflection amplitude strength and sandstone thickness is of a positive correlation when sandstone thickness is less than 30m. by means of building the relationship between amplitude attribute and sandstone thickness, we are able to predict he8 sandstone thickness. according to the wedged sandstone forward models (figure 6b), well data analysis results，and combined with reprocessed 9 seismic data resolution (6-40hz of frequency band), we think that 10m above single sand-body or sand group can be identified by using rms amplitude attribute. avo attribute. avo forward modelling results of target zone in the work area show: he8 gas-bearing sand exhibits class ⅲ avo response characteristics (zou et al. 2005), which means as the incidence increases (or offset increases), the amplitude energy gradually enhances (figure 7). through comparative analysis between avo forward modelling results of target zone from 33 drilled wells and corresponding amplitude features on the substack data, the coincidence rate of wells with good match is 73% (previous one is 42%). thus we can predict the gas-bearing reservoir qualitatively by using avo attribute analysis. vp/vs ratio. the rock physics analysis of he8 reservoir in the work area (figure 8a) shows: the vp/vs ratio is of higher sensitivity and discrimination to sandstone, mudstone and gas-bearing sand. therefore, it can be used to predict he8 reservoir quantitatively. according to the well-seismic data analysis in the work area, the vp/vs ratio from prestack seismic inversion can be applied to identify 5m above gas sands (figure 8b). although the vp/vs ratio is of higher sensitivity and discrimination to sandstone and mudstone, abnormal values often exist in the seismic inversion results, which usually show lower vp/vs ratio, and with impedance value too high or too low. thus, by using the crossplot interpretation between vp/vs ratio and s-impedance, we can predict sandstone and gas sand more accurately. (a) 10 (b) figure 6—the seismic response characteristics of wedged sandstone forward modeling. (a)wedged sandstone forward modeling. (b)wedged sandstone forward models and seismic data recognizable scales. figure 7—avo forward modeling of different gas sand thickness in he8 zone. the refined prestack seismic inversion the fundamental principles of prestack simultaneous inversion. the prestack simultaneous inversion is a technique that uses prestack migration crp(common reflection point) gather data, and well logging data, such as vp,vs and density, to simultaneously produce various rock physics parameters, such as p-impedance, s-impedance, vp/vs ratio, and pr(poisson ratio), which can be used to 11 differentiate the lithology, properties, and oil and gas bearing of the reservoir (shao et al. 2016). the technique is classified as travelling time method and amplitude method. the latter is often applied, and its basic theory is from the matrix expression of zoeppritz equation. data preparation. for the sonic and density log, it is necessary to conduct environmental correction and normalization processing respectively to eliminate the curve distortion. and for the multi-well logs, it is necessary to conduct crossplot and histogram analyses to remove the data which are not able to meet the need of prestack inversion. generally, 3 to 5 substack data volumes are used in the prestack simultaneous inversion. in this study, based on the prestack amplitude reserved processing results, we determined to use three substack data volumes as 3°-14°,13°-22° and 21°-35° (i.e. near, mid and far angle stack, respectively) to conduct the inversion. (a) (b) figure 8—the rock physics analysis of he8 reservoir in the work area. (a) well log interpretation and rock physics chart on the well snx-08. (b) wedged gas sand forward models and seismic data recognizable scales. 12 key steps and qc(quality control) the key steps of prestack simultaneous inversion include angle wavelet extractions and refined horizon calibrations. the qc in the inversion mainly consists of model creation, selection of λ value，design of the low frequency filter, and control of the trend restriction lines. prestack simultaneous inversion effect analysis. three data volumes such as p-impedance, s-impedance and vp/vs ratio were obtained from prestack simultaneous inversion. the inversion sections through a drilled well (figure 9) show higher s-impedance at the well location, which indicates the developed sandstone; and p-impedance and vp/vs ratio at the well location are lower, which indicates the better reservoir properties and gas-bearing sand. for the drilled well with 25.9 m of he8 sandstone and 13.3 m of gas sand, the inverted results are well matched with the real drilling ones. in this study, five wells were involved in the prestack simultaneous inversion, and other 28 wells were used to verify the inversion effect as blind ones. we can evaluate the quality of inversion results by the comparative analyses between inverted logs at well locations and real logs. the statistical analysis results from 28 validated wells indicate that 21 wells are of good and moderate well-seismic fit. under the same evaluation criterion, the proportion of well-seismic fit has increased significantly from 44% to 75%, which indicates a better inversion effect. furthermore, seven wells are of poor well-seismic fit due to poor migration imaging quality, which is caused by non-uniform far offset distribution at boundary of the work area. figure 9—prestack simultaneous inversion sections through drilled well snx-08. results and discussions this study has created a set of high-resolution reprocessing workflow with amplitude and fidelity reserved for the seismic data in cooperation block, and it has formed seismic data processing technology series based on tomostatics, prestack fidelity reserved denoising, well-control wide frequency processing, 13 and ovt domain processing. meanwhile, in the pilot area, we also obtained prestack gathers and migration stack data with high fidelity, moderate s/n and wider frequency band, which are able to meet the needs of reservoir prediction. by the crossplot interpretation between vp/vs ratio and s-impedance from prestack simultaneous inversion, we got the map of he8 sandstone thickness in the pilot area (figure 10a), and obtained better prediction effect with 82% of coincidence rate. on the basis of avo characteristics of he8 reservoir in the pilot area, we qualitatively predicted the gas-bearing property (figure10b) by analyzing seismic amplitude variation in the target zone on near and far offset stack sections, and the coincidence rate is 73%. at the same time, by using crossplot interpretation between vp/vs ratio and s-impedance from prestack simultaneous inversion, we got the map of he8 gas-bearing sand thickness in the pilot area (figure 10c), and the coincidence rate is 75%. the effective reservoir prediction obtained satisfied results. figure 10—(a) map of he8 sandstone thickness. (b) map of avo attribute analysis of he8 reservoir. (c) map of gas-bearing sand thickness of he8 zone. conclusions 1. for the most of raw single shot data in the pilot area, the high frequency constituent is still preserved but of weaker energy. by applying prestack seismic data processing techniques with wide frequency, fidelity reserved and amplitude reserved at its core, the energy of high frequency constituent in the data was enhanced, and we obtained the reprocessed data with high fidelity, wide frequency band, high resolution and good consistency, compared to the previous processing results. 2. the reprocessed seismic data can be used to identify 10m above single sandbody or sand group, and 5m above gas sand. avo attribute analysis can be used to qualitatively predict gas-bearing property of he8 reservoir. by using crossplot interpretation between vp/vs ratio and s-impedance, we can quantitatively predict thickness of he8 sandstone and gas sand. 3. both well-seismic match of avo characteristics of he8 reservoir in the pilot area and well-seismic fit of prestack seismic inversion results are improved significantly, compared to the previous studies. 14 4. the techniques and results from this study in the pilot area can be applied to the whole cooperation block, and it plays an important guidance role to the development of international cooperation block in sulige gas field. acknowledgements we would like to thank fiedc for providing us with this technical exchange opportunity. and we also would like to extend deep gratitude to three senior geophysicists from changqing branch of geophysical research institute, bgp, cnpc: changliang shang, jinfu li, and faming gu, for their help. conflicts of interest the author(s) declare that they have no conflicting interests. references ding, x., zhang, s., zhou, w., et al. 2007. characteristics and genesis of the upper paleozoic tight sandstone reservoir in the northern ordos basin. oil & gas geology 28(4):492-496. duan, w., li, f., wang, y., et al. 2013. offset vector tile for wide–azimuth seismic processing. ogp 48(2):206-213. li, m., dou, w., lin, h., et al. 2009. model for tight lithologic gas accumulation in upper paleozoic, east of ordos basin. petroleum exploration and development 36(1):56-61. li, x. 2008. an introduction to common offset vector trace gathering. cseg recorder 33(9):28-34. schapper, s., jefferson, r., calvert, a., et al. 2009. anisotropy velocities and offset vector tile prestack-migration processing of the durham ranch 3d. northwest colorado. the leading edge 28(11):1352-1361. shao, l., wang, j., zhang, l., et al. 2016. application of pre-stack simultaneous inversion in low porosity and permeability sandstone reservoirs prediction and hydrocarbon detection. geological science and technology information 35(3): 145-150. stein, j. a., wojslaw, r., langston, t., et al. 2010. wide-azimuth land processing: fracture detection using offset vector tile technology. the leading edge 29(11):1328-1337. zou, x., sun, w., wang, d., et al. 2005. the reservoir prediction of low permeability sandstone in sulige gas field. gpp 44(6): 621-626. xinning zou is a senior engineer of changqing oilfield company, petrochina. zou specializes in geology of unconventional reservoirs. tao lu is a senior engineer of changqing oilfield company, petrochina. lu specializes in geology of tight gas reservoirs. jinbu li is a senior engineer of changqing oilfield company, petrochina. li specializes in geology of tight gas reservoirs. bin fu is a senior engineer of changqing oilfield company, petrochina. fu specializes in geology of tight gas reservoirs. abstract introduction previous seismic data analysis in the pilot area seismic data reprocessing techniques seismic data reprocessing effect analysis seismic reservoir prediction research in the pilot the refined prestack seismic inversion key steps and qc(quality control) results and discussions conclusions acknowledgements conflicts of interest references a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.458 received november 21, 2019; revised december 12, 2019; accepted january 15, 2020. *corresponding author: minh.vo@chevron.com 1 surface pressure data for well-test analysis at a joint venture gas project in sichuan minh vo*, yue yu, and jianjiang lv, chevron unocal east china sea ltd, chengdu, china; junliang zhang，southwest oil and gas company, cnpc, chengdu, china abstract pressure transient analysis (pta) of bottom-hole pressure (bhp) data is a well-established method for estimating reservoir dynamic parameters and determining well behavior under different production stages. unfortunately, permanent recording of bottom-hole data is not always operationally possible, particularly in the case of horizontal/high deviated wells and/or h2s (sour gas) reservoirs, for safety and cost-effective reasons. however, most wells are equipped with real time and digital gauges at the wellhead, which record well head pressure (whp) and temperature (wht) data continuously. what to do to maximize the value of the available information and to minimize the operational cost and execution risk? this paper is to present the current experience at the joint venture gas project, utilizing the new converting technology, with which, whp data can be converted to bhp data accurately during well shutin. with this success, the surface wellhead pressure whp can be used for well-test analysis (i.e., pta). there are several advantages in deriving the useful information from wellhead surface data: (a) the cost of recording wellhead data is much less than that of a downhole survey; (b) the risks associated with running tools in the wellbore are eliminated, particularly useful in horizontal/high deviated wells where tools cannot be run deeply enough; (c) the work can be done any time where well shut-in is possible (both planned and unplanned downtime); and (d) this can reduce the significant production loss for any well intervention, particularly when spare gas supply capacity is low. in brief, effective use of wellhead data is considered as an excellent technology application in china to minimize the traditional well-test intervention, which is with high cost and potential h2s risk. operational lessons learned and case studies on pta will be shared. introduction this greenfield sour gas project is developed in sichuan, china. the full field development schematics is shown in figure 1. the project involves development of gas resources in triassic carbonate reservoirs. the field of interest is made up of bedded dolostone and limestone facies of early triassic age. the depositional environment is carbonate platform and ramp with oolitic shoals. gas is trapped in thrust-related anticlinal structures and seals comprise tight limestones and anhydrites. the structure is normally large. rock porosity ranges from 3 to 20% and permeability ranges from 0.01 to 1,000 millidarcy (md). the reservoir fluid is dry gas, with h2s and co2. mailto:minh.vo@chevron.com 2 figure 1—sour gas development project. wellbore structure. most of the development wells in this field were drilled and completed in the 2000s. the wells are either horizontal or high angle deviated directional wells to maximize the deliverability potential and to minimize the development footprint. in 2012-2013, the wells were worked over by removing the existing completion string, running and cementing an inner combination string of 4 1/2in.×7-in. casing with gas tight connections and h2s service metallurgy. the wells were then recompleted with 4 1/2-in. h2s service metallurgy production tubing. the wells remained shut-in until mid-2015. a well schematic after recompletion is shown in figure 2. figure 2—typical wellbore schematic. 3 historical test results and key challenges. most of the development wells were tested right after they were drilled and completed, with the primary goal to unload the completion fluid, to clean up the formation, and to ensure a sustainable deliverability of the well during the production phase. during this testing, five wells obtained large production rates. the goal was thus fully achieved. most of the tests were short. furthermore, to reduce potential so2 emissions of testing, there was an attempt to conduct a well-test using the wellhead pressure survey (convert wellhead pressure to bottom hole pressure by using the static gas column method), and perform well-test analysis, which has been proven successful in many locations worldwide. if wellhead pressure survey could be conducted to perform dynamic monitoring, work load, cost and execution risk of a well-test would be cut down significantly. a well had been selected with the pressure transient tests conducted with both surface pressure and downhole pressure surveys. while the downhole pressure test was successful performed, and the testing goals were met, the data obtained from the wellhead pressure survey behaved abnormally, with a build-up test behaviour like a drawdown test; more specifically, after shut-in, wellhead pressure rebounded to the peak very quickly (by leaps), and then declined continuously, as seen in figure 3. figure 3—change of tubing pressure at wellhead during shut-in period after stable test. one possible reason for this behaviour could be that vaporous or annular liquid in the tubing could have segregated to the bottom-hole after shut-in and formed a section of slugged liquid column. another possible reason could be a segregation of the fraction of h2s and co2 to the bottom-hole. new well design and reservoir surveillance. in an effort to understand the well deliverability potential, a new well has been designed and drilled. to support a long-term reservoir surveillance strategy, the well location was optimally selected, with the downhole pressure gauges (dhpg) installed. to ensure the reliability and the accuracy of the data recorded downhole, the operator selected a halliburton welldynamics roc (2012), which was the first application of this technology in china. the down-hole reservoir pressure data is the most important reservoir surveillance measurement, which is to provide invaluable information about the reservoir behaviours at different production arrangements. a well schematic after completion is shown in figure 4, with the dhpg located above the reservoirs where gas is produced. specifications of the surface pressure gauges and dhpgs can be summarized in table 1. 4 table 1—specifications of permanent gauges. surface gauges downhole gauges pressure 0-10,000 psi 0-16,000 psi temperature -40~121゜c 25-177゜c figure 4—schematic of new wellbore design. with the full equipment for real time surveillance, both the wellhead and downhole pressure survey can be conducted at the same time. after the project reached first gas, the operator followed reservoir management and a field performance surveillance program. the well-test data that was collected is shown in figure 5. note that, the well behaviour is similar to what was observed in the previous pressure transient test; however, it cannot definitely be concluded “abnormal” as the well has completely been cleaned up after an extensive production period and tested at the flow rate greater than the critical liquid segregation rate. so, what explains the results? from the subject matter experts of pressure transient tests, this is one of the most significant challenges to surface test, a so-called the wellbore cooling effect. the operator has kicked off a further investigation on the issue as detailed below. 5 figure 5—“conflicting” surface and downhole pressures. wellhead pressure to bottom-hole pressure. calculating bottom-hole pressures from surface data has been extensively studied (cullender and smith 1956; fair et al. 2002). the basic equation governing the conversion of wellhead pressure (whp) to bottom-hole pressure (bhp) is the following, bhp = whp + ρgh + f + a……………………………………………………………………….(1) in eq. 1, ρgh is the fluid hydrostatic head component, f is friction pressure loss along wellbore, and a is the kinetic energy loss, which is small and normally negligible. by estimating the change of both wellbore fluid hydrostatic head and friction loss, the total change of bottom-hole pressure can be calculated. δbhp = δwhp+ δ(ρgh)+ δf.…………………………………………………………………………(2) wellbore cooling effect is widely observed on gas wells, mostly wells with high gas flow. when a well is flowing, the wellhead temperature is increased since reservoir heat is brought by flowing fluid to surface, with some heat spreading to near wellbore formation. the deeper the reservoir, the higher gas rate, the more water, then the higher the wellhead temperature. when a well is shut-in for a relatively short period, wellhead temperature starts to cool down. with temperature dropping, both wellbore fluid density and hydrostatic head increase. figure 6—wellbore cooling effect (halliburton, 2012). 6 for well shut-in, friction loss is zero. for big wells with good deliverability, bottom-hole pressure drawdown is small. wells in this jv gas project normally have pressure drawdown smaller than fluid hydrostatic head change. for these types of wells, counterintuitively, it results in a negative wellhead pressure change. this means the surface pressures will decline when well is closed. figure 6 illustrates the wellhead pressure change when wellhead cooling effect is applied. pilot test and testing goals the test procedures have been designed to determine the following reservoir properties: 1. permeability; 2. skin; 3. reservoir pressure; 4. reservoir characteristics (fracture/dual porosity); and 5. non-darcy skin (multi-rate test required). test design given the reservoir characteristics (i.e., fractured dolomite), with a long bottom-hole well and reservoir interaction, associated with operational constraints prevent a long shut-in (i.e., production target to deliver), a multi-rate test is preferred. it is a combination of both drawdown test and build-up test, with different desired flow rates.  build-up test: the simplest test to perform would be a basic pressure build-up. ideally, the well to be tested would be flowing stably for at least 1-2 days prior to the start of the build-up. the goal of this stable flow is to minimize any transient behavior around the wellbore prior to the start of the shut-in, and to stabilize the wellbore thermal profile. at the end of this stable flow period, shut-in the well for 3-4 days to capture the build-up. this test will accomplish goals one through four as listed above.  drawdown test: this type of test is simply an extension of the build-up test mentioned above. instead of completing the test at the end of the build-up, it is continued by monitoring pressures as the well is returned to production on a constant rate/choke drawdown. the drawdown data should be recorded for the same duration as the previous build-up. for the drawdown analysis to be viable, the flowing tubing pressure (ftp) during the drawdown should exceed the flow line pressure by at least a ratio of about 2.2:1. this ensures that there is an adiabatic shock front across the choke, isolating the well from downstream operations. this test accomplishes goals one through four as listed above and, provides a second confirmation of the test analysis.  multi-rate test: this test begins with the build-up procedure, and followed up a drawdown test procedure. however, instead of single flow rate drawdown test, an adjustment to the choke is made to have a new gas rate. the well should be held on this constant rate/choke for about 1-2 days (like the build-up). the rate change should be significant to induce a noticeable transient in the reservoir, and the ftp constraints also apply as in the above procedures. this test could be then extended to multi-rates by making a second choke adjustment to a third flow rate. this test would accomplish goals one through five (multi-rate only). in practice, the type of multi-rate test is less desirable given the fact that it is often difficult to maintain a constant rate/choke drawdown, and drawdown data is inherently noisier and more difficult to interpret. however, it is selected for this test as to fully understand if the new technology could help deliver the testing goals. figure 7 shows the conceptual well-test design. 7 figure 7—conceptual well-test design. case study the pilot test was conducted on the well equipped with downhole gauge. the purpose was to compare the conversion from whp to bhp with the measured downhole gauge data during pressure build-up test. halliburton’s in-house developed model was used to conduct the conversion. figure 8 shows the comparison result and the converted bhp curve was almost parallel with the measured curve indicating the conversion achieved a good build-up trend. however, the gap still existed, around 40 psi, because halliburton’s pressure conversion model is based on large amount of well-test data collected worldwide, which may not accurately match with the specific well conditions in sichuan (such as wellbore schematic, wellbore fluid, formation stratigraphy, reservoir temperature and reservoir pressure) for the pilot test. figure 8—bhp conversion vs. downhole gauge measurement before thermal decay model tuning. then the specific well-data was incorporated to the thermal decay model resulting in a slower cooling down profile in the well, as illustrated in figure 9. 8 figure 9—model tuning with wht change rate. figure 10 shows the converted bhp after model tuning, which almost overlaps with the downhole gauge data. in other words, no obvious gaps can be visually seen. figure 10—bhp conversion vs. downhole gauge measurement after thermal decay model tuning. the results of pta for both the dhpg and converted bhp at well a are quite similar. figure 11(a) shows the test interpretation using the pressure conversion data and figure 11(b) using the pdhg data. note that the data from surface gauges results in similar reservoir parameters, such as skin and permeability. 9 1e-4 1e-3 0.01 0.1 1 time [day] 1e+5 1e+6 1e+7 g as p ot en tia l [ ps i2 /c p] log-log plot: m(p)-m(p@dt=0) and derivative [psi2/cp] vs dt [day] 1e-4 1e-3 0.01 0.1 1 10 100 time [hr] 1e+5 1e+6 1e+7 g a s p o te n tia l [ p s i2 /c p ] log-log plot: m(p)-m(p@dt=0) and derivative [psi2/cp] vs dt [hr](a) (b) figure 11—pta results. (a) pta with converted data. (b) pta with pdhg data. to ensure the result is reliable and the work can be repeatable, the test has been extended to well b, where an obviously “abnormal” reservoir behaviour was observed. the thermal decay conversion model established based on the pilot test can be utilized on the other wells with the same wellbore structure, the same wellbore fluid and the same reservoir formation as the well installed with downhole gauge. because the thermal cooling effect in the adjacent wells shall be like the pilot test well. figs. 12 through 14 are the pta plots for well b. the good matching of the log-log plot, semi-log plot and history plot indicates high quality bhp conversion. therefore, with the mature thermal decay model, the reservoir properties such as permeability, skin damage, dual porosity parameters, and outer boundary can be analysed with whp during pressure build-up test. 1e-4 1e-3 0.01 0.1 1 10 100 time [hr] 100 1000 10000 g a s p o te n tia l [ (m p a )? c p ] log-log plot: m(p)-m(p@dt=0) and derivative [(mpa)?cp] vs dt [hr]figure 12—log-log plot of well b pta. -5 -4 -3 -2 -1 superposition time 61000 66000 71000 76000 g as p ot en tia l [( m pa )? cp ] semi-log plot: m(p) [(mpa)?cp] vs superposition timefigure 13—semi-log plot of well b pta. 10 4800 5200 5600 p re ss ur e [p si g] 8/13/2016 8/15/2016 8/17/2016 8/19/2016 8/21/2016 8/23/2016 8/25/2016 0 25 g as ra te [m m sc f/d ] hi st or y pl ot ( pr essur e [ psi g] , gas r at e [ mmscf / d] vs ti me [ hr ] )figure 14—history plot of well b pta. lessons learned several lessons were learned through this process:  for a reservoir where fracture flow contribution is dominant, the surface pressure data during the build-up test will behave as the “normal” drawdown test. pressure data conversion needs calibration.  for the wells with the two-choke configuration, the adjustment automation of the second choke to stabilize the output pressure of the production system has created extra “noise” during draw-down test. therefore, extra care is needed in the well test interpretation,  even with detailed well configuration modeling, the well configuration has a minimum impact on the data conversion, as all will be grouped under “skin” factor (i.e. formation damage).  before any installation and disconnection of wellhead gauges, ensure that double mechanical blocks to isolate pressure source shall be in place, by checking integrity of the needle valves and gate valves on the x-mas tree. best practices several best practices have been developed through this process:  well locations can have health, safety, and environment (hse) hazards. great care must be exercised when operating in such high-risk areas, which include wearing the proper personal protective equipment (ppe), knowing and following the proper procedures, job safety analysis (jsa), and permit to work (ptw) to operate safely, and checking the area for high levels of h2s. stop work authority is the right of all personnel when on any location; if an unsafe situation exists, stop the operation until the unsafe condition is resolved or mitigated to a safe level.  as of the ambient temperature variance, any surface pressure survey, if possible, should be insulated from the external source; i.e., do not install surface pressure gauges near extreme ambient temperature, such as a heater, or the wellhead area should be shielded from direct sunlight to reduce the large differential between day and night.  liquid accumulation or drop-off may deviate the calibration of thermal cooling effect.  due to a high-pressure resolution, particularly high deliverability wells, the surface pressure gauges should be in a location that should be less impacted / interfered by the noise of daily production operations. 11 conclusions the data conversion technology is not new, and has been used in china in the past. however, it is the first application of this technology to sour gas field development project in china. all the primary goals for the well-test requirement have been achieved:  avoided the cost and risk of running equipment downhole for the conventional well-tests.  acquired pressure data with high resolution, high accuracy, high repeatability and effective thermal compensation for pressure transient analysis. the test can be monitored in real-time.  leveraged the conversion technology from surface pressure data to bottom-hole pressure data and elementary analysis with halliburton in-house developed mode, which helped to ensure highquality work. acknowledgment the authors thank the management of uecsl and cnpc for their permission to publish this paper. the authors also thank all the personnel, particularly halliburton engineers, who involved in the execution of the operations at the field site and in the well-test interpretation to ensure the highest quality received. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature bhp = bottom-hole pressure, psia bht = bottom-hole temperature, °f whp = wellhead pressure, psia dpskin = pressure drop due to skin, psi ρo = oil density, lbm/ft3 references cullender, m.h. and smith, r.v. 1956. practical solution of gas-flow equations for wells and pipelines with large temperature gradients. journal of petroleum technology 207(12):281-287. fair, c., cook, b., brighton, t., et al. 2002. gas/condensate and oil well testing--from the surface. paper spe77701-ms presented at the spe annual technical conference and exhibition, san antonio, texas, 29 september-2 october. halliburton. 2012. understanding wellbore cooling. downloaded 16 december 2017. http://www.spidr.com. minh vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 4+ years. he has had 25 years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. yue yu, spe, is production engineer in unocal east china sea ltd., where he has worked for 6 years. his research interests are in production and reservoir engineering. he holds master’s degree from china university of petroleum, beijing. jianjiang lv, spe, is production engineer in unocal east china sea ltd., where he has worked for 7 years. his research interests are in production and reservoir engineering. he holds master’s degree and ph.d. from southwest petroleum university, both in petroleum engineering. http://www.spidr.com 12 junliang zhang, is a production engineer in southwest oil & gas field company, where he has worked for 13 years. his research interests are in production engineering and daily field operations. he holds master’s degree from southwest petroleum university in petroleum engineering. abstract introduction pilot test and testing goals test design case study lessons learned best practices conclusions acknowledgment conflicts of interest nomenclature references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1187 received march 23, 2021; revised may 15, 2021; accepted june 18, 2021. *corresponding author: dongzz@xsyu.edu.cn 1 research on oil-co2-water relative permeability of the low permeability reservoir based on history matching fengli zhang, tianjin branch of cnooc, tianjin, china; wenfeng lv, research institute of petroleum exploration and development (riped), petrochina, beijing, china; yongyi zhou, north china petroleum bureau, sinopec, zhengzhou, china; bochao qu,yawen he, xinle ma, weidong tian, and zhenzhen dong*, xi’an shiyou university, xi’an, china abstract accurate prediction of the relative permeability curve provides the basis for study of the co2 flooding effects (such as swept volume and oil displacement efficiency) and optimization of the co2 flooding plan. considering that laboratory experiments are time-consuming and effort-consuming, and experimental results are easily affected by external factors, a method was proposed to calculate the relative permeability curve of the oil-co2-water multiphase fluid based on particle swarm optimization (pso). the typical co2 flooding experiments in the low-permeability cores were performed, a multiphase flow numerical model was established in cmg-gem, and 26 parameters of the model were optimized using the pso method. the results of the model fitting are consistent with the results of the experiment, and the relative permeability of oil-co2 water, the capillary pressure of oil-water and the capillary pressure of gas-liquid of the low-permeability core were obtained. the validity of the model was verified in the research that the prediction from the numerical model is consistent with the laboratory experiment results. this study provides guidance for determining the oil-co2-water relative permeability of the low-permeability core. introduction the relative permeability curve, a parameter reflecting the seepage law of multi-phase fluids in the porous media, is used to describe the movement of each fluid phase in the reservoir and predict the basic production index such as oil recovery rate, ultimate recovery factor, and water cut, and it is an important indicator in reservoir evaluation(zhang et al. 2010). the relative permeability curve is of great significance to the study of fluid distribution in the process of co2 flooding, and it is used to understand the characteristics of both miscible and immiscible co2 flooding(zhang et al. 2019). therefore, accurate prediction of the relative permeability curve in co2 flooding provides the basis for the study of the swept volume, the oil displacement effect, fine reservoir description, and plan optimization in co2 flooding(zhang et al. 2016). currently, the oil-water relative permeability curve is obtained through the steady-state method, the transient method, and the history matching method(toth et al. 2002; li et al. 2018; li 1989; eydinov et al. 2009). mailto:dongzz@xsyu.edu.cn 2 typical co2 flooding experiment of low-permeability cores experimental materials and fluids. the co2 flooding device in the low-permeability core is shown in figure 1. figure 1—device of displacement in the low-permeability core: 1.displacement pump; 2.oil vessel; 3.co2 gas vessel; 4.brine vessel; 5.long core clamp; 6.thermostat; 7.pressure sensor; 8.inspection window; 9.pressure relief valve; 10.separation bottle; 11.sample tap; 12.gasometer. constant composition expansion experiments of the oil from lowpermeability reservoirs were carried out to obtain the in-place oil and its volume factor. the fluid model was established by dividing the pseudocomponents through pvt fitting. the compositions of original components and pseudo-components are listed in table 1. table 1—pseudo-components of fluids in low-permeability reservoirs. original components mole compositions, mol% post-division components mole compositions, mol% co2 0.113 co2 0.11 n2 1.39 n2 -ch4 22.90 ch4 21.533 c2h-c3h 5.26 c2h6 3.148 ic4-c6 1.76 c3h8 2.119 c7-c11 23.31 i-c4h10 0.348 c11-c20 23.31 n-c4h10 0.658 c21+ 23.31 i-c5h12 0.167 n-c5h12 0.216 c6h14 0.367 c7+ 69.941 total 100 100 the fitting error of fluid viscosity and density with the pressure of the experiment is less than 5% (figures 2 and 3). 3 figure 2—fitting result of the oil viscosity at the formation temperature. figure 3—fitting result of the oil density at the formation temperature. experimental method. the experiments of water flooding in the cores under the formation state were performed. water flooding continued until the water cut is above 98% and is stabilized for a period of time. then, co2 flooding started and continued until the core is at the residual oil state. in the experiments, the displacement pressure and the oil, water and gas production were recorded at the designed time interval. the basic parameters of the displacement experiment of the cores from the low permeability reservoirs are listed in table 2. table 2—basic parameters and conditions of the displacement experiment of the cores from the low permeability reservoirs. parameters values experimental temperature (oc) 75.0 experimental pressure (mpa) 17 water injection rate (cm3/min) 0.1 co2 injection rate (cm3/min) 0.1 air permeability (md) 1.2 porosity (%) 13.2 irreducible water saturation (%) 35 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 0 5,000 10,000 15,000 20,000 25,000 30,000 35,000 o il v is co si ty ( c p ) pressure(kpa) oil visc. exp. oil visc. legend 640 660 680 700 720 740 760 780 800 0 5000 10000 15000 20000 25000 30000 35000 o il d e n si ty ( k g /m 3 ) pressure(kpa) oil density exp oil density(kg/m3) legend 4 results. the experimental results are shown in figure 4, which include gas-oil ratio, water cut, injection well bottom-hole pressure, and oil recover. in the water flooding period, the water cut increases to 98%, the gas-oil ratio is zero, and the recovery factor increases to 41%. during co2 flooding period, gas-oil ratio rises up quickly in the beginning and stabilizes around 14900 m3/m3, water cut drops dramatically and then increases to 80%, and the oil recovery increases from 41% to 89%. (a)gas-oil ratio, m3/m3 (b)water cut, % (c) injection well bottom-hole pressure, kpa (d)oil recovery, % figure 4—results of displacement experiment of the low-permeability cores. theoretical model relative permeability curve model of co2 flooding. the compositional model in the commercial software cmg was used to simulate co2 flooding, and the corey model of the relative permeability model in cmg was first proposed and has been widely adopted(cmg manual 2015). the corey model is expressed as follows. oil and water relative permeability 𝑘𝑟𝑤 = 𝑘𝑟𝑤𝑖𝑟𝑜 × ( 𝑆𝑤−𝑆𝑤𝑐𝑟𝑖𝑡 1−𝑆𝑤𝑐𝑟𝑖𝑡−𝑆𝑜𝑖𝑟𝑤 ) 𝑛𝑤 ,…………………………………………………………....………(1) 𝑘𝑟𝑜𝑤 = 𝑘𝑟𝑜𝑐𝑤 × ( 𝑆𝑜−𝑆𝑜𝑟𝑤 1−𝑆𝑤𝑐𝑜𝑛−𝑆𝑜𝑟𝑤 ) 𝑛𝑜𝑤 .…………………………………………………..………….........(2) gas and liquid relative permeability 5 𝑘𝑟𝑜𝑔 = 𝑘𝑟𝑜𝑔𝑐𝑔 × ( 𝑆𝑙−𝑆𝑜𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 1−𝑆𝑔𝑐𝑜𝑛−𝑆𝑜𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 ) 𝑛𝑜𝑔 ,……………………….…………………………......……...(3) 𝑘𝑟𝑔 = 𝑘𝑟𝑔𝑐𝑙 × ( 𝑆𝑔−𝑆𝑔𝑐𝑟𝑖𝑡 1−𝑆𝑔𝑐𝑟𝑖𝑡−𝑆𝑜𝑖𝑟𝑔−𝑆𝑤𝑐𝑜𝑛 ) 𝑛𝑔 ..…………………………..…………………..………......……(4) the relationship between the capillary pressure and the saturation of core is expressed as follows. oil and water 𝑝𝑐𝑜𝑤 = [𝑝𝑐𝑜𝑤(𝑆𝑤 = 𝑆𝑤𝑐on ) − 𝑝𝑐𝑜𝑤(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑤)] × [ (1−𝑆𝑜𝑟𝑤−𝑆𝑤) (1−𝑆𝑤𝑐𝑜𝑛−𝑆𝑜𝑟𝑤) ] 𝑛𝑜𝑤 + 𝒑𝒄𝒐𝒘(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑤).………………….……………………(5) gas and liquid 𝑝𝑐𝑜𝑔 = [𝑝𝑐𝑜𝑔(𝑆𝑙 = 𝑆𝑙𝑐𝑜𝑛) − 𝑝𝑐𝑜𝑔(𝑆𝑙 = 1 − 𝑆𝑔𝑐𝑜𝑛)] × [ (1−𝑆𝑜𝑟𝑔−𝑆𝑔) (1−𝑆𝑔𝑐𝑜𝑛−𝑆𝑜𝑟𝑔) ] 𝒏𝒐𝒈 + 𝑝𝑐𝑜𝑔(𝑆𝑤 = 1 − 𝑆𝑜𝑟𝑔).…………………….……………….(6) in the cmg-gem module, the relative permeability curve is interpolated with the interfacial tension method. fluids are considered immiscible when the interfacial tension is relatively large. the relative permeability curve and the capillary curve are assigned to both oil and gas. when the interfacial tension drops to the critical value, interpolation is performed with the formulas method to obtain the relative permeability curve and the capillary curve of oil and gas. the fluids are miscible when the interfacial tension is lower than the critical value. the relative permeability curves are selected according to the miscible modes. the effect of interfacial tension on relative permeability is considered to obtain the linear functions of gas and oil saturation from gas and oil relative permeability curves when the fluid phases are miscible (the dual phase interfacial tension approaches 0). the corrected kro and krg are expressed with krot and krgt as follows. 𝑘𝑟𝑜𝑡 = 𝑓 ∗ 𝑘𝑟𝑜 − (1 − 𝑓) ∗ 𝑘𝑟𝑜 𝑆𝑜 (1−𝑆𝑤) ,……………………………………………….….……….……..(7) 𝑘𝑟𝑔𝑡 = 𝑓 ∗ 𝑘𝑟𝑔 − (1 − 𝑓) ∗ 𝑘𝑟ℎ 𝑆𝑔 1−𝑆𝑤 ,………..……………………...………………..………….……..(8) where, 𝑘𝑟ℎ = 0.5 ∗ (𝑘𝑟𝑜𝑤(𝑆𝑤)) + 𝑘𝑟𝑔(𝑆𝑔 = 1 − 𝑆𝑤) ,…………………………………..…….…………….…(9) 𝑓 = { 1, 𝑖𝑓(𝜎 > 𝜎0) ( 𝜎 𝜎0 ) ^𝑒𝑘𝑠𝑖𝑔, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 ,……………..…………...……………...………………….……..…...(10) 𝜎 1 4 = [𝑃](𝜌𝐿 − 𝜌𝑔) .……………………….………………………………………….………………..(11) where [p] is a temperature-independent parameter, which is estimated by molecular structure. when the interfacial tension is determined using this method, the unit of interfacial tension is dyn/cm and the unit of density is mol/cm3. when eksig>1 and 𝜎 < 𝜎0 , the function is transformed into the linear function. when eksig<1, the transformation is delayed. when 𝜎 drops to a small part of 𝜎0, the function is transformed into the linear function. when eksig=1, the function is in a transition to an asymptotic linear function. the effect of interfacial tension on the gas-oil capillary pressure causes the dual-phase pressure difference approach zero. the modified pcog is expressed with pcogt as, 6 𝑝𝑐𝑜𝑔𝑡 = { 𝑝𝑐𝑜𝑔, 𝑖𝑓 𝜎 > 𝜎0 𝑝𝑐𝑜𝑔 ∗ ( 𝜎 𝜎0 ) 𝑒𝑝𝑠𝑖𝑔 , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .…………….……..…………………..(12) parameter selection. in this paper, based on the known core data and by integrating eqs. 1 through 12, the parameters listed in table 3 are selected to fit the data from the co2 flooding experiments. table 3—model parameters and their value. model parameters parameters range co2 miscible interpolation parameters eksig 0.01~1 epsig 0.01-1 𝜎0 0.01~20 sigms 0.0005-0.0015 oil and water permeability parameters swcon(%) 0.46 swcrit(%) >0.46 1-sorw(%) 0.5-0.9 1-soirw(%) >1-sorw krowmax 0.1-1 krwmax 0.1-1 no 0.5-5 nw 0.5-5 gas and liquid permeability parameters soirg(%) 0.05-0.3 sorg(%) >soirg sgcon(%) 0-0.1 sgcrit(%) >sgcon krgmax 0.1-1 krogmax =krowmax nl 0.5-5 ng 0.5-5 capillary pressure parameters pcowmax(kpa) 120-300 pcogmax(kpa) 30-100 pcowmin(kpa) 0-400 pcogmin(kpa) 0-100 npow 1-10 npgl 1-10 particle swarm optimization (pso) algorithm. the parameters are optimized with the pso method, where each particle has a memory to track the optimum iteration positions of the previous generation of particles. one position is found by the particle itself and is called the best position of the individual particle, and the other position is found by the entire particle group currently and is called the global best particle position. it is assumed that there are n particles in the d-dimensional search space, i.e., the population size of the particle swarm is n, where the position parameter of the ith particle in the d-dimensional position is expressed as 𝑥𝑖(𝑘) = (𝑥𝑖1(𝑘), 𝑥𝑖2(𝑘),⋅⋅⋅, 𝑥𝑖𝐷(𝑘)) …………..…………………….…...……………………..…..….(13) the cost function of the optimization problem is used to judge whether the current position of the particle is superior to its history positions (zhang 2017).the individual optimum position parameter (pbest) searched by the ith particle is expressed as 7 𝑝𝑏𝑒𝑠𝑡 = (𝑝𝑖1, 𝑝𝑖2,⋅⋅⋅, 𝑝𝑖𝐷) .………………………………………………………….....………..….……(14) the optimal position parameter (gbest) of the population searched by all particles is expressed as 𝑔 best = (𝑝𝑔1, 𝑝𝑔2,⋅⋅⋅, 𝑝𝑔𝐷) .……………………………………..…………………………….……...…(15) the velocity is expressed as 𝑣𝑖(𝑘) = (𝑣𝑖1(𝑘), 𝑣𝑖2(𝑘),⋅⋅⋅, 𝑣𝑖𝐷(𝑘)) .…………..…………………………………………...….….…...(16) the velocity and position of the ith particle are updated in kth iteration as follows 𝑣𝑖(𝑘 + 1) = 𝜔𝑣𝑖(𝑘) + 𝑐1𝑟1(𝑝𝑖(𝑘) − 𝑥𝑖(𝑘)) + 𝑐2𝑟2(𝑝𝑘(𝑘) − 𝑥𝑖(𝑘))𝑥𝑖(𝑘 + 1) = 𝑥𝑖(𝑘) ,………...…(17) where k is the iteration times, ω is the weight of inertia, and c1 and c2 are acceleration factors, which control individual information feedback and group information communication of the particles, and causes the particles approach the potential optimal position through judgments based on the information from individual and group optimization and adjustment of the position. r1 and r2 are random numbers between 0 and 1, which improves the fault tolerance and optimization ability of the particles. analysis of pso-based automatic history matching results numerical fitting of experimental data. the relative permeability curve and capillary curve were calculated by controlling points of the relative permeability curve. the value of parameters is listed in table 3. the pso algorithm was used to perform history matching for 3,000 times to obtain the recovery degree, injection pressure, water cut and gas-oil ratio of cores from the low-permeability reservoir. the results are shown in figure 5, and the error is less than 2%. (a)gas-oil ratio,m3/m3 (b)water cut,% (c)injection well bottom-hole pressure, kpa (d)oil recovery,% figure 5—fitting of data from the flooding experiment of the low-permeability cores. 8 the variation of the global error of historical matching with the test trial is shown in figure 6. it shows that the model error is less than 3% after 500 trials, but more trials are required to reduce the error. the distribution of model parameters optimized with the pso algorithm in 3000 times is shown in figure 7. figure 6—global error of historical matching vs the trial number. (a)eksig (b)epsig (c) 𝝈𝟎 (d)sigms (e)krowmax (f)no 9 (g)pcowmax (h)1-sorw (i)krwmax (j)nw (k)pcowmin (l)npow (m)soirg (n)krgmax (o)ng (p)pcogmax 10 (q)sgcon (r)nl (s)pcogmin (t)npg figure 7—distribution of parameters 3000 times during optimization. a total of 51 cases of historical matching with an error of less than 2% were selected, and the distribution of the model parameter in the optimization of pso is shown in figure 8. it can be seen that the parameter uncertainty has been searched to a range small enough with the pso optimization. (a)eksig (b)epsig 11 (c) 𝝈𝟎 (d)sigms (e)krowmax (f)no (g)pcowmax (h)1-sorw 12 (i)krwmax (j)nw (k)pcowmin (l)npow (m)soirg (n)krgmax 13 (o)ng (p)pcogmax (q)sgcon (r)nl (s)pcogmin (t)npg figure 8—distribution of 51 groups of model parameters with an error of less than 2%. analysis of relative permeability curve characteristics. the capillary curves (figure 9) and the relative permeability curves (figure 10) of the low permeability reservoir cores were obtained by normalization of the capillary curves and the relative permeability curves from 51 cases of history matching with an error of less than 2%, and the characteristics of the curve endpoints are illustrated in table 4. as shown in figure 9a, the oil-water capillary pressure of low-permeability reservoirs is low, ranging from 0 to 3 mpa, and the gas-liquid capillary pressure is even lower, ranging from 0 to 0.2 mpa (figure 9b). 14 (a)oil-water (b)gas-liquid figure 9—capillary curve of low-permeability cores. the characteristics of the relative permeability curves are summarized as follows. oil-water relative permeability curve: (1) the water saturation at the same permeability point of the oil-water relative permeability curve is 56.2%, which is greater than 50%, indicating that the reservoirs in the study area are hydrophilic. (2) the oil-water relative permeability curve shows obvious characteristics of the displacement of water by oil in low-permeability reservoirs. the irreducible water saturation of the cores exceeds 30%, while the residual oil saturation exceeds 20%, and the range of common permeability is 33%. (3) as water saturation increases, the relative permeability of the oil decreases rapidly and the relative permeability of the water increases. gas-liquid relative permeability curve: (1) the irreducible liquid saturation exceeds 30%, and the residual gas saturation is 11%. (2) as the gas saturation increases, the relative permeability of the liquid decreases significantly, and the relative permeability of the gas increases significantly, indicating that the oil flow is affected both by gas and liquid. (3) the gas-liquid common permeability range is 54%. the common permeability range of oil and gas is larger than that of oil and water, which is conducive to more oil displacement. this indicates that compared to the development of water flooding, co2 injection is more conducive to improving oil recovery of this type of reservoir and increases oil recovery by more than 10%. table 4—relative permeability of low permeability reservoirs. oil-water permeability (md) porosity (%) swcon (%) sorw (%) krwiro (%) sw @ isosmotic point (%) two-phase flow region (%) 1.2 13.2 35 32 18 56.2 33.0 gas-liquid permeability (md) porosity (%) slcon (%) sgcrit (%) krgcl (%) sl @ isosmotic point (%) two-phase flow region(%) 1.2 13.2 35 11 42.4 60.1 54.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.4 0.5 0.6 0.7 0.8 o il -w at er c ap il la ry p re ss u re , m p a sw,% 0.00 0.05 0.10 0.15 0.20 0.4 0.5 0.6 0.7 0.8 g as -l iq u id c ap il la ry p re ss u re , m p a sl,% 15 (a)oil-water (b)gas-liquid figure 10—relative permeability curve of low permeability cores. conclusions in this paper, a pso-based method of fitting the relative permeability was proposed. the co2 flooding experiments in long cores from low-permeability reservoirs were performed to obtain flow and pressure data. the corey model was used to characterize the permeability curve, where the permeability and capillary pressure models include 26 parameters. the core experimental data were fitted by adjusting the corey model and the capillary curve with the pso method, and the fitting error is less than 2%. the relative permeability curve and the capillary curve of the experimental core were obtained. the curve characteristics are as follows. 1. the water saturation at the same permeability point of the oil-water relative permeability curve is 56.2%, which is higher than 50%, indicating that the reservoirs in the study area are hydrophilic. the oil-water relative permeability curve shows obvious characteristics of the displacement of water by oil in low-permeability reservoirs. 2. the common permeability range of oil and gas is larger than that of oil and water, which is conducive to more oil displacement. this indicates that compared to the development of water flooding, co2 injection is more conducive to improving the oil recovery of this type of reservoir. 3. the oil-water capillary pressure of low-permeability reservoirs is low, ranging from 0 to 3 mpa, and the gas-liquid capillary pressure is even lower, ranging from 0 to 0.2 mpa. nomenclature krg = relative permeability of gas krgcl = krg at connate liquid saturation krw = relative permeability of water krwiro = krw at irreducible oil saturation krow = krw in the presence of the given water saturation krocw = krw at connate water saturation krog = krw in the presence of the given water saturation krogcg = krog at connate gas saturation ng = exponent for calculating krg nw = exponent for calculating krw 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 k rw ， kr o sw krw_dst1(1.2md) kro_dst1(1.2md) 0.0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1 k rl ， kr g sl krl_dst1(1.2md) krg_dst1(1.2md) 16 now = exponent for calculating krow nog = exponent for calculating krog sgcon = connate gas saturation sgcrit = critical gas saturation sl = liquid saturation slcon = irreducible liquid saturation, swcon+soirg so = oil saturation sorg = residual oil saturation for gas-liquid table sorig = non-reducible oil saturation for oil-gas table soirw = non-reducible oil saturation for oil-water table sorw = residual oil saturation for oil-water table sw = water saturation swcrit = critical water saturation swcon = connate water saturation pcow = oil-water capillary pressure pcog = gas-liquid capillary pressure swcon = connate water saturation swcrit = critical water saturation sorw = residual oil saturation soirw = irreducible oil saturation for oil-water table krowmax = maximum krow krwmax = maximum krw no = exponent for calculating krow from krocw nw = exponent for calculating krw from krwiro soirg = irreducible oil saturation for gas-liquid table sorg = residual oil saturation for gas-liquid table sgcon = connate gas saturation sgcrit = critical gas saturation krgmax = maximum krg krogmax = maximum krog ng = exponent for calculating krog from krogcg nl = exponent for calculating krg from krgcl pcowmax = maximum oil-water capillary pressure pcogmax = maximum oil-gas capillary pressure pcowmin = minimum oil-water capillary pressure pcogmin = minimum oil-gas capillary pressure npow = exponent for calculating oil-water capillary pressure npgl = exponent for calculating gas-liquid capillary pressure greek letters σ = oil-gas interfacial tension calculated through the macleod-sugden correlation 𝜎0 = referenced interfacial tension when calculating the relative permeability eksig = gas-oil relative permeability index (dimensionless) epsig = gas capillary pressure index (dimensionless) 17 acknowledgements the authors are grateful for financial support from the national science and technology major project (grant no. 2016zx05016-005 and 2016zx05016-001), the major project of china national petroleum corporation (grant no. riped-2020-js-50214) and (grant no. riped-2020-js-50215), the project of sinopec north china petroleum bureau (grant no. 290018276) and project of petroleum engineering technology institute of sinopec shengli oilfield (grant no. 290018276). conflicts of interest the author(s) declare that they have no conflicting interests. references cmg manual 2015. computer modeling group. eydinov, d., gao, g., li, g., et al. 2009. simultaneous estimation of relative permeability and porosity/permeability fields by history matching production data. journal of canadian petroleum technology 48(12):13-25. li, k.1989. an optimization method for calculating the relative permeability curve of oil and water based on the experimental data of dynamic displacement. journal of oil and gas technology 11(3) :45-54. li, y., li, y., yu, l., et al. 2018. review of history matching method for calculating oil-water relative permeability curves. journal of longdong university 29(3):55-58. toth, j., tibor, b., peter, s., et al. 2002. convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs. journal of petroleum science and engineering 36(1):33-44. zhang, f., wang, z., cheng, y., et al. 2010. processing methods for relative-permeability curves in reservoir numerical simulation. natural gas geoscience 21(5):859-862. zhang, q. 2017. research on the particle swarm optimization and differential evolution algorithms. phd dissertation, shandong university, jinan, china. zhang, x., du, j., bai, l., et al. 2016. new calibration method for oil-water relative permeability curves based on unsteady state method. fault-block oil & gas field 23(2):185-188. zhang, z., tong, y., and wu, y. 2019. effects of diffusion on relative permeability curves of co2 flooding in low permeability reservoirs. journal of xi'an shiyou university (natural science edition) 34(2):73-77. weiling zhang is a engineer in tianjin branch of cnooc. his research interests include numerical simulation and field development of offshore reservoirs. wenfeng lv is a senior engineer at the research institute of petroleum exploration and development (riped), petrochina. he holds a phd degree from china university of petroleum. his research interest includes numerical simulation and gas flooding. yongyi zhou, north china petroleum bureau, sinopec. his research interest includes numerical simulation and field development for unconventional reservoirs. bochao qu is a master candidate in petroleum engineering department at xi’an shiyou university. his research interests include reservoir simulation and production analysis. 18 yawen he is a master candidate in petroleum engineering department at xi’an shiyou university. her research interests include reservoir simulation and hydraulic fracturing design. xinle ma is a master candidate in petroleum engineering department at xi’an shiyou university. her research interests include big data, reservoir simulation, and production analysis. weidong tian is a master candidate in the department of petroleum engineering at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing and production analysis. zhenzhen dong is a professor in the department of petroleum engineering at xi’an shiyou university. she worked as a reservoir engineer at schlumberger from 2012 to 2016. her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dr. dong holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development (riped), china; and a phd degree in petroleum engineering from texas a&m university. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1194 received october 01, 2021; revised november 15, 2021; accepted december 23, 2021. *corresponding author: sedaee@ut.ac.ir 1 numerical investigation of the most affecting parameters on foam flooding performance in carbonate naturally fractured reservoirs seyyed ali ghoreishi, university of calgary, calgary, canada; behnam sedaee*, university of tehran, tehran, iran abstract as one of the methods for reducing gas mobility and delaying gas breakthrough time, foam flooding has potentials to play a crucial role in the oil industry. thus, being used in highly heterogeneous reservoirs, e.g., naturally fractured reservoirs, it can increase sweep efficiency. in this paper, a conceptual 3d model has been used for demonstration of influential factors on foam flooding in naturally fractured reservoirs. a series of numerical analysis on fracture and matrix permeability, fracture spacing, wettability, and foam parameters have been conducted. furthermore, an investigation of certain phenomena, including diffusion and the block-toblock effect, has been conducted. based on the simulations, increasing fracture permeability increased gor in foam flooding, while increasing matrix permeability decreased it. moreover, regardless of the intensity of the fracture in the models, the foam decreased the gas rate and increased the oil recovery. however, cases with higher fracture spacing ended up having higher gors. foam injection performed very well in both water-wet and oil-wet scenarios; however, it performed better in the oil-wet case. while consideration of diffusion increased gor in model with very low matrix permeability, taking the block-to-block effect decreased gor and increased oil recovery in all scenarios. furthermore, the foam injection rate was one of the most critical variables that needed to be optimized. in conclusion, the foam flooding not only tended to decrease gor drastically but also increased oil recovery significantly in naturally fractured reservoirs. however, different rock, fluid, and injection properties can significantly change the results. introduction oil is known to be one of the most important elements of modern industry. taking into account the growing demand for energy in the following decades, it is vital to meet the needs. in this sense, carbonate reservoirs, as one of the most significant sources of oil, have the potential to play a significant role in filling the gap. however, the heterogeneous nature of carbonate oil reservoirs has made not only oil production but also enhancing oil recovery very challenging. the contrast between fracture and matrix media has rendered co2 flooding less effective (trivedi and babadagli 2010; shedid 2009), which is mainly the result of co2 mobility and viscose fingering. in this regard, gas injection and even water injection have poor results because of the early breakthrough. to face the challenge, varied solutions have been proposed, including foam injection. the purpose of this approach is to reduce gas mobility and divert the gas to the matrix to increase sweep efficiency. this aim is to be claimed by having foam lamella to provide resistance to gas flow and increase oil recovery. mailto:sedaee@ut.ac.ir 2 in addition, the jamin effect tends to create higher resistance in high-permeable parts compared to lowpermeable areas, allowing foam to block fractures and causing gas to divert into the matrix. many experimental studies have investigated the application of co2 foam as a means of reducing gas mobility and increasing sweep efficiency (khalil and asghari 2006; farzaneh and sohrabi 2013; zhang et al. 2014). experimental and simulation results indicate that co2 foam can be used to improve macroscopic sweep efficiency and recover more oil from fractured reservoirs (john et al. 2010; farajzadeh et al. 2010). furthermore, although the improvement in the sweep in the more heterogeneous reservoirs was smaller than that in the less heterogeneous reservoirs when the foam was present, there was an improvement in the breakthrough time and incremental oil recovery in more heterogeneous reservoirs as well (tham 2015). moreover, many other investigations have shown that foam injection can yield a higher oil recovery compared to other eor methods such as water alternating gas (wag) or co2 injection. when comparing wag injection and surfactant alternating gas (sag) injection at the same condition, the pressure buildup in the wellbore could be very different, inferring blockage and reduction of permeability due to the presence of foam (foo et al. 2014). the simulation study indicates that the performance of co2 foam flooding on oil recovery and displacement efficiency is better than that obtained by water flooding, co2 flooding, and wag (farajzadeh et al. 2009; tham 2015). furthermore, fractured reservoirs can have a different distribution of heterogeneities, all of which can contribute to many problems in the implementation of eor schemes. however, based on research conducted by tham (2015), as the heterogeneity of the reservoir increases, the degree of improvement using sag increases. in more recent research carried out at the university of harriot-watt, it was pointed out that the ratio of surfactant to the gas used in sag is also very important, and higher ratios of surfactant to gas yield higher recovery as the fracture intensity increases. modelling foam is very complicated as foam is not only very unstable, but also it is a combination of gas and liquid. as a result, it cannot be studied and considered as a different phase (almaqbali et al. 2017; hematpur et al. 2018). there are various models used to simulate foam flow, including the population balance model, the limiting capillary pressure model, fractional flow theory, and the stone model for continuous foam injection (falls et al. 1988; friedmann et al. 1991; kovscek et al. 1995; farajzadeh et al. 2012; ma et al. 2015). based on our best knowledge, the role of the most affecting parameters were not comprehensively studies at nfrs. in this study, the effects of rock and fluid properties on foam flooding in naturally fractured reservoirs were numerically simulated and the most affecting parameters were discussed, compared, and addressed. simulations rock and fluid properties. the stars module of the cmg™ package software was used to build a simple 3d model with 20×20×1 grid blocks. all grids had the height, width, and depth of 100 m. table 1 summarises the properties of the dual-porosity model (dp). the transmissibility in the fracture-matrix fluid flow term used in this dual-porosity model has been calculated using the gilman and kazemi (1988) formulation. the base dp model was water-wet, and its capillary pressure and relative permeability for the water-wet and oil-wet model curves are presented in figures 1 and 2. the reservoir fluid is saturated under flood conditions with a gas cap. furthermore, gas and foam were injected from this cap. the fluid properties of the models, including density and viscosity, are presented in table 2. the initial conditions of the model are summarized in table 3. a vertical production well with a constant maximum rate of 800 m3/d and a minimum pressure of 1,500 kpa was considered; furthermore, a vertical injection well with a constant pressure of 20,000 kpa was considered perforated through the first layer. 3 table 1—reservoir properties of the model used in this study. parameters value matrix porosity 0.1 fracture porosity 0.01 matrix permeability, md 10 fracture permeability, md 1000 table 2—fluid properties of the model used in this study. water dead oil solution gas surfactant densities, kg/m3 978 843 15 379.1 viscosity @80°c , cp 0.38 0.38 2.28 0.16 live oil viscosity @ 26013 kpa, cp 0.42 critical pressure of live oil, kpa 137895 critical temperature of live oil, °c 760 table 3—initial conditions of the reservoir. parameters value initial pressure, kpa 17500 initial temperature, °c 80 initial water saturation, fr 0.27 initial oil saturation, fr 0.73 initial oil saturation in gas cap, fr 0.20 initial gas saturation in gas cap, fr 0.53 figure 1—capillary pressure and relative permeability curve (water-wet). figure 2—relative permeability curve (oil-wet). 4 foam model and foam properties. the foam is generated in-situ by injecting gas and alpha-olefin sulfonate (aos) solution. the success of foam as a displacing fluid in porous media depends on the longevity and strength of foams in the presence of nonaqueous phase liquids such as hydrocarbons, which are controlled by several factors, including critical water and surfactant concentration, brine salinity, oil saturation, and so on. many different models have been developed to describe foam through porous media; generally, there are two main modelling approaches used to simulate foam in commercial simulators: empirical and mechanistic (abbaszadeh et al. 2018), which use different parameters for simulating foam’s stability and performance. the approach used in this study is the empirical method, which tends to modify the relative permeability in the presence of foam; however, the texture of the foam is not considered directly in the calculations. { krg f = krg × fm fm = [1 + 𝑓𝑚𝑚𝑜𝑏 ∙ 𝑓1 ∙ 𝑓2 ∙ 𝑓3 ∙ 𝑓4 ∙ 𝑓5 ∙ 𝑓6 ∙ 𝑓𝑑𝑟𝑦] −1 𝑓1 = ( 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛(𝐼𝐶𝑃𝑅𝐸𝐿) 𝑓𝑚𝑠𝑢𝑟𝑓 ) 𝑒𝑝𝑠𝑢𝑟𝑓 𝑓2 = ( 𝑓𝑚𝑜𝑖𝑙−𝑠𝑜 𝑓𝑚𝑜𝑖𝑙−𝑓𝑙𝑜𝑖𝑙 ) 𝑒𝑝𝑜𝑖𝑙 𝑓3 = ( 𝑓𝑚𝑐𝑎𝑝 𝑐𝑎𝑝𝑖𝑙𝑙𝑎𝑟𝑦 𝑛𝑢𝑚𝑏𝑒𝑟 ) 𝑒𝑝𝑐𝑎𝑝 𝑓4 = ( 𝑐𝑎𝑝𝑖𝑙𝑙𝑎𝑟𝑦 𝑛𝑢𝑚𝑏𝑒𝑟−𝑓𝑚𝑔𝑐𝑝 𝑓𝑚𝑔𝑐𝑝 ) 𝑒𝑝𝑔𝑐𝑝 𝑓5 = ( 𝑓𝑚𝑜𝑓−𝑥𝑛𝑢𝑚𝑥 𝑓𝑚𝑜𝑓 ) 𝑒𝑝𝑜𝑚𝑓 𝑓6 = ( 𝑚𝑜𝑙𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛−𝑓𝑙𝑠𝑎𝑙𝑡 𝑓𝑚𝑠𝑎𝑙𝑡−𝑓𝑙𝑠𝑎𝑙𝑡 ) 𝑒𝑝𝑠𝑎𝑙𝑡 𝑓𝑑𝑟𝑦 = 0.5 + arctan (𝑠𝑓𝑏𝑒𝑡(𝑠𝑤−𝑆𝐹) 𝜋 ,…………….……………………………………………………(1) where, fmmob is the pressure gradient function that represents the reduction in foam mobility when all conditions are favorable, which can be a good indication of foam strength; f1 is the surfactant concentration function; f2 is the oil saturation function; f3 and f4 are the capillary number functions; f5 is the critical oil mole fraction; f6 is the salinity function. this model takes various parameters that affect foam mobility into account, including sharpness of transition zone (epsurf), critical oil saturation (fmoil), lower oil saturation (floil), exponent of oil saturation (epoil), reference capillary number (fmcap), exponent of capillary number (epgcp), exponent of critical oil mole fraction (epomf), lower salt mole fraction (flsalt), critical salt mole fraction (fmsalt), dry out function (fdry) and a parameter to control the sharpness of transition zone between two foam regimes (sfbet). defining foam parameters can be very challenging and has inherited uncertainty due to non-uniqueness of the calibration of the foam model parameters with experimental data. as a result, the foam parameters presented in this study have been matched by in-situ generation of foam in fractured carbonate rocks. the foam parameters used in this study are listed in table 4. table 4—experimental foam parameters for foam. results and discussions the base model with a gas injection had a breakthrough time of two years. furthermore, the ultimate gor after 10 years of gas injection was 1.0×105 (m3/m3) and oil production rate of 253 m3/day which was half of its initial production rate of 500 m3/day. this gas injection performance was improved by using foam injection. foam experiments fmmob sdfdry sfbet fmacap epcap foam 7,720 0.13 5,224 0.02 0.03 5 in this study, various properties, including fracture permeability, matrix permeability, spacing, and wettability, were investigated to find out their effects on breakthrough time, gor, and oil recovery. fracture permeability. effect of fracture permeability was investigated from 100 md to 4000 md to study its influence on breakthrough time and gor. it is shown in figure 3, as the heterogeneity of the reservoir increases, the gas-oil ratio also increases. furthermore, foam injection tends to decrease the gor ratio more significantly in higher fracture permeabilities as a result of the jamin effect. besides, although the difference of gas-oil ratio between the most and the least homogeneous model was about an order of magnitude, it was very subtle in case of foam injection. however, the permeability variations did not have a very significant impact on the gas breakthrough time after foam injection, while they caused a difference of approximately two years in gas injection (figure 3). generally, as can be observed in table 5, foam tended to increase oil recovery for all models. however, it improved oil production much more in the more homogeneous ones (table 5). table 5—effect of fracture permeability on oil recovery after 10 years. kf=100 md kf=1000 md kf=4000md gas injection 0.11 0.15 0.18 foam injection 0.15 0.17 0.20 figure 3—effect of fracture permeability on gor for gas injection and foam injection. matrix permeability. effect of matrix permeability was investigated using 1md to 50md models for clarifying its impact on the gas rate and breakthrough time. as presented in figure 4, foam decreased gor in all the models dramatically, while there was not a consistent relation between matrix permeability and breakthrough time. furthermore, the gor of foam injection decreased as the matrix permeability increased, due to the fact that the increased matrix permeability tended to conduct gas to infiltrate the matrix more and result in a better sweep of oil at higher matrix permeabilities (figure 5). 6 figure 4—effect of matrix permeability on the gas oil ratio for foam injection. figure 5—oil saturation in the matrix after foam injection in a) matrix permeability=1 md, b) matrix permeability=10 md, c) matrix permeability=20 md, and d) matrix permeability=50 md. fracture spacing. effect of fracture spacing on gas breakthrough time, gor, and oil recovery was investigated by changing it from 0.01 m to 70 m. as can be seen in figure 6, the foam performed well in all cases. breakthrough time decreased as the fracture intensity increased, which can be due to the fact that the lower fracture spacing helped the foam to spread better in the reservoir and decreased the chance of fingering. furthermore, models with higher fracture intensity ended up with higher cumulative gor (figure 6). to end it, the foam drastically decreased the gor and increased oil production in all cases. 7 figure 6—effect of fracture spacing on gas breakthrough time for foam injection. gas diffusion effect. gas diffusion has a major impact on models with very low matrix permeability. however, its influence decreased as the matrix permeability increased, to the point that it was almost nonexistent at a matrix permeability of 1 md (figure 7). one of the main factors that controls foam stability is coarsening, the growth of the average bubble size, which is greatly affected by gas diffusion (attia et al. 2013). to further elaborate, the diffusion of gas through the lamellae can lead to an increase in bubble size and end up making the foam less stable. as a result, the consideration of diffusion tended to increase the ultimate gasoil ratio in all scenarios. this was especially important in ultra-low matrix permeabilities since the contribution of molecular diffusion in oil recovery is higher at lower flow rates in the matrix (table 6). as a result, increasing matrix permeability reduced the importance of diffusion in gor and oil recovery. in another scenario, the foam was injected for two years, followed by gas injection for eight years. the impact of diffusion was studied for lower matrix permeabilities. on the basis of simulations, foam tended to delay gas breakthrough and significantly decreased gor significantly; however, foam flood performed better than foam injection for two years, since it decreased gor more. moreover, consideration of diffusion had much less impact in the second scenario. although the gor increased by more than an order of magnitude after considering diffusion during foam flood, it tended to increase less significantly in the latter (figures 7 and 8). this results from continuous injection of foam in the first scenario. continuous degradation of the foam until the end of the flood causes an acceleration of the rate of increase in gor. in the latter case, the foam disappears after a while, resulting from instability of the foam; therefore, the rate of increasing the gor becomes constant after some time. consequently, although the gor in the first scenario is lower than that in the second, the consideration of diffusion had a much greater impact on foam flood compared to foam injection for two years followed by eight years of gas injection. 8 figure 7—effect of diffusion on gor for foam flooding in different matrix permeabilities. figure 8—impact of diffusion during foam injection in the second injection mode. table 6—impact of diffusion on oil recovery in different matrix permeability. oil recovery (fr) km=0.01 md km=0.1 md km=1 md with diffusion 0.08 0.10 0.12 without diffusion 0.11 0.12 0.14 wettability effect. the main model in this study was water-wet. however, an investigation was conducted with an oil-wet model (figure 2). the model shared all the properties of the water-wet model except wettability. in this model, gas injection and foam injection were performed. while gor is higher during gas injections in the oil-wet systems (figure 9), it does not change dramatically during foam injections in the same models. furthermore, for higher fracture permeabilities, the difference between the ultimate gor was greater in foam injection. the breakthrough time did not change significantly by altering the wettability (figure 10). 9 figure 9—gor in oil-wet and water-wet models with different fracture permeabilities (gas injection). figure 10—breakthrough time in oil-wet models with different fracture permeabilities (foam and gas injection) re-infiltration effect. all previous studies had used standard dual-porosity model; however, in order to study the effect of re-infiltration, a subdomain model has been used. the matrix element is divided into several nested volume domains that communicate with each other (figure 11). therefore, pressure, saturation, and temperature gradients are established inside the matrix, allowing transient interaction between fracture and matrix. consequently, the fracture and matrix will start communicating earlier due to matrix sub-blocks. matrix sub-blocks, as well as the fracture, have different depths and, hence, this model is suitable to simulate the gravity drainage process this study investigates the block-to-block effect in the presence of gravity drainage. reimbibition of oil to the lower block matrix can have significant impacts on gas breakthrough since considering this effect will increase sweep efficiency and conduct more gas to the matrix compared to the scenario that is not considered (figure 12). as it can be observed in figure 13, gas tends to breakthrough earlier when there is no block-toblock effect since it mainly sweeps the fracture. although the block-to-block effect had postponed the breakthrough, the ultimate gor was higher. higher gor in the second scenario can be explained by acknowledging that in the first scenario, no block-to-block effect, even after the breakthrough foam diverts some gas into the matrix while in the second scenario, foam has already conducted a considerable amount of 10 gas into the matrix and not much of it is sweeping the matrix after breakthrough. furthermore, cumulative oil production is also higher in the second model, which can approve higher sweep efficiency (table 7). figure 11—subdomain model to investigate the re-infiltration effect. figure 12—gor in models with different fracture permeabilities with and without consideration of re-infiltration effect. table 7—block-to-block effect on oil recovery with different fracture permeabilities. oil recovery kf=500 md kf=1000 md kf=2000 md with block-to-block effect 0.41 0.42 0.44 without block-to-block effect 0.33 0.34 0.35 11 figure 13—effect of re-infiltration on oil saturation in the matrix: models without re-infiltration effect with fracture permeability of a) 500 md and b) 1000 md, models considering re-infiltration with fracture permeability of c) 500 md and d) 1000 md. foam injection rate. impact of the rate of foam injection on gor and oil recovery has been investigated using the dual-porosity model for a wide range of rates. increasing the injection rate did not have the same impact on the results. increasing foam rate tended to increase oil recovery at a lower injection rate since it not only increased the sweep efficiency but also maintained the reservoir pressure. however, increasing the rates had adverse effects at higher injection rates. as a result, there is an optimum rate for maximizing the oil recovery in this period. this results from the fact that, while higher injection rates improve oil recovery before the breakthrough, they decrease it afterward, as they drastically increase gas production and gor (figure 14). in this study, the optimal rate was around 500 m3/day, after which the increase in the rate had the opposite influence on oil recovery and significantly decreased gor. it is important to point out that this is the technical optimum rate, however, this rate is always calculated based on economic variables and may be different in real reservoirs. figure 14—impact of injection rate on cumulative gor and oil recovery. 12 conclusions gas injection and foam injection simulations were performed on a 3d reservoir model and the following conclusions can be drawn from this study: 1. foam injection tends to decrease gor, delay gas breakthrough, and increase oil production in all the cases of naturally fractured reservoirs studied; however, its impact was much notable in models with higher heterogeneities. 2. although increasing matrix permeability and fracture intensity decreased gor, the differences were not as striking as the changes caused by fracture permeability alterations. 3. furthermore, although consideration of diffusion did not result in much change in higher matrix permeabilities, it increased gor and decreased oil recovery in the cases with lower matrix permeability. this impact decreased as the matrix permeability increased. 4. the change in wettability from water-wet to oil-wet increased the gor in gas injection; however, the foam model performed better and significantly decreased the gor, even lower than that of the waterwet system. 5. the consideration of the block-to-block effect had significant impacts on the result. while for the scenarios with the reinfiltration option, it took longer for the gas to breakthrough, the ultimate gor was higher for them. 6. an investigation of the injection rate clarified that increasing the injection rate does not necessarily increase oil recovery; in fact, it can decrease oil recovery after the breakthrough. however, increasing the rate before the breakthrough increases oil recovery. as a result, the optimal rate should be calculated. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature fmmob = pressure gradient function f1 = surfactant concentration function f2 = oil saturation function f3 = capillary number function f4 = capillary number function f5 = critical oil mole fraction f6 = salinity function epsurf = sharpness of the transition zone fmoil = critical oil saturation floil = lower oil saturation epoil = exponent of oil saturation fmcap = reference capillary number epgcp = exponent of capillary number epomf = exponent of critical oil mole fraction flsalt = lower salt mole fraction fmsalt = critical salt mole fraction fdry = dry out function sfbet = parameter to control the sharpness of the transition zone between two foam regimes 13 references abbaszadeh, m., varavei, a., garza, f.r., et al. 2018. methodology for the development of laboratory-based comprehensive foam model for use in the reservoir simulation of enhanced oil recovery. spe reservoir evaluation & engineering 21(2): 344-363. almaqbali, a., spooner, v.e., geiger, s., et al. 2017. uncertainty quantification for foam flooding in fractured carbonate reservoirs. paper presented at the spe reservoir simulation conference montgomery, texas, usa, 2023 february. spe-182669-ms. attia, j.a., kholi, s., and pilon, l. 2013. scaling laws in steady-state aqueous foams including ostwald ripening. colloids and surfaces a: physicochemical and engineering aspects 436:1000-1006. hematpur, h., mahmood, s.m., nasr, n.h., et al. 2018. foam flow in porous media: concepts, models and challenges. journal of natural gas science and engineering 53: 163-180. falls, a.h., hirasaki, g.j., patzek, t.w., et al. 1988. development of a mechanistic foam simulator: the population balance and generation by snap-off. spe reservoir engineering 3(3): 884-892. farajzadeh, 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k., ren, g., mateen, k., et al. 2015. modeling techniques for foam flow in porous media. spe journal 20(3): 453-470. shedid, s.a. 2009. influences of different modes of reservoir heterogeneity on performance and oil recovery of carbon dioxide miscible flooding. journal of canadian petroleum technology 48(2): 29-36. farzaneh, s.a. and sohrabi, m. 2013. a review of the status of foam applications in enhanced oil recovery. paper presented at the eage annual conference & exhibition, london, uk,10-13 june. spe-164917-ms. su, s., gosselin, o., parvizi, h., et al. 2013. dynamic matrix-fracture transfer behavior in dual-porosity models. paper presented at the eage annual conference and exhibition incorporating spe europec, london, uk, 10-13 june. spe-164855-ms. trivedi, j.j. and babadagli, t. 2010. experimental investigations on the flow dynamics and abandonment pressure for co2 sequestration and oil recovery in artificially fractured cores. journal of canadian petroleum technology 49(3): 22-27. tham, s. 2015. a simulation study of enhanced oil recovery using carbon dioxide foam in heterogeneous reservoirs. paper presented at the spe annual technical conference and exhibition, houston, texas, 28-30 september. spe-178746-stu. zhang, y., zhang, l., chen, b., et al. 2014. evaluation and experimental study on co2 foams at high pressure and temperature. j. chem. eng. chin. univ. 28(3): 535-541. 14 s. a. ghoreishy received his bachelor's degree in petroleum engineering from the university of tehran. he is currently a master student and researcher at the university of calgary. he mainly focuses on different phenomena that affect the fluid flow in porous media, including foam flow in porous media and flow alongside on the surface of porous media. behnam sedaee is currently an assistant professor of institute of petroleum engineering at university of tehran. behnam has authored several peer-reviewed journal publications and conference papers. he has been heavily involved in research on various aspects of reservoir engineering including natural fractured reservoir simulations (nfr), enhanced oil recovery (eor), gas condensate, underground gas storage (ugs), and acidizing. his research has also included laboratory measurement and characterization of enhanced oil recovery (eor). he developed several software for ugs, eor and reservoir applications. dr.sedaee earned a bs in chemical engineering and a ms, phd in petroleum engineering from polytechnics university. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1148 received december 30, 2019; revised february 23, 2020; accepted april 12, 2020. *corresponding author: dongzhenzhen1120@hotmail.com 1 horizontal well productivity evaluation for stress sensitive elliptical reservoirs weidong tian, zhenzhen dong* and jiaen lin, xi’an shiyou university, xi’an, china abstract well productivity model is one of the vital tools required to evaluate well performance. most horizontal well productivity models are idealistic in nature, mainly developed for homogeneous reservoirs and conventional reservoirs, and ignore the influences of the pore pressure and stress changes. however, as the capillary in low permeability porous media is tiny, the medium permeability is quite sensitive to pressure change. thus, there is an urgent need for new realistic productivity models that describe the actual reservoir inflow performance behavior more efficiently than the available models. this paper presents a new horizontal well productivity model which accounts for the stress sensitive permeability in an elliptical reservoir. then, the proposed model was extended to investigate the effects of reservoir heterogeneity, eccentricity, and formation damage on horizontal well productivity. the results show that the thinner the formation is, the greater the impact of the horizontal well lengths on production. as the horizontal well length is longer, the impact of stress sensitivity on the production becomes more significant. horizontal well would be a better well type option for elliptical reservoirs. the longer the horizontal well is, the more impact of heterogeneity, eccentricity distance, as well as skin factor on productivity. the new model provides a simpler and more reliable means to optimize horizontal well length and efficiently forecast well behavior in stress sensitive reservoirs, such as tight gas reservoir and shale oil reservoirs, with respect to horizontal well productivity to vertical well productivity. introduction to determine the economic feasibility of drilling a horizontal well, the engineers need reliable methods to estimate its expected productivity. there have been attempts to describe and estimate horizontal well productivity. joshi (1988a) further illustrates the principle of horizontal well production through electrical simulation, and the calculation of steady-state production of horizontal well was derived in detail. up to now, most of the steady-state horizontal well productivity formulas proposed by many authors are similar to the formulas. larsen (1996) proposed a method for calculating the productivity equation of multilateral wells, branch wells and other generalized wells. babu and odeh (1989) calculated the productivity equation of the horizontal well in a pseudo-steady state. billiter et al. (2001) proposed the dimensionless inflow dynamic curve of the non-fracture horizontal gas well. the flow equation of the babu and odeh’s horizontal well is transformed into the pseudo-pressure form of the gas well, and the non-darcy flow effect as well as the mechanical skin effect are considered. furthermore, the pseudo-steady horizontal well productivity of anisotropic reservoir (lu and tiab 2007), mailto:dongzhenzhen1120@hotmail.com 2 constant rate and constant pressure (hagoort 2011) are given. salam (2019) presents a new practical method for determining the start time of pseudo-steady flow and constant-behavior productivity index (pi). other scholars have considered the wellbore flow into the productivity formula. penmatcha and khalid (1999) proposed a semi-analytical model for homogeneous reservoirs that can quantify the impact of wellbore single-phase and two-phase oil and gas in wellbores on productivity. anklam and wiggins (2005) presented a model for estimating horizontal well productivity, which combined wellbore fluid dynamics to calculate the well pressure for the entire wellbore. zhu et al. (2002) (for multilateral wells) and yildiz (2003) (for perforated horizontal wells) have done similar research. guo, et al. (2006) developed a general mechanistic model combining the fluid flow of a single branch. the model strictly considers the pressure drop in the vertical and inclined wellbore sections. in recent years, scholars have been mainly devoted to the study of the productivity of horizontal wells with tight reservoirs, taking into account the factors such as multi-layer reservoir, capillary force, hydraulic fracturing and so on. tabatabaei et al. (2009) in studying the yield of horizontal wells for hydraulic fracturing in bakken shale reservoir, established an analytical model to predict the horizontal well yield for longitudinal fractures in multi-layer reservoirs. kewen and chen (2012) derived formulas for calculating water cut and dimensionless total and oil productivity indices (pis) by considering capillary pressure, to study the effect of capillary pressure on production performance in low-permeability oil wells or reservoirs. bin et al. (2015) present a new analytical solution to study the interplay between flowing pressure and production rate for horizontal well completed within stimulated reservoir volumes (srv) in tight gas reservoirs. chen et al. (2019) presented the calculation method of fracturing production of horizontal well through layer, considering the inter-slit interference and wellbore interference. sun et al. (2019) set up a seepage model for the tiny reservoir by coupling the elliptical flow in the matrix and the near radial flow in the fracture. all of the above pseudo-steady state equations are either too complicated to use or very time consuming. moreover, they all ignored the influences of the pore pressure and stress changes on horizontal wells. however, as the capillary in low permeability porous media is tiny, the medium permeability is quite sensitive to pressure change. the effect of pressure on permeability cannot be ignored, especially for the abnormally high pressure and low permeability reservoirs. this paper provides analytical equations to calculate productivity of horizontal wells in low-permeability reservoirs with considering the effect of stress on permeability. then, the effect of shape of drainage area, heterogeneity, eccentricity and formation damage on the proposed horizontal well productivity model were studied. the work discussed here was carried out at xi’an shiyou university, from june to december 2019. materials and methods physical model figure 1 is a schematic of a horizontal well. the following assumptions are made: 1. the horizontal well is in the middle of an elliptical reservoir. 2. the horizontal well is in the middle of the formation, with an impermeable top and bottom boundary. 3. the reservoir is homogeneous and isotropic. 4. the length of horizontal well is l and the width of reservoir is h. 5. the flow of fluid is slight compressible single-phase flow of oil which corresponds to the low-speed non-darcy flow law. 6. ignore the effect of gravity and capillary forces. 3 figure 1—the horizontal well scheme of low permeability reservoir productivity formula derivation the horizontal flow calculations. the horizontal flow of well keeps its shape in ellipses, introducing the ru koves ki function 𝑧 𝐿/2 = 1 2 (𝜔 + 1 𝜔 )...……………………..……………………………………………………………….(1) utilize conformal mapping and transfer the area of elliptical shape with semi-major axis of a as well as semi-minor axis of b into the circular area with radius of 𝑎+𝑏 𝐿/2 . the segment from (-l/2, 0) to (+l/ 2, 0) is imaged into the unit circle, as shown in figure 2. the flow on ω surface can be considered as the supply which is provided from the circular with radius of 𝑎+𝑏 𝐿/2 to a vertical well with radius of 1. figure 2—scheme of horizontal conformal mapping most horizontal well productivity models ignored the influences of the pore pressure and stress changes. however, as the capillary in low permeability porous media is tiny, the medium permeability is quite sensitive to pressure change. the effect of pressure on permeability cannot be ignored, especially for the abnormally high pressure and low permeability reservoirs. many research efforts have shown that the permeability changes exponentially with the pressure. thus, 𝐾𝐷 = 𝑘 𝑘ℎ = 𝑒−𝛼𝑘(𝑝𝑖−𝑝).……………………….…………………………………………………………(2) consider the existence of starting pressure gradient, so the fluid velocity can be defined as ν = 𝑘 𝜇 [ 𝑑𝑝 𝑑𝑟 − 𝐺𝑝].………...………………………………………………………………………………(3) substitute eq. 2 into eq. 3 and replace the fluid velocity with production to yield h/2 h x y z (-l/2,0) o (l/2,0) x y          1 2 1 2/l z o   z  b a 4 qμb 85.2618×2πrhkh = e−αk(pi−p) [ dp dr − gp],……………………………………………….………………...(4) based on the research of chen et al. (2006, 2007), the oil production formula is as follows. q = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{−𝛼𝑘[𝑝𝑖−𝑝𝑤−𝐺𝑝(𝑟𝑒−𝑟𝑤)]} 𝑙𝑛 𝑟𝑒 𝑟𝑤 ....………………………………..……….………………(5) consider the property of elliptical b = √𝑎2 − (𝐿/2)2, the horizontal flow of the production wells can be expressed as q𝐻 = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{ −𝛼𝑘 [ 𝑝𝑖−𝑝𝑤−𝐺𝑝 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 −1 ) ] } 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 ) ,……....…………….……………………………(6) where 𝑎 = 𝐿 2 √1 2 +√ 1 4 + ( 2𝑟𝑒𝐻 𝐿 ) 4 , 𝑟𝑒𝐻 = √𝐴/𝜋...……………..….…………………………...…………...…(7) the vertical flow calculations. the vertical flow of horizontal well can be regarded to be a junction of supply from the top and bottom boundaries. the diagram of vertical conformal transformation is shown in figure 3. figure 3—vertical conformal transformation convert the band-shaped region (-h/2<y<h/2) on z plane to the unit circle domain on ω plane. then, the junction of (0, 0) on z plane will be converted to the b point (1, 0) on ω plane and the well radius of rw on z plane will be converted to ρw on ω plane. on ω plane, the complex potential of any points can be obtained through mirror image theory. thus, u = 𝑞 2𝜋 𝑙𝑛(𝜔 − 1)(𝜔 + 1) + 𝐶 = 𝑞 4𝜋 𝑙𝑛[(𝜍2 + 𝜂2 + 1)2 − 4𝜍2] + 𝑖 𝑞 2𝜋 (𝑎𝑟𝑐𝑡𝑔 𝜂 𝜍−1 + 𝑎𝑟𝑐𝑡𝑔 𝜂 𝜍+1 ) + 𝑐2,……….(8) where 𝜍2 = 𝑒 2𝜋𝑥 ℎ 𝑐𝑜𝑠2 𝜋𝑦 ℎ ; 𝜂2 = 𝑒 2𝜋𝑥 ℎ 𝑠𝑖𝑛2 𝜋𝑦 ℎ . therefore, the potential function (pressure function) is given as, 𝛷 = 𝑞 4𝜋 𝑙𝑛 [(𝑒 2𝜋𝑥 ℎ + 1) 2 − 4𝑒 2𝜋𝑥 ℎ 𝑐𝑜𝑠2 𝜋𝑦 ℎ ] + 𝑐2,………………………………………………………..(9) o x y o   h z e    a(-1,0) b(1,0) h/2 h/2 z  5 when x=0，y=h/2, then 𝜙ℎ 2 = 𝑞 4𝜋 𝑙𝑛4 + 𝑐2. the potential of the junction b on the wall of well can be defined as φw and it is always divided into two parts, which is brought by the junction a and junction b, respectively. the distance from junction a to junction b can be approximately equal to 2 and the radius of junction b is ρw. thus, 𝜌𝑤 = 𝑑(𝜔−1)(𝜔+1) 𝑑𝑧 |(0,0)𝑟𝑤 = 2𝜋 𝑑𝑧 𝑒 𝜋𝑧 ℎ |(0,0)𝑟𝑤 = 2𝜋𝑟𝑤 ℎ ,…………....…..………………………………….(10) 𝛷𝑤 = 𝑞 2𝜋 [𝑙𝑛2 + 𝑙𝑛 2𝜋𝑟𝑤 ℎ ] + 𝑐2.…………………………….…………………………………………..(11) the non-darcy flow equation can be expressed as follows 𝑑𝛷 𝑑𝑟 = 𝑘 𝜇 ( 𝑑𝑝 𝑑𝑟 − 𝐺𝑝),…………………………………………………….………….…………………....(12) the flow on ω plane can be regarded as the unitary circular supply for a vertical well in one area with radius of ρw (which will be corrected to the effective caliper using peaceman method (1990)) whose discharge area is a rectangle with h/2 as long side and h/2π as short side. the area of this rectangle is equivalent to the area of the circle with a radius of h/2π. do integration to the eq.11 within (rw, h/2) and according to the dupuit formula, the shunt volume on the vertical direction of horizontal wells is q𝑣 = 𝑘ℎ𝐿 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒 {−𝛼𝑘[𝑝𝑒−𝑝𝑤−𝐺(1−𝑙𝑛 2𝜋𝑟𝑤 ℎ )]} 𝑙𝑛( ℎ 2𝜋(𝑟𝑤+1) ) ......…………………………………………………..(13) horizontal well productivity. the oil flow resistance on horizontal direction (ωh) and on vertical direction (ωv) which are based on eq. 6 and eq.13 can be expressed as follows ω𝐻 = 1.8665×10−3𝛼𝑘𝜇𝐵 𝑘ℎℎ 𝑙𝑛 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )....……………………….……………………………………..(14) ω𝑣 = 1.8665×10−3𝛼𝑘𝜇𝐵 𝑘ℎ𝐿 𝑙𝑛 ( ℎ 2𝜋(𝑟𝑤+1) )....………………………….…………………………………….(15) total production of the horizontal well resulting from these two flow components is obtained by adding the respective flow resistances, ∆p q = ( ∆p q𝐻 ) + ( ∆p q𝑣 ),…………………………………………...………………………………………..(16) or pressure drawdown per unit volumetric flow rate, q = (𝑝𝑒 − 𝑝𝑤)/(ω𝐻 − ω𝑣),…………………………………………………………………………..(17) thus, the horizontal well flow rate can be given as, q = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{ −𝛼𝑘 [ 𝑝𝑒−𝑝𝑤−𝐺 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 −𝑙𝑛 2𝜋𝑟𝑤 ℎ ) ] } 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )+ ℎ 𝐿 𝑙𝑛( ℎ 2𝜋(𝑟𝑤+1) ) .......…………………..……………………..(18) expansion of the proposed productivity model the proposed productivity model (eq. 18) was extended to consider more practical conditions, such as heterogeneous reservoir, off-center wells, and formation damage. heterogeneity. with considering reservoir heterogeneity, the steady flow percolation equation is given as, 𝑘𝑥 𝜕2𝑝 𝜕𝑥2 + 𝑘𝑦 𝜕2𝑝 𝜕𝑦2 + 𝑘𝑧 𝜕2𝑝 𝜕𝑧2 = 0....………………………………………….…………………………...(19) 6 according to the assumption of joshi (1988b), the horizontal wells flow in the three-dimensional system is always divided into the horizontal flow and the vertical flow. therefore, the stable seepage can be simplified as, ( 𝜕2𝑝 𝜕𝑥2 ) + 𝑘𝑣 𝑘ℎ ( 𝜕2𝑝 𝜕𝑧2 ) = 0..…………………………………………………………………………………(20) introduce z = z√ 𝑘ℎ 𝑘𝑣 , then the heterogeneous problem of eq. 20 can be transformed into a homogeneous problem, expressed in eq. 19. ( 𝜕2𝑝 𝜕𝑥2 ) + ( 𝜕2𝑝 𝜕𝑧2 ) = 0..……………………………………………………………………………………(21) substitute ℎ√ 𝑘ℎ 𝑘𝑣 for h in eq.20 and eq.21, and substitute the average permeability√𝑘ℎ𝑘𝑣 or ki in eq.19, then the horizontal well production formula with considering heterogeneity can be expressed as, q = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{ −𝛼𝑘 [ 𝑝𝑒−𝑝𝑤−𝐺 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 −𝑙𝑛 2𝜋𝑟𝑤 ℎ ) ] } 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )+𝐼𝑎𝑛𝑖 ℎ 𝐿 𝑙𝑛( ℎ𝐼𝑎𝑛𝑖 2𝜋(𝑟𝑤+1) ) ,……………………………………………..(22) where 𝐼𝑎𝑛𝑖 = √ 𝑘ℎ 𝑘𝑣 . eccentricity. the eccentricity only affects the vertical plane of horizontal well productivity. introducing transformation ω = z + iδ will transform the problem solving with eccentricity into the problem solving without eccentricity, seen in figure 4. figure 4—vertical conformal transformation affected by eccentricity introduce conformal transformation, ω = 1−𝑒 𝜋 ℎ (z+iδ) 1+𝑒 𝜋 ℎ (z+iδ) ,…………………………………………………………………………………………(23) and convert the band-shaped region with eccentricity on z plane to the unit circle domain on ω plane. then, the junction of (0, 0) on z plane will be converted to the original point (0, 0) on ω plane and the production well radius of rw on z plane will be converted to ρw on ω plane. thus, 𝜌𝑤 = 𝑑𝜔 𝑑𝑧 |(0,0)𝑟𝑤 = 2𝜋𝑟𝑤 ℎ(2+𝑒 𝑖 𝜋δ ℎ +𝑒 −𝑖 𝜋δ ℎ ) = 𝜋𝑟𝑤 2ℎ𝑐𝑜𝑠2 𝜋δ 2ℎ ,…………………………………..…………………(24) according to the study of yuan et al. (2009 and 2015) and chen et al.(2009, 2012), for the reservoirs with anisotropic permeability, there is 0.5h 0.5h (0,0) 𝛿 𝑥 𝑦 0.5h 0.5h (0,0) 𝜂1 z w 𝜁1 7 𝐽ℎ = 0.543𝑘ℎℎ/(𝜇𝑜𝐵𝑜) 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )+( 𝛽ℎ 𝐿 )𝑙𝑛( ( 𝛽ℎ 2 ) 2 +𝛽2𝛿2 𝛽ℎ 2 𝑟𝑤 ) ,…………………………………………………………………(25) therefore, horizontal well production formula considering the existence of eccentricity can be expressed as, q = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{ −𝛼𝑘 [ 𝑝𝑒−𝑝𝑤−𝐺 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 −𝑙𝑛 2𝜋𝑟𝑤 ℎ ) ] } 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )+𝐼𝑎𝑛𝑖 ℎ 𝐿 𝑙𝑛 ℎ𝐼𝑎𝑛𝑖+(2𝐼𝑎𝑛𝑖𝛿) 2 2𝜋(𝑟𝑤+1) ………………………………………………(26) formation damage. compared with vertical wells, the drilling time of horizontal wells in the oil layer is much longer, so the contact area between producing formation and drilling fluid is larger. therefore, under the same drilling conditions, the contamination of horizontal well reservoir is much severer than that of the vertical wells reservoir, resulting in the production difference between horizontal wells and vertical wells. the parameter which is used to represent the horizontal wellbore damage is usually called skin factor, abbreviated as s. it is be obtained through drill-stem testing (dst) or pressure recovery testing. the value of s can affect the flow efficiency of the fluid, but it is not the unique factor and it does not exist independently. the flow efficiency of the fluid also can be affected by the vertical penetration level (giger et al. 1984). therefore, when the effect of formation damage on horizontal well productivity was studied, the effect of skin and permeability anisotropy should be considered. according to the study of renard and dupuy (1991), the value of skin can be estimate roughly based on the following equation, 𝑆ℎ = 𝐼𝑎𝑛𝑖ℎ𝑆 𝐿 ……….……………………………………………………………………………………(27) thus, horizontal well production formula considering the existence of formation damage can be expressed as follows. q = 𝑘ℎℎ 1.8665×10−3𝛼𝑘𝜇𝐵 1−𝑒{ −𝛼𝑘 [ 𝑝𝑒−𝑝𝑤−𝐺 ( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 −𝑙𝑛 2𝜋𝑟𝑤 ℎ ) ] } 𝑙𝑛( 𝑎+√𝑎2− 𝐿2 4 𝐿/2 )+𝐼𝑎𝑛𝑖 ℎ 𝐿 (ln ℎ𝐼𝑎𝑛𝑖+(2𝐼𝑎𝑛𝑖𝛿) 2 2𝜋(𝑟𝑤+1) +𝑠) ………………………………………….(28) results and discussion in this section, the proposed production model (eq. 28) was applied to study the impact of horizontal well length (l), reservoir thickness (h), medium deformation coefficient (ak), shape of drainage area (a/b), anisotropy index (𝐼𝑎𝑛𝑖), eccentric distance(𝛿) and formation damage (s) on horizontal well production (q). the basic data that used to calculate production rate are listed in table 1. 8 table 1—basic data used in the calculation parameters value parameters value kh, μm2 0.1 pw, mpa 8 αk, mpa-1 0.1 g, mpa/m 0.001 μ, mpa.s 0.9 rw, m 0.1 b 1.2 a, m2 300000 pe, mpa 10 h, m 40 𝐼𝑎𝑛𝑖 1 𝛿,m 0 s 0 horizontal well length and reservoir thickness. figure 5 shows that the production increases as the reservoir thickness and horizontal well length increase. the thinner the formation is, the greater the impact of the horizontal well lengths on production. for instance, as the reservoir thickness increases from 5 m to 50 m, the horizontal well production increases from 1280.7 to 9941.5 105m3/d (7.8 times) when horizontal well length is set to be 1000 m. while the well length is 3000 m, the production only increases by 5.5 times. thus, horizontal well is suggested in a thin formation. figure 5—effect of reservoir thickness on production at different horizontal well length medium deformation coefficient. medium deformation coefficient, 𝛼𝑘, is an indicator of the degree of stress sensitivity (eq. 2). its influence on productivity is shown in figure 6, which indicates that medium deformation coefficient has a negative linear correlation with production on the semi-log plot. the larger the coefficient, the smaller the production. in other words, the more stress sensitive the formation is, the lower the production. as the horizontal well length is longer, the impact of medium deformation coefficient on the production becomes more significant. 0 1 2 3 4 5 6 7 5 10 15 20 25 30 35 40 45 50 p ro d u ct io n ,1 0 5 m 3 /d reservoir thickness,m l=1000m l=1500m l=2000m l=2500m l=3000m 9 figure 6—effect of the medium deformation coefficient on production at different horizontal well length shape of drainage area. the shape of drainage area is determined by the ratio a/b in figure 2. the influence of the medium deformation coefficient on production with various ratio of a/b is shown in figure. 7. the horizontal well length l was set to be 1000 m, other parameters are listed in table 1. fig 6 shows that the smaller a/b (the closer reservoir shape is to the circle), the lower the production of horizontal well. thus, horizontal well would be a better well type for elliptical reservoirs. figure 7—effect of different a/b on production anisotropy index. anisotropy index is an indicator is an indicator of the degree of reservoir heterogeneity (eq. 22). the influence of the permeability anisotropy index on production is shown in figure 8 in terms of different horizontal well length. it shows heterogeneity has great impact on production. the smaller the vertical permeability (the greater the anisotropy index), the lower the horizontal well production. as 0.1 1 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p ro d u ct io n ,1 0 5 m 3 /d medium deformation coefficient l=1000m l=1500m l=2000m l=2500m l=3000m 0 0.2 0.4 0.6 0.8 1 1.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 p ro d u ct io n ,1 0 5 m 3 medium deformation coefficient a/b=1.5 a/b=2 a/b=2.5 a/b=3 a/b=3.5 10 anisotropy index increases from 1 to 10, the production decreases from 41,024 to 6,019 105m3/d (6.8 times) when the horizontal well length is 3000m. while the horizontal well length is 1000m, the production only decreases 2.6 times. thus, it can be concluded that the stronger the heterogeneity, the more impact of horizontal well length on productivity. figure 8—effect of the anisotropy index on production at different horizontal well length eccentric distance. the influence of the eccentric distance (𝛿) on production was investigated versus various horizontal well length. the anisotropy index (iani), was set to be 1. figure 9 shows that the larger the eccentricity distance, the smaller the production, and the degree of influence gradually decreases. the longer the horizontal well is, the more impact of eccentricity distance on productivity. figure 9—effect of the eccentricity distance on production at different horizontal well length formation damage. figure 10 depicts the influence of formation damage. it indicates that the longer the horizontal well is, the more impact of skin factor(s) on horizontal well production. 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 p ro d u ct io n ,1 0 5 m 3 /d anisotropy index l=1000m l=1500m l=2000m l=2500m l=3000m 0 1 2 3 4 5 6 0 2 4 6 8 10 12 14 16 18 20 p ro d u ct io n ,1 0 5 m 3 /d eccentricity distance,m l=1000m l=1500m l=2000m l=2500m l=3000m 11 figure 10—effect of the formation damage on production at different horizontal well length conclusions a new horizontal well productivity evaluation model based on stress sensitive permeability in an elliptical reservoir is established. and the proposed productivity model was extended to consider the effects of reservoir heterogeneity, eccentricity, and formation damage on horizontal well productivity. the following conclusions can be drawn: 1. the thinner the formation is, the greater the impact of the horizontal well lengths on production. thus, horizontal well is suggested in a thin formation. 2. the more stress sensitive the formation is, the lower the production. as the horizontal well length is longer, the impact of stress sensitivity on the production becomes more significant. 3. the closer reservoir shape is to the circle, the lower the production of horizontal well. thus, horizontal well would be a better well type option for elliptical reservoirs. 4. the longer the horizontal well is, the more impact of heterogeneity, eccentricity distance, as well as skin factor on productivity. acknowledge acknowledgment to the following projects for supporting the research work of this paper: scientific research project of key laboratory of education department in shaanxi province: "research on well test evaluation technology of unconventional horizontal well exploitation" (13js090) conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature a = the semi-major axis of the elliptical drainage area formed in the horizontal wells, m b = the short half axis of the ellipsoidal drain region formed in the horizontal wells, m b = formation volume factor h = reservoir thickness, m 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 3 6 9 12 15 p ro d u ct io n ,1 0 5 m 3 /d skin factor l=1000m l=1500m l=2000m l=2500m l=3000m 12 iani = permeability anisotropy index kh = horizontal permeability, μm2 l = horizontal well length, m pe = supply pressure, mpa pwf = wellbore flowing pressure, mpa q = production, m3/d rw = wellbore radius, m s = pseudo-skin factor δ = eccentric distance, m αk = medium 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generalized and extended well concepts. paper presented at spe annual technical conference and exhibition, denver, colorado, 6-9 october. spe-36754-ms. lu, j. and tiab, d. 2007. a simple productivity equation for a horizontal well in pseudo-steady state in a closed anisotropic box shaped reservoir. paper presented at production and operations symposium, oklahoma city, oklahoma, u.s.a., 31 march-3 april. spe-106970-ms. peaceman, d.w. 1990. discussion of productivity of a horizontal well. spe reservoir engineering 5(2): 252-253. spe-31025-pa. penmatcha, v.r. and khalid, a. 1999. effects of pressure drop in horizontal wells and optimum well length. paper presented at spe production operations symposium, oklahoma city, oklahoma, 9-11 march. spe-37494-ms. renard, g. and dupuy, j. m. 1991. formation damage effects on horizontal-well flow efficiency. journal of petroleum technology 43(7):786-869. spe-19414-pa. salam, a. 2019. revisiting current techniques for analyzing reservoir performance: a new approach for horizontal-well pseudosteady-state productivity index. spe journal 24(1):71-91. spe-191139-pa. sun, r., zhang, y., and zhang, x. 2019. productivity prediction model and parameter analysis for fractured horizontal wells in double medium tight oil reservoirs. science technology and engineering 19(10):89-96. tabatabaei, m., mack, d.j., and daniels, n.r. 2009. evaluating the performance of hydraulically fractured horizontal wells in the bakken shale play. paper presented at spe rocky mountain petroleum technology conference, denver, colorado, 14-16 april. spe-122570-ms. yildiz, t. 2003. mutilateral pressure-transient response. spe journal 8(1):234-245. spe-83631-pa. yuan, b., su, y., and rouzbeh, g.m. 2015. a new analytical multi-linear solution for gas flow toward fractured horizontal wells with different fracture intensity. journal of natural gas science and engineering 23(2015):227-238. yuan, y., zhang, l., wang, j., et al. 2009. a binomial deliverability equation for horizontal gas wells in formations with nonlinear seepage flow features. oil＆gas geology 30(1):122-126. zhu, d., hill, a. d., and landtum, w. r. 2002. evaluation of crossflow effects in multilateral well. paper presented at spe/doe improved oil recovery symposium, tulsa, oklahoma, 13-17 april. spe-75250-ms. weidong tian, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. tian holds an bs degree in petroleum engineering from xi’an shiyou university. zhenzhen dong is a professor in the petroleum engineering department at xi’an shiyou university. she worked as a reservoir engineer with schlumberger from 2012 to 2016. her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dong holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. jiaen lin is a professor of petroleum engineering department at xi’an shiyou university, where he has worked as faculty for the last 30 years. he focuses his research in well testing and production analysis. a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1145 received december 12, 2019; revised march 2, 2020; accepted april 10, 2020. *corresponding author: guqingjie1218@163.com 1 study on technical and economic limit of layer-recombination and well pattern adjustment qingjie gu*, daqing oilfield company ltd., daqing, china abstract three types of displacement mode coexist in ns development area at present, including water flooding, polymer flooding, alkaline surfactant polymer flooding. the well patterns and the injection-production relationship is complex, which leads to many difficulties on the adjustment of development plan. combining with reservoir characteristics and well pattern deployment, this study investigates the limit of exploitable reserve and the economic limit of effective thickness of single new drilled well under the different crude oil price. through numerical simulation, the limits of injector-producer spacing, permeability differential and maximum production well segment span were obtained. at the same time, the water flooding and the chemical flooding well patterns were considered coordinately, and the technical policy limits were summarized. the results of the study can help the well pattern adjustment for both the water flooding and the chemical flooding, and also help to lay the foundation for the long term development. introduction the ns development area has experienced a course of continuous research and practice since it was put into production. with a very good development effect, it also led to many problems, such as multiple well patterns and layer systems, and the injection-production relationship is complex, the existing development adjustment methods can not satisfy the need of ultra-high water cut oilfield. the technical and economic limits in the field of the recombination layer system and optimize well pattern were obtained by using numerical simulation with economic assessment. limit of recoverable resources the principle of economic efficiency should be adopted in the well pattern adjustment. recoverable resource of single well is the material base limit for determining the scale of infill well. according to the material balance principle, considering the parameters such as drilling, capital cost, operation cost, tax and internal rate of return (irr), the lower limit of recoverable resource is estimated with the following equation, 𝑁𝑅𝑚𝑖𝑛 ≥ 𝑛𝑎(1+𝑎)𝑛 (1+𝑎)𝑛−1−1+𝑎 (𝑆𝑍+𝑆𝐽) 𝐽(1+𝑌)−𝐶𝑑−𝐶𝑠 ,………………………………………………………………...………….(1) where, nrmin is the lower limit of recoverable resource of single well; sz is the drilling cost per well; j is crude oil price; sj is the capital cost per well; cs is the oil tax; cd is the oil cost; n is the economic life; a is the rate of discount; y is internal rate of return. as shown in table 1, with the increase of single well investment, the recoverable resource of single well also increases. when the internal rate of return (irr) is set to be 12%, single well investment costs is 2.4 mailto:guqingjie1218@163.com 2 million rmb, and crude oil prices is $50/barrel, the lower limit of exploitable reserves of single well is estimated to be 2669 t. table 1—the limit of recoverable resources under different single well investment. crude oil price ($/ barrel) limit of recoverable resources (t) single well investment is 2.0 million rmb single well investment is 2.2 million rmb single well investment is 2.4 million rmb 50 2218 2440 2669 60 1638 1802 1971 70 1298 1427 1561 80 1075 1182 1293 90 917 1009 1103 limit of effective thickness—water flooding recoverable resources can be calculated as control in-place resources multiplying recovery. control resources is defined as the control area multiplies by porosity and oil saturation. so the lower limit of effective thickness can be calculated as eq. 2 and the results are shown in table 2. ℎ = 𝑁𝑅𝑚𝑖𝑛 𝜋𝑟2𝜙𝑆𝑜(𝐸𝑅−𝑅) ,………………..……….……………………………………………………………..(2) where, h is the lower limit of effective thickness; r is the well control radius, which equal to half of the well spacing; 𝜙 is the porosity; so is the oil saturation; r is the recovery percent; er is recovery. table 2—the limit of effective thickness under different well spacing. crude oil price ($/ barrel) limit of recoverable resources (t) lower limit of effective thickness under different well spacing (m) 125 150 175 200 225 250 50 2669 25.2 17.5 12.9 9.9 7.8 6.3 60 1971 18.6 12.9 9.5 7.3 5.7 4.7 70 1561 14.8 10.2 7.5 5.8 4.6 3.7 80 1293 12.2 8.5 6.2 4.8 3.8 3.1 90 1103 10.4 7.2 5.3 4.1 3.2 2.6 limit of effective thickness-chemical flooding of class iii reservoirs two scenarios were carried out, 1) with new drilling wells; 2) with using existing water flooding wells to save drilling investment, but additional cost was added to the investment for polymer flooding project, such as chemical cost and extra capital. the lower limit of effective thickness under different crude oil price for alkaline surfactant polymer flooding was estimated and shown in figure 1. 3 figure 1—limit of effective thickness in alkaline surfactant polymer flooding of class iii reservoir. limit of injector-producer spacing the recovery speed was estimated and compared with increasing well spacing between injectors and producers. the smaller the well spacing is, the faster to reach the maximum recovery (figure 2). figure 2—relation curve between recovery ratio and time with different well spacing. figure 3—relation curve between well spacing and oil production rate. with the increase of well spacing, the oil production rate decreases theoretically (blue curve in figure 3). at present, the oil production rate of b oilfield is 0.45% (red curve in figure 3), and that of c oilfield is 0 10 20 30 40 50 60 70 80 90 t h ic k n es s, m crude oil price ($/bbl) with new wells with exsiting wells 0 0.5 1 1.5 2 2.5 100 125 150 175 200 225 250 采 油 速 度 （ % ） 井距（m） 采油速度 北二西采油速度 北三西采油速度 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 采 收 率 （ % ） 时间（年） 100m 125m 150m 175m 200m 225m 250m time(years) re c o v e ry r a ti o ( % ) well spacing(m) o il re c o v e ry r a te (% ) oil recovery rate of models oil recovery rate of b2x oil recovery rate of b3x fig. 3 relation curve between recovery ratio and time under different well spacing fig. 4 relation curve between well spacing and oil production rate 0 0.5 1 1.5 2 2.5 100 125 150 175 200 225 250 采 油 速 度 （ % ） 井距（m） 采油速度 北二西采油速度 北三西采油速度 0 5 10 15 20 25 30 35 40 0 10 20 30 40 50 采 收 率 （ % ） 时间（年） 100m 125m 150m 175m 200m 225m 250m time(years) re c o v e ry r a ti o ( % ) well spacing(m) o il re c o v e ry r a te (% ) oil recovery rate of models oil recovery rate of b2x oil recovery rate of b3x fig. 3 relation curve between recovery ratio and time under different well spacing fig. 4 relation curve between well spacing and oil production rate 0 0.5 1 1.5 2 2.5 100 125 150 175 200 225 250 采 油 速 度 （ % ） 井距（m） 采油速度 北二西采油速度 北三西采油速度 well spacing(m) o il r e c o v e ry r a te (% ) oil recovery rate of models oil recovery rate of b oil field oil recovery rate of c oil field fig. 4 relation curve between well spacing and oil production rate 4 0.38% (green curve in figure 3), intersecting theoretical curve at 200 m and 220 m, respectively. so the reasonable well spacings were estimated to be 200 m for b oilfield, and 220m for c oilfield. similarly, the theoretical models were established for saertu, putaohua, gaotaizi layers, respectively. as a result, their reasonable well spacing is 200m, 225m and 175m, respectively. limit of permeability ratio by means of numerical simulation, models for different permeability ratio levels (1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 6, 8, 10 respectively) were designed. comparing the development indexes under different permeability ratio by setting the same mining methods and conditions such as the well pattern, the production intensity and the production pressure, conclusions can be drawn. with the increase of permeability ratio, the recovery rate decreases. as the permeability ratio is greater than 4, the recovery rate decreases rapidly and the development effect is poor. as a result, the upper limit of permeability ratio is estimated to be 4, as shown in figure 4. figure 4—relation curve between recovery and permeability ratio. limit of production well spacing by means of numerical simulation, three theoretical models were established and compared (figure 5). middle is interlayer, the upper part is layer 2 and the lower part is layer 1, the reservoir thickness is designed as 10 m, the permeability is designed for an average of 350 md, porosity is 0.2773. by controlling the thickness of the interlayer, the development effects under different production wells spacing were simulated. 11 comparative schemes were designed to compare the development effect, including the production wells spacing of 10m, 40m, 70m, 100m, 130m, 160m, 190m, 220m, 250m, 280m, 300m. with the increase of spacing, the recovery of all the wells decreases gradually, because the recovery of the layer 1 is gradually reduced, and that of layer 2 increases gradually. when the production well spacing is greater than 100 m, the recovery efficiency decreases rapidly and the development effect is poor. so the reasonable production well spacing is less than 100 m. 15 19 23 27 31 35 0 2 4 6 8 10 采 收 率 ， % 渗透率级差 re c o v e ry r a ti o ( % ) permeability ratio 15 19 23 27 31 35 0 2 4 6 8 10 采 收 率 ， % 渗透率级差 re c o v e ry r a ti o ( % ) permeability ratio 5 figure 5—relation curve between recovery efficiency and production well span. conclusions when the oilfield enters into the ultra-high water cut stage, more and more development problems will appear. the layer-recombination and well pattern adjustment should hold the principle of economic efficiency. reuse the existing injectors will reduce the development investment in a large scale. some guidelines for adjustment plan were estimated and summarized as follows.  when the crude oil price is 50 dollars/barrel, the lower limit of effective thickness is 12.9 m with 175 m well spacing;  when the crude oil price is 70 dollars/barrel, the limit of effective thickness in alkaline surfactant polymer flooding of class iii reservoirs is 17.0 m under the condition of using existing water flooding wells;  the reasonable well spacing of injector/producer for saertu, putaohua, gaotaizi layers respectively are 200m, 225m and 175m.  the upper limit of permeability ratio is 4.  the reasonable production well spacing is less than 100m. to improve the recovery efficiency as much as possible, the above technical and economic limits should be followed when compiling the adjustment plan. conflicts of interest the author(s) declare that they have no conflicting interests. references hu, g. 2012. study on limitation of production well segment span in multi-layer reservoirs. xinjiang petroleum geology 33: 72-78. ju, h. 2008. study on rational well density and rational well spacing in tx oilfield. inner mongolia petrochemical industry 16: 78-83. liu, z., wang, q., and sun, y. 2014. study and application of new technological limit for polymer flooding in field application. petroleum geology and recovery efficiency 21:22-30. wu, j., zuo, s., and zhao, x. 2015. technical and economic boundaries on formation and well pattern adjustment in lazhong block. petroleum geology and recovery efficiency 22:113-118. yang, x. 2006. determination of rational well spacing in low permeability sandstone reservoir by dynamic analysis. special oil & gas reservoirs 13: 64-70. qingjie gu is a senior engineer of daqing oilfield company. dr. gu specializes in enhance oil recovery and economic analysis. 34 35 36 37 0 50 100 150 200 250 300 采 出 程 度 ， % 生产井跨度，m 全井 1号层 2号层 re c o v e ry e ff ic ie n c y ( % ) production well segment span(m) 34 35 36 37 0 50 100 150 200 250 300 采 出 程 度 ， % 生产井跨度，m 全井 1号层 2号层 re c o v e ry e ff ic ie n c y ( % ) production well segment span(m) whole well layer 1 layer 2 34 35 36 37 0 50 100 150 200 250 300 采 出 程 度 ， % 生产井跨度，m 全井 1号层 2号层 re c o v e ry e ff ic ie n c y ( % ) production well segment span(m) 34 35 36 37 0 50 100 150 200 250 300 采 出 程 度 ， % 生产井跨度，m 全井 1号层 2号层 re c o v e ry e ff ic ie n c y ( % ) production well segment span(m) whole well layer 1 layer 2 whole well layer 1 layer 2 a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1146 received december 23, 2019; revised march 13, 2020; accepted april 10, 2020. *corresponding author: lpyan07@petrochina.com.cn 1 using dynamic monitoring data to calculate remaining oil saturation liping yan*, daqing oilfield company ltd, daqing, china abstract the dynamic remaining oil saturation of each oil layer is based on the two phase (oil/water) percolation theory. the correlation equation was established by using dynamic monitoring data and regression analysis. the dynamic parameters include the various layer water cut, interstitial oil saturation, current water saturation, etc. the accuracy and feasibility of this research results have been verified by means of numerical reservoir simulation, carbon-oxygen-log results and neutron-lifetime-log data. as the dynamic monitoring data reflect current reservoir productivity, so the remaining oil saturation (ros) can be the realtime dynamic data. the value and distributing of ros can be obtained whenever necessary. the field example proved the accuracy of the proposed method in x oilfield. the calculated ros can provide quantitative evidence for the dynamic adjustment and development strategy for oilfield. introduction the dynamic monitoring data is the objective reflection of the oil productivity in specific phase and working system. it has the necessary internal relationship with the dynamic parameters of the oil reservoir. this study is based on the two phase (water/oil) flow theory. with the dynamic monitoring data, the remaining oil saturation (ros) can be calculated. the method is simple and easy to be applied. in reservoir condition, oil, gas and water all comply with two phase (water/oil) flow theory. according to the theory, the property of reservoir fluid can be described by the fractional flow equation, which can be expressed as, 𝑄𝑜 = 𝐴𝐾𝑜 𝜇𝑜 ∆𝑃 ∆𝐿 .……………………………………………..….…………….……………………………(1) the relative permeability is usually applied to understand fluid flowing capacity, and describe the multiphase fluid flow. it is the ratio of the effective permeability and the absolute permeability. 𝐾𝑟𝑜 = 𝐾𝑜/𝐾.……………………………………………………………………………………...…….(2) according to the equation, the relative percentage of each-phase can be deduced. it equals the ratio of fractional flow and the total flow. in the water-oil system, the water production rate in reservoir can be given as, 𝑓𝑤 = 𝑄𝑤/(𝑄𝑜 + 𝑄𝑤)..………………..…………...………………………………………..……..……(3) integrate eq. 1 and 2 into eq. 3, the expression can be obtained as, 𝑓𝑤 = 1 1+ 𝐾𝑟𝑜 𝐾𝑟𝑤 𝜇𝑤 𝜇𝑜 ,……………………….………………………………………..………………..……….(4) as for polymer injection wells, the calculation of water production rate must take the polymer residual resistance factors and the effect of the polymer concentration-viscosity into account. depending on the research of correction coefficient by daqing petroleum institute, the water production rate can be expressed as, 2 𝑓𝑤 = 𝐾𝑟𝑤 𝜇𝑤𝑅𝑘 𝐾𝑟𝑤 𝜇𝑤𝑅𝑘 + 𝐾𝑟𝑜 𝜇𝑜 .…………………….…………….….…………………………..…………………..….(5) jone’s formula (yong and zhang 1996; zhao et al. 1997; yu 1992) about the water-oil relative permeability curves is given as, 𝐾𝑟𝑤 = | 𝑆𝑤−𝑆𝑤𝑖 1−𝑆𝑤𝑖 | 2 , 𝐾𝑟𝑜 = | 1−𝑆𝑤−𝑆𝑜𝑟 1−𝑆𝑤𝑖−𝑆𝑜𝑟 | 3 .………………….…………………………..……………….…..(6) integrate eq. 6 into eq. 4 or into eq. 5. according to the water or polymer injection, the calculation equation of water saturation can be deduced as eq. 7 (zhang et al. 1998; chen 1990), which can be used to calculate the remaining oil saturation. 𝑆𝑜 = 1 − 𝑆𝑤 = 1 − (1−𝑆𝑤𝑖)(1−𝑆𝑜𝑟)+𝐿(1−𝑆𝑤𝑖−𝑆𝑜𝑟)𝑆𝑤𝑖 𝐿(1−𝑆𝑤𝑖−𝑆𝑜𝑟)+(1−𝑆𝑤𝑖) ,…….…...…………………………………………..(7) where, 𝐿 = √| 1 𝑓𝑤 − 1| 𝜇𝑜 𝜇𝑤𝑅𝑘 3 .…………………………………..…………………….…………………………..(8) production profile application and parameters determination the dynamic monitoring data includes the oil production profile and water injection profile. oil wells and water wells have the different methods to determine the parameters. it needs to discuss respectively. water production rate in reservoir (fw).reservoir production rate usually comes from interpreting production log profile. the results provide the information of effective thickness, permeability, liquidproducing capacity and water-cut, etc., of oil reservoir. if the oil well does not have the dynamic monitoring data, water production rate can be predicted by using the comprehensive producing water data and permeability. referring to the research results about the development performance of heterogeneous reservoir, the high permeability part of reservoir comes to certain moisture content, the water content of the other lower permeability part depends on the ratio, which is its permeability k divide by the highest permeability kmax. they follow inverse linear relationship. here, kmax is defined as weighted average, �̅� = ∑ ℎ𝑖×𝑘𝑖 ∑ ℎ𝑖 𝑛 𝑖=1 𝑛 𝑖=1 ,…….………………………..…………………………….…………………………..(9) where, ki is permeability of layer i in the same oil well, i=1,2,…,n; n is number of layers; hi is the thickness of layer i. the water production rate fwi and �̅�/𝐾𝑖 follows negative linear relationship as, 𝑓𝑤𝑖 = 𝑎 − 𝑏 �̅� 𝐾𝑖 ,………………………………………………………………..………………………..(10) where the coefficient a and b can be estimated by regression analysis using the log data. irreducible water saturation (swi). irreducible water saturation mainly is affected by porosity and shale content. the more shale content in the reservoir is, the smaller the rock particles is. the narrower the pore throat is, the higher the irreducible water saturation. at present, the methods which confirm the irreducible water saturation by using the logging data are based on core analysis and logging data analysis. according to the correlation analysis of 128 cores obtained from 9 sealed coring wells in x oilfield, the original water saturation is considered as the irreducible water saturation. if the saturation data pool is insufficient, the irreducible water saturation can be estimated from the formula which regressed by the coring well data, 𝑆𝑤𝑖 = 31.98 [1.26 − 𝑙𝑔 ( 𝜙 𝑉𝑠ℎ − 0.15)].………………………………………………………………..(11) residual oil saturation (sor). residual oil saturation and irreducible water saturation are opposite but related. they reflect the bending property of reservoir acting on the inner liquids. this theory has been 3 verified by the test. depending on the cores relativity analysis, eq. 12 can be obtained by using the relative permeability curves of x oilfield (figure 1). the correlation coefficient is about 0.99. 𝑆𝑜𝑟 𝑆𝑤𝑖 = 3.158 − 9.762𝑆𝑤𝑖 + 8.94𝑆𝑤𝑖 2 .………………………………………………………………….(12) 𝑆𝑜𝑟 𝑆𝑤𝑖 swi figure 1—irreducible water saturation versus residual oil saturation relation. water saturation (sw). with the development of the oilfield, oil saturation of the reservoir decreases gradually, water saturation increases continuously. the relationship of water saturation, irreducible water saturation and residual oil saturation can be expressed as 𝑆𝑤𝑖 ≤ 𝑆𝑤 ≤ 1 − 𝑆𝑜𝑟 .water saturation can be calculated by the formula which is deduced from the water production rate and oil-water relative permeability equation (hu and zhang 2002). input each parameter into the eq. 7, the remaining oil saturation in reservoir can be calculated. using injection profile data to calculate the residual oil saturation the remaining oil saturation calculation methods are different between injection wells and producing wells. the residual oil saturation of injection well is dynamic. due to water washing the reservoir in the long term waterflooding, the lithology and property of the water-absorbing layer has changed. so the residual oil saturation is not a fixed value any more, but a range (chen 1999). for most of injection wells, at the beginning of water injection, the residual oil saturation is regarded as the lower limit of the remaining oil saturation in waterflooding reservoir. long term waterflooding will decrease the residual oil saturation slowly. the calculated remaining oil saturation will be the dynamic residual oil saturation. residual oil saturation determination. in x oilfield which is an extra high water-cut reservoir, especially when each oil layer is the serious water flooded layer, the residual oil saturation can be obtained with oil/water relative permeability curve. as the residual oil saturation is regarded as zero corresponding to relative permeability of oil phase (hearn et al. 1984). the higher the porosity and permeability are, the smaller the residual oil saturation is. regressing the relative permeability curve data, eq. 13 can be obtained, 𝑆𝑜𝑟 = 62.440 + 1.3212𝜙 − 3.4028𝑙𝑔𝐾.…..…………..…………………………………………….(13) dynamic residual oil saturation determination. the decreasing speed of the dynamic residual oil saturation relates to many factors, such as water injection rate, reservoir heterogeneity, pressure, permeability, thickness, etc. but the accumulative water injection rate per meter reflect water absorption ability of the waterflooding layer. this parameter can be determined with all the previous water injection profile logging data. according to the data of core experiment and sidetracking well, the following formula can express the slow decreasing process of dynamic residual oil saturation in water-absorbing layer, 𝑆𝑜𝑟𝑐 = 𝑆𝑜𝑟𝑒 −𝐴𝑄/𝐷...………………..……………………………………..……………………………(14) y = 8.94x2 9.7629x + 3.1584 r2 = 0.9994 0.5 0.6 0.7 0.8 0.9 1 1.1 0.3 0.35 0.4 0.45 0.5 4 single layer accumulative water injection rate, q, can be obtained by using the water injection profile logging data. factor a in eq. 14 is measured by the core waterflooding experiment. in conclusion, the calculation methods of remaining oil saturation in injection wells is as follows,  using eq. 13 to calculate the residual oil saturation of each oil layer when injection begins;  to determine the accumulative water injection rate and effective thickness of each layer according to all the previous water injection profile data. thus, current dynamic residual oil saturation can be determined. that is the value of remaining oil saturation. methods verification take the block of x oilfield for instance to verify the feasibility of using dynamic monitoring data to calculate the remaining oil saturation. logging data method. comparing the calculation value and logging data which were measured in 2009, including carbon oxygen log and neutron lifetime log from 4 wells, the comparison results verified the feasibility of the proposed calculation methods (table 1). the errors are less than 3.3%. table 1—2009 logging data and calculation value comparison. numerical simulation method (cheng et al. 2000). taking a block of x oilfield as the study area, which has developed the numerical simulation in 2010, the remaining oil saturation has been understood clearly. taking the oil layer gi1, gii1+2 for instance, using the data of the output profile and the injection profile from 2008 to 2010, plugging the data into the eq. 4 through 7, eq.13 , and eq.14, the remaining oil saturation can be calculated. the calculated remaining oil saturation of each well match with the numerical simulation results very well. the error is only 4.6% (table 2). so the numerical simulation method verified the feasibility of the proposed methods as well. well logging mode layer effective thickness (m) permeability (μm2) porosity (%) shale content (%) irreducible water saturation producing water rate (%) logging data of dos (%) calculated ros si 1 0.6 0.256 25.978 24.325 21.45 0.923 19.239 22.34 sii 1+2 0.9 0.171 26.636 17.924 22.38 0.911 22.777 20.54 sii 15+16 2.5 0.232 28.737 14.961 21.14 0.966 32.623 31.58 siii5+6 2.7 0.396 20.115 22.849 19.25 0.945 14.624 17.88 pi 5-7 6.3 0.5 26.216 19.697 19.39 0.899 36.559 35.45 gi2+3 1.8 0.052 26.618 10.694 29.18 0.901 33.583 33.456 gi4+5 1.4 0.077 26.596 11.881 29.18 0.917 27.944 31.242 si4+5 0.8 0.124 21.521 24.107 27.45 0.846 29.397 29.041 sii1+2 1.2 0.186 26.456 10.103 32.1 0.892 32.588 30.353 gi1 0.7 0.053 27.813 18.34 38.16 0.948 27.562 28.034 sii4 1.4 0.44 28.28 16.598 28.37 0.953 35.604 32.436 pii4+5 1.7 0.08 25.37 20.12 30.04 0.925 41.6 40.55 gi2 3.3 0.44 26.88 18.44 27.49 0.891 39.1 38.92 sii13+14 3.1 0.34 28.02 22.57 26.89 0.904 36.1 35.46 gi8 0.9 0.04 22.42 25.397 33.7 0.939 25.93 28.45 nllm4 c/om1 c/om2 nllm3 5 table 2—comparison of calculated ros value and numerical simulation results (part of wells). wells irreducible water saturation residual oil saturation weighted average permeability permeability water cut original oil saturation current water cut current oil saturation remaining oil a 0.214 0.316 0.263 0.13 0.812 0.457 0.639 0.361 0.507 b 0.215 0.316 0.012 0.05 0.825 0.512 0.629 0.371 0.376 c 0.251 0.319 0.214 0.14 0.871 0.602 0.601 0.399 0.385 d 0.209 0.315 0.311 0.211 0.792 0.588 0.617 0.383 0.388 e 0.256 0.319 0.345 0.314 0.845 0.577 0.667 0.333 0.215 f 0.239 0.319 0.154 0.11 0.756 0.58 0.622 0.378 0.398 g 0.244 0.319 0.078 0.09 0.895 0.67 0.689 0.311 0.342 h 0.242 0.319 0.031 0.04 0.887 0.619 0.429 0.571 0.531 i 0.196 0.351 0.027 0.03 0.862 0.601 0.599 0.401 0.329 j 0.255 0.319 0.247 0.12 0.785 0.524 0.627 0.373 0.398 k 0.264 0.318 0.314 0.21 0.801 0.63 0.657 0.343 0.352 l 0.232 0.319 0.471 0.33 0.789 0.587 0.544 0.456 0.379 m 0.23 0.319 0.061 0.04 0.844 0.587 0.627 0.373 0.397 n 0.252 0.319 0.201 0.19 0.865 0.609 0.594 0.406 0.426 o 0.243 0.319 0.245 0.22 0.792 0.602 0.656 0.344 0.386 p 0.315 0.306 0.354 0.301 0.907 0.562 0.598 0.402 0.418 q 0.388 0.278 0.621 0.058 0.914 0.612 0.527 0.473 0.347 r 0.291 0.313 0.175 0.251 0.868 0.411 0.615 0.385 0.397 field application 2d remaining oil distribution. table 3 is a comparison between the measured remaining oil saturation in 1994 and the calculated remaining oil saturation according to the dynamic monitoring data in 2010. the average remaining oil value equals to 0.51. at present, this oil layer remaining oil saturation is 0.37. the numerical value decreased obviously. it indicates that the remaining oil saturation will change dynamically along with the time goes on and developing adjustment. as the dynamic monitoring data reflects current reservoir productivity, so the ros can be real-time dynamic data. table 3—comparison between current remaining oil value and initial measured value. wells 1994 remaining oil saturation 2010 remaining oil saturation wells 1994 remaining oil saturation 2010 remaining oil saturation a1 0.618 0.407 a17 0.664 0.46 a2 0.524 0.3 a18 0.377 0.3 a3 0.436 0.429 a19 0.451 0.34 a4 0.487 0.373 a20 0.467 0.375 a5 0.45 0.412 a21 0.516 0.334 a6 0.48 0.347 a22 0.49 0.409 a7 0.485 0.38 a23 0.398 0.346 a8 0.49 0.379 a24 0.42 0.408 a9 0.561 0.347 a25 0.389 0.36 a10 0.589 0.368 a26 0.452 0.36 a11 0.682 0.34 a27 0.511 0.34 a12 0.714 0.375 a28 0.498 0.382 a13 0.45 0.334 a29 0.419 0.38 a14 0.55 0.409 a30 0.419 0.385 a15 0.51 0.346 a31 0.499 0.378 a16 0.46 0.408 a32 0.736 0.339 6 3d remaining oil distribution. for a long term, the remaining oil in the upper part of the thick oil-layer has been described qualitatively in the oilfield. the dynamic monitoring data can be used to calculate the current remaining oil saturation in reservoir of which effective thickness is greater than two meters. comparing current ros with its initial value listed in table 4, it shows that the remaining oil saturation of the upper and lower part in the thick oil layer changes with time. in the upper part of thick oil layer, the ros value has decreased by 15.1%, from initial 0.47 to 0.399 at present. in the lower part, the value decreases by 50.2%, from 0.457 to 0.284. it proves that ros will decreased along with development. especially, the lower part of a thick oil layer will be flooded more throughoutly. as a result, remaining oil is enriched in the upper part of oil layer. it proves that ros calculation method can describe the remaining oil quantitatively. table 4—three-dimensional ros calculation results. wells layers effective thickness (m) initial ros current ros 01 pii101 0.8 0.369 0.353 pii102 1.6 0.388 0.339 sii1+21 0.6 0.477 0.39 sii1+22 1.4 0.572 0.385 02 gi2+31 2.6 0.562 0.419 gi2+32 0.8 0.388 0.359 03 si15+61 1.1 0.449 0.418 sii5+62 1.3 0.387 0.125 04 pii7+81 0.8 0.375 0.344 pii7+83 1.2 0.592 0.187 05 sii10+111 1.3 0.699 0.432 sii10+113 0.4 0.567 0.285 06 gi2+31 1 0.391 0.369 gi2+32 0.6 0.422 0.212 07 pii8+91 0.4 0.439 0.411 pii8+92 1.8 0.344 0.319 conclusions in conclusion, using the dynamic monitoring data, the relationship between water production rate and ros was established in this study. the developing example has verified that the proposed method of calculating ros by using dynamic monitoring data is feasible. as the dynamic monitoring data reflects current reservoir productivity, so the ros can be the real-time dynamic data. it can provide quantitative data for dynamic adjustment and development strategy. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature ko = effective oil permeability, md kw = effective water permeability, md kg = effective gas permeability, md k = absolute permeability kro = oil relative permeability, md krw = water relative permeability, md krg = gas relative permeability, md 7 ∆𝑝 ∆𝐿 = pressure gradient upon the seepage direction qo = oil rate, m3 qw = water quantity, m3 μo = oil viscosity μw = water viscosity rk = correction factor q = cumulative water absorption per-layer, m3 d = monolayer thickness, m references chen y. 1990. calculation method of oil and gas reservoir engineering. beijing, china: china petroleum industry press. chen, y. 1999. practical methods of petroleum reservoir engineering. beijing, china: china petroleum industry press. cheng, l., wang, j., li, w., et al. 2000. oil and gas reservoir research technology. beijing, china: china petroleum industry press. hearn, c. l., ebanks, w. j. jr, and tye, r. s. 1984. geological factors influencing reservoir performance of hartog draw field, wyoming. journal of petroleum technology 36(8):1335-1344. hu, j. and zhang, d. 2002. symposium of practical forecasting method for oil & gas reservoir engineering. beijing, china: china petroleum industry press. yong, s. and zhang, c. 1996. logging data processing and comprehensive interpretation. beijing, china: china petroleum industry press. yu, h. 1992. research on development dynamic caused by two-dimensional heterogeneity in oil-layer. petroleum exploration and development 19(2): 49-55. zhang, j., lei, g., and zhang, y. 1998. fluid mechanics in oil and gas reservoir. dongying, china: petroleum university press. zhao, p., tan, y., song, s., et al. 1997. using dynamic monitoring data to determine ros in waterflooding reservoir. acta petrolei sinica 18(2):54-60. liping yan is a senior reservoir engineer of daqing oilfield company of petrochina. dr. yan specializes in enhance oil recovery of conventional oil reservoirs. spe international symposium & exhibition on formation damage control copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.422 received april 5, 2017; revised april 26, 2017; accepted may 4, 2017. *corresponding author: kai.dong@aliyun.com 1 analysis of fracture design in a vertical well with a horizontal fracture kai dong*, china national petroleum corporation, beijing, china; xiao jin and jie he, texas a&m university, college station, usa abstract the overwhelming majority of hydraulic fractures are vertical and methods for designing them in both vertical and horizontal wells are well understood. in shallow and over-pressured formations there is a strong likelihood for horizontal fractures. hence, horizontal fractures are common in shallow coalbed methane formations and may occur in highly over-pressured shale formations. models for the transient flow and pressure behavior of horizontal fractures emanating from vertical wells exist and show highly distinct behavior from those for vertical fractures. consequently, fracture design based on maximizing well productivity for a horizontally fractured well is distinct from the unified fracture design (ufd) strategies described previously for vertically-fractured vertical or horizontal wells. this study shows well productivity behavior for horizontal fractures in homogeneous formations with or without vertical to horizontal permeability anisotropy as a function of suitably-defined proppant number, dimensionless fracture conductivity, and fracture penetration index parameters. for low penetration index, a relationship among fracture half-length, conductivity, and skin is provided. this work provides a simple framework for horizontal fracture design. introduction hydraulic fracturing was first reported in the early 1950s (grossman 1951) and has been extensively used to improve the well productivity in the oil and gas industry. different fracturing techniques have been developed in the past 60 years, but the overwhelming majority of hydraulic fractures are vertical in the field practice, and the methods for designing them in both vertical and horizontal wells have been widely studied and well understood. the idea of horizontal fractures, however, does not receive much attention, and a limited volume of literature can be found about it in contrast to vertical fractures. the application of horizontal fractures was greatly restricted because it was generally believed that in conventional reservoirs the vertical permeability is much lower than the horizontal (usually one tenth of the horizontal permeability), so that vertical fractures will be more beneficial than horizontal ones. landrum and crawford (1957) also found that horizontal fractures are not every effective in thick pays and if the well is not centered in the drainage area. a third reason is the old “common wisdom” (gidley et al. 1989) that horizontal fractures cannot occur below 2,000 feet since the maximum stress direction is usually vertical, but wright et al. (wright et al. 1997) challenged it and reported a case of horizontal fractures at the depth of 7,500 feet due to high horizontal reservoir stress. there is another technical issue (lowe and huitt 1966) that proppants may deposit and form a dune around the wellbore in the horizontal fracture at high proppant concentration or low fluid velocity during the fracturing process, which is not likely for vertical fractures due to gravity. the dune will block the whole flow path and reduce the fracture flow capacity, resulting in shorter fracture length than designed. despite of these shortcomings of horizontal fractures, it has been recognized nowadays that horizontal fractures are far more common than generally believed. in fact, it was reported as early as in 1960 (morrisson and henderson 1960) that horizontal fractures were created to produce gravity drainage reservoirs. horizontal fractures are also applicable to thin pays because of their low cost even though it has mailto:kai.dong@aliyun.com 2 been shown by sung et al. (sung and ertekin 1987) that horizontal wells have better performance. moreover, horizontal fractures are common in unconventional reservoirs like shallow coal bed methane or heavy oil formations and highly over-pressured shale formations (valko and economidies 1998; chhina et al. 1987; britt et al. 2006). in addition, in-situ stress state change due to geological movements (e.g. a thrust fault) (maxwell et al. 2007), secondary or enhanced oil recovery (wright et al. 1997; wong and chau 2004) may result in significant growth of horizontal fractures during fracturing. daal and economides (2006) studied hydraulically fractured wells in square and rectangular patterns, and they concluded that a dimensionless fracture conductivity of 1.6 will yield the highest productivity for production systems with proppant number below 0.1. recently, larsen (2011) did a type curve study of horizontal fractured wells in single and multilayer reservoirs. their work brought up our interest in horizontal fractures and initialized this paper. we wanted to provide a simple framework for horizontal fracture design. and in our study we investigated well productivity behavior for horizontal fractures in homogeneous formations with or without vertical to horizontal permeability anisotropy as a function of suitably-defined proppant number, dimensionless fracture conductivity, and fracture penetration index parameters. we used the software eclipse to build our models and run the simulation. upon completion of our simulation using our eclipse model, we found that in a circular reservoir, the maximum cfd is no longer 1.6 but changes even at low proppant number below 0.1. the maximum jd is also seen to be greater than 6/π as seen in a square or rectangular reservoir. upon doing sensitivity analysis, we also found that changing the effective radius increases the dimensionless productivity index at a constant value of dimensionless conductivity. also, we found that by changing kv/kh, we are exponentially increasing the dimensionless production index. model description this section will introduce the model used in this work, its validity for this work, and data treatment after the simulation. reservoir simulator eclipse was used to build the model. after the model was set up, we run some known cases from other papers to verify our model. finally, the calculation based on the simulated data was introduced. model for simulation. the model used is a radial reservoir, with a well fully penetrating the formation right in the center. the fracture is created as radial fracture, with the radius of rf. this model is shown in figure 1. figure 1—reservoir model with fracture. in figure 1, different colors represent different layers. in this model, we divide the formation into 11 layers, with one layer containing the horizontal fracture. the horizontal fracture is contained in the middle layer. note that only 10 layers can be observed in figure 1 as the middle layer is too thin to be observed. if we make the middle layer thicker, shown in figure 2, the layer with fracture can be seen, but this is just for illustration. in the model calculation, the middle layer is assigned to a very small thickness. 3 figure 2—reservoir model with visible fracture in the middle layer. radial coordinated was used for this theoretical model. the radial direction is discretized into 50 grids, theta direction is treated as one grid, and vertical direction is discretized into 11 even grids. the algorithm for discretizing radius is eq. 1, ni i e i i r r r r )1( 11 )(    ,…………………..…..………………………………………..….….…...………….(1) in this equation, i is the grid number in radial direction while n is the total grid number in radial direction, which is 50 in this case. the fracture is treated by changing the layer thickness and grid permeability and porosity. the desired grid permeability can be calculated by the eq. 2 which provides the proppant number and reservoir properties. 2 ev ff hfp rk wrk n  ,……………………………………..…………………..…..…...……………..…….(2) note that in our model, the fracture width is not calculated but selected by us. as the fracture permeability need to be set a reasonable value, neither too large nor too small, to avoid simulation failure. and we can see, inside the fracture, the permeability is different in different radial grids. in our simulator, we assigned the whole layer with the same thickness as fracture width. the fracture may not necessarily penetrate fully the whole formation, so that each layer has two different permeability and porosity, with inner part for the fracture and outer part for the reservoir. model verification. since we treat the hydraulic fracture as formation with high permeability, porosity and tiny width, we need to verify whether this method is appropriate or not. this part provides the simulated results for a horizontal fracture in a large reservoir. the input data is from larsen (2011). after the simulation, the flowing bottom-hole-pressure with time can be exported. thus a log-log diagnostic plot can be generated as shown in figure 3. this graph is consistent with the graph in larsen’s paper (2011). in conclusion, the model can be used to simulate the horizontal fracture. 4 figure 3—simulated log-log diagnostic plot based on larsen’s input. calculation based on the simulated data. the methods for calculating the dimensionless productivity index and dimensionless horizontal fracture conductivity are illustrated in this part. the dimensionless horizontal fracture conductivity measures the relative ease of the fluid flowing from reservoir to fracture and then to the wellbore. it can be calculated as eq. 3. fv f hffd rk wk c  ,..……..…………......……………………..…………………………………..……....(3) cfd-hf has the following relationship with proppant number. provided a fixed fracture radius and drainage area radius, the dimensionless horizontal fracture conductivity is proportional with the proppant number. 2 2 2 2 )( e f hffd e f fv f ev ff hfp r r c r r rk wk rk wrk n   ,………………..…………………………………..…….(4) after the model was set up, we can easily calculated cfd-hf as we know the reservoir properties and simulation fracture properties. the dimensionless well conductivity is defined as eq. 5. j kh b j d 2.141  ,…………………………………..…………………………………..……........…...(5) after each simulation, the average reservoir pressure pave, and flowing bottom-hole-pressure, pwf can be obtained. thus, the well productivity can be calculated as eq. 6. wfave pp q j   ,………………………………………………..………………………………...……..(6) results analysis in order to achieve our goal of analyzing horizontal fractures in homogenous formations with a vertical well as a function of proppant number, dimensionless fracture conductivity, and fracture penetration index parameters, eclipse was used to design the model. the following sections will include the actual problem statement, reservoir properties of the formation which are the inputs of our eclipse model. and we will take an in-depth look at nine different cases of jd versus cfd-hf with changes in np-hf, xe/h, and also differences in isotropic and anisotropic reservoirs. problem statement. given a specific set of reservoir properties for designing a vertical well with horizontal fractures, we analyzed the scenario of jd versus cfd–hf. table 1 describes the reservoir properties we used to design the problem solution. 5 table 1—reservoir properties for model analysis. parameters values units pi 3000 psi rw 0.3 ft ϕ 0.1 μ, 1 cp ct, 13.10*10-6 1/psi nf 1 ft xf 200 s 0 case analysis. there are nine different cases for analysis using the reservoir model designed in eclipse as shown in table 2. table 2—cases designed for eclipse model. case 1 kv/kh = 0.1 xe/h = 10 case 2 kv/kh = 0.1 xe/h = 20 case 3 kv/kh = 0.1 xe/h = 50 case 4 kv/kh = 1 xe/h = 10 case 5 kv/kh = 1 xe/h = 20 case 6 kv/kh = 1 xe/h = 50 case 7 kv/kh = 10 xe/h = 10 case 8 kv/kh = 10 xe/h = 20 case 9 kv/kh = 10 xe/h = 50 among the cases we have cases four, five, six being isotropic cases and cases one, two, three, seven, eight, nine being anisotropic cases. to fully understand the plot it is possible to use a sensitivity analysis with variation of xe/h, kv/kh, and different proppant numbers. we observed the effect of proppant number (np-hf) on dimensionless well conductivity (jd) at different dimensionless horizontal fracture conductivity (cfd-hf) in case 7 (figure 4). as we increase the proppant number, we also increase jd-hf opt, and cfd-hf opt. while it is a great thing to increase the productivity index to as high as possible, it might not be the most efficient way to design the treatment because increasing the proppant number costs money. 6 figure 4—case 7 with kv/kh = 10 and proppant number from 0.00001 to 100. with a skin factor of zero, the effective radius re is the same as the wellbore radius rw. as we are increasing the effective radius, we are also increasing the dimensionless productivity index at every value of dimensionless conductivity. this is shown in figure 5 as we look at a sensitivity analysis of with different values of re. this makes sense because as we have more effective radius holding the permeability constant, we will have more production due to the increase drainage area. figure 5—sensitivity analysis with varying values of effective radius. the increase in kv/kh versus jd is an exponential increase. this is important because in designing a reservoir to maximize jd to minimize proppant cost, we want to have a higher kv/kh ratio while increasing the dimensionless conductivity. as shown in figure 6, a sensitivity analysis of kv/kh by a power of 10. figure 6—sensitivity analysis with varying kv/kh ratio. the consistency with all case scenarios shown in the appendix (figures 7 through 14) also proves the importance of designing with the optimum kv/kh ratio in mind as it has the greatest effect on the productivity index. knowing the optimum dimensionless conductivity (cfd) also makes the hydraulic fracture stimulation more cost-effective to enhance production due to reducing unnecessary proppant. 7 figure 7—case 1 with xe/h = 10 and kv/kh = 0.1. figure 8—case 2with xe/h = 20 and kv/kh = 0.1. figure 9—case 3 with xe/h = 50 and kv/kh = 0.1. figure 10—case 4 with xe/h = 10 and kv/kh = 1. figure 11—case 5 with xe/h = 20 and kv/kh = 1. figure 12—case 6 with xe/h = 50 and kv/kh = 1. figure 13—case 8 with xe/h = 20 and kv/kh = 0.01. figure 14—case 9 with xe/h = 50 and kv/kh = 0.01. 8 conclusions 1. at a higher proppant number we will see a higher dimensionless productivity index at every value of conductivity 2. in order to maximize productivity we need maximum the effective drainage radius. 3. we want a higher kv/kh ratio when producing in a vertical well with a horizontal fracture to minimize cost of proppant. nomenclature b = formation volume factor, rb/stb cfd-hf = dimensionless horizontal fracture conductivity h = formation height, ft hf = horizontal fracture j = well productivity index, stb/d/psi jd = dimensionless well productivity index kf = fracture permeability, md kv = formation vertical permeability, md kh = formation horizontal permeability, md µ fluid viscosity, cp np-hf = horizontal fracture proppant number pave = average reservoir pressure, psi pwf = bottom hole flowing pressure, psi q = production rate, stb/d ri = radial position of i-th grid, ft re = reservoir radius, ft rf = fracture radius, ft w = fracture width, ft acknowledgement we would like to express our gratitude to dr. christine ehlig-economides, professor of petroleum engineering at texas a&m university, for her continuous guidance and invaluable advice in our preparation of this paper. we would also like to thank kappa engineering and schlumberger for providing the software ecrin and eclipse, without which this study would not have been possible, as well as our classmates in course pete 648 pressure transient testing su2012 for sharing their data with us. conflicts of interest the author(s) declare that they have no conflicting interests. references britt, l. k., dunn-norman, s., smith, m. b, et al. 2006. characterization of a shallow horizontal fracturing treatment in western missouri. paper presented in spe annual technical conference and exhibition, san antonio, texas, usa, 24-27 september. spe-102342-ms. chhina, h.s., luhning, r.w., bilak, r.a., et al. 1987. a horizontal fracture test in the athabasca oil sands. paper presented in annual technical meeting, calgary, alberta, 7-10 june. petsoc-87-38-56. daal, j. a. and economides, m. j. 2006. optimization of hydraulically fractured wells in irregularly shaped drainage areas. paper presented in international symposium and exhibition on formation damage control, lafayette, louisiana, usa. 15-17 february. spe-98047-ms. gidley, j. l., holditch, s. a., nierode, d. e., et al. 1989. recent advances in hydraulic fracturing. monograph series:12. grossman, w. l. 1951. hydrafrac operations in the spraberry production, west texas. paper presented in fall meeting of the petroleum branch of aime, oklahoma city, oklahoma, 3-5 october. spe-128-g. 9 landrum, b. l. and crawford, p. b. 1957. estimated effect of horizontal fractures in thick reservoirs on pattern conductivity. journal of petroleum technology 9(10):50-52. larsen, s. l. 2011. horizontal fractures in single and multilayer reservoirs. paper presented in canadian unconventional resources conference. society of petroleum engineers, alberta, canada, 15-17 novemer. spe147004-ms. lowe, d. k. and huitt, j. l. 1966. propping agent transport in horizontal fractures. journal of petroleum technology 18(6): 753-764. spe-1285-pa maxwell, s. c., zimmer, u., and gusek, r.w. 2007. evidence of horizontal hydraulic fracture at depth due to stress rotations across a thrust fault. paper presented in spe annual technical conference and exhibition, anaheim, california, usa, 11-14 november. spe-110696-ms. morrisson, t. e. and henderson, j. h. 1960. gravity drainage of oil into large horizontal fractures. spe j 219(1):20-25.spe-1330-g. sung, w. and ertekin, t. 1987. performance comparison of vertical and horizontal hydraulic fractures and horizontal boreholes in low permeability reservoirs: a numerical study. paper presented in low permeability reservoirs symposium, denver, colorado, usa, 18-19 may. spe-16407-ms. wright, c. a., davis, e., weijers, l., et al. 1997. horizontal hydraulic fractures: oddball occurrences or practical engineering concern? paper presented at spe western regional meeting, long beach, california, usa, 25-27 june. spe-38324-ms. wong, r. and chau k. 2004. propagation of in situ horizontal fractures in shale due to steam injection. journal of canadian petroleum technology 43(1):41-46. valko, p. p. and economidies, m. j. 1998. heavy crude production from shallow formations: long horizontal wells versus horizontal fractures. paper presented in spe international conference on horizontal well technology, calgary, alberta, canada, 1-4 november. spe-50421-ms. kai dong is a production engineer at china national petroleum corporation (cnpc) in beijing, working on shale gas reservoirs in southwest china. before joining cnpc, he worked as a production technologist with baker hughes, houston. dong’s specialties and research interests include well stimulation in all kinds of reservoirs, well-performance optimization and general production engineering. he is an active spe member. dong holds a bachelor’s degree in petroleum engineering from china university of petroleum, beijing, and master’s and ph.d degrees in petroleum engineering from texas a&m university. jie he is a quantitative associate at wells fargo. before joining wells fargo, he worked as a research intern at halliburton. he specializes in computational mathematics and reservoir simulation. he holds a be in chemical engineering from tsinghua university, an ms in chemical engineering from washington university in st. louis, and a phd in petroleum engineering from texas a&m university. xiao jin is a ph.d. candidate currently studying petroleum engineering at texas a&m university. previously, he has worked full-time for baker hughes, a ge company as a hydraulic fracturing engineer and interned with exxonmobil upstream research company as an unconventional research engineer. jin has authored and co-authored 4 technical papers and currently serve as a technical editor for the spe journal. his research interests include hydraulic fracturing and matrix acidizing. he also obtained both b.s. and m.s. degrees all in petroleum engineering at texas a&m university. jin is a member of spe. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.430 received september 1, 2019; revised october 12, 2019; accepted october 20, 2019. *corresponding author: neogi@mst.edu 1 extraction rate in vapor assisted extraction of heavy oil (vapex) vijitha mohan and parthasakha neogi*, missouri university of science and technology, rolla, usa abstract heavy oil recovery requires either heat (sagd) or a solvent (vapex) to reduce its high viscosity first and then the less viscous oil can be recovered. we show here that the existing data, on the rate of oil recovered in vapex process in sandpacks show a square root dependence on the height of pay zone, following expectation. this dependence had remained uncertain and is of importance in oil field operations. we have used dimensional analysis and inverse viscosity-diffusivity dependence to obtain an expression for the rate that agrees well with the available sandpack data. the dimensional analysis overcomes the uncertainty in the number of independent variables and leads to standard dimensionless groups. the inverse dependence is based on the free volume theory which we have tested earlier successfully for heavy oils. the final correlation is shown to work well in the limit where we go from sandpacks to reservoir. introduction highly viscous heavy oil (above 100 mpa.s) cannot be recovered from underground reservoirs without the aid of an external resource like heat or solvents, which reduces its viscosity before recovery. steam assisted gravity drainage (sagd) process is a thermal process where steam is used as a heat source to heat up the heavy oil, reducing the viscosity to ~5-10 mpa.s. the less viscous oil flows under gravity to the drainage well. the alternate, which requires no water, is the vapor assisted petroleum extraction (vapex) process that uses gases (above critical temperature) or vapors (below critical temperature) which form a part of products on condensation. they dissolve in the oil at the interface and diffuse into the bulk. in the process, the viscosity of the solution is brought down and it drains under gravity (banerjee 2012). the rate of oil recovery that has been predicted by theory, is not fully backed by the experimental data. specifically, it is the role of h, the height of the pay zone, which does not appear to conform to any pattern. the results by mokrys and butler (1993) provides the recovery rate, 𝑄𝑏 = √2𝑘𝑔𝜙δ𝑆𝑜ℎ𝑁𝑠 ,…………….………….………..…………………………………………….……..(1) in m3/(m-width.s), where δ𝑆𝑜 is the difference between the fractional pore volume containing oil before and after displacement. for perfect displacement, δ𝑆𝑜 =1. others parameters in the eq. 1 are permeability k, acceleration due to gravity g, and porosity 𝜙. ns is defined as, 𝑁𝑠 = ∫ δ𝜌𝐷(1−𝜑) 𝜇 𝑑𝑙𝑛𝜑 1 𝜑𝑚𝑖𝑛 ,……………….…….……………………………………………………...…(2) where δ𝜌 is the density difference between pure oil and displacing fluid (vapor). 𝜑 is the volume fraction of the solvent in oil, and 𝜑min is the solvent concentration at the end of the front of the solvent that has penetrated the oil. mohan et al. (2019) improved the earlier model using mass transfer boundary layer theory. but their final results are not that different. mailto:neogi@mst.edu 2 𝑄𝑏 = 2√ 𝑘𝑔𝜙δ𝜌ℎ𝐷𝑜 𝜇𝑜 ∫ 𝑒𝛼𝜑𝑜𝜓(1 − 𝜑𝑜𝜓)𝑑𝜓 𝑢 0 .…………………………………………………………….....(3) the terms under the square-root sign (only) also appears in eq. 1 if we express d = do × function of 𝜑, and µ = µo × function of 𝜑. here, 𝑢 = 𝛿 √4𝜇𝑜𝐷𝑜𝜂𝜙/(𝑘δ𝜌𝑔𝑠𝑖𝑛𝜃) ,……………………………………………………….………………………....(4) where δ is the thickness over which solvent concentration in oil falls from volume fraction of 𝜑𝑜 to 𝜑𝑚𝑖𝑛 in the direction normal to the interface, η is the direction tangential to the interface, and u is taken to be a constant. if we use a vapor which can condense and the condensate is miscible in oil, then 𝜑𝑜 = 1. for most solvents, known to us �̅� = 𝛼𝜑𝑜~10 where the free volume theory (mohan et al. 2017) is used to write the diffusivity as, 𝐷 = 𝐷𝑜𝑒𝛼𝜑 ,…………………………………………………………………………………………..…….(5) and the viscosity as, 𝜇 = 𝜇𝑜𝑒−𝛼𝜑 ,…………………………………………………………………………………………..……(6) mokrys and butler (1993) conducted experiments in vertically held hele-shaw cells and verified the above k and h dependence. the vapor is introduced from the side as shown in figure 1. figure 1—schematic view of the recovery experiments. in hele-shaw cells the gap between the two parallel plates is empty and then is filled with oil. in sandpack experiments the gap is filled with sand and oil mixture which is then packed. other experiments using twodimensional sandpacks followed and showed a result that was proportional to h rather than h½ as in above (karmakar and maini 2003; yazdani and maini 2005; haghighat and maini 2012). one numerical simulation also showed such a result (cuthiell and edmunds 2013). nenninger and dunn (2008) put together a large number of data from sandpacks and hele-shaw cell and found, 𝑊𝑏 = 43550(𝑘𝜙/𝜇𝑜)0.51,…………………………………………………………………..………..…...(7) where, 𝑊𝑏 = 𝑄𝑏𝜌𝑜/ℎ .………..……………………………………………………………………………….......(8) 3 note that the terms under the square-root appear in both eqs. 1 and 2. however, the correlation failed to show an h dependence although some dependence is seen. thus, we face a situation where we cannot be sure what the experiments have to say regarding h, an important field variable. formulation we note that eq. 7 is somewhat along the lines of dimensional analysis. however, if we try to fit variables 𝑦 = m𝑥1 𝑚1𝑥2 𝑚2 ,……………………………………………………………………………………………..(9) there is no reason to suppose that the constants m, m1, m2, etc. are independent of one another. this problem is eliminated by buckingham-pi theorem which gives us the correct number of independent variables. we take wb to be a function of 𝜇𝑜 , 𝜙, δρ, 𝑘, ℎ from nenninger and dunn (2008) where we have omitted surface tension. because of the way 𝜙 is associated with k in eq. 7, 𝜙 has been considered only as a product 𝜙𝑘. we now add to these all mass transfer variables 𝐷𝑜 , 𝛼, 𝜑𝑜 . since 𝛼𝜑𝑜~10, it is not considered to be a variable here. similarly, most of the data compiled have 𝜑𝑜 = 1 and it is not considered to be a variable. hence, there are seven variables and three dimensions leading to four dimensionless groups. these groups are found to be 𝑅𝑒 = 𝑊𝑏ℎ/𝜇𝑜 ,…..………………………………………………………………………………..……...(10) 𝐹𝑟 = 𝜙𝑘δ𝜌 𝜇𝑜 √ 𝑔 ℎ ,…….……………………………………………………………..…………………….…(11) 𝐴𝑟 = 𝜙𝑘/ℎ2 ,……………………………………………………………………………………………..(12) 𝑆𝑐 = 𝜇𝑜 δ𝜌𝐷𝑜 ,………………………………………….……………………………………………..….…..(13) where re is the reynolds’ number, which is the ratio between the inertial and the viscous forces; fr is the froude number, which is the square-root of the ratio between kinetic energy and potential energy due to gravity; ar is a square of aspect ratio; and sc is schmidt’s number. note that h plays an important role of providing a length scale. finally, δ𝜌~𝜌𝑜where two values of specific gravities of oil, 0.8 and 0.9 are used. diffusivity at infinite dilution do is difficult to find, and stokes-einstein’s equation is used to calculate this value following mohan et al. (2017). note the inverse relation do is defined as 𝐷𝑜 = 𝐵/𝜇𝑜 ,…………………………………………………………………………..…………………..(14) where b is a constant. since re (flow rate) and fr (gravity) are the two important variables, we plotted re versus fr and found that the data compiled by nenninger and dunn (2008) lay on a straight lines. thus, we take 𝑅𝑒 = λ𝐹𝑟𝑎𝐴𝑟𝑏𝑆𝑐𝑐,………………………………………………………………………………….……(15) where λ, a, b and c are unknown and set a to 1. we look at how wb is affected by 𝜙𝑘 from eq. 7 and set the net power on it to ½. similarly, the power on 𝜇𝑜 is set to -½. as a result, b and c were calculated to be ½ and -¼. λ can be determined by fitting to the data (figure 2) and the result is shown below. 𝐹𝑟 𝑅𝑒 = 4 × 10−6𝐴𝑟1/2𝑆𝑐1/4...………………………………………………………………………….…...(16) results and discussion eq. 16 and the data (nenninger and dunn 2008) have been plotted in figure 2 using the specific gravity of heavy oils to be 0.9. there are 6 outliers in their group of 43 on sandpacks that have been omitted. of these, three points are outliers to eq. 7 as well and the other three have combined heat and mass transfer. the fit has been stretched in figure 3 to show that it is excellent at small values. this is good, as the rock data will show at even smaller values of √𝑘/ℎ. 4 figure 2—plots of fr/re against √𝑨𝒓√𝑺𝒄 in sandpacks from the compilation by nenninger and dunn (2008). specific gravity of heavy oil is taken to be 0.9. figure 3—plots of fr/re against √𝑨𝒓√𝑺𝒄 in logscale. same as in figure 2 to show the fit at small values of ar. there is more scatter at small values of h (or large ar) than large values. nenninger and dunn (2008) have also compiled data on hele-shaw cells (higher ar values), which however had too much scatter and were not considered. eq. 16 can be re-expressed as 𝑊𝑏 = 25 × 104√ 𝜙𝑘 𝜇𝑜 (δ𝜌)5/4𝑔1/2𝐵1/4 ℎ1/2 ,……………………………………………..…………………….....(17) or in terms of qb, 𝑄𝑏 = 25 × 104√𝜙𝑘(δ𝜌)1/2𝑔ℎ𝐷𝑜 1/2 𝜇𝑜 1/2 ,………………………………………………..…………………..…..(18) which supports the result that 𝑄𝑏 ∝ ℎ1/2. 0.0e+00 5.0e-06 1.0e-05 1.5e-05 2.0e-05 2.5e-05 3.0e-05 3.5e-05 0 1 2 3 4 5 6 f r/ r e √(𝐴𝑟√𝑆𝑐) 0.00e+00 5.00e-06 1.00e-05 1.50e-05 2.00e-05 2.50e-05 3.00e-05 0.01 0.1 1 10 f r/ r e √(ar√sc) 5 conclusions thus, the sandpack data does indeed agree with the result that for small values of √𝑘/ℎ, we should see a ℎ1/2 dependence. however, if we had done a curve fit using eq. 18 then we may not have obtained the h dependence fully as nenninger and dunn (2008) had experienced. eq. 2 can be expressed as eq. 16 if the inverse dependence between diffusivity and viscosity with b and δρ ~ ρo are taken to be constants. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature d = diffusivity do = diffusivity at infinite dilution fr = froude number g = acceleration due to gravity h = total pay zone height of the system k = permeability qb = recovery rate re = reynolds’ number sc = schmidt’s number wb = mass flux greek letters 𝛼 = concentration dependence term δ𝜌 = density difference between oil and the vapor δ𝑆𝑜 = difference in fractional pore volume 𝜇 = viscosity 𝜇𝑜 = viscosity of pure oil 𝜌 = total density 𝜌𝑜 = density of pure oil 𝜑 = volume fraction of solvent 𝜑𝑜 = solubility of solvent in oil 𝜙 = porosity references banerjee, d. k. 2012. oil sands, heavy oil and bitumen, from recovery to refinery. tulsa, ok, us: penn well corp. mokrys, i. j. and butler, r. m. 1993. the rise of interfering solvent chambers: solvent analog model of steamassisted gravity drainage. journal of canadian petroleum technology 32(3): 26-36. cuthiell, d. and edmunds, n. 2013. thoughts on simulating the vapex process. journal of canadian petroleum technology 52(3):192-203. spe-158499-pa. haghighat, p. and maini, b. b. 2012. experimental evaluation of heated vapex process. paper presented at spe heavy oil conference, alberta, canada, 12-14 june. spe-157799-ms. karmakar, k. and maini, b. b. 2003. experimental investigation of oil drainage rates in vapex process for heavy oil and bitumen reservoirs. paper presented at spe annual technical conference and exhibition, denver, colorado, 5-8 october. spe-84199-ms. mohan, v., neogi, p., and bai, b. 2019. revisiting butler-mokrys model for vapex process. soc. pet. eng, j. 24(2): 511-521. spe-194212-pa. mohan, v., neogi, p., and bai, b. 2017. concentration dependent diffusivities of model solvents in heavy oil. diffusion fundamentals 27(3):1-27. 6 nenninger, j. e. and dunn, s. g. 2008. how fast is solvent based gravity drainage? paper presented at canadian international petroleum conference, calgary, alberta, canada, 17-19 june. petsoc-2008-139. yazdani, a. and maini, b. 2005. effect of drainage height and grain size on production rates in the vapex process: experimental study. soc. pet. eng. res. eval. eng. 8(3): 205-212. spe-89409-pa. vijitha mohan received her phd in chemical engineering from missouri university of science and technology and served as a lecturer after graduation. her research interests lie in heavy oil recovery. she acquired her b.tech in chemical engineering from university of madras and m.s in chemical engineering from mississippi state university. she is now employed in alberta, canada. parthasakha neogi, spe, is a professor of chemical engineering at missouri university of science and technology, where he has worked as faculty for the last 36 years. his research interests are in wetting, surfactants and polymers, and in interfacial transport phenomena. he holds b.tech. (hons.) from the indian institute of technology kharagpur, m. tech. from the indian institute of technology kanpur, and ph.d. from carnegie-mellon university, all in chemical engineering. a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.447 received september 3, 2019; revised november 10, 2019; accepted december 12, 2019. *corresponding author: xuqingyan007@163.com 1 comparison of development effects for two different combined well patterns with horizontal wells and vertical wells qingyan xu*, research institute of petroleum exploration and development, petrochina, beijing, china; rongliang guan, daqing no.1 drilling company of daqing drilling ltd, petrochina, daqing, china; cong wu, research institute of petroleum exploration & development, huabei oilfield branch, petrochina, zhengzhou, china abstract in recent years, horizontal wells have been widely utilized in low permeability reservoirs of china. normally horizontal wells are deployed combined with vertical wells, in which way effective injectionproduction well network system could be established. however, horizontal wells could be water injectors as well as oil producers and the same is true for vertical wells. the adoption of which kind of combined well pattern has been in dispute for a long time. in response to this issue, a novel physical simulation system is utilized to contrast the development effect of two well patterns with horizontal wells and vertical wells together. by comparing pressure gradient and flow velocity, the better scenario can be selected. if the horizontal well is not fractured, well pattern of horizontal wells as injectors with vertical wells as producers has a remarkable advantage. while the horizontal well is fractured, well pattern of horizontal wells as producers with vertical wells as injectors has a clear advantage. from another perspective to analyze the result, if an oilfield needs horizontal well to inject water for vertical wells, then the horizontal well is suggested not to be fractured. if an oilfield needs horizontal wells to produce much more oil with vertical injection wells, then horizontal wells with multiple hydraulic fractures could obtain better effect. as a rule of thumb, deployment of horizontal wells as oil producers is more common in oilfields. introduction application of horizontal wells and vertical wells combined is an effective technology to improve the development effect of low permeability reservoirs in china (cai et al. 2009; zeng et al. 2010). with respect to the combined well patterns (cai et al. 2010; xiong et al. 2012), there are two entirely different modes. one is setting horizontal wells as injectors and vertical wells as producers (hivp), and the other one is on the contrary, i.e. horizontal wells as producers and vertical wells as injectors (hpiv). the adoption of which kind of combined well pattern has been in dispute for a long time and little literature involves research for this issue. large-scale slab model made of natural outcrop core is an effective tool to study seepage mechanism in low permeability reservoirs. in this paper, we present a novel physical simulation system to contrast the two approaches to optimize the more reasonable scenario. mailto:xuqingyan007@163.com 2 manuscript presentation to carry out the slab model physical simulation experiment, several working procedures are essential, including natural outcrop screening, flat model fabrication, packaging, vacuum, water saturation, and flow field measurement. detailed process of the large-scale slab model can be found in the following reference (xu et al. 2012). the system of physical simulation has four sections：injecting system, natural outcrop slab, producing system and measuring system, as shown in figure 1. figure 1—flow diagram of physical simulation in order to determine the better well pattern, horizontal well with fracture and without fracture are both considered, as shown in figures 2 and 3. pressure gradient distribution and flow velocity can be obtained by pressure patrol instrument and micro-flow meter respectively. according to darcy law, flow rate or flow velocity in porous media is proportional to the pressure gradient. in other words, the value or level of pressure gradient can reflect the degree of difficulty for displacement. figure 2—hpvi without fractures and with fractures figure 3—hivp without fractures and with fractures the size of the slab model is 0.4m×0.4m and the length of two fractures is 0.05 m. as shown in figures 4 and 5, pressure gradient distribution of the two well patterns is provided when the displacement pressure difference is 30 kpa. pressure gradient around injectors and producers is higher than the region between wells. also when the horizontal well is fractured, the pressure gradient nearby the fractures becomes higher. low pressure gradient reveals high degree of difficulty for displacement, while high pressure gradient is the opposite. while the horizontal well is not fractured, as a whole the pressure gradient of hivp pattern is slightly greater than that of hpvi pattern, reflecting horizontal well as injectors has an advantage. while the horizontal well is fractured, the pressure gradient of hpvi pattern is significantly higher than that of hivp pattern, reflecting horizontal well as produces has a clear advantage. 3 0.15 0.10 0.05 0.1 0.40.2 0.30.0 0.15 0.10 0.05 0.1 0.2 0.30.0 0.4 0.54 0.02 0.10 0.18 0.26 0.34 0.40 0.46 figure 4—pressure gradient distribution of hpvi without fractures and with fractures 0.15 0.10 0.05 0.1 0.40.2 0.30.0 0.15 0.10 0.05 0.1 0.2 0.30.0 0.4 0.54 0.02 0.10 0.18 0.26 0.34 0.40 0.46 figure 5—pressure gradient distribution of hivp without fractures and with fractures as shown in figures 6 and 7, the flow velocity of hivp pattern is slightly greater than that of hpvi pattern, also reflecting horizontal well as injectors has an advantage when the horizontal well is not fractured. while the horizontal well is fractured, the flow velocity of hpvi pattern is significantly higher than that of hivp pattern, also reflecting horizontal well as produces has a clear advantage after hydraulic fractured. figure 6—flow velocity of hivp and hpvi without fractures 4 figure 7—flow velocity of hivp and hpvi with fractures conclusions and discussions the present result may be useful for combined well pattern selection and adoption when horizontal wells are involved in the oilfield development. if the horizontal well is not fractured, well pattern of horizontal wells as injectors with vertical wells as producers could obtain better development effect. while the horizontal well is fractured, well pattern of horizontal wells as producers with vertical wells as injectors may result in better performance. from another perspective to analyse the result, if an oilfield needs horizontal well to inject water for vertical wells, then the horizontal well is suggested not to be fractured. if an oilfield needs horizontal wells to produce much more oil with vertical injection wells, then horizontal wells with multiple hydraulic fractures could obtain better effect. in general, deployment of horizontal wells as oil producers is more common in oilfields. acknowledgments we sincerely thank the supports from national science and technology major project of china (no. 2011zx05032 and no. 2011zx05058). also we thank the support from cnpc project (no.2016d-4402). conflicts of interest the author(s) declare that they have no conflicting interests. references cai, w., li, z, and zhang, x. 2009. horizontal well fracturing technology for reservoirs with low permeability. petroleum exploration and development 36(1):80-85 cai, x., tang, h., and zhou, k. 2010. pattern optimization of hydraulically fractured horizontal wells in low permeability and thin interbedded reservoirs. special oil and gas reservoirs 17(4):72-74. xiong, y., liu, l., and zhang, l. 2012. present status and development comments on horizontal well completion techniques in china. petroleum drilling techniques 40(1):1-6. xu, x., liu, x., and yang, z. 2012. an experimental study on single-phase seepage characteristics with a largescale model made of ultra-low permeability sandstone outcrops. acta petrolei sinica 33(3):454-458. zeng, b., cheng, l., and li, c. 2010. development of evaluation of fractured horizontal wells in ultra-low permeability reservoirs. acta petrolei sinica 31(5):791-796. qingyan xu is a senior reservoir engineer at cnpc research institute of petroleum exploration and development (beijing), where he has worked for 7 years. his research interests are in low permeability reservoir development, complex fault block reservoir development, and super-deep water gas reservoir 5 development. he holds bachelor and master degree from the china university of petroleum, and ph.d. from chinese academy of sciences, all in oil & gas field development. rongliang guan is a senior drilling engineer at daqing no.1 drilling company of daqing drilling ltd, where he has worked for 12 years. his research interests are in directional drilling and horizontal drilling. he holds bachelor degree from the china university of petroleum in drilling. cong wu is a senior reservoir engineer at research institute of petroleum exploration & development of huabei oilfield branch, where he has worked for 15 years. his research interests are in formation testing, acidizing and fracturing. he holds bachelor and master degree from the china university of petroleum, both in oil & gas field development. abstract introduction manuscript presentation conclusions and discussions acknowledgments conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.425 received july 5, 2018; revised august 30, 2018; accepted september 18, 2018. *corresponding author: ouodi7@gmail.com 1 incorporation of homogenizer in nanoemulsion injection scheme for enhanced oil recovery uchenna odi*, devon energy, houston, usa abstract this work presents a theoretical approach of incorporating a homogenizer within a nanoemulsion injection scheme for enhanced oil recovery (eor). nanoemulsions are kinetically stable emulsions stabilized by surfactants with droplet sizes ranging from 20 to 500 nm and have the potential to deliver chemical agents depending on their application. for eor, nanoemulsions have the potential to be more effective than the often used microemulsion which are thermodynamically stable and thus may break due to the heterogeneous conditions inherent in oil and gas reservoirs. there are two primary categories of nanoemulsion formulation which are high energy methods and low energy methods. high energy methods involve creating nanoemulsions using a high energy process such as high pressure homogenization. these methods can be expensive due to the energy applied to the nanoemulsion formulation process. low energy methods involve manipulating the chemistry of the oil and surfactant formulation and are thus low cost due to the low energy input. current technology illustrates that nanoemulsion size control is relatively straightforward using high energy methods such as high pressure homogenization. injecting incompressible fluids into a reservoir requires substantial energy in the form of pumps. incorporating a homogenizer in the injection scheme gives an opportunity for the homogenizer to utilize the high energy inherent in the injection process. this is illustrated using the mechanical energy balance that combines the potential, kinetic, friction, and homogenizer pressure drops inherent in the incorporation of a homogenizer in the injection of nanoemulsions. analysis shows the relative contributions of each of these pressure effects in the overall determination of the bottom hole injection pressure. incorporating a homogenizer into a nanoemulsion eor process would schematically give direct control over nanoemulsion size while conserving energy by using the high energy inherent in an eor injection process. this would be a novel direct approach of controlling the stability of nanoemulsions (by controlling the size) while not producing extra costs associated with high energy nanoemulsion creation methods. the describe procedure illustrates how to design an injection performance curve that can schematically give control of nanoemulsion size. introduction nanoemulsion eor is an emerging smart fluid technology that has the potential to substantially increase ultimate recovery rates of reservoirs in the tertiary stages of recovery. nanoemulsion formation is characterized as two methods which are high energy and low energy (koreleva and yurtov 2012). low energy methods, which include phase inversion (by temperature or composition) and spontaneous emulsification, have been demonstrated but control of nanoemulsion diameter is not as straightforward as high energy methods. high energy methods which include high shear stirring, ultrasonic emulsification and high pressure homogenization are more energy intensive (and thus expensive) but give greater control of nanoemulsion diameter and therefore control of stability. a breakdown of nanoemulsion stability can be caused by gravitational separation (creaming/sedimentation), flocculation, coalescence, and ostwald ripening (mcclements 2012). kinetic stability is critical to avoiding nanoemulsion breakage. kinetic mailto:ouodi7@gmail.com 2 stability of a nanoemulsion can be maintained as long as the energy barrier height between the nanoemulsion and separated state of the surfactant and oil mixture is greater than 20kt, where k is the boltzman constant and t is the absolute temperature (mcclements 2012). in addition, mcclements has remarked that radius’s less than 90 nm show ability to avoid gravitational separation (creaming/sedimentation) due to brownian forces dominating gravitational forces. some authors have commented on the use of nanoemulsions for eor. del gaudio et al. (2007) remarked on the potential application of nanoemulsions to deliver chemical agents that can increase oil recovery. in addition, del gaudio et al. were successful in creating several nanoemulsion formulations for eor (del gaudio et al. 2013). mandal et al. (2012) showed that nanoemulsions (consisting of mineral oil and a series of nonionic ethoxylated surfactants) in a core flood setup increased oil recovery up to 30% more after a water flood. mandal et al. (2012) and del gaudio et al. (2007 and 2013) methods of nanoemulsion preparation were both categorized as low energy methods which have indirect control over nanoemulsion size. no authors have commented on the simultaneous injection of nanoemulsions of eor while controlling nanoemulsion size. the original work here utilizes an existing nanoemulsion fluid and illustrates how to create injection performance curves that have the ability to control nanoemulsion size. control of nanoemulsion size is essential for successful nanoemulsion eor. a high energy nanoemulsion system is presented in this work that utilizes the existing energy inherent in eor injection to create and inject stable nanoemulsions. this process is verified by merging the theory of nanoemulsion creation into the mechanical energy balance of an eor injection process. as examples, several nanoemulsion injection scenarios are presented that utilize this process using an example nanoemulsion, vertical well configuration, and several homogenizer dimensions. statement of theory and definitions consider the diagram in figure 1 which illustrates an injection scheme that is connected to a nanoemulsion formulation process which includes a mixing system, centrifugal pump and high pressure homogenizer. the first stage of this process is the mixing process. the purpose of the mixer is to create low energy emulsions by mixing the brine, surfactant, and oil phases together. in addition the mixer can also be used to mix already prepared nanoemulsions. after this mixing stage, the mixture is transported to the second stage by a centrifugal pump. the centrifugal pump pressurizes and transports the emulsion mixture to the third stage which is the high pressure homogenizer. the purpose of the homogenizer is to further reduce the nanoemulsion diameter to a desired value that ensures kinetic stability (radiuses less than 90 nm) (mcclements 2012). after going through the homogenizer, the fluid is transported (still using the head of the centrifugal pump) to the fourth stage which is transport through the wellbore to the reservoir’s sand face. as an assumption, every stage in the nanoemulsion injection process occurs at a steady state injection rate. all four stages are linked and have an associated effect on one another. as an example, the emulsion diameter after the pumping stage can be large enough to warrant multiple passes through the homogenizer. multiple passes through the homogenizer will reduce the overall bottom hole pressure. if the bottom hole pressure is less than the reservoir pressure than no injection can take place. therefore, it is important to consider emulsion size in conjunction with a mechanical energy balance so that the bottom hole injection pressure is above the reservoir pressure. 3 figure 1—nanoemulsion injection system. nanoemulsion size control. the emulsion mixture goes through several processes that have the ability to impart energy in various forms which may have wide implications on nanoemulsion size. the primary difference in each of the processes is the turbulent energy of dissipation. each process imparts a form of energy onto the emulsion. for the mixer, it has been remarked that the turbulent energy of dissipation is in the order of 10-100 w/kg (davis 1987). this range is miniscule when compared to homogenizers and other high energy methods which are 108 w/kg and greater (davis 1987). davis (1987) proposed a widely used expression for emulsion diameter as a function of the turbulent energy of dissipation and emulsion properties. the expression for emulsion diameter, dne, is conveyed in the following relationship. 𝑑𝑛𝑒 = ( 4 𝐶1𝐶2 ) 3/5 (1 + ( √𝐶2 4 ) 𝜇𝐷𝜀1/3𝑑𝑛𝑒 1/3 𝜎 ) 3/5 (𝜎3/5𝜌𝐶 −3/5 𝜀−2/5),…………...……………………………(1) where c1 and c2 are constants equal to 0.7 and 2 respectively; µd is the dispersed phase viscosity; ε is the turbulent energy of dissipation; ρc is the density of the continuous phase; and σ is the interfacial tension between the oil and aqueous phases. the turbulent energy of dissipation is the key factor in controlling the nanoemulsion diameter. using davis’s equation and assuming the physical properties of a typical emulsion, it is possible to see the relationship between the energy of dissipation and emulsion droplet size. this relationship is expressed in the following figure for emulsions where the continuous phase density is approximately 1000 kg/m3 and the interfacial tension is .001 n/m. 4 figure 2—turbulent energy of dissipation as a function of emulsion droplet size using davis's expression. figure 2 (in diameter length scales) illustrates that stable nanoemulsions (radiuses less than 90 nm or 180 nm diameter) can be made using turbulent energy of dissipations greater than approximately 5×103 mw/kg for dispersed phase viscosities of approximately .001 pa*s. to make stable nanoemulsions with an increased dispersed phase viscosity of .01 pa*s, results in a required turbulent energy of dissipation of approximately 3×106 mw/kg or greater. to make stable nanoemulsions with a decreased dispersed phase viscosity of .0001 pa*s, results in a required turbulent energy of dissipation of approximately 7×102 or greater. these results indicate that amount of energy needed to reduce emulsion size substantially increases as the dispersed phase viscosity increases. additionally, these results show that the energy of dissipation can be used to directly control nanoemulsion size. for a homogenizer, the energy of dissipation can be directly controlled using the dimensions of the homogenizer. these dimensions are illustrated in figure 3. figure 3—homogenizer valve cross section (rotate along axis of symmetry for complete cross section, not drawn to scale). using this active zone, the energy of dissipation for the homogenizer is the following (hakansson 2007). 𝜀𝐻 = 𝛥𝑃𝐻𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ,……..………………………………………….....……………………………..(2) where rin is the homogenizer inlet radius, rout is the homogenizer outlet radius, hgap is the gap height of the 5 homogenizer, q is the volumetric flow rate of emulsion, ρm is the density of the emulsion, and δph is the pressure drop through the homogenizer. several homogenizers placed in series is equivalent to multiple passes through one homogoenzier. the energy of dissipation for n passes through the homogenizer is derived to be the following (see appendix). 𝜀𝐻 = 𝑁𝛥𝑃𝐻𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ,.……………………………………….…………...…………………………...(3) observing the expressions for the energy of dissipation from one pass in the homogenizer and n passes through a homogenizer, it is evident that the total turbulent energy of dissipation is directly proportional to the number of passes or number of identical homogenizers in series. when several homogenizers are placed in series together, the equivalent total energy of dissipation can be found by substituting the energy of dissipation for each individual homogenizer. this results in the following expression for the total energy of dissipation. 𝜀𝐻 = 𝜀𝐻1 + 𝜀𝐻2 + ⋯ + 𝜀𝐻𝑁 = ∑ 𝜀𝐻𝑖 𝑁 𝑖=1 ,.…………………..…………………..………………………(4) this result states that for identical homogenizers in series, the total energy of dissipation is the summation of their respective turbulent energies of dissipation. this conclusion can be extended to multiple emulsion droplet reducing machines in series. the sum of their turbulent energies of dissipations can be used to effectively determine resulting droplet size. as an example, consider an emulsion with properties listed in figure 4 that undergoes several passes using a homogenizer with specifications listed in figure 4. this emulsion’s size is simulated in figure 4 as a function of number of passes in the homogenizer. a decay relationship, first proposed by hatton et al. (2014) described the eventual decline of emulsion size as the number of passes. this relationship is described in the following expression. 𝑑𝑛𝑒 = 𝑑∞ + 𝐴𝑛𝑒−𝑁/𝑁𝑏,...…………………………………..………………..…………………………(5) where an is a parameter in the fit, nb is the number of passes until emulsion breakage and d∞ is the emulsion size after an infinite amount of passes. the parameter an can be quantified by understanding that before the emulsion enters the homogenizer, the parameter nh is 0. therefore, 𝑑𝑛𝑒 = 𝑑∞ + 𝐴𝑛 which is essentially the initial emulsion diameter size before homogenization. figure 4 illustrates this best fit line using the previous relationship and the simulated data. figure 4—simulated emulsion as a function of homogenizer passes. because the sum of the turbulent energy of dissipations is the total contribution of the energy imparted onto the emulsion, the emulsion diameter is then a function of the total turbulent energy of dissipation along with the specific properties of the emulsion. for the nanoemulsion injection system, the total energy of dissipation can be modeled using the following expression. 6 𝜀𝑇 = 𝜀𝑀 + 𝜀𝐶𝑃 + 𝜀𝐻,..………………………..………………………………………………………..(6) where εm is the turbulent energy of dissipation for the mixer, εcp is the turbulent energy of dissipation for the centrifugal pump, and εh is the turbulent energy of dissipation for the homogenizer(s). the starting point of the nanoemulsion injection system is the mixer. the turbulent energy dissipation for a mixer is function of the impeller diameter and impeller speed. the expression for the turbulent energy of dissipation in a mixer is represented in the following expression (morales et al. 2013). 𝜀𝑀 = 𝜅𝑀𝑁𝑀 3 𝐿𝑀,………..…………………..…………………………………………………………..(7) where κm is the mixing turbulent energy of dissipation for the mixer, nm is the mixing impeller angular velocity, and lm is the mixing impeller diameter. the mixing system used in this work has the general ability to mix the aqueous and oil phases for pressurization through the centrifugal pump. all specifications for the mixing system are listed in table 1. table 1—mixing system specifications. mixing impeller diameter .232 m mixing turbulent energy of dissipation 0.0019 mixing impeller angular velocity 150 rpm to determine the emulsion size as a result of passing through a centrifugal pump requires quantifying the turbulent energy of dissipation for the centrifugal pump. the turbulent energy dissipation for a centrifugal pump is a function of the hydraulic power performed on the fluid. specifically, it can be represented using the following expression (morales et al. 2013). 𝜀𝐶𝑃 = 𝜅𝐶𝑃 𝛥𝑃𝐶𝑃𝑄 𝜌𝑀𝑉𝐶𝑃 ,.……………………..………………..….…………………………………………..(8) where κcp is the fraction of total dissipated energy by turbulence for the centrifugal pump, ∆pcp is the change in pressure caused by the centrifugal pump and vcp is the volume of the centrifugal pump. using the previous expression and the davis expression for emulsion diameter, it is possible to estimate the emulsion size as a result of pumping the emulsion product from the mixing system through the centrifugal pump. the resulting high pressured emulsion from the centrifugal pump is the premix feed into the high pressure homogenizer. emulsion size can be further controlled by using the homogenizer’s ability to pass the emulsion mixture through several homogenizer passes. it is possible to incorporate emulsions size control in the injection scheme of nanoemulsions by performing a mechanical energy balance on the nanoemulsion injection system. description and application of equipment and processes the injection bottom hole pressure is a function of the fluid changes due to the pump, potential energy, kinetic energy, and friction (with full discussion in the appendix). a homogenizer can be added to this conventional setup by adding another pressure drop attributed to 𝑁 passes through the homogenizers in series. quantitatively this pressure drop is 𝑁∆𝑃𝐻. the bottom hole pressure from the mechanical energy balance across an injection system incorporating a homogenizer is then represented using the following equation. 𝑃𝐵𝐻𝑃 = 𝑃𝑡ℎ + 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓 − 𝑁𝐻𝛥𝑃𝐻,..…………….…………………………………………(9) where pth is the pressure contribution due to the pump, ∆ppe is the pressure drop due to potential energy, ∆pke is the pressure drop due to kinetic energy, and ∆pf is the pressure drop due to friction. using the previous expression, nanoemulsion size control can be incorporated into the mechanical energy balance. the primary challenge in implementing the nanoemulsion injection scheme is ensuring that there is enough pressure to inject and enough turbulent energy of dissipation to control the nanoemulsion size. these goals are counterintuitive because ensuring emulsion radiuses of 90 nm or less (for stability) requires large turbulent energies of dissipation which correspondingly require large pressure drops through the 7 homogenizers. large pressure drops through multiple homogenizers would reduce the bottom hole injection pressure to values less than the reservoir pressure which would result in nanoemulsion injection failure. conversely, only ensuring bottom hole pressures larger than the reservoir pressure would result in small pressure drops in the homogenizers which would then result in low turbulent energies of dissipation. radiuses greater than 90 nm would then be created and would cause nanoemulsion failure because these diameters are outside the stable nanoemulsion class. a generalized algorithm can be created that ensures that nanoemulsions with radiuses less than 90 nm (diameter less than 180 nm) are created with sufficient pressure for injection against a reservoir pressure, presv. illustrated in figure 5, this algorithm shows that for a limit of nlimit homogenizers in series it is possible to create stable nanoemulsions by systematically going through a three step checklist after each homogenizer pass. after each homogenizer pass, this checklist consists of first verifying if 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is true. if 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is false than there can be no injection of nanoemulsion. if 𝑁∆𝑃𝐻 < 𝑃𝑡ℎ is true then the second point on the checklist, 𝑑𝑛𝑒 ≤ 180 nm, needs to be checked. if the second point, 𝑑𝑛𝑒 ≤ 180 nm, is false then the emulsion needs another pass through a homogenizer. if 𝑑𝑛𝑒 ≤ 180 nm is true then the third point on the checklist, 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣, needs to be checked. if the third point, 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣, is false than there can be no injection of nanoemulsion. if 𝑃𝐵𝐻𝑃 > 𝑃𝑟𝑒𝑠𝑣 is true, than there is successful nanoemulsion injection. applying this algorithm for a desired nanoemulsion injection rate, it is possible to create stable nanoemulsions with sufficient injection pressure. figure 5—generalized nanoemulsion injection algorithm. proper homogenizer dimensions can be used to mitigate the two conflicting goals of nanoemulsion injection and nanoemulsion size control. homogenizer dimensions can do this by creating enough turbulent energy of dissipation to reduce emulsion diameter at moderate homogenizer pressure drops that minimize the deduction from the bottom hole injection pressure. to adequately compare homogenizer performance, innings and tragardh (2007) proposed dimensionless groups and length scales which are represented in the 8 following expressions. 𝑁𝑅𝑒, 𝐺𝑎𝑝 = 𝜌𝑀𝑄 2𝜋𝑟𝑜𝑢𝑡𝜇𝑀 ,..…………………………….……………………………………………………(10) 𝑁𝐺,𝐾𝑜𝑙 = ℎ𝐺𝑎𝑝 𝜂 ,……………………..…………………………………………………………………...(11) 𝜂 = ( 𝜇𝑀 𝜌𝑀𝜀 ) 1 4,…………………….…………..…………………………………………………………(12) 𝑙0 = 𝜂 ⋅ 𝑁𝑅𝑒, 𝐺𝑎𝑝 3 4,.……………………..……………………………………………………………...(13) where nre,gap is the gap reynolds number, ng,kol is the turbulent gap height, ƞ is the kolmogorov length scale, and l0 is the largest eddy scale. these groups can be used to compare the performance of different homogenizer dimensions. they will also give insight on homogenizer dimensions that are essential to successful nanoemulsion injection. presentation of data and results to illustrate the effectiveness of the nanoemulsion injection system a tween 80/span 80 and diesel fuel nanoemulsion injection is simulated using nanoemulsion experimental data from noor el-din et al. (2013). specifically, this system is a water in oil nanoemulsion that contains 9 wt% water and 10 wt% active surfactants (53.3wt% tween 80 and 46.7wt% span 80) in the aqueous phase and diesel fuel as the oil phase. noor el-din et al. (2013) measured the hlb of the aqueous phase as 10, the critical micelle concentration of the mixed surfactant system as 14.3x10-4 mol/l, and the interfacial tension between the oil and aqueous phase at the critical micelle concentration as 3.8 mn/m. noor el-din et al. (2013) also measured the density and kinematic viscosity of the nanoemulsion system for different volume fractions of the aqueous phase illustrated in figure 6 and figure 7. using the density and kinematic viscosity as functions of temperature, dynamic viscosity values were determined as a function of temperature. as previously discussed, nanoemulsion viscosity and density are critical parameters in the calculation of the bottom-hole injection pressure. these parameters are essential in quantifying viscosity and density changes caused by temperature increases in the injection tubing as the nanoemulsion is transported from the homogenizer and through the wellbore to the reservoir’s sand face. figure 6—0-9 wt% water and 10 wt% surfactant mixture (53.3 wt% tween 80 and 46.7 wt% span 80) in diesel nanoemulsion density as function of temperature (noor el-din et al. 2013). 9 figure 7—0-9 wt% water and 10 wt% surfactant mixture (53.3 wt% tween 80 and 46.7 wt% span 80) in diesel nanoemulsion kinematic viscosity as function of temperature (noor el-din et al. 2013). noor el-din et al. (2013) experimental nanoemulsion diameter was measured as 49.55 nm and was obtained using a high pressure homogenizer. for this work, 49.55 nm is the target diameter because it represents the minimum diameter obtained experimentally. using this target diameter, noor el-din’s emulsion properties, and a test injection rate of 1000 stb/day (159 m3/day), homogenizer gap heights were determined for four cases of homogenizer dimensions. homogenizer gap heights were determined by first solving for the turbulent energy of dissipation for a diameter equal to 49.55 nm. from there, the turbulent energy of dissipation was used along with user defined homogenizer inlet and outlet radiuses to solve for the gap height in the homogenizer turbulent energy of dissipation expression. using this procedure, gap heights were determined for four homogenizer dimensions labeled accordingly in the following table along with their characteristic properties. observing table 2, it is apparent that the pressure drop is reduced for the same turbulent energy of dissipation as the homogenizer dimensions progress from production scale to the 2nd proposed nano scale. this is an important result because it shows that the homogenizer pressure drop can be reduced without adversely affecting the homogenizer’s ability to produce nanoemulsions. in addition, turbulence is increased as the homogenizer dimensions progress to the 2nd nano scale which may be an indication that more energy is utilized in the process of reducing the emulsions diameter. a vertical well configuration with a target reservoir temperature of 99oc (210of) and other parameters listed in table 3 was used to illustrate the nanoemulsion injection system. using the vertical well configuration, several homogenizer scenarios indicated in table 2 were simulated. table 2—homogenizer dimensions (dne=49.55 nm, q=1000 stb/day (159 m3/day), temp.=60of (15.6oc)). production scale pilot scale 1st proposed nano scale 2nd proposed nano scale rout, mm 16 4 2 1 rin, mm 15 3 1 0.5 hgap, µm 170 291 413 696 ∆ph, mpa 5,290 2,050 1,250 524 ε, mw/kg 677,000 677,000 677,000 677,000 nre,gap 2,140 8,570 17,200 34,300 ƞ, µm 59.6 59.6 59.6 59.6 l0, mm 18.8 53.1 89.3 150.2 ng,kol 2.85 4.89 6.93 11.7 10 table 3—well parameters. pipe roughness 0.0006 tubing inner diameter 0.0762 m (3 inches ) surface temperature 15.6oc (60of) geothermal gradient 8.33oc per 304.8 m, (15of per 1000 ft) injection tubing length 3048 m (10000 ft) inclination angle 90o total depth 3048 m (10,000 ft) change in depth 3.048 m (10 ft) the results of these simulations are illustrated in figure 8 through figure 11. observing the pressure contributions illustrated in figure 8, it is apparent that the bottom hole injection pressure increases for the same nanoemulsion injection rate as the homogenizer dimensions progress from production scale to the 2nd proposed nano scale. this occurs primarily because the pressure drop due to homogenization is minimized as the homogenizer dimensions progress from the production scale to the 2nd proposed nano scale. a reduction of the homogenizer pressure drop ensures larger range of positive bottom hole injection pressures. (a) (b) (c) (d) figure 8—bottom hole pressure and pressure drops for nlimit = 1 (a) production scale (b) pilot scale (c) 1st proposed nano scale (d) 2nd proposed nano scale. 11 (a) (b) (c) (d) figure 9—turbulent energy of dissipation for nlimit = 1 (a) production scale (b) pilot scale (c) 1st proposed nano scale (d) 2nd proposed nano scale. as a consequence of extending the bottom hole pressure over a larger range of injection rates for specific homogenizer dimensions, there is a larger range of turbulent energies of dissipation and thus a larger range of emulsion diameters. this is portrayed in figure 9 and figure 10 which show that as the homogenizer dimensions progress from the production scale to the 2nd proposed nano scale there is larger amount of energy dissipated in the creation of smaller diameter emulsions. observing all the presented homogenizer dimensions, it is apparent that the 2nd proposed nano scale had the largest impact on emulsion diameter reduction. the injection range in which positive injection pressures and kinetically stable emulsion diameters occurred for this homogenizer was an injection flow rate of 32 m3/day at a bottom hole injection pressure of 251 mpa to an injection flow rate of 107 m3/day at a bottom hole injection pressure of 0.585 mpa. when compared to the 2nd proposed nano scale, the other homogenizer specifications did not have the same success in reducing the emulsion diameters as conveyed by table 4. overall, all of the homogenizers exhibited the same trend of having the emulsion diameters decrease. this decrease was limited by the homogenizer pressure drop. because of this, it is essential to choose the right homogenizer dimensions so as to ensure stable nanoemulsions and adequate nanoemulsion injection. table 4—minimum diameters obtained for nanoemulsion injection. minimum diameter, nm injection rate at minimum diameter, m3/day bottom hole pressure at minimum diameter, mpa production scale 235 20.2 0.259 pilot scale 138 39.7 0.530 1st proposed nano scale 105 58.0 0.492 2nd proposed nano scale 67.8 107 .585 12 (a) (b) (c) (d) figure 10—emulsion diameter for nlimit = 1 (a) production scale (b) pilot scale (c) 1st proposed nano scale (d) 2nd proposed nano scale. in addition to the homogenizer dimension study presented earlier, an additional study was conducted to see if adding homogenizers in series according to the algorithm presented in figure 5 is beneficial. this scenario was conducted using the dimensions of the 2nd proposed nano scale. the emulsion diameter results are illustrated in figure 11. these results show that increasing the amount of homogenizers results in no beneficial decrease in nanoemulsion diameter. this occurs because increasing the amount of homogenizers correspondingly increases the total homogenizer pressure drop. increasing the total homogenizer pressure limits the bottom hole injection pressure range which thus reduces the injection rate range of how far the emulsion diameter can be reduced. 13 (a) (b) (c) figure 11—diameter using 2nd proposed nano scale (a) nlimit=1, (b) nlimit=3, (c) nlimit=5. economics equipment and transportation costs are the primary differences between onsite and offsite production of nanoemulsions for the oil field. onsite production of nanoemulsions which utilizes a homogenizer incorporated into an eor injection scheme requires capital investment due to homogenizers, mixers, and centrifugal pumps. while a single homogenizer and single mixer could be sized accordingly to service several wells in a field (estimated total capital cost ranging from 1-10 million usd), the cost of several centrifugal pumps for injection depends on the number of wells in a field. because of this, the total cost of the nanoemulsion injection system depends on the number of wells utilized in the field. the final decision to use the onsite option depends on if the capital costs of the onsite implementation are less than the transportation costs to deliver offsite produced nanoemulsions. regardless of the choice between onsite and offsite options, the one similarity between these two options is the chemical cost associated with creating the nanoemulsion. nanoemulsions fundamentally contain oil, water, and surfactants. considering these components it is possible to determine the chemical cost per volume of a nanoemulsion by utilizing the following equation. 𝐶𝑁𝐸 = 𝜌𝑀 ( 𝑓𝑚,𝑊𝐶𝑊 𝜌𝑊 + 𝑓𝑚,𝑆𝐶𝑆 + 𝑓𝑚,𝑂𝐶𝑂),.………………………………………………………….....(14) where fm,w is the mass fraction of water in the nanoemulsion, cw is the cost per volume of water, ρw is the density of water in the nanoemulsion, fm,s is the mass fraction of surfactants in the nanoemulsion, cs is the cost per mass of surfactants in the nanoemulsion, fm,o is the mass fraction of oil phase in the nanoemulsion, and co is the cost per mass of oil in the nanoemulsion. considering the nanoemulsion investigated in this 14 work and the chemical costs of each component the nanoemulsion costs is approximately $5.98 per liter. this costs is relatively expensive due to the expensive cost of surfactants (tween 80 is $114 per gallon, span 80 is $96.20 per liter) and diesel (3.65 per gallon). in addition, the majority of the investigated nanoemulsion is diesel by mass. these costs are lab scale and can be further reduced using carefully selected suppliers or cheaper chemical substitutes when scaled up to field use. to ensure profitability for the nanoemulsion injection system, the current commodity price of oil must be more than the cost of delivering the nanoemulsion to the reservoir. when considering the numerous possible nanoemulsions (water in oil and oil in water) it is possible to determine the range of chemical cost associated with nanoemulsion formulation by using montecarlo simulation. these simulation results using the uniform distributed parameters in table 5 and a range of 800 kg/m3 to 1200 kg/m3 for the nanoemulsion density gives a nanoemulsion cost ranging from $.0044 to $21.62 per liter. additional specifics regarding the possible nanoemulsion costs are illustrated in figure 12. (a) (b) figure 12—results of montecarlo simulation of nanoemulsion cost (a) probability distribution function (b) cumulative distribution function. table 5—parameters for montecarlo simulation of nanoemulsion cost. water phase surfactant phase oil phase minimum mass fraction .01 .01 .01 maximum mass fraction .90 .10 .98 minimum density 1000 maximum density 1200 minimum cost $.01 per barrel $.01 per kg $.01 per kg maximum cost $10 per barrel 100 per kg 10 per kg these results show that it is important to have low cost surfactants and low cost oil. having low cost nanoemulsion components ensures that the margin between nanoemulsion chemical cost and oil price is large enough to justify nanoemulsion eor. conclusions it is theoretically possible to create nanoemulsions within an eor injection scheme. proof of this concept is accomplished by incorporating the production of nanoemulsions into the mechanical energy balance. successful nanoemulsion injection is strongly dependent on the homogenizer dimensions. inadequate homogenizer dimensions cause too much of a pressure drop or too small of an energy of dissipation. proper 15 homogenizer dimensions have adequate pressure drops with substantial turbulent energies of dissipation that reduce the emulsion to stable nanoemulsion sizes. utilizing the 2nd proposed nano scale, it is possible to combine the production of nanoemulsions into a nanoemulsion injection scheme. acknowledgement eni is gratefully acknowledged for promoting this research towards understanding implementation of nanoemulsion eor in the field. mit is also acknowledged for collaboration. conflicts of interest the author(s) declare that they have no conflicting interests. references del gaudio, l., bortolo, r., and lockhart, t. p. 2007. nanoemulsions: a new vehicle for chemical additive delivery. paper presented at the 2007 spe international symposium on oilfield chemistry. houston, tx, 28 february-2 march. spe-106016-ms. del gaudio, l., lockhart, t. p., belloni, a., et al. 2013. process for the preparation of water-in-oil and oil-in-water nanoemulsions. u.s. patent application 13/845,515, filed march 18, 2013. economides, m. j., hill, a. d., and ehlig-economides, c. 1994. petroleum production systems. englewood cliffs, n.j.: ptr prentice hall. hakansson, a. 2007. dynamic modelling of high pressure high pressure homogenizer. master thesis. department of food technology, engineering and nutrition. lund university, sweden. hakansson, a., tragardh, c., and bergenstahl, b. 2009. dynamic simulation of emulsion formation in a high pressure homogenizer. chemical engineering science 64(12):2915-2925. hatton, t. a., doyle, p. s., doyle, g. a., et al. 2014. nanoemulsions: mechanistic evaluation of formation, stability and applications. massachusetts institute of technology. innings, f. and tragardh, c. 2007. analysis of the flow field in a high-pressure homogenizer. experimental thermal and fluid science 32(2):345-354. mandal, a., bera, a., ojha, k., et al. 2012. characterization of surfactant stabilized nanoemulsion and its use in enhanced oil recovery. paper presented at the 2012 spe international oilfield nanotechnology conference. noordwijk, the netherlands, 12-14 june. spe-55406-ms. mcclements, d. j. 2012. nanoemulsions versus microemulsions: terminology, differences, and similarities. soft matter 8(3):1719-1729. morales, r., pereyra, e., wang, s., et al. 2013. droplet formation through centrifugal pumps for oil-water dispersions. spe journal 18(2013):172178. spe-163055-pa. noor el-din, m. r., el-hamouly, s. h., mohamed, h. m., et al. 2013. water-in-diesel fuel nanoemulsions: preparation, stability, and physical properties. egyptian journal of petroleum 22(2013):517-530. the mathworks. 2014. centrifugal pump. http://www.mathworks.com/help/physmod/hydro/ref/centrifugalpump.html?refresh=true. appendix energy of dissipation through a homogenizer derivation. the energy of dissipation using the homogenizer dimensions can be quantified by assuming that the major fragmentation and coalescence occurs in the gap just after the seat and before the forcer as a consequence of the pressure drop through the gap. using this active zone, the energy of dissipation for the homogenizer is the following (hakansson 2007). 𝜀𝐻 = 𝛥𝑃𝐻𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ,………….…….……………………………………………………………..(a1) where rin is the homogenizer inlet radius, rout is the homogenizer outlet radius, hgap is the gap height of the homogenizer, q is the volumetric flow rate of emulsion, ρm is the density of the emulsion, and δph is the pressure drop through the homogenizer expressed as the following (hakansson et al. 2009). 𝛥𝑃𝐻 = 𝜌𝐶 4 ( 𝑄 2𝜋𝑟𝑖𝑛ℎ𝑔𝑎𝑝 ) 2 + 5𝜌𝐶𝜇𝐶 3/5𝑄7/5 (2𝜋)7/5ℎ𝑔𝑎𝑝 3 ( 1 𝑟𝑖𝑛 2/5 + 1 𝑟𝑜𝑢𝑡 2/5 ) + 𝜌𝐶 2 ( 𝑄 2𝜋𝑟𝑜𝑢𝑡ℎ𝑔𝑎𝑝 ) 2 …...…………….………..(a2) http://www.mathworks.com/help/physmod/hydro/ref/centrifugalpump.html?refresh=true 16 substituting the pressure drop expression in the turbulent energy of dissipation expression results in the following expression which illustrates that the turbulent energy of dissipation is a function of the homogenizer dimensions which are rin, rout, and hgap. 𝜀𝐻 = ( 𝜌𝐶 4 ( 𝑄 2𝜋𝑟𝑖𝑛ℎ𝑔𝑎𝑝 ) 2 + 5𝜌𝐶𝜇𝐶 3/5𝑄7/5 (2𝜋)7/5ℎ𝑔𝑎𝑝 3 ( 1 𝑟𝑖𝑛 2/5 + 1 𝑟𝑜𝑢𝑡 2/5) + 𝜌𝐶 2 ( 𝑄 2𝜋𝑟𝑜𝑢𝑡ℎ𝑔𝑎𝑝 ) 2 ) ( 𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ).……(a3) ideally, it is desired to create nanoemulsions after one pass in the homogenizer. however it may not be possible to do this depending on the dimensions of the homogenizer. because of this, it is important to model the homogenizer for n passes. this can be done by first considering homogenizers with the same dimensions in series as illustrated in figure 13a. these homogenizers have the same pressure drop through them (∆𝑃𝐻1 = ∆𝑃𝐻2 = ⋯ = ∆𝑃𝐻𝑁) and therefore have the same turbulent energy of dissipation (𝜀𝐻1 = 𝜀𝐻2 = ⋯ = 𝜀𝐻𝑁). effectively, this means that each homogenizer has the same ability to change emulsion size. (a) (b) figure 13—pressure drops in a series of homogenizers (a) individual in series (b) summation of individual in series. as the emulsion passes through each homogenizer, it has a pressure drop equal to the summation of pressure drops as illustrated in figure 13b. using the analogy presented in the previous figure, it is possible to deduce the total turbulent energy of dissipation as a result of passing through a series of these homogenizers. this expression is derived by starting with the expression for turbulent energy of dissipation and the total pressure drop through the homogenizer. 𝜀𝐻 = 𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 [𝛥𝑃𝐻1 + 𝛥𝑃𝐻2 + ⋯ + 𝛥𝑃𝐻𝑁 ]...…………………..…………………………...(a4) multiplying out the pressure drop terms results in the following expression. 𝜀𝐻 = 𝛥𝑃𝐻1𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 + 𝛥𝑃𝐻2𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 + ⋯ + 𝛥𝑃𝐻𝑁 𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ........……………………………(a5) there are two conclusions that can be made from the previous expression. since ∆𝑃𝐻 = ∆𝑃𝐻1 = ∆𝑃𝐻2 = ⋯ = ∆𝑃𝐻𝑁, there are n pressure drops with a pressure drop of ∆𝑃𝐻. therefore, the total pressure drop through the system of homogenizers is 𝑁∆𝑃𝐻 . using this statement, the first conclusion is the final expression for the turbulent energy of dissipation for n homogenizers in series. 𝜀𝐻 = 𝑁𝛥𝑃𝐻𝑄 𝜋(𝑟𝑜𝑢𝑡 2 −𝑟𝑖𝑛 2 )ℎ𝑔𝑎𝑝𝜌𝑀 ......………………………………………..…………………………………...(a6) mechanical energy balance. nanoemulsion injection is possible when the bottom hole injection pressure (pbhp) at the reservoir’s sand face is greater than the pressure in the reservoir. the bottom hole injection pressure is determined by first performing an energy balance on the injection system which includes everything downstream from the pump to the sand face of the reservoir system. the following equation describes the energy balance for a production/injection system (economides et al. 1994) excluding a homogenizer. 17 𝑑𝑃 𝜌𝑀 + 𝑢𝑑𝑢 𝑔𝑐 + 𝑔 𝑔𝑐 𝑑𝑧 + 2𝑓𝑓𝑢2𝑑𝐿 𝑔𝑐𝐷 + 𝑑𝑊𝑠 = 0,..….…………………..……………………………………(a7) where p corresponds to pressure, u is the injection velocity, z is the height from the injection site to the reservoir’s sand face, ff is the friction factor, d is the wellbore diameter, and ws is the shaft work. integrating the previous equation from the injection site (stage 2) to the reservoir’s sand face (stage 4) and solving for the total pressure drop leaves the following expression. 𝛥𝑃 = 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓.....………………..………………………………………………..……..(a8) the total pressure drop, δp, is the pressure loss experienced from transporting a fluid from the pump to the reservoir’s sand face (without a homogenizer). this pressure drop is the sum of pressures which include the pressure increase due to the weight of fluid (δppe, potential energy), the pressure loss due to decreasing the diameter of flow (δpke, kinetic energy), and the pressure loss due to friction (δpf). it is possible to determine each of these contributions by first dividing the length of the wellbore into nl segments with each segment being of length dl. the pressure drop due to kinetic energy in a section of pipe can be determined using the following relationship. 𝛥𝑃𝐾𝐸 = 8𝑄2 𝜋2𝑔𝑐 ∑ 𝜌𝑀𝑖 ( 1 𝐷𝑖 4 − 1 𝐷𝑖−1 4 ) 𝑁𝐿 𝑖=1 .……………………………..……………………………..……..(a9) the parameter i corresponds to the ith segment along the length of the wellbore. the pressure drop due to potential energy can be determined using the following relationship. 𝛥𝑃𝑃𝐸 = 𝑔 𝑔𝑐 ∑ 𝜌𝑀𝑖𝑑𝐿𝑖 𝑠𝑖𝑛 𝜃𝑖 𝑁𝐿 𝑖=1 .………………………………..…………………………………….(a10) the parameter θ is the angle of well inclination. the pressure drop due to friction can be determined using the following relationship. 𝛥𝑃𝑓 = 2 𝑔𝑐 ∑ 𝜌𝑀𝑖𝑓𝑓𝑖𝑢𝑖 2𝑑𝐿𝑖 𝐷𝑖 𝑁𝐿 𝑖=1 .……………………….………………………………………………….(a11) the fanning friction factor, ff, for the ith segment can be determined by first calculating the reynolds number (nre) illustrated in the following expression (economides et al., 1994). 𝑁𝑅𝑒 = 𝜌𝑀𝑢𝐷 𝜇𝑀 ,.………………………………………………………………………………………...(a12) where μm is the viscosity of the nanoemulsion mixture. using the reynolds number, the fanning friction factor can be calculated using the laminar (nre ≤2100) or turbulent (nre >2100) flow regimes (economides et al. 1994).                                             2100for 1497 82572 log 04525 70653 log4 2100for 16 re 289810 re 10981 re re re n n . . ε n . . ε n n f .. rr f ,……………….(a13) the parameter, εr, is the relative pipe roughness. incorporating the pressure contribution due to the pump (pth) it is possible to determine the bottom hole injection pressure, pbhp, using the following relationship. 𝑃𝐵𝐻𝑃 = 𝑃𝑡ℎ + 𝛥𝑃𝑃𝐸 − 𝛥𝑃𝐾𝐸 − 𝛥𝑃𝑓...…………………………………………………………...….(a14) the pressure contribution due to the pump can be determined by using a pumping curve (for a centrifugal pump) and common affinity laws that scale pump performance as a function of required injection rate (mathworks 2014). these affinity laws can be utilized by first relating the required injection rate, q, and the pumps impeller angular velocity, ω, to the rate provided by the pumping curve, qcurve, and the pumping curve’s angular velocity, ωcurve. this relation is expressed as the following equation. 𝑄𝑐𝑢𝑟𝑣𝑒 = 𝑄 ( 𝜔𝑐𝑢𝑟𝑣𝑒 𝜔 ).....………………..….………………………………………………………...(a15) the pressure contribution due to the pump can then be determined by first finding its equivalent, pth,curve, on the pumping curve using qcurve. the pressure contribution due to the pump can be determined using the following equation.                  curve m curve curvethth pp     2 , ,.………….……..…………………………………………………….(a16) where ρcurve refers to the reference density in the centrifugal pump used to make the pumping curve. the 18 centrifugal pump used in this work is a high capacity pump that has the ability to increase the pressure of the nanoemulsion from the mixing stage. a synthetic pumping curve in conjunction with pump affinity relationships were used to describe the relationship between the pressure and flow rate for the centrifugal pump. the pumping curve used for this work is illustrated in figure 14. previously discussed pump affinity laws were used to scale the pumping curve for several impeller angular velocities. in addition, the pump had several more specifications listed in table 6. figure 14—high capacity centrifugal pump curve. table 6—centrifugal pump parameters. pump impeller diameter (morales et al. 2013) .231775 m fraction turbulent energy of dissipation (morales et al. 2013) 0.0019 pump active volume .05 m3 ( 50 l) pump impeller angular velocity 5000 rpm uchenna odi is a data scientist at devon energy corporation. he was previously a research scientist at eni petroleum and a visiting scientist at the massachusetts institute of technology on behalf of eni. he holds a b.s. degree in chemical engineering and an energy focused executive mba both from the university of oklahoma. he also holds m.s. and ph.d. degrees in petroleum engineering from texas a&m university. his interests are in optimization algorithms, risk analysis, emulsion systems, enhanced oil recovery, carbon dioxide sequestration, reservoir fluids, and machine learning. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1184 received february 3, 2021; revised march 23, 2021; accepted april 2, 2021. *corresponding author: neogi@mst.edu 1 heavy oil and vapex process: a brief review vijitha mohan, university of calgary, calgary, canada; parthasakha neogi* and baojun bai, missouri university of science and technology, rolla, usa abstract heavy oil recovery requires either heat or solvent assistance to reduce its high viscosity first, and then the less viscous oil can be recovered. processes that use vapor assisted petroleum extraction (vapex) utilize vaporized solvent. solvent vapors are introduced through a top injection well to induce viscosity reduction and the less viscous oil is collected at the bottom production well. it is noteworthy, that the solvent itself when recovered, can be seen as an integral part of oil. the exact molecular weight and chemistry of heavy oil are uncertain making analysis of thermodynamic properties difficult; however, this is overcome by making use of volume fractions of heavy oil and solvent used. it is possible to correlate all properties of heavy oil with or without solvent using the volume-based approach. to understand transport properties of heavy oil, studies have focused on free volume theory, which is also a volume-based approach. the diffusion of solvent in heavy oil is seen to be highly concentration-dependent. both thermodynamic and transport properties using volume fractions, are discussed first. the efforts at introducing these properties to simulate production are then discussed. also reviewed are work on sandpacks, which show good agreement with the theory when properly correlated. on the whole, it is found that the present day effectiveness of vapex has some important shortcomings. we mention some suggestions for improvement from literature. introduction highly viscous heavy oil (above 100 cp) cannot be recovered without the aid of an external resource like heat or solvents. the high viscosity provides impediment to easy recovery, making the reduction of the viscosity of oil a necessary precursor to oil recovery. steam assisted gravity drainage (sagd) process is a thermal process where steam is used as a heat source to reduce the viscosity of heavy oil to ~1cp. the less viscous oil flows under gravity to the drainage well. the water requirement, fuel usage to produce steam and discharge of a large amount of contaminated water, make the process, while still in use, expensive with future liabilities. vapor assisted petroleum extraction (vapex) process uses gases (above critical temperature) or vapors (below critical temperature). these are usually called solvents even though they play the role of solutes in crude oil. they dissolve in the oil at the interface and diffuse into the bulk. in the process, the viscosity of the solution is brought down ~5cp, and it drains under gravity. the drainage is collected at the production well (banerjee 2012; speight 2009). quantitative understanding of the process is divided into two parts. in the first case, we look at the thermodynamic and transport properties of the oil-solvent mixture. in particular, the solubility has less variation, but the viscosity and diffusivity have very large variations with solvent concentrations. the solvent itself varies in its properties. at the reservoir temperatures, methane would be well above the critical temperature and would not condense. co2 is below its critical temperature and will condense but appears to be immiscible with heavy oil even at very high pressures (chung et al. 1988). higher alkanes are below the critical temperature and will condense, and the condensate is miscible with oil. prausnitz et al. (1999) have provided a list of specific mailto:neogi@mst.edu 2 volumes of mainly noncondensable gases in a liquid. they appear to be the same as those of organic liquids. thus, the specific volume of co2 at 25ºc is shown as 1.25 cm3/g. the difficulty in characterizing heavy oil is significant. it is a mixture of high molecular weight compounds that has a variety of structures. when we look at the molecular weight distribution, such fractionation does not imply that in a cut, the chemistry of oil molecules is the same. similarly, if we fractionate the oil by chemical types, it does not mean that in a fraction the constituents have close molecular weights. in addition, different oil fields yield different oil types (banerjee 2012; speight 2009; subramanian et al. 1996). all thermodynamic and transport properties are reported after they have been suitably weighted by the above distribution, where these weights change according to the property under consideration. further along these lines, the higher molecular weight fraction contains a group of compounds called asphaltenes. these are primarily aromatic but quite complex in structures, often containing heavy metals, and vary not only from one molecule type to another but also from one oil field to another. asphaltenes precipitate in presence of solvents of small molecular weights. the precipitates appear as small gelatinous masses, and the largest amount is seen with propane and the lowest with co2. there has been considerable amount of work in the thermodynamics of asphaltene precipitation (burke et al. 1990; nghiem and coombe 1997; buckley et al. 1998). asphaltene precipitation is not important in this work but will appear from time to time. the reason is that when the dynamics are studied for either measurement of transport properties or displacement process in the laboratory, the asphaltene precipitation is seen well after the experiments are over, that is, it appears to be a very slow process. when we look at the process itself, we exclude those with the same outlet well as inlet (upreti et al. 2007), although many remarks of what we say for systems with separate injection and production wells also hold there. the schematic is shown in figure 1. the original experiments by butler and mokrys (1989) in a vertical heleshaw cell showed small recovery. however, later work on two-dimensional sand packs showed much higher yields and since then has received the attention of many investigators. the yield is also low when co2 is used. co2 is still a suitable gas for sequestering in heavy oil reservoirs (bachu and shaw 2003; shaw and bachu 2002). small oil production can be enough to pay for the project. in sections below, we have looked at suitable correlations of both thermodynamic and transport properties, followed by models on the recovery process where these properties come into play. figure 1—schematic view of a vapex process. the height of the pay zone h is shown and a sharp solventheavy oil interface is shown. physical properties of oil with solvent physical properties in general can be divided into thermodynamic and transport properties. there have been good amount of measurements reported, but their correlations are scattered. as mentioned earlier, there is one solvent vapor zone solvent injection interface drained oil collection oil zone h 3 key difficulty in characterizing chemistry and molecular weight distribution of the components in heavy oil; hence, how to arrive at properly weighted physical properties continues to be debated. one feature of heavy oil is that the molecular weights of all molecules are large, a situation found in polymers where individual molecules are all large even though a molecular weight distribution exists. there can also be chemical differences among polymer molecules, such as chain branching. flory (1953) has shown that in polymer solutions, the thermodynamic properties should be expressed in terms of volume fractions rather than mole fractions. in crude oils, the specific chemistry of oil is bundled under the name of the oil field from which it was extracted. flory had problems in getting his point of view accepted, and one editor turned down request of our manuscript for review with a comment that they only look at materials with fully specified chemistry. as discussed later, the same volume based approached can be taken to understand the transport properties. thermodynamic properties one key assumption made here is that, for an oil-solvent pair, their volumes are assumed to be additive. when the solvent is co2, it becomes difficult to determine what its specific volume will be in oil. in this case, it is back calculated from the data. chung et al. (1988) have reported extensive data on bartlett heavy crude and co2. under additivity of volumes, 𝜌 = 𝜌𝑠𝜙 + 𝜌𝑜(1 − 𝜙),……………………………….………..…………………………………..……….(1) and 𝑓𝑇 = 𝑐𝜙 + 𝑓(1 − 𝜙),………………….…………………………..………………………….……..……..(2) where ρ is the density, the volume fraction of the solvent and the subscripts s and o stand for solvent and oil. now, oil and solvent can be split into the hard molecular dimensions and free volume. here, f and c are the free volume fractions of oil and co2 and the subscript t stands for total. chung et al. (1988) provide the densities of oil, with or without co2, at three different temperatures, and pressures going up to 5000 psi. these provided tran et al. (2012) with a way of calculating f and c and the pressure and temperature dependence of f (namely, through the isothermal compressibility and the thermal expansion) but the data were sensitive enough to obtain the temperature dependence of c only (and not the pressure dependence). the free volume c was about four times the value of f. in co2 oil recovery, co2 swells oil and this feature is thought to be important in squeezing oil out of narrow pores and crevices. tran et al. (2012) found that dissolved co2 has a specific volume similar to organic liquids, and this volume adds to the volume of oil. the resulting swelling gave then the welker and dunlop (1963) correlation for swelling in day crude, kansas: 𝑆𝐹 = 1 + 3.5 × 10−4𝑆,……………………….………………....…………………………………..…….(3) in eq. 3 the swelling factor sf=volume occupied by oil containing co2/(volume occupied by the same mass of oil without co2 at 1 atm and the same temperature) and s=standard cubic feet of co2/bbl. the result of welker and dunlop (1963) has been checked out with a number of other oils by chung et al. (1988). in addition, eq. 3 led them to the specific volume of co2 in oil of 1.06 cm3/g, where prausnitz et al. (1999) suggested 1.25 cm3/g. another discovery of tran et al. (2012) was that the co2 solubility data in chung et al. (1988) fitted henry’s law well. henry law coefficients themselves at different temperatures showed an activation energy. furthermore, for the subcritical case (temperature below tc) henry’s law held even during the phase change of co2 from vapor to liquid. due to the large types of solvents available, as discussed earlier, mohan et al. (2017a) performed a volume fraction-based analysis of solubility following flory-huggins theory (1953) and the data on lloydminster crude by yang and gu (2006a). the additivity of volumes was assumed. supercritical gases, methane and co2 which condensed but the condensate was not miscible with oil, both showed constant henry’s law type behavior. however, the condensable higher alkanes did not, particularly when the saturation vapor pressure was approached. there are two parameters in the system. the first is x, the ratio between the size of an average oil molecule to that of a solvent molecule, which was found to be very high for all the above 4 solvents. it can be set to infinity. the second is χ, flory-huggins coefficient, which was found to be greater than ½ for ethane and propane. this crosses the limit of solution stability, and it was assumed that asphaltene will precipitate. finally, the surface tension of co2-oil solution exposed to pure co2 has been modeled (tran et al. 2012). there are two aspects to the chemical potential of co2 at the interface. the first is the usual mixing entropy, which can be modeled using simplified flory theory using volume fractions. the second is the surface work, which uses work done by surface tension over a reference state (miller and neogi 2008). the results fit the data of rojas and ali (1988) of aberfeldy heavy oil, alberta, canada, quite well. the model comes with three parameters, all of which have physical interpretations. it should be emphasized here that, in the correlations discussed so far, there is no need to know the molecular weight or molecular weight distribution, or information on species distribution. like in polymers, volume fractions are all we need. further, the assumption of additivity of volumes does not lead to problems where we end up with results that cannot be fitted to the data, or on fitting yields unphysical values of parameters. transport properties the diffusivity of a solvent in heavy oil is very concentration dependent. when the solvent enters the oil, the leading toe which is at very low solvent concentration shows a very low diffusivity. it severely limits the rate of penetration. further, the solvent also decreases the viscosity of oil. thus, the viscosity of oil fell to 2% and to 10%, both for co2 in heavy oil (welker and dunlop 1963; chung et al. 1988). consequently, it is not just the viscosity, but also its concentration dependence, that is of importance, and the lack of penetration. considered below are some theories of diffusivity and the difficulties in measuring those. when the liquid under consideration has a high density in its pure form, its free volume (total volume less the hard volumes of the molecules) is low. generally, when a solvent molecule or a segment of oil moves, it has to overcome an arrhenius type of activation energy barrier. as a result, both diffusivity and viscosity show such temperature dependence. however, when the free volume is low, the available space becomes restricted, and this restriction controls mobility. fujita (1961) argued that as the free volume of the solvent was much larger (earlier we had said that c was four times larger than f for co2 in heavy oil) the free volume grows as the solvent enters oil and viscosity of the solution drops. the free volume theory provides the expression for viscosity of the form (cohen and turnbull 1959), 𝜇 = 𝑅𝑇𝐴𝜇𝑒 𝐵𝜇 𝑓𝑇 ,…….……………………………………..………..………………………………...……..(4) where aμ and bμ are constants and ft is given by eq.2. eq.4 can be rewritten for convenience as 𝜇 = 𝜇𝑜𝑒 𝐵𝜇(𝑓−𝑐)𝜙 𝑓.𝑓𝑇 ,……….…………………………...……………...……………………………….………(5) where μo is the viscosity of the pure oil. since c is larger than f, the argument in the exponential of eq. 5 is negative. tran et al. (2012) compared the extensive data by chung et al. (1988) on bartlett oil to eq. 5. at the end, after all parameters were obtained, they could actually predict the viscosity at one temperature as a function of co2 partial pressure which showed excellent comparison with the actual data. two fitted results are of interest, bμ = 1.000 and f* the reference free volume fraction in pure oil at 1 atm and 75ºf is 0.02088. in general, the free volume fraction of oil decreases with increasing pressure and increases with temperature. under free volume theory diffusivity becomes (vrentas and duda 1979) 𝐷 = 𝐷𝑜𝑒 𝐵𝑑(𝑐−𝑓)𝜙 𝑓.𝑓𝑇 ,………………………………..…..……………...………………..…………….….……(6) note that this time the argument is positive and bd is generally set to bµ. there are a large number of diffusivity data of solvents in heavy oil. the difficulty with these is that to obtain diffusivity, one needs the solution to a boundary value problem where the diffusivity is a strong function of solvent concentration. one such solution exists (neogi 1988). if a mathematical solution is obtained by assuming that the diffusivity is a 5 constant, it leads to a concentration averaged diffusivity which is not possible to interpret and difficult to use. in addition, there are some items in solving a boundary value problem that need to be addressed. to write the diffusive flux as 𝑗𝐴 𝑜 = −𝐷∇𝜌𝐴 = − 𝐷 𝑣𝐴 ∇𝜙,………………..…………..……………..………...………….……….……….. (7) where 𝜌𝐴and 𝑣𝐴mass concentration and specific volume of the diffusing species a, it is necessary to use volume average velocity, and assume that the specific volumes are constants, that is, volumes are additive (bird et al. 2002) . in general, there will be a convective flux (from the volume average velocity above) in addition to eq. 7, whether or not convection is being forced. consider also a special case where there is a drop of heavy oil exposed to a vapor or half-filled test tube with oil exposed to vapor. the vapor will enter the oil through dissolution and diffusion and swell it. if the volume of oil under consideration is increasing, then that alone will give rise to a convective term. when the problem under consideration is a moving boundary problem, the boundary condition at the liquid-vapor interface becomes a jump boundary condition. slattery (1972) has provided proofs of the above. as mentioned earlier, there are a large number of experimental works, a review by ghanavati et al. (2014), and papers by afsahi and kantas (2007), fedai et al. (2013), zhang et al. (2007), yang and gu (2006a, 2006b, 2008) all of which contain the above errors in some form or another. however, we do not know the magnitude of the error. returning to free-volume theory and eq. 6, if numbers are used there, then eq. 6 approximates as 𝐷 = 𝐷𝑜𝑒𝛼𝜙,…………….………………...….……………………………..………………………..……..(8) where 𝛼 ≈ 𝐵𝑑 𝑓 , which is property of the oil. tran et al. (2012) found �̄� = 𝛼𝜙𝑜~ 10 for co2, and about the same value was found by mohan et al. (2017b) for hexane, heptane and toluene in heavy oil. here, 𝜙𝑜is the solubility of the solvent in oil. one peculiarity of eq. 8 is that at moderate solvent concentrations not much variation in diffusivity with concentration is observed with diffusivities ~10-5 cm2/s. however, it plunges sharply to low values to ~10-9 cm2/s at less than 1% solvent concentrations. this is also seen in solid polymers, where free volume theory holds (vrentas and duda 1979). the consequence is that when the solvent enters oil, the toe is at this small concentration and the small diffusivity controls the rate of penetration into oil. it leads to selfsharpening of the solvent profile which gives rise to a pseudo-interface, sometimes called a concentration shock. instead of looking at the concentration profile in this pseudo-shock region, mohan et al. (2017b) monitored the location of the shock front as a function of time. the changes in the location of the interface is δ𝑥𝑜 = [ 2𝐷𝑜(𝑒𝛼𝜙𝑜−1)𝑡 𝛼(𝜙𝑜−𝜙𝑖) ] 1/2 ,………………………..…………………..……...…………………….….……..(9) where 𝜙𝑜 = 1 as pure solvent was introduced and the initial concentration in oil was 𝜙𝑖 = 0. they contacted heavy oil with solvent (hexane, heptane and toluene) for that purpose and followed the front shown in figure 2. they supplemented this set of experiments with desorption with the object that between the two experiments they would get the two parameters, 𝐷𝑜and �̄� = 𝛼𝜙𝑜. however, desorption was too slow to use and an estimate of 𝐷𝑜was obtained from stokes-einstein equation. note that as in eq. 8, eq. 5 yields 𝜇 = 𝜇𝑜𝑒−𝛼𝜙,……………………………………..……………………...………………………….….…..(10) where viscosity decreases with solvent concentration. like in the stokes-einstein equation, eq. 8 and eq. 10 share exact inverse relation. if only arrhenius type behavior is expected, 𝐷 ∝ 𝜇−2/3 for very viscous liquids (hiss and cussler 1973). in many cases, the entire concentration profile is measured. however, low solute concentrations are not usually reached. fadaei et al. (2013) using light absorption and ghanavati et al. (2014) using x-ray absorption go down to 10 wt % solvent but not less. they find, with some exceptions, diffusivities ~10-5 cm2/s as mentioned earlier. at lower solvent concentrations than above, afsahi and kantas (2007) reach d~10-7 cm2/s using nmr, that is, 6 in the right direction but still a long way to go. where needed, the arrhenius equation is used for viscosity (chun et al. 1988). figure 2—a case where liquid hexane is contacted with heavy oil ( a hauser, kansas) is shown by mohan et al. (2017b) with permission. process design the first to be considered are the recovery and the mechanism of oil production. before offering results on oil recovery in processes in a porous medium as in figure 1, we first look at displacement inside a single pore modeled as a cylinder. tran et al. (2015) observed that the penetration of co2 into oil was extremely low under dynamic conditions. consequently, the line of thought that dissolved co2 penetrated the oil and decreased the oil viscosity does not quite work. however, the displacement velocity seemed relatively unaffected when the viscosity of the liquid increased. a thin film of oil was left clinging to the wall during displacement, which probably offered much less resistance to the displacing co2 than the bare solid wall. so, the conclusion was that heavy oil to very heavy oil does not change the displacement process and remain virtually unaffected by carbonation, actually by the lack of it. note that the velocity of displacement front in an oil reservoir medium is same as that in a single pore. one other feature in mass transfer in porous media is that we should be using dispersivity (gardner et al. 1981). however, when we look at interphase mass transfer, it shows that dispersivity which is an averaged value cannot be used and molecular diffusivity will have to be used (tran et al. 2016). further, lake (1989) has shown that the velocity associated with oil displacement (~1ft/day) is so low that the dispersivity is equal to the diffusivity. consequently, molecular diffusivity is all we need for simulation. the convective-diffusive transport in an oil reservoir of the configuration in figure 1 was first given by butler and mokrys (1989). it provides the recovery rate of 𝑄𝑏 = √2𝑘𝑔φδ𝑆𝑜ℎ𝑁𝑠,……………………………….……………….……………….…..………………(11) where 𝛥𝑆𝑜is the difference between the fractional pore volume containing oil before and after displacement. for perfect displacement 𝛥𝑆𝑜= 1. others are k permeability, g acceleration due to gravity, φ porosity and h is the pay zone height. further, 𝑁𝑠 = ∫ 𝛥𝜌𝐷(1−𝜙) 𝜇 1∫ 𝑙𝑛 𝜙 𝜙𝑚𝑖𝑛 where δ𝜌 is the density difference between pure oil less the solvated oil. ϕmin is the solvent concentration at the end of the shock front of the solvent that has penetrated the oil. finally, h is the height of the pay zone. mohan et al. (2019a) found the concentration profile assumed by butler and mokrys (1989) to be inconsistent with the conservation of solvent equation. however, their final results are not that different even after the concentration dependence of the transport properties as described above, are used. these are 7 𝑄𝑏 = 2√ 𝑘φδ𝜌𝑔𝐷𝑜ℎ 𝜇𝑜 ∫ 𝑒𝛼𝜙𝑜𝜓𝑢 0 (1 − 𝜙𝑜𝜓)𝑑𝜓,………...……………………………....………..………….. (12) where δ𝜌is the density difference between solvated oil and solvent (vapor). here,𝑢 = 𝛿 √4𝜇𝑜𝐷𝑜𝜂𝛷/𝑘𝛥𝜌𝑔 𝑠𝑖𝑛 𝜃 where δ is the thickness over which solvent concentration in oil falls from ϕo to ϕmin in the direction normal to the interface and 𝜓 = 𝜙/𝜙𝑜. this definition of the boundary layer and the profile itself are used to obtain the value of u. if we use a vapor which has a condensate that is miscible in oil, then the ϕo=1. the resulting drainage is calculated in this case to be mainly the solvent. for most solvents, known to us �̄� = 𝛼𝜙𝑜~10. this case corresponds to low solvent penetration and low oil recovery in general. the region occupied by can be divided roughly into a dry part and a thin sliver of oil at the interface with very high amount of solvent. the end result is that if free volume theory and 𝐷 ∝ 1/𝜇are used then both production and fraction oil at the effluent end will be very low, perhaps unacceptably low. if arrhenius equation and 𝐷 ∝ 1/𝜇2/3are used, then there will be a small amount of improvement. finally, if d~10-5 cm2/s and arrhenius equation are used then both quantities will improve to possibly acceptable results. the second feature is that there are many sandpack results but they are not fully organized. butler and mokrys (1989) conducted experiments in hele-shaw cells and verified k and h dependence. many other experiments using two-dimensional sand packs followed and showed often a result that was proportional to h rather than ℎ 1/2 as in above. nenninger and dunn (2008) correlated results of many experiments and showed that the recovery was given by mass flux (or mass velocity) 𝑊𝑏 = 43550(𝑘φ/𝜇𝑜)0.51,. …………………………..…………………….……………..……………(13) where 𝑊𝑏 = 𝑄𝑏𝜌𝑜/ℎ. note that the variables on the right appear in the same manner as in eq. 12. eq. 13 is in a form of results of dimensional analysis. for a more formal dimensional analysis, if we take 𝑊𝑏to be a function of other variables 𝜇𝑜 , 𝐷𝑜 , 𝛼, 𝛷, 𝛥𝜌, 𝑔, 𝑘, 𝜙𝑜 , ℎ then there are 7 variables and 3 dimensions (mass, length and time) leading to 4 dimensionless groups (leaving aside the quantities that are already dimensionless) according to buckingham-pi theorem (buckingham 1914). these groups are found to be reynolds’ number 𝑅𝑒 = 𝑊𝑏ℎ/𝜇𝑜the ratio between the inertial and the viscous forces, froude number 𝐹𝑟 = 𝛷𝑘𝛥𝜌 𝜇𝑜 √ 𝑔 ℎ the square-root of the ratio between kinetic energy and potential energy due to gravity, a square of aspect ratio 𝐴𝑟 = 𝛷𝑘/ℎ2 , and schmidt’s number 𝑆𝑐 = 𝜇𝑜 𝛥𝜌𝐷𝑜 . because of the way φ is associated with k in eq. 13, φ has been considered only in a product φk. it is reasonable to assume that in most cases 𝛼𝜙𝑜~ 10 and it is not considered to be a variable (mohan et al. 2017b). do that occurs is difficult to find, and stokes-einstein’s equation is used to calculate this value (mohan et al. 2017b). note that because of the inverse relation between viscosity and diffusivity in stokes-einstein equation, 𝐷𝑜 = 𝐵/𝜇𝑜where b is a constant. fr/re has been plotted against √(ar√.sc) using the data compiled by nenninger and dunn (2008) in figure 3a for sandpacks and fit to 𝐹𝑟/ 𝑅𝑒 = 4 × 10−6𝐴𝑟1/2𝑆𝑐1/4 ,………..……..…....……………..….……………………..……..….. (14a) there are 8 outliers in their group of 43 on sandpacks that have been omitted. the fit has been stretched in figure 3b to show that the fit is excellent at small values near the origin. this is good, because field results will have values of ar close to zero on this scale. the data on hele-shaw had scatter that was too high and were dropped. eq. 14a can also be re-expressed as 𝑊𝑏 = 25 × 104√(𝑘𝛷/𝜇𝑜) (δ𝜌)5/4𝑔1/2𝐵1/4 ℎ 1/2 ,………..…………….……………..……………..……..…..(14b) or, in terms of qb, 𝑄𝑏 = 25 × 104√(𝑘𝛷/𝜇𝑜)(δ𝜌)1/4𝑔1/2𝐵1/4ℎ1/2,………………..………………………..……..……...(14c) which supports the result that 𝑄𝑏 ∝ ℎ 1/2 (mohan et al. 2019b). the above theoretical results assume that flow is given by darcy’s law, 8 𝑣 = − 𝑘 𝜇 𝛻𝑃,……………………………………………….………………………………..………..…….(15) where p is the dynamic pressure, a sum of static pressure p and the potential energy due to gravity. brinkman equation is (brinkman 1947) ∇[𝜇∇𝑣] − 𝜇𝑣 𝑘 − ∇𝑃 = 0,……………………………………………………………………..………..…..(16) quantities in bold in the above equations are vectors. note that if the first term in eq. 16 is omitted, eq. 15 results. the velocity here is the superficial velocity. however, in conservation of species equation, the interstitial velocity 𝒗/𝛷 is used. when flow profile is introduced, mohan et al. (2019a) used an approximation to show that 𝑄𝑏could reach a height dependence of h but only at larger values of k. cuthiell and edmunds (2012) using tetrad, have provided the results of their simulation that shows 𝑄𝑏is proportional to h. it is concluded that as sandpacks offer large values of k only, those result may well support h instead of h1/2. the vapor oil-interface is not sharp, and cuthiell and edmunds (2012) put together a model expression for fractional flow as a function of fractional volume occupied by the oil, to obtain a diffuse interface. mohan et al. (2019a) obtained an approximate shape of the vapor-oil interface as linear except at very large times and near the top end. finally, there is the issue of stability of the interface. tran et al. (2016) have shown that when displacement is accompanied by mass transfer, the interface is stable to disturbances of large wavelengths but unstable to disturbances of small wavelengths. mass transfer and accompanied reduction of viscosity of the oil play important roles. if there is no mass transfer, the situation is reversed where disturbances of large wavelengths are unstable and those at small wavelengths are stable. there are some differences between the above stability results and the present case in that the directions of flow here are mainly parallel to the interface, and the displacement velocities are conventionally about 1 ft/day which appears to be a lot larger than in the present case. (a) (b) figure 3—(a) plot of fr/re against √𝑨𝒓√𝑺𝒄 in sandpacks from the compilation by nenninger and dunn (2008). (b) the same data as in figure 3(a) replotted differently to show the region near the origin. from mohan et al. (2019). on solvent species in the immiscible displacement study of heavy oil in a sand pack with co2, rojas and ali (1988) found that the reduction of surface tension was the most important reason for improved oil recovery. the data compiled by nenninger and dunn (2008) contain measured values of surface tension where the vapor phase is almost saturated. the values are often low. since the vapor phase is posed to condense, the question arises as to what the dynamics of an oil drop floating on surface the solvent liquid will look like. heavy oil when contacted with 0.0e+00 5.0e-06 1.0e-05 1.5e-05 2.0e-05 2.5e-05 3.0e-05 3.5e-05 0 2 4 6 f r/ r e √(𝐴𝑟√𝑆𝑐) 0.00e+00 5.00e-06 1.00e-05 1.50e-05 2.00e-05 2.50e-05 3.00e-05 0.01 0.1 1 10 f r/ r e √(ar√sc) 9 a solvent, shows a very clear interface as shown in figure 4a and 4b. the interface looks clean but subsequently deformation show a wavelike character that suggests rayleigh-taylor instability due to gravity imbalance, figure 4a, observed when the liquid on the top is heavier than the liquid at the bottom (miller and neogi 2008). the wavelengths associated with this instability should be of the order of basic dimension of the drop ~0.5 mm. however, one wave very quickly develops which is pointed and sharp, figure 4b. this “wave” would correspond to that of zero wavelength and zero surface tension. in general, there can be a dynamic surface tension, that is small but positive, but quickly disappears to the equilibrium value of zero which is the accepted value for miscible systems. all photographs were taken almost instantaneously after layering the drop of oil on the surface of the solvent. (a) (b) figure 4—inverted drop of heavy oil on glass substrate at 30oc flooded with (a) hexane and heptane, where heptane shows a pointed end corresponding to zero surface tension for rayleigh-taylor instability and (b) shows the rayleigh-taylor waves eq. 12 shows that the choice of the solvent species is felt through 𝐷𝑜, 𝜙𝑜 and 𝛼𝜙𝑜. there are practically no data on diffusivity at infinite dilution in species of interest, however, the estimates show that there is not much difference among species (mohan et al. 2017b). similar estimates show that usually 𝛼𝜙𝑜~10 (tran et al. 2012; mohan et al. 2017b). further, as the temperatures of operation are below the critical temperatures of solvents used, the vapor will condense and be miscible with oil. thus, in that case 𝜙𝑜 = 1. thus, one does not expect any differences in performance among species in the first approximation. this is observed by nenninger and dunn (2008) who have surveyed results for co2, ethane, propane and butane. however, one point needs to be cleared up. activity is defined as the pressure of the vapor p/saturated vapor pressure pv. in most cases the data tabulated by nenninger and dunn (2008) show activity of ~1. however, there are some which are below to well below that activity and are expected to show lower values of 𝜙𝑜 and 𝛼𝜙𝑜. to the first approximation, activity ~𝜙𝑜, yet even at below 0.5, this co2 data show no significant deviation from nenninger and dunn (2008) correlation, eq.12. on the other hand, the outliers to nenninger and dunn (2008) correlation have activity below 1 but not so much below as 0.5. it is necessary to go through experiments which attempt to correlate qb to the activity of the vapor. such data do not exist at present. none of these show asphaltene precipitation which according to mohan et al. (2017b) is very slow. they also discuss the bounds of operation for an extremely fast rate of precipitation and for extremely slow rate of precipitation. if steam is used (in conjunction with vapor) the end results could be oil-in-water (o/w) or water-in-oil (w/o) emulsion. this issue has been addressed by abdulmohsein et al. (2021) using sodium dodecyl sulfate or sds, an anionic surfactant, cetyl trialkyl ammonium bromide, ctab a cationic surfactant, and igepal co-530, a nonionic surfactant c9e6 close to the hydrophile-lipophile balance. the emulsion samples, viewed under microscope of o/w emulsions are shown in figure 5. experiments also had sio2 or al2o3 nanoparticles. the systems containing the nonionic surfactant were difficult to flocculate in presence of nanoparticles, even on raising temperatures when the surface active property of nonionics, disappear. in general, the phase separation 10 was very quick, but some water was left in the oil and did not separate in a day’s time, because of high viscosity of oil. figure 5—confocal microscopy images of o/w emulsion using sds on the left and a bicontinuous structure using igepal co-530 at high oil: water ratio on the right. oil is fluorescent and water appears black. discussion we were not able to find examples of vapex process used in industry. it appears that the fall in price of oil has made this technology into one that is unsuitable for a long time, but trade journals suggest that view is changing (rassenfoss 2017). one issue is where one would get the solvent from, and one interesting feature here is an unconventional oil source of shale oil, which on pyrolysis provides naphtha, typically 5-6 or 6-12 carbon aliphatics (beckwith 2012). if we look at the process itself, the correlation by nenninger and dunn (2008), eq. 13 speaks a volume that higher the oil viscosity, the output will be lower. further, the formation cannot be “tight.” one key feature that has been obtained is the fact that solvents like propane and butane would have a very high value of 𝛼𝜙𝑜 ~10. if we use co2 at a very high pressure of ~3000 psi, there too, we will see high value of 𝛼𝜙𝑜. solvents with high values of 𝛼𝜙𝑜do not penetrate the oil much hence give rise to low recovery. consider now co2 where the pressure is lowered. the solubility 𝜙𝑜 is proportionately lowered. now, a lower value of 𝛼𝜙𝑜implies more penetration of co2 and better recovery but lower value of 𝜙𝑜 also implies lower carbonation. it would seem to suggest that there could be an optimum pressure. other than changing pressures, other features have been suggested (and we merely note these without review) are that the gas used be heated. heat transfer by itself would be good in lowering the viscosity of the crude oil, and then mass transfer would lower the viscosity still further. gas mixtures have also been proposed for use. however, if a gas mixture is made of one condensable and other non-condensable (such as methane) gases, then the non-condensable gas would form a “vapor blanket” and the condensable gas has to diffuse through it. it sets up a significant mass transfer resistance in the gas phase where for a single component there is none. further, some more complex molecules such as dimethyl ether, are receiving attention at present, but nothing is known about its impact here. finally, it is worth reminding that no report of field study has appeared yet although there are some indications that some start has been made. the field test by itself will show another set of problems and improvements. 11 conclusions vapex process uses no water to extract heavy oil, and that is its main advantage. more recent results than the seminal ones by butler and mokrys (1989) have shown yields to be significant in sandpacks and hence have been pursued vigorously. we have reviewed here the components needed for a simulation and find the perhaps the present call for success may be premature but show that the process could be improved. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature 𝐴𝜇 = constant 𝐵𝜇 = constant 𝐵𝑑 = solvent segment needed for a jump during diffusion 𝑐 = free volume fraction of co2 𝐷 = diffusivity 𝐷𝑜 = diffusivity at infinite dilution 𝑓 = free volume fraction of oil 𝐹𝑟 = froude number 𝑓𝑇 = total free volume fraction of oil 𝑔 = acceleration due to gravity ℎ = total pay zone height of the system 𝑗𝐴 ° = diffusive flux 𝑘 = permeability 𝑃 = dynamic pressure 𝑄𝑏 = recovery rate 𝑅 = gas constant 𝑅𝑒 = reynold’s number 𝑡 = time 𝑇 = temperature 𝑆𝐹 = swelling factor 𝑆𝑐 = schmidt’s number 𝑣𝐴 = specific volume of the diffusing species a 𝑊𝑏 = mass flux greek letters 𝛼 = concentration dependence term δ𝜌 = density difference δ𝑆𝑜 = difference in fractional pore volume δ𝑥𝑜 = changes in location of interface 𝜇 = viscosity 𝜇𝑜 = viscosity of pure oil 𝜌 = total density 𝜌𝐴 = mass concentration of the diffusing species a 𝜌𝑜 = density of pure oil 𝜌𝑠 = density of pure solvent dissolved in oil 12 𝜙 = volume fraction of solvent 𝜙𝑜 = solubility of solvent in oil 𝜙𝑖 = initial concentration of solvent in oil 𝛷 = porosity references afsahi, b. and kantzas, a. 2007. advances in diffusivity measurement of solvents in oil sands. j. can. pet. technol. 46(11): 56–61. petsoc-07-11-05. bachu, s. and shaw, j. 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zhang, x., fulem, m., and shaw, j.m. 2007. liquid-phase mutual diffusion coefficients for athabasca bitumen+pentane mixtures. j. chem. eng. data. 52(3):691–694. vijitha mohan received her phd in chemical engineering from missouri university of science and technology and served as a lecturer after graduation. her research interests lie in heavy oil recovery. she acquired her b.tech in chemical engineering from university of madras and m.s in chemical engineering from mississippi state university. she is at present a research associate at university of calgary, canada. she has three prior publications in this area. parthasakha neogi, spe, is a professor of chemical engineering at missouri university of science and technology, where he has worked as faculty for the last 36 years. his research interests are in wetting, surfactants and polymers, and in interfacial transport phenomena. he holds b.tech. (hons.) from the indian institute of technology kharagpur, m. tech. from the indian institute of technology kanpur, and ph.d. from carnegie-mellon university, all in chemical engineering. baojun bai, spe, is the lester r. birbeck endowed chair professor of petroleum engineering at missouri university of science and technology. previously, bai was a reservoir engineer and head of the conformance control team at the research institute of petroleum exploration and development, petrochina. he also was a post-doctoral scholar at the california institute of technology and a graduate research assistant at the new mexico petroleum recovery research center for eor projects. bai has over 20 years of experience in the area of eor. he holds phd degrees in petroleum engineering from new mexico institute of mining and technology and in petroleum geology from china university of geoscience-beijing. bai has published more than 130 papers in peer-reviewed journals and international conferences. he served on the jpt editorial committee for the feature “eor performance and modeling” during 2007-2013. he is a technical editor for spe journal and spe reservoir evaluation and engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1185 received february 23, 2021; revised march 15, 2021; accepted april 6, 2021. *corresponding author: dongzhenzhen1120@hotmail.com 1 optimization of flowback operations for shale gas wells cheng dai, research institute of petroleum exploration and development, sinopec group, beijing, china; zhenzhen dong*, xi’an shiyou university, xi’an, china; xiang li, ennosoft ltd, beijing, china; weidong tian, xi’an shiyou university, xi’an, china abstract hydraulic fracturing has become one of the most important aspects of well completion because of the everincreasing development of unconventional oil and gas reservoirs. uncontrolled fluid flowback after the fracture treatment has the potential to impact well productivity and profitability, as aggressive flowback strategies can damage a well’s completion while conservative flowback procedures may hinder near-term economic performance. the goal of this study was to develop an integrated flowback model of fracturing fluid that can accelerate production while minimizing the risk of a decrease in the estimated ultimate recovery or a damage to the productivity of the well. first, by considering the complex situations occurring during fracturing fluid flowback, a fluid-solid coupling numerical model corresponding to fracture closure was established and solved with the finite-element method. a proppant transport model was established to investigate the time and displacement of proppant migration within the fracture. fluid velocity in the fracture created as a result of flowback was considered, along with its effects on proppant movement and localized fracture closure. finally, by integrating the two-phase tubing flow model, the proppant transport model, and the fluid-solid coupling model, an integrated reservoir-fracture-wellhead model was established, and the principles and methods for designing the flowback scheme were determined. the work considered actual data and information on flowback in shale gas wells from the available literature, as well as our own experiences. the results reveal how choke management, or flowback strategies, can impact potential damage mechanisms in the reservoir, completion, and wellbore. the proposed model can provide optimum flowback design and therefore lead to maximized near-wellbore fracture conductivity and maximum-attainable conductive length in communication with the wellbore. introduction multistage fracturing technology for horizontal wells has been applied to shale gas development for many years and has achieved great success within the history of the oil and gas industry. to create hydraulic fractures in horizontal wells, a high volume of fracturing fluid, potentially including slick water and various additives, is injected into the shale formation, along with proppant. the oil industry has developed a suite of tools or models to mitigate proppant flowback, including forced closure, resin-coated sands, deformable proppants, mechanical screens, fracture packs, resin injection, and surface modification agents (shor and sharma 2014). however, there are no standard industry practices or recommendations for well flowback to maximize well productivity and minimize proppant flowback. current practices for flowback operations are, in general, based on rules-of-thumb and are embodied in mailto:dongzhenzhen1120@hotmail.com 2 the confidential flowback operational procedures of various well operators. such rule-of-thumb flowback practices can cause extensive tensile rock failure, excessive proppant flowback, fines migration, and scale formation (barree and mukherjee1995). in tight sandstone gas reservoirs usually produced by single-wing hydraulically induced fractured wells, the forced closure flowback process is used for fracturing fluid flowback within 20 to 30 minutes after the treatment of the fracturing pump (canon et al. 2003). while for shale gas wells, most multistage fracturing horizontal wells undergo more than 3 days of soaking, coiled tubing is used to drill and grind the bridge plug of the wellbore, and then multistage mixed flowback testing is carried out. fracturing fluid loss, microfracture communication, and shale immersion in artificial fractures during soak affect reservoir properties near the wellbore and then affect gas well productivity. according to the fracturing technology, string characteristics and formation, the flowback process of shale gas wells usually goes through three stages: closed control, maximum production, and stable production. according to our experience, the whole flowback period lasts around 2 weeks, and flowback rate could be up to 30% to 40%. thus, unlike tight gas wells, procedure and time for flowback operations are dictated by economic considerations and reservoir properties for shale gas wells. sometimes, it is desirable to conduct flowback operations immediately after the fracturing treatment so that the well can benefit from nondissipated reservoir pressure. there are also reservoirs where wells show better production performance after “seasoning,” when fracturing fluid is allowed to dissipate in the formation for several weeks before initiating flowback procedures. in all cases after the flowback is initiated, it is desirable to flow the well back at the maximum technically and operationally allowable rate so that the well can be put into production quickly. at the same time, the flowback rate should not exceed certain limits defined by the formation and type of injected materials, as exceeding these limits may result in excessive flowback of propping material, formation destabilization, and, as a result, poorer well production performance. thus, the optimization of fracturing fluid flowback strategy is mainly embodied in optimizing flowback timing and flowback rate. early modeling work to understand proppant transport behavior was based on fluid flow velocity, proppant transport, and settling velocity predicted by broad correlations (bratli and risnes 1981). later work (robinson et al. 1988; ely et al. 1990; biezen et al. 1994) used probabilistic methods to calculate two-dimensional (2d) grid block failure of fracture proppant packs. a critical flow rate depended on proppant size, and closure stress was the key cause of catastrophic pack failure. shortly after, a different approach based on novotny’s work was introduced that described the movement of individual proppant grains. rather than directly modeling the effects of fluid, these studies (asgian et al. 1995; gidley et al. 1995; andrew and kjorholt 1998; parker et al. 1999; crafton 2010; wang et al. 2020) added point-drag forces to grains to calculate the viscous effect of fluid. now, a fluid-solid coupling numerical model corresponding to fracture closure has been established and solved with the finite-element method (fem). this paper presents this model, along with a coupled proppant transport model to investigate the stability of proppant packs, and makes recommendations on flowback procedures. flowback mechanism model the flowback model is a system of mathematical equations that characterize the pressure distributions and fluid flow in hydraulically fractured reservoir rock and well piping over time as a function of wellhead pressure or choke size. the mathematical model of reservoir fluid flow showing fracturing fluid flowback is the same as the model showing fracturing fluid injection. the proppant particles suspended in the fracturing fluid enter the hydraulic fracture system during the course of fracturing fluid injection, but they cannot enter the matrix pore given the size scale (nanoscale matrix pore versus millimeter diameter proppant). during flowback, proppant particles in the hydraulic fracture system flow under natural 3 convection, as does the fluid. if reservoir pressure drops, the fluid leaked into the matrix during the fracturing fluid injection period may gradually release into the fracture during the flowback period. the flow of fluid through the fracture system is driven by viscous and gravity forces, simultaneously carrying suspended proppant particles. proppant particle flow is propelled by both vertical forces, such as gravity and buoyancy, and horizontal forces, such as drag, inertia, and collision. fluid flow in the matrix is propelled by viscous and gravity forces, and does not carry proppant particles. during the flowback of the fracture fluid, the fluid first flows to the fracture, flows next to the horizontal wellbore along the fracture, and then arrives at the wellhead along the wellbore (horizontally and vertically). thus, to simulate the whole process of fracturing fluid flowback, one should simulate the flow in the well, as well as through the reservoir and/or along the hydraulic fracture. figure 1 illustrates an embodiment of the flowback model including submodels. it incorporates a horizontal well model, reservoir model, and fracture flow model. 1) the horizontal well model is a two-phase pressure loss correlation that calculates the fracturing fluid and gas flow rates in the well over time as a function of the wellhead pressure. the horizontal well model receives input (bottomhole pressure and fluid velocity) from a proppant transport model and a fluid-solid coupling flow model. 2) the proppant transport model simulates the movement of particles along the fracture. 3) the fluid-solid coupling flow model incorporates the output of a fluid-fluid displacement model within the fractures, a model of the geomechanical behavior of the formation rock, and a reservoir model that models the inflow of fluid from the reservoir into the fractures.  the geomechanical model models the interaction among the stresses, pressures, and temperatures in the reservoir rock and the hydraulic fracture.  the fluid-fluid displacement model models the displacement of gas by hydraulic fracturing fluid in the reservoir rock and also the displacement of the hydraulic fracturing fluid by the resident reservoir fluids.  the reservoir model models the physical space of the reservoir by an array of discrete cells delineated by an irregular grid. due to the high conductivity of hydraulic fractures, the flow of the fracturing fluid can be considered darcy’s flow. the interaction of the fracturing fluid and the proppant flow is coupled by the equivalent viscosity. figure 1—schematic representation of the component parts of a flowback model. mathematical model and discretization assumptions. the following assumptions were made: (1) the flowback model comprises four interconnected domains, including wellhead, horizontal well, proppant transport model horizontal well model fluid-solid coupling flow model geomechanical model fluid-fluid displacement model reservoir model c o u p li n g 4 fractures, and matrix. (2) a set of fine grids with high permeability was used to characterize the primary fracture, which has a half-length (lf), width (wf), and height (hf). (3) proppant transport includes the drag force, inertia force, and collision force. (4) the proppant settlement and the change in proppant bed height occur due to hydraulic fracture closure. horizontal well flow model. fluid flowing in a wellbore will experience pressure loss. pressure loss can be categorized as hydrostatic, frictional, or kinetic. for wellbores, kinetic loss is often minimal and can be ignored. many fluid correlations can be derived empirically that account for hydrostatic and frictional fluid losses in a wellbore under various flow conditions, including modified beggs and brill, petalas and aziz, flanigan, and modified flanigan. in this study, the modified beggs and brill method was used to calculate the pressure loss along the wellbore. fluid-solid coupling model. geomechanical governing equation. we treated the porous medium as the superimposition of two continua: skeleton and fluid. the physical model was based on the governing equations of quasistatic poroelasticity (biot 1941, 1956; rice and cleary 1994). we assumed the porous medium to be of isotropy and of infinitesimal transformation and the fluid in the porous medium to be isothermal, single-phase, and compressible. the governing equations for fluid flow and mechanics were taken from mass and linear-momentum balance, respectively. constitutive relationship for solid rock can be written as (cook et al. 1974): (𝜎 − 𝜎0) + b(𝑝− 𝑝0)𝑰 = 𝑫휀̃,…………………………………………………………………………….….(1) where σ is the cauchy total stress tensor; b is the biot’s coefficient; p is the pore fluid pressure; i is thee unit matrix, i = [1 1 1 0 0 0]𝑇; d is the elastic tensor matrix; and 휀̃ is the linearized strain tensor under the assumption of infinitesimal transformation. the strain tensor, 휀̃ , is related to the displacement vector, �̃�, via the kinematic compatibility relations as follows: 휀̃ = 1 2 (∇�̃� + (∇�̃�)𝑇),……………………………………………………………………………………(2) the governing equation for mechanical deformation of the rock mass can be written as follows. ∇𝛔 + 𝜌𝑏𝒈 = 0,………………………………………………………………………………………….(3) where g is the gravity vector; 𝜌𝑏 = 𝜙𝜌𝑓 + (1 − 𝜙)𝜌𝑠 is the bulk density; 𝜌𝑓 is the fluid density; 𝜌𝑠 is the solid density; and 𝜙 is the true porosity. true porosity is defined as the ratio between current void volume and current bulk volume. substituting eqs. 1 and 2 in eq. 3, the governing equation for rock can be expressed as: ∇ [ 1 2 𝐷(∇�̃� + (∇�̃�)𝑇) + 𝜎0 − b(𝑝 − 𝑝0)𝑰] + 𝜌𝑏𝒈 = 0…………………………….…………………...(4) fluid flow governing equation. fluid flow in the fractured porous medium during the flowback period experiences three stages: flow in the porous matrix, flow in the fracture, and cross-flow between the matrix and fracture. the governing equations for the three stages of fluid flow are described in the following paragraphs. the fluid flow constitutive equation can be expressed as: 𝜕(𝜌𝑓𝑉𝑝) 𝑉𝑏𝜕𝑡 + ∇(𝜌𝑓𝒗𝑓) = 𝑞 𝑉𝑏 ,………………………………………………………………………………..(5) where 𝑉𝑝 is the pore volume; 𝑉𝑏is the bulk volume; 𝜌𝑓 is the fluid density; q is a sink/source term for 5 fluid; and 𝒗𝑓is the fluid velocity vector, which can be expressed by darcy’s law: 𝒗𝑓 = − 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈),………………………………………………………………………………….(6) where 𝜇 is the fluid dynamic viscosity; k is the permeability vector; and p is the pressure. based on poroelastic theory and darcy’s law, the governing equation for single-phase fluid flow (eq. 5) in porous media can be derived as (see derivative details in attachment 1): 𝑏 𝜕𝜀𝑏 𝜕𝑡 + 1 𝑀 𝜕𝑝 𝜕𝑡 = 𝑞 𝜌𝑓𝑉𝑏 + ∇ [ 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)],………………………………………………………………(7) where 휀𝑏is the bulk stress tensor; m is biot’s modulus, 1 𝑀 = ϕ𝑐𝑓 + 𝑏−𝜙 𝐾𝑠 ; 𝑐𝑓 is the fluid compressibility; k is the skeleton modulus; and 𝑏 = 1 − 𝐾𝑑 𝐾𝑠 . eqs. 4 and 7 constitute the governing equations for the rock and fluid, respectively. after discretizing the equations, the pressure and displacement fields of the model could be determined. numerical discretization. time discretization was applied using a backward first-order and a fully implicit finite-difference scheme. we adopted fem to discretize the objective domain, both for fluid flow and geomechanics (nassir 2013). the benefit of adopting the same method is that fem can easily handle general boundary conditions, complex geometry, and variable material properties. for most heterogeneous grid blocks, permeability is understood to be a 3×3 second-order tensor with stress-dependent elements. because in fem, the governing differential equation for flow is integrated over each discretized domain, permeability can be considered in its full tensor form. in fem, we rewrote eqs. 4 and 7 in an equivalent weak variation form. we partitioned the domain into nonoverlapping elements, ω = 𝑈𝑗=1 𝑛𝑒𝑙𝑒𝑚ω𝑗,…………………………………………………………………………………………..(8) where nelem is the number of elements. a linear space was defined as v={functions v: v is a continuous function in the domain ω and has a piecewise continuous and bounded first partial derivatives in ω, and ν(γ) = 0} the discrete approximation of the continuum problem of eqs. 4 and 7 could then be given as: ∫ ∇𝑁𝑢: 𝜎𝑑ω = ∫ 𝑁𝑢𝜌𝑏𝑔𝑑ω + ∫ 𝑁𝑢𝑡̅𝑑γ γωω ,…………………………………………………………..(9) ∫ 𝑁𝑝 𝜕 𝜕𝑡 ( 𝑝 𝑀 + 𝑏휀𝑏)𝑑ω + ∫ 𝑁𝑝∇𝒗𝑓𝑑ω = ∫ 𝑁𝑝�̅�𝑑γ. γωω ..…………………………………………….(10) when the weight coefficients of solid and fluid were discretized by fem, the variables of displacement field and pressure field were placed on the element vertex. the form of the coefficient matrix is shown in figure 2. it can be concluded that the dimension of coefficient matrix for a model with n nodes is 4n×4n, with the coefficient matrix being a sparse matrix. to reduce the storage space, the coefficient matrix was stored in compressed sparse row (csr) format. the calculation unit used in this study was hexahedron element, as shown in figure 2. 6 figure 2—stiffness matrix form for fem. proppant transport model. proppant transport grid. in a quasicontinuous medium, the flow passage of proppant does not really exist. to visualize the flow passage of proppant, a flow passage of proppant was made equivalent to the fracture element generated by the above algorithm, and the topological relationship between these flow passages was established, as shown in figure 3. figure 3—a schematic illustration of the topological structure of proppant. proppant-governing equation. in the framework of a quasicontinuous medium, the proppant transport process satisfies the mass conservation equation (boronin and osiptsov 2014): 𝜕(𝐶𝜙𝐹) 𝜕𝑡 + ∇(𝐶𝜙𝐹�⃗� 𝑝) = 𝑞𝑖𝑛𝑗,……………..…….………………………………………………………(11) where c is the concentration of proppant in the fracturing fluid, cm3/cm3; ∅𝐹 is the fracture porosity (percentage of the fracture volume in the grid); �̅�𝑝 is the proppant migration velocity, cm/s; and 𝑞𝑖𝑛𝑗 is the proppant injection rate, cm3. proppant migration velocity in a fracture is determined by fracturing fluid flowback velocity (blyton et al. 2015): 7 �̅�𝑝 = 𝑘𝑟𝑒𝑡�̅�𝑓 ,...…………………………………………………………………………………………(12) where 𝑘𝑟𝑒𝑡 is the retardation factor derived from an experiment of fluid-particle flow considering the drag force, inertia force, and particle-to-particle and particle-to-wall collision forces. 𝑘𝑟𝑒𝑡 = 1 + ( 𝑑𝑝 𝑤𝑒 ) − 2.02 ( 𝑑𝑝 𝑤𝑒 ) 2 ,…………..…………………………………………………………..(13) where 𝑑𝑝 is the diameter of proppant, cm; and we is the effective fracture width, cm, which is related to the proppant diameter and the concentration. 1 𝑤𝑒 2 = 1.411 ( 1 𝑑𝑝 2 − 1 𝑤2 ) 𝐶0.8,………………….……………………………………………………......(14) where w is the fracture width, cm. there is an additional settling velocity of the proppant in the vertical direction: { 𝑢𝑝,𝑥 = 𝑘𝑟𝑒𝑡𝑢𝑓,𝑥 𝑢𝑝,𝑦 = 𝑘𝑟𝑒𝑡𝑢𝑓,𝑦 𝑢𝑝,𝑧 = 𝑘𝑟𝑒𝑡𝑢𝑓,𝑧 + 𝑢𝑠 ,.……….………………………………………………………………………(15) where 𝑢𝑠 is the proppant-settling velocity, cm/s, which is generally used as the corrected velocity based on stokes’ law: 𝑢𝑠 = 𝑢𝑠𝑡𝑜𝑘𝑒𝑠𝑓(𝑅𝑒𝑝, 𝐶) = 𝑔𝐷𝑝 2(𝜌𝑝−𝜌𝑓) 18𝜂𝑓 𝑓(𝑅𝑒𝑝, 𝐶, 𝑤𝐹),……….……………………………………….(16) where dp is the proppant diameter, cm; 𝜌𝑝 and 𝜌𝑓 are the particle and fluid densities, g/cm3, respectively; 𝜂𝑓is the hydrodynamic viscosity, mpa.s; and 𝑓(𝑅𝑒𝑝, 𝐶, 𝑤𝐹) is the correction factor, which is related to the particle reynolds number, concentration, and fracture width. it is commonly believed that the reynolds number, particle concentration, and fracture width are independent, so 𝑓(𝑅𝑒𝑝, 𝐶, 𝑤𝑓) can be expressed as: 𝑓(𝑅𝑒𝑝, 𝐶, 𝑤𝑓) = 𝑓1(𝑅𝑒𝑝)𝑓2(𝐶)𝑓3(𝑤𝑓),………………………………………………………………(17) 𝑓2(𝐶) = 𝑒−5.9𝑐,……………………………………………………………………………………….(18) 𝑓3(𝑤𝑓) = ∑ 𝑅𝑖 ( 𝐷𝑝 𝑤𝑓 ) 𝑖 𝑛 𝑖=0 ,……………………………………………………………………………..(19) where ri is a calibrating model parameter. 𝑓1(𝑅𝑒𝑝) has no implicit expression. it is usually calculated iteratively based on the traction model and gravity balance as: 𝑑�⃗⃗� 𝑝 𝑑𝑡 = 𝐷𝑝(�⃗� 𝑓 − �⃗� 𝑝) + (1 + 𝜌𝑓 𝜌𝑝 )𝑔 = 0,………………………………………………………………(20) where: 𝐷𝑝 = 3𝜌𝑓 8𝜌𝑝 𝐶𝑑 |�⃗⃗� 𝑓−�⃗⃗� 𝑝| 𝑟 ,…………………………………………………………………………………..(21) 𝐶𝑑 = { 24 𝑅𝑒𝑝 (1 + 1 6 𝑅𝑒𝑝 2/3) 𝑅𝑒𝑝 < 103, 0.44 103 ≤ 𝑅𝑒𝑝 ≤ 3 × 105. ,……………………………….……………….(22) thus, by combining eq. 20 with eqs. 18 and 19, the particle settlement velocity due to inertial effects can be calculated by eq. 16. numerical discretization. we applied finite volume methodology to discretize proppant-governing 8 equation eq. 11. before presenting the discretization of eq. 11, we present a discussion here. note that in the quasicontinuous medium method, the real fracture structure is not analyzed. the existence of the fracture in the mesh and the direction of fracture propagation are determined by current stress conditions. correspondingly, when calculating proppant migration, the macroscopic migration behavior should be considered with the grid as the basic control body, and the proppant flow between the grids depends on the fluid flow in the fracture. no matter how complex the fracture network is, the change in proppant concentration can be calculated by calculating the interposition equation of the channeling flow in the fracture between different grids. in the framework of a quasicontinuous medium, the total flow between grids can be obtained by darcy's law, and the flow through the fracture can be separated by the average permeability law. if using the explicit central second-order scheme to discretize the flow term in the proppant-governing equation, the discrete form can be written as follows (li et al. 2016): (𝐶𝜙𝐹)𝐶 𝑛+1−(𝐶𝜙𝐹)𝐶 𝑛 δ𝑡 δ𝑉 + ∑ [𝑤𝑐(𝐶𝜙𝐹)𝐶 𝑛 + 𝑤𝑛(𝐶𝜙𝐹)𝑁 𝑛 ](�⃗� 𝑝,𝐼 𝑛+1�⃗� δ𝑆)𝑠 = 𝑞𝑖𝑛𝑗,𝐶δ𝑉,………....……………..(23) where subscriptions c and n are the current grid and neighboring grid, respectively; �⃗� 𝑝,𝐼 𝑛+1 is the particle transport velocity at the interface in time step n+1, which is precalculated; and 𝑤𝑐 and 𝑤𝑛 are the weights of the first-order approximation at the interface between the current grid and the adjacent grid. the explicit discretization mentioned above is obviously unstable (referring to the explicit second-order central difference scheme). in order to ensure accuracy, some variables must be treated implicitly, and a set of linear equations must be constructed to solve them. the first-order upwind scheme is absolutely stable, but its accuracy is low. combining the advantages and disadvantages of the two schemes, we implicitly dealt with the convective upwind scheme and modified the right hand of equation (rhe) by using the second-order margin. thus, eq. 23 can be discretized as: (𝐶𝜙𝐹)𝐶 𝑛+1−(𝐶𝜙𝐹)𝐶 𝑛 δ𝑡 δ𝑉 + ∑ [𝑤𝑐(𝐶𝜙𝐹)𝐶 𝑛+1 + 𝑤𝑛(𝐶𝜙𝐹)𝑁 𝑛+1](�⃗� 𝑝,𝐼 𝑛+1�⃗� δ𝑆)𝑠 = ∑ [𝑤𝐷(𝐶𝜙𝐹)𝑢 𝑛 + 𝑤𝑛(𝐶𝜙𝐹)𝑁 𝑛 ](�⃗� 𝑝,𝐼 𝑛+1�⃗� δ𝑆)𝑠 + 𝑞𝑖𝑛𝑗,𝐶δ𝑉……………………(24) the relationship among the upwind grid, dead-wind grid, current grid, and adjacent grid should be determined according to the flow velocity. the above analysis is based on the suspending region. if the case of sand heap is considered, the firstorder dead scheme must be adopted; otherwise, the result will be nonphysical. for this reason, when the concentration of the upwind grid in the direction of particle settlement approaches the limit accumulation concentration, the interface between the two grids must be corrected to adopt the first-order dead scheme. critical flow rate of proppant flowback. the maximum stable pressure drop gradient for the proppant flowback within the fracture after closure can be obtained with the sum of the pressure drop gradients that the proppant adhesion force and fracture closure stress can resist. ( 𝑑𝑝 𝑑𝑥 ) 𝑚𝑎𝑥 = ( 𝑑𝑝 𝑑𝑥 ) 𝑠𝑡𝑎 +( 𝑑𝑝 𝑑𝑥 ) 𝐹𝑉 ,……………...…………………………………………………………..(25) where ( 𝑑𝑝 𝑑𝑥 ) 𝑠𝑡𝑎 is the pressure drop gradient that the fracture closure stress can resist (mpa/m); and ( 𝑑𝑝 𝑑𝑥 ) 𝐹𝑉 is the pressure drop gradient that the proppant adhesion force can resist (mpa/m), ( 𝑑𝑝 𝑑𝑥 ) 𝐹𝑉 = 3𝐹𝑛 106×4𝜋𝑅3.……………………………………………………………………………………(26) the effective cohesion force can be expressed as a function of cohesion, gravity, and buoyance. 9 𝐹n = 𝑎𝑐 ( 𝛾0 𝛾0∗ ) 2.5 𝜋 2 𝜌𝑓휀𝑑 5 3 √3 − (𝜌𝑠 − 𝜌𝑓) 1 6 𝜋𝑑3g,……………………………………….……………(27) where 𝜌𝑠 is the proppant density, kg/m3; 𝜌f is the fluid density, kg/m3; and 휀 is a constant, 1.75 cm3/s2. the pressure that the fracture closure stress can resist is a function of fracture width and fracture closure stress, ( 𝑑𝑝 𝑑𝑥 ) 𝑠𝑡𝑎 = 𝑊𝑇𝑒𝑥𝑝 [−0.5 ( 𝑙𝑛𝑝𝑛𝑒𝑡−𝑎′ 𝑆𝑇 ) 2 ],………………………………………………………………(28) 𝑊𝑇 = 1422.5exp(−1.0483𝑊𝑟),…………………………………………………………………….(29) 𝑊𝑟 = 𝑊𝑓 𝑑 ,……………………………………………………………………………………………..(30) where wf is the fracture width, cm; d is the proppant diameter, cm; pnet is the fracture net closure pressure, pa; 𝑎′ is a constant, 7.7172; and st is a function of apparent strength of proppant. 𝑆𝑇 = 3 × 10−5s𝑀𝑎𝑥 + 0.22368,……………………………………………………………………..(31) where smax is the apparent proppant strength. according to the stress and deformation of the element, the fracture width is calculated by the constitutive model of the fracture. in this study, we adopted barton et al.’s (1985) constitutive model to calculate fracture width. barton et al. (1985) proposed an empirical correlation between mechanical aperture, am, and hydraulic aperture, wf, on the basis of experimental data: 𝑤𝑓 = { 𝑎𝑚 2 𝐽𝑅𝐶−2.5 𝛿ℎ ≤ 0.75𝛿𝑝𝑒𝑎𝑘 √𝑎𝑚𝐽𝑅𝐶𝑚𝑜𝑏 𝛿ℎ > 𝛿𝑝𝑒𝑎𝑘 , ,……….……………………………………………….....(32) where jrc is the joint roughness coefficient; jrcmob is the mobilized value of jrc; 𝛿 is the shear displacement in the horizontal direction; h and v are horizontal and vertical, respectively; and 𝑤𝑓is the fracture width of the smooth fracture wall, which is the fracture width used in this study. note that a linear interpolation determines the hydraulic aperture value when 0.75 < 𝛿ℎ/𝛿𝑝𝑒𝑎𝑘 < 1.0, and both am and wf are in the unit of mm. given the fracture stress state, the mechanical aperture can be calculated as (li et al. 2017): 𝑎𝑚 = 𝑎0 − ∆𝑎𝑛 + 𝛿𝑣 ……………………………………………………………………………….....(33) fracture closure stress refers to the force on the fracture wall required to close the fracture after shut-in. fracture closure stress is an important factor that affects fracture conductivity and can be calculated from the instantaneous shut-in pressure at the wellhead, the fluid column pressure, and the reservoir pressure. in addition, the minimal horizontal stress of the formation affects the fracture closure stress. on the basis of the study of triaxial stress and mechanical parameters of rock, an equation for closure stress was derived as 𝑝𝑛𝑒𝑡 = 𝛾 1−𝛾 s𝑣+𝑆ℎ𝑖+𝐴𝑝𝑒× 𝑝𝑖 2 1− 𝐴𝑝𝑒 2 ………………………...……………………………………………………...(34) the closure stresses in different regions can be obtained in field tests. if conditions permit, the best methods for obtaining closure stress are stepped injection, flowback, and equilibrium tests prior to hydraulic 10 fracturing. otherwise, the closure stress can be estimated with eq. 33. if the stability of the proppant filling layer is characterized with the critical flow rate, the darcy equation can be introduced. 𝑁𝑅𝑒 < 10 𝑑𝑝 𝑑𝑥 = 𝜇 𝐾 𝑣,…………………………………………………………………….(35) 𝑁𝑅𝑒 > 10 𝑑𝑝 𝑑𝑥 = 𝜇 𝐾 𝑣 + 𝛽𝜌𝑣2,………..………………………………………………………(36) where μ is the fluid viscosity (pa·s); v is the seepage velocity (m/s); ρ is the fluid density (kg/m3); p is the pressure (pa); β is the seepage velocity (m–1); and k is the permeability (m2). eqs. 35 and 36 were transformed to obtain the critical fluid velocity for zero proppant production after fracture closure. 𝑁𝑅𝑒 < 10 𝑣 = 𝐾 𝜇 ( 𝑑𝑝 𝑑𝑥 ) 𝑚𝑎𝑥 ,……………………………..…………………………………(37) 𝑁𝑅𝑒 > 10 𝑣 = − 𝜇 𝐾 +√( 𝜇 𝐾 ) 2 +4𝜌𝛽( 𝑑𝑝 𝑑𝑥 ) 𝑚𝑎𝑥 2𝜌𝛽 ……..…………………………………………………….(38) according to eqs. 37 and 38, the fluid within the closed fracture exhibits mainly a gas-liquid flow for shale gas wells. thus, calculating the critical fluid velocity for the zero proppant production after the fracture closure requires the maximum stable pressure drop gradient of the proppant-filling layer, mixed fluid viscosity, and mixed fluid density within the fracture. full model coupling. by coupling the proppant transport model, fluid-solid coupling model, and gasliquid two-phase tubing flow models, the optimal flowback velocity for the stable proppant-filling layer and minimal fluid loss could be calculated with the optimization algorithm; in addition, the choke size for the fluid flowback was adjusted by observing the wellhead pressure. explicit iteration was used to couple the fracture model and the proppant migration model (figure 4). firstly, fem was used to simulate the current time-step evolution process of fracture width, and then the proppant migration was simulated to obtain the concentration distribution. then, the proppant distribution was used to update the viscosity of sand-carrying fluid and the fracture-equivalent conductivity, and it was substituted into the model of the average permeability tensor of a quasicontinuous medium to achieve coupling. 11 figure 4—schematic of the fully coupled model. optimization of fracturing fluid flowback in a shale gas well as an example, the flowback scheme of well a in the fuling shale gas field (a horizontal multistage fractured gas well) was established with the reservoir and fracturing treatment parameters. fracturing fluid flowback was simulated using the proposed integrated model for a hydraulically fractured horizontal well with a 1,000-m horizontal wellbore and 10 fracture stages located in the center of a shale reservoir. each stage created transverse primary fractures along the horizontal wellbore with a fracture spacing of 25 m. all primary hydraulic fractures were assumed to be identical and to penetrate the whole reservoir. a specific fracturing fluid flowback scheme was planned for a horizontal shale gas well in fuling. the reservoir and fracturing treatment parameters of the gas well are listed in table 1. 12 table 1—reservoir and fracturing treatment parameters of a shale gas well (well a) in fuling. parameter type parameter unit value reservoir parameter effective reservoir thickness m 12 poisson's ratio dimensionless 0.23 young's modulus mpa 28,000 fracture closure pressure mpa 52 reservoir pressure mpa 64.2 shut-in pressure at wellhead mpa 69 reservoir permeability 10–3μm2 0.003 filter-cake permeability 10–3μm2 1.6 relative permeability 10–3μm2 0.02 reservoir porosity dimensionless 0.09 comprehensive compressibility mpa–1 0.001 fracturing treatment parameter proppant density kg/m3 2,650 proppant particle size mm 0.8 fracturing fluid density kg/m3 1020 fracturing fluid viscosity mpa·s 2 fracture half-length m 200 fracture height m 40 fracture dynamic maximum width mm 6 adhesion force coefficient dyn/cm 2.6 filtrate viscosity mpa·s 1.6 borehole vertical height m 2300 borehole radius m 0.05 horizontal section length m 500 stage number dimensionless 5 nozzle outlet pressure mpa 0.1 local resistance coefficient dimensionless 0.5 treatment displacement m3/min 3 total leak-off coefficient m/min0.5 0.00029 absolute roughness of the borehole mm 2 model validation. to validate the proposed fracturing flowback model, we matched the measured casing pressure with the predicted pressure from the injection period to the flowback period, as shown in figure 5. they were in good agreement. consequently, the fracture width was predicted and is illustrated in figure 6. the fracture width clearly declined as pressure dropped during the flowback period. 13 figure 5—history match of bottomhole pressure for well a during fracture treatment. figure 6--predicted fracture width for single fracture of well a during fracture treatment. in the first couple of days, well a flowback showed a relatively high flow rate and a choke size of 8 mm, which caused sand production (orange dots in figure 7a and 7b). the proposed model was run to calculate critical flow rate and corresponding critical choke size, which is the maximum flow rate that will not cause proppant flowback (blue curves in figure 7 and 7b, respectively). as actual flow rate is greater than critical flow rate and actual choke size is larger than the estimated choke size, proppant flowed back with fracturing fluid. after controlling flow rate by reducing choke size to be smaller than critical choke size, there was no sand production anymore. thus, the proposed model was proved to be robust enough to optimize the flow rate and choke size. 0 20 40 60 80 0 50 100 150 200 p re ss u re , m p a t,min field data simulated result 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0 50 100 150 200 f ra ct u re w id th , m t, min 14 (a) (b) figure 7—flowback performance versus (a) flow rate and (b) choke size. proppant transport. in addition to flow pressure and flow rate, the proposed model can also display the progress of proppant migration from injection period to flowback period. figure 8 shows proppant concentration profiles perpendicular to the fracture. the x-axis is the position along the fracture, which refers to the center of the fracture. the proppant concentration during the fracturing period ranged from 1.5% to 2.5%. from the concentration change curve in figure 8, an area of high proppant concentration was found to form at the fracture tip due to the severe filtration. after stopping pumping (“end of fracturing” curve in figure 8), the proppant concentration in the fracture front decreased gradually, but fracturing fluid in the fracture continued to advance because of high pressure in the fracture. at this time, the velocity of fluid in the fracture decreased and the distribution of fluid in the fracture gradually became uniform. however, it should be noted that the fluid continued to move forward. figure 9 is the 2d distribution of proppant concentration in a single fracture in the course of fracturing to flowback. 0 50000 100000 150000 200000 250000 1 7 13 19 25 31 f lo w b ak r at e, m 3 /d flowback time, days critical flow rate field flow rate flow with sand 0 1 2 3 4 5 6 7 8 9 1 7 13 19 25 31 c h o k e si ze , m m flowback time, days critical choke size field choke size 15 figure 8—proppant concentration profiles perpendicular to the fracture in the course of injection and flowback. (a) 48 min (b) 72 min (c) 113 min (d) end of fracturing (e) start of flowback (f) flowback for 20 min figure 9—2d proppant distribution in the fracture in the course of injection and flowback. fracturing fluid flow. the model was run to investigate the factors that affect fracture closure time. the pressure profiles of the wellhead during the fracturing fluid flowback period were established with the basic data in table 1 by changing the matrix permeability (figure 10) and the choke size (figure 11). when the wellhead pressure was lower than the fracture closing pressure (53 mpa in this case), the fracture was considered closed. it was obvious that the fracture closure time gradually increased with decreasing matrix permeability and choke size. the lower the matrix permeability, the slower the fracture pressure drop and the longer the fracture closure time. and with decreased permeability, the decreasing trend of fracture 16 pressure was slower. in other words, for shale gas reservoirs, it takes longer for a fracture to close because of the extremely low permeability. but by increasing choke size in the wellhead, it is possible to obtain an optimal flow rate that can reduce fracture closing time and prevent proppant flowback. figure 10—wellhead pressure in the fracture with various matrix permeabilities. figure 11—wellhead pressure in the fracture with various choke sizes. optimization of flowback scheme.on the basis of the above analysis, we applied the proposed model to optimize the flowback mode and choke size corresponding to measured wellhead pressure. traditional flowback mode. the traditional flowback mode refers to the choke size (radius of 2 mm) not vary during fracturing fluid flowback. the wellhead pressure profile obtained by the proposed model is shown in figure 12. the result shows that the fracture closed at 1,440 minutes and the pressure decreased by 32.4 mpa in 30 days. 20 30 40 50 60 70 80 0 10 20 30 40 50 w el lh ea d p re ss u re , m p a time, days k=0.001md k=0.003md k=0.005md k=0.01md fracture closure pressure (52 mpa) 20 30 40 50 60 70 80 0 10 20 30 40 50 w el lh ea d p re ss u re , m p a time, days r=2mm r=3mm r=4mm r=5mm r=6mm fracture closure pressure (52 mpa) 17 figure 12—wellhead pressure curve in the traditional flowback scheme. natural closure mode. in natural closure mode, the well is shut in until the fracture is closed after fracturing, and then the flowback initiates. the predicted wellhead pressure is presented in figure 13. the fracture closed at 1,584 minutes, and then choke size increased from 4 to 8 mm at 7.6 days. the pressure decreased by 34.5 mpa in 30 days. it was observed that when the fracture closed and the choke size increased, the pressure decreased suddenly. figure 13—wellhead pressure in natural fracture closure mode. forced closure mode. in forced closure mode, flowback is performed immediately with a choke size of 2 mm after fracturing. the estimated wellhead pressure is presented in figure 14. the fracture closed and the choke size increased to 4 mm at 1,044 minutes. after 7.1 days, the choke size increased to 8 mm. the pressure dropped by 35.8 mpa in 30 days. 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 w el lh ea d p re ss u re , m p a time, days fracture closure pressure (52 mpa) 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 w el lh ea d p re ss u re , m p a time, days no choke choke size=4mm choke size=8mm 18 figure 14—wellhead pressure curve in forced closure mode. the comparison of the above three schemes shows that in the forced closure mode of the fracture, the pressure decreased more rapidly, the fracture closed earlier, and the final stress equilibrium time was shorter, causing less damage to the reservoir. optimization of choke size. according to the above analysis, the optimal choke size under forced closure mode without proppant production corresponding to wellhead pressure is presented in figure 15. the fracture was closed when the wellhead pressure was 53 mpa. before fracture closure, the critical flowback rate was 2.5 m3/h and the safe choke size was 2 mm; after fracture closure, the critical flowback rate was 4 to 14.6 m3/h, and the choke size without proppant production was 4.2 to 7.8 mm. one can refer to figure 15 to adjust the choke size based on the measured wellhead pressure during the fracturing fluid flowback period. figure 15—maximum choke size and flow rate without proppant production for different wellhead pressures. conclusions an integrated reservoir-fracture-wellbore model was successfully applied to evaluate the stability of the proppant pack and optimize fracturing fluid flowback procedures based on wellhead pressure in multistage fractured horizontal shale gas wells. the model accuracies were verified with an example, and the following conclusions were drawn. 0 10 20 30 40 50 60 70 80 0 5 10 15 20 25 30 35 w el lh ea d p re ss u re , m p a time, days choke size=2mm choke size=4mm choke size=8mm 0 4 8 12 16 20 0 2 4 6 8 10 20 30 40 50 60 70 80 f lo w r at e, m 3 /h c h o k e si ze , m m wellhead pressure, mpa choke size critical flow rate 19 1. through simulations, the effects of the different parameters on wellhead pressure, fracture closure time, and final equilibrium time during fracturing fluid flowback were determined: larger choke size and higher reservoir permeability result in faster wellhead pressure drop, shorter fracture closure time, and shorter equilibrium time (figures 10 and 11). 2. during fracturing fluid flowback, several parameters influence the critical flow rate and choke size required for proppant pack stability: as the fracture is closed, the critical flowback rate and choke size increase rapidly because of the stress acting on the proppant. higher proppant density allows a higher critical flow rate and larger choke size before the fracture closure, but the choke size required for stable proppant pack after the fracture closure does not vary. the larger particle size of the proppant results in a higher critical flow rate and larger choke size for a safe blow-off before fracture closure. the opposite is the case after the fracture closure. the higher viscosity of the fracturing fluid corresponds to a lower critical flow rate and a smaller choke size for safe blow-off. 3. the proposed model for fracturing fluid flowback in a shale gas well considers the reservoir, fracture, and wellbore. thus, the model provides the theoretical basis for the optimization of postfracture flowback time, fracture closure mode, and choke management. on the basis of the model, the flowback process of a horizontal shale gas well with multistage fracturing in fuling was optimized. according to the results, the choke size should be increased from 2 to 4 and 8 mm in forced closure mode (figure 15). acknowledgements we would like to thank the sponsors of the project entitled “study on fracturing fluid flowback model and flowback scheme for shale gas well” (g5800-18-zs-kfgy002) from state key laboratory of shale oil and gas enrichment mechanisms and effective development, sinopec group, for financial support. we also would like to thank prof. zhenzhen dong from xi’an shiyou university and dr. xiang li from ennosoft ltd. for technical support. conflicts of interest the author(s) declare that they have no conflicting interests. reference andrew, j.s. and kjorholt, h. 1998. rock mechanical principles help to predict proppant flowback from hydraulic fractures. paper presented at spe/isrm rock mechanics in petroleum engineering, trondheim, norway, 8-10 july. spe-47382-ms. asgian, m.i., cundall, p. a., and brady, b.h.g. 1995. the mechanical stability of propped hydraulic fractures: a numerical study. journal of petroleum technology 4(3):75-78. spe-28510-pa. asadollahi, p. and tonon, f. 2010. constitutive model for rock fractures: revisiting barton's empirical model. engineering geology 113(4):11-32. barton, n., bandis, s., and bakhtar, k. 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𝐾𝑠−𝐾𝑑 𝐾𝑠𝐾𝑑 + 1 𝐾𝑠 = 1 𝐾𝑑 ,………………………………..……………………..(a5) 𝑐𝑏𝑝 = 𝑏 𝐾𝑑 ,…..…………………………………………………………………………………………(a6) 𝑐𝑝𝑐 = 𝑏 𝜙𝐾𝑑 ,……………………………………………………………………………………………(a7) 𝑐𝑝𝑝 = 𝑏 𝜙𝐾𝑑 − 1 𝐾𝑠 ,………………………………………………………………………………………(a8) where 휀𝑏 is the bulk stress tensor; 휀𝑝 is the pore stress tensor; 𝜙 is true porosity; ks and kd are the skeleton modulus. fluid compressibility is given as 𝑐𝑓 = 1 𝜌𝑓 𝑑𝜌𝑓 𝑑𝑝 ,……………………………………………………………………………………………(a9) 𝜕(𝜌𝑓𝑉𝑝) 𝑉𝑏𝜕𝑡 = 𝜌𝑓 𝜙 𝑉𝑝 𝜕𝑉𝑝 𝜕𝑡 + 𝜙 𝜕𝜌𝑓 𝜕𝑡 = 𝜌𝑓 𝜙 𝑉𝑝 𝜕𝑉𝑝 𝜕𝑡 + 𝜙𝜌𝑓 1 𝜌𝑓 𝜕𝜌𝑓 𝜕𝑝 𝜕𝑝 𝜕𝑡 .…….…...………..….…………………….(a10) substituting eqs. a2 and a9 into eq. a10 𝜕(𝜌𝑓𝑉𝑝) 𝑉𝑏𝜕𝑡 = 𝜙𝜌𝑓 ( 𝜕𝜀𝑝 𝜕𝑡 + 𝑐𝑓 𝜕𝑝 𝜕𝑡 )…..………………………………..…………..……………………….(a11) from eq. a2 𝜕𝜀𝑝 𝜕𝑡 + 𝑐𝑓 𝜕𝑝 𝜕𝑡 = 𝑐𝑝𝑐𝜕𝜎+𝑐𝑝𝑝𝜕𝑝 𝜕𝑡 + 𝑐𝑓 𝜕𝑝 𝜕𝑡 = 𝑐𝑝𝑐 𝜕𝜎 𝜕𝑡 + (𝑐𝑓 + 𝑐𝑝𝑝) 𝜕𝑝 𝜕𝑡 ……….....…………………………….(a12) substituting eqs. a11 and a12 into eq. a10 𝜕(𝜌𝑓𝑉𝑝) 𝑉𝑏𝜕𝑡 = 𝜙𝜌𝑓 (𝑐𝑝𝑐 𝜕𝜎 𝜕𝑡 + (𝑐𝑓 + 𝑐𝑝𝑝) 𝜕𝑝 𝜕𝑡 ),………………………...…………………………………(a13) substituting eq. a13 into the fluid constitutive equation (eq. 5) and dividing 𝜌𝑓 on both sides of eq. 5, eq. 5 can be simplified as 𝜙𝑐𝑝𝑐 𝜕𝜎 𝜕𝑡 + 𝜙(𝑐𝑓 + 𝑐𝑝𝑝) 𝜕𝑝 𝜕𝑡 + ∇(𝜌𝑓𝒗𝑓) 𝜌𝑓 = 𝑞 𝜌𝑓𝑉𝑏 .………………....……………………………………..(a14) from eq. a1 𝜕𝜎 𝜕𝑡 = 𝜕𝜀𝑏−𝑐𝑏𝑝𝜕𝑝 𝑐𝑏𝑐𝜕𝑡 ……………………………………………….………………………………………(a15) thus, 22 𝜙𝑐𝑝𝑐 𝜕𝜎 𝜕𝑡 = 𝑏 𝐾𝑑 𝜕𝜎 𝜕𝑡 = 𝑏 𝐾𝑑 𝜕𝜀𝑏− 𝑏 𝐾𝑑 𝜕𝑝 1 𝐾𝑑 𝜕𝑡 = 𝑏 𝜕𝜀𝑏 𝜕𝑡 − 𝑏2 𝐾𝑑 𝜕𝑝 𝜕𝑡 ……………......……………………………………(a16) from eq. a8 𝜙(𝑐𝑓 + 𝑐𝑝𝑝) 𝜕𝑝 𝜕𝑡 = 𝜙 (𝑐𝑓 + 𝑏 𝜙𝐾𝑑 − 1 𝐾𝑠 ) 𝜕𝑝 𝜕𝑡 ,…..………………….…………………………………….(a17) ∇(𝜌𝑓𝒗𝑓) 𝜌𝑓 = ∇𝒗𝑓 + 𝒗𝑓 ∇(𝜌𝑓) 𝜌𝑓 = ∇𝒗𝑓 + 𝒗𝑓𝑐𝑓∇𝑝…………………………………………………………(a18) substituting eq. a16 through a18 into eq. a14 𝑏 𝜕𝜀𝑏 𝜕𝑡 + [𝜙 (𝑐𝑓 + 𝑏 𝜙𝐾𝑑 − 1 𝐾𝑠 ) − 𝑏2 𝐾𝑑 ] 𝜕𝑝 𝜕𝑡 + ∇𝒗𝑓 + 𝒗𝑓𝑐𝑓∇𝑝 = 𝑞 𝜌𝑓𝑉𝑏 ………....………………………….(a19) in eq. a19 𝜙 (𝑐𝑓 + 𝑏 𝜙𝐾𝑑 − 1 𝐾𝑠 ) − 𝑏2 𝐾𝑑 = 𝜙𝑐𝑓 + 𝑏(1−𝑏) 𝐾𝑑 − 𝜙 𝐾𝑠 = 𝜙𝑐𝑓 + 𝑏 𝐾𝑑 𝐾𝑠 𝐾𝑑 − 𝜙 𝐾𝑠 = 𝜙𝑐𝑓 + 𝑏−𝜙 𝐾𝑠 ...…..………………(a20) let 1 𝑀 = 𝜙𝑐𝑓 + 𝑏−𝜙 𝐾𝑠 ….…………………………………………………………………………………...(a21) eq. a19 can be finally simplified as 𝑏 𝜕𝜀𝑏 𝜕𝑡 + 1 𝑀 𝜕𝑝 𝜕𝑡 + ∇𝒗𝑓 + 𝒗𝑓𝑐𝑓∇𝑝 = 𝑞 𝜌𝑓𝑉𝑏 ………...………………………..……………………………(a22) based on darcy’s law 𝒗𝑓 = − 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)………………………………………………………………………………(a23) eq. a22 can be expressed as 𝑏 𝜕𝜀𝑏 𝜕𝑡 + 1 𝑀 𝜕𝑝 𝜕𝑡 = 𝑞 𝜌𝑓𝑉𝑏 + ∇ [ 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)] + 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)𝑐𝑓∇𝑝,...……………..………………….(a24) 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)𝑐𝑓∇𝑝 is negligible as it is a second derivative. thus, the governing equation of fluid flow can be expressed as 𝑏 𝜕𝜀𝑏 𝜕𝑡 + 1 𝑀 𝜕𝑝 𝜕𝑡 = 𝑞 𝜌𝑓𝑉𝑏 + ∇ [ 𝐾 𝜇 (∇𝐩 − 𝜌𝑓𝒈)]…………...……………………..………………………...(a25) cheng dai is a senior engineer in petroleum exploration and development research institute, sinopec. dr. dai holds a bachelor's degree and a ph.d. degree from peking university. his research interest includes numerical simulation and shale gas development. zhenzhen dong is a professor in the department of petroleum engineering at xi’an shiyou university. she worked as a reservoir engineer at schlumberger from 2012 to 2016. dong holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from the research institute of petroleum exploration and development, china; and a ph.d. degree in petroleum engineering from texas a&m university. xiang li is the technical director of beijing energy innovation software company. his work includes scientific computing, fracture modeling, and reservoir simulator development. dr. li holds a bachelor’s degree and a phd degree from peking univerisy. 23 weidong tian is a master's candidate in the department of petroleum engineering at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. tian holds a bs degree in petroleum engineering from xi’an shiyou university. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.456 received september 22, 2019; revised november 30, 2019; accepted december 12, 2019. *corresponding author: minh.vo@chevron.com 1 reservoir surveillance and production optimization workflow from real time data advantage at a joint venture gas project yue yu, minh vo*, chevron unocal east china sea ltd, chengdu, china; and chaohong xiao, southwest oil and gas company, cnpc, chengdu, china abstract with the advancement of computer science and information technology, the oil and gas industry has been well positioned in the data-driven business. all kinds of data, from every phase of production, are useful if they can be interpreted in a real-time manner to support optimization and development. reservoir surveillance, starting with the data acquisition from the well and the production network, is the driver for evaluating well and reservoir performance, then ogip/reserves evaluation, and finally, the foundation development, on which development options are optimally selected and production optimization decisions can be made. this paper here presents the practice that a greenfield gas field adopted and many other aspects of reservoir characterization and production optimization. focal point is to start with the permanent downhole pressure gauge (pdhg) and then, application of the real time wellhead data monitoring and recording system are the best use when putting together with the well-defined engineering methodology to support for decision making. this is even more beneficial in the context of high operational cost and inherent high environmental risk of the high h2s operating exposure, for the joint venture gas project in sichuan. introduction the green-field sour gas project is developed in sichuan, china. the full field development schematic is shown in figure 1. the project involves development of gas resources in triassic carbonate reservoirs. the field of interest is made up of bedded dolostone and limestone facies of early triassic age. the depositional environment is carbonate platform and ramp with oolitic shoals. gas is trapped in thrustrelated anticlinal structures and seals comprise tight limestones and anhydrites. the structure is normally large. rock porosity ranges from 3 to 20%, and permeability ranges from 0.01 to 1,000 millidarcies (md). the reservoir fluid is dry gas, with h2s and co2. the unique challenges for this project are sour gas, rugged terrain, large operating area, and high population. therefore, optimizing production and maximizing the value for the field development is the primary goal for the field development plan. 2 figure 1—sour gas development project. reservoir surveillance goal and workflow reservoir surveillance, starting with the data acquisition from the wells and the production network, is to obtain data for evaluating well and reservoir performance, reserves evaluation and finally, the foundation development, on which development options are optimally selected and decisions are made. the primary objectives of reservoir surveillance are to ensure gas availability meets all contractual agreements and timely promotion of resources to reserves. this is aligned well with the goals of the field development plan. contractual production demand. to achieve this goal, well and reservoir performance should be evaluated frequently to identify any signposts for upside / downside potentials. this is to: • maintain predicted well deliverability; • determine the optimal well-count and the preferred location / placement of wells; and • support production accounting and allocation. figure 2—rolling reservoir surveillance workflow. 3 timely promotion of resources to reserves. to effectively develop the field, timely execution of downside mitigation and upside capture strategies are needed. this requires the operator to: • establish reservoir in-place gas volumes; and • establish reservoir connectivity, both areally and vertically. in brief, to achieve these goals, the team develops and follows the rolling reservoir surveillance workflow, conceptually described in figure 2. the effectiveness of any decision will therefore dictate what data to collect and when to collect it (satter et al. 1994). data collection and challenges typical gas field development will start from the wells, then connect to the gathering station(s), and finally to the processing system via pipeline. in this case study of the field development application, the gas field has been developed with six producing wells, of which one well is equipped with permanent downhole gauge (pdhg), or down hole pressure gauge (dhpg). the schematics in figure 3 will provide a better picture how the system works. figure 3—real time recording system. as seen in figure 3, only one well was equipped with a pdhg in this field, whereas the other five wells have a wellhead data monitoring system in place. to ensure the reliability and the accuracy of the data recorded downhole, the operator selected a halliburton welldynamics roc (satter et al. 1994), which was the first of its application in china. the downhole reservoir pressure data is the most important reservoir surveillance measurement, and provides invaluable information about the reservoir behaviors at different production arrangements. key surveillance data are thus composed of wellhead and bottom-hole-pressure and temperature, gas and water rate, and gas composition. real time monitoring of well operating conditions will help collect the data from the wells to server. except for limited downhole data available, a challenge for any field development also is the high production requirement from the wells. each well is therefore planned to produce at the high flow rate, ~85% – 95% of the well constraints (e.g., pressure safety valve limit, flare limit, erosional limit). with a limited cushion of production, well intervention operations of any well will lead to a large production loss, associated with an execution risk of well intervention and also high operations cost. data analysis a question then follows of how to make the best use of available data to conduct reservoir surveillance to optimize production and to maximize the value for the entire life of field development. 4 since limited bottom-hole data is available, if the wellhead data including pressure, flow rate and temperature from the real time recording system is used, it would be an advantage. several well-recognized methodologies can successfully be used in the oil industry to convert the wellhead data into the bottom hole data, such as cullender and smith (1956), beggs and brill, dukler flannigan, fancher brown (william 2004). at this gas project, an internal petroleum engineering toolkit has been available to use, with more than 20 different correlations available. the workflow is described below in figure 4. starting with the well where both surface and downhole pressure data are available, the petroleum engineering model has been built and it helps calculating the gas compressibility z factor under specific production condition (i.e., from gas composition, including h2s and co2, and non-linear temperature profile along the wellbore). the uncertainty on fluid pvt (pressure temperature volume) and tubing roughness can be eliminated as having a low impact. appropriate correlations are loaded to convert the surface pressure data to downhole pressure data, and the results are compared with the actual pdhg data measured directly from the downhole gauge. figure 4—using pdhg data for best fit correlation. the correlation with a minimal gap is then selected and calibrated to match with the pdhg, by adjusting friction and gravity loss in tubing. since all six wells have similar structures in this project, this calibration exercise can be applicable to the other five wells without the pdhg, and all are with the good quality conversion. once wellbore flowing data and bottom-hole data are determined with above method, the data can be further linked to selected inflow performance relationship ipr model. by observing the change of intersection, we can monitor how the performance of the wells has changed with time. the work can be illustrated in figure 5. in this plot, the results from all six wells, using the wellhead pressure data and the converted downhole pressure data to evaluate well performance and benchmark their potential to identify wells with formation damage. 5 figure 5—use wellhead and downhole data for well performance update. to maximize the value of this workflow with real-time data, an analytical model has been developed at this gas development project. the work started from pdhg data to select the best fit model and then, used that to convert all the wellhead data available in the other wells. the data is then used for formation damage estimate. the workflow is summarized as figure 6. figure 6—data conversion and well performance evaluation model. note that skin, as normally used in the oil and gas development, is defined as the level of formation damage; the higher the value of skin, the more the formation was damaged by drilling, completion, and production activities. more specifically, several wells in this field development were identified with formation damage, whereas the others showed gradual cleaning (skin is reaching zero or even negative). more benefits from the usage of this analytical model are shared below. 6 decision analysis it is hard to overstate the importance of integrating reservoir surveillance together with performance forecast, production optimization and field development. different engineering tools such as production optimization and reservoir simulation are also being used to help understanding the reservoir. meanwhile, cross-functional teams such as operations, geophysics, economics and planning are also involved when making any decision of field development (thakur 1990). what we learned from reservoir surveillance, such as reservoir connection, formation damage, and ogip/reserves of each well should be treated as input for any field development decision, such as infill drilling, stimulation, and expansion. implementation besides of reliably and economically executing an optimization project, health, safety and environment (hse) is always the top criteria in performing any development plan at this gas project. therefore, any decision will be evaluated together with its value creation.  when opportunities are identified, and evaluated, cross-functional team such as subsurface, facilities, operations, commercial and planning, economics should be involved.  with clearly and transparently defined goals, several doable and practical alternatives can be evaluated. the project scope can be varied, as small as stimulating a well, or as big as project scope expansion. reservoir surveillance always provides the first and invaluable information in selecting the best alternatives.  after determining the preferred alternative, a detailed plan will be developed. at this phase, reservoir surveillance doesn’t go alone. simulation, geophysics, operation, hse, etc. are involved to develop the detailed project plan. after implementation, a lookback is normally conducted to see the performance and if there are any lessons learned or best practices. in terms of reservoir surveillance, input data quality and ensuring operations fully followed the procedure are the keys. case study: benefits of reservoir surveillance and production optimization several key uncertainties were identified before first gas from the project, mainly reservoir connectivity and other characteristics, and well deliverability. real time data were collected before, during, and after first gas in an effort to narrow these uncertainties. interference test for compartmentalization. recognition of compartmentalization is especially critical to help identify signposts of both low side and high side for the real-time optimization decision. interference test between these wells provided relevant data for well connectivity and so, reservoir compartmentalization. 7 figure 7—pressure response on pdhg when the other well pad started production. figure 8—pressure response on pdhg days after the other well pad stopped production. to support this test, production started from one well pad and gradually ramped up. just days after that, pressure drop was observed from pdhg installed on the well at another well pad. not only pressure drop, the lateral communication was also confirmed by plant shut down that pdhg reading increased accordingly. this is clearly shown in figures 7 and 8. well test analysis for formation damage evaluation. understanding well skin damage is critical for estimating the well deliverability and making any intervention decision. after days of trial and calibration, the wellhead pressure can be consistently converted into downhole pressure with minimal error. in most cases with stable production, the gap between converted bottom-hole pressure and pdhg data is within 10 psi. to understand more about the value of pressure conversion, a case study has been done at well a where we have both the surface and downhole pressure data. figure 9a shows the test interpretation using the pressure conversion data and figure 9b from the pdhg data. note that the data from surface gauges results in similar reservoir parameters such as skin and permeability. also, with multiplewell tests done at different times, reservoir characteristics (e.g., fractures and no flow boundaries) can be characterized and understood. 8 (a) (b) figure 9—pressure transient analysis (pta). (a)pta with converted data. (b) pta with pdhg data. the biggest benefit from this pressure conversion work (from data surveillance) could be highlighted at well b, when consistently poor performance indicated a large formation damage (i.e., skin factor greater than +30). the decision was made to acidize this well. from figure 10, it can be seen that the deliverability improved after stimulation and the skin factor reduced sharply. in brief, the timely evaluation of formation damage from real time data is used to help understand well performance change during liquid unloading and ramp-up period. this helps guide well intervention decisions to optimize field development. figure 10—well well performance monitoring and update. with production, it is critical to monitor well performance changes. since there is little spare capacity in the whole production system, one failed well will lead to production loss. wellhead and pdhg data are monitored real time to see if there are any changes. as we see in this field, most producers get better performance after ramp-up due to cleaning of the near wellbore area damage by continued big gas flow (figure 11). 9 figure 11—well production improvement monitoring. tracking and plotting the well performance variance helps optimize production from each well. production optimization aims to sustain production, manage reservoir depletion and extend plateau production by allocating production target to each well. to perform this, the 3-step process starts with real time data collection, then, frequent well tests with the orifice meters to validate flow rate and update gas compositions; and finally, update well performance curve with above petroleum engineering tool kit to determine an optimal production rate target for each well. reservoir performance monitoring and update. well performance monitoring is the first step for reservoir performance monitoring. ogip cannot be changed by any artificial lift or stimulation. however, a recovery factor can be improved with good reservoir performance monitoring. in this case, well shut-ins when appropriate provide invaluable information for the field development evaluation. well shut-ins can be managed during planned maintenance such as turnaround and pigging to minimize production loss. by estimating the change of reservoir pressure, the speed of reservoir depletion and ogip can be derived. the ultimate goal of all above surveillance techniques is to maximize plateau of the gas field, optimize infill drilling time, and determine well location and well count. with the well performance, deep understanding of reservoir characteristics, and reservoir depletion estimate, the value of field development can be effectively maximized, illustrated in figure 12. 10 figure 12—timely decision of drilling for field development optimization. reservoir surveillance in long run surveillance conducted after the plant has achieved full throughput is very important, particularly when all wells are producing near maximum capability and stabilized operating rates. if it can be managed properly, it will provide invaluable information to achieve the critical subsurface objectives.  surveillance data to achieve the above objectives are required as frequent as practical, and with the workflow and analytical model set up, routine well shut-in data can prove a very valuable sources of reservoir information.  well shut-in pressure data are critical to accurately estimate well ogip, and therefore proven reserves by well. this in turn is the most reliable method to confirm the extent of reservoir compartmentalization, and, in severe instances of such, enables an assessment of undrilled resource which is critical for determining the feasibility of further development.  except for well shut-in, other common surveillance methods at gas field development include deliverability testing, transient pressure analysis and production logging, fluid sampling. selecting the most appropriate surveillance methods to acquire the most valuable information at different phases of field development is important for all reservoir engineers when involved in development decision making. conclusions advancement of computer science and information technology is a key driver to support the oil and gas industry and makes the reservoir surveillance effort more effective and efficient. this paper detailed several examples of how realtime data, new technologies, and standardized processes could be used to support interpretation and analyses for decision making. specific cases from well performance analysis (e.g., formation damage) to pressure transient analysis (e.g., interference test for reservoir connectivity and pta for reservoir characteristics), and eventually, to ogip and reserves evaluation are shared to demonstrate how the new information and techniques can be used to support production optimization and a long-term development value maximization. 11 acknowledgment the authors thank the management of uecsl and cnpc for their permission to publish this paper. the authors also thank all the personnel, particularly halliburton engineers, who were involved in the execution of the operations at the field site and in the well-test interpretation to ensure the highest quality received. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature pdhg = permanent downhole gauge ogip = original gas in place sitp = shut in tubing pressure h2s = hydrogen sulphide fdp = field development plan pvt = pressure temperature volume ipr = inflow performance relationship pta = pressure transient analysis references satter, a., varnon, j. e., and hoang, m. t. 1994. integrated reservoir management. journal of petroleum technology 46(12):23-27. spe-22350-pa. cullender, m.h. and smith, r.v. 1956. practical solution of gas flow equations for wells and pipelines with large temperature gradients. journal of petroleum technology 207(12): 281-287. spe-696-g. william, c. l. 2004. standard handbook of petroleum and natural gas engineering. thakur, g. c. 1990. reservoir management: a synergistic approach. paper presented at permian basin oil and gas recovery conference, midland, 8-9 march. spe-20138-ms. yue yu, spe, is production engineer in unocal east china sea ltd., where he has worked for 6 years. his research interests are in production and reservoir engineering. he holds master’s degree from china university of petroleum, beijing. minh vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 4+ years. he has had 25 years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. chaohong xiao, is a production engineer in southwest oil & gas field company, where he has worked for 32 years. his research interests are in production engineering and daily field operations management. he holds bs degree from southwest petroleum university in petroleum engineering. abstract introduction reservoir surveillance goal and workflow data collection and challenges data analysis decision analysis implementation case study: benefits of reservoir surveillance and reservoir surveillance in long run conclusions acknowledgment conflicts of interest nomenclature references a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1155 received february 28, 2020; revised may 4, 2019; accepted may 13, 2020. *corresponding author: minh.vo@chevron.com 1 reservoir modeling and production history matching in a triassic naturally fractured carbonate reservoir in sichuan, china minh vo*, san su, and jianjiang lv, chevron unocal east china sea ltd, chengdu, china; chaohong xiao, southwest oil and gas company, cnpc, chengdu, china abstract fractures are observed on the image log data in many triassic carbonate gas fields in the block located in sichuan basin, china, and clearly matched at the equivalent analogy outcrops. the pressure transient analysis test (pta) after the field’s first gas clearly implies a dual porosity dual permeability system. sustained high gas rate from all producing wells and the communication between two well pads in distant indicate the significant role fractures play in well deliverability. to support flow simulation, discrete fracture networks (dfn) modelling was conducted with various static data as inputs. multivariate analysis (mva) was carried out to ensure a quality correlation between reservoir and fracture properties which is the key for fracture modelling. the kmax/kmin ratio of the resulting elliptical fracture permeability tensors were scaled to an uncertainty range defined by integrating the core and fmi interpretation, equivalent outcrop study, and analogy data. the tensors throughout the model were then calibrated to the fracture component of isotropic permeability derived from well test. prior to the simulation, the single well inflow performance relationships (ipr) was calibrated to actual flow test results by adjustment in the simulation model. the production forecast shows that the reservoir depletion profile from the simulation model overlaps well with p/z versus three-year cumulative production based on pta results, and the single well production from the simulation model matches actual data, indicating a reliable static reservoir model and dynamic simulation process. in brief, this presentation is to share the fit-for-purpose approach of reservoir modelling and history matching which has greatly helped better understand the dynamic performance of the reservoir, and therefore to guide optimal field development. the success can be tailored to other fields of similar kind. introduction this greenfield sour gas project is developed in sichuan, china. the full field development schematics is shown in figure 1. mailto:minh.vo@chevron.com 2 figure 1—sour gas development project. the project involves development of gas resources in triassic carbonate reservoirs. the field of interest is made up of bedded dolomite and limestone lithofacies of early triassic age. the depositional environment is carbonate platform margin and ramped with oolitic shoals. gas is trapped in thrust-related anticlinal structures and seals comprise tight limestones and anhydrites. the structure is normally large. the reservoir fluid is dry gas, with h2s and co2. fractures in reservoir and their impact fractures are a universal element in sedimentary rock layers (nelson 2001), and they are more common in carbonate rocks with higher brittleness than in sandstones (crain 2017; kuchuk et al. 2015). natural fractures in carbonate reservoir can help create secondary porosity and promote communication between reservoir compartments. however, fractures may sometimes short-cut fluid flow within a reservoir, causing early water production (bratton et al. 2006). therefore, it is very important to characterize and model fractures to determine their effect in our reservoir performance. with the understanding of the regularity of fractures distribution, wells can be planned effectively and efficiently to maximize production. in development drilling program (if there are any), appreciation of fractures’ impact on reservoir connectivity can prevent from drilling redundant wells to manage cost and to maximize the value of the field development. in fact, naturally fractured reservoirs are very complicated and difficult to evaluate due to: 1) lack of in-depth quantitative approaches for the description and characterization of highly anisotropic reservoirs; 2) failure to recognize fractures and their distribution; 3) over-simplistic approaches in the description of fractures distributions and morphologies; and 4) data limitations only allowing stochastic rather than deterministic fluid flow simulation (nelson 2001; bourbiaux et al. 2005). within the area of interest in this study, there are 5 triassic dolomite gas fields. both static information from cores, logs and equivalent outcrops, and dynamic information from well-test data since field production demonstrate the presence of natural fracture development in the carbonate reservoirs. in recognizing the challenges and significance of natural fractures, this paper is trying to fully utilize all sorts of static and dynamic fracture data to characterize and model fractures in the reservoirs, which therefore enables us to evaluate the impact of fractures on production and guide optimal future development. 3 fracture characterization various approaches can be carried out to characterize natural fractures in the reservoirs to assist fracture modelling, including equivalent outcrop study, fmi interpretation, and well-test analysis. application of 3d seismic attributes, unfortunately not applicable in this study due to data quality and resolution, is also proved to be an effective way to characterize fracture network (angerer et al. 2011). equivalent outcrop analog. as showing in figure 2, vertical fractures can be observed in the equivalent outcrop of reservoir rocks. as the outcrops are in the cliffs near top of the mountain, fracture parameters such as density, aperture, length, dip and azimuth data could not be obtained due to the inaccessibility. given reservoir model cell size of 200 m×200 m×7 m in this study, fractures in the photo would penetrate multiple vertical cells. fmi interpretation of fracture density & orientation. interpretation of images logs has suggested that open fractures should play an important role in the reservoir flow. however, the absence of important ancillary flow data (such as production logging test) hinders determination of fracture system flow effectiveness. in fact, it is only through interrogation of a variety of different data types that the characteristics of fractured reservoir are revealed (narr et al. 2006). figure 2—persuasive large-scale vertical fractures on equivalent outcrops. figure 3 shows the fracture interpretation from fmi image logs. the same fracture interpreted from image log is also identified in the equivalent core. 4 figure 3—fracture interpreted from fmi in comparing with the fractures observed on core of well a. figure 4 shows the fracture parameters interpreted from fmi log of well a in field a. fracture density is calculated using the methodology as described by wayne narr (narr 1996). fracture orientations are plotted in rose diagram for easy visualization. the fractures interpreted from well a image log are parallel to the strike of the anticline (figure 5), which is the dominant fracture orientation in field a as well as the other offset fields. another well in field a has a majority fracture orientation perpendicular to the strike of the anticline, and it represents the secondary fracture orientation. the conceptual fracture model can be constructed based on fracture parameters interpretation, rock competency evaluation, tectonic stress analysis and analogous structures. in a typical asymmetric anticline, there are three types of fractures, including hinge-parallel fractures, hinge-perpendicular fractures and oblique fractures (figure 5) (price 1966; stearns and friedman 1972; aguilera 1980; price and cosgrove 1990; awdal et al. 2016; galuppoc et al. 2016). the hypothesis is that hinge-perpendicular fractures are pre-folding whereas hinge-parallel and oblique fractures are fold-related or post-folding fractures. figure 4—fracture density and orientation interpreted from fmi image log fromwell a. 5 figure 5—observed fracture sets shown in price's classification of fracture sets typical for asymmetric anticlines. the field a in this study is characterized as an asymmetric anticline trending ne-sw by 3d seismic data and well data. based on the limited fmi data (2 wells in the field) and fmi data from the offset fields, the conceptual fracture sketch for field a is generated as shown in figure 6. the dominant fracture orientation is parallel to the strike of the anticline, with secondary fracture orientation being perpendicular or oblique to the strike. figure 6—field a conceptual fracture development and distribution (courtesy wayne narr). fracture characteristics from well-test data. diagnostic plot can be constructed to identify various flow regimes and reservoir heterogeneities as these affect the pressure response during well-test (satter and iqbal 2015). naturally fractured reservoirs have two distinct porosities, one in the matrix and one in the irregular fractures (fekete 2017), and they can be represented by equivalent homogenous dual porosity systems (lee and wattenbarger 1996). in a dual porosity system, flow from both the fractures and matrix are assumed. a characteristic “dip” is observed in the derivative plot (figure 7) beyond the wellbore storage effects. flow from a highly conductive fracture system leads to less pressure change over time, causing the apparent dip, which is often referred as “dual porosity dip” (satter and iqbal 2015), and is defined by two parameters including ω and λ. ω is the storability ratio and is essentially the fraction of hydrocarbon stored in the fracture system. it determines the depth of the dip, with smaller ω corresponding to deeper dip. λ is the interporosity flow coefficient that characterizes the ability of gas flowing from matrix to fractures. 6 figure 7—signature of a dual porosity reservoir on a diagnostic plot. it also determines the time of start of transition (from fracture dominated flow to matrix dominate flow) and controls the speed at which the matrix will react, with smaller λ corresponding to later dip. a reservoir with a big λ has relatively high matrix permeability, so it will start to give up its fluid almost as soon as the fracture system starts to produce, and vice versa (kappa 2017). prior to the field production, the well-test data is limited as the duration was not long enough to represent the full reservoir behavior. quality well-test data after field a on production was recorded through permanent downhole pressure gauge during the pressure build-up test when the well was shut in. the interpretation of the well-test data clearly indicates a dual porosity system (figure 8) (satter and iqbal 2015; kappa 2017). the shallower “dip” on the pta analysis plot implies a relatively large ω, and that the pressure support from the matrix during the transition is relatively less substantial. such feature indicates that the fractures account for a large portion of pore volume. the λ in this case is about 10-7, a moderate value which might show that the matrix is neither too tight nor too porous, and moderate pressure drawdown will have to be established in the fractures system before the matrix will appreciably give up any fluid (kappa 2017), and the transition starts neither too early nor too late. figure 8—well b dual porosity model as interpreted from pta. the dynamic characteristics of permeability of the fractures and matrix as revealed by well-test data should be integrated with static characterization to construct the fracture model. fracture modeling workflow with relatively good understanding of the fracture characteristics in the reservoirs, static fracture modeling can be carried over to further assist flow simulation. the fracture modeling workflow consists two parts. the first part is to model the fractures using fit-forpurpose fracture modeling technique based on mainly on static reservoir information prior to field 7 production. the second part is to calibrate the above fracture model to dynamic reservoir parameters as derived from production performance and well-test. the fracture modeling workflow suggested by smes is showing in figure 9. firstly, the fractures are interpreted from available image logs, the fracture density curves are calculated, and the fracture orientation and distribution regularity with regarding to the structure are understood. secondly, the correlations between calculated fracture density and reservoir properties which have been populated in the reservoir model is established. this step is usually very challenge due to limit fracture density data, and the correlation coefficient largely determines the quality of the resulting fracture model. with the establishment of such correlation, fracture density in each grid cell can be predicted from the reservoir property in the same cell. the potential reservoir properties that can be used to correlate with and predict fracture density include but not limit to facies, porosity, formation, seismic anomaly and geometric factor, etc.(narr et al. 2004). the next step is to develop reasonable uncertainty ranges for a series of fracture parameters including fracture density, azimuth, length, mean aperture, and through-going fracture length cutoff, aiming to capture a wide yet realistic range of simulation outcomes. the final step is to create a discrete fracture model using fracture density which already populated in the whole grid model and the fracture parameters as defined above. the discrete fractures are then effectivized into permeability tensor. the output of the fracture modeling is the horizontal fracture permeability tensor in each grid cell. the tensor can be then combined with matrix permeability as the composite horizontal permeability. the fracture parameters’ sensitivity on gas production can be evaluated. the big hitters identified from the sensitivity study could be included in the dynamic experimental design to optimize the flow simulation while capturing all possible scenarios. the modeled fracture permeabilities based on static data usually have a large uncertainty range, and they should be scaled and calibrated to dynamic permeability as derived from well test analysis. fracture model calibrated with dynamic data the static fracture model constructed following the above steps has several limitations. firstly, the input data availability and quality are usually limited and compromised. secondly, the static fracture model normally has multi-million grid cells depending on the reservoir areal extension and thickness, while the popular flow simulator usually cannot handle model with so many grid cells efficiently, thus requiring an up-scaling process before the actual flow simulation. the up-scale process shall of course lose part of the reservoir information. the advances in technology such as next generation simulator which is deemed to handle a larger number of cells in a less time-consuming manner should help to eliminate the issues brought by up-scaling process. therefore, it is of necessity to update the static fracture model with dynamic performance data after the field is on production for a reasonable amount of time. the authors herein introduce a fit-for-purpose adjustment technique to revise the model. the permeability derived from well-test (kiso) is a composite property of matrix and fracture permeability. the fracture permeability (kisof) can be calculated by subtracting matrix permeability (kisom) from well-test permeability kiso (i.e. kisof = kiso kisom). the fracture model adjustment is indeed the calibration of fracture permeability only. the adjustment of fracture permeability includes two steps.  the first step is to scale the permeability tensor to the desired major-axis / minor-axis ratios (i.e. kmaxf /kminf ratios). this step can be skipped if the static fracture model is considered as reasonable.  the second step is to calibrate the static fracture permeability in the model to fracture permeability derived from well-test. 8 figure 9—fracture modelling workflow (courtesy eric a. flodin and jerome glass). scaling permeability tensor. due to the availability and quality of input data for fracture modelling, the ratio between kmaxf and kminf of the permeability tensor in the fracture model may not be reasonable. therefore, it is necessary to scale the ratio and confine it to an uncertainty range of min-mid-max, which is defined by fracture smes based on the understanding of reservoirs of similar kinds, and of course, local and regional benchmark data. to achieve the desired uncertainty range, firstly the kmaxf /kminf ratio in each grid cell in area of interest (aoi) needs to be scaled to “mid” ratio while keeping the average isotropic fracture permeability in aoi unchanged. the next step is to scale the ratios to “min” and “max” in the regions where the kmaxf /kminf ratio is less than “min” and greater than “max” respectively and keep the average isotropic fracture permeability in the regions unchanged as well (figure 10). the scaling process ensures the kmaxf /kminf ratio in the aoi falling in the desired uncertainty ratio of min-mid-max, while the average fracture permeability is unchanged. 9 figure 10—scaling of kmax/kmin ratio in fracture model. static permeability to dynamic permeability. the static fracture permeability tensors after scaling need to be calibrated to fracture component of permeability derived from well-test (kisof). as shown in figure 11, kiso can be considered as an equivalent isotropic permeability of the kmax and kmin on permeability tensor. kiso is the geometric mean of kmaxf and kminf as shown ����� 2 = �����_� × �����_�....….……………………….………….….…...............................................(1) similarly, the well-test derived fracture permeability kisof should be equal to geometric mean of calibrated kmaxf_c and kminf_c, as shown ����� 2 = �����_� × ������,.……….……………..…………….……………….……………………….(2) to keep the ratio between major axis and minor axis of the fracture permeability tensors unchanged during the calibration process, we have �����_� �����_� = ����� ����� ....…….………………………………………………………….…….............................(3) solve eqs. 2 and 3, the �����_� and �����_� as final anisotropic fracture permeability can be calculated as �����_� = ����� 2 × ����� ����� ,…………….....……………………………….………….………..………..(4) �����_� = ����� 2 × ����� ����� .…………...…………………………............................................................(5) figure 11—permeability tensor and the equivalent isotropic permeability (courtesy wayne narr). 10 after the above scaling and calibrating process, the fracture permeability tensor in each grid cell of aoi should have a reasonable kmaxf /kminf ratio and the average fracture permeability in aoi should match the fracture permeability derived from well-test. the adjusted fracture permeability is then added back to matrix permeability in corresponding grid cells as the final composite permeability for flow simulation. ipr and vlp, basics for well performance calculation well-performance analysis, or ‘nodal analysis’, dictates that any single point (i.e. the bottom hole) must observe mass balance and can only have one pressure associated with it (lyons and plisga 2004). it is the normal practice that every petroleum engineer will do to understand the well potential and any improvement needed. a simplified model of nodal analysis is illustrated as a node in figure 12. figure 12—nodal analysis for well performance. to make it simple, everything at upstream of the solution node will be treated as the ‘ipr’ and everything at downstream of the node will be part of the ‘vlp’. the ipr & vlp calculation allows to determine the production of a well for a set of conditions by combining the vlp and ipr curves in one plot. this means that the rate at which the vlp and ipr curves across (figure 13) is the rate which the well will produce under these conditions such as wellhead pressure, water gas ratio, vertical lift correlation, solution, and wellbore structure. figure 13—ipr & vlp calculation concept. best fit inflow performance relation (ipr) the workflow can be illustrated in figure 14. the first step is to figure out the best fit correlation from a built-in pool to convert whp to bhp. starting with the well that has both surface and downhole pressure gauges installed, the appropriate correlations are loaded to convert the surface pressure data to downhole pressure data, then the conversion results are compared with the actual pdhg data. once the most 11 appropriate correlation is selected, two adjusting parameters can be applied to further calibrate it to match the exact data. one parameter is used to control the gravity (related to pvt) and the other is to control the friction loss (related to tubing roughness). all the flow rates are thus determined from the actual well test performance as shown in figure 15. figure 14—using pdhg data for best fit correlation. figure 15—well performance from history match. this calibration workflow is applied to the other wells of similar structures but without pdhg, and all conversion results are with the good quality. 12 best fit fractured reservoir performance in addition to adjust the kmaxf /kminf ratio to a reasonable min-mid-max range (mid case model) as illustrated above, the ratios in the aoi are also re-scaled to generate the min and max case models to test the sensitivity of permeability tensor (i.e. kmaxf /kminf ratio). in the min case model, the kmaxf /kminf ratio in all grid cell are scaled to the early-defined min value, and similarly, the kmaxf /kminf ratio in all grid cell are scaled to the early-defined max value to generate the max case model. flow simulation were then run on the min, mid and max case models to quantify the impact of fracture permeability tensors. figure 16 displays the production profiles generated from the min, mid, and max case models. the sensitivity analysis results as shown in table 1 conclude that the kmaxf /kminf ratio uncertainty in field a does not have a significant impact on either plateau length or pulse test response. figure 16—production profiles generated frommin, mid and max case fracture models. table 1—kmaxfx/kminfx ratio sensitivity analysis. scenario impact plateau length pulse test average ratio of mid, with min and max cutoff extend by 6 months 0.06 psi/week ratio of min in all grid cells extend by 6 months 0.06 psi/week ratio of max in all grid cells extend by 13 months 0.06 psi/week forward plan with the pressure decline from the field production, the reservoir behavior may change with time and this can help understand more on the interaction between fracture and matrix. therefore, with the reservoir surveillance program, reservoir pressure and field production should be monitored closely. dual-porosity dual-permeability model may also be considered if the current pseudo-fracture model is deemed insufficient. fracture data acquisition during future infill drilling will also help to characterize the fractures and evaluate their impact on reservoir performance. production implications from offset fields of similar kind may also shed light on field development. it should be kept in mind that reservoir modelling effort never stops. rather, it is an ever-green process that dynamic reservoir performance information should be incorporated to update the model periodically or when seeing any gaps to improve its accuracy of prediction to assist optimal reservoir management. 13 acknowledgment the authors thank the management of uecsl and cnpc for their permission to publish this paper. special thanks to fracture subject matter experts smes for their advices and support on fracture characterization and reservoir modelling and history match. conflicts of interest the author(s) declare that they have no conflicting interests. references aguilera, r. 1980. naturally fractured reservoirs. tulsa, usa: pennwell publishing company. angerer, e., neff, p., and abbasi, i. et al. 2011. integrated reservoir characterization of a fractured basement reservoir. the leading edge 30(12):1408-1413. awdal, a., healy, d., and alsop, g. i. 2016. fracture patterns and petrophysical properties of carbonates undergoing regional folding: a case study from kurdistan, n iraq. marine and petroleum geology 71(8): 149-167. bourbiaux, b., basquet, r., and daniel, j. 2005. fractured reservoirs modelling: a review of the challenges and some recent solutions. first break 23(9):33-40. kuchuk, f., biryukov, d., and fitzpatrick, t. 2015. fractured-reservoir modeling and interpretation. spe journal 20(5):78-96. spe-176030-pa. bratton, t., canh, d., and que, n. 2006. the nature of naturally fractured reservoirs. oilfield review 18(2): 4-23. crain, e. 2017. crain's petrophysical handbook (online). https://www.spec2000.net/22-fracloc1.htm, accessed june 2017. fekete associates inc., dual porosity. http://www.fekete.com/san/theoryandequations/welltesttheoryequations/dual_porosity.htm, accessed june 2017. galuppoc c., toscani, g., turrini, c., et al. 2016. fracture patterns evolution in sandbox fault-related anticlines. italian journal of geosciences 135(1):5-16. kappa dda book v4.30.01. https://www.kappaeng.com/documents/flip/dda/, accessed june 2017. lee, j. and wattenbarger, r.1996. gas reservoir engineering. textbook series, spe, richardson, texas. lyons, w.c and plisga, g. j. 2004. standard handbook of petroleum & natural gas engineering (second edition). oxford, uk: gulf professional publishing. narr, w. 1996. estimating average fracture spacing in subsurface rock. aapg bulletin 80(10): 1565–1586. narr, w., schechter, d., and thompson, l. 2006. naturally fractured reservoir characterization. society of petroleum engineers, richardson, texas. narr, w., fischer, d., harris, m., et al. 2004. understanding and predicting fractures at tengiz–a giant, naturally fractured reservoir in the caspian basin of kazakhstan. search and discovery article #20057. nelson, r.a. 2001. geologic analysis of naturally fractured reservoirs (second edition). oxford, uk: gulf publishing. price, n. 1966. fault and joint development in brittle and semi-brittle rock. pergamon press 32(5):176-190. price, n. and cosgrove, j. 1990. analysis of geological structures. cambridge university press 128(3)502-510. stearns, w. and friedman, m. 1972. reservoirs in fractured rock: geologic exploration methods. in stratigraphic oil and gas fields—classification, exploration methods, and case histories ed. gould, h.r. chap 16, 82– 106. satter a. and iqbal g. 2015. reservoir engineering: the fundamentals, simulation, and management of conventional and unconventional recoveries. oxford, uk: gulf professional publishing. minh vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 4+ years. he has had 25 years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. http://earthdoc.eage.org/publication/search/?pubjournal=3&pubvolume=2005 https://www.spec2000.net/22-fracloc1.htm http://www.fekete.com/san/theoryandequations/welltesttheoryequations/dual_porosity.htm https://www.kappaeng.com/documents/flip/dda/ 14 san su, aapg, is a development geologist in unocal east china sea ltd., where he has worked for 11 years. his research interests are in geology and geophysics, carbonate formation evaluation and characteristics. he holds bachelor’s and master’s degree in geoscience from china university of geoscience, beijing. jianjiang lv, spe, is production engineer in unocal east china sea ltd., where he has worked for 7 years. his research interests are in production and reservoir engineering. he holds master’s degree and ph.d. from southwest petroleum university, both in petroleum engineering. chaohong xiao, is a production engineer in southwest oil & gas field company, where he has worked for 32 years. his research interests are in production engineering and daily field operations management. he holds bsc. degree from southwest petroleum university in petroleum engineering. abstract introduction fractures in reservoir and their impact fracture characterization fracture modeling workflow fracture model calibrated with dynamic data ipr and vlp, basics for well performance calculati best fit inflow performance relation (ipr) best fit fractured reservoir performance forward plan acknowledgment conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.428 received june 29, 2018; revised july 19, 2018; accepted july 26, 2018. *corresponding author: happidence1@tamu.edu 1 dynamic study on the fracture interaction and the predominant frequency of the induced microseismic signals during hydraulic fracturing zhenhua he* and benchun duan, texas a&m university, college station, usa abstract hydraulic fracturing has been used as a successful well stimulation method for decades. the created hydraulic fractures interact with the pre-existing fractures in a naturally fractured reservoir. microseismicity is induced during the treatments. microseismic monitoring has been a routine service to determine the geometry of the hydraulic fractures for over a decade. however, studies on the source mechanisms, the signal characteristics and predominant frequencies are still very limited, and many related problems remain ambiguous. most of the current hydraulic fracturing models are based on a quasi-static framework. however, activation of the natural fractures and microseismicity generation and radiation during hydraulic fracturing are dynamic processes. we apply our in-house dynamic finite element geomechanics code to investigate these problems. first, the slip distributions and the ruptures along the activated natural fractures in the models with different cohesion are studied. we find that some activated natural fractures could have a partial failure while some others could fail entirely. the ruptures could be either unilateral or bilateral and the speeds may vary. the natural fractures and the hydraulic fracture can interact with each other. different patterns of microseismic signals could be induced by different sources. second, the effects of model parameters such as injection rate and young’s modulus on the predominant frequency of the microseismic signals are investigated. we find that injection rate doesn’t affect the predominant frequencies much and a higher young’s modulus could shift the predominant frequencies to the high side. rupture patterns (i.e., directionality and speed) along the natural fractures could affect the spectrum of the induced microseismic signals. the spectrum could either have multiple predominant frequencies or be relatively flat over the investigated frequency range. introduction hydraulic fracturing is a critical well stimulation technology for economically producing oil and gas from unconventional reservoirs (warpinski et al. 2012). natural fractures are present in most unconventional reservoirs and could affect the behaviors of the hydraulic fractures (gale et al. 2007; wu and olson 2014). extensive research including experimental (e.g., blanton 1986; warpinski and teufel 1987; renshaw and pollard 1995; beugelsdijk et al. 2000; gu et al. 2011; bahorich et al. 2012; yang et al. 2016) and numerical (e.g., zhang and jeffrey 2006; dahi-taleghani and olson 2011; gu and weng 2010; olson and wu 2012; chuprakov et al. 2013; wu and olson 2014; zhang et al. 2015; duan 2016) work has been conducted to study the interaction between the natural and hydraulic fracturs. akulich and zvyagin (2008) and duan (2016) presented that the activation of the natural fractures could change the opening profile of the hydraulic fracture. when the fracturing fluid pressure within a hydraulic fracture accumulates and the effective mailto:happidence1@tamu.edu 2 normal stress reached the rock tensile strength, the rock breaks and abrupt or jerky opening (hu et al. 2017) occurs. most of these studies are based on a quasi-static framework, while abrupt opening and unstable shear slip of fractures are dynamic processes. in this study, we investigate dynamic interactions between a hydraulic fracture and pre-existing nature fractures. when a hydraulic fracture is propagating in a naturally fractured reservoir, seismicity could be induced. warpinski et al. (2012) studied the induced seismicity in many fracturing treatments in all the major shale basins in north america and found the magnitudes are very small (i.e., -3.0 mw ~ 1.0 mw and typically around -2.5 mw). so, the induced events are called microseismic events. warpinski et al. (2013) also pointed out the source mechanisms of the microseismicity still remains ambiguous. zeng et al. (2014) presented that the opening and growth of tensile fractures and shear slip along fractures during hydraulic fracturing are the major source mechanisms for the induced microseismic events and showed microseismic traces recorded on six stations. and these traces include some specific patterns of signals such as isolated spiky signals and continuous signals with coda waves. similar patterns of microseismic signals can also be found in song et al. (2010). duan (2016) numerically studied and also presented such characteristics of the induced microseismic signals from different sources. different sensors are used to record the microseismic signals in the petroleum industry. warpinski (2009) stated that the best sensors used to acquire the microseismic data will be those with high sensitivity, low self-generated noise and a flat response over the frequency range of interest. in microseismic monitoring, there are two main types of sensors: ‘omnigeophone’ and ‘gac’ (geophone accelerometer) sensor. an omni-geophone can be placed in any orientation and a gac sensor can provide acceleration data. geophones measure velocity and accelerometers measure acceleration. however, they respond well to different ranges of frequency (warpinski 2009). determination of predominant frequencies could be helpful for sensor selection (maxwell, 2014). in this study, we investigate whether some model parameters such as the rock properties and injection parameters could affect the predominant frequencies of microseismic signals. model and methods figure 1 shows the model setup. there is one hydraulic fracture (hf) and one set of inclined natural fractures (nfs) in the model. this set of nfs includes eight uniformly distributed nfs. their length is about 58 meters and spacing is about 35 meters. the red triangles in the model indicate the location of the receivers. the parameters are listed in table 1. the reservoir is assumed to be at around 2500 meters in depth. the maximum and minimum horizontal stresses and initial reservoir pore pressure are 55, 40 and 25 mpa, respectively. based on the data from stanford rock physics laboratory (i.e., mavko, 2005), the rock property values are selected. kohli and zoback (2013) presented that some shale samples show frictional coefficients around 0.4. the fracturing fluid with a viscosity of 0.02 pa ∙ s is injected at a rate of 0.053 m3/s (i.e., about 20 bpm). figure 1—model setup. 3 table 1—model parameters. parameters model a model b (base model) model c density ρ (kg/m3) 2400 young’s modulus e (gpa) 10.0 poisson’s ratio ν 0.2 p wave velocity 𝑉𝑝 (m/s) 2200 s wave velocity 𝑉𝑠 (m/s) 1300 static friction 𝜇𝑠 0.35 dynamic friction 𝜇𝑑 0.25 critical slip distance 𝑑0 (m) 0.001 cohesion 𝑐𝑜 (mpa) 1.05 0.35 0.70 skempton’s coefficient b 0.8 tensile strength t (mpa) 1 initial 𝜎𝑥𝑥 (mpa) 55 initial 𝜎𝑦𝑦 (mpa) 40 initial 𝜎𝑥𝑦 (mpa) 0 initial pore pressure p (mpa) 25 injection fluid viscosity η (pa ∙ s) 0.02 hydraulic fracture height ℎ𝑓 (m) 50.0 injection rate 𝑖 (m3/s) 0.053 in this study, a dynamic finite element method (duan 2016) is applied to perform numerical simulations. eqdynafrac is developed from another dynamic fem code eqdyna (duan and oglesby 2006; duan and day 2008; duan 2010; duan 2012) for rupture dynamics and seismic wave propagation. eqdyna follows the standard procedure of fem (e.g. hughes 2000) to solve a dynamic problem and has been verified on many benchmark problem (harris et al. 2009;2011;2018). the dynamic fem solves the equations of motions as below. 𝑑𝑖𝑣(𝝈) + 𝜌𝒃 = 𝜌�̇�,…………………………………………………....………………………………..(1) where, 𝝈 is the stress tensor, ρ is density, b is body force vector and �̇� is the acceleration vector. in the models, eqdynafrac treats fractures as surfaces across which a discontinuity in the displacement vector is permitted. on a fracture, one fem node is split into two halves and the two halves interact with each other by the traction acting on the surface between them. hydraulic fracturing opening and propagation are the source of deformation in each model. the hydraulic fracturing propagation and fracturing net pressure follows the non-leak off pkn model (valko and economides 1995). the equations are as below, 𝑙𝑓(𝑡) = ( 625 512π3) 1 5 ( 𝑖3𝐸′ 𝜂ℎ𝑓 4 ) 1 5 𝑡 4 5,……………….…....……………..…………………………………………………(2) 𝑝𝑛(𝑥, 𝑡) = ( 32𝜂𝑖 𝜋 ) 1 4 𝐸 ` 3 4 ℎ𝑓 (𝑙𝑓(𝑡) − |𝑥| 1 4) 1 4 , |𝑥| ≤ 𝑙𝑓(𝑡),…………………………...………………………………....(3) where 𝑖 is the injection rate, e’ is the plane strain modulus and calculated as e’=e/(1-v2), e is the young’s modulus, v is the poisson ratio, η is the fluid viscosity, and ℎ𝑓 is the fracture height. the injection well is assumed at the origin point in figure 1. 4 the coulomb failure criterion and a linear slip-weakening law (e.g., andrews 1976) which is widely used in the earthquake community control the shear failure along the fractures. the two equations are as below. 𝜏𝑐 = 𝜇(𝜎𝑛 − 𝑝) + 𝑐,……………………..……………………………………………………………..(4) 𝜇(𝑙) = { 𝜇𝑠 − (𝜇𝑠 − 𝜇𝑑) × 𝑙 𝑑0 𝑤ℎ𝑒𝑛 𝑙 ≤ 𝑑0 𝜇𝑑 𝑤ℎ𝑒𝑛 𝑙 > 𝑑0 ,…………………………………………………………..(5) where 𝜏𝑐 is the shear strength, 𝜇 is the frictional coefficient, 𝑐 is cohesion, 𝜎𝑛 is the normal stress, and 𝑝 is the pore pressure, 𝑙 is the slip distance, 𝜇𝑠 and 𝜇𝑑 are static and dynamic frictional coefficients, respectively, and 𝑑0 is the critical slip distance. so, (𝜎𝑛 − 𝑝) is the effective normal stress. when the effective normal stress along a fracture reaches the rock tensile strength, the fracture opens. the friction disappears, and the tensile strength becomes zero where the fracture opens. the two walls are regulated not to interpenetrate each other. we assume the medium in the models is undrained, fluid saturated and linearly elastic. the pore pressure is time-dependent. according to harris and day (1993), its increment is a function of the skempton coefficient b, undrained poisson ratio υ, and the time dependent normal stress changes in the xand ydirections ∆𝜎𝑥𝑥(t) and ∆𝜎𝑦𝑦(t). the equation is shown below. ∆p(t) = −b[(1 + υ)/3][∆𝜎𝑥𝑥(t) + ∆𝜎𝑦𝑦(t)].…………………………………………………………(6) in our models, the main model region (i.e., figure 1) that includes all fractures is at the center. a buffer region surrounding the main model region is set to prevent the reflections at the model boundaries from traveling back to the main model region. results and analysis activation of the nfs in different models. when the hf is propagating in the model, the induced stress perturbations could activate some of the nfs. the activation of the nfs of the three models (i.e., models a, b and c in table 1) is shown in figure 2. in model a, the cohesion of the nfs is the largest and we can see no nfs are activated. model b has a much smaller cohesion (i.e., 0.35 mpa), and all the nfs are activated along the whole length. model c has a little larger cohesion (i.e., 0.7 mpa) than model b, and only some of the nfs are activated. we can see the lower (i.e., the region with negative y values in figure 1) fourth (counted from left to right) and the upper first nfs are entirely activated, and the lower second and the upper third nfs are partially activated although the slip magnitudes are very small comparatively (i.e., the inset plots in figure 2). 5 figure 2—activation of the nfs in the models a, b and c. displacement profiles along the hf in different models. in figure 3, the top panel (a) shows the displacement profile of the two hf walls in the three models, the middle panel (b) shows the width profile along the hf, and the bottom panel (c) shows the shearing profile (i.e., the relative displacement of the two walls in the shear direction) along the hf. in model a, there are no nfs activated as shown in figure 2, and the two hf walls open in the opposite directions. the open width profile is almost elliptical as shown in figure 3(b) and there is no shearing between the two walls as shown in figure 3(c). in model b, all the nfs are activated. the displacement profiles of the two hf walls are greatly distorted. the flow channel along this hf is very tortuous. in figure 3(b), the width profile has three peaks at x = -50, 0 and 50 meters corresponding to the effect of the slip of the nfs intercepting x-axis at x = -50, 0 and 50 meters. from figure 3(b), we can see that the hf only propagates to 80 meters. so, the other two nfs intercepting x-axis at -100 and 100 meters do not have much impact on the width profile. figure 3(c) shows there is shearing along the hf. in model c, the lower fourth and upper first nfs are entirely activated, and the lower second and upper third nfs are partially activated with very small slip at one end respectively. in figure 3(b), the width profile has significant change at x = -50 and 50 meters corresponding to the effect of the activated nfs intercepting x-axis at -50 and 50 meters. also, there is shearing along the hf, and different senses of shear can occur. 6 figure 3—the top panel shows the displacements of the two hf walls in the three models; the middle panel shows the width profile along the hf; and the bottom panel shows the shearing profile along the hf. figure 4 shows the evolution of the hf width at the wellbore in the three models. in model a, no nfs are activated. there is no interaction between hf and nfs and thus no abrupt change in the width. however, models b and c have abrupt/jerky opening during the hydraulic fracturing process. the abrupt opening occurs at around 98 seconds in model b and 163 seconds in model c and are caused by the interaction between the hf and the activated nfs. after this abrupt opening, the hf width gradually gets back to the normal trend (i.e., green line in figure 4). by looking at the curve of the hf width evolution more closely (i.e., the inset plot of figure 4), the hf has closing and opening motions. 7 figure 4—evolution of the hf width at the wellbore in the three models. rupture along the nfs in different models. the rupture along the nfs in models b and c are shown in figures 5 and 6, respectively. from figure 5, we can see that the nfs are activated and slide at around 98 seconds, which is corresponding to the time when the abrupt opening of the hf at the wellbore occurs. the patterns of the rupture (i.e., rupture directionality and speed) along the nfs could be very different. the ruptures could be unilateral (i.e., figures 5(a) and 5(h)) and bilateral (i.e., figures 5(b), 5(c), 5(d), 5(e), 5(f) and 5(g)). the rupture speeds in the figures 5(a) and 5(h) are almost constant along the nfs and they are 2173 m/s and 2157m/s, respectively. the speeds of the other ruptures vary along the nfs. we take figures 5(c) and 5(f) for examples. both the ruptures initiate from an inner location on the nfs and then propagate bilaterally to the two ends. from the initiation point to the two ends, the rupture starts from a very slow speed and then gradually accelerates to a high speed respectively. in figure 6, there are some blank plots (i.e., figures 6(b), 6(d), 6(e) and 6(g)), which indicate that the nfs are not activated. by looking at the figures 2 and 6 together, we can see that the ruptures in figures 6(a) and 6(h) are large while the ruptures in figures 6(c) and 6(f) are very small and would not affect the hf opening much. therefore, the abrupt opening of the hf in model c shown in figure 4 is caused by the activation of the upper first (i.e., figure 6(a)) and lower fourth (i.e., figure 6(h)) nfs. the activation of these two nfs occurs around 163 seconds, which is corresponding to the time when the abrupt opening of the hf happens. 8 figure 5—rupture along the nfs in model b (i.e., cohesion = 0.35 mpa). figure 6—rupture along the nfs in model c (i.e., cohesion = 0.7 mpa). induced microseismicity in different models. the xand ycomponents of the seismogram of the induced microseismicity during hydraulic fracturing in models a, b and c are shown in figures 7 and 8, respectively. in model a, there are no nfs activated. so, the only source of the microseismic signals is the non-smooth opening (e.g., the slightly wiggly opening profile in figure 4) of the hf as suggested by duan (2016). isolated spiky signals are generated in both xand ycomponents and they are seismic signals with very short rise time as shown in the inset plot of figure 7. therefore, these isolated spiky signals are induced by hf non-smooth opening, as proposed by duan (2016). in model b, there are nfs activated at around 98 seconds. comparing the models a and b in figures 7 and 8, the microseismic signals are the same from 0-98 seconds. when the nfs are activated at about 98 seconds, continuous signals with relatively large amplitude and long-duration and low-amplitude coda waves are generated. these signals are caused by the unstable shear sliding along the nfs as presented in duan (2016). this is similar in model c when the nfs are activated at around 163 seconds. 9 figure 7—the x-component of the induced microseismicity during hydraulic fracturing. the seismic signals are obtained from the lower first receiver, whose location is shown in figure 1. figure 8—the y-component of the induced microseismicity during hydraulic fracturing. the seismic signals are obtained from the lower first receiver, whose location is shown in figure 1. predominant frequency of the induced microseismicity. to eliminate the impact of the activation of other nfs on the microseismic signals, in this section we keep only one nf in each model. figure 9 shows the model configurations with only one nf. in the left plot (i.e., l1 model), only the lower first (l1) nf exists. the black solid line indicates the location of the nf. the black dashed lines indicate the locations of the other nfs in the previous models, but they do not exist in this model. in the right plot (i.e., l4 model), only the lower fourth (l4) nf exists. in these models, the element length in the x-direction is 1 meter. six elements are used to represent a full wavelength. so, the highest frequency that can be resolved is 𝑓𝑚𝑎𝑥 = 𝑉𝑠 6×𝑑𝑥 = 1300 6×1 = 216.6 (𝐻𝑧). 10 figure 9—model setup with only one nf. the seismogram of the induced microseismicity, the spectrum and the rupture along the nfs in these two models are studied and shown in figure 10. the top half is for l1 model. in the subplot l1(a), we can see that a continuous signal with a coda wave starts to occur around 212 seconds. there are multiple distinct predominant frequencies of 17 hz, 100 hz, and 170 hz as shown in the subplot l1(b). the subplot l1(c) shows the rupture along the nf. it initiates around the center and then propagates bilaterally to the left and right sides. the speed varies along each rupture path. the bottom half is for l4 model. a continuous signal appears at about 155 seconds (i.e., subplot l4(a)). its spectrum is relatively flat over the frequency range. the predominant frequencies are not distinct, and the spectrum mainly lies in the high frequency band. the subplot l4(c) shows that the rupture initiates from the left end, and then propagates unilaterally to the right end. the speed varies at the beginning and then remains almost a constant afterwards. figure 10—the x-component of the seismogram of the induced microseismicity, the spectrum and the rupture along the nfs in the two different models (i.e., l1 and l4). the top half is for the model with only the lower first (i.e., l1) nf, and the bottom half is for the model with only the lower fourth (i.e., l4) nf. 11 effect of injection rate on the predominant frequency. the effect of injection rate on the predominant frequency is studied. the l1 and l4 model configurations are also used in this section. the base model parameters are shown in table 1 (i.e., the base model column). for each model configuration, the injection rate is varied in three different cases. the injection rates in the other two cases double and triple the injection rate in the base case, respectively. at the end of the simulation, the hydraulic fractures propagate to the same length in all three cases. figure 11 presents the spectrums of the induced microseismicity in the three cases under l1 and l4 model configurations, respectively. the top panel shows the spectrums in l1 model configuration. we can see that there are three distinct predominant frequencies in each of the three cases and the three predominant frequencies in one case are very close to those in the other two cases correspondingly. however, the amplitudes in the higher-injection-rate case are greater than those in the lower-injection-rate case. the bottom panel shows the spectrums in l4 model configuration. in general, the spectrums are all relatively flat and mainly lie in the high frequency band. the predominant frequencies of the three cases are all around 150 hz. the amplitude also increases with injection rate. figure 11—comparison of the spectrums of the microseismicity induced in the models with different injection rates. effect of young’s modulus on the predominant frequency. we also investigate the effect of young’s modulus on the predominant frequency and make use of the l1 and l4 model configurations in this section. the base model parameters are also as in table 1 (i.e., the base model column). for each model configuration, the young’s modulus is varied in three different cases and are 10.0, 10.8, 11.6 gpa, respectively. at the end of the simulation, the hydraulic fractures propagate to the same length in all three cases. the spectrums of the induced microseismicity in the three cases under l1 and l4 model configurations respectively are shown in figure 12. the top panel shows the spectrums in l1 model configuration. for each spectrum, there are multiple distinct predominant frequencies. comparing different cases and the 12 second predominant frequency, we can see the predominant frequency shifts to the right (i.e., high frequency) when the young’s modulus increases. the spectrums in l4 model configuration are shown in the bottom panel. all the spectrums are relatively flat over the investigated frequency range and it is hard to distinguish the change or shift of the predominant frequencies with the young’s modulus. figure 12—comparison of the spectrums of the microseismicity induced in the models with different young’s modulus. in summary, from the study on the effects of injection rate and young’s modulus on the predominant frequency of the induced microseismicity, we can see that the spectrum could either have multiple distinct predominant frequencies or could be relatively flat over the investigated frequency range. the injection rate doesn’t affect the predominant frequencies much, however, a higher young’s modulus could shift the predominant frequency to the high side. discussion during hydraulic fracturing, the activation of nfs and the associated microseismic generation and radiation are dynamic processes. dynamic modeling is needed to accurately model the fracture interaction and induced microseismicity. in this study, we do not attempt to simulate the fluid flow in a hydraulic fracture. the well-known non-leak-off pkn model is implemented. although the models may lack of acute fluid pressure response when the hydraulic fracture has sudden opening and/or closing, they still capture the main characteristics of all the processes associated with hydraulic fracturing. in our models, some frequency spectrums have multiple distinct predominant frequencies (e.g., l1(b) in figure 10) and others could be relatively flat over the investigated frequency range (e.g., l4(b) in figure 10). maxwell and cipolla (2011) presented similar frequency spectra of microseismic events induced by hydraulic fracturing. for natural earthquakes, martin (2016) proposed that the controlling factors of the frequency are the size, geometry and the rupture pattern of the earthquake source. we also studied the 13 rupture patterns in our models and found that rupture directionality could affect the frequency spectrum. bilateral ruptures may induce multiple predominant frequencies, while unliteral ruptures may induce relatively fat frequency spectrums. effect of young’s modulus on the predominant frequency is studied. young’s modulus is not a direct input parameter in our dynamic models while p and s wave velocities, 𝑉𝑝, 𝑉𝑠 are. mavko (2005) in stanford rock physics lab presented a saturated shale rock (pore pressure, 𝑃𝑝 around 25 mpa) has 𝑉𝑠 of 1300-1500 m/s under the confining pressure of 40-55 mpa. in these studies, varying young’s modulus is achieved by varying 𝑉𝑝 and 𝑉𝑠 and 𝑉𝑝/𝑉𝑠 is assumed to be about 1.7 for the rocks. conclusions we apply our in-house finite element geomechanics code to study the fracture interaction and the predominant frequency of the induced microseismic signals. some conclusions are achieved as below. 1. cohesion affects the activation of the nfs during hydraulic fracturing process. the nfs are easier to be activated in the low-cohesion models. the nfs could be activated to different extents. some nfs may slide along the whole lengths, while some others may slide along just part of the whole lengths. 2. the opening of the hf could be affected by the activation of the nfs, which changes the width profile along the hf. abrupt opening or closing (i.e., increase or decrease in hf width) could occur when nfs are activated. 3. when a nf is activated, the rupture could be unilateral or bilateral along the nf. the speed of the rupture could be constant or varying along the path. 4. rupture patterns (i.e., directionality and speed) along the nfs could affect the spectrum of the induced microseismicity. the spectrum could have multiple predominant frequencies or could be relatively flat over the investigated frequency range. 5. injection rate doesn’t affect the predominant frequencies much. a higher young’s modulus could shift the predominant frequency to the high side. acknowledgement we appreciate the funding support from the crisman institute and the berg-hughes center at texas a&m university. conflicts of interest the author(s) declare that they have no conflicting interests. references akulich, a. and zvyagin, a. 2008. interaction between hydraulic and natural fractures. fluid dynamics 43(3): 428435. andrews, d. 1976. rupture velocity of plane strain shear cracks. journal of geophysical research 81(32): 56795687. bahorich, b., olson, j. e., and holder, j. 2012. examining the effect of cemented natural fractures on 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warpinski, n. and teufel l. 1987. influence of geologic discontinuities on hydraulic fracture propagation (includes associated papers 17011 and 17074). journal of petroleum technology 39(2): 209-220. wu, k. and olson j. e. 2014. mechanics analysis of interaction between hydraulic and natural fractures in shale reservoirs. paper presented at unconventional resources technology conference (urtec), denver, colorado, usa, 25-27 august. urtec-1922946. yang, x., burghardt, j., zhang, h., et al. 2016. experimental study of hydraulic fracture/natural fracture interaction on a tight sandstone formation. paper presented at unconventional resources technology conference (urtec), san antonio, texas, usa, 1-3 august. urtec-2460449. https://www.quora.com/seismology-what-is-the-frequency-in-hz-of-an-earthquakes-p-wave 15 zeng, x., zhang, h., zhang, x., et al. 2014. surface microseismic monitoring of hydraulic fracturing of a shale‐ gas reservoir using short‐period and broadband seismic sensors. seismological research letters 85(3): 668677. zhang, f., qiu, k., yang, x., et al. 2015. a study of the interaction mechanism between hydraulic fractures and natural fractures in the ks tight gas reservoir. paper presented at europec 2015, madrid, spain, 1-4 june. spe-174384-ms zhang, x. and jeffrey, r. g. 2006. the role of friction and secondary flaws on deflection and re-initiation of hydraulic fractures at orthogonal pre-existing fractures. geophysical journal international 166(3): 1454-1465. zhenhua he currently is a ph.d. candidate in the department of geology and geophysics of texas a&m university. he received the m.s. degree in petroleum engineering from texas a&m university (college station) and the b.s. degree in petroleum engineering from china university of petroleum. his interests are dynamic geomechanical modeling, hydraulic fracturing, induced seismicity, source mechanisms, microseismic clouds, carbonate acidizing, reservoir simulation, data analysis and machine learning. benchun duan is a professor in the department of geology and geophysics of texas a&m university. he received his ph.d. degree in geological science from university of california, riverside in 2006 and joined texas a&m university as a faculty in 2007. his research interests include earthquake source physics, geomechanics, and computational seismology. a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.453 received july 11, 2019; revised august 18, 2019; accepted september 8, 2019. *corresponding author: xiangwang@cczu.edu.cn 1 well production real-time intelligent monitoring based on convolutional neural network zhen wang, luming oil and gas exploration and development co., ltd, shengli oilfield, dongying, china; xiang wang*, changzhou university, changzhou, china; weigang duan, fajun li and fei chen, luming oil and gas exploration and development co., ltd, shengli oilfield, dongying, china abstract based on the theory of deep learning, this paper proposes the use of convolution neural network (cnn) method to identify the working condition of pumping unit of an oil well by indicator diagram. the structure and principle of cnn are introduced, and the cnn-based indicator diagram identification model is established. over 180,000 pieces of indicator diagram data from a real oilfield are collected and the working conditions corresponding to each indicator diagram are manually labeled as the training set for cnn model. using this training set, the cnn-based indicator diagram identification model is trained and tested. the training and test results show that the accuracy of the cnn-based indicator diagram identification model is more than 90%. compared with the traditional neural network models, cnn model can learn from the image directly and avoid the complex process of artificial extraction of features, hence lead to a better performance. the cnn-based indicator diagram classification and recognition model can be combined with the real-time data acquisition system of the well to realize the real-time intelligent monitoring of the oil well working condition. introduction rod pumping is the most commonly used method in oil production. monitoring the working conditions in real time is very important to avoid the inefficient production, reduce the production cost, and improve the oil production capacity. the working conditions diagnose is mainly conducted by using the indicator diagram of pumping well (wang et al. 2001). with the continuous improvement of information construction in the oilfield, real-time online measurement of well indicator diagram has been achieved. the sensors installed in the wells can collect the indicator diagram data by a certain frequency and upload the data to the management terminal (wang 2006). if the data is collected every 30 minutes, for a management region of an oilfield which has 100 wells, 144,000 pieces of data will be collected within one month. for such a large number of data, the traditional indicator diagram identification method, which identifies each diagram manually, will bring a huge workload, and the identification accuracy is affected by the experience and knowledge of the field engineer. there are also many automatic methods were introduced for indicator diagram identification, such as the decision tree method (gong 2016), gray correlation analysis (xu and yang 2013), pattern recognition method (schirmer et al. 2013), etc. however, these methods also have the issues of low accuracy. in recent years, with the development of machine learning technology, researchers start to apply the machine learning methods to identify the indicator diagram automatically (nazi et al. 2013; martinez et al. 1993; pan and ge 1996; yue et al. 1999; li et al. 2014; meng 2012). the main ideas of these methods are: firstly, extract the feature vectors (e.g. area of the indicator diagram, the maximum/minimum value, etc.) from the indicator diagram. then, use the traditional neural network method to identify the working mailto:xiangwang@cczu.edu.cn 2 conditions of the indicator diagram according to the feature vectors. the selection of features and the quality of these features have a significant influence on the identification results. too many features lead to a large computation budget and noise may involve. but if we consider too few features, the indicator diagram cannot be fully reflected and leads to a low identification accuracy. moreover, lots of useful information is lost during the feature extraction process (li 2015). to address these problems, the convolution neural network was introduced. the convolution neural network (cnn) model animal visual perception and avoid the explicit feature extract process. this makes cnn a great success in many visual recognition tasks. in this paper, a cnn based identification model is proposed and is used in indicator diagram identification. results show that cnn method can identify the working conditions by the indicator diagram with over 95% accuracy and high efficient. convolution neural network convolution neural network (cnn) is a type of feed-forward artificial neural network in which the connectivity pattern between its neurons is inspired by the organization of the animal visual cortex (lisa lab 2017; matsugu et al. 2003). it is a variation of a multilayer perceptron (mlr). cnn has wide applications in image and video recognition, recommender systems (aaron et al. 2013), and natural language processing (collobert and weston 2008). in this section, we introduce the structure of cnn and its training method. structure of cnn. cnn includes several feature extraction stages and a classifier in structure. in each feature extraction stage, a higher level of features is obtained through convolution operations. each feature extraction stage includes a convolution layer and a sub-sampling layer. the output of each layer is a series of feature maps. the output of feature maps obtained in the last feature extraction stage is used as input to the classifier. the classifier of cnn generally uses back propagation (bp) network (cun et al. 1990; simard et al. 2003) and radial basis function (rbf) network (lecun et al. 1998), etc. figure 1 shows a typical structure of cnn with two feature extraction stages. figure 1—a typical structure of cnn with two feature extraction stages. convolution layer. a convolution layer contains a series of feature maps, each of which is connected to one or more of the feature maps in the previous layer by a convolutional kernel. the convolutional kernel of k×k size defines the connection weight. for cnn in figure 1, a feature map in layer c3 can be connected to multiple feature maps in layer s2. all neurons in the same feature map share the same convolutional kernel and bias, and the convolution kernel and bias are determined by training/learning method. each neuron in the convolution layer extracts the local features at the same position in the previous part of the feature map by convolution. taking the element of the jth feature map of the ith convolution layer as an example, the convolution operation is calculated as, input 6464 c1 4@6060 s2 4@3030 c3 14@2626 s4 14@1313 c5 120 f6 84 output 8 convolutions subsampling convolutions subsampling full connection 3 𝑜𝑖𝑗(𝑥, 𝑦) = tanh [ 𝑏𝑖𝑗 + ∑ ∑ ∑ 𝑤𝑖𝑗𝑘(𝑟, 𝑐)𝑜(𝑖−1)𝑘(𝑥 + 𝑟, 𝑦 + 𝑐) 𝐶𝑖 𝑐=0 𝑅𝑖−1 𝑟=0 𝑘∈𝐾𝑖𝑗 ] ,………………(1) where tanh denotes the hyperbolic tangent activation function; bij denotes the bias parameter of the feature map; kij denotes the set of feature maps in the (i-1)th layer connected to oij; wijk denotes the convolution kernel between the feature map oij and the feature map o(i-1,k); ri and ci denote the number of rows and the number of columns of the convolution kernel correspondingly. assuming that the size of the feature map in (i-1)th layer is n1×n2. if we do convolution operation to the feature map using a l1×l2 convolution kernel, the size of feature map obtained for the ith layer is (n1l1+1)×(n2-l2+1). we can see that the convolution operation can reduce the dimension of the data. generally, the size of the convolution kernel is 5×5. if the size of the convolution kernel is too small, it cannot obtain the local characteristics between the adjacent regions of the image. but if the size is too large, the calculation budget of the convolution operation will be increased and the calculation speed will be slow. sub-sampling layer. the sub-sampling layer uses the region filter to reduce the resolution of the feature map in the convolution layer. the sub-sampling operation can extract the important features for classification, and ignore the useless details and noise. this gives cnn a good noise resistance ability. the feature maps of the sub-sampling layer are one-to-one corresponding to the feature maps of the previous convolution layer. assuming the resolution of the sub-sampling operation is n, the resolution of feature map in sub-sampling layer becomes the 1/n2 of the original map. the sub-sampling operation can decrease the number of data significantly. there are two main sub-sampling methods, the mean sampling, and the maximum sampling. the sub-sampling operation makes the output of the convolution neural network invariance in spatial. taking the element of the jth feature map of the ith layer as an example, the subsampling operation is calculated as follows. 𝑜𝑖𝑗(𝑥, 𝑦) = tanh [𝑏𝑖𝑗 + 𝑔𝑖𝑗 ∑ ∑ 𝑜(𝑖−1)𝑗(𝑥𝑁𝑖 + 𝑟, 𝑦𝑁𝑖 + 𝑐) 𝑁𝑖−1 𝑐=0 𝑁𝑖−1 𝑟=0 ] ,………………………........(2) where gij denotes the gain parameter of the feature map oij; ni denotes the sub-sampling rate of the ith layer. the step size of the feature combination is equal to the side length of the sub-sampling operation, and ni>1. assuming that the size of the feature map of the (i-1)th layer is n1×n2, the ith layer is obtained through a sub-sampling operation with a l×l sub-sampling rate. then the size of the ith layer should be n1/l×n2/l, where   denotes rounded down operation. classifier. cnn extracts the feature of the input image and reduces the dimension of data through the convolution operation and sub-sampling operation in its hidden layers. that makes cnn can obtain the effective features and filtering the interference information for identification and classification. because cnn uses the backpropagation algorithm to train the weight of the entire network, so the classifier for cnn usually chooses the fully connected bp network classifier (cun et al. 1990; simard et al. 2003), polynomial logic regression classifier (jarrett et al. 2010), radial basis function network classifier (lecun et al. 1998), and so on. training of cnn. the cnn obtains the mapping relationship between input and output through learning. this mapping relationship is finally reflected in the network weight, which makes cnn have the ability to extract features of input data layer by layer. in this paper, a supervised error backpropagation algorithm is used to train the cnn network. the sum of squared the output errors is used as the system error function. the weights are updated according to the error backpropagation algorithm during the training process. the training process can be divided into two stages, they are, the forward propagation of the input signal and the backpropagation of the output error. in the process of forward propagation, the sample image data is input directly into the input layer of cnn, and the result is extracted and transformed by layer-by-layer of the middle hidden layer, and finally to the output layer. in the backpropagation process, the error between 4 the sample label and the forward propagated output is calculated, and the weights of the entire network are adjusted by the backpropagation algorithm to achieve the best performance. the detailed training process of cnn is as follows: (1) forward propagation process a. take a sample from the training set (x, dp) and put the sample data x into cnn; b. forward propagation the input data according to the convolution operation calculation eq. 1, the sub-sampling operation calculation eq. 2 and the classifier, and obtains the actual output yp of the input data x. (2) backpropagation process a. calculate the error e from the actual output yp and the ideal output dp; b. back propagate the error e to update the weight of the entire network. in practical application, the training process usually uses the batch training technology, which weights and biases are updated after multiple of the inputs and targets are presented. the detailed descriptions of the error estimate method and the weights update method can be found in li (2015). cnn based indicator diagram identification model the process of indicator diagram identification based on cnn is shown in figure 2. figure 2—the process of indicator diagram identification based on cnn. pretreatment of indicator diagram. in order to keep the quality of the training and learning of the cnn network, it is necessary to standardize the input data of the network. standardized indicator diagram drawing. in order to reduce the training time and improve the convergence speed of learning, the original indicator diagram is pre-processed to a normalized binary image as the input of cnn. in our model, the displacement vector s and the load vector f measured from the pumping unit are plotted as 64×64 binary image. the plot uses displacement vector as the x-axis and the bound is set to [min(s), max(s)]; and uses load vector as the y-axis and the bound is set to [min(f), max(f)]. cnn output definition. in this paper, all the samples are classified into eight categories of working conditions of pumping unit, of which seven are the most common types of working conditions, and the rest of the conditions is classified as unknown. figure 3 shows the typical indicator diagram of the well and the corresponding working conditions. 5 figure 3—the typical indicator diagram. the number of neurons in the output layer of cnn equals the number of categories of working conditions we defined. when we input an indicator diagram to cnn, only one of all the neurons in the output layer obtain value 1, and the remaining neuron output is 0. the ideal output mode for cnn is shown in table 1. table 1—ideal output mode for cnn model. index working condition output vector 1 unknown [1 0 0 0 0 0 0 0] 2 normal [0 1 0 0 0 0 0 0] 3 insufficient liquid [0 0 1 0 0 0 0 0] 4 gas influence [0 0 0 1 0 0 0 0] 5 travelling valve loss [0 0 0 0 1 0 0 0] 6 standing valve loss [0 0 0 0 0 1 0 0] 7 piston out [0 0 0 0 0 0 1 0] 8 gas locking [0 0 0 0 0 0 0 1] model description. in this study, we use lenet-5 (elsawy et al. 2016), the most commonly used structure of cnn, as the cnn structure of indicator diagram identification model. lenet-5 contains two feature extraction stages and a neural network classifier (figure 1). the input for our cnn model is a normalized 64×64 binary image of indicator diagram, and output is an 8×1 column vector. the first feature extraction stage of cnn consists a convolution layer c1 and a sub-sampling layer s2. the c1 layer is obtained by convolution of the original image through four 5×5 convolution kernels. that makes c1 layer contains four 60×60 feature maps. there are one 5×5 convolution kernel and one bias normalunknown piston out insufficient liquid gas locking gas influence standing valve losstravelling valve loss 6 between the original image and each feature map in the c1 layer. the number of weights needs training is 4×(5×5+1)=104. the s2 layer is obtained by one-to-one sub-sampling operation on the feature maps of the c1 layer. the sub-sampling resolution is set to 2×2. hence the size of feature maps in the s2 layer is 30×30, and the number of the maps is 4. each sub-sampling operation contains two training parameters, which are multiplicative bias and additive bias. the s2 layer has 4×(1+1)=8 weights. the second feature extraction stage of cnn consists of convolution layer c3 and subsampling layer s4. the convolution layer c3 contains 14 feature maps, corresponding to the size of 14 convolution kernels is 5×5, so the layer of the feature map resolution of 26×26. each of the feature maps in the c3 layer is connected to one or more maps of the s2 layers. this not only reduces the number of connections between the c3 and s2 layers but more importantly, it can destroy the symmetry of the network connection. the connection between the c3 layer and the s2 layer is shown in figure 4. the number of weights required for the c3 layer is 5×5×14+14×1=364. figure 4—the connection between the c3 layer and s2 layer. the sub-sampling resolution of the subsampling layer s4 is still 2×2, so s4 outputs 14 13×13 feature maps. each sub-sampling operation requires two training parameters. the number of weights required in the s4 layer is 14×2=28. the c5 layer is a convolution layer, and each feature map is connected to all the feature maps of the s4 layer. this connection type usually is called as full connections. c5 layer contains 120 1×1 feature maps, which can also be seen as a 120-dimensional column vector. the convolutional kernel size for this layer is 13*13. the number of connections between the s4 layer and c5 layer is 120×(13×13×14+1)=284,040, i.e. the number of weights is 284,040. the f6 layer is a hidden layer of bp neural network with 84 nodes. there are 84×(120+1) = 10164 weights for this layer. the output layer contains 8 nodes, and a 1×8 output column vector is obtained. the position of the element with the largest value in the vector corresponds to the classification result of the network. experimental results the indicator diagram set collected from a real oilfield are used to training our proposed cnn model and verify its effectiveness. the data set includes 180,000 indicator diagram from 39 wells. all indicator diagrams are labelled by means of manual identification and can be divided into 8 categories. 2/3 of each category are randomly selected as training set and the rest as the test set. the total number of training 1 2 3 4 1 2 3 4 5 6 7 8 9 10 11 12 13 14 7 samples is 120,000 and the number of test samples is 60,000. the number of samples for each type of working condition is shown in figure 5. figure 5—distribution of experiment samples. the structure of cnn used in our model is lenet-5, which shows good performance in the experiments of image recognition and speech recognition. the detail description of the cnn is given in section 3. before training our cnn model, we need to determine the learning rate η and the training times s. for the learning rate η, a too large training rate may lead to an unstable training process, and a too small rate will slow down the convergence rate of training, hence make the training cycle too long and is easy to fall into local optima. according to li’s work (2015), we choose the learning rate η=0.5 in our model. for the training times s, the training times should be decided carefully to make sure cnn will be trained adequately without overfitting. according to li’s work (2015), we choose the training times s=20 in our model. the training time for our cnn model is 6,235s. when training process is completed, the test samples and training samples are used to verify the identification accuracy of the model, results show that the recognition error of the training sample is 1.79%, and the recognition error of the test sample is 2.00%. the accuracy of the cnn-based indicator diagram recognition model is more than 90%. the average time required for our cnn model to identify an indicator diagram is 3.0 ms. from the result, we can see that the performance of cnn model is excellent. the cnn-based indicator diagram classification and recognition model can be combined with the real-time data acquisition system of the well to realize the real-time intelligent monitoring of the oil well working condition. conclusions based on the theory of deep learning, this paper proposes the use of convolution neural network method to study the massive indicator diagram collected in the pumping unit of oil well, and identify the working conditions of the oil well. the structure and principle of cnn are introduced and the cnn based indicator diagram recognition model is established. the accuracy of the cnn-based indicator diagram recognition 0 10000 20000 30000 40000 50000 unknown normal insufficient liquid gas influence travelling valve loss standing valve loss piston out gas locking number of training samples number of test samples 8 model is more than 90%. the efficiency of the identification process is excellent. the cnn based indicator diagram recognition model can be combined with the real-time data acquisition system of the well to realize the real-time intelligent monitoring of the oil well working condition. acknowledgments this work is supported by open fund (plc20190803) of state key laboratory of oil and gas reservoir geology and exploitation (chengdu university of technology) and the natural science research project of higher education of jiangsu, china (no. 17kjb440001). we would like to thank luming oil and gas exploration and 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2003. subject independent facial expression recognition with robust face detection using a convolutional neural network. neural networks 16(5): 555-558. martinez, e.r., moreno, w.j., castillo, v.j., et al. 1993. rod pumping expert system. paper presented at petroleum computer conference, new orleans, united states, 7-9 january. meng, q. 2012. theoretical research on recognition of rod pumped well working condition through dynamometer card based on cellular neural network theory. master thesis, china university of petroleum (east china), qingdao, china. nazi, g. m., ashenayi, k., lea, j. f., et al. 2013. application of artificial neural network to pump card diagnosis. spe computer applications 6(6): 9-14. pan, z. j., and ge, j. l. 1996. an adaptive neural networks for identification of dynamometer card. acta petrolei sinica 17(3): 104–109. schirmer, p., gay, j. c., and toutain, p. 2013. use of advanced pattern-recognition and knowledge-based system in analyzing dynamometer cards. spe computer applications 3(6): 21-24. simard, p. y., steinkraus, d., and platt, j. c. 2003. best practices for convolutional neural networks applied to visual document analysis. paper presented at international conference on document analysis and recognition, edinburgh, uk, 2-5 august. http://deeplearning.net/tutorial/lenet.html 9 wang, z., xue, g., jin, z., et al. 2001. using human nerve network for indicator diagram identification. petroleum drilling techniques 29(2): 56–57. wang, y. 2006. remote monitoring and fault diagnosis system of sucker road oil well. master thesis, wuhan university of technology, wuhan, china. xu, g. and yang, s. 2013. application of grey theory in fault diagnosis of rod-pumped well. journal of hefei university of technology (natural science) 36(10): 1265–1268. yue, j., zuo, j., and li, h. 1999. distinguishing method to characteristics of dynamometer diagram moment of pumping wells. oil-gas field surface engineering 18(3): 15–16. zhen wang is an engineer at luming oil and gas exploration and development co., ltd, shengli oilfield. he holds a master’s degree in oil and gas field development engineering from china university of petroleum (east china). his expertise is oil well production management and smart oilfield. xiang wang is an assistant professor at school of petroleum engineering, changzhou university. he got his phd degree from china university of petroleum (east china). his research interests are the interface of mathematics, computer science, and engineering to better understand and optimize the development of oil and gas reservoirs. weigang duan is a senior engineer at luming oil and gas exploration and development co., ltd, shengli oilfield. he has over 20 years of experience in oil and gas production and management. fajun li is a senior engineer at luming oil and gas exploration and development co., ltd, shengli oilfield. he has long been engaged in research and management of oil well production technology and has rich experience. fei chen is an engineer at luming oil and gas exploration and development co., ltd, shengli oilfield. he is currently engaged in research and management of oilfield information construction. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1183 received january 3, 2021; revised march 2, 2021; accepted april 3, 2021. *corresponding author: neogi@mst.edu 1 dynamics in drops as confined systems containing nanoparticles: reformation of nanoparticles and evaporation of water vijitha mohan, university of calgary, calgary, canada; xianjie qiu, and parthasakha neogi*, missouri university of science and technology, rolla, usa abstract brine is used to displace crude oil in a reservoir and its performance improves when brine contains nanoparticles. it is the presence of nanoparticles in confinements, such as at dynamic contact lines and in thin films, which is of importance. the investigators here have determined a fast way to obtain confined systems by evaporating a small drop of water containing nanoparticles. water droplets containing nanoparticles of alumina or silica were evaporated on surfaces of polyethylene terephthalate sheets, which are partially wet by water, and glass which is fully wet. after the liquid in the drops evaporated, the residues were examined under a microscope and sintering and melting effects, crystals growth and dendritic formations for alumina and monoliths for silica were seen. the coffee stains are seen in most cases; however measurements show that the contact lines are not always pinned. turbidity measurements showed that no significant reformation could have taken place in the bulk liquid. a simple model for evaporation, based on geometric measurements, showed that much of the film seen on the solid arose out of evaporation of water that forced the particles down. sintering rates into the interior could be quantified and shown to be unstable. introduction deegan and coworkers (deegan et al. 1997; deegan et al. 2000; and deegan 2000) studied small drops of water containing small particles, evaporating from a glass surface. they found that the basal radius of the drop did not change. the particles migrated to the contact line due to a flow that was generated and pinned the foot of the drop there. the rate of evaporation at the contact line was shown to be infinite in a simple model and gave rise to this flow. much more theoretical and experimental work followed and have been cited in a recent review (mampallil and eral 2018). most work continues to deal with low particle concentrations and/or larger particles. the particles used by deegan et al. (1997; 2000; deegan 2000) also showed that the pinning broke down at a very late stage. their particles were 1µm and, in one case 0.1 µm in diameter, that is, had no brownian motion (less than 0.1 µm diameters are suggested for significant brownian motion). the concentrations of the particles were at 2% or less by volume. researchers have been interested in looking at the effect of nanoparticles (diameters less than 30 nm) at interfaces and in higher amounts for the of crude oil (bera and belhaj 2016; zhang et al. 2014; cheringhian and hendraningrat 2018; ko and huh 2019). we have examined below, the footprints of evaporating drops of water containing larger amounts of alumina (al2o3) and silica (sio2) nanoparticles with water containing 1 wt% nacl on surfaces of polyethylene terephthalate (pet) and glass. we confine ourselves to liquid-air systems here and not liquid-liquids system in oil recovery because of the ease in achieving films and analyzing the results. mailto:neogi@mst.edu 2 evaporating drops were considered because the dynamics of confined systems in crude oil displacement, such as in thin films and the dynamic contact lines, play key role in the displacement process (norman 1991). nanoparticles at large concentrations show extensive reformation. sintering (ristić and milosević 2006) is common. the first layer of molecules on the solid surface is more mobile and can cause two particles to stick. further, the laplace pressure, which is the product of curvature and surface tension is very high for the nanoparticles. this gives rise to melting at room temperature and below (nanda et al. 2003). finally, as the chemical potentials are high, nanoparticles dissolve faster in the dispersion medium. as a result, the smaller particles dissolve and disappear while the larger ones grow. this is ostwald ripening (mcnaught and wilkinson 1997). 1% nacl has been added to water to mimic oil field water, however, it would also discourage ostwald ripening by reducing the solubility of the solid. some of these issues have been long known and have been reviewed (shrestha et al. 2020). we do not know the difference between the behavior in three dimensions versus in two, which is of significance here. we also do not have time scales for comparison. we have shown below using turbidimetry, that in three dimensions, reformation does not happen over the time scale of interest. we have measured drop dimensions using a contact angle goniometer and used a model to show that the confinement model is good. finally, we have shown that the footprints left after drying show extensive reformation for which we have identified the ingredients of a quantitative model in one case. model material balance. small drops on a horizontal solid surface have a profile that is a segment of sphere, indicating that the effects of gravity were insignificant. for such a system, the change in water content in the drops is given by: −𝜌𝐿 𝑑𝑉𝐿 𝑑𝑡 = 𝑆𝑘𝑝𝑝𝑠(1 − 𝜙)𝑒𝜙,………………………………………………………………………………(1) where 𝑉𝐿 is the volume of water in the drop and 𝜌𝐿 is the density of water. the exponential term has been added on the right following flory, to take into some effects of higher concentrations. also s is the drop-air interfacial area, 𝑘𝑝 is the averaged mass transfer coefficient and 𝑝𝑠 is the saturated vapor pressure of water. the term (1 − 𝜙) is the activity, valid in dilute suspensions, and 𝜙 is the volume fraction of the particles. the total volume is 𝑉 = 𝑉𝐿 + 𝑉𝑆where the volume of the solids, 𝑉𝑆 = 𝑉𝑜𝜙𝑜 = 𝑉𝜙, is a constant. this relationship can be used to track 𝜙 in eq. 1. the subscript o denotes the initial values. finally, the rate of evaporation is assumed to be distributed instead of being concentrated near the contact line. a sedimentation model. if we assume instead that the concentration of the particles remains constant and that the particles that occupied the evaporated space have been deposited on the solid surface as in sedimentation (probstein 1994) , we obtain: − 1 𝑆 𝑑𝑉 𝑑𝑡 = 𝑘𝑝𝑝𝑠 𝜌𝐿 𝑒𝜙𝑜,…………..……………………………………………………………………………..(2) for the deposition model. in a sedimentation experiment, the top of the liquid is clear and the particles have deposited at the bottom. in between, we have the original particle concentrations. here, we assume that the clear liquid at the top has evaporated away. both models given by eqs. 1 and 2 have two dependent variables each, to be identified later. as a consequence, an additional constraint will have to be sought, possibly from the experimental data to determine the validity of these equations. 3 experiments materials. nacl was added to distilled water. polyethylene terephthalate sheets were cleaned using methanol and, under a microscope, showed sparse sets of scratches. the glass substrate was in the form of coverslips, which being float glass, has roughness less than 2 nm. the coverslips were cleaned with koh-isopropyl alcohol and then thoroughly rinsed with distilled water. water does not wet pet and, thus, pinning in some form or other is expected. however, water wets glass and hence pinning will have to overcome spreading. silica particles had a nominal diameter of 12 nm and the alumina a diameter less than 50 nm. these were used as supplied by aldrich. turbidimetry. the first experiments were to determine how the particles behaved in bulk suspension using a turbidimeter. water and the particles were mixed and a vibrating table was used to obtain better dispersion. turbidimeter was calibrated only once using a standard solution. the turbidity of the mixture was measured in the sample holder as a function of time. the results are shown in figures 1 and 2. all particles and many aggregates will be in the rayleigh scattering regime. thus, the turbidity (in national turbidity units, ntu) will be proportional to the number of scattering centers. however, at the large concentrations used here of 550 wt%, multiple scattering will take place, so that the functionality will not be a simple proportionality. at large degrees of aggregation, which occurs because of high concentrations, sedimentation will begin. in general, we see a fine sediment often in 2 hours. figure 1—national turbidity units ntu as a function of time for alumina and silica at different starting mass fractions. both figures are plotted with same symbols for the same weight fractions. 0 200 400 600 800 1000 1200 0 5 10 15 n t u time h al2o3 0.05 0.1 0.3 0.4 0.5 0 50 100 150 200 250 0 5 10 15 n t u time h sio2 0.05 0.1 0.3 0.4 0.5 4 figure 2—residual turbidity in national turbidity unit ntu of al2o3 and sio2. concentrations are in weight fractions. contact angle goniometry. the drops of suspensions were layered on the horizontal surface of pet or glass inside the environmental chamber of the ramé-hart contact angle goniometer. we needed drops smaller than 10 µl as they are free of the effects of gravity. the drops could not be delivered with the standard microliter syringe and a hypodermic syringe was used. for sufficiently small drops, unaffected by gravity, the drop profiles would have the shape of spherical caps. this was determined by measuring the contact angle α and checking that tan(α/2)=height of the drop at the middle/radius of the base. the two sides of this equation could be obtained independent of one another and compared well. only a few drops were examined for this sphericity, and data were taken for ro, basal radius, and α, contact angle, as functions of time. the chamber protects the drop. the best results for the evaporation rates were obtained by keeping the top of the chamber partially open. it was assumed that because of the smallness of the drop, the humidity in the chamber was not too high to affect evaporation. full evaporation occurred in about 30 minutes. the height of the drop in the middle was monitored to check if full evaporation had taken place. the coverslip was then put in a covered dish and examined under the microscope. during the experiments, the radius of the base was measured to check if pinning occurred. results and discussion turbidity. as shown in figure 1, the turbidity of alumina fluctuates greatly but the turbidity of silica does not and shows a continual decrease with time. figure 2 shows that two mechanisms may be operating for al2o3. there is another time scale of half an hour, over which the drop evaporates, where a constant value of turbidity can be assumed. it means that the particle microstructures seen in figures 3 and 4 are formed after the deposition and not before. 0 300 600 900 0 0.1 0.2 0.3 0.4 0.5 0.6 n t u initial weight fractions sio2 al2o3 5 figure 3—alumina drop on pet. the bar shown is 250 µm. initial concentration of alumina is 0.40 weight fraction. figure 4—sio2 drop on pet. the bar shown is 250 µm. initial concentration of silica is 0.40 weight fraction. analysis of the evaporation process. in the next step, the data are analyzed using a sequence that helps us to determine a mechanism. these are in the form of ro and α as a function of time. because of the very large amount of data and calculations that result, we have provided the numerical details mainly for two systems below; sio2 on glass and al2o3 on pet. their values of ro and α are shown in figure 5 as functions of time. shown in figure 6 are the volumes calculated from 𝑉 = 𝜋𝑟𝑜 3 24 (2−3𝑐𝑜𝑠𝛼+𝑐𝑜𝑠3𝛼) 𝑠𝑖𝑛3𝛼 .…………………………………………………………………………………..(3) we also note that 𝑆 = 2𝜋𝑟𝑜 2 1+𝑐𝑜𝑠𝛼 .………………………………………………………………………………………………..(4) also shown in figure 6 are the dotted lines that fit to 𝑉 = 𝑉𝑜𝑒−𝜔𝑡 which appear to be good. we have added in appendix why this is expected. this is the additional constraint that we need. we use this fit in eqs. 1 and 2 to get, for confinement 𝑌 = 𝑉/𝑉𝑜 𝑉 𝑉𝑜 −𝜙𝑜 𝑉/𝑉𝑜 𝑆/𝑉𝑜 𝜔𝑒𝜙𝑜𝑉𝑜/𝑉 = 𝑘𝑝𝑝𝑠 𝜌𝐿 ,..…………………………………………………………………………(5) and for sedimentation 𝑍 = 𝑉𝜔 𝑆 𝑒𝜙𝑜 = 𝑘𝑝𝑝𝑠 𝜌𝐿 .………………………………………………………………………………………..(6) 6 sio2 on glass al2o3 on pet figure 5—basal radius r0 and contact angle α shown for two systems as functions of time. the measurements were taken using a contact angle goniometer. note that at the smallest concentrations there is a continuous drop in r0. the measurements were problematic in case of 50 wt% particles. figure 6—volumes calculated by assuming that the profiles are given by segments of spheres, and plotted as functions of time. the curves represent exponential fits. 0 0.4 0.8 1.2 1.6 2 0 5 10 15 20 r 0 (m m ) time (min) 5% 10% 30% 40% 50% 0 20 40 60 80 0 5 10 15 20 co n ta ct a n g le ( d eg re e) time (min) 5% 10% 30% 40% 50% 0 0.4 0.8 1.2 1.6 2 0 5 10 15 20 r 0 (m m ) time (min) 5% 10% 30% 40% 50% 0 20 40 60 80 0 5 10 15 20 co n ta ct a n g le ( d eg re e) time (min) 5% 10% 30% 40% 50% 0 0.05 0.1 0.15 0.2 0.25 0 5 10 15 20 v o lu m e (μ l ) time (min) sio2 on glass 5% 10% 30% 40% 50% 0 0.2 0.4 0.6 0.8 1 1.2 0 5 10 15 20 v o lu m e (μ l ) time (min) al2o3 on pet 5% 10% 30% 40% 50% 7 y as a function of time is plotted in figure 7. figure 7 shows that all values of y are positive and there are most often independent of time, both expected. for a particular type of nanoparticle, alumina or silica, and for a particular substrate, pet or glass, the plots should be independent of concentrations and coincide. the results are less satisfactory though not too far away. in general, the cases of the top two concentrations show irregularities. when z from eq. 6 is plotted as a function of time, the plots are spaced even more and show more time dependence. thus, they have not been shown here, although some effects of sedimentation exist. sio2 on glass sio2 on pet al2o3 on glass al2o3 on pet figure 7—y in eq. 5 has been plotted against time for sio2 and al2o3 on glass and pet. on pet, the drops do not spread, that is, the drop border is pinned except for the 5 wt% for silica and 5 and 10 wt% for alumina which retract very slowly at first, then in a significant way at later times (figure 5). the images of alumina and silica are shown enlarged in figures 3 and 4 where silica is seen to spread more. the drop edge is practically never smooth but our measurements in figure 5 do not show fluctuations except at high particle concentrations. alumina and silica on glass are shown in figures 8 and 9. both have spread over larger distances such that lower magnification was required to capture the full image. -0.0005 0.0000 0.0005 0.0010 0.0015 0.0020 0.0025 0.0030 0.0035 0.0040 0 5 10 15 20 25 y time (min) 5% 10% 30% 40% 50% 0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007 0 5 10 15 20 25 y time (min) 5% 10% 30% 40% 50% 0 0.00001 0.00002 0.00003 0.00004 0.00005 0.00006 0 5 10 15 20 25 y time (min) 5% 10% 30% 40% 50% 0 0.0002 0.0004 0.0006 0.0008 0.001 0.0012 0.0014 0.0016 0.0018 0.002 0 5 10 15 20 25 y time (min) 5% 10% 30% 40% 50% 8 figure 8—alumina drop on glass. the bar shown is 1000 µm. initial concentration of alumina is 0.40 weight fraction. figure 9—sio2 drop on glass. the bar shown is 1000 µm. initial concentration of silica is 0.40 weight fraction. analysis of the reformation process. for alumina/pet (figure 3) and alumina/glass (figure 8), one can see a moving boundary with the boundary (interline) separating a reformed region from the initial one. the reformed region looks like sintering has happened, that is, nearly uniform and matte. the dynamics of the interline can be expressed through a conservation equation 𝜕𝑐 𝜕𝑡 = 𝐷𝑠 𝑟 𝜕 𝜕𝑟 (𝑟 𝜕𝑐 𝜕𝑟 ),…………………………………………………..……………………….………………(7) where radial symmetry is being assumed. the concentration c is number of particles per unit area and ds is the surface diffusivity. it is subject to finiteness and c = c* a fixed concentration at the interline at r = r*, where particles are converted to a sintered mass (as in alumina/pet figure 3 or as in alumina/glass figure 8. a change of variable leads to 𝑑𝜏 = 𝐷𝑠𝑑𝑡 𝑟∗2 ,………………………………………………………………………..…………………………(8) where τ→0 as t→0 and 𝜉 = 𝑟/𝑟∗. taking laplace transform and inverting using standard tables, one has: 𝑐∞−𝑐 𝑐∞−𝑐∗ = 1 − 2 ∑ 𝑒−𝜆𝑘 2 𝜏𝐽𝑜(𝜆𝑘𝜉) 𝜆𝑘𝐽1(𝜆𝑘𝜉) ∞ 𝑘=1 ,……………………..……………………………………………….……(9) where 𝑐∞ is the initial concentration, ji are the bessel functions and λk are the zeros of jo. the solution is used in the jump balance at the interline 𝑅∗ = −𝑐∗ 𝑑𝑟∗ 𝑑𝑡 − 𝐷𝑠 ∂c 𝜕𝑟 |𝑟∗ ,…………….…………………………………………………………………..(10) 9 where r* is the rate of sintering in terms of number of particles per unit time per unit interline length and the first term on the right hand side is the effect of moving boundary and is followed by diffusion. substituting the solution in there we have 𝑅∗ = −𝑐∗ 𝑑𝑟∗ 𝑑𝑡 + 2𝐷𝑠 𝑐∞−𝑐∗ 𝑟∗ ∑ 𝑒−𝜆𝑘 2 𝜏 𝜆𝑘 ,………..……………………………………………………………..(11) is obtained which gives us an integro-differential equation for r* as a function of time. an approximation at short times is possible by setting r* to ro, the initial drop radius, to calculate 𝜏 = 𝐷𝑠𝑡/𝑟𝑜 2, substituting this τ into eq. 11 and then integrating to get a better expression for r*. however, the diffusion limited growth in a moving boundary problem is often unstable (probstein 1994). linear stability analysis that is performed by assuming that the rate of change of interline is much slower than the rate of growth of the instabilities, gives us a fastest growing wavelength, which is the length scale observed in the unstable growth. a length scale can be obtained from the balance between the two rates of mass transfer mechanisms to obtain: 𝜆 = 𝐷𝑠(𝑐∞−𝑐∗) 𝑅∗ ,……………………………………………………………………………………………..(12) which usually differs from the fastest growing wavelength by a dimensionless number of the order of 1. from figure 3, λ~266 µm, where interline is sinuous suggesting that the instability has just begun. in figure 8, is 402 µm, where the interline is jagged which cracks separating growth, suggesting that we have looked at the specimen in the late stage of instability. it is noteworthy that in all photographs shown here on silica, the sintering is over and the material has cracked. on pet, a clear “coffee stain” is seen for alumina, but not as clearly seen in silica as the rim is a lot thinner. coffee stain refers to the unusually high rates of deposition along the drop periphery. dendritic growths are common in alumina but not seen as often in silica. in general, dendrites here are due to mass transfer effects that arise from surface diffusivity (miller 1978) and also known in two dimensions (neogi and wang 2011). in addition, large crystals are seen for alumina but not for silica. silica system shows only small clusters that are barely visible under a microscope. large crystals are usually due to ostwald ripening which for, some reason, is more pronounced in alumina. possibly alumina is more soluble in water. the very large laplace pressures, due to the smallness of the particles, can lower the melting point at the surface as stated earlier. in the photographs, the dendrites glisten, which led us to conclude that these are melts. finally, we look at the footprints left by the dried drops in all cases for comparison; on pet in figure 10 and on glass on figure 11. systematic changes are seen in all cases with increasing initial concentrations; however, for alumina there is a break between 10 and 30% initial concentrations and such a break also occurs in the turbidimetry results in figure 2. nanoparticles show such a high reformation that it is possible to speculate that, in oil reservoirs, they may choke fine pores. in general, the properties of thin films and contact angles will change with time. it also appears that there are significant differences between the footprints left by alumina and by silica, which can be used as markers. however, the main difficulty here is that the process is very fast and may have deleterious effects such as the haphazard nature of reformation. one way of slowing down the system is to add a low molecular weight water soluble oligomer. conclusions all the changes in morphology that were observed could have occurred only on the surface, as demonstrated by the turbidity studies and studies on evaporation rates. reformation is brought about by sintering and melting, and sintering starts at the coffee stain along the drop periphery and moves inwards. this is the main conclusion, other effects are seen but appear to be secondary. 10 dried droplets of al2o3 on pet 0.05 wt.fr 0.1wt. fr 0.3 wt.fr 0.4 wt.fr 0.5 wt.fr dried droplets of sio2 on pet 0.05 wt.fr 0.1wt. fr 0.3 wt.fr 0.4 wt.fr 0.5 wt.fr figure 10—dried droplets of al2o3 and sio2 suspensions where dendrites can be seen in all frames with al2o3 but only in the first two in sio2. at lowest concentration of al2o3 we see large crystals. we see coffee stain behavior for al2o3 but it is not so clear in sio2. significant cracks are seen in sio2 but not in al2o3. small white horizontal bars in every frame is 250 µm. 11 dried droplets of al2o3 on glass 0.05 wt.fr 0.1wt. fr 0.3 wt. 0.4 wt.fr 0.5 wt.fr dried droplets of sio2 on glass 0.05 wt.fr 0.1wt. fr 0.3 wt.fr 0.4 wt.fr 0.5 wt.fr figure 11—dried droplets of al2o3 and sio2 suspensions where dendrites can be seen only for al2o3 at lower concentration and some at the highest concentration. none appear in sio2. crystals appear everywhere for al2o3 and this feature in not clear in silica. we see coffee stain behavior in all. small horizontal bar in every frame is 1000 µm indicating larger areas involved due to drop spreading. conflicts of interest the author(s) declare that they have no conflicting interests. references bera, a. and belhaj, h.j. 2016. application of nanotechnology by means of nanoparticles and nonodispersions in oil recovery. nat. gas sci. eng. 34: 1284-1309. 12 cheringhian, g. and hendraningrat, l. 2018. a review on applications of nanotechnology in enhanced oil recovery part b: effects of nanoparticles on flooding. int. nano letts. 6: 1-10. deegan, r.d. 2000. pattern formation in drying drops. phys. rev. e. 61: 475-48. deegan, r.d., bakajin, o., dupont, t.f., et al. 1997. capillary 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dekker, m. 1991. interfacial phenomena in petroleum recovery. new york: marcel dekker. probstein, r.f. 1994. physicochemical hydrodynamics. 2nd ed. new york: john wiley and sons. ristić, m.m. and milosević, s.d. 2006. frenkel's theory of sintering. science of sintering 38: 7-11. shah, r. and neogi, p. 2002. interfacial resistance in solubilization kinetics. j. colloid interface sci 253: 443-454. shrestha, s., wang, b., and dutta, p. 2020. nanoparticle processing: understanding and controlling aggregation. adv. colloid interface sci. 279:102-122. zhang, h., nikolov, a., and wasan, d. 2014. enhanced oil recovery (eor) using nanoparticle dispersions: underlying mechanism and imbibition experiments. energy fuels 28: 3002-3009. appendix previously for a drop of oil on a solid disappearing under surfactant solution, (shah and neogi 2002) we had assumed for the conservation equation eq. 1 that 𝑆 ∝ 𝑉2/3 and obtained excellent results. this is not a first order processes. shah and neogi (2002) calculated the proportionality constant numerically but found that it failed for flat and thin drops. for this case where drops are flat and thin, eqs. 3b and 4b can be combined to show that 𝑉 = ℎ 2 𝑆or 𝑉 = <ℎ> 2 𝑆 where < ℎ > is an appropriate average height at the center of the drop. here, we have 𝑉 = 𝜋 3 ℎ 2(3𝑅 − ℎ),.……………………………………………………………..……………………….(a-1) 𝑆 = 2𝜋𝑅ℎ..………………………………………………………………………………………………(a-2) we calculated v/s and found the ranges in the four cases to be narrow. they range from 0.0258 to 0.0341, 0.0258 to 0.0356, 0.0100 to 0.0224 and 0.0357 to 0.0545 mm, for sio2 (on glass then on pet) followed by al2o3 in the same order. 5% solids was always an outlier, showing twice as much change. the systems at 40% and 50% were erratic and were not considered. it is seen that v/s can be approximated as a constant which when substituted in eq. 1 leads to 𝑉 = 𝑉𝑜𝑒−𝜔𝑡used after eq. 4. vijitha mohan received her ph.d. in chemical engineering from missouri university of science and technology and served as a lecturer after graduation. her research interests lie in heavy oil recovery. she acquired her b.tech in chemical engineering from university of madras and m.s in chemical engineering from mississippi state university. she is at present a postdoctoral associate at university of calgary, canada. xianjie qiu received the ph.d., master and bachelor’s degree in chemical engineering department from missouri university of science and technology. his research interests in convective-diffusive transport. 13 parthasakha neogi, is a professor of chemical engineering at missouri university of science and technology, where he has worked as faculty for the last 36 years. his research interests are in wetting, surfactants and polymers, and in interfacial transport phenomena. he holds b.tech. (hons.) from the indian institute of technology kharagpur, m. tech. from the indian institute of technology kanpur, and ph.d. from carnegie-mellon university, all in chemical engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.429 received september 5, 2018; revised october 30, 2018; accepted november 8, 2018. *corresponding author: wanghao1202@petrochina.com.cn 1 sensitivity calculation by adjoint method: an application to reservoir simulation hao wang*, liaohe oilfield company, petrochina, panjin, china abstract scope of this paper is the sensitivity calculation by using adjoint method. we have a 9×9 two phase twodimension quarter five spot model with one injector and one producer. the high uncertainty of the permeability field gives us the data mismatch in the model, and we set the permeability as model parameter (uncertainty). the data distribution we get is bottom-hole pressure at injector and water cut at producer for 10 time steps. to get the optimal permeability field, we first calculate the sensitivity coefficients for permeability by using adjoint method. we already have a forward simulator for this problem that is the fully implicit black-oil simulator. hence, we need to extract necessary information from the forward simulator, i.e. jacobian matrix, transmissibility, and accumulation etc. advantage of the adjoint method is that it enables us to reduce the considerable amount of computation time for calculating the sensitivity matrix compared with gradient simulator method. the forward simulation we need at each minimization step is only one time for calculating the sensitivity. then we minimize the objective function by levenbergmarquardt algorithm. introduction the quality of the reservoir model, i.e., the degree to which it represents the actual reservoir, directly affects reservoir management. this model helps the manager to analyze the behaviors of the reservoir and also it is helpful in production forecasting and optimization. the reservoir model creates on the basis of valuable data obtained during the reservoir life. in the exploration phase, the reservoir model is constructed using 3d seismic data, geologic knowledge of the surrounding area, and log/core measurements from a few exploration wells. these kinds of data are called “static data in the appraisal phase, drilling additional wells provide new information about the reservoir as a well test. production data and 4d seismic data are available during the production time of a reservoir. these kinds of information are categorized as “dynamic data”. conditioning reservoir model to the new information obtained about the reservoir is called history matching process, i.e. history matching is the process by which the geological model properties are modified to fit the production data. the objective of history matching is to build a reservoir model that integrates available data and yields production forecasts that are accurate. incorrectly identifying structural features, such as fluvial channels, can have very serious consequences such as badly placed wells, by-passed hydrocarbon, and failure to find trapped hydrocarbons. a reservoir model is described by many parameters, and each parameter can generate millions of pieces of data. some parameters are specified per grid block (e.g., permeability and porosity) and others for the entire model or a particular layer (e.g. relative permeability and capillary pressure). due to insufficiency of available data about the reservoir, history matching is an ill-posed problem. it means that it is possible to obtain reservoir models that honor observed measurements but provide incorrect predictions. to deal with the ill-posed of history matching, the number of parameters has to be reduced. also, parameterization preserves important geological features and their connectivity that has a significant effect on fluid flow within the reservoir. mailto:wanghao1202@petrochina.com.cn 2 several methods have been investigated to reduce the number of unknown parameters. jacquard and jain (1965) used simple zonation approach to assign one value to a region of the reservoir. other researchers (jahns 1966; bissel et al. 1994; chavent and bissell 1998) modified the jacquard et al.’s method to adaptive one. some authors (grimstad et al. 2003; sahni and horne 2005) worked on different techniques for parameterization and history matching at different scales. another powerful approach that is suitable for history matching is klt. klt is mathematically defined as an orthogonal linear transformation that transforms a set of possibly correlated data into a smaller number of uncorrelated variables called principal components. klt is theoretically the optimum transform for given data in least square terms. but for the standard klt model, it is necessary to carry out an eigendecomposition of the covariance matrix of the random field, which is expensive for large models. in this research study, we use adjoint method to calculate the sensitivity matrix, thus to reduce the overall computation time during simulation. figure 1 shows the work flow for the history matching. figure 1—history matching flow chart. sensitivity calculation based on adjoint method the simulator used in ajoint-based sensitivity calculation is based on fully implicit finite-difference method of the two-phase blackoil model. several literatures refer to the derivation of adjoint system with fully implicit formulation (wu et al. 1999; li et al. 2003). in this chapter, i briefly show the formulation of adjoint method, used in the algorithm for sensitivity calculation. first equation derived from the finitedifferent equation is as follows. [𝛻𝑦𝑛(𝑓𝑛)𝑇]𝜆𝑛 = −[𝛻𝑦𝑛(𝑓𝑛+1)𝑇]𝜆𝑛+1 − 𝛻𝑦𝑛𝛽,…………..………………..……………….…………(1) where 𝜆𝑛 is the vector of adjoint variables at timestep n, and given by 𝜆𝑛 = [𝜆1 𝑛, 𝜆2 𝑛, … , 𝜆2𝑁 𝑛]𝑇,…………………..………………..……..….……………………………..(2) where 𝑁 is number of gridblock. returning to eq. 1, [𝛻𝑦𝑛(𝑓𝑛)𝑇] is transpose of jacobian matrix at 𝑛, which can be extracted from forward simulation. [𝛻𝑦𝑛(𝑓𝑛+1)𝑇] is the gradient matrix (derivative of finitedifference equation at 𝑛 + 1 with respect to the primary variables at 𝑛). 𝛻𝑦𝑛𝛽 is the sensitivity matrix with respect to the primary variable. using following initial and boundary conditions, eq. 1 can be solved backwards in time for n=l, l-1, …, 1. the initial condition and boundary condition are fixed. 𝑑𝑦0 = 0.……….………….……………………………………………………………………………(3) the boundary condition is as follows. 3 𝜆𝐿+1 = 0.……….………………………………………………………………………………………(4) the gradient matrix, [𝛻𝑦𝑛(𝑓𝑛+1)𝑇] is the derivative of accumulation term at 𝑛, because all terms in 𝑓𝑛+1 are independent to the primary variables at 𝑛 except for the accumulation at 𝑛 as shown in eq. 5. 𝜕𝑓𝑛+1 𝜕𝑦𝑛 = 𝜕{(𝑇𝑡𝑎𝑛𝑠×𝛻𝑝)𝑛+1−(𝐴𝑐𝑐𝑢𝑚𝑛+1−𝐴𝑐𝑐𝑢𝑚𝑛)−(𝑆𝑖𝑛𝑘/𝑆𝑜𝑢𝑟𝑐𝑒) 𝑛+1} 𝜕𝑦𝑛 .........…………………………………..(5) hence, 𝜕(𝐴𝑐𝑐𝑢𝑚𝑜,𝑖,𝑗 𝑛) 𝜕𝑝𝑖,𝑗 𝑛 = ∆𝑥𝑖,𝑗∆𝑦𝑖,𝑗∆𝑧𝑖,𝑗 1 ∆𝑡𝑛−1 𝑆𝑜,𝑖,𝑗 𝑛 ( 𝜕𝜑𝑖,𝑗 𝑛 𝜕𝑝𝑖,𝑗 𝑛 𝐵𝑜,𝑖,𝑗 𝑛−𝜑𝑖,𝑗 𝑛 𝜕𝐵𝑜,𝑖,𝑗 𝑛 𝜕𝑝𝑖,𝑗 𝑛 𝐵𝑜,𝑖,𝑗 𝑛2 ),…..........….………………………(6) 𝜕(𝐴𝑐𝑐𝑢𝑚𝑤,𝑖,𝑗 𝑛) 𝜕𝑝𝑖,𝑗 𝑛 = ∆𝑥𝑖,𝑗∆𝑦𝑖,𝑗∆𝑧𝑖,𝑗 1 ∆𝑡𝑛−1 𝑆𝑤,𝑖,𝑗 𝑛 ( 𝜕𝜑𝑖,𝑗 𝑛 𝜕𝑝𝑖,𝑗 𝑛 𝐵𝑤,𝑖,𝑗 𝑛−𝜑𝑖,𝑗 𝑛 𝜕𝐵𝑤,𝑖,𝑗 𝑛 𝜕𝑝𝑖,𝑗 𝑛 𝐵𝑤,𝑖,𝑗 𝑛2 ),……….......…….……………….(7) 𝜕(𝐴𝑐𝑐𝑢𝑚𝑜,𝑖,𝑗 𝑛) 𝜕𝑆𝑤,𝑖,𝑗 𝑛 = −∆𝑥𝑖,𝑗∆𝑦𝑖,𝑗∆𝑧𝑖,𝑗 1 ∆𝑡𝑛−1 ( 𝜑𝑖,𝑗 𝑛 𝐵𝑜,𝑖,𝑗 𝑛),…………………......……….………..……………….(8) 𝜕(𝐴𝑐𝑐𝑢𝑚𝑤,𝑖,𝑗 𝑛) 𝜕𝑆𝑤,𝑖,𝑗 𝑛 = ∆𝑥𝑖,𝑗∆𝑦𝑖,𝑗∆𝑧𝑖,𝑗 1 ∆𝑡𝑛−1 ( 𝜑𝑖,𝑗 𝑛 𝐵𝑤,𝑖,𝑗 𝑛).…........………………….………….…………………..(9) the gradient matrix, [𝛻𝑦𝑛(𝑓𝑛+1)𝑇] form the following matrix 𝛻𝑦𝑛(𝑓𝑛+1)𝑇 = 𝜕(𝐴𝑐𝑐𝑢𝑚𝑛)𝑇 𝜕𝑦𝑛 = [ 𝜕(𝐴𝑐𝑐𝑢𝑚𝑜 𝑛)𝑇 𝜕𝑝𝑛 𝜕(𝐴𝑐𝑐𝑢𝑚𝑤 𝑛)𝑇 𝜕𝑝𝑛 𝜕(𝐴𝑐𝑐𝑢𝑚𝑜 𝑛)𝑇 𝜕𝑆𝑤 𝑛 𝜕(𝐴𝑐𝑐𝑢𝑚𝑤 𝑛)𝑇 𝜕𝑆𝑤 𝑛 ].………......….…………………………..(10) because 𝛽 is assumed as bottomhole pressure at injector and water cut at producer in this project, 𝛻𝑦𝑛𝛽 can be analytically calculated by using following formulation 𝑊𝐶𝑇 = 𝑘𝑟𝑤𝜇𝑜𝐵𝑜 𝑘𝑟𝑜𝜇𝑤𝐵𝑤+𝑘𝑟𝑤𝜇𝑜𝐵𝑜 ,………………………………...…………………………………..………(11) 𝑝𝑤𝑓,𝑖,𝑗 = 𝑝𝑖,𝑗 + 𝑙𝑛(𝑟𝑜,𝑖,𝑗/𝑟𝑤,𝑖,𝑗)+𝑠𝑖,𝑗 (2𝜋)1.127×10−3ℎ𝑘𝑖,𝑗 ( 𝐵𝑚,𝑖,𝑗𝜇𝑚,𝑖,𝑗 𝑘𝑟𝑚,𝑖,𝑗 ) 𝑞𝑚,𝑖,𝑗,……...........………………..…….……………..(12) 𝑟𝑜,𝑖,𝑗 = 0.14036√∆𝑥2 + ∆𝑦2 ..…………………………..…………………………….…………….(13) the adjoint system is ended up computing as shown in figure 2. the sensitivity coefficients for 𝐽 are given by, 𝛻𝑚𝐽 = 𝛻𝑚𝛽 + ∑ [𝛻𝑚(𝑓𝑛)𝑇](𝜆𝑛)𝐿 𝑛=1 .………………..…………………………………………………(14) we already know 𝜆𝑛 from the computation of eq. 1. the gradient matrix, [𝛻𝑚(𝑓𝑛)𝑇] is 𝑀 × 2𝑁 sparse matrix as follows 𝛻𝑘(𝑓 𝑛)𝑇 = 𝛻𝑘[(𝑇𝑡𝑎𝑛𝑠 × 𝛻𝑝)𝑛]𝑇 = [ 𝜕𝑓𝑜,1 𝑛 𝜕𝑘1 𝜕𝑓𝑤,1 𝑛 𝜕𝑘1 𝜕𝑓𝑜,1 𝑛 𝜕𝑘2 𝜕𝑓𝑤,1 𝑛 𝜕𝑘2 𝜕𝑓𝑜,2 𝑛 𝜕𝑘1 𝜕𝑓𝑤,2 𝑛 𝜕𝑘1 𝜕𝑓𝑜,2 𝑛 𝜕𝑘2 𝜕𝑓𝑤,2 𝑛 𝜕𝑘2 ⋯ 𝜕𝑓𝑜,𝑁 𝑛 𝜕𝑘1 𝜕𝑓𝑤,𝑁 𝑛 𝜕𝑘1 𝜕𝑓𝑜,𝑁 𝑛 𝜕𝑘2 𝜕𝑓𝑤,𝑁 𝑛 𝜕𝑘2 ⋮ ⋮ ⋮ 𝜕𝑓𝑜,1 𝑛 𝜕𝑘𝑀 𝜕𝑓𝑤,1 𝑛 𝜕𝑘𝑀 𝜕𝑓𝑜,2 𝑛 𝜕𝑘𝑀 𝜕𝑓𝑤,2 𝑛 𝜕𝑘𝑀 ⋯ 𝜕𝑓𝑜,𝑁 𝑛 𝜕𝑘𝑀 𝜕𝑓𝑤,𝑁 𝑛 𝜕𝑘𝑀 ] ........….(15) figure 3 shows the computation of sensitivity matrix. 4 figure 2—computation of adjoint system. figure 3—computation of sensitivity matrix. minimization the levenberg–marquardt algorithm, which was independently developed by kenneth levenberg and donald marquardt, provides a numerical solution to the problem of minimizing a nonlinear function. it is fast and has stable convergence. in the artificial neural-networks field, this algorithm is suitable for training smalland medium-sized problems. the levenberg–marquardt algorithm blends the steepest descent method and the gauss–newton algorithm. fortunately, it inherits the speed advantage of the gauss–newton algorithm and the stability of the steepest descent method. it’s more robust than the gauss–newton algorithm, because in many cases it can converge well even if the error surface is much more complex than the quadratic situation. although the levenberg marquardt algorithm tends to be a bit slower than gauss–newton algorithm (in convergent situation), it converges much faster than the steepest descent method. the basic idea of the levenberg– marquardt algorithm is that it performs a combined training process: around the area with complex curvature, the levenberg–marquardt algorithm switches to the steepest descent algorithm, until the local curvature is proper to make a quadratic approximation; then it approximately becomes the gauss–newton algorithm, which can speed up the convergence significantly. 5 gauss–newton algorithm. the relationship between hessian matrix h and jacobian matrix j can be rewritten as, 𝐻 = 𝐽𝑇𝐽.………………………………………………………………..………………………….….(16) levenberg's contribution. replace the above equation by a "damped version", 𝐻 = 𝐽𝑇𝐽 + 𝜆𝐼,…………………………………………………………………………………………(17) where λ is always positive, called combination coefficient. i is the identity matrix levenberg's algorithm has the disadvantage that if the value of damping factor, λ, is large, inverting jtj + λi is not used at all. marquardt modification. replaced the identity matrix, i, with the diagonal matrix consisting of the diagonal elements of jtj, resulting in the levenberg–marquardt algorithm 𝐻 = 𝐽𝑇𝐽 + 𝜆𝑑𝑖𝑎𝑔(𝐽𝑇𝐽)...…………………………………..………………………………………….(18) from above equation, one may notice that the elements on the main diagonal of the approximated hessian matrix will be larger than zero. therefore, with this approximation, it can be sure that matrix h is always invertible. for our problem, we drive the objective function without prior information 𝑂(𝑚) = 1 2 [𝑔(𝑚) − 𝑑𝑜𝑏𝑠] 𝑇𝐶𝐷 −1[𝑔(𝑚) − 𝑑𝑜𝑏𝑠],…..………………………………………….………(19) 𝑂(𝑚 + 𝛿𝑚) = 𝑂(𝑚) + 𝐽𝑇𝑒𝛿𝑚 + 1 2 𝛿𝑚𝑇𝐽𝑇𝐽𝛿𝑚...…………………………………………………….(20) set 𝜕𝑂(𝑚+𝛿𝑚) 𝜕𝛿𝑚 ≈ 0.…………………………………………………………………………………………(21) we have 𝐽𝑇𝐽𝛿𝑚 = −𝐽𝑇𝑒.………………………………………………………………………………………..(22) hence, apply levenberg-marquardt algorithm, we get 𝛿𝑚 = −[𝐽𝑇𝐽 + 𝜆𝑑𝑖𝑎𝑔(𝐽𝑇𝐽)] −1(𝐽𝑇𝑒),…………………………………………………………………(23) where, 𝑂(𝑚) = 1 2 𝑒𝑇𝑒,.......................................................................................................................................(24) 𝑒 = 𝐶𝐷 1/2[𝑔(𝑚) − 𝑑𝑜𝑏𝑠],........................................................................................................................(25) 𝐽 = 𝜕𝑒 𝜕𝑚 ,.................................................................................................................................................(26) 𝐽 = 𝐶𝐷 −1/2 𝜕𝑔(𝑚) 𝜕𝑚 = 𝐶𝐷 −1/2 𝐺𝑙 ,..................................................................................................................(27) 𝐽𝑇𝐽 = 𝐺𝑙 𝑇𝐶𝐷 −1𝐺𝑙 .....................................................................................................................................(28) the simplest way to obtain the correction 𝛿𝑚 is to use cholesky decomposition on the linear system. the main advantage of the nodal equations is speed. 𝑚𝑙+1 = 𝑚𝑙 + 𝛼𝛿𝑚𝑙+1 ,………………………………………………………………………………..(29) where, 𝒍 is iteration number. the (non-negative) damping factor, λ, is adjusted at each iteration. 𝑂(𝑚𝑙+1) > 𝑂(𝑚𝑙) → 𝜆𝑙+1 = 𝜌𝜆𝑙,…………………………………………………………………….(30) 𝑂(𝑚𝑙+1) < 𝑂(𝑚𝑙) → 𝜆𝑙+1 = 𝜆𝑙 𝜌 ,………………………………………………………………………(31) 6 where 𝝆 > 1; 𝝀𝟏 is between √ 𝑂(𝑚0) 𝑁𝑑 and 𝑂(𝑚0) 𝑁𝑑 ; f 𝝀 = 0, we have gauss-newton method. if the reduction of objective function is rapid, a smaller value can be used, bringing the algorithm closer to the gauss-newton algorithm, whereas if one iteration gives insufficient reduction in the residual, λ can be increased, giving a step closer to the gradient descent direction. result figure 4 and 5 show the wct and bhp sensitivity comparison between our adjoint sensitivity calculation and sensitivity calculated using perturbation. we are able to capture the trend of both wct and bhp, the relative difference is generally less than 10%. figure 4—sensitivity comparison of wct. perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 x 10 -9 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 x 10 -9 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 x 10 -9 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -8 -6 -4 -2 0 2 x 10 -8 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 x 10 -9 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 7 figure 5—sensitivity comparison of bhp. figure 6 and 7 shows the model calibration history and results. we are able to match both bhp and wct quite well. the updated permeability field keeps the high permeability region in the center. it does not give quite similar results mainly due to the non-uniqueness of solution. figure 6—history of model calibration (bhp and wct). perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10 -5 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10 -5 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10 -5 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 perturbation sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 adjoint sensitivity 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -2 -1 0 1 x 10 -4 sensitivity difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 x 10 -5 % difference 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0 0.05 0.1 0.15 0.2 0.25 100 200 300 400 500 600 700 800 900 1000 2975 2980 2985 2990 2995 3000 bhp time (days) p re s s u re ( p s i) 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 wct time (days) reference permeability (log10 scale) 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 updated permeability (log10 scale) 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 100 200 300 400 500 600 700 800 900 1000 2975 2980 2985 2990 2995 3000 bhp time (days) p re s s u re ( p s i) 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 wct time (days) reference permeability (log10 scale) 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 updated permeability (log10 scale) 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 8 figure 7—model calibration results (bhp and wct). figure 8 shows the history of objectives. the data misfit decrease dramatically, even in the semilog plot. figure 8—history of objective (normal and semilog coordinate). physical explanation of sensitivity the effect of permeability change on the bhp and wor is studied. figure 9 shows the sensitivity of bhp with the permeability. 100 200 300 400 500 600 700 800 900 1000 2975 2980 2985 2990 2995 3000 bhp time (days) p re s s u re ( p s i) reference initial updated 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 wct time (days) reference initial updated reference permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 updated permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 100 200 300 400 500 600 700 800 900 1000 2975 2980 2985 2990 2995 3000 bhp time (days) p re s s u re ( p s i) reference initial updated 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 wct time (days) reference initial updated reference permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 updated permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 100 200 300 400 500 600 700 800 900 1000 2975 2980 2985 2990 2995 3000 bhp time (days) p re s s u re ( p s i) reference initial updated 100 200 300 400 500 600 700 800 900 1000 0 0.2 0.4 0.6 0.8 1 wct time (days) reference initial updated reference permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 updated permeability (log10 scale) 2 4 6 8 1 2 3 4 5 6 7 8 9 0.5 1 1.5 2 2.5 3 3.5 0 10 20 30 40 50 60 70 80 90 0 200 400 600 800 1000 1200 1400 iterations o b je c ti v e obj decrease ratio(obj initial /obj final ) = 0.00099719 0 10 20 30 40 50 60 70 80 90 10 0 10 1 10 2 10 3 10 4 iterations o b je c ti v e obj decrease ratio(obj initial /obj final ) = 0.00099719 9 figure 9—sensitivity of bhp. we can see from the colorbar that most the grid cells have negative value, which means if the permeability increases, the bhp decreases. it is easy to understand that higher permeability is more conductive for water than lower permeability. besides, with the time increasing, the cells around the producer are becoming more sensitive to the bhp. figure 10 shows the sensitivity of wor with the permeability. figure 10—sensitivity of wor. 10 we can see there is a channel connecting injector and producer. the sensitivity of these channel cells are positive, which means if the permeability increases in these areas, the wor increases. more water tends to flow in this channel. the sensitivity of cells in the edge part is negative, meaning higher permeability in these areas can decrease the wor. more water flow to this area. effect of α and λ in the lm minimization process. α is the searching step in the lm algorithm. small α results in more iterations while large α may lead to convergence failure. large searching step may make the derivative stepping cross the minimization point. figure 11 shows the comparison of history matching process between α=0.01 and 3. figure 11—comparison of history matching process between α=0.01 and 3. the left part of figure 11 shows the history matching process with α equals 0.01. we can see the converging process is slow. the blue line is the final curve. it is limited by the iteration numbers. if given sufficient iterations, it can converge. the right part shows history matching process with α equals 3. we can see the matching curve jumps around, and the convergence is failed. figure 12 below shows the objective function behavior with iteration numbers for nine different α. we can see if α equals 0.2, the objective function converges slowly and smoothly, although 68 iterations are needed. but if the α equals 3, the objective function fluctuates without tendency to converge. these are two extreme cases. additionally, if α equals 1.7, it converges very fast with only 8 iterations. figure 12—objective function behavior with iteration numbers for different α. 11 λ in the lm algorithm is the perturbation added to the original function, to avoid the singular matrix. if λ is too small, the original function may still be singular, while if λ is big, more iterations will be needed to converge the objective function. figure 13 below shows the trend. figure 13—objective function behavior with iterations for different λ. we can see if the λ equals 0.001, the objective function fluctuates a lot, and the code gives the warning that the objective matrix is badly conditioned. the result is not correct. for λ of 10, it converges slowly and smooth, but 72 iterations are needed. for λ of 20, it does not converge with the limited iterations, but it will converge given sufficient iterations. additionally, λ of 0.5 gives very fast convergence. we can see both α and λ affect the history matching process, and good combination of them is desired. conclusions 1. we successfully incorporate the sensitivity calculation with adjoint method into the software, and the sensitivity results are quite close to the results calculated by perturbation. 2. the adjoint method only need one-time simulation to give the sensitivity calculation, instead of m times (the number of parameters), which show great advantages in computational efficiency. 3. we can carry out history matching using levenberg-marquardt method to match both wct and bhp. we are also able to keep the high permeability trend of the permeability field. 4. more suitable search step lengths and perturbation in levenberg-marquardt method will give faster converge. integrated with adjoint method, it is a fast and accurate history matching workflow. conflicts of interest the author(s) declare that they have no conflicting interests. references wu, z., reynolds, a.c., and oliver, d.s. 1999. conditioning geostatistical models to two-phase production data. paper presented at spe annual technical conference and exhibition, new orleans, louisiana, september 27-30. spe-56855-ms. li, r., reynolds, a.c., and oliver, d.s. 2003. history matching of three-phase flow production data. spe journal 8(4):25-31. spe-87336-pa. oliver, d.s., reynolds, a.c., and liu, n. 2008. inverse theory for petroleum reservoir characterization and history matching: front matter. journal of affective disorders 2008(175):488-493. jacquard, p. 1965. permeability distribution from field pressure data. spe journal 5(4): 281-294. spe-1307-pa. 12 jahns, o.h. 1966. a rapid method for obtaining a two dimensional reservoir description from well pressure response data. spe journal 6(4): 315-327.spe-1473-pa chavent, g. and bissell, r. 1998. indicator for the refinement of parameterization in inverse problems in engineering mechanics. ed. m. tanaka and g.s. dulikravich, 309-314. oxford, uk: elsevier science. grimstad, a.a., mannseth, t., nævdal, g., et al. 2003. adaptive multiscale permeability estimation. computational geosciences 7(1): 1-25. sahni, i. and horne, r.n. 2005. multiresolution wavelet analysis for improved reservoir description. spe reservoir evaluation & engineering 8(1): 53-69. spe-87820-pa. hao wang is a petroleum engineer at liaohe oilfield company, a subsidiary of petrochina. wang’s specialties include viscous oil development technologies, like sagd and steam drive. wang holds a bachelor’s degree in petroleum engineering from china university of petroleum, beijing, and master’s degree in petroleum engineering from northeast petroleum university. a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.444 received september 10, 2019; revised october 22, 2019; accepted november 10, 2019. *corresponding author: jiangyun119@petrochina.com 1 water block damage and its solutions for tight gas reservoirs in dabeikeshen area yun jiang*, yang shi, liang zhao, xianyou yang, research institute of petroleum exploration & development, petrochina, beijing, china; yue li, cnooc(china) co., ltd. tianjin branch, tianjin, china; yue yu, southwest oil & gasfield company, petrochina, chengdu, china; ying gao, and meng wang, research institute of petroleum exploration & development, petrochina, beijing, china abstract water block damage may arise in tight gas reservoirs in dabei-keshen area as the reservoir is associated with low porosity, low permeability and strong capillary forces, which results in worthless industrial exploitation. to investigate the mechanism of water block and put forward corresponding measures, water block index (wbi) is developed to estimate the damage degree of water block and thermo-stable surfactant systems are optimized to clean up water block through interfacial tension tests, wettability tests and spontaneous imbibition. the result of wbi for core samples from the targeted zone is 70%, belonging to the type of strong water block. sensitivity analysis shows that matrix permeability and displacement pressure are in positive correlation with wbi, while water saturation, content of clays, fluid viscosity and interfacial tension are in negative correlation with wbi. thermo-stable surfactant systems jy-2(0.05fs31+15%methanol) and jy-3(0.5%hsc-25+15%methanol) are preferentially optimized. and jy-3 works best to reduce wbi from 66.2% to 30.4%. surfactant in composite system contributes to reducing interfacial tension and altering wettability, and methanol is benefit for reducing water saturation through accelerating evaporation in a short time. this synergy promotes the clean-up process of water blocks. based on the study of mechanism of water blocks and experimental results, we are able to provide reference for economic and efficient development of gas fields. introduction tight gas reservoirs in china contain large amount of resources with ultra-low permeability, porosity and productivity. it must be successfully stimulated to produce commercial productivity (khlaifat et al. 2011). however, many problems may arise during the process of stimulation, including fines migration, incompatible fluid, water block, etc. among these problems, water block seriously limits the successful development of tight gas reservoirs, and problems become more complicated when encounters high temperature and high pressure. dabei-keshen area is a typical ht/hp tight gas reservoir and the targeted zone mainly consists of feldspar sandstone, litharenite and arcose. multi high angle fractures grew in the formation where feldspars and calcites are the main interstitial fillings. clays consist of kaolinite (67~74%), illite mixed with smectite (16~22%) and chlorite, which results in the increase of connate water saturation and flow resistance due to high content of illite and smectite. the petrophysical properties of the reservoir include permeability (0.011×10-3-0.424×10-3μm2), porosity (2.09-7.91%), drainage pressure (1-8mpa), average pore radius (0.1μm), contact angle (18~40°), pressure coefficient (1.54-1.65), temperature (2.10°c/100 m), etc. it can be concluded that the target zone is a ht/hp and low mailto:jiangyun119@petrochina.com 2 porosity and permeability formation, and water block may exist during the process of stimulation (xu 2016; mei 2014). there have been numerous experimental and field studies (penny et al. 1983, bennion et al. 2006, liu et al. 2015; rostami et al. 2016) on water block trapping. ding and kantzas (2003) studied the imbibition mechanism with nmr technique and attributed the cause of water block to capillary forces. mahadevan and sharma (2005) studied the affecting factors of water block, including permeability, wettability, and temperature on clean-up of water block by measuring relative gas permeability with berea sandstone and texas cream limestone cores. based on the analysis of these factors, many formulas have been proposed to clean up water block in consideration of reducing interfacial tension, altering wettability and reducing water saturation (adejare et al. 2012; tang and firoozabadi 2002; fahes and firoozabadi 2007; fernandez et al. 2011; liu 2015; li 2017; jiye et al. 2016; yuan et al. 2016;). but few studies of water block characteristics on tight gas reservoirs with ht/hp were conducted as it is difficult to simulate ht/hp conditions. in this study, we focused on core’s relative gas permeability from dabei-keshen area to investigate the cause of water block and put forward corresponding measures. first of all, water block index was initially established to evaluate the damage degree of water block and then five factors related to water block were systematically analysed. then, four kinds of composite surfactant system were used to optimize the thermos-stable surfactant through interfacial tension, wettability and spontaneous imbibition tests. finally, the optimized surfactant was used to prevent water block by measuring water block index. materials and apparatus materials: 25 core samples (d=2.54cm, l=4.06-5.08cm) selected from 6 wells (5850.3-5885.8m) in dabei-keshen; 4 surfactants purchased from 3m corporation in usa. apparatus: dcat11 interfacial tension meter, dsa-30 contact angle meter, self-made spontaneous device, ht/hp acidizing simulation device, displacement simulation device. methods damage degree of water block. 11 cores were applied to evaluate damage degree of water blocks by testing the relative gas permeability. the experimental procedure was as follows: (1) dry the cores in the oven at 50°c for 24 hours; (2) take out the cores, record the dry weight m0 and calculate initial gas permeability k0 using steady state method as listed in eq. 1; (3) set the sample in the core holder and flood it with simulated formation water with a salinity of 62000 mg/l, record the wet weight m1; (4) flood the core with n2 for 50-60 hours until the weight of the core ceases to change, set confining pressure as 4mpa and constant injecting pressure to be 2 mpa; (5) record the flow rate and weight the core per 1-2 hours, record as mi (i=2,3,…n); (6) calculate sw (eq. 2) for a given time, and calculate ki for gas phase under different water saturation according to sy/t 5345-2007; (7) calculate the damage degree of water blocks according to eq. 3 and plot sw vs. krg (kg/k0). �� = ���(�)��� � �ln( ������ 2 −�������� 2 ������ 2 −������� 2 �� ,……………………………………..…………………..……………(1) �� = ��−�0 �1−�0 ,…………………………………………..…………………………………………….(2) ��� = �0−�� �0 × 100%.……………………..………………………………………...…………….(3) criterion for damage degree of water block index (wbi) is listed in table 1. table 1—criterion for damage degree of water block. wbi, % 0-30 30-60 60-90 >90 damage degree weak neutral severe extremely severe 3 optimization of thermo-stable surfactants system. dcat11 interfacial tension meter was firstly used to measure the interfacial tension of four kinds of composite surfactants system according to platinum plate method. dsa-30 contact angle meter was then used to measure the contact angle before and after adding surfactants. finally, self-made spontaneous imbibition device (figure 1) was employed to observe the variation law of sw. figure 1—apparatus of spontaneous imbibition. clean-up of water block. the optimized composite surfactant system was utilized to clean up water block and the procedure was as follows: (1) evacuate the core in the sealed container and saturate it with simulated formation water; (2) set the sample in the core holder and heat it to 160°c, flood the core with 2pv surfactants, and then cool down to room temperature; (3) take out the core sample and weight it; (4) place the sample in the core holder again and flood it with n2, measure the flow rate and weight until the weight stops changing; (5) calculate relative gas permeability under different water saturation. results and discussion damage degree of water block. 11 cores (as listed in table 2) were selected to evaluate water block index (wbi) and relative gas permeability (krg). the average value of wbi is 69.8%, which indicates that the damage from water block is extremely severe. table 2—results of wbi for 11 cores. sample no. porosity(%) k1(10-3 μm2) kg(10-3 μm2) swir(%) wbi(%) 1 6.41 0.092 0.032 35.82 65.59 2 6.51 0.098 0.029 41.68 70.41 3 7.91 0.424 0.231 29.78 45.52 4 5.05 0.061 0.019 34.96 68.85 6 3.07 0.013 0.003 42.14 76.92 7 3.34 0.011 0.002 46.51 81.82 11 2.09 0.016 0.002 49.76 87.50 12 2.49 0.021 0.003 48.69 85.71 18 6.47 0.083 0.031 34.74 62.65 21 6.53 0.115 0.044 36.85 61.73 22 5.61 0.151 0.058 31.74 61.59 4 sensitivity analysis. sensitivity analysis was performed to investigate the effect of water saturation, matrix permeability, and content of clays. water saturation. figure 2 shows the results of relative gas permeability under different water saturation. when sw is between 40% and 80%, krg decreases drastically and the concave curves is observed. while for the high sw (80~100%), krg is less than 15% for all 11 curves and its change interval is relatively small. figure 2 reveals that the damage degree of water block increases significantly in the early time and then remains stable while the pore volume is almost occupied by water. 20 30 40 50 60 70 80 90 100 0 10 20 30 40 50 60 70 80 kr g / % sw / % 1# 2# 3# 4# 6# 7# 11# 12# 18# 21# 22# figure 2—relative gas permeability under different sw. matrix permeability. figure 3a and 3b present the results of krg and wbi for three cores (#11, #18, #3), whose matrix permeability is 0.016×10-3, 0.031×10-3 and 0.424×10-3μm2, respectively. the results indicates that krg is in positive correlation with matrix permeability while wbi displays the negative law. this is subjected to the higher porosity and higher matrix permeability as the capillary force is lower, so the invaded fluid is more easily to be displaced. as a result, the fluid retained in the cores is less, which decreases the damage degree of water block. (a) (b) figure 3—results for #3, #18, #11. (a) curves of relative permeability. (b) wbi. content of clays. figure 4a and 4b show the results of krg and wbi for three cores (#6, #7, #11) whose matrix permeabilities are close but contents of clays are 14.9%, 20.1% and 23.6%, respectively. the results indicate that the degree of water block damage is more serious for the cores with higher content of clays, especially, when illites and smectites are rich. this is mainly attribute to the strong suction effect of illites and smectites, which induces the increase of water saturation and flow resistance. therefore, the damage degree of water block increases. 5 (a) (b) figure 4—result for #6, #7, #11. (a) curves of relative gas permeability. (b) wbi. displacement pressure. the tests were performed at 1mpa and 2mpa (#4 and #5). figure 5 shows that the water saturation decreases with time. the results show that sw is almost the same when t<200 min, but sw of #5 decreases more rapidly as time increases. it can be concluded that displacement pressure mainly affects the clean-up time, and higher pressure tends to lower sw and wbi. figure 5—saturation curves of 4# and 5#. fluid type. three cores were employed to compare the effect of different fluid type to wbi. the result presented in table 3 shows that the order of damage degree was surfactant jy-2 < simulated formation water (a) < filtrate of guar gum fracturing fluid (b). the main differences among these fluids are viscosity and interfacial tension. the invaded fluid is more difficult to be displaced if the viscosity and interfacial tension are higher. table 3—results of wbi for different liquids. no. fluid type swir (%) μ (mpa/s)  (mn/m) wbi (%) #15 a 38.62 1.48 48.24 68.42 #16 b 51.35 4.00 62.61 90.24 #25 jy-2 21.51 1.42 20.58 37.25 water block damage and sensitivity analysis indicates that the main factors that affects water block can be divided into inertial ones and external ones. among them, the lower water saturation, matrix 6 permeability, content of clays (inertial factors) will result in less damage. fluid type and displacement pressure are the external factors. lower viscosity, lower interfacial tension and higher pressure will decrease degree of water block. optimization of composite surfactant system. wettability alteration and reduction of interfacial tension are two major means to clean up water block. selecting proper surfactant is the most economical method to clean up water block. combined with the geological properties of targeted zone, four kinds of composite surfactants system were used for further assessment. they are jy-1 (0.05% fc4430+15% methanol), jy-2 (0.05% fs-31+15% methanol), jy-3 (0.5% hsc-25+15% methanol), and jy-4 (0.5% f108+15% methanol). among them, fc4430 and fs-31 are fluorocarbon surfactants, hsc-25 is cationic surfactant and f108 is bio surfactant. three sets of tests were conducted to optimize the appropriate system, including interfacial tension tests, wettability tests and spontaneous imbibition tests. interfacial tension tests. table 4 shows the interfacial tension of four composite surfactants at 180°c and 25°c. the results presented in the table indicate that they are all thermos-stable under both conditions. the interfacial tensions at 180°c is improved slightly than that at 25°c. four systems all meet the requirements. table 4—interfacial tension of composite surfactants. no. (mn/m) 180°c (mn/m) 25°c jy-1 20.34 19.86 jy-2 20.58 19.88 jy-3 22.81 22.41 jy-4 26.16 25.42 wettability tests. figure 6 shows the result of wettability alteration by measuring the contact angle before and after adding surfactants. the contact angles were transferred from 20~30° to 60~65° by injecting jy-1 and jy-4, and the contact angles increased to 70~78°by injecting jy-2 and jy-3. the result indicates that jy-2 and jy-3 are more effective for wettability alteration. figure 6—wettability before and after adding surfactants. spontaneous imbibition tests. spontaneous imbibition tests were conducted to observe whether the surfactants could shorten the time of displacement so that water saturation could be decreased. figure 7a and 7b show the results of water saturation with time increasing. the imbibed fluid consists of simulated formation water, simulated formation water mixed with surfactants, and simulated formation water with pre-treated surfactants. the results indicate that water saturation and imbibition rate could be reduced by injecting mixed system and pre-treatment system. as a result, the imbibition process was prohibited to a certain extent. in other words, surfactants jy-2 and jy-3 are both able to reduce imbibition rate. 7 (a) (b) figure 7—spontaneous imbibition curves. (a) #21. (b) #22. clean-up of water block damage. figure 8a and 8b show the result of wbi by injecting simulated formation water, jy-2 and jy-3. the average wbi for simulated formation water and jy-2 are reduced from more than 62.6% to 42.4%. and wbi for simulated formation water and jy-2 are reduced from 66.2% to less than 30.4%. the results indicate that the surfactants in the composite system reduce the interfacial tension and alter the wettability, leading to a considerable decrease in capillary force. meanwhile, the methanol in the composite system can accelerate the evaporation process and reduce water saturation. eventually, water block is effectively cleaned up through injecting composite surfactant system, and jy-3 is the best choice. (a) (b) figure 8—results of wbi. (a) jy-2. (b) jy-3. conclusions 1) water block index, wbi, is applied to evaluate the damage degree of water block, and wbi of selective core samples from the targeted zone is 70%, belonging to the type of strong water block. 2) sensitivity analysis shows that the factors that affects wbi are divided into inertial ones and external ones. matrix permeability and displacement pressure are in positive correlation with wbi, while water saturation, content of clays, fluid viscosity and interfacial tension are in negative correlation with wbi. 3) thermo-stable surfactant systems jy-2 (0.05 fs-31+15% methanol) and jy-3 (0.5% hsc25+15% methanol) are optimized through interfacial tension tests, wettability tests and spontaneous imbibition tests. surfactant in the composite system plays a role of reducing 8 interfacial tension and altering wettability, and methanol is favorable for reducing water saturation. they are mutually effective to clean up water block damage. 4) composite system jy-3 works best to reduce wbi from 66.2% to less than 30.4%. acknowledgments foundation: national science and technology major project (2011zx05046005). conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature qg = gas flow rate gas, cm3/s l = sample length, cm a = sample cross sectional area, cm2 pinlet/outlet = are inlet pressure and outlet pressure, respectively, mpa mi = i core weight at different sw, respectively, g vd = downstream reservoir volume, ml pinitial = initial pore pressure, mpa wbi = water block index, % k0 = initial gas permeability, 10-3μm2 ki = gas permeability at sw, 10-3μm2 kn = gas permeability at swi, 10-3μm2 krg = relative gas permeability, %. references adejare, o.o., nasralla, r.a., and nasr-el-din, h.a. 2012. a procedure for measuring contact angles when surfactants reduce the interfacial tension and cause oil droplets to spread. paper presented at the spe saudi arabia section technical symposium and exhibition, al-khobar, saudi arabia, 8-11 april. spe-160876-ms. bennion, d. b., thomas, f. b., schulemeister, b., et al. 2006. water and oil base fluid retention in low permeability porous media—an update. paper presented at the petroleum society’s 7th canadian international petroleum conference in calgary, alberta, canada, 13-15 june. petsoc-2006-136. ding, m. and kantzas, a. 2003. investigation of liquid imbibition mechanisms using nmr. sca 2003(39): 1-6. fahes, m.m. and firoozabadi, a. 2007. wettability alteration to intermediate gas wetting in gas-condensate reservoirs at high temperatures. spe j. 12(4): 397-407. fernandez, r., fahes, m. m., zoghbi, b., et al. 2011. wettability alteration at optimum fluorinated polymer concentration for improvement in gas mobility. paper presented at the europec/eage annual conference and exhibition, vienna, austria, 23-26 may. spe-143040-ms. jihye, k., ahmed, m.g., scott, g.n., et al. 2016. engineering hydraulic fracturing chemical treatment to minimize water blocks: a simulated reservoir on-a-chip approach. paper presented at the spe international conference and exhibition on formation damage control, lafayette, louisiana, usa, 24-26 february. spe178959-ms. khlaifat, a., qatob, h., and barakat, n. 2011. tight gas sands development is critical to future world energy resources. paper presented at spe middle east unconventional gas conference and exhibition, muscat, oman, 31 january-2 february. spe-142049-ms. li, s., ding, y., gu, d., et al. 2017. enhancing oil recovery by wettability alteration during fracturing in tight reservoirs. journal of shenzhen university science and engineering 2017(1): 98-104. liu, x. kang, y., luo, p., et al. 2015. wettability modification by fluoride and its application in aqueous phase trapping damage removal in tight sand stone reservoirs. j. pet. sci. eng. 133(2): 201-207. mahadevan, j. and sharma, m. m. 2005. factors affecting clean-up of water blocks: a laboratory investigation. paper presented at the spe annual technical conference and exhibition in denver, 5-8 oct. spe-84216-ms. mei, j. 2014. water locking damage evaluation and prevention countermeasures of tight gas reservoir in hangjinqi area. petroleum geology and engineering 4(1):132-135. 9 penny, g. s., soliman, m. y., conway, m. w., et al. 1983. enhanced load water-recovery technique improves stimulation results. paper presented at the spe annual technical conference and exhibition in san francisco, ca. 5-8 oct. spe-12149-ms. rostami, a., nguyen, d.t., and nasr-ei-din, h.a. 2016. laboratory studies on fluid recovery enhancement and mitigation of phase trapping by use of microemulsion in gas sandstone formations. spe prod. oper. 31(2): 120-132. spe-178421-pa. tang, g. and firoozabadi, a. 2002. relative permeability modification in gas/liquid systems through wettability alteration to intermediate gas wetting. spe reserv. eval. eng. 5(6): 427-436. xu, p. 2016. damage analysis of tight sandstone gas reservoir and control measures of kupa piedmont structure. science technology and engineering 6(2):172-177. yuan, b., moghanloo, r.g., and pattamasingh, p. 2016. analytical model of nanofluid injection to improve the performance of low salinity water flooding in deepwater reservoirs. paper presented at the offshore technology conference asia, kuala lumpur, malaysia, 22-25 march. otc-26363-ms. yun jiang is a reservoir engineer in research institute of petroleum exploration & development, petrochina. his research interests include unconventional reservoir stimulation. he holds a phd in reservoir stimulation from research institute of petroleum exploration & development and a master’s degree in reservoir stimulation from china university of petroleum (beijing). yang shi is a reservoir engineer in research institute of petroleum exploration & development, petrochina. his research interests include unconventional reservoir stimulation. he holds a master’s degree in reservoir stimulation from research institute of petroleum exploration & development. liang zhao is a reservoir engineer in research institute of petroleum exploration & development, petrochina. his research interests include numerical reservoir simulation. he holds a phd in reservoir stimulation from research institute of petroleum exploration & development and a master’s degree in reservoir stimulation from china university of petroleum (beijing). xianyou yang is a reservoir professor in research institute of petroleum exploration & development, petrochina. his research interests include reservoir stimulation. he holds a phd in reservoir stimulation from research institute of petroleum exploration & development and a master’s degree in reservoir stimulation from china university of petroleum (beijing). yue li is a reservoir engineer in cnooc(china) co., ltd. tianjin branch. his research interests include unconventional reservoir stimulation. he holds a master’s degree in reservoir stimulation from china university of petroleum (beijing). yue yu is a reservoir engineer in central sichuan oil and gas district, southwest oil & gasfield company, petrochina. her research interests include unconventional reservoir stimulation. she holds a master’s degree in reservoir stimulation from china university of petroleum (beijing). ying gao is a reservoir engineer in research institute of petroleum exploration & development. her research interests include unconventional reservoir stimulation. she holds a master’s degree in reservoir stimulation from beijing institute of technology. meng wang is a reservoir engineer in research institute of petroleum exploration & development, petrochina. his research interests include unconventional reservoir stimulation. he holds a phd in reservoir stimulation from china university of petroleum (beijing) and a master’s degree in reservoir stimulation from sichuan university. abstract introduction materials and apparatus methods results and discussion conclusions acknowledgments conflicts of interest nomenclature references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1203 received may 1, 2022; revised june 15, 2022; accepted july 22, 2022. *corresponding author: minh.vo@chevron.com 1 smart seismic modeling artificial intelligence in the petroleum industry binh nguyen kieu and minh van vo*, unocal east china sea ltd, chengdu, china abstract vertical seismic profile (vsp) data have many known advantages, if being compared to seismic data such as broader bandwidth, less attenuation, clearer under well true depth (td) image, multiple noise differentiation, shear wave information, direct attenuation and anisotropy measurements, higher fidelity amplitude versus offset (avo) effect, etc. in this paper, we share the bottom-up approach that aims to maximize the information extracting from borehole seismic, in conjunction with seismic and well log data, to generate a geological model by integrating full wave-field modeling (fwm) to deep learning techniques, called smart seismic modeling (ssm) project. the study starts using data at well locations, with vertical seismic profile (vsp) forward modeling process. the 2d rock physics model is thus built from the prior well logs and the major interpreted seismic horizons and faults. by altering rock-physics properties values and thickness of each layer, the model has been multiplied thousand times. the rock-physics models and their simulated seismic traces are fed, as labels and inputs, respectively, into a 2d deep learning network. the network then extracts the non-linear relationships between inputs and labels so that thickness and rock-physics properties can simultaneously be regressed with least squared error loss function. optimal trained weight set (artificial intelligence engine) is finally used to predict wellbore’s surrounding geologic structures and rock properties for all the wells in the study area. to make sure machine learning can provide a good work, similar training and prediction process is carried out from surface seismic forward modeling. not only is it used for rock property prediction at the area apart from wells, but also for cross checking the prediction at well location. all 2d predicted rock-property models are merged by multi-point statistics (mps) method using hard data from wells’ prediction and trends from actual vsp processing, such as anisotropy, 2d qp, qs, for a complete 3d geologic model. by doing with two different modeling processes, i.e., vsp forward modeling and surface seismic forward to cross check the results, results can obtain from this study are: 1)high quality static model for field development; 2)high quality dynamic model for field monitoring; 3)robust artificial intelligence engines for variety types of geology. in this study, we introduce the smm approach and share promising successes in applying deep learning in rock property inversion process. the successful showcase has proved that deep learning technique can be used to extract any kind of rock properties from the big data of vsp, well log and of seismic. introduction one of the subsurface modeling challenges is to deal with the random walks of geology at the areas, where well data are missing and/or complex geologic structure beyond seismic resolution. many studies have been continuously conducted to enhance the seismic quality by researching new approaches, algorithms, tools, 2 techniques, etc. in all areas from seismic acquisition, processing, to interpretation. however, extracting net pay directly from seismic data remains a major challenge. chopra et al. (2006) presented their effort on increasing vertical seismic resolution by removing wavelets from conventional seismic data through thin-bed spectral inversion and their upgraded version (chopra and marfut, 2007) was sparse-layer inversion that reduced the effects of wavelet side-lobe inference. both the studies have not worked well unless there is not much lateral geological structure and wavelet changes and the impedance structure of the earth is blocky, rather than transitional. zhang and castagna (2011) enhanced seismic frequency content by applying q-compensation on seismic data for frequency attenuation due to hydrocarbon collision and friction. recently, zhang et al. (2016) conducted a study using deep learning (dl) to automatically detect geophysical features (faults, geo-bodies…) from pre-migrated raw seismic data to steer interpretation and modeling processes. their concepts and projects have showed potential applications to the industry and motivated the effort for an integration solution. more recent, walker et al. (2017) came up with a stochastic inversion method known as one dimension stochastic inversion (odisi) that ignored the above assumptions and requested more simple prior information such as processed well logs and high-level interpreted seismic horizons, bayesian machine learning was used for the regression process. however, it recommends the inputs are impedance cubes, which are projected by chi angles for lithology and fluid enhancement (paramo et al. 2019). at the thin bed and complex structures where amplitude variation with offset (avo) effect is usually not clear for lithology and fluid projections, this method might not effectively support. furthermore, the cost function between synthetic and observed seismic trace to vote for 100 best correlation cases might suffer the cumulative error from previous seismic processing steps (not true amplitude and phase fluctuation). synthrock module, opendtect, can even match with pre-stack seismic angle data and integrate physics law into the deep learning loss function (physics-inform neural network), but hardly does it consider the vertical seismic profile (vsp) advantages in the workflow. full waveform inversion (fwi) is the most recent advanced seismic imaging (high resolution) technology that utilizing supercomputing and advanced algorithms process all the sound wave components then create a model to simulate synthetic seismic and compare to the field recorded data. supercomputers iterate through possibilities until they develop a model where the synthetic traces match those recorded data. the rock layers and its properties (velocity) will be updated during the iteration (inversion)(saraiva et al. 2021). the method suffers several bottlenecks such as time-consuming due to the curse of dimensionality, heavily sensitive on proper velocities selection and requires low frequency information (ma and zhang 2021). in this study, we would share the smart seismic modeling (ssm) approach, which utilizes full wave-field modeling (fwm) technique in building datasets for the deep learning network. by doing this, it will help relieve the fwi’s bottlenecks from several angles. it is a bottom-up method, simply starting from well data that are less noise, high resolution, higher quality, and then the work scales up to “up level” of seismic. moreover, ssm considers geo-statistical analysis when working in 3d reconstruction under constraints of hard data, such as vsp, well logs, core, and fluid sample, and trends from borehole seismic. to illustrate the success of this approach, we have presented several case studies to support the conclusion that deep learning can be used to provide a reasonable prediction in vsp rock property inversion process. methodology ssm is a multidisciplinary project, across several subsurface disciplines: geophysics, geology, and reservoir engineers, and most importantly, with the participation of machine learning engineers. the target is to create an artificial intelligence (ai) engine, which is mainly driven by the characteristics of training data (datadriven learning), rather than the latent theories, assumptions, and domain expertise to outperform human limitation. ai engines could flexibly promote self-adaptive learning to any new geology. the most important indicator of seismic quality is seismic resolution. it depends on wavelets, signal/noise and geologic contents as shown in figure 1. more detail, seismic resolution is subdivided to vertical and lateral ones. it depends on the frequency content of the seismic wavelet and aperture of migration. https://www.earthdoc.org/search?value1=m.+walker&option1=author&noredirect=true https://www.earthdoc.org/search?value1=p.+paramo&option1=author&noredirect=true 3  wavelet is affected by amplitude and frequency decaying (geometrical spreading, absorption, inter-bed reflection, refraction, scattering…); noise interference; human bias whilst processing.  geologic contents include complex or simple geological structure, thin or thick layers, and high or low impedance contrast. figure 1—some of the key variables that affect seismic detectability. there is a large range of seismic resolution, it depends on different frequency regimes: 25m for seismic in a general case of 3000m/s rock velocity and 30hz peak/dominant frequency wavelet (source); vsp is 10m, sonic is few cm (chabot et al., 2002) (figure 2). vsp stands at the center as a bridge connecting the large lateral coverage of seismic (time domain) and high resolution of sonic (depth domain) data. below 10m thickness (stratigraphic targets) seismic may suffice for structural objectives (prior information), the detailed reservoir scale will be fitted by sonic, vsp and full waveform sonic or cross well seismic (mondol 2015). the output from wells needs to be up sampled back to seismic frequency range for later up-scaling purposes. the “grey zone” and “not visible seismically” zones contribute about a half of the seismic volume in figure 1, these are the challenging part to the conventional approach, it is beyond the geoscientists’ (human) bare eyes’ interpretation capacity. moreover, to invert seismic to geological domain in conventional manner, even the most modern fwi, accurate wavelets still are extremely sensitive and crucial to the success of the inversion (feng et al. 2018). figure 2—range versus resolution of various geophysical techniques (chabot et al. 2002). project foundation bases on forward modeling and deep learning inversion techniques (figure 3), where x(x1, x2,…,xn) is a multi-channel tensor; of which x1 is density vector, x2 is compression velocity vector, …, xn is compression absorption q; y(i,j) is a set of seismic (vsp) traces/gathers/stacks; f(x), is a convolutional 4 function. and f-1(y) is a non-linear deep learning function (optimum set of weights) taking seismic images and original earth model as inputs and labels in the inversion process. figure 3—project conceptual model ssm approach is not subject to the accuracy of the wavelet, it also digs into the “grey zone” and “not visible seismically” zones to get the insights from the raw seismic and the other hard data thus skips huge workloads of processing and interpretation. technically, the project is divided into three stages (figure 4).  stage 1: the “bottom level” is built at well locations. rock properties derived from well logs and surrounding geological structures from seismic will be utilized to build 2d viscoelastic forwarding models which include vp, vs, density, qp and qs. by altering rock properties values and thickness of each layer, the model will be multiplied thousand times. synthetic seismic will be simulated on the models following single source common midpoint (cmp) seismic and vsp recording geometries. actual field recorded surface hydrophone source signatures can be used as convolution wavelets. these generated synthetic seismic will be fed into deep learning networks as inputs, meanwhile the forwarding models will be the labels in the inversion processes. vsp inversion will compute sensitive rock properties: vs, density, qp, qs while seismic inversion will cross check the inverted properties computed from vsp. the deep learning model will be trained for many epochs, the optimum weight scheme will be saved as an ai engine for further predictions.  stage 2: is spreading out the engine to areas apart from wells.  stage 3: is another extension with the integration of dynamic data. figure 4—project workflow comprises three stages 5 in more detailed, stage 1 is shown as in figure 5, starting at a well which has at least vp, vs, density, vsp and simple interpreted seismic horizons/faults. a 2d structure model across the well will first be constructed from seismic structure interpretation results. the intra-layers and rock-physics properties will be filled up by well logs following seismic intra-layer facies. for the quick computation, well logs can be blocked at seismic or vsp scale (5-10m or 1-5m). forward modeling process will be carried out on that model for seismic and vsp survey geometries to generate synthetic seismic traces. this process will be replicated hundred to thousand times by iterating randomly the thickness and rock-properties within their statistical tolerances to create a dataset for deep learning model. the rock-physics models and their synthetic seismic images will be fed into a deep learning network as labels and multi-channel inputs for model training. an optimum set of weight (ai engine) will be captured to predict 2d rock physics models simultaneously from actual seismic and vsp data. figure 5—stage 01-forward modeling products are the materials for deep learning network model training; an ai engine will be saved to predict rock-properties from real seismic and vsp data. those steps will be replicated to other wells then. consequently, a set of ai engines representing specific geology (well locations) are ready for next steps. stage 2 is the extension of stage 1 into 3d scale. the conflict of mismatching among inverted 2d rockphysics models will be encountered and really a challenge. outputs of stage 1 will be considered as hard data/input. forward modeling process will be continued in other directions and areas apart from wells. study area can be subdivided to smaller partitions following geology, normally faults act as natural partition boundaries. multi-source forward modeling will be applied for seismic survey geometry for further migration and stacking processes that generate 3d seismic cubes which will be fed into a 3d deep learning network model to create an engine for quick 3d seismic to geology inversion. to overcome the conflict of miss-matching at boundaries intersection among partitions, multi-point statistics (mps) algorithm is introduced in merging these 2d rock-physics models into a 3d one. the merging process integrates hard data from stage 1 and trends from actual vsp processing results, such as anisotropy (walk-away, 3d vsp), 2d qp, and qs distribution (walk-above vsp). similarly, as stage 1, 2d deep learning network will be trained by ingesting inputs and labels but controlled by hard data and trends following mps method (sun et al. 2014), the optimum set of weights will also be achieved for future prediction. synthetic seismic can be processed and stacked to 3d cubes then fed into a 3d deep learning network to create an engine for quick seismic to geology inversion. expected outputs are a set of 2d ai engines for partitions, 3d geological model and a 3d ai engine for quick 3d rock-physics model prediction. 6 stage 3 is an extended phase of stage 2. dynamic data will feed into the model for the matching process. it is aiming for field monitoring after a period of producing time. it is also applied in other engineering processes, such as co2, h2 storage. new data will come during the field life cycle, the process then re-run and update. proof of concept forward modeling and deep learning regression processes have been built following the concept of the threestage approach (ma and zhang 2021) and run through. this is a crucial positive indication showing the ssm project feasibility. acoustic velocity (vp) model comprises a simple set of nine flat and thick layers. it has been replicated to 600 models (450 models are used for training and validation, 150 for testing processes) by keep v0=1,500m/s and thickness = 200m, meanwhile changing velocity of following layers as vlayer + 1 = (vlayer + 190) ± 380 and no greater than vmax = 4,000m/s. a 12 hz seismic source time signature, modeled using the theory ricker wavelet, injects waves to those velocity models following acoustic wave equation (louboutin et al. 2020). 100 downhole hydrophones, 15m separate to each other, are used to record the pressure field from the surface source. the acquisition geometry is zero offset vsp, and synthetic vsp image as in figure 6. figure 6—single source zero offset vsp for single hydrophone receiver forward modeling process these 1d velocity curves and their synthetic seismic images are fed into a two simple hidden layers neural network, followed by sigmoid activation functions for 1d regression process (figure 7a). total of 5 million model parameters have been trained through 1000 epochs, stochastic gradient descent with decay learning rate was used. the best model is converged at epoch 999 with validation loss of 495.03 (mean squared error) which is still high (figure 7b). 7 figure 7—a) 2 simple hidden neural network layers, loss function: mean_squared_error, optimizer: stochastic gradient descent; b) training and validation loss functions the predicted vp indeed shows a limited match to the ground truth (figure 8). predicted vp tends to oscillate around vp label mean and shows poor matches at the small and large velocity variation among layers. the result is very positive and there is room for improvement. figure 8—1d acoustic velocity inversion: a) vsp synthetic images’ inputs. b) labels vs predicted vp with the success of 1d acoustic velocity inversion, the modeling work has been upgraded by using 2d multi-channel inputs (seismic gathers, vsp 4 components) and outputs (by generating vp, vs, qp, qs, density, etc. simultaneously) regression and more complicated deep learning networks such as physics-informed deep learning where physics laws can be integrated to machine learning (ml)/deep learning (dl) network loss functions (raissi et al. 2019). 8 discussion the 1d acoustic velocity inversion results could be enhanced by using more appropriate network such as convolutional neural network (cnn, a typical image processing network), increasing data volume (with more powerful computational computer) to avoid over-fitting. despite the limitation in the result from a simplified regression model, it obviously does fulfill its role in proving the feasibility of deep learning in rock property inversion from vsp data. that is the achievement that is an encouraging support for the project execution. to minimize the multi-root problem of inference result from non-standard data, which is the biggest challenge of all rock property inversion approaches, physics-informed neural networks (pinns) is introduced to converge the regression process with the least error, meanwhile multi-point statistics (mps) helps to interpolate and extrapolate the discrete rock property profiles into a 3d model under the constrains of training images and trends from vsp data. conclusions this paper has outlined the 3-stage approach project with the application of ai, deep learning, and the illustration case successes. there have been several identified working items to optimize the project execution. 1. the bottom-up approach integrates as much as possible the availability of borehole seismic data with their advantages such as image in both time and depth domains, less frequency and amplitude decaying and absorption, quantitatively measure shear waves and its absorption, anisotropy, avo estimation and better subsurface images. 2. the flexibility of deep learning from 1d to 3d scales under the modern constraints such as physicsinformed base and geo-statistics interpolation technique helps more easily converge the “random walk” of the subsurface geology in the inversion process. those are the key elements of the project and expected to overcome the difficulties of the conventional approach. acknowledgement the authors would like to thank the software underground community for their excellent open-source dsl devito free license usage and their great support through the slack channel. conflicting interests the author(s) declare that they have no conflicting interests. references chabot, l., brown, r.j., henley, d.c., et al. 2002. henley, and john c. bancroft. single-well imaging using full waveform sonic data. crewes research report 14: 1-14. chopra, s., castagna, j., and portniaguine, o. 2006. seismic resolution and thin-bed reflectivity inversion. cseg recorder 12: 19-25. chopra, s. and marfut, k.j. 2007. seismic attributes for prospect identification and reservoir characterization. seg geophysical developments series 11:180-185 feng, j., teng, q., he, x., et al. 2018. accelerating multi-point statistics reconstruction method for porous media via deep learning. acta materialia 159:296-308. louboutin, m., luporini, f., witte, p., et al. 2020. scaling through abstractions high-performance vectorial wave simulations for seismic inversion with devito. computational physics 3(3):12-25. ma, y. and zhang, j. 2021. velocity model building from one-shot vsp data via a convolutional neural network. paper presented at the international meeting for applied geoscience and energy, denver, colorado, usa, 26 september-1 october. 9 mondol, n.h. 2015. seismic exploration. in petroleum geoscience from sedimentary environments to rock physics. 2nd ed. ed. knut bjørlykke, chap. 4, 427-454. berlin: springer. paramo, p., chauhan, a., grant, s., et al. 2019. using one dimension stochastic inversion to characterize reservoir facies in a deep water turbidite field. paper presented at the 81st eage conference and exhibition, london, uk, 1-5 june. raissi, m., perdikaris, p., and karniadakis, g. e. 2019. physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. journal of computational physics 378(1): 686-707. saraiva, m., forechi, a., de oliveira neto, j., et al. 2021. data-driven full-waveform inversion surrogate using conditional generative adversarial networks. paper presented at the 2021 international joint conference on neural networks (ijcnn), virtual. sun, d., jiao, k., vigh, d., et al. 2014. source wavelet estimation in full waveform inversion. seg technical program expanded abstracts 4: 1184-1188. walker, m., grant, s., pham huu, h., et al. 2017. comparing the odisi integrated stochastic seismic inversion method to an equivalent bayesian inversion method. paper presented at the 79th eage conference and exhibition, paris, france, 1-5 april. yu, s. and ma, j. 2021. deep learning for geophysics: current and future trends. reviews of geophysics 59(3): 120122. zhang, c., frogner, c., poggio, t., et al. 2016. automated geophysical feature detection with deep learning. paper presented at the gpu technology conference, silicon valley, california, usa, 4-7 april. zhang, r. and castagna, j. 2011. seismic sparse-layer reflectivity inversion using basis pursuit decomposition. geophysics 76(6) :147–158. binh nguyen kieu, spe, received a b.e in geophysics from hanoi university of mining and geology humg (2005) and an m.e in applied petroleum geology from hochiminh city hcmc university of technology hcmut (2012). he has been working as an exploration and development geophysicist for cuu long joc, pvep poc, and schlumberger in vietnam. for 14 years of working experience, he had involved in many projects spreading in all major offshore basins of vietnam, malaysia, myanmar, thailand, kuwait, and china, in many types of reservoirs of sandstone/carbonate/fractured granite basement bearing oil and gas. he has been recently pursuing the continuing education in web development, data science and machine learning engineering (in madrid, spain since 2019). he has been an active member of spe, seg&vag in promoting the industry values to community through leading local young professional activities, visiting lecturer in hcmut, hcm university of science hcmuos, and petrovietnam university pvu. minh van vo, spe, is currently subsurface manager in unocal east china sea ltd., where he has worked for the last 7+ years. he has had 28+ years of experience in the oil and gas industry with multiple global locations. his research interests are in reservoir engineering, production optimization, and systems engineering. he holds several master’s degrees from unsw in petroleum engineering, from rmit in systems engineering, and mba from nyu. https://www.earthdoc.org/search?value1=p.+paramo&option1=author&noredirect=true https://www.earthdoc.org/search?value1=a.+chauhan&option1=author&noredirect=true https://www.earthdoc.org/search?value1=s.+grant&option1=author&noredirect=true https://www.earthdoc.org/content/proceedings/london2019 https://www.earthdoc.org/search?value1=m.+walker&option1=author&noredirect=true https://www.earthdoc.org/search?value1=s.+grant&option1=author&noredirect=true https://www.earthdoc.org/search?value1=h.+pham+huu&option1=author&noredirect=true https://www.earthdoc.org/content/proceedings/paris2017-annual abstract introduction methodology proof of concept discussion conclusions acknowledgement conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1189 received april 12, 2021; revised july 2, 2021; accepted august 9, 2021. *corresponding author: liushiqi@cumt.edu.cn 1 effects of co2 on the micron-scale porefracture structure and connectivity in coals from the qinshui basin shiqi liu*, shuxun sang, tian wang, yi du, and huihuang fang, china university of mining and technology, xuzhou, china abstract changes in the micron-scale pore and fracture structure in coal caused by co2 are critical for co2 injection and ch4 production in coal seams. to investigate the effects of co2 on the characteristics and connectivity of micrometer-scale pores and fractures in coal, four coal samples from the qinshui basin were selected. these samples were exposed to co2 and water for 240 hours at 80 °c and 20 mpa using a co2 geochemical reactor. x-ray micro-ct (computed tomography), field emission scanning electron microscopy (fesem), and energy dispersive spectroscopy (eds) were used to identify the characteristics and connectivity of micron-scale pores and fractures in the coal samples before and after co2 treatment. then, the influence of mineral dissolution on micrometer-scale pores and fractures was discussed. after co2 treatment, the massive dissolution of carbonate minerals significantly increased the pore contents and volumes of the coal samples. for this reason, the grain size and volume of carbonate minerals determined the increase in pore number and volume after co2 treatment. the dissolution of calcite, dolomite, and other carbonate minerals in the coal matrix formed a large number of pores created by dissolution <10 μm in diameter, which affected the number of pores in the coal after co2 treatment, but contributed little to the connectivity of the coal at the micro-scale. the carbonate minerals that filled the microfractures were heavily dissolved in co2, increasing the aperture and connectivity of the microfractures. the dissolution of carbonate minerals in microfractures was the major contributor to the increase in the volume of pores >50 μm in diameter and the main reason for the increase in coal connectivity at the micrometer scale. introduction the adsorption of co2 is superior to that of ch4 in coal seams (day et al. 2008; white et al. 2005). by injecting and storing co2 in coal seams, ch4 can be displaced by co2 and expelled from the coal seam, thereby improving ch4 recovery and reducing co2 emissions (white et al. 2005; hol et al. 2014; fujioka et al. 2010). this technique is called co2 geological storage-enhanced coalbed methane recovery (co2ecbm). co2-ecbm has environmental and energy benefits and has quickly become one of the hot spots in research on coalbed methane and emissions reduction (hol et al. 2014; fujioka et al. 2010). the united states, canada, the netherlands, japan, and china have conducted pilot tests of co2-ecbm, and the results are satisfactory (fujioka et al. 2010; faiz et al. 2007; pan et al. 2018; wong et al. 2007). mixing of co2 and water forms an acid fluid containing h2co3, which can dissolve calcite, dolomite, magnesite, and other minerals and promote ca and mg migration (bertier et al. 2006; dawson et al. 2015; du et al. 2018; hayashi et al. 1991; kolak and burruss 2014; liu et al. 2018). the co2-induced migration, dissolution and precipitation of inorganic minerals in coal change the structure of the coal, eg, opening some closed and semi-closed pores in the coal, changing the distribution of pore size in the coal, and increasing the porosity and permeability of the coal (anggara et al. 2013; kutchko et al. 2013; liu et 2 al. 2015; liu et al. 2010 ;massarotto et al. 2010; liu et al. 2019). co2 can also dissolve minerals filling coal fractures, thus increasing the aperture and connectivity of coal fractures and changing the mechanical properties of the coal (anggara et al. 2013; massarotto et al. 2010; perera et al. 2011; ranjith and perera 2012). other scholars have suggested that the reaction between the co2-h2o system and coal is a longterm process in which dissolved mineral components can migrate and precipitate in fractures that have not been filled with minerals or dissolved with co2, thus reducing their connectivity (du et al. 2018; kutchko et al. 2013; xu et al. 2016; zerai et al. 2006). the characteristics and connectivity of pores and fractures in coal determine the storage, diffusion, and migration of ch4 and co2 in coal (liu et al. 2015; wang et al. 2017; zhou et al. 2018). it is generally believed that the micron-scale pores in coal are mainly secondary gas pores and dissolution-created pores, while the fractures are micro-fractures and some small-scale cleats (liu et al. 2015; liu et al. 2016; liu et al. 2017). these pores and fractures are the main seepage channels of ch4 and co2 and connect the microscopic structure (e.g., adsorption pores and diffusion pores) and the macroscopic structure (e.g., macroscopic fractures) of the coals (liu et al. 2015; liu et al. 2016; liu et al. 2017). therefore, changes in the characteristics and connectivity of micron-scale pores and fractures in coal determine the injectivity and storage capacity of co2 and the production of ch4, which are crucial factors in co2-ecbm. research on changes in coal structures caused by co2 reactions was mainly focused on the nanoto submicrometer scale and the macroscale. the changes in the characteristics and connectivity of pores and fractures at the micron-scale are still unclear. in this paper, using typical low-volatile bituminous coal and anthracite coal as examples, x-ray microct (computed tomography), field emission scanning electron microscopy (fesem), and energy disperse spectroscopy (eds) were used to study the effects and mechanisms of co2 on the characteristics and connectivity of micrometer-scale pores and fractures in coal. this study aims to provide a better understanding of the effectiveness of co2 injection and ch4 production. samples and methodology samples. four groups of coal samples were collected from the qinshui basin, china, including lowvolatile bituminous coal from the xinyuan mine, semi-anthracite coal from the yuwu mine and the xinjing mine, and anthracite coal from the sihe mine. these samples were named coal #1 to coal #4 (table 1). the coal samples were systematically collected from the working faces of the coal mines. the collection, retention, and preparation of the coal samples were conducted in line with the relevant standard gb/t 19222-2003 in china and the international standard iso 7404-2:1985. to prevent further oxidization, coal samples were wrapped in absorbent paper, hermetically sealed in plastic bags and stored at 5 °c after sample collection. the key properties of these samples are shown in table 1. table 1—properties of the coals used. samples sampling location ro, max (%) proximate (wt. %) ultimate (wt. %) mad aad vdaf fcad odaf cdaf hdaf ndaf #1 xinyuan mine 1.81 0.81 5.35 15.26 80.20 9.30 80.32 4.43 1.14 #2 yuwu mine 2.19 1.10 11.98 13.44 76.19 2.44 91.73 4.12 2.44 #3 xinjing mine 2.64 1.66 10.02 10.10 80.89 3.05 91.52 3.96 1.06 #4 sihe mine 3.33 1.48 13.12 6.32 81.39 2.98 93.45 2.15 1.00 note: ro, max, the mean maximum reflectance values of vitrinite; wt. %, weight percent; mad, moisture; aad, ash yield; vdaf, volatile matter; fcad, fixed carbon content; odaf, oxygen content; cad, carbon content; had, hydrogen content; nad, nitrogen content; “ad” means air-dried basis; “daf” means dry ash-free basis. co2 treatment. co2 treatments were performed to replicate a burial depth of 2000 m. the temperature and pressure at this burial depth (80 °c and 20 mpa, respectively) were calculated from the temperature and depth of the sub-surface constant temperature zone, the average geothermal gradient, and the average pressure gradient at the sampling location. the coal samples chosen for co2 treatment consisted of small coal pillars for x-ray ct and bulk coal for scanning electron microscopy (sem) analysis. details of the high-pressure reactor and the experimental duration used in co2 treatment can be found in our previous 3 studies (liu et al. 2018; liu et al. 2019). after the co2 treatment, the coal samples were vacuum dried at 50 °c for 24 hours for the x-ray ct scan and sem analysis. pore-fracture network modelling. x-ray ct scan. x-ray ct scanning was performed with an xradia 520 versa x-ray ct scanner produced by the carl zeiss foundation group. samples for x-ray ct scanning were small coal pillars approximately 2 mm in diameter and 2 mm in height. these were drilled from bulk coal samples using a mechanical sampler. the scanning area of the x-ray ct scan was 1 mm in diameter and 1 mm in height. the total scan number was 1000 and the voxel resolution was 1.0 μm. after the x-ray ct scan, the small coal pillars were loaded into 800 mesh nylon bags that are resistant to high temperatures and corrosion for co2 treatment. after co2 treatment, x-ray ct scans were taken again of the small coal pillars. to compare the x-ray ct results, the scanning range, total scan number, voxel resolution, and scanning position of the small coal pillars before and after co2 treatment were the same. to ensure the same scanning areas before and after co2 treatment, the central point of each small coal pillar was identified as the center of the scanning area. due to the manually set scanning area, slight errors may exist. however, the x-ray ct results show that these errors have a weak impact on the research and can be ignored. establishing the pore-fracture network model. three-dimensional (3d) digital models of coal were established using avizo 9, which is professional software for 3d digital cores based on x-ray ct images. the process of establishing the 3d digital model of the coal includes several steps, such as 3d imaging reconstruction, image denoising, image binarization, and model construction. threshold selection is the key to identifying pores and fractures during the binarization process. in this paper, the x-ray ct images were first converted into 8-bit tiff bitmaps (tag image file format), and then their greyscales were normalized to the range of 0-255. thus, all bitmaps had 256 greyscales and the same grey range. threshold segmentation of the x-ray ct images revealed that the grey ranges for pore fractures, organic matter and minerals are 0-110, 110-180 and 180-255, respectively. based on the 3d digital model of coal, the characteristics of pores, fractures and minerals, including porosity, pore size distribution, pore volumes, mineral grain size distribution, and mineral volumes, were further extracted. the maximum inscribed ball method was used to extract the pore size and grain size of the mineral, and the equivalent diameters (eqdiameters) of the pores and minerals were obtained. furthermore, the equivalent pore-fracture network models which are ball-and-stick models, and interconnected pore-fracture models, were established, and the coordination numbers of pores and fractures and throat lengths were extracted. due to the large number of calculations and limited calculation capacity of the workstation, cubic ball-and-stick models and interconnected pore-fracture network models of coal samples that were 500 μm on each side were established. according to the maximum inscribed ball method, the fractures are filled with a number of balls and cut into a number of pores. therefore, the contents, volumes, and numbers of pores extracted from the 3d digital model contain the contents, volumes, and numbers of fractures. when establishing the ball-andstick model, a series of balls filling the fractures are identified as throats. for this reason, fractures are generally considered throats in the ball-and-stick model. scanning electron microscopy analysis. pores, micro-fractures, and minerals in coal before and after co2 treatment were investigated using a sigma 300 fesem instrument produced by the carl zeiss foundation group, germany, with a quantax 200 eds produced by bruker company, usa, with amplification from 103 to 105. samples used for fesem were bulk coal. the coal samples were polished into small samples approximately 10-30 mm across and 4-5 mm high using a polishing and burnishing machine. then, the small samples of coal were polished using a cross section polisher. after fesem analysis, coal samples were first loaded into 800 mesh nylon bags for co2 treatment and then investigated again using fesem to observe changes in pores, fracture, and minerals after co2 treatment. coal is known as a non-conducting substance. therefore, to achieve better experimental results, a thin gold coating is commonly applied to coal samples by sputtering. in this study, the gold coating can hamper reactions between coal samples and co2. therefore, instead of a gold coating, before co2 treatment, the sub-face and side faces of each coal sample were wrapped in conductive tape. after co2 treatment, to achieve better experimental results, a thin gold coating was applied to the coal samples by sputtering. the grain size of the mineral is small in coal and the minerals are difficult to locate. a 4 photograph of the minerals was first taken using the back-scattering mode with low amplification. with the help of the advanced mineral identification and characterization system (amics), the mineral compositions were initially identified, and the typical minerals were marked in the photographs. then, using the secondary electron mode and increasing the amplification step by step, details on the surface of typical minerals were observed. amics is the latest software package for automated identification and quantification of minerals and synthetic phases (du et al. 2018). combined with eds, amics can be used to synthesize sem images and automatically determine the compositions of minerals with grain sizes greater than 4 μm via an amplification of 200 (du et al. 2018). results and discussion changes in pore structure. pore content. before co2 treatment, the pore contents of the coal samples are relatively low, ranging from 0.84-2.18 % (table 2). after co2 treatment, the pore contents (1.225.93 %) of the coal samples increase significantly, with an average increase of 82.61 % (table 2). changes in pore volumes show the same trend as changes in pore contents (table 2). table 2—volumes and contents of pores and minerals in coal samples based on x-ray ct. samples pore content, % mineral content, % pore volume, μm3 mineral volume, μm3 before after before after before after before after #1 2.18 3.33 5.43 3.33 1.62e+07 2.46e+07 4.01e+07 2.46e+07 #2 1.20 1.54 3.77 2.83 8.86e+06 1.14e+07 2.78e+07 2.09e+07 #3 1.95 5.93 8.18 3.73 1.48e+07 4.50e+07 6.22e+07 2.83e+07 #4 0.84 1.22 3.19 2.40 2.03e+07 2.98e+07 7.72e+07 5.86e+07 pore number. before co2 treatment, the pores in the coal samples are primarily <5 μm in eqdiameter, and the pore number decreases rapidly with increasing pore eqdiameter (figure 1). the number of pores >10 μm in eqdiameter is small (figure 1). after co2 treatment, the number of pores <2 μm of coal sample #2 changes slightly, while the number in the other coal samples decreases (figure 1). the number of pores ranging from 2-10 μm in eqdiameter of coal sample #3 decreases, while the number of the other coal samples increases slightly (figure 1). moreover, the number of pores >10 μm in eqdiameter changes slightly (figure 1). in general, changes in pore number are not significant, indicating that changes in pore content and volume are not determined by changes in pore number. pore volume. before co2 treatment, the pore volumes of the coal samples are primarily associated with pores <10 μm in eqdiameter, with pores >10 μm in eqdiameter accounting for a small volume (figure 2). the volumes of pores <50 μm in eqdiameter follow normal distribution, and the peak of pore volume ranges from 3 to 4 μm (figure 2). with the increase and decrease in the pore eqdiameter, the pore volumes of the coal samples decrease rapidly (figure 2). coal sample #3 and #4 have larger pores >50 μm in eqdiameter, which may result from the presence of micro-fractures (figure 2). combined with the pore number distribution, pores >10 μm in eqdiameter contribute greatly to the pore volume. after co2 treatment, the pore volume distribution of the coal samples changes significantly, which is mainly caused by the significant increase in the volumes of pores >50 μm in eqdiameter (figure 2). in addition, the volumes of pores <50 μm in eqdiameter of coal sample #2 exhibit no marked changes, while the volumes of pores <4 μm in eqdiameter in coal sample #1, #3, and #4 decrease slightly (figure 2). 5 figure 1—pore number distribution of coal samples based on x-ray ct. figure 2—pore volume distributions of coal samples based on x-ray ct. changes in connectivity. interconnected pore models of coal samples. before co2 treatment, there are a large number of pores and a certain number of micro-fractures in the 3d digital models of the coal samples (figure 3a). the 3d digital models and the ball-and-stick models show that micro-fractures are throats in the ball-and-stick models (figure 3b). although some pores and microfractures are connected 6 (figure 3b), the connectivity is weak, resulting in poor connectivity in the coal samples. therefore, the interconnected pore models of the coal samples cannot be extracted (figure 3c). notes: a, 3d digital models of coal; in cubes, pores and microfractures are red, minerals are blue, and organic matter is grey; b, ball-and-stick models of pores and throats; in ball-and-stick models, the pores are red, and the throats are green; and c, interconnected pore models. figure 3—3d digital models, ball-and-stick models, and interconnected pore models of coal samples based on x-ray ct before co2 treatment. after co2 treatment, some minerals filled the pores and microfractures, increasing the connectivity of the pores and microfractures (figure 4a). ball-and-stick models show that the number of pores and throats interconnected in the coal samples increases (figure 4b). however, the increase in connectivity of pores and micro-fractures caused by co2 does not obviously improve the connectivity of the coal samples on the macro-scale (figure 4c), and the connectivity of pores and micro-fractures is still limited to local areas in the coal samples and does not extend throughout the whole coal samples (figure 4c). after co2 treatment, the interconnected pore models of coal sample #1 and coal sample #2 were successfully extracted (figure 4c). by comparing the interconnected pore models and 3d digital models of coal samples #1 and #2, the connectivity of coal samples is improved by a micro-fracture (figure 4a and 4c), which means that the connectivity of coal samples on the micron-scale is mainly contributed by micro-fractures, while the contribution of pores is weak. figure 4—3d digital models, ball-and-stick models, and interconnected pore models of coal samples based on x-ray ct after co2 treatment. coordination numbers. the coal samples are dominated by isolated pores (pores with a coordination number of 0), and the number of pores with coordination numbers > 0 only accounts for 0.56-7.83 % (table 3). the coordination numbers of the interconnected pores (pores with coordination numbers >0) are low, mainly 1-2 (figure 5). the number of pores with a coordination number >2 decreases rapidly 7 (figure 5), indicating that the connectivity of pores and fractures on the macro-scale is weak and that pores are only connected with 1-2 adjacent pores and throats. table 3—numbers and contents of pores with different coordination numbers. samples pore number pore content, % before after before after 0 >0 total 0 >0 total 0 >0 0 >0 #1 1029934 16289 1046223 1005892 34226 1040118 98.44 1.56 96.71 3.29 #2 961181 81686 1042867 948262 94502 1042764 92.17 7.83 90.94 9.06 #3 1021998 5804 1027802 343714 69641 413355 99.44 0.56 83.15 16.85 #4 982578 60727 1043305 968959 73782 1042741 94.18 5.82 92.92 7.08 notes: “0”, pores with a coordination number of 0; ”>0”, pores with coordination numbers >0. figure 5—coordination numbers of coal samples based on x-ray ct. after co2 treatment, the total number of pores in coal samples remained unchanged, except for coal sample #3 (table 3). the number of pores with coordination numbers >0 increases, while the number of pores with a coordination number of 0 decreases correspondingly (table 3), indicating that co2 improves the connectivity of the pores in coal and has little influence on the number of pores. although the total number of pores and the number of pores with a coordination number of 0 in coal sample #3 decrease, the number of pores with coordination numbers >0 increases significantly (table 3). this is because a large number of pores in coal sample #3 become connected to form larger pores. the number of pores with coordination numbers >1 in coal samples all increases (figure 5), indicating that co2 improves the connectivity of pores and fractures in coal to a certain extent. throat lengths. a throat is the connecting channel between pores and is representative of the connectivity of pores and fractures (song et al. 2018). before co2 treatment, throats <20 μm in length and >100 μm in length are the most common (figure 6). throats >100 μm in length are mainly composed of microfractures. 8 figure 6—throat lengths of coal samples based on x-ray ct. after co2 treatment, the number of throats >100 μm in length obviously increases (figure 6). the number of throats <100 μm in length in coal samples #2 and #4 changes weakly (figure 6). the number of throats <20 μm in length in coal sample #1 increases obviously, while the number in coal sample #3 decreases (figure 6). the number of 20-100 m long throats in coal sample #1 does not show obvious changes, while the number in coal sample #3 obviously increases (figure 6). changes in mineral. similarly to the distribution of the pores, the mineral grain size is mainly <5 μm, and as the grain size increases, the mineral number decreases rapidly (figure 7). minerals with a grain size <50 μm are normally distributed, and the peaks of mineral volume are distributed at 3-6 μm (figure 8). with the increase and decrease in the grain size, the mineral volumes of coal samples decrease rapidly (figure 8). the volumes of minerals with grain sizes ranging from 10-50 μm are small, while those with grain sizes >50 μm are large (figure 8), indicating that there is a large amount of minerals with grain sizes >50 μm or a large amount of minerals filling the micro-fractures. after co2 treatment, mineral numbers show a significant decrease trend, while the number of minerals with grain sizes <6 μm in coal samples #1, #3 and #4 increases significantly, indicating that minerals with grain sizes >6 μm are partially dissolved, resulting in a decrease in grain size (figure 7). after co2 treatment, the volume of minerals with grain sizes >50 μm largely decreases greatly (figure 8). moreover, the 3d digital models of the coal samples (figure 5a, figure 4a) show that the minerals that fill the micro-fractures are largely dissolved by co2, which improves the connectivity of the microfractures and increases the pore volume in the coal samples. therefore, the dissolution of minerals with grain sizes >50 μm and filling microfractures is the main contributor to the decrease in mineral volume in the coal samples and the increase in the volume of pores >50 μm. some minerals with grain sizes <50 μm are not completely dissolved, resulting in a significant decrease in the volume of minerals with grain sizes of 6-50 μm and a slight increase in the volume of minerals with grain sizes <6 μm in some coal samples (figure 8). 9 figure 7—mineral number distributions in the coal samples based on x-ray ct. figure 8—mineral volume distributions of coal samples based on x-ray ct. effects of mineral dissolution on pore structure. the relationship between pore content and mineral dissolution. the mineral contents of the coal samples range from 3.19 % to 8.18 %, and these values decrease significantly (2.40-3.73 %) after co2 treatment, with an average decrease of 35.69 % (table 2). after co2 treatment, there are significant positive correlations between increased pore content and decreased mineral content and between pore volume and mineral volume, with r2=0.8851 and 10 r2=0.9624, respectively (figure 9). these relationships show that the change in the pore content of the coal samples is closely related to the mineral dissolution caused by co2. figure 9—relationships between pores and minerals before and after co2 treatment. the effect of mineral dissolution on pore structure. the minerals with grain sizes >1 μm in the coal samples are mainly clay minerals and carbonate minerals. clay minerals are mainly kaolinite (46.01 %) and muscovite (13.52 %), and carbonate minerals include calcite (15.98 %), ankerite (1.60%), and dolomite (0.15 %). in addition, there is a certain amount of gibbsite (2.48 %) and organic-clay complex (mainly organic-kaolinite complex) (5.28 %) (figure 10, table 4). clay minerals are mainly distributed in the coal matrix, and minerals filling the microfractures and pores are mainly carbonate minerals and gibbsite, as well as some organic-clay complexes (figure 10). table 4—area percentages of minerals in coal sample #2 before and after co2 treatment. minerals kaolinite calcite muscovite ankerite gibbsite dolomite organic-clay complexes other minerals area percentage, % before 46.01 15.98 13.52 1.60 2.48 0.15 5.28 14.98 after 69.17 0.20 6.14 0.62 3.50 0.20 4.54 15.63 figure 10—the fesem and eds images of coal sample #2 before and after co2 treatment. after co2 treatment, carbonate minerals are largely dissolved and disappear (figure 10 aa’, bb’). among them, calcite has the highest degree of dissolution and disappears almost completely (0.20%) (table 4, figure 10 aa’), followed by microfractures filled with ankerite (0.62%) (table 4, figure 10 bb’). the dolomite in the coal matrix has a relatively low degree of dissolution (0.20 %) (table 4, figure 10 aa’), while the dolomite filling micro-fractures is largely dissolved (figure 10 cc’). therefore, the dissolution of carbonate minerals is the main reason for the decrease in the mineral content in the coal. kaolinite reacts weakly with co2. therefore, kaolinite shows no significant change after co2 treatment 11 (69.17 %) (table 4, figure 10 aa’). the gibbsite in the coal matrix is difficult to dissolve with co2 (figure 10 dd’), while the gibbsite filling the micro-fractures is partially dissolved (figure 10 cc’). muscovite mainly exists in the coal matrix and can be partially dissolved by co2 (figure 10 aa’). organic-clay complexes mainly fill microfractures and are partially dissolved by co2 (figure 10 bb’). after co2 treatment, calcite, dolomite, and other carbonate minerals in the coal matrix (including those that fill pores) dissolve or partially dissolve, forming a large number of pores created by dissolution (figure 11a and 11c). the shape of these dissolution-created pores is irregular, and the pore diameter is generally <10 μm. residual carbonate minerals can be found in these pores. these dissolution-created pores are the primary cause of the changes in the number and volume of pores <10 μm in diameter, and they control the changes in the pore number distribution in the coal samples (figure 11a and 11c). some of the pores created by dissolution become connected to each other (figure 11a) and with microfractures (figure 11c); however, most of them are associated with local connectivity in a small part of coal samples, which are characterized by overall poor connectivity. therefore, these pores make a weak contribution to the connectivity of the coal samples. note: a and c are coal samples from the xinjing mine; c is a coal sample from the sihe mine; d is a coal sample from the yuwu mine. figure 11—pores, microfractures, and minerals in coal samples before and after co2 treatment. after co2 treatment, the carbonate minerals, such as calcite and dolomite, with grain sizes >50 μm in the coal matrix (including those filling pores) are dissolved or partially dissolved, forming dissolutioncreated pores with diameters >50 μm (figure 11b). residual carbonate minerals can also be found in the pores created by dissolution (figure 11b). these dissolution-created pores have a relatively large contribution to the number of pores >50 μm in diameter after co2 treatment, while they have a relatively small contribution to the pore volume. similar to the dissolution-created pores <10 μm in diameter, the connectivity of the dissolution-created pores with diameters >50 μm is weak. a large number of carbonate minerals filling the micro-fractures are dissolved by co2, resulting in a partial or complete opening of the micro-fractures and significantly increasing the apertures of the micro-fractures (figure 11c). although the number of micro-fractures is less than the number of dissolution-created pores >50 μm in diameter caused by co2 and has a much smaller contribution to the pore number, the volume of microfractures is much larger than that of dissolution-created pores >50 μm in diameter, and micro-fractures are the main contributor to the increase in the volume of pores >50 μm in diameter. this increase is also the reason why the pore volumes of the coal samples increase significantly after co2 treatment, while the pore numbers change only slightly. furthermore, according to section 3.2.3, the connectivity of coal samples on the micrometer scale is mainly contributed by microfractures. therefore, increasing the microfracture aperture significantly improves the connectivity of the coal samples and throat lengths. moreover, some micro-fractures are filled with organic-clay complexes. after co2 treatment, several organic-clay complexes that fill the microfractures are removed, which also increase the apertures and connectivity of the microfractures. in general, microfractures in coal samples are mainly filled with carbonate minerals (figure 10), and the removal of organic-clay complexes from microfractures has a 12 relatively weak effect on microfractures. furthermore, neither the clay minerals in the coal matrix nor the clay minerals that fill the microfractures exhibit obvious changes after co2 treatment, and their influence on the structure of the pore fracture and the connectivity of the coal is weak (figure 11d). conclusions in this paper, taking low-volatile bituminous coals and anthracite coals collected from the qinshui basin as examples, changes in pore fracture structure and connectivity on the micron scale after co2 treatments were studied using x-ray micro-ct, fesem and eds. the following conclusions can be drawn from this study. 1. after co2 treatment, the pore contents and volumes of low-volatile bituminous and anthracite coal increase significantly and the changes in pore numbers are small. the increase in pore volume is mainly caused by pores > 50 μm in diameter, while the change in pore number is related to pores <10 μm in diameter. the connectivity of low-volatile bituminous coal and anthracite coal on the micron-scale is mainly contributed by micro-fractures. 2. after co2 treatment, the number of pores with coordination numbers >1 and the number of throats >100 μm in length increase significantly, confirming that co2 improves the connectivity of pores and fractures; however, the improvement in pore-fracture connectivity is not enough to improve the connectivity of the coal on the micron-scale. 3. after co2 treatment, the changes in pore numbers and volumes are mainly caused by the dissolution of carbonate minerals. calcite, dolomite and other carbonate minerals in the coal matrix dissolve to form a large number of dissolution-created pores <10 μm in diameter. these dissolution-created pores are the main causes of the increase in the number and volume of pores <10 μm in diameter and determine the changes in pore numbers in coal samples. the carbonate minerals that fill the microfractures are greatly dissolved by co2, which increases the apertures and connectivity of the microfractures. these microfractures are the main contributor to the increase in the volume of pores >50 μm in diameter and improve the connectivity of coal on the micrometer scale. acknowledgments this study was supported by the national key research and development plan (no. 2018yfb0605601), the china national natural science foundation (no. 41972168), and the jiangsu key laboratory of coalbased greenhouse gas control and use (no. 2019a001). we would like to thank engineers from the shanxi cbm branch of huabei oilfield company and lu’an group and a number of research students from china university of mining and technology for their assistance in the coal sampling and some experiments. conflicts of interest the author(s) declare that they have no conflicting interests. references 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recovery-a review. energy & fuels 19(3): 659-724. wong, s., law, d., deng, x.h., et al. 2007. enhanced coalbed methane and co2 storage in anthracitic coalsmicro-pilot test at south qinshui, shanxi, china. international journal of coal geology 1(2): 215-222. xu, y., liu, x., zhang, p., et al. 2016. role of chlorine in ultrafine particulate matter formation during the combustion of a blend of high-cl coal and low-cl coal. fuel 184: 185-191. zerai, b., saylor, b.z., and matisoff, g. 2006. computer simulation of co2 trapped through mineral precipitation in the rose run sandstone, ohio. applied geochemistry 21(2): 223-240. 14 zhou, h.w., zhong, j.c., ren, w.g., et al. 2018. characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using x-ray μct and a fractal method. international journal of coal geology 189:35-49. shiqi liu is a professor of geological resources and geological engineering at china university of mining and technology, where he has worked as faculty for 9 years. his research interests are in the exploration and development of unconventional gas (coalbed methane, shale gas, coal measure gas), and co2 geological storage and utilization. he holds b.s. from the china university of petroleum (east china) in information and computer science, m.s. from the china university of petroleum (east china) in oil and gas field development engineering, and ph.d. from china university of mining and technology in geological resources and geological engineering. shuxun sang is a professor of geology at china university of mining and technology, where he has worked as faculty for 28 years. his research interests are in the exploration and development of unconventional gas (coalbed methane, shale gas, coal measure gas) and in geological storage and utilization of co2. he holds a b.s., m.s., and ph.d. from china university of mining and technology, all in geology. tian wang is a doctoral candidate at china university of mining and technology. her research interests are in co2 geological storage and utilization. she holds a b.s. from china university of mining and technology in geology. yi du is a doctoral candidate at china university of mining and technology. her research interests are in co2 geological storage and utilization. she holds a b.s. from china university of mining and technology in geology. huihuang fang is a doctoral candidate at china university of mining and technology. his research interests are in co2 geological storage and utilization. he holds m. s. from china university of mining and technology in geological resources and geological engineering. abstract introduction samples and methodology results and discussion conclusions acknowledgments conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1275 received february 1, 2024; revised march 14, 2024; accepted april 19, 2024. *corresponding author: osamaajaz99@gmail.com 1 carbon sequestration in unmined coalbeds of pakistan osama ajaz*, lmk resources pakistan (pvt) limited, islamabad, pakistan; saleem qadir tunio, cyrpus international university, nicosia, north cyprus; jahangeer zafar, united energy pakistan limited, karachi, pakistan abstract exponential increment in carbon dioxide (co2) emissions into the atmosphere has become a serious threat to global security. many reports concluded that maintaining <2oc is mandatory to avoid severe consequences associated with the environment and global warming. pakistan is indexed in a region of high vulnerability to climate change. thus, the country has faced severe reflection of the deteriorated environment in terms of drought, floods, and uncertain climatic conditions. the country’s recent development has increased emissions as many power plants are being run on coal. it implies that significant efforts must be made to emphasize limiting emissions and environmental damage. carbon storage technology is a way forward for continuous utilization of fossil fuels. coalbeds ensure secure storage of co2 for long term. carbon storage in subsurface beds will minimize the ongoing greater impact on environment of pakistan. thar coalfield offers great potential for co2 storage due to the largest reserves in the country. this study contributes towards further steps needed for practical implementation of carbon capture and sequestration in thar coalfield. the analogy among different coal sites for carbon storage was drawn to project potential of thar coalfield along with other coalfields in pakistan. thar coalfield properties, being lignite in rank, resemble north dakota coalfield, whereas some properties resemble rajasthan coals. hence, north dakota coalfield and rajasthan can be effective reference projects for practical implementation of co2 storage in thar coalfields. the research study has recommended further directions for study to calculate exact amount of co2 storage. the study was concluded with the future implication of potential carbon storage in the coalfield of thar. introduction rising greenhouse gas concentrations in atmosphere are causing a rapid increase in average temperatures globally. evidence shows that global surface temperature rose 0.6u±0.2oc over the 20th century (balat and oz 2007). the environment model projections suggest that temperature will rise sharply in the next century and this could go beyond 2oc. to avoid such an increment in temperature, intergovernmental panel on climate change (ipcc) has stated that greenhouse gas (ghg) emissions should be reduced to 80% by 2050 (li et al. 2019). primarily co2 is responsible for alteration in environment and global warming (nunes 2023). among current viable mitigation environmental strategies, carbon capture gathered many interests of experts and policymakers that could enable the continuous use of fossil energy. carbon sequestration with advanced technologies causes low (or almost zero) emissions into environment. countries should emphasize this low emission to contribute to reaching a temperature of less than 2oc by 2050. besides furnace oil, pakistan’s power sector has been relying on natural gas (having the lowest carbon intensity), and a lower fraction of coal (highest carbon intensity) for the purpose, which is in utter contrast to energy consumption for electricity generation worldwide. thus, pakistan has been a lesser contributor to co2 mailto:osamaajaz99@gmail.com improved oil and gas recovery 2 emissions. however, modern life have changed fuel-type preferences and pakistan has no alternative but to utilize only sizable coal reserves of 185 billion tons to meet increasing energy needs. since coal is a high carbon-intensity fuel as shown in figure 1, so emissions have drastically increased, as shown in figure 2. the country’s vulnerability to the effects of climate change is well documented and recognized. over the last decade, repeated periods of extreme weather had a negative impact on the country’s economic growth. figure 1—carbon dioxide emissions for different fossil fuels (carbon dioxide emissions coefficients 2023). figure 2—annual co2 emissions from burning fossil fuel and cement production since 1970 (our world in data 2024). clean coal technology is a viable approach to adopt for medium-term planning in order to mitigate carbon emissions which are continuously on the rise. the creative energy and environmental framework design may help in reducing ghg emissions along with meeting energy demands. co2 capture extracted from different large-scale firms and deposited far below the ground provides a unique design and is widely adopted for the purpose. this prevents and eliminates a larger fraction of co2 exposure to the environment. improved oil and gas recovery 3 carbon capture and storage appears to be a workable choice for removal of 50-85% of ghg emissions by 2050 (shukla et al. 2020). role of gdp in co2 emissions energy intensity is calculated on energy consumption per unit of gdp. this derives a direct relationship between energy use and co2 emissions. higher co2 emissions reflect greater use of fossil fuel energy. co2 emissions and gdp are related as (balat and oz 2007), co2 emissions = gdp × energy consumption per unit gdp × co2 emissions per unit energy consumption.(1) the relation implies that a country having a higher gdp leads to higher co2 emissions, whereas developing countries tend to increase emissions with a higher gdp. to meet demands, electricity generation potential is being expanded in pakistan and many plants are consuming coal as fuel.thus, emissions are on the rise. this situation could lock the country into a carbon-intensive region due to emissions from coal. whereas, increasing gdp guarantees the development of the country. pakistan, like any other developing countries, tends to increase gdp, as shown in figure 3, which results in increasing emissions as shown in figure 4. figure 3—gdp of pakistan over years (the world bank 2024). figure 4—cumulative co2 emissions from burning fossil fuel since 1970 by pakistan (our world in data 2024). improved oil and gas recovery 4 carbon capture and sequestration carbon capture and sequestration (ccs) technology is an important portfolio option in mitigating atmospheric greenhouse concentrations. the process consists of co2 capture from energy-related sources mainly power plants, cement plants, steel mills, and refineries. the captured co2 is then transported to storage sites and thus isolates co2 from the atmosphere in the long term. the capture and storage site should be near enough to minimize costs. co2 capture. co2 can be captured by any of the following technologies (sifat and haseli 2019): 1. pre-combustion: co2 and hydrogen are separated from the primary fuel in a shift reaction. this hydrogen can be used as a fuel. 2. oxy-fuel combustion: oxygen is used for combustion instead of air for producing co2 and h2o, after which water vapor is condensed and co2 is captured. 3. post-combustion: it captures co2 combustion of a primary fuel in air. co2 storage. following the capture process, co2 is stored underground so that it will remain stored preferably for hundreds to thousands of years. by this way, co2 is prevented from being exposed to the atmosphere. the geological structure must have the ability to contain co2 over a long period. table 1 shows international treaties that come into force for the geological storage of co2. table 1—international treaties for consideration of geological co2 storage 9 (metz 2005). treaty adoption (signature) entry into force number of parties/ratifications unfccc 1992 1994 189 kyoto protocol (kp) 1997 2005 132* unclos 1982 1994 145 london convention (lc) 1972 1975 80 london protocol (lp) 1996 no 20* (26) ospar 1992 1998 15 basel convention 1989 1992 162 *several other countries have also announced that their ratification is under way. there are differences in the physical features of oceans, geological formations, saline aquifers, and mineralized solids for the retention of co2. there could be a chance that injected gas leaks or is exposed to surface depending upon the subsurface structure. the amount of co2 stored over time interval is given by (balat and oz 2007): co2 stored = 0 t co2 injected t − co2emitted t dt� ,............................................................................(2) where t is time, and t is length of assessment time period. improved oil and gas recovery 5 economics of ccs. the vital consideration for implementing ccs is the cost. the cost of capturing carbon depends upon the capturing mechanism, which is being optimized with the developments made in technology. the storage and monitoring are based on the geologic area, in which co2 is injected for storage. however, transportation costs can be eliminated from the process, when the capture and storage sites are near or in the same area. this greatly reduces the whole cost. the cost of ccs, therefore, consists of (balat and oz 2007): cccs = ccapture + ctranportation + cstorage + cmonitoring,.........................................................................................(3) capturing co2 from the power plant at thar coalfield and then injecting it into the coalbed would reduce overall cost for ccs. potential storage sites international treaties endorsed geological sites as reliable places for co2 storage. following are underground formations that could be used for co2 storage, 1. saline formations 2. oil and natural gas reservoirs 3. unmineable coal seams 4. organic-rich shales 5. basalt formations coalbed seams could be abandoned due to many reasons including unmineable, inadequate technology, and government policies. however, this geological formation shows great potential to storage great amounts of co2 depending upon the depth and rank of coal. there needs comprehensive study including pilot tests to evaluate the exact potential of coalbed to store co2. thar coalfield–pakistan largest potential sequestration site thar coalfield reserves account for 175 billion tons over a single geological area, as shown in figure 5 and table 2 in appendix i. the coal reflects a high volatile rank of lignite b type. tharcoal offers the largest site of co2 storage in the country. coal shows potential sites for geological storage in a way that it has a greater affinity towards co2. due to this, there are lower or no chances of leakage to the atmosphere even at lower depths, if coal remains undisturbed after co2 storage. figure 5—coal type reserves in pakistan (data collection survey on thar coal field in pakistan: final report. 2013). improved oil and gas recovery 6 although lower-rank coals show less co2 adsorption capacity as compared to higher ranks ( li et al. 2022), coal seams present a great amount of co2 that can be stored in large available areas. figure 5 shows dark coal (high rank) shows better adsorption capacity than brown coal (low rank). coal micro pores contain around 98% of co2 as an adsorbed phase, whereas the rest exists as free gas in cleats (perera et al. 2012). hence, this stable storage phenomenon neglects the idea of back migration. the co2, after reaching the coal seam layer, occupies the spaces around cleats and adorbs onto to coal surface. this action of co2 displaces any gas residing previously in cleats (li et al. 2022). the cleats provide the means of co2 flow in the extended section of the seam. the tharcoal field, comprising several blocks and having different properties, shows variations in carbon storage potential depending upon the characteristics of a block, as shown in figure 6. after an initial assessment of data and properties, blocks show storage potential for co2 correspondingly. it is pertinent that all blocks cannot be assigned for storage, however, blocks showing greater potential could be allocated for the purpose. similarly, considering whole thar coal reserves as not feasible for mining smaller parts or sections could be dedicated to mitigating the environment. figure 6—block wise co2 storage potential in thar coalfield (zahid 2017). analogy among coalfields since no detailed studies have been carried out on carbon storage in the thar coalfield, an analogy using given data from the world’s numerous fields is drawn to estimate possibilities. the data analogy focuses on thar coalfields along with other potential coalfields in pakistan for co2 storage. however, due to the largest reserves, thar coal is highlighted in this paper. the available data on properties relevant to carbon storage are discussed in table 3. effect of ash content. co2 sequestration potential decreases with increasing ash content. the adsorption content is also one of the important parameters in deciding the pore volume of coal. higher ash content reduces the adsorption capacity of methane, which leaves a significant part of methane present in cleats. this presence of methane restricts the addition of any phase onto the coal surface. due to this reason, only a small amount of co2 can fill up the space available in cleats of coal. the ash content of tharcoal resembles with north dakota coals, shown in figure 7. improved oil and gas recovery 7 table 3—analogy among pakistan’s largest coalfields with world’s cbm coalfields. country pakistan (harpalani and schraufnagel 1990) india (prabu and mallick 2005) china (yu et al. 2007) australia (victorian brown coals) (bachu et al. 2005) japan (yamaguchi et al. 2005) united states (hares 1928) project thar coalfield lakhra sondhajerruk rajastan northeast otway gippsland murray ishikari north dakota (lignite) ash content, % 2.9011.50 4.3049.00 2.7052.00 15.5 11.62 4 4.4 10.8 3.62 9 moisture content, % 29.6055.50 9.7038.10 9.0048.00 41.5 35 44 51.7 56 0.87 32.17 fixed carbon, % 14.2034.00 9.8038.20 8.9058.80 19 52.04 66 66.7 61 n/a 65.6 depth, m 120-200 80-450 1-85 450 (avg.) n/a n/a n/a n/a 890 (avg.) 335 estimated co2 storage , mtco2 200.7 n/a n/a 0.552 2862.92 n/a n/a n/a 480 10.3 figure 7—ash content of different coalfields. improved oil and gas recovery 8 effect of moisture content. the higher moisture content of coal decreases carbon storage potential. this is due to the presence of water restricting the entrance of co2 within cleats. also, the co2 flow rate decreases, with increasing injection pressure, due to the swelling of cleat structures (zhang et al. 2023). the data of different coalfields shows that higher moisture coal has a lower volume for co2 sequestration. lignite coals of north dakota show a similarity of moisture content with thar coals, shown in figure 8. north dakota field (usa) presents lower storage, which corresponds to lower carbon storage in the thar coalfield. figure 8—moisture content of different coalfields. effect of carbon content. carbon content is related to the rank of coal. the higher-rank coals show more co2 storage potential than that of lower rank (li et al. 2022). the data in table 2 shows higher carbon ensures greater carbon sequestration. figure 9 shows rajasthan coalfield carbon content provides better similarity than the others in table 2. figure 9—carbon content of different coalfields. improved oil and gas recovery 9 critical analysis pakistan, being among the most affected countries by global warming, has to take initiatives towards minimizing emissions of ghg to let its inhabitants survive. the country’s fragile economy does not allow lower its gdp and development for the sake of emissions. carbon sequestration in coalbeds provides a way forward and a win-win position for the cause. the co2 occupies the space and displaces methane gas from coalbeds hence making it enhanced coal bed methane (ecbm) recovery. methane recovery depends upon the properties of coal and eventually offsets the cost of co2 storage. figure 10 illustrates the process of co2 injection and ch4 (methane) production from coal seams. figure 10—vertical well showing co2-ecbm recovery. the uncertain and unpredictable nature of climate change poses an added challenge to policymakers who are tuned to make decisions based on historical and known denominators. the climate change challenge that we are facing could be turned into a new opportunity based on cleaner technology and a low-carbon economy. the country needs to start planning for its long-term implementation. for reliable calculation of storage capacity following methodology may be employed: 1. calculate the coal mass available for co2 storage for each field. 2. based on experimental investigation, calculate the average co2 mass storage per tonne. many coalbeds at different depths should be studied for this. to obtain the best possible storage mass of co2. conclusions and recommendations increasing emissions are part of the progress of developing countries. the emissions associated with coal consumption can be prevented from damaging the environment. since many coal power plants were built near coalfields, this significantly reduces the cost of transporting co2 for storage. also, the carbon storage process in coalbeds depends upon several factors, including coal mass, coal permeability, gas desorption, and adsorption. the properties of thar coalfield provided similarities as rajasthan and north dakota coalfields. the features of these two projects could help in the practical implementation of carbon storage in thar coals. the concept of clean coal technology should be implemented keeping a view of a low-carbon economy. besides of passive strategies of planting trees, pakistan should take aggressive steps to reduce up to 20% of projected ghg emissions by 2030, as ratified under the paris agreement. current technologies need to cater according to conditions to apply lignite coals of thar coalfields. however, the following challenges are coming across, which delay or prevent practical applications, improved oil and gas recovery 10 1. lack of knowledge of coal seam permeability before co2 sequestration. 2. extensive laboratory tests are to be carried out for samples of lignite (thar coalfield) for calculation of adsorption, and desorption at different depths. 3. post-co2 storage risk assessment studies, economic optimization studies, project-screening models, etc. are to be carried out. the following sequence was proposed for maximum sequestration in given coalbeds. 1. water production stage: producing water will leave space for other fluids to adsorb onto coal. 2. gas production stage: unloading of water allows gas to flow towards the wellbore. this gas production will increase empty spaces in the cleat/pores of coalbeds. 3. co2 injection: after the creation of empty spaces due to gas flow, more spaces are held in pores/cleats for co2 storage. conflicting interests the author(s) declare that they have no conflicting interests. references balat, h. and oz, c. 2007. technical and economic aspects 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(accessed 24 march 2024). perera, m.s.a., ranjith, p.g., viete, d.r., et al. 2012. parameters influencing the flow performance of natural cleat systems in deep coal seams experiencing carbon dioxide injection and sequestration. international journal of coal geology 104(30): 1-12. prabu, v. and mallick, n. 2015. coalbed methane with co2 sequestration: an emerging clean coal technology in india. renewable and sustainable energy reviews 50: 229-244. shukla, a.k., ahmad, z., sharma, m., et al. 2020. advances of carbon capture and storage in coal-based power generating units in an indian context. energies 13(16):4124. sifat, n.s. and haseli, y. 2019. a critical review of co2 capture technologies and prospects for clean power generation energies 12(21):4143. the world bank. 2024. https://data.worldbank.org/indicator/ny.gdp.mktp.kd.zg?locations=pk. (accessed 13 march 2024) yamaguchi, s., ohga, k., fujioka, m., et al. 2005. prospect of co2 sequestration in the ishkari coalfield japan. greenhouse gas control technologies 7(1):425-430. https://www.eia.gov/environment/emissions/co2_vol_mass.php https://openjicareport.jica.go.jp/643/643/643_117_12113221.html https://ourworldindata.org/fossil-fuel-subsidies https://data.worldbank.org/indicator/ny.gdp.mktp.kd.zg?locations=pk improved oil and gas recovery 11 yu, h. zhou, g., fan, w., et al. 2007. predicted co2 enhanced coalbed methane recovery and co2 sequestration in china. international journal of coal geology 71(2) :345–357 zahid, u. 2017. application case study of enhanced coal bed methane recovery process in thar coal fields. environmental progress & sustainable energy 37(2):900-911. zhang, x., jin, c., zhang, d., et al. 2023.carbon dioxide flow behaviour in macro-scale bituminous coal: an experimental determination of the influence of effective stress. energy 268:1-15. osama ajaz is working under the capacity of petroleum engineer with landmark resources pakistan (pvt) limited. he holds b.e and m.s. in petroleum engineering. his research areas include drilling engineering, artificial lifting methods, enhanced oil & gas recovery, and engineering aspects of carbon storage. saleem qadir tunio is serving as assistant professor at faculty of engineering, cyprus international university. he obtained his b.e in petroleum and natural gas from mehran university of engineering and technology, m.s in petroleum engineering from the university of adelaide, australia, and holds ph.d.in petroleum engineering from universiti teknologi petronas (utp), malaysia. he has expertise in the areas of unconventional hydrocarbons and enhanced hydrocarbons recovery. jahangeer zafar is working under the capacity of petroleum engineer with united energy pakistan limited. he holds b.e and m.s. in petroleum engineering. his research areas include production engineering, well testing, and enhanced oil & gas recovery. improved oil and gas recovery 12 appendix i table 2—coal reserves in pakistan (data collection survey on thar coal field in pakistan: final report. 2013) province location quantity (million tones) type moisture content (%) ash content (%) heating value (btu/lb) fixed carbon (%) si nd h thar 175,506 lignite b-a 29.60-55.50 2.90-11.50 1072311353 (dry basis) 14.2034.00 lakhra 1328 lignite -a 9.70-38.10 4.30-49.00 5503-9158 9.80-38.20 sondha-jherruch 5523 9.00-48.00 2.70-52.00 5219-13555 8.90-58.80 meting-jhimpir 473 lignite data not availableindus east 1777 badin 16 total 184,623 b al uc hi st an sor-range/degari 50 subbituminous 3.90-18.90 4.9-17.20 1124513900 41.0050.80 khost/harnai/ziarat 88 1.70-11.20 9.30-34.00 9637-15499 25.5043.80 mach 23 7.10-12.00 9.60-20.30 1111012937 32.4041.50 duki 56 3.50-11.50 5.00-38.00 1013114164 28.0042.00 total 217 pu nj ab salt-range 213 subbituminous 3.20-10.80 12.3044.20 9472-15801 25.7044.80 makarwal 22 2.80-6.00 6.40-30.80 1068814029 34.9044.90 total 235 k pk cherat 9 subbituminous 0.10-7.10 5.30-43.30 9386-14217 21.8076.90hungu 82 total 91 ajk kotli 9 subbituminous 0.20-6.00 3.30-50.00 7336-12338 26.3069.50 total 9 total pakistan 185,175 abstract introduction role of gdp in co2 emissions carbon capture and sequestration potential storage sites thar coalfield–pakistan largest potential sequestr analogy among coalfields critical analysis conclusions and recommendations conflicting interests references appendix i an new analytical equation to predict gas-water two-phase relative permeability curves in fractures copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.424 received march 15, 2017; revised april 7, 2017; accepted april 14, 2017. *corresponding author: lg1987cup@126.com 1 an analytical equation to predict oil-gas-water three-phase relative permeability curves in fractures gang lei* and cai wang, peking university, beijing, china; yuan tian, tongji university, shanghai, china; limin yang, china university of petroleum, beijing, china abstract as fractures are the major flow channels for multiphase flow in naturally and hydraulically fractured reservoirs, the accurate prediction of multiphase flow in fractures is highly important. the oil-gas-water three-phase relative permeability relations in fractures define the hydrodynamics of multiphase fluids flow and are necessary for modeling of multi-phase flow in fractured reservoirs. in this work, a novel flow model based on the concept of shell momentum balance, newton's law of viscosity, and the cubic law, is derived to determine analytic functions for the three-phase relative permeability curves versus phase saturation and viscosity in a single fracture. the results show that the equations describing three-phase relative permeability curves in a fracture are function of saturations and viscosities. water phase relative permeability depends on water saturation, gas phase relative permeability depends on gas saturation when µg is much lower than µo and µw. however, oil phase relative permeability is function of all-phase saturations. the isoperms of water phase and gas phase are straight lines. however, oil phase isoperms are functions of all phase saturations and have significant curvature. the curvatures of oil phase isoperms increase with the increase of µo. gas saturation decreases oil phase relative permeability with a given oil saturation, while the viscosity ratio increases it. introduction multiphase flow in naturally fractured reservoirs and hydraulically fractured reservoirs, which holds major part of the world's remaining hydrocarbon reservoirs, is strongly influenced by fractures in the geological formations (lei et al. 2014). fractures are the major flow channels for fluid flowing in fractured reservoirs. thus, it is highly important to predict multiphase flow in fractures accurately. the three-phase relative permeability relations for fractures defines hydrodynamics of fluid flow and are necessary for modeling of multiphase flow in reservoirs. the study of three-phase relative permeability was reported as early as 1941 by leverett and lewis (1941). they conducted steady-state three-phase relative permeability measurements in a tightly packed sand core. corey et al. (1956) reported results of three-phase relative permeability measurements in berea sandstone and proposed a model for prediction of three-phase relative permeability with assuming that the oil relative permeability depends on two saturations due to the dependence of residual oil saturation on two saturations. they suggested that the water phase isoperms and gas phase isoperms were straight lines. sarem (1966) modified three-phase relative permeability measuring techniques by using unsteady-state technique. donaldson and dean (1965) used sarem’s technique to measure three-phase relative mailto:lg1987cup@126.com 2 permeability in berea sandstone. saraf and fatt (1967) developed a new technique using nmr for in-situ saturation measurements in three-phase flow system. stone (1970) proposed the stone i model for prediction of three-phase relative permeability. stone (1973) proposed the stone ii model using four two-phase flow relative permeability curves (two oil-water and two oil-gas) for predicting three-phase relative permeability. dietrich and bonder (1976) proposed a model accounted for reduction in oil relative permeability due to the presence of a third phase. spronsen (1982) measured a three-phase system in berea sandstone using the centrifuge method. saraf et al. (1982), grader and o’meara (1988) and maini et al. (1990) measured the three-phase relative permeability using steady-state and unsteady-state methods. in addition, there have been more models (maini et al. 1989; hustad and hansen 1995; oosrom and lenhard 1998; balbinski et al. 1999) proposed for prediction of three-phase relative permeability. oak et al. (1990) and oak (1990) conducted a three-phase relative permeability measurement on water-wet fired berea sandstone core and presented about 1,800 data collected for three-phase measurements for different saturation paths to investigate the effect of saturation history on relative permeability curves. these studies have great significance for studying three-phase relative permeability. however, these studies are for multiphase flow in porous media but not for fracture systems. compared with the studies on relative permeability in porous medium, relative permeability in fractures has received less attention. many researchers have studied flow regimes in a fracture (persoff et al. 1991; persoff and pruess 1995; diomampo 2001; fourar et al.1993; fourar and bories 1995; pan 1999; chen 2005) and revealed that the flow patterns not only depend on fracture geometry but also on phase properties. in order to examine flow of multiphase flow in fractures, some researchers have done different experimental studies (chen et al. 2004; chen 2005; habana 2002; kneafsy and pruess 1998; nicholl and glass 1994; nicholl et al. 2000; pan 1999). the first relative permeability models for fracture systems were established by romm (1966) based on experimental results using kerosene and water. romm suggested that two-phase flow in fractures can be modeled by straight-line. however, many scholars (mcdonald et al. 1991; pieters and graves 1994; fourar and bories 1995; diomampo 2001; speyer et al. 2007) had proved that relative permeability curves in fractures were not a simple linear function of saturation with experimental evidence. many different theoretical studies have been conducted to examine multiphase flow in fractures (bodin et al. 2003; iwai 1976; reis 1990; shad and gates 2010; chima et al. 2010; chima and geiger 2012). shad and gate (2010) developed a new model for multiple-phase layer flow in a single fracture and concluded how relative permeability in fractures depended on flow structures as well as fluid properties. chima et al. (2010) derived an analytical equation to calculate oil-water relative permeability curves in fracture systems. and they concluded that relative permeability curves in two-phase flow in fractures are not a linear function of saturation. chima and geiger (2012) presented a new model to predict gas-water relative permeability curves in a fracture. the model was validated with experimental data and showed much better agreement than original models. although these experimental and theoretical studies relative permeability in a fracture and the influence of flow structures and fluid properties on relative permeability, they are not for oil-gas-water three-phase relative permeability. based on chima and geiger’s (2012) two-phase models, a novel model that can predict three-phase relative permeability in fracture systems was proposed in this paper. although our three-phase relative permeability model is for fracture systems and different from previous models, the results of our studies match the previous studies (corey et al. 1956; donaldson and dean 1966; saraf et al. 1982; oak 1990; and maini et al. 1990). mathematical model the following assumptions are made to derive the proposed mathematical model of oil-gas-water relative permeability curves in the fracture: 3 1. flow is laminar and in steady-state; 2. fluids are newtonian. gas is compressible, oil and water are slightly compressible, all the phases have constant properties; 3. no phase transformation between the three phases; 4. fracture walls are planar and impermeable, e.g. no fluid is exchanged between matrix and fracture; 5. the wettability of fracture walls sequences from water>oil>gas. water phase flow occurs close to fracture surface, gas phase flows in the center of the fracture, oil phase flow occurs in-between water phase and gas phase; 6. flow occurs in an open fracture, e.g. the planar surfaces representing the fracture walls remain parallel and thus are not in contact at any point; 7. the fracture is oriented horizontally and gravity is negligible. figure 1—proposed fracture model used in the mathematical model. for a perfectly smooth fracture placed horizontally with negligible gravity and buoyancy effects. applying the shell momentum balance to the fracture configuration shown in figure 1 leads to the following equations that allow reservoir engineers to estimate oil-gas-water relative permeability curves in fractures. the detailed mathematical derivation is given in appendix a. 𝑘𝑟𝑤 = 𝑆𝑤 3 2 (3 − 𝑆𝑤),…………….………………………………..……………………………..……....…(1) 𝑘𝑟𝑔 = 𝑆𝑔 2 (𝑆𝑔 2 + 𝜇𝑔 𝜇𝑤 (3𝑆𝑤 − 3 2 𝑆𝑤 2 ) + 𝜇𝑔 𝜇𝑜 (3𝑆𝑔𝑆𝑜 + 3 2 𝑆𝑜 2)),..…….………..…………………..………(2) 𝑘𝑟𝑜 = 𝑆𝑜 2 ( 𝜇𝑜 𝜇𝑤 (3𝑆𝑤 − 3 2 𝑆𝑤 2 ) + 3 2 𝑆𝑔𝑆𝑜 + 𝑆𝑜 2),…………….…………..…………………………..………...(3) eqs. 1 through 3 are applied to water phase, gas phase, and oil phase, respectively. eq. 1 implies that water relative permeability is only function of its saturation. eq. 2 illustrates that gas relative permeability depends on all other phases’ saturation. eq. 3 reveals that oil relative permeability is not only function of saturation but also depends on water and gas saturations and oil-water two-phase viscosities. however, if µg is much lower than µw and µo, eq. 2 can be simplified as, 𝑘𝑟𝑔 = 𝑆𝑔 4,……………………………………………………..……………….………….……………..(4) eq. 4 illustrates that gas relative permeability is only function of gas saturation when gas viscosity is much lower than all other phases’ viscosity. 4 model validation and model analysis with the basic parameters (table 1) applied in the novel model, the oil-gas-water three-phase relative permeability curves in the fracture systems was estimated by the eq. 1 to 3 and oil-gas-water three-phase isoperms of the study are given in figure 2. the results of this study confirm the dependency of water and gas relative permeabilities on their own saturations, and oil phase relative permeability to all the phases. the study also shows that the isoperms of water and gas phases are function of their own saturations. however, oil isoperms are not only function of oil saturation but also had significant curvature (concave towards the 100% oil saturation) which has the same conclusions with the previous studies (corey et al. 1956; donaldson and dean 1966; saraf et al. 1982; oak 1990; and maini et al. 1990). table 1-basic parameters applied in the model. parameters value fracture length [m] 1.15 fracture width [m] 2.25 fracture thickness [mm] 0.75 gas bed thickness [mm] 0.30 water bed thickness [mm] 0.25 oil bed thickness [mm] 0.20 inlet pressure [mpa] 1.50 gas density [kg/m3] 0.82 water density [kg/m3] 1000 oil density [kg/m3] 810 gas viscosity [cp] 0.017 water viscosity [cp] 1.0 oil viscosity [cp] 4.5 outlet pressure [mpa] 1.45 5 (a) (b) (c) figure 2—the isoperms of different phase for fracture systems calculated for the example. (a) gas phase. (b) water phase. (c) oil phase. with the proposed model, series of three-phase relative permeability calculations at various oil viscosities were performed. the results show that the trend and curvature of oil isoperms varied with oil viscosity. the larger the viscosity of oil phase is, the greater the curvatures of oil isoperms are. oil isoperms (kro=0.08) with different oil viscosities of the data sets are shown in figure 3. figure 3—oil isoperms for fracture systems with different viscosities of oil phase (kro=0.08). 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 s w krg=0.01 sg (a) krg=0.05 s o krg=0.1 krg=0.2 krg=0.4 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 sw krw=0.2 s o 0.00 0.25 0.50 0.75 1.00 (b) s g krw=0.1 krw=0.05 krw=0.01 krw=0.4 s g kro=0.001 s w 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00 so kro=0.01 0.00 0.25 0.50 0.75 1.00 kro=0.05 kro=0.08 kro=0.1 (c) kro=0.4 kro=0.2 kro=0.6 kro=0.65 0.00 0.25 0.50 0.75 1.00 s g  w =1cp, o =1.45cp s w so 0.00 0.25 0.50 0.75 1.00 0.00 0.25 0.50 0.75 1.00  w =1cp, o =1cp  w =1cp, o =0.59cp  w =1cp, o =0.71cp 6 figure 4 shows the predicted oil phase relative permeability results at various water saturations. and oil viscosity is 1.45 cp. the results of this study show that oil phase relative permeability increased with the decrease of gas saturation (e.g. oil phase relative permeability increased with the increase of water saturation) with the same oil saturation. the study illustrates that gas saturation decreased oil relative permeability for the same oil saturation. the reason for this is that water phase flow occurs close to fracture surface, gas phase flows in the center of the fracture and oil phase flow occurs in-between water phase and gas phase. under the same oil saturation, gas saturation decreases with the increase of water saturation. for the same thickness of oil bed, the larger water saturation is (e.g. the larger the thickness of water bed in the fracture is), the lower the thickness of gas bed is, the closer to the center of the fracture oil phase flow occurs and the faster oil phase flows in the fracture. figure 4—oil relative permeabilities for fracture systems. the curves represent three-phase data at various water saturations when oil viscosity is 1.45 cp. figure 5 shows oil phase relative permeability results at various water saturations and viscosities of oil phase (as µw=1cp, µo represents viscosity ratio). the results show that oil phase relative permeability increases with the increase of viscosity ratio. the result can be explained as: wetting phase (water phase) flow occurs close to fracture surface, the flow of the adjacent high-viscosity non-wetting phase (oil phase) passing by it, to some extent, can be considered as a sliding motion in which the wetting phase (water phase) provides lubrication. figure 5 also shows that water saturation intensifies the influence of viscosity ratio to oil relative permeability. the effect increases with the increase of water saturation. (a) (b) (c) figure 5—oil relative permeabilities for fracture systems. the curves represent three-phase data at various oil viscosities with different water saturations. (a) the value of water saturation is 0.1. (b) the value of water saturation is 0.2. (c) the value of water saturation is 0.3. 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 o il r e la ti v e p e rm e a b il it y oil saturation sw=0 sw=0.1 sw=0.2 sw=0.3 sw=0.4 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 o il r e la ti v e p e rm e a b il it y oil saturation s w =0.1  o =1.45cp  o =1cp  o =0.85cp  o =0.75cp  o =0.65cp  o =0.55cp  o =0.45cp (a) 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8 1.0 (b) o il r e la ti v e p e rm e a b il it y oil saturation s w =0.2  o =1.45cp  o =1cp  o =0.85cp  o =0.75cp  o =0.65cp  o =0.55cp  o =0.45cp 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.0 0.2 0.4 0.6 0.8 1.0 (c) o il r e la ti v e p e rm e a b il it y oil saturation s w =0.3  o =1.45cp  o =1cp  o =0.85cp  o =0.75cp  o =0.65cp  o =0.55cp  o =0.45cp 7 conclusions the following main conclusions can be drawn from this study: 1. a novel analytical model for oil-gas-water three-phase relative permeability in fracture systems has been proposed in this study. the equations describing oil-gas-water three-phase relative permeability curves in a fracture are function of saturations and viscosities. 2. the novel model was validated with the previous studies. the isoperms of water and gas phases are function of their own saturations, however, oil isoperms are not only function of oil saturation but had significant curvature. 3. the study illustrated that the trend and curvature of oil isoperms varied with oil viscosity. the curvatures of oil isoperms increase with the increase of the viscosity of oil phase. gas saturation decreases oil relative permeability, however, the viscosity ratio increases it. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature as = area of the fracture aw = area of water bed in the fracture ag = area of gas bed in the fracture ao = area of oil bed in the fracture c1 = integration constant c11 = integration constant c12 = integration constant c13 = integration constant c14 = integration constant c15 = integration constant 𝐶1 𝑤𝑏 = integration constant of water phase at the bottom 𝐶1 𝑔 = integration constant of gas phase 𝐶1 𝑤𝑡 = integration constant of water phase at the top 𝐶1 𝑜𝑏 = integration constant of oil phase at the bottom 𝐶1 𝑜𝑏 = integration constant of oil phase at the top hg = thickness of gas bed in the fracture hw1 = thickness of water bed in the fracture ho1 = thickness of oil bed in the fracture krw = relative permeability to water phase krg = relative permeability to gas phase kro = relative permeability to oil phase ke = absolute permeability l = fracture length p1 = pressure in z=0 p2 = pressure in z=l sw = water saturation sg = gas saturation 8 so = oil saturation 𝑣𝑧 𝑤𝑏 = velocity of water phase at the bottom 𝑣𝑧 𝑤𝑡 = velocity of water phase at the top 𝑣𝑧 𝑜𝑏 = velocity of oil phase at the bottom 𝑣𝑧 𝑜𝑡 = velocity of oil phase at the top 𝑣𝑧 𝑔 = velocity of gas phase 𝑉𝑧 𝑤 = average velocity of water phase 𝑉𝑧 𝑜 = average velocity of water phase 𝑉𝑧 𝑔 = average velocity of gas phase w = width of fracture δx = difference operator µg = viscosity of gas µo = viscosity of oil µw = viscosity of water 𝜏𝑥𝑧 𝑤𝑏 = shear stress for the water phase at the bottom 𝜏𝑥𝑧 𝑤𝑡 = shear stress for the water phase at the top 𝜏𝑥𝑧 𝑜𝑏 = shear stress for the oil phase at the bottom 𝜏𝑥𝑧 𝑜𝑡 = shear stress for the oil phase at the top 𝜏𝑥𝑧 𝑔 = shear stress for the gas phase references balbinski, e. f., fishlock, t. p., goodyear, s. g., et al. 1999. key characteristics of three-phase oil relative permeability formulations for improved oil recovery predictions. petroleum geoscience 5(4): 339-346. bird, r. b., stewart, w. e., and lightfoot, e. n. 2002. transport phenomena, second edition. new york, us: john wiley & sons, inc. bodin, j., delay, f., and de marsily, g. 2003. solute transport in a single fracture with negligible matrix permeability 1: fundamental mechanisms. hydrogeology journal 11(4): 418-433. chen, c., li, k., and horne, r. n. 2004. experimental study 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(english translation, w. r. balke, bartlesville, ok, 1972). saraf, d. n. and fatt, i. 1967. three-phase relative permeability measurements using a nuclear magnetic resonance technique for estimating the fluid saturation. spe journal 7(3): 235-242. spe-1760-pa. saraf, d. n., batycky, j. p., jackson, c. h., et al. 1982. an experimental investigation of three-phase flow of water-oil-gas mixtures through water-wet sandstones. paper presented at spe california regional meeting, san francisco, california, 24-26 march. spe-10761-ms. sarem, a. m. 1966.three-phase relative permeability measurements by unsteady-state method. society of petroleum engineers journal 6(3): 199-205. spe-1225-pa. shad, s. and gates, i. d. 2010. multiphase flow in fractures: co-current and counter-current flow in a fracture. journal of canadian petroleum technology 49(2): 48-55. snow, d. t. 1965. a parallel plate model of fractured permeable media. phd dissertation, university of california, berkeley, california. speyer, n., li, k., and horne, r. 2007. experimental measurement of two-phase relative permeability in vertical fractures. paper presented at thirty-second workshop on geothermal reservoir engineering. stanford university, stanford, california, 22-24 january. sgp-tr-183. stone, h. l. 1970. probability model for estimating three-phase relative permeability. journal of petroleum technology 22(2): 214-218. spe-2116-pa. golf-racht, t. d. v.1982. fundamentals of fractured reservoir engineering. amsterdam, holland: elsevier. spronsen, e. v. 1982. three-phase relative permeability measurements using the centrifuge method. paper presented at spe enhanced oil recovery symposium, tulsa, oklahoma, 4-7 april. spe-10688-ms. witherspoon, p. a., wang, j. s. w., iwai, k., et al. 1980. validity of cubic law for fluid flow in a deformable rock fracture. water resource research 16(6): 1016-1024. stone, h.l. 1973. estimation of three-phase relative permeability and residual oil data. journal of canadian petroleum technology 12(4): 53-61. appendix a the fracture geometry and flow configuration for the proposed model is shown in figure 1. for the proposed model, the modeled fracture comprises two smooth and planar fracture walls. within the fracture, oil-gas-water three fluids are flowing in a steady-state condition. the wettability of fracture walls sequences from water>oil>gas. gas phase flows in the center of the fracture. water phase flow occurs close to fracture surface. oil phase flow occurs in-between water phase and gas phase. applying the shell momentum balance (bird et al. 2002; chima et al. 2010; chima and geiger 2012) in the fracture, the following equation can be written as, ∂𝜏𝑥𝑧 ∂𝑥 = 𝑃1−𝑃2 𝐿 ,………………..………………………………………………………………………..(a-1) 11 with the integration of the eq. a-1 for the five regions, the shear stress for water phase at the bottom, oil phase at the bottom, gas phase, oil phase at the top and water phase at the top can be written as, 𝜏𝑥𝑧 𝑤𝑏 = 𝑃1−𝑃2 𝐿 𝑥 + 𝐶1 𝑤𝑏,…………………………………………………..………..…..……...….……(a-2) 𝜏𝑥𝑧 𝑜𝑏 = 𝑃1−𝑃2 𝐿 𝑥 + 𝐶1 𝑜𝑏,…………………….…………………………….………..….…………….….(a-3) 𝜏𝑥𝑧 𝑔 = 𝑃1−𝑃2 𝐿 𝑥 + 𝐶1 𝑔 ,…………..………………………………………...…………..………....……..(a-4) 𝜏𝑥𝑧 𝑜𝑡 = 𝑃1−𝑃2 𝐿 𝑥 + 𝐶1 𝑜𝑡,.……………………………………………………………….…….……..……(a-5) 𝜏𝑥𝑧 𝑤𝑡 = 𝑃1−𝑃2 𝐿 𝑥 + 𝐶1 𝑤𝑡,...……….………………………………………………….…………………..(a-6) based on the boundary conditions (chima et al. 2010; chima and geiger 2012; lei et al. 2014) in the fracture, the following equations can be written as, condition 1: at 𝑥 = 0, 𝜏𝑥𝑧 𝑤𝑏 = 𝜏𝑥𝑧 𝑜𝑏; 𝑣𝑧 𝑤𝑏 = 𝑣𝑧 𝑜𝑏 condition 2: at 𝑥 = ℎ𝑜1, 𝜏𝑥𝑧 𝑔 = 𝜏𝑥𝑧 𝑜𝑏; 𝑣𝑧 𝑔 = 𝑣𝑧 𝑜𝑏 condition 3: at 𝑥 = ℎ𝑜1 + ℎ𝑔, 𝜏𝑥𝑧 𝑔 = 𝜏𝑥𝑧 𝑜𝑡; 𝑣𝑧 𝑔 = 𝑣𝑧 𝑜𝑡 condition 4: at 𝑥 = 2ℎ𝑜1 + ℎ𝑔, 𝜏𝑥𝑧 𝑤𝑡 = 𝜏𝑥𝑧 𝑜𝑡 , 𝑣𝑧 𝑤𝑡 = 𝑣𝑧 𝑜𝑡 condition 5: at 𝑥 = −ℎ𝑤1, 𝑣𝑧 𝑤𝑏 = 0 condition 6: at 𝑥 = ℎ𝑤1 + 2ℎ𝑜1 + ℎ𝑔, 𝑣𝑧 𝑤𝑡 = 0 with the boundary conditions 1-4, we can find that 𝐶1 𝑔 = 𝐶1 𝑤𝑏 = 𝐶1 𝑜𝑏 = 𝐶1 𝑜𝑡 = 𝐶1 𝑤𝑡 = 𝐶1. when newton's law of viscosity is substituted into eqs. a-2 through a-6, the velocity equations for water phase at the bottom, oil phase at the bottom, gas phase, oil phase at the top and water phase at the top can be written as, 𝑣𝑧 𝑤𝑏 = − ( 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑤 + 𝐶1 𝜇𝑤 𝑥) + 𝐶11,………………………………………….………........................(a-7) 𝑣𝑧 𝑜𝑏 = − ( 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑜 + 𝐶1 𝜇𝑜 𝑥) + 𝐶12,………………………………………….………..…….....……...(a-8) 𝑣𝑧 𝑔 = − ( 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑔 + 𝐶1 𝜇𝑔 𝑥) + 𝐶13,……………..………………………………..…….……….....….(a-9) 𝑣𝑧 𝑜𝑡 = − ( 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑜 + 𝐶1 𝜇𝑜 𝑥) + 𝐶14,……………………………………………..…….….............….(a-10) 𝑣𝑧 𝑤𝑡 = − ( 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑤 + 𝐶1 𝜇𝑤 𝑥) + 𝐶15,……………………………………………….…..………..…...(a-11) with the boundary conditions 1-5, the velocity profiles for the oil-gas-water three-phase can be written as, 𝑣𝑧 𝑤𝑏 = − 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑤 + 𝑃1−𝑃2 𝐿 ℎ𝑔+2ℎ𝑜1 2 𝑥 𝜇𝑤 + 𝑃1−𝑃2 𝐿 ℎ𝑤1 2 +ℎ𝑤1ℎ𝑔+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 ,………………............................(a-12) 𝑣𝑧 𝑜𝑏 = − 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑜 + 𝑃1−𝑃2 𝐿 ℎ𝑔+2ℎ𝑜1 2 𝑥 𝜇𝑜 + 𝑃1−𝑃2 𝐿 ℎ𝑤1 2 +ℎ𝑤1ℎ𝑔+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 ,……………..……......…………..(a-13) 12 𝑣𝑧 𝑔 = − 𝑥2 2𝜇𝑔 𝑃1−𝑃2 𝐿 + ℎ𝑔+2ℎ𝑜1 2 𝑃1−𝑃2 𝐿 𝑥 𝜇𝑔 + 𝑃1−𝑃2 𝐿 ( ℎ𝑤1 2 +ℎ𝑔ℎ𝑤1+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 + ℎ𝑔ℎ𝑜1+ℎ𝑜1 2 2𝜇𝑜 − ℎ𝑔ℎ𝑜1+ℎ𝑜1 2 2𝜇𝑔 ),…………..……(a-14) 𝑣𝑧 𝑜𝑡 = − 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑜 + 𝑃1−𝑃2 𝐿 ℎ𝑔+2ℎ𝑜1 2 𝑥 𝜇𝑜 + 𝑃1−𝑃2 𝐿 ℎ𝑤1 2 +ℎ𝑔ℎ𝑤1+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 ,…………………………………..(a-15) 𝑣𝑧 𝑤𝑡 = − 𝑃1−𝑃2 𝐿 𝑥2 2𝜇𝑤 + 𝑃1−𝑃2 𝐿 ℎ𝑔+2ℎ𝑜1 2 𝑥 𝜇𝑤 + 𝑃1−𝑃2 𝐿 ℎ𝑤1 2 +ℎ𝑔ℎ𝑤1+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 ,………………….…………......(a-16) the average velocities for each phase are calculated as (chima et al. 2010; chima and geiger 2012; lei et al. 2014), 𝑉𝑧 𝑤 = 𝑉𝑧 𝑤𝑏 = 𝑉𝑧 𝑤𝑡 = 1 ℎ𝑤1 ∫ 𝑣𝑧 𝑤𝑏𝜕𝑥 0 −ℎ𝑤1 = 𝑃1−𝑃2 𝐿 4ℎ𝑤1 2 +3ℎ𝑤1ℎ𝑔+6ℎ𝑤1ℎ𝑜1 12𝜇𝑤 ,………..……..….………....(a-17) 𝑉𝑧 𝑜 = 𝑉𝑧 𝑜𝑏 = 𝑉𝑧 𝑜𝑡 = 1 ℎ𝑜1 ∫ 𝑣𝑧 𝑜𝑏 ∂𝑥 ℎ𝑜1 0 = 𝑃1−𝑃2 𝐿 ( ℎ𝑤1 2 +ℎ𝑤1ℎ𝑔+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 + 3ℎ𝑔ℎ𝑜1+4ℎ𝑜1 2 12𝜇𝑜 ),…….………….(a-18) 𝑉𝑧 𝑔 = 1 ℎ𝑔 ∫ 𝑣𝑧 𝑔 ∂𝑥 ℎ𝑜1+ℎ𝑔 ℎ𝑜1 = 𝑃1−𝑃2 𝐿 ( ℎ𝑔 2 12𝜇𝑔 + ℎ𝑤1 2 +ℎ𝑔ℎ𝑤1+2ℎ𝑤1ℎ𝑜1 2𝜇𝑤 + ℎ𝑔ℎ𝑜1+ℎ𝑜1 2 2𝜇𝑜 ),……….……..………..(a-19) with the darcy law, the following equations for oil-gas-water three-phase can be written as, 𝑘𝑟𝑜𝑘𝑒𝐴𝑠 𝜇𝑜 𝛥𝑃𝑜 𝐿 = 𝐴𝑜𝑉𝑧 𝑜,………………………………..……………………..……………..…........….(a-20) 𝑘𝑟𝑔𝑘𝑒𝐴𝑠 𝜇𝑔 𝛥𝑃𝑔 𝐿 = 𝐴𝑔𝑉𝑧 𝑔 ,………………………………..……………………….…………..…...…..…(a-21) 𝑘𝑟𝑤𝑘𝑒𝐴𝑠 𝜇𝑤 𝛥𝑃𝑤 𝐿 = 𝐴𝑤𝑉𝑧 𝑤,………………………………………………………………………......…...(a-22) where (see appendix b for details), 𝛥𝑃𝑜 = 𝑃1−𝑃2 𝑆𝑜 ; 𝛥𝑃𝑔 = 𝑃1−𝑃2 𝑆𝑔 ; 𝛥𝑃𝑤 = 𝑃1−𝑃2 𝑆𝑤 𝐴𝑜 = 2𝑊ℎ𝑜1;ℎ𝑜1 = 𝑆𝑜𝐻 = (1 − 𝑆𝑔 − 𝑆𝑤)𝐻 𝐴𝑔 = 𝑊ℎ𝑔; ℎ𝑔 = 𝑆𝑔𝐻; 𝐻 = ℎ𝑔 + 2ℎ𝑤1 + 2ℎ𝑜1 𝐴𝑠 = 𝑊𝐻 ;𝐴𝑤 = 2𝑊ℎ𝑤1 ;ℎ𝑤1 = 𝑆𝑤 2 𝐻 ;𝑘𝑒 = 𝐻2 12 (snow 1965; witherspoon et al. 1980; golf-racht 1982). rearranging eqs. a20 to a22 give the relative permeability for oil-gas-water three-phase, 𝑘𝑟𝑜 = 𝑆𝑜 2 ( 𝜇𝑜 𝜇𝑤 (3𝑆𝑤 − 3 2 𝑆𝑤 2 ) + 3 2 𝑆𝑔𝑆𝑜 + 𝑆𝑜 2),…………………………………………………...….(a-23) 𝑘𝑟𝑔 = 𝑆𝑔 2 (𝑆𝑔 2 + 𝜇𝑔 𝜇𝑤 (3𝑆𝑤 − 3 2 𝑆𝑤 2 ) + 𝜇𝑔 𝜇𝑜 (3𝑆𝑔𝑆𝑜 + 3 2 𝑆𝑜 2)),..……………………......…………....…(a-24) 𝑘𝑟𝑤 = 𝑆𝑤 3 2 (3 − 𝑆𝑤),………..…….…………………………………….…………..........……….....(a-25) eqs. a-23 through a-25 are the proposed equations to estimate oil-gas-water relative permeability curves in fractures. 13 appendix b for the fracture geometry and flow configuration shown in figure 1, the following equations can be obtained as, ℎ𝑜1 = 𝑆𝑜 𝐻 2 ,………………………………………………..………………..…..……..……....…...…(b-1) ℎ𝑔 = 𝑆𝑔𝐻,…………………………………………………………………….………..………….…(b-2) 𝑆𝑤 = 𝑊𝐿(2ℎ𝑤1) 𝑊𝐿𝐻 = 2ℎ𝑤1 𝐻 ,……………………………………………………………………………….(b-3) the equalities 𝛥𝑃𝑜, 𝛥𝑃𝑔 and 𝛥𝑃𝑤 are given below (chima et al. 2010; chima and geiger 2012; lei et al. 2014), 𝛥𝑃𝑜 = 𝑃1−𝑃2 𝑆𝑜 = 𝑃1−𝑃2 1−𝑆𝑤−𝑆𝑔 ,……………………………………………………………..……………….(b-4) 𝛥𝑃𝑔 = 𝑃1−𝑃2 𝑆𝑔 ,…………………………………………………..…………...……….……….………..(b-5) 𝛥𝑃𝑤 = 𝑃𝑤1 − 𝑃𝑤2 = 𝑃1−𝑃2 𝑆𝑤 ,………………………….………………………..……………….….….(b-6) gang lei is a postdoctoral fellow at the peking university. his research interests include theory and laboratory studies of the fundamental properties and behavior of fractured reservoirs, numerical modeling of fractured horizontal wells, and enhanced oil recovery of tight sandstone reservoirs. lei holds a phd degree from the china university of petroleum, beijing. he is a member of spe. cai wang is now a postdoctoral fellow in peking university, beijing, china. his research interests mainly contain contamination of shale gas development on underground water, productivity analysis and numerical modeling of shale gas and tight gas reservoirs. wang hold a doctoral degree and a bachelor degree in china university of geosciences (beijing). yuan tian is now an undergraduate student at the school of civil engineering of tongji university. her research interests mainly contain mathematical modeling and fluid flow law in porous media. limin yang is associate professor of the department of mathematics at the china university of petroleum, beijing. her research interests include multi-phase percolation theory in unconventional reservoirs. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1207 received december 2, 2021; revised march 14, 2022; accepted april 20, 2022. *corresponding author: dongzz@xsyu.edu.cn 1 interfacial characterization and minimum miscible pressure study of co2 flooding based on molecular dynamics bochao qu, xinle ma, and zhenzhen dong*, xi’an shiyou university, xi’an, china abstract co2 flooding can not only effectively improve the recovery of oil reservoirs, but also permanently store co2 underground to alleviate the greenhouse effect. in the process of co2 flooding, co2 is injected into the oil reservoirs to affect the properties of crude oil through adsorption on oil interface, which reduces the interfacial tension and the density of the crude oil, thereby enhancing the recovery factor. conventional core flooding experiments can only observe the oil displacement effect from a macroscopic perspective, but it is difficult to characterize the interface of co2 flooding from a microscopic perspective. furthermore, the experiment to obtain the minimum miscible pressure (mmp) usually requires a long time and high cost. in this study, an all-atom molecular dynamics simulation method was used to establish a co2 model and a crude oil model. using the co2 force field of zhu and the alkane force field of nerd, the interface interaction, interface characteristics, and minimum miscible pressure between co2 and crude oil were analyzed. the research results show that when co2 mixes with the crude oil, co2 accumulates at the interface to form an adsorption layer; with the increase of system pressure, the phase interface and the co2 adsorption layer gradually become thicken, and the interfacial tension (ift) between co2 and crude oil decreases linearly. the addition of the light hydrocarbon component allows co2 to be more readily miscible with crude oil. at a low pressure, ift decreases with increasing temperature, while at a high pressure, ift increases with increasing temperature and mmp increases with increasing temperature as well. the mmp calculated using linear extrapolation of the interfacial tension was in good agreement with the experiment measurements. the main innovations of this study was the use of molecular dynamics analysis to simulate the interfacial properties of a system composed of co2 and n-alkanes, and it is applicable to apply the simulated mmp in real oilfields.this study can significantly reduce the human, material and financial resources of the experiment in estimating mmp and also provide constructive suggestions on the practical application of co2 flooding on oil reservoirs. introduction in domestic and international reservoir development, co2 flooding can not only enhance oil recovery, but also achieve co2 sequestration and reduce the greenhouse effect. when the pressure is high enough, the ability of the crude oil to dissolve bitumen and paraffin decreases after co2 precipitates the lighter mailto:lichen1125@foxmail.com 2 components in the crude oil, and the heavy components precipitate out of the crude oil, the crude oil viscosity decreases significantly and the oil flow ability is improved to achieve the purpose of mixed-phase oil drive. under certain temperature and pressure conditions, when the crude oil is miscible with co2, the interfacial tension of the crude oil is eliminated, and the pressure at this point is the minimum miscible pressure (mmp) for co2 miscible flooding. therefore, understanding the interfacial properties of processes, such as the dissolution of co2 into crude oil, is particularly important for co2 miscible flooding technology. the mmp is the minimum pressure at which the interfacial tension between oil and gas disappears. the most commonly used experiments for determining mmp are the fine tube test method, the bubbler method, and the vanishing interfacial tension method. the fine tube experiments is a standard method widely used and accepted in the petroleum industry to measure mmp and usually the measured mmp is reliable (elsharkaw1996; flock and nouar 1984). yelling et al. (1980) used sand-filled long fine tubes to simulate the co2 repulsion process in real reservoirs to determine mmp, and investigated the effect of reservoir temperature and oil compositions on mmp. nouar and flock(1984) performed a parameter analysis of the mmp determination using a thin-tube test and suggested that increasing the length of the thin-tube could result in more accurate mmp values. however, the fine tube test is very expensive and time consuming (zhang and gu 2015). the bubble-lift method is an relative cheap and fast method for determining mmp. the movement of co2 bubbles in oil is observed through a high-pressure window, and the oil-gas miscible state is determined by the change in appearance of the bubbles as they move at different pressures. however, the method relies on human observations and is subjective (elsharkaw 1996; dong 2001). the vanishing interfacial tension method was used to determine the interfacial tension between the injected gas and oil at constant temperature and pressure, and the pressure at which the interfacial tension is zero is obtained by extrapolation, i.e. the mmp (rao 1997; rao and lee 2002; 2003). ayirala and rao demonstrated that the mmp determined using the vanishing interfacial tension method was similar to that was determined by the fine tube experiment and the bubble lifter method. the experiment results clearly supported that the use of vanishing interfacial tension for the rapid and economical determination of mmp (ayirala and rao 2011). due to the complex composition of crude oil, there are too many influencing factors if the properties of the system composed of co2 and crude oil are studied directly in the co2 flooding process. therefore, researchers generally take the major components of oil to represent crude oil, such as n-alkanes, cycloalkanes aromatic hydrocarbons, etc. shaver et al. (2001) experimentally measured the phase fraction, phase density and interfacial tension of co2 and n-decane in the pressure range of 1~13mpa at 344 k. hsu et al.(1985) measured the oil composition, oil density, and interfacial tension of co2 and n-butane system at the temperature of 319k~378k until the pressure achieved the mmp. spee and schneider (1991) measured the change of oil composition with pressure in a co2/dodecane system and co2/1,8-octanediol system at 393 k and 10~100 mpa. in recent years, molecular simulations have been widely applied to study the co2 and crude oil systems. makimura et al. (2012) investigated two characteristics of co2-eor based on molecular simulations, including interfacial properties and phase equilibrium. neyt et al. (2011) used gibbs ensemble monte carlo and two-phase monte carlo to calculate the interfacial tension between co2 and water, the interfacial tension between co2 and n-butane system. the calculated results were in good agreement with the experiment results. müller et al .(2009) used molecular dynamics to calculate the oil composition, oil density, interfacial tension and interfacial structure of n-hexane and n-decane system, co2 and n-decane system, and ethane and n-eicosane system. the simulation results agreed well with the experiments. de 3 lara et al. (2012) used molecular dynamics to investigate the interfacial properties of brine/light oil, co2/light oil, n2/ light oil and ch4/light oil systems. they showed that the co2/light oil system had the advantage of lower interfacial tension and enhancing diffusion of co2 in the oil phase. the diffusion coefficients of n-alkanes from methane to tetradecane in co2 at infinite dilution were calculated by feng et al. (2013). the results obtained from the simulations were reliable. compared to experimental methods, molecular simulations can be used to calculate the interfacial tension between co2 and crude oil, to reveal the interfacial properties of co2 and oil, and to observe microscopic mixing processes. these are difficult or impossible to be observed and measured using experimental methods. in addition, molecular dynamics simulations can be used to predict the interfacial properties of co2 and oil with low cost and fast calculation time. in this study, the molecular dynamics simulation method was proposed to study the miscibility characteristics of injected co2 and oil in a block of yanchang oilfield. the paper is structured as follows: section 2 describes the proposed methodology in details, including force field and mmp calculation methods; section 3 describes the model used for the molecular simulations; section 4 presents the main results of the study. methodology force field. the potential energy function describing the forces interacting between atoms in a system is called the force field. constructing an accurate potential energy function for a system is an important step in molecular dynamics calculations. in general, molecular force fields mainly include bond stretching potential energy, bond angle bending potential energy, dihedral angle distortion potential energy, and non-bonding potential energy. non-bonding potential energy includes van der waals potential energy and coulomb electrostatic potential energy. force fields have been developed for each system and are basically suitable for molecular dynamics simulation studies in various fields. different force fields include different atom types, so before selecting a force field one should first check the list of atom types for the force field and whether the force field covers the atom types in the simulated system. the available co2 molecular force fields are mainly divided into a rigid force field containing the trappe force field, a semi-flexible force field with the epm2 force field and a flexible force field with the zhu force field (potoff and siepmann 2001; harris and yung 1995; zhu 2009). the molecular force fields of n-alkanes can be divided into two categories: joint atomic force fields and all-atomic force fields. joint atomic force fields are those that equate ch3 and ch2 of n-alkanes as one atom, such as opls-ua, trappe-ua and nerd (jorgensen 1984; martin and siepmann 1998; nath 1998). all-atomic force fields are those all atoms expressed in n-alkanes explicitly, such as opls-aa and charmm (jorgensen 1996; price 2001; davis 2008). the zhu force field was proposed by zhu et al. (2009), which can accurately predict the saturated gas-liquid phase density, critical point properties, while taking into account the molecular structure properties of supercritical co2, and is therefore suitable for the simulation of systems containing supercritical co2. the calculated gas-liquid equilibrium curves from the nerd force field are in good agreement with experimental data for both shorter chain alkanes and longer chain alkanes (müller 2009; nath 1998). therefore, the zhu co2 force field and the nerd n-alkane force field were used in this study. the nerd molecular force field defines the total potential energy function of an alkane as shown in eq. 1. 4 �total = bonds ��� � 2 ��� − ���� 2 + ������ ���� � 2 ���� − ����0� 2 + ��ℎ�������0 + �1 1 + ���� +� �2 1 − ��� 2� + �3 1 + ��� 3� + ���������4���� ��� ��� 12 − ��� ��� 6 + ���� 4��0����� .............................................(1) the zhu co2 force field function takes the form shown in eq. 2. �total = bonds ��� � 2 ��� − ���� 2 + ������ ���� � 2 ���� − ����0� 2 + ���������4���� ��� ��� 12 − ��� ��� 6 + ���� 4��0����� ,...............................................(2) van der waals interactions between atoms describe the interactions between atoms that are caused by non-covalent and non-hydrostatic forces that attract or repel each other. the lennard-jones potential function is a function that describes the van der waals interactions between atoms and has the form shown in eq. 3. ��� ��� = 4��� ��� ��� 12 − ��� ��� 6 .............................................................................................................(3) the sums between the different atoms are obtained by means of a mixing rule, the common lorentz-berthelot mixing rule, as shown in eq. 4 and 5, respectively. ��� = ��+�� 2 ,...............................................................................................................................................................................(4) ��� = ����...............................................................................................................................................(5) simulation method. in this study, lammps molecular simulation software was used for the simulations. during the molecular dynamics (md) simulations, periodic boundary conditions were used, the equations of motion were solved for integration using the velocity-verlet method. the long-range force electrostatic interactions used the particle-particle-particle-mesh (pppm) summation method with an accuracy of 1.0×10-4. the non-bonded van der waals forces used the 12-6 lennar-jones potential function with a truncation radius of 2 nm and a time step of 1 fs. the temperature coupling was performed using the nosé-hoover algorithm. the entire simulation time was 10 ns of relaxation time, 30 ns of calculation time, with data collected at 0.1 ps intervals. finally, the ift of the system was calculated. there are many ways to obtain the mmp, the most common ones are to calculate the number of co2 and alkanes that cross the phase interface at the same temperature and different pressures as a percentage of the total number of co2 and alkanes, and to obtain the mmp when the number of ratios drops to a stable pressure. there are also methods to obtain the mmp by the disappearance of interfacial tension. in this study, the mmp was obtained by the disappearance of interfacial tension, as the method has a clear definition of parameters. when the interfacial tension is zero, the interface between the two phases disappears, then the two phases can completely become a miscible phase. the gibbs interfacial tension equation was used to calculate the variation of the two-phase interfacial tension with pressure, from which mmp is indirectly calculated. the specific expression is given as eq. 6. � = 1 2 0 �� �� � − �� � ��� = 1 2 ��� − ���+��� 2 ��,..........................................................................(6) where γ is the interfacial tension, and �� � and �� � represents the normal and tangential pressures, ��� is the amount on the diagonal of the pressure tensor, and �� is the length in the z-direction of the simulated system. 5 modeling. the force field parameters for this study are shown in table 1. the initial systems of two cases are given in figure 1, with a oil (liquid phase) in the middle and co2 (gas phase) in the two side. the oil phase consists of alkanes of different chain lengths, depending on the case. for the co2/n-decane system, the oil contains 800 n-decane molecules. the system pressure was varied with the number of co2 molecules in the gas phase on both sides. the size of the simulated system was taken to be 5×5×30 nm3. table 1—force field parameters. atom σ(nm) εij(kj/mol) ct_ch3 0.3910 0.8647 ct_ch2 0.3930 0.3808 c 0.2800 0.23397 o 0.3028 0.66824 bond r0(nm) kb(kj/(mol/nm2) ) ch3_ch2 0.1540 80235.0280 ch2_ch2 0.1540 80235.0280 c-o 0.1162 60000.0000 angle θ0(deg) kθ（kj/mol/rad2) ch3_ch2—ch2 114 519.657 ch2_ch2—ch2 114 519.657 c-o-c 180 110.000 torsion v0（kj/mol) v1（kj/mol) v2（kj/mol) v3（kj/mol) ch3_ch2—ch2—ch2 0.0000 5.9038 -1.1339 13.1590 ch2_ch2—ch2—ch2 0.0000 5.9038 -1.1339 13.1590 (a) case 1 (b) case 2 figure 1—initial structure of the two systems. 6 results and discussion interfacial tension and mmp. the disappearance of interfacial tension method was used in the md simulation to indirectly calculate the mmp of co2 with n-decane at 334k. because shaver (2001) experimentally measured the phase fraction, phase density and interfacial tension of co2 and n-decane in the pressure range of 1~13mpa at 344 k, the simulation results in this section are compared with the experimental values. as shown in figure 2(a), the calculated ifts by this work were in very good agreement with shaver (2001) method. the interfacial tension decreases with increasing pressure and displays a linear relationship, which indicates that the interface between co2 and alkane becomes increasingly blurred and gradually tends to a miscible phase. in addition, the linear relationship enables a reliable extrapolation to obtain the pressure when the interfacial tension is zero. thus, the mmp was determined to be 11.89 mpa when ift equal 0. the estimated mmp is very close to that measured mmp (12.74 mpa) by shaver et al (2001). as can be seen from figure 2(b), the relationship between interfacial tensions and pressure obtained by müller and mejía (2009) using the epm2 co2 model and the nerd n-decane model were in good agreement with the experiments. mejia et al. (2014) used coarse-grained molecular model to simulate co2/n-decane system. but the estimated interfacial tensions were slightly higher than the measured values. the estimated ifts by this work agreed well with the measured values. therefore, zhu co2 model and the nerd n-alkane model used in this paper are an effective, convenient and low-cost method for predicting the mmp for co2 and alkane systems compared to coarse-grained simulations. (a) (b) figure 2—interfacial tension between carbon dioxide and n-decane with pressure. to validate the effectiveness of the proposed method in estimating mmp, the proposed method was compared to the empirical formulas. the comparison results are shown in table 2. the national petroleum council (npc) empirical equation estimates mmp roughly, mainly by using api and temperature as parameters, and obtains results with large errors. yellig and metcalfe (1980) proposed a method to predict mmp according to the temperature, which is one of the most common methods. the temperature is the only parameter in the formula: ���=1833.7217+2.2518055(t-460)+0.01800674(t-460)2 − 103949.93 �−460 ......................................(7) as can be seen from table 2, the results of the npc empirical formula approach are poor. the molecular simulation used in this study has a higher prediction accuracy than the yellig-metcalfe model. 7 it indicates that the empirical formula has certain limitations, such as the composition of different oil fields, the composition of the injected gas, and the range of working conditions. thus, the results obtained by the empirical formulas are difficult to be generalized. in contrast, the working conditions of the molecular simulation method proposed in this study is easy to set, and the calculated values agree well with the experimental values, so it has a wider applications. table 2—comparisons between the proposed method and the empirical formulas. mmp from experiment (mpa) npc yellig-metcalfe (1980) this study 12.74 mmp (mpa) error (%) mmp (mpa) error (%) mmp (mpa) error (%) 10.69 2.05 13.78 1.04 11.89 0.85 phase interface properties. the phase interface properties of co2 and n-decane systems, such as interfacial structure and interfacial thickness, are difficult or impossible to be measured by experiments. however, molecular dynamics has the advantage of being intuitive and convenient for this purpose. in this section, the mixing process, interfacial structure and interfacial thickness of the co2 and n-decane system at 344 k were investigated. the dynamic mixing process of the co2/n-decane system at 344 k are shown in figure 3. a small amount of decane molecules were extracted by co2 and moved towards the co2 phase, and the phase interface gradually disappeared; a large number of co2 molecules formed clusters around the decane molecules, and the two gradually miscible, and finally the phase interface disappeared and reached the mixed-phase state after 40ns. (a) 0ns (b) 5ns (c) 15ns 8 (d) 30ns (e) 40ns co2, n-decane figure 3—co2/n-decane mixed-phase microscopic processes. the variation of the gas-liquid phase density with pressure for the co2 and n-decane system at 344 k is shown in figure 4. as the pressure of the system increases, the system in the liquid phase area gradually expands, the gas-liquid phase density also increases and the phase interface gradually becomes thicker. figure 4—variation of gas-liquid phase density with pressure of co2/n-decane system. the density distribution of co2 and n-decane in the system at different pressures is shown in figure 5. as the pressure of the system increases, the density of n-decane decreases and the density of co2 increases. part of the co2 in the system gathered at the interface to form a co2 adsorption layer, and the adsorption layer gradually became thicker as the pressure increased, which surface more and more co2 gathered at the interface as the pressure increased. 9 (a)2.72mpa (b)4.51mpa (c)5.91mpa (d)7.06mpa (e)8.1mpa (f)9.09mpa (g)9.76mpa figure 5—density distribution of components of co2/n-decane system at different pressures. 10 base on the above analytical simulations, a mixture of n-decane and n-hexane was used to replace the oil from the yanchang field and the mmp was determined. the results are shown in figure 6, which shows an mmp of 11.4 mpa at 344 k. and the effect of the oil components on the mmp can also be illustrated with figure 6, which shows that the addition of n-hexane has a significant effect on the mmp of n-decane and co2. the addition of n-hexane makes the mmp decrease, because the light hydrocarbon components can be extracted from oil phase by co2, when co2 contacts with the oil, while the light components originally were dissolved in the oil. as a result, it makes co2 become hydrocarbon rich. the enriched co2 then contacts with the oil to further extract the light components. the process repeats until co2 extracts enough alkanes. in contrast, when n-hexane is dissolved in the oil to contain more light components, so co2 can be more easier to extract enough light hydrocarbons to accelerate enrichment and make co2 be more easy miscible with the oil. figure 6—effect of oil composition on mmps. the effects of temperature on mmp. it has been proven by numerous experiments that reservoir temperature has a significant effect on mmp and it is an important variable affecting mmp (zolghadr 2013). the variation of mmp with temperature for the co2/n-decane system is shown in figure 7. at a low pressure, ift decreases with increasing temperature. but at a high pressure, ift increases with increasing temperature and mmp increases with increasing temperature. this is because the density of co2 is controlled by temperature and pressure. as can be seen in figure 8, at a constant pressure, the density of co2 decreases with increasing temperature, leading to a decrease in the solubility of co2 and in the extraction ability of light hydrocarbons. thus, to give co2 sufficient solubility to achieve a mixed phase, it is necessary to increase the density of co2 by increasing pressure, so the mmp increases with increasing temperature. 11 figure 7—effect of temperature on mmps. figure 8—the density distribution of co2/n-decane at 4.5 mpa. conclusions in this paper, we simulated the phase density and interfacial tension of the co2 and n-decane system at 334 k under different pressures using molecular dynamics methods, analyzed the interfacial characteristics of the system, and investigated the effect of the addition of hexane on the minimum miscibility pressure of the co2 and n-decane system, and the main conclusions are as follows. 1. the mmp of co2 with n-decane at 334 k was predicted to be 11.89 mpa using the molecular simulation method, which has the advantage of being less costly and more efficient than the experimental methods, and the prediction is more realistic and reliable than the theoretical equations. 2. the proposed molecular dynamics simulation displayed the mixing process of co2/n-decane system. in the process, co2 is dissolved into n-decane, while n-decane is continuously extracted by co2. the interface between co2 and n-decane gradually disappears and the interfacial tension gradually decreases, and finally reaches the miscible state. 12 3. as the pressure of the system increases, the thickness of the phase interface between co2 and n-decane increases, and the co2 adsorption layer on the interface also gradually becomes thicker, and the density of n-decane decreases with the increase of pressure, while the density of co2 is the opposite. 4. when a certain amount of hexane is dissolved to the system of co2 and n-decane, the mmp of the system decreases. at a low pressure, the ift decreases with increasing temperature; while at a high pressure, both the ift and mmp increases with increasing temperature. conflicts of interest the author(s) declare that they have no conflicting interests. 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different technical criteria for determining the minimum miscibility pressures (mmps) from the slim-tube and coreflood tests. fuel 161(1): 146-156. zhu, a., zhang, x., liu, q., et al. 2009. a fully flexible potential model for carbon dioxide. chinese. j. chem. eng. 17(2): 268-272. zolghadr, a., escrochi, m., and ayatollahi, s. 2013. temperature and composition effect on co2 miscibility by interfacial tension measurement. j. chem. eng. data. 58(5): 1168-1175. bochao qu, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. tian holds a bs degree in petroleum engineering from xi’an shiyou university. xinle ma, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. tian holds a bs degree in petroleum engineering from xi’an shiyou university. zhenzhen dong is a professor in the petroleum engineering department at xi’an shiyou university. she worked as a reservoir engineer with schlumberger from 2012 to 2016. her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. 14 dong holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. abstract introduction methodology results and discussion conclusions conflicts of interest references ieee paper template copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.455 received october 3, 2019; revised november 19, 2019; accepted december 11, 2019. *corresponding author: zhangrixing1983@gmail.com 1 multiscale investigation of a lessdamaging friction reducer to mitigate formation damage in unconventional shale reservoirs rixing zhang* and hisham nasr-el-din, texas a&m university, college station, usa; xiaochun jin, ultrecovery, houston, usa; jun jim wu, phoenix c&w, houston, usa; lisa m. pérez, texas a&m university, college station, usa abstract among the additives in slickwater fracturing, only friction reducers (frs) are heavy molecular polymers, many of which are polyacrylamide-based. although they are useful for their intended purpose, frs rapidly decrease the production rate in shale by damaging the formation. this paper describes the damage mechanism in detail and proposes a less-damaging fr. molecular dynamics simulation was used to evaluate how salts potentially encountered during fracturing treatments affect polyacrylamide-based frs (pam and hpam). this work focuses on identifying an ideal less-damaging fr and proposes one based on predictions verified by the experimental results of coreflood simulation tests. field cases were also conducted, and results show that this less-damaging fr can better mitigate formation damage compared with conventional frs. although production decline still occurs in a treated well, it is slower than that of a control well treated with a conventional fr. the radius of gyration results from molecular dynamics simulations show the salt-tolerant patterns of pam and hpam follow a trend in which trivalent ions affect polymers more than bivalent ones, and monovalent ions affect the polymers the least. this result is consistent with results reported in the literature. this research predicts that the polymer chains in a less-damaging fr should be in the medium to shortrange, the polymer concentration should be much lower, and nanoparticle fillers are necessary. the turbidities of the less-damaging fr solutions are almost ten times lower than those of hpam. in addition, this new fr has only a negligible reaction with selected salts. coreflood test results indicate that the permeability lost via conventional fr is 92.6% to 99.8%. in contrast, the permeability damage via the lessdamaging fr is 0.8%. in the field test, two wells on the same platform were treated with two different frs. after three months of production, a comparative decline of gas production rate in measurable formation damaged by the less-damaging fr (10% reduction of initiated production rate) and a conventional inverse emulsion fr (30% reduction of daily gas production) was observed. this work simulates the trend of conventional frs affected by salts for the first time. it further provides a systematic method to mitigate formation damage caused by frs by combining molecular dynamics simulation, prediction, lab tests, and field tests. this procedure is useful for future work as well. a new less-damaging fr has been identified that will prove beneficial for the industry. introduction oil and gas have been produced economically from shale plays by combining the horizontal drilling and hydraulic fracturing, ushering in a revolution in the shale oil and gas industry. however, the production of oil and gas from shale has declined rapidly over the past few years. for example, in the present study, the mailto:zhangrixing1983@gmail. mailto:zhangrixing1983@gmail. 2 first three months of operation saw a 30% decline in production, followed by a 70% reduction over three years. the overall estimated ultimate recovery (eur) is less than 10%. it is well known that slickwater is the most commonly used fracturing fluid system. however, this popular method may actually be the cause of the low eur and rapid production decline. among the chemicals used in slickwater, only the friction reducer (fr) is a heavy, polyacrylamide-based molecular polymer. all other slickwater components are of such small molecular weight that they cannot be considerable factors in formation damage. slickwater treatments do perform generally well, barring any external effects, such as encountering metal ions during the treatment procedure. however, in shale formations, there are several metal ions (ca2+, mg2+, etc.). during fracturing, pad acid reacts with the metal tubulars, and, as a result, fe3+ is produced. this iron precipitation proves very damaging to shale formations, and all of the metal ions mentioned here affect frs. some biocides also degrade the performance of slickwater fracturing treatments. researchers have studied formation damage caused by frs in different ways; however, no systematic multiscale research has to date been conducted. this paper explains the mechanisms of frs in shale formation damage caused by slickwater fracturing at the molecular scale, pore scale, core scale (permeability change) and reservoir scale (field case). an effective method is found to improve eur. the present work focuses on samples obtained from the otter park and evie shales. formation damage causes oil and gas production rate decline. as noted in the previous section, frs are essential to any slickwater fracturing fluid system in shale. however, the chemical components can damage the formation and reduce production (figure 1). the other elements in figure 1 includes zn, ba, cu, and mn elements. si is excluded from the acid digestion results (peña-icart et al. 2011; tessier et al. 1979). although the majority of the previous research focused on evaluating the friction-reducing performance of these chemicals, only a few studies have addressed the potential formation damage (ibrahim et al. 2018). because of the polymeric nature of these chemicals (typically polyacrylamide (pam)), a fr can cause damage either by creating a barrier on the surface of the formation or by penetrating deeply to plug the pores. in addition, breaking these polymers at temperatures lower than 200°f remains challenging (woodroof and anderson 1977). (a) (b) figure 1—the six major elements of the (a) otter park and (b) evie shale samples obtained by acid digestion. the structure of shale.the pore-size distribution of shales is mainly small, down to several nanometres. relatively large pores with poor connections can be up to four microns. pores can also be connected by thin conduits down to 15 nanometres (figure 2) (sisk et al. 2010; kuila and prasad 2011). if big polymers are injected to the formation flocculate, the pore throats most likely would be plugged. 3 (a) (b) figure 2—(a) rendered volume of shale at the highest nano-resolution. (b) kerogen (green), disconnected pores (red) and connected porosity (blue). the scale is 500 nanometres. fracturing fluids. slickwater fracturing was developed and used in other unconventional reservoirs, such as tight gas sand and shale (carman and cawiezel 2007). the evolution of fracturing fluids has alternated between oil-based, water-based, and liquefied natural gas fracturing fluids (barati and liang 2014). because the frs primarily used for slickwater fracturing are polyacrylamides, which are synthetic polymers, the perception was that they would be difficult to break. the components of slickwater. in slickwater fracturing fluid, water, and proppant occupy 99% of the fluid-system volume (jackson et al. 2011). other additives like acid, frs, surfactant, potassium chloride, scale inhibitor, ph adjusting agent, iron control agents, corrosion inhibitors, and biocides are also added to fracturing fluid at low concentrations to fulfil different purposes for different fracturing jobs (figure 3). figure 3—volumetric composition of a general slickwater system for the us shale plays (edited with source data from www.fracfocus.org). metal ions in flowback. in flowback, different ions may affect friciton reducers (montgomery 2013) or other long-chain polymers pumped into reservoirs (table 1). pam and hpam polymers are unstable when temperature increases. pam-based fr can precipitate in the presence of divalent and trivalent cations, so formation damage could occur (seright et al. 2009). the cations in flowback water should be considered carefully to prevent the fr from precipatating. http://www.fracfocus.org/ 4 table 1—the surface charge density of the focus ions (essington 2005). ion charge[c] ion radius [pm] surface area [m2] surface charge density[c/m2] na+ 1.60e-19 116 1.69e-19 0.9462 k+ 1.60e-19 152 2.90e-19 0.5511 ca2 + 3.20e-19 114 1.63e-19 1.9594 ba2 + 3.20e-19 149 2.79e-19 1.147 cl-1.60e-19 167 3.50e-19 -0.4565 so4 2-3.20e-19 290 1.06e-19 -0.3028 hydrochloric acid (hcl) in pre-production can react with tubing steel. in us shale fracturing, an acid stage is always used before the slickwater stage. hydrochloric acid plays a key role in the hydraulic fracturing process. after a natural gas well’s hole is bored, drillers will pu mp thousands of gallons of water mixed with acid (typically a 15 wt% hcl solution) into the well. the point is to clear out cement debris left over from the drilling stage, and to help open the underground shale fractures. after the acid stage is completed, slickwater and proppant are injected into the well to flush the natural gas out. although this acid stage serves a useful purpose, the hcl can corrode the tubulars used for pumping. hcl not only corrodes the tubing steel, but also releases ferrous and ferric ions. the pam-based frs participate when encountering ferric ions. carbon steel composition summary. during the fracturing treatment, the fracturing fluid must pass through many different tubulars made of several kinds of steel (table 2). the materials selected are representative of alloys used as tubular goods or downhole equipment. table 2—the representative material of tubulars that fracturing fluids pass through. generic name c mn s ni cr mo others 4130(a) 0.31 0.46 0.018 0.03 0.88 0.20 - cu-0.11 cu-0.10 n-0.23 cb+ta-5.25 ti-0.95 al-3.4 v-8.2 zr-3.1 9 cr(a) 0.13 0.48 0.010 0.057 8.27 0.96 420(a) 0.38 0.36 0.010 0.37 12.70 0.05 2205(a) 0.02 1.83 0.003 5.82 22.33 2.77 718(a) 0.04 0.13 0.0002 53.20 18.18 3.12 bc-ti(b) 0.02 ---5.90 4.10 (a)balance fe (b)balance ti fecl3 always forms after acid flush. in fracturing treatments, among other chemicals, hydrochloric acid is largely used to dissolve minerals and initiate cracks in a formation. during the operation, the acid readily dissolves rust in the tubing or casing and corrodes steel equipments where it is mixed and pumped through. the acid also attacks iron-containing minerals in a formation under treatment. iron could also be presented in dissolved or suspended form in produced water. when the fracturing fluid mixes with subsurface water and reacts with carbonate rocks and shale, the ph increases as the acid/fracturing fluid is consumed, and the dissolved iron starts to precipitate in the form of gelatinous iron hydroxide unless an effective iron control system is applied. the insoluble iron precipitation may accumulate in the reservoir and near the wellbore, thereby plugging or reducing the created and natural permeability of the reservoir. dill and smolarchuk (1988) have indicated that the above phenomenon, i.e. precipitation of iron in natural and newly developed fractures, is one of the main causes of formation damage. the iron can also precipitate and form scale within the tubing, which also reduces production. 5 the dissolved trivalent ferric ions react with polyacrylamide and flocculate in water (kaşgöz et al. 2003). water treatments always use this mechanism to remove tervalent ferric ions from water. but this reaction will damage the formation and decrease the friction-reduction rate during slickwater fracturing. typical treatment procedure of slickwater fracking. several metal ions are generated and dissolved in fracturing fluid and flowback fluid. in the whole procedure, the fr is in a kind of brine environment. polyacrylamide-based frs will precipitate when they meet with different salts in water. the sizes of pam/hpam polymers are larger than most formation pores but smaller than fracture size. without metal ions, the formation damage caused by frs may not be that severe. reacting with metal ions, however, the pam/hpam frs coil or precipitate, the sizes are much bigger, and the formation damage becomes more serious. this paper further discusses uv-vis transmittance tests that indicate how metal ions in water affect hpam frs. a new less-damaging fr has much better results in the comparison tests. to summarize, the typical slickwater-fracturing treatment includes the following steps (table 3). table 3—different stages of slickwater fracturing (holloway and rudd 2015). no. pumping steps of slickwater fracturing fluid injected in each stage function 1 an acid stage several thousand gallons of water mixed with a dilute acid such as hydrochloric or muriatic acid this serves to clear cement debris in the wellbore and provide an open conduit for other frac fluids by dissolving carbonate minerals and opening fractures near the wellbore. 2 a pad stage approximately 100,000 gallons of slickwater without proppant material the slickwater pad stage fills the wellbore with the slickwater solution (described below), opens the formation and helps to facilitate the flow and placement of proppant material. 3 a prop sequence stage may consist of several substages of water combined with proppant material (consisting of a fine mesh sand or ceramic material, intended to keep open, or “prop” the fractures created and/or enhanced during the fracturing operation after the pressure is reduced) this stage may collectively use several hundred thousand gallons of water. proppant material may vary from a finer particle size to a coarser particle size throughout this sequence. 4 a flushing stage a volume of fresh water sufficient flush the excess proppant from the wellbore experimental studies molecular dynamics simulations for pam and hpam frs in different salt water. molecular dynamics (md) simulation helps determine the structures and interactions of molecular components in certain force-filled solutions. md is also a complement to conventional experimental approaches and enables observation of the different processes microscopically. md serves as a link between microscopic and macroscopic scales of time and length, predicts the bulk properties by simulating molecular interactions and behaviors, and provides a link between theoretical hypothesis and experimental results in this paper. the mechanism of formation damage caused by polyacrylamide-based frs is also further explained in a later section. fr selection. pam (polyacrylamide) and hpam (partially hydrolyzed polyacrylamide) are commonly used frs. the concentration of pam and hpam in slickwater typically ranges from 0.25 to 2 gal/1000 gal. considering the less fr concentration, the longer the simulation takes, it is better to use relative higher fr concentration during simulations to accelerate this simulation procedure. and fr-related formation damage always happens in reservoirs or after flowback, when much water molecues already filtrate into 6 rocks. in that condition, the real fr concentration is high. so, finally, the fr concentration in molecular dynamics simulations was 1.5 wt%, relative higher than normal dose in real treatment on site. main simulation steps. the main simulation steps included amorphous cells installation, forcite geometry optimization, npt (npt means the condition of constant particle number n, constant pressure p, and constant temperature t), nvt (nvt means the condition of constant particle number n, constant volume v, and constant temperature t), forcite analysis, and comparison of results and variables optimization. parameters for characterizing polymer solutions. the radius of gyration (rg) is used to quantify the conformation alteration of polymer chains. for the same polymer chain in salt water, the smaller the rg, the more the polymer chain coils. then, the coiled pam/hpam chains affected by metal ions lost the friction-reduction function and tend to flocculate. the radius of gyration, rg, is defined as the root mean square distance of the atoms in the molecule from their common center of mass, that is (eq. 1), 𝑅𝑔 = √(∑ 𝑚𝑖𝑠𝑖 2𝑁 𝑖=1 )/(∑ 𝑚𝑖 𝑁 𝑖=1 ),………………………………………………………………………..(1) where mi is the mass of atom i, si is the position of atom i with respect to the center of mass of the molecule, and n is the total number of atoms. pam polymer in salt solutions. material studio 2017r2 software was used to simulate molecular dynamics of pam-based frs in different salt solutions. for pam amorphous cells, one 20-repeat units pam, 5200 h2o molecules and different number of metal ions (ca2+, mg2+, fe2+ or fe3+) with corresponding number of chlorine ion, clconstituted a 53.8×53.8×53.8 å (1 angstrom (å) = 1×10-10 meters (m) = 0.1 nanometer (nm)) cube. smart algorithm, compass force field, 298k temperature, and 20ps simulation time were chosen. as a synthetic fr, pam is a long-chain polymer composed of repeating units of acrylamide (am) (figure 4). figure 4—molecular structures of polyacrylamide (pam). in this study, 20 repeated units were chosen for molecular dynamics simulations. 3d structure of pam in this simulation is shown as follows (figures 5 and 6). figure 5—non-ionic pam with 20 repeated units. in figure 5, the red dots are oxygen atoms, the blue dots are nitrogen atoms, the grey ones are carbon atoms, and the white ones are hydrogen atoms. the whole molecule is composed by 20-repeat units of pam polymer. 7 figure 6—pam polymer's 3d configuration alteration before nvt beginning (left) and after 20ps simulation (right). purple dots around the 20-unit pam molecule are fe2+. take the fecl2 solution simulation as an example. from the 3d configuration of the pam molecule changing along with simulation time, it is obviously that the pam polymer coiled in different metal ions’ solutions (figure 7). the radius of gyration evolution for non-ionic pam was analysed. the result shows that pam coils in all studied solutions. and the calcium ions affects pam-based solutions less than magnesium, but more than ferrous iron. the pam polymers coils in all solution candidates. as the concentration of salt goes up, the radius of gyration for pam becomes smaller. this result means that pam coils more. this trend matches hydraulic fracturing treatment industrial field experience. pam frs, interacting with ferric ions, lose more frictionreduction rate than when interacting with calcium ions. therefore, ferrous ions affect pam frs less than ferric ions and calcium ions. figure 7—radius of gyration evolution as pam interacts with various metal ions in different concentration. 0.24 0.26 0.28 0.30 0.32 0.34 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 rg , a concentration of metal ion , mol/l concentration of salt vs. radius of gyration for polyacrylamide polymer in salt solution (15gpt, 25℃) pam in fecl3 solution pam in cacl2 solution pam in mgcl2 solution pam in fecl2 solution 8 hpam in salt solutions. hpam (partially hydrolyzed polyacylamide) is the most common fr available. it is made by reacting sodium acrylate with acrylamide so that approximately 30% of the acrylamide groups are in the hydrolyzed form (figure 8). this hydrolyzed form improves the solubility in water, and makes the polymer more compatible with cationic minerals, and is commonly marketed as a 50% active dispersion in mineral oil. because it is widely used as a flocculant for water in paper manufacture and the cheapest fr, it is the most widely used in the fracturing treatment(montgomery 2013). figure 8—repeating monomer units of hpam. in this study, the structure of hpam (yegin et al. 2017) appears below (figure 9). the value of n is 5 and that of m is 2. as shown in figure 10, by converting concentration unit from weigh percentage to mol/l, it clearly shows that all radius of gyrations trend lines with monovalent metal ions are overlapped. the trend lines of bivalent metal ions are together in the plot. the trivalent ions’ line is far beneath the ones of bivalent metal ions. with the same mole of metal ions, the higher the electrovalence, the more severely the metal ion affect the hpam polymers. figure 9—hpam polymer with 4-repeat units. figure 10—radius of gyration evolution when hpam interacts with different metal ions in different concentration. md simulations of hpam also follow a trend that trivalent ions affect polymers more than bivalent ones, and the monovalent affect the polymers the least. 0.25 0.27 0.29 0.31 0.33 0.0 0.5 1.0 1.5 2.0 2.5 3.0 rg , a concentration of metal ion, mol/l concentration of salt vs. radius of gyration for hydrolyzed polyacrylamide polymer in salt solution(15gpt, 25℃) hpam in fecl3 solution hpam in cacl2 solution hpam in mgcl2 solution hpam in fecl2 solution hpam in nacl solution hpam in kcl solution 9 verifying the short-time simulations with long-time simulations. to accelerate simulations, one molecule of pam polymer with 20 repeating units was used instead of hundreds of thousands of repeating units pam in each cell. after comparing 20ps with 200ps simulation time, the radius of gyration results matched. it means 20ps simulation time is enough for all pam and hpam simulations (figures 11 through 13). figure 11—20ps md simulations vs. 200ps md simulations in ferric chloride solutions (1ps=10-12 s). figure 12—20 ps md simulations vs. 200ps md simulations in calcium chloride solutions. 0.321 0.3204 0.3197 0.3188 0.3179 0.3168 0.321 0.3197 0.3169 0.3165 0.3175 0.3185 0.3195 0.3205 0.3215 0 0.2 0.4 0.6 0.8 1 1.2 rg , a concentration of fe3+, wt% concentration of fe3+ vs. radius of gyration for polycrylamide polymer in polyacrylamide solution (1.5wt%) 20ps simuation 200ps simuation 0.321 0.3207 0.32 0.3194 0.3186 0.3178 0.3146 0.3123 0.3099 0.321 0.3201 0.318 0.3099 0.307 0.310 0.313 0.316 0.319 0.322 0 0.5 1 1.5 2 2.5 3 rg , a concentration of ca2+, wt% concentration of ca2+ vs. radius of gyration for polycrylamide polymer in polyacrylamide solution (1.5wt%) 20ps simuation 200ps simuation 10 figure 13—20ps md simulations vs. 200ps md simulations in magnesium chloride solutions. summary of simulations results. the molecular dynamics simulations for typical pam and hpam frs illustrated intra-molecular aggregation so that the rg decreases. pam-based frs coil in salt water. intramolecular interactions are obvious with formation damage risk. long chain and being charged are the two main inherent defects. prediction of a new fr for slickwater without formation damage.the simulations results show that pam-based frs coil in salt water. formation damage tends to happen after hydraulic fracturing with slickwater. in the molecular dynamics simulations, it shows that long chain and being charged are the two main inherent defects when using pam-based frs. a new frs can be predicted, at least including the following features. 1. relatively shorter polymer chain. the shorter, the better, even a chain as short as one micron. even if the short-chain polymer coils in salt water, its size is small enough to pass the fractures without plugging or blocking the pores. 2. without the long chain, the friction-reduction rate could be low. thus, nanoparticles may be introduced to the low velocity flow zone next to tubing walls. with these two features as guidelines, one new fr mixture is found. effects of metal ions on hpam frs in water few papers have shown transmittance results that frs affected by metal ions in water. metal ions force pam-based frs coil, so frs will lose friction-reduction rate. the transmittance tests show how the pure hpam frs are affected by each salt solution. fe3+, ca2+, mg2+ and na+ are the representative metal ions that hpam frs can encounter during the whole procedure in a slickwater fracturing job. experiments. the formula for calculating transmittance is transmittance equals light exiting the sample divided by light striking the sample. in the experiment, wavelength was 600nm. the hpam concentration was 0.12v%, based on field treatment experience. the molecular weight of hpam was around 12 million. normalized transmittance data was used to eliminate the time effect of friction-solution change. the hpam solution samples without salt were set to 100 and all the transmittance test results were compared, allowing for a determination of which kind of salt affects the polymers more than others (tables 4 and 5). 0.321 0.3209 0.32 0.3193 0.3187 0.318 0.321 0.3201 0.318 0.3175 0.3183 0.3191 0.3199 0.3207 0.3215 0 0.1 0.2 0.3 0.4 0.5 rg , a concentration of mg2+, wt% concentration of mg2+ vs. radius of gyration for polycrylamide polymer in polyacrylamide solution (1.5wt%) 20ps simuation 200ps simuation 11 table 4—transmittance results of hpam fr solution with different salts. salt ppm concentration,w% molarity transmittance, % normalized transmittance fecl3 0 0 0.00 7 100.00 10000 1 0.06 1 14.29 42300 4.23 0.26 1.9 27.14 cacl2 0 0 0.00 5.2 100.00 24200 2.42 0.22 6 115.38 155900 15.59 1.40 11.3 217.31 mgcl2 0 0 0.00 6.8 100.00 51100 5.11 0.54 7.9 116.18 209000 20.9 2.20 13.2 194.12 nacl 0 0 0.00 7.3 100.00 97100 9.71 1.66 11.3 154.79 198800 19.88 3.40 17.3 236.99 table 5—transmittance results of the less-damaging fr solution with different salts. salt ppm concentration, w% molarity transmittance, % normalized transmittance fecl3 0 0 0.00 101 100.00 6100 0.61 0.04 104 103.48 29500 2.95 0.18 98 97.51 cacl2 0 0 0.00 101 100.00 29800 2.98 0.27 98 97.51 67600 6.76 0.61 93.6 93.13 mgcl2 0 0 0.00 97.2 100.00 35900 3.59 0.38 99.9 102.78 57200 5.72 0.60 96.8 99.59 nacl 0 0 0.00 99 100.00 41100 4.11 0.70 100 101.01 81500 8.15 1.39 99 100.00 the transmittance results indicate that with the same concentration, hpam solutions have a lower transmittance value. compared with water, the transmittance of hpam solution with different salts is less than 20%, while the less-damaging fr solutions are almost the same, clear as distilled (di) water. except for fecl3, the transmittance value becomes smaller as the metal ion concentration increases. metal ions force polymers to bend or coil. without salts, the hpam polymers mostly relax in water. most light hits the polymers, and certain wavelength lights are absorbed. so, transmittance is low. as the hpam polymers are forced to bend or coil as metal ion concentrations increase, more and more space becomes available for light to escape. therefore, the transmittance becomes smaller and the solutions are clearer (figure 14). 12 figure 14—transmittance results of the less-damaging fr vs. hpam. for the less-damaging fr solutions, almost without any large polymers, very few light beams can hit the polymers and be absorbed while penetrating the solutions. in ferric chloride solutions, hpam reacted with ferric ions and flocculation formed, as shown in figure 15. there is no flocculation for the lessdamaging fr. figure 15—hpam vs. a less-damaging fr in fecl3 solutions (hpam: reacted with ferric ions and flocculated; less-damaging fr: no flocculation). in hpam solutions with calcium chloride (figure 16) and the ones with magnesium chloride (figure 17), as the salt concentration increases, some little white dots can be observed. it could be the very early stage of flocculation. for all the salt solutions in tests, the less-damaging fr does not precipitate or flocculate. except for fecl3 solution, the less-damaging fr’s solutions remained as clear as di water, as shown in figures 15 through 17. although, sodium chloride is one of the monovalent salts that affect polymers the least compared with divalent salts and trivalent salts. however, the colors of the solutions with different concentrations are different in figures 15 through 17. the background is black by design for better clarification of the flocculation process. the higher the concentration of nacl is, the clearer the solution, i.e., the black background appears unobstructed. it means hpam polymers stretch like barriers without 0% 20% 40% 60% 80% 100% 0% 3.76% 18.19% t ra n sm it ta n ce concentration of metal ion, mol/l concentration of salt vs. transmittance for new fr and hpam in salt solution (0.12v%, 25oc) new fr in fecl3 solution new fr in cacl2 solution new fr in mgcl2 solution new fr in nacl solution hpam in fecl3 solution hpam in cacl2 solution hpam in mgcl2 solution hpam in nacl solution 13 nacl, and the more na+, the more the polymers bend, so more space is available for light to pass through. the dark background (black) intensifies as sodium ion concentrations increase, as shown as figure 18 (right), which indicates a clearer solution with fewer flocculates. figure 16—hpam vs. a less-damaging fr in cacl2 solutions. figure 17—hpam vs. a less-damaging fr in mgcl2 solutions. 14 figure 18—hpam vs. a less-damaging fr in nacl solutions. viscosity concerns. for fracturing operations, proppant screenout in treatments is risky for wellbore integrity and equipment safe. conventionally, viscosity is one of the most important variables for proppant suspension in fracturing fluid (feng et al. 2017). stokes’ law was applied to designing most types of fracturing fluids, including guar-based fluids, cellulose-based fluids, and pam-based fluids, in which the sedimentation velocity is inversely proportional to the medium viscosity. later, the fluid elasticity was found to be another important variable that dominates proppant suspension (harris and harold 2000, naval and shah 2001; hu et al. 2015). in slickwater fracturing in shale reservoirs, the mechanism of proppant transport is different. since slickwater has only a small concentration of polymers (up to 2 gpt), it does not have high enough viscosity or elasticity required to keep the proppant in suspension. in this case, the proppant settles faster under static conditions, and proppant transport may be dominated by the movement of the proppant bank itself. three proppant transport mechanisms in slickwater have been proposed (coker and mack 2013; sun 2015). at very low velocity, little or no proppant is moved. at higher velocity, proppant grains roll or slide along the surface of the settled proppant bank (reptation creep). at even higher velocity, proppant grains bounce off the surface back into the flow stream (saltation). dufek and bergantz (2007) demonstrated that saltation depends on the coefficient of restitution which is defined as the ratio of the velocity with which the object leaves after a collision to the velocity with which it enters the collision. proppants with a higher coefficient of restitution and a lower friction coefficient than other proppants will be transported deeper into the fracture. coreflood experiment. the goal of fracking is to maximize production, the extent of which is directly linked to how much the formation is damaged after fracking. table 6 is a set of coreflood data corroborating the less-damaging nature of less-damaging fr (without using any breaker), which shows greater than 99% regained permeability. 15 table 6—cores data for coreflood. items value material synthetic quartz dimensions 2.5cm×8cm porosity 20% permeability 40-200 md n 2 flow time > 1 hour variables to measure the flow rate and the pressure of n 2 gas in contrast, industrial regulars fr-a and fr-b lead to less than 10% regained permeability, under presumably identical conditions. fr-a is a commercial dry powder fr, and fr-b is a regular emulsion fr. k1 (md) is the initial permeability, and k2 is the regained permeability (wu et al. 2017). arising from this less-damaging nature, the use of the less-damaging fr showed astonishing production enhancement of 56 folds or more than conventional means (table 7). table 7—coreflood results comparison between less-damaging fr to common commercial frs without breakers. frs k1 (md) k2 (md) regained permeability fr-a 172.7 12.76 7.4% fr-b 166.3 0.5 0.3% less-damaging fr 147.7 146.5 99.2% field tests comparative daily gas production through two wells on the same platform: one well fractured by slickwater with less-damaging fr (gas well #1); the other by a conventional inverse emulsion fr (gas well #2) (figure 19). figure 19—gas production rate: less-damaging fr (red) vs. conventional fr (blue). 16 results show that the less-damaging fr is three times more effective at increasing daily gas production than conventional inverse emulsion fr. • gas well #1: decline rate was 10% after three months of production. • gas well #2: decline rate was 30% after three months of production. gas well #2 production regime follows the statistical data. the literature reports an average 30% decline after three months of gas production on 838 wells (figure 20). however, the well fractured by slickwater with the less-damaging fr saved 20% of gas production, just by not damaging the formations. figure 20—barnett shale first-year production rates. conclusions results of the experimental studies and field tests conducted during this research lead to the following conclusions: 1. a systematic method is found to mitigate formation damage caused by frs. 2. the md simulations systemically explain how the commonly used frs interact with different metal ions in water. potential formation damage caused by frs in slickwater is confirmed by both md simulations and lab tests (uv-vis tests and coreflood tests). 3. md simulation saved time and cost for new formula inventions. 4. the coreflood and field results substantiate the finding/guidance for a less-damaging fr as impressive and directional. 5. the finding that the shrinkage/aggregation of pam is most sensitive to fe3+, then ca2+/mg2+, then na+/k+ is consistent with the typical fr performance. most frs lose performance in the presence of fe3+. one frequently reduces ferric (by iron reducer) to ferrous to minimize the negative influence of ferric, which is also consistent with our md simulations. 6. by combining molecular dynamics simulation, prediction, lab tests, and field tests, one more effective fr is found for slickwater with high salt-tolerant, almost non-damage to formations and more gas production. 17 acknowledgment gia alexander is acknowledged for editorial assistance in preparing this paper. conflicts of interest the author(s) declare that they have no conflicting interests. references barati, r. and liang, j. 2014. a review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells. journal of applied polymer science 131(16):1-9. carman, p.s. and cawiezel, k.e. 2007. 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spe-174801-ms. 18 tessier, a., campbell, p. g. c., and bisson, m. 1979. sequential extraction procedure for the speciation of particulate trace metals. analytical chemistry 51(7): 844-851. woodroof, r. a. and anderson, r. w. 1977. synthetic polymer friction reducers can cause formation damage. paper presented at the spe annual fall technical conference and exhibition, denver, colorado, 9-12 october. spe-6812-ms. wu, j.j., yu, w., ding, f., et al. 2017. a breaker-free, non-damaging friction reducer for all-brine field conditions. journal of nanoscience and nanotechnology 17(9): 6919-6925. yegin, c., jia, b., zhang, m., et al. 2017. next-generation supramolecular assemblies as displacement fluids in eor. paper presented at the spe europec featured at 79th eage conference and exhibition, paris, france, 1215 june. spe-185789-ms. rixing zhang is in the ph.d. program of petroleum engineering at texas a&m university. his research is mainly on the failure mechanism of common friction reducers used in slick-water. he has more than 14 years of experience in completion engineering, especially in high-pressure high-temperature (hpht) ultra-deep wells. hisham nasr-el-din is a professor in petroleum engineering department at texas a&m university. his research interests include well stimulation, formation damage, enhanced oil recovery, conformance control, interfacial properties, adsorption, rheology, cementing, drilling fluids, two-phase flow, and non-damaging fluid technologies. nasr-el-din has nearly twenty patents and has published and presented more than 575 technical papers. he has received numerous awards within saudi aramco for significant contributions in stimulation and treatment-fluid technologies and stimulation design, and for his work in training and mentoring. he serves on the society of petroleum engineers (spe) steering committees on stimulation and oilfield chemistry, is a review chairperson for the society of petroleum engineers journal (spe j.), and is a technical editor for spe production & operations (spepo) and spe development & completion (spedc). xiaochun jin has integrated industry, academic, management, and investment experience across asia, america, and the middle east. he has been dedicated to commercializing clean technology in the fossil industry, and industrializing clean energy. his investment portfolio includes biotechnology, geothermal energy, smart microgrid, hydrocarbon exploration & production, etc. he worked at bp america, weatherford, and blade energy partners, energy & geoscience institute at the university of utah. he has published 20+ papers in peer-reviewed journals and spe conferences. dr. jin holds a ph.d. degree in petroleum engineering from the university of oklahoma. jun jim wu is the president & cto of phoenix c&w, inc. he received his ph.d. from the university of toronto in 2004 and held various technical and managerial positions in multinational companies. his accomplishment is manifested by over 20 peer-reviewed journal publications in prestigious journals such as journal of the american chemical society and macromolecules, as well as 20 granted patents. lisa m. pérez is the manager of the laboratory for molecular simulation at texas a&m university. she strives to reveal the benefits of molecular modeling and computational chemistry to researchers and students at texas a&m university and to curious minds of all ages through outreach events. she has more than 10 years of research experience in the theoretical investigation of reaction mechanisms for transition metal containing enzyme systems. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1263 received june 2, 2023; revised september 14, 2023; accepted december 20, 2023. *corresponding author: eng_mrm@yahoo.com 1 optimization of oil-gas separation in the production stations at abo-sannan field case study mohamed ramadan mohamed kotb*, general petrolem company, cairo, egypt; galal mohamed abdelalim and said mohamed abdall aly, suez university, suez, egypt abstract the study employs aspen hysys simulation and optimization tools to investigate three different scenarios. this optimization aims to determine the optimal separator pressures for a two-stage gas-oil separation plant (gosp) as well as modified configurations for threeand four-stage separations while targeting maximum profit and best results. the study consists of three case scenarios. the first case study deals with the existing base station under normal and optimal operating conditions. the second case study involves modifying an existing t-oil plant by rearranging the separators to create sequential separators that operate under ideal conditions. the third case study explores adding one additional separator in series to the three existing separators in the series, all of which operate under optimal conditions. extracting oil and gas, reducing energy consumption. the crude oil reed vapor pressure (rvp) is set to 10 psi for all scenarios. this study resulted in significant improvements, including a daily increase in oil recovery of 1.8%, 2.3% and 2%, as well as a daily increase in net profit of 6.4%, 5.8% and 4.3%, respectively. specifically, simulations conducted in the three case studies revealed significant daily increases in oil recovery also highlight the potential for improved performance and economic benefits through improved t-oil plant and gosp operations, contributing to a more sustainable and profitable crude oil processing industry. the crude oil stabilization unit known as the t-oil plant within the gas-oil separation plant (gosp) is greatly enhanced by using the multiple separation stages. introduction the well stream typically contains a mixture of gas, oil, water, and condensates. to separate these components effectively, a series of separators are employed. the primary purpose of these separators is to utilize gravitybased forces to divide the extracted well fluid into its constituent parts (olugbenga et al. 2021). during this separation process, pressure plays a crucial role in determining the flow of liquids, and the resulting fractions are subsequently transported to a laboratory for analysis. this analysis allows us to discern the composition of gas, oil, and condensates within the well stream. therefore, not only does pressure impact well flow, but the separation of well fluids also provides valuable insights into each well's conditions (zeng et al. 2021). the initial phase of separation focuses on removing water from the well stream, followed by the separation of oil and gas in the production separator. both of these separation processes are gravity-driven, ensuring the efficient division of the different fluid components (wang et al. 2022). the objective of liquid separation is to generate a gas stream that is devoid of propane, as well as other hydrocarbons and crude oil constituents. this gas stream should remain stable under storage conditions to prevent the evaporation of crude oil during transfer to storage tanks. this is particularly important because 2 crude oil often contains light components that can evaporate due to slight variations in storage pressure and temperature (al-mhanna 2018). the process for achieving this separation involves a three-stage approach that is employed for separating well fluids. these stages consist of high-pressure, medium-pressure, and low-pressure separators. to reduce the water content in well fluids from 0.4 parts to approximately 0.05 parts, a three-phase high-pressure separator can be utilized. it's crucial to note that the initial stage of oil-gas separation from the well stream is the most critical step in the crude oil field processing. in the reservoir, high-pressure crude oil contains a significant number of dissolved gases (tian et al. 2022). to effectively separate the crude oil and obtain it in a stable state, it's essential to gradually reduce both its pressure and velocity. this reduction occurs within the gas oil separation plant (gosp). however, a challenge arises during this pressure reduction process in the gosp, as some of the lighter and more valuable oily hydrocarbons may escape with the gas into the vapor phase (mosleh et al. 2022). the purpose of crude oil stabilization is twofold: to align with market specifications and minimize the loss of liquid hydrocarbons within atmospheric storage tanks. this process reduces the volume of intermediate hydrocarbon components like propane and butane that transition to a vapor state, thereby increasing sales liquid volume while reducing vapor pressure (bakyani et al. 2018). one of the methods employed in crude oil stabilization is stage separation. in this process, the well stream undergoes a series of equilibrium flashes within a gas oil separation plant (gosp), gradually reducing the pressure until it matches atmospheric tank pressure. this results in a more stable tank liquid (alireza et al. 2008). while increasing the number of separation stages can yield more valuable recovered liquids, practical constraints often limit the actual number of separations due to operational costs (sarvestani et al. 2009). for low water and gas oil preparation plants dealing with oils containing minimal water and gas (less than one-third of the total mixture), a single-stage separation is typically sufficient. however, in cases involving oils with higher water and gas content, a two-stage separation system is recommended and commonly employed (andreasen 2020). when comparing the three-stage separation process to the four-stage separation process, it has been observed that the four-stage separation provides a higher liquid recovery, with an increase of up to 25%. however, it is important to note that these units are constrained by both capital and operating costs, which can be substantial in many separation facilities (mahmoud et al. 2019). while it is theoretically true that increasing the number of consecutive separation stages should result in higher liquid recovery, practical limitations come into play. factors such as available space, fixed costs, and operating expenses impose constraints on the number of stages that can be effectively employed (al-jawad et al. 2010). in practice, the number of stages typically falls within the range of two to four, and the choice depends on variables such as the gas-to-oil ratio (gor) and the well stream pressure (wsp), as illustrated in table 1. table 1—stages of oil specifications. no. of stages oil specifications 2 stages low gor and wsp 3 stages medium gor and intermediate wsp 4 stages high gor and wsp usually, the three-stage separation process represents the economic optimum, offering a liquid recovery rate that is 2-12% higher than that of a two-stage separation process. in certain cases, it can even achieve liquid recovery rates up to 25% higher (al-maliki and and madhi 2019). the quantities of recovered gas and oil at a specific pressure are determined through equilibrium flash calculations, using an equation of state (eos) (edwin et al. 2017). 3 the existing gas/oil separation plant is a two-stage separation gas/oil separation plant (gosp) consisting of two parallel separators and an atmospheric tank in series. the plant receives two different pressure streams (high and medium pressures), which are pre-heated and directed to two parallel separators (high and medium pressure separators). these separators separate the oil to meet the required specifications (rvp) for the sales pipeline and send the gas to a compression station to increase its pressure to 650 psig. the operating pressure significantly influences separator performance as it determines the liquid exit rate and can be regulated using a back valve that controls the air pumping, thereby affecting the flow of separated gas into the gas pipeline (kylling 2009). while both pressure and temperature are factors in controlling fluid recovery, the ambient temperature within the separators remains consistent, resulting in them operating at the same surface temperature. consequently, pressure is the primary factor influencing improved results, leading to higher separator pressures and a larger presence of light components in the liquid phase (kim et al. 2014). conversely can lead to the separation of many light components in the liquid phase, while conversely, it can attract significant quantities of medium and heavier contents. therefore, it is advisable to adjust the separator pressure during both winter and summer seasons to maximize fluid recovery (hajivand and vaziri 2015). this study comprises four hysys simulation cases. the first case represents the existing two-stage separation plant, with the process flow outlined in table 1. the second case involves optimizing the first case to identify the most efficient operating conditions that yield the highest net profit, balancing oil recovery and energy consumption. the third case investigates the impact of rearranging the separators, transforming the two separators into a series of three-stage separations, on oil recovery, energy consumption, and net profit. the fourth case assesses the effects of adding an additional separator in series, resulting in a four-stage separation, on oil recovery, energy consumption, and net profit. methodology the study employed aspen hysys process simulation (version 8.8) using the peng-robison equation of state as the primary tool. the main focus of this simulation was the optimization of an existing gas oil separation plant (gosp) with the aim of maximizing profit while achieving a reid vapor pressure (rvp) within the range of 10-12 psia. the process involves two manifold streams: one operating at high pressure and the other at medium pressure. table 2 displays the composition of crude oil feeds and the operating conditions of the crude oil streams from the manifold to the gosp inlet. table 2—feed streams composition. hp crude oil feed-1 mp crude oil feed-2 s. pressure (psi) 250 s. pressure (psi) 35 component mole % component mole % c1 56.14 c1 31.09 c2 7.24 c2 10.31 c3 5.58 c3 15.56 ic4 1.55 ic4 3.00 nc4 2.28 nc4 4.67 ic5 1.47 ic5 1.74 nc5 1.37 nc5 0.74 nc6 3.14 nc6 3.22 c7+ 20.39 c7+ 29.35 n2 0.09 n2 0.01 co2 0.65 co2 0.05 h2s 0.00 h2s 0.00 h2o 0.09 h2o 0.25 4 additionally, figure 1(a) illustrates the pressure-temperature envelope of the high-pressure crude oil stream, while figure 1(b) presents the pressure-temperature envelope of the medium-pressure crude oil stream. in figure 2, a process flow diagram of the aspen hysys simulation for the gosp is depicted. (a) (b) figure 1—pressure-temperature envelope diagram of crude oil flow under different pressures: (a) high-pressure region; (b) medium-pressure region. figure 2—aspen hyses simulation process diagram. table 3(a) provides a detailed overview of the operating conditions, including separator pressure, separator temperature, energy consumption, oil recovery, and gas recovery. these streams pass through pre-heaters to adjust the fluid temperature before entering the high-pressure separator (operating at 250 psig and 25°c) and the medium-pressure separator (operating at 35 psig and 30°c). gases separated in the process are collected and sent to the abu-sannan condensate recovery plant via compressors. the oil stream is directed through a heater to raise its temperature to achieve the target rvp of 10-12 psia before being stored in a tank. furthermore, table 3(b) provides details on the optimum operating conditions, including separator pressure, separator temperature, energy consumption, and oil recovery, for the actual two-stages gosp optimization case (the second case) with an rvp of (10-12) psia. in the third case of gosp modification, the parallel separators in the main hysys case were rearranged into series separators, resulting in a three-stage separation plant. this configuration was then optimized to determine the optimum operating conditions, energy consumption, oil/gas recovery, and net profit, as detailed in table 3(c). figure 3 illustrates the simulation process flow diagram for the three-stage gosp modification. 5 figure 3—pfd for the three-stage gosp modification. in the fourth case of gosp modification, an additional separator was installed in the third case, resulting in a four-stage separation plant. this configuration was subsequently optimized to determine the optimum operating conditions, as presented in table 3(d). figure 4 depicts the simulation process flow diagram (pfd) for the four-stage gosp modification. figure 4—pfd of the four-stage gosp modification. results and discussion there exists a great effect of separators pressure on the oil, gas recoveries, the required heaters duty, compressors power and therefore the net profit of the gosp. the idea of stage separation is essential as it reduces the propensity of intermediate and heavy hydrocarbons to be vaporized as the pressure decreases gradually. 6 table 3—all scenarios’ operating conditions. (a) actual 2 stages separation operating conditions pressure psig temp. ⁰c pr-heater duty kw gas comp. power kw gas rate mmscfd oil production bbl/d gas recovery mmscfd hp separator 250 25 250.2 2192 23.63 18410 33.56 mp separator 35 30 178.6 721.7 9.93 rvp (psig) h.v. (mj/m3) lp separator 7 66 2831 77.59 3.5 -4.729 54.41 (b) optimization of 2 stages separation operating conditions pressure psig temp. ⁰c pr-heater duty kw comp. power kw gas rate mmscfd oil production bbl/d gas recovery mmscfd hp separator 281 23 0 1604 23.29 18750 33.2 mp separator 20 14 23.02 1127 9.903 rvp (psig) h.v. (mj/m3) lp separator 0 31 1240 147.1 3.556 -4.697 53.09 (c) optimization of 3 stages separation operating conditions pressure psig temp. ⁰c pr-heater duty kw gas comp. power kw gas rate mmscfd oil production bbl/d gas recovery mmscfd hp separator 400 27 0 958 22.42 18830 33.09 mp separator 30 23 383 1230 10.67 rvp (psig) h.v. (mj/m3) lp separator 0 39 1224 82 1.482 -4.697 52.84 (d) optimization of 4 stages separation operating conditions pressure psig temperature ⁰c pr-heater duty kw gas comp. power kw gas flow mmscfd oil production bbl/d gas recovery mmscfd hp separator 440 27 0 758 22.22 18770 33.14 mp separator 200 28 0 195 5.648 rvp (psig) h.v. (mj/m3) 3rd stage 36 51 2000 614 3.592 -4.793 53.09 lp separator 0 43 0 104 1.679 actual two-stages separation case without optimizer. table 3(a) presents the initial separators’ pressure in the un-optimized two-stage gosp. this pressure is notably influenced by wellhead pressures and pressure losses incurred through production pipelines. furthermore, table 3(a) displays the operating conditions of the high pressure separator (250 psig, 25°c), the medium pressure separator (35 psig, 30°c), the low pressure stage (7 psig, 66°c), which was achieved by a 3259.8 kw pre-heating process, aimed at meeting the final product of 18,410 bbl/d of oil recovery while maintaining a reid vapor pressure of 10 psia. the effect of separators pressure on the oil/gas recovery in two-stage gosp. figures 5 illustrate the pressure effects on oil and gas recovery in a two-stage separation plant. figure 5(a) demonstrates how the highpressure separator reduces oil recovery while increasing gas recovery. figure 5(b), on the other hand, shows how the medium pressure separator initially increases oil recovery but decreases gas recovery. 7 (a) (b) figure 5—the influence of pressure on oil and gas recovery in a two-stage separation plant. optimization of two-stages separation. table 3(b) presents the separators’ operating conditions obtained after optimizing the two-stage gas oil separation plant (gosp), along with the corresponding the highpressure separator (283 psig, 23°c), the medium pressure separator (20 psig, 14°c), the low pressure stage (0 psig, 31°c), achieved through a pre-heaters duty of 1263.02 kw. these adjustments were made to fulfill the reid vapor pressure requirement of 10 psia for a final product of 18,750 bbl/d oil recovery. optimization of three-stages separation. in table 3(c), the separators’ operating conditions for the optimized three-stage gosp are displayed, along with the high-pressure separator (400 psig, 27°c), the medium pressure separator (30 psig, 23 °c), the low-pressure stage (0 psig, 39 °c). to meet the reid vapor pressure specification of 10 psia for a final product of 18,830 bbl/d oil recovery, a pre-heaters duty of 1607 kw was necessary. the effect of separators pressure on the oil/gas recovery in three-stage gosp. we examine the pressure effects on oil and gas recovery in a three-stage separation plant (figure 6). figure 6(a) reveals that the highpressure separator leads to a dome-shaped curve for oil recovery (an initial increase followed by a decrease) while increasing gas recovery. figure 6(b), focusing on the medium pressure separator, shows a similar pattern with an initially increasing curve for oil recovery and an initially decreasing curve for gas recovery. （a) (b) figure 6—the influence of pressure on oil and gas recovery in a three-stage separation plant. optimization of four-stages separation. table 3(d) illustrates the separators’ operating conditions for the optimized four-stage gosp, which involves the addition of a third separator incurring an additional cost. the corresponding high-pressure separator (440 psig, 27°c), the 1st medium-pressure separator (200 psig, 28°c), the 2nd medium-pressure separator (36 psig, 51°c), the low-pressure stage (0 psig, 43°c) were achieved through a 8 pre-heater ’s duty of 2000 kw, aiming to meet the vapor pressure requirement of 10 psia for a final product of 18,770 bbl/d oil recovery. (a) (b) (c) figure 7—the influence of pressure on oil and gas recovery in a four-stage separation plant. 9 the effect of separators pressure on the oil/gas recovery in four-stage gosp. figure 7 explore the pressure effects on oil and gas recovery in a four-stage separation plant. figure 7(a) displays a dome-shaped curve for oil recovery with the high-pressure separator, along with an increase in gas recovery. figure 7(b) depicts the impact of medium pressure separator 1, resulting in a decrease in oil recovery and an initial decrease followed by an increase in gas recovery. figure 7(c), focusing on medium pressure separator 2, shows a similar pattern to figure 7(b), with an initially increasing curve for oil recovery and an initially decreasing curve for gas recovery. summary of result. the summary table of optimization results (table 4) reveal the following findings for various scenarios. comparison of multistage optimizers with actual gosp case (table 4(b)), which provides a comparison between the actual and optimization cases, reveals significant improvements in oil recovery, energy efficiency, and overall profitability across the different scenarios. case-1 represent actual gosp scenario. the actual gas-oil separation plant (gosp) consumed 3259 kw of energy by pre-heaters and achieved an oil recovery rate of 18410 barrels per day (bbl/d) with a net profit of $1,530,000 per day. case-2 is the optimization case for actual gosp. in this scenario, optimization reduced the energy consumption to 1263 kw by pre-heaters, increased the oil recovery rate to 18750 bbl/d, and raised the net profit to $1,630,000 per day. the comparison table 4(b) showed that an increase in oil recovery achieved by 1.8%, a reduction in total energy consumption by 34%, and an increase in net profit by 6.4% in comparison with the actual gosp. case-3 represents optimization scenario for three-stage separation modified plant. the optimization of a modified plant with a three-stage separation process resulted in an energy consumption of 1607 kw by preheaters, an oil recovery rate of 18830 bbl/d, and a net profit of $1,620,000 per day. the comparison table 4(b) showed an increase in oil recovery by 2.3%, a reduction in total energy consumption by 38%, and an increase in net profit by 5.8%. case-4 is the optimization result for four-stage separation modified plant. the optimization led to an energy consumption of 2000 kw by pre-heaters, an oil recovery rate of 18770 bbl/d, and a net profit of $1,597,000 per day. the comparison table (4b) showed an increase in oil recovery by 2.0%, a reduction in total energy consumption by 41%, and an increase in net profit by 4.3%. through optimization efforts, the energy consumption of the gosp was significantly reduced to only 1263 kw, indicating a substantial improvement in energy efficiency.the optimization also led to an increase in the oil recovery rate, reaching 18750 bbl/d, which is higher than the initial scenario.these findings highlight the positive impact of optimization on the gosp’s performance in several key aspects. 1. energy efficiency. the optimization efforts led to a remarkable reduction in energy consumption by the pre-heaters, indicating a more energy-efficient operation. this not only reduces operating costs but also contributes to environmental sustainability by lowering energy usage. 2. increased oil recovery. the gosp's ability to recover more oil per day is a crucial metric in the oil and gas industry. the optimization resulted in a significant increase in oil recovery, which can lead to higher revenue generation for the company. 3. improved profitability. the combination of reduced energy costs and increased oil recovery directly contributed to a higher daily net profit. this is a clear indicator of the financial benefits of optimization efforts. in summary, the optimization of the gas-oil separation plant had a positive impact on both its operational efficiency and financial performance. these improvements not only enhance profitability but also demonstrate a commitment to resource conservation and environmental responsibility. further analysis and monitoring may be necessary to ensure the sustainability and long-term success of these optimization efforts. the provided information discusses the optimization of a modified plant with three-stage and four-stage separation processes in the context of the gas oil separation plant (gosp) industry. the goal of these optimizations is to improve oil recovery, reduce energy consumption, and increase net profit. let's break down the key findings and implications of these optimization cases. 10 the four-stage separation process, despite slightly lower oil recovery, benefited from optimizer-3 by achieving significant reductions in energy consumption and a moderate increase in net profit. overall implications. these optimization cases demonstrate that investing in advanced optimization strategies can lead to substantial improvements in the gosp industry. optimizations across different scenarios consistently showed enhanced oil recovery, reduced energy consumption, and increased profitability. the choice between four-stage and three-stage separation processes depends on a trade-off between energy efficiency and oil recovery, with the three-stage process showing better performance in these specific cases. these findings underscore the importance of ongoing research and optimization efforts in the energy sector to maximize resource utilization and economic benefits. table 4—results summary and comparisons. (a) final results summary energy consumed oil recovery gas recovery net profit ($/d) heaters (kw) comp.s (kw) prod. (bbl/d) prod. (mmscfd) case 1: one-stage separation 3259 2991.29 18410 33.56 1532285 case 2: one-stage separation optimization 1263.02 2878.1 18750 33.2 1630396 case 3: two-stages separation optimization 1607 2270 18830 33.09 1621818 case 4: three-stages separation optimization 2000 1671 18770 33.14 1597739 (b) multistage profits’ comparisons with actual case energy consumed diff. oil recovery diff. gas recovery diff. net profit diff. $/d total energy diff. 2&3 stages kw heaters (kw) comp.s kw prod. bbl/d prod. mmscfd 1 stage comparison (actual /optimization cases) -1995.98 -113.19 340.00 -0.36 98111.00 -2109.17 -61.2% -3.8% 1.8% -1.1% 6.4% -33.7% 1&2 stages comparison (actual /optimization cases) -1652.00 -721.29 420.00 -0.47 89533.75 -2373.29 -50.7% -24.1% 2.3% -1.4% 5.8% -38.0% 1&3 stages comparison (actual /optimization cases) -1259.00 -1320.29 360.00 -0.42 65453.91 -2579.29 -38.6% -44.1% 2.0% -1.3% 4.3% -41.3% 11 conclusions the study focused on simulating and optimizing the gas-oil separation plant (gosp) process using the aspen hysys model, considering real-world conditions and fluid compositions. the main objectives were to maximize oil recovery, minimize energy consumption, and maintain a target reid vapor pressure. key findings include: 1.optimizing the existing two-stage separation process was the most economically advantageous scenario, increasing net profit by $98,000 per day (a 6.4% improvement). 2.the optimization significantly reduced energy consumption, with heaters using 61% less energy and gas compression seeing a 4% decrease. 3.the optimization also increased oil recovery by 2.3%, demonstrating its effectiveness. 4.separator pressure was crucial in optimizing the process for maximum profit and minimal energy consumption, emphasizing the need for careful control and adjustment. 5.considering wellhead pressure and pressure drop in upstream pipelines impacting delivered pressure and separation stages is essential for optimization. in summary, this comprehensive 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interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1196 received october 21, 2021; revised november 13, 2021; accepted december 29, 2021. *corresponding author: jiangshl3@cnooc.com.cn 1 data mining: caliper prediction based on gamma logging while drilling shaolong jiang*, supervision & consultancy center, cnooc, tianjin, china; guoqiang zhang, well construction and intervention center, cnooc, tianjin, china; renguo yuan, xin li, and enlong feng, supervision & consultancy center, cnooc, tianjin, china abstract during offshore drilling and completion operations of production adjustment wells, logging while drilling (lwd) is often adopted to improve the timeliness of drilling. in order to provide more reliable decisionmaking basis under limited data conditions, a study on data mining is needed. by collecting and analyzing 55 sets of data on wells in the pl block of bohai oilfield, the main controlling environment factors of the gamma geophysical response were identified. and based on adjacent well interpolation prediction, a mathematical model of predicted gamma/measured gamma difference versus caliper curve was built. this model was applied to e59 well, providing a decision-making basis for its subsequent casing running operation. it is found that: (1) with increasing potassium ion concentration and mud specific gravity, the geophysical response of gamma logging while drilling (glwd) increases gradually; potassium ions have the most significant influence on gamma, and the influence increases with increasing caliper; (2) the caliper prediction model built based on the gamma-difference scatter fitting function and measured caliper has some engineering applicability in pl block; (3) the in-depth mining of the glwd geophysical response data is of directive significance to field drilling and completion operations, yet various sources of data need to be utilized for comprehensive analysis. the successful application of this method provides an idea for accurately guiding drilling and completion operations, a way to increase the utilization rate of logging data, and an important technical support to increase reserve and production and promote engineer-geology integration in the bohai sea. introduction in modern offshore drilling and completion operations, lwd is usually adopted to lower production cost and improve operational safety and quality. due to the limitation by the features of lwd and in order to reduce the operation cost of the development adjustment well, there are generally only two curves in lwd–gamma curve and resistivity curve, which often leads to a lack of caliper curve data of the development adjustment well. different from an exploratory well, a development adjustment well usually has a large deviation or it can even be a horizontal well, so decision making is more dependent on the understanding of the sidewall conditions. however, the missing of caliper curve data in lwd poses great challenges for understanding of the sidewall conditions and providing a decision-making basis for subsequent drilling and completion operations (xu et al. 2019). in view of this, we hope to obtain more efficient geological engineering information only by the gamma curve and the resistivity curve, thus providing support for decision-making in subsequent operations (shen et al. 2015). the main direction of the study is to further perform data mining mailto:jiangshl3@cnooc.com.cn 2 based on large data analysis, to find relationships between data and data, to allow full use of existing log data and to solve the geology-engineering integration problem (ma et al. 2014). figure 1—gamma geophysical logging response and data application. in the field, the gamma geophysical logging response is affected by two aspects the formation and the engineering, as shown in figure 1. the formation influences include radioactive material, lithology, particle distribution characteristics, sedimentation characteristics, and waterflooding characteristics. the response rule in this aspect can be used to interpret the glwd data, such as the calculation of the mud content, the classification of the lithology, the evaluation of the reservoir, the study of the characteristics of the particle distribution, the evaluation of sedimentary facies, the evaluation of the water flooded layer and the analysis of the injectivity of water injectors (cripps and mccann 2000). the engineering influences include mud barite, potassium ion content, caliper size, and mud specific gravity (wang 2011). since our study focuses on formation, we usually use the type curve to correct and eliminate engineering influences, to ensure that the gamma geophysical logging response merely contains formation information without interference from engineering information (liu 2006). in the main direction of the geology-engineering integration study, the main technical challenge is how to explore more values of existing data and how to provide more reliable decision-making for subsequent drilling and completion operations (frahm and lemke 2010). for this purpose, we studied the main factors influencing glwd, tried to make an interpolation prediction for the target well data based on the existing adjacent well data, used the difference between the gamma value and the measurement gamma value to fit the measured caliper, and built a model (klaus 2010 ). we studied glwd data mining and found a method to predict the caliper and to understand the stability status of the sidewall through glwd. this method can provide efficient technical support and a decision-making basis for subsequent drilling and completion operations. influence factors in glwd influence of potassium ions on glwd curve. to identify the environmental influence factors and the main controlling factors during field operation of glwd, we collected 55 sets of logging data of 40 development adjustment wells operating in pl block of bohai oilfield from 2018 to 2019, and analyzed the 3 glwd distribution of sandstone and mudstone formation under different potassium ion concentrations, as shown in figure 2. (a) (b) figure 2—distribution of the mean glwd of sandstone and mudstone formation under different concentrations of potassium ions. figure 2a shows the distribution of glwd mean values in dimensions of sandstone formation and mudstone formation at different potassium ion concentrations. figure 2b is the dimensionless relationship diagram. as can be seen in the figure, with the increase in potassium ion concentration, the glwd response value exhibits a gradual increase trend and the trend is almost the same for sandstone and mudstone (we can see from figure 2a that the slope adjusted for the formation of mudstone is 8.95, while that of sandstone is 7.53), indicating that potassium ions have the same influence on the sandstone formation and mudstone formation, which is in agreement with the phenomena we usually observe in field operation. the fitted rsquared ranges from 0.59-0.62, indicating that such fitting relationship is significant, in other words, potassium ions have a significant influence on gamma geophysical response. to better understand the influence of potassium ions on the glwd curve, we collected logging data from 40 development adjustment wells and analyzed the distribution of glwd of 8.5-inch and 12.25-inch borehole sizes under different concentrations of potassium ions, as shown in figure 3. (a) (b) figure 3—distribution of the mean glwd of different borehole sizes at different concentrations of potassium ions. 4 figure 3a shows the distribution of glwd mean values of different borehole sizes in dimensions under different concentrations of potassium ion; figure 3b is the dimensionless relationship diagram. as can be seen in the figure, with the increase in potassium ion concentration, the geophysical response of glwd increases gradually. from the fitted curve (figure 3a), we can see that the fitted slope of the 8.5-inch borehole is 10.27, while that of the 12.25-inch borehole is 14.41, indicating that the rate of increase in gamma response of the 8.5-inch borehole with increasing potassium ion concentration is smaller than that of 12.25-inch. this is because the increase of the caliper causes an increase of the response of the logging instrument to the mud in the wellbore. influence of mud specific gravity on glwd curve. through literature research, we have known that the geophysical response of glwd is influenced by the specific gravity of the mud. to understand the degree of such influence on logging data of the study area, we collected 55 sets of logging data of 40 development adjustment wells operating in pl block of bohai oilfield from 2018 to 2019, and analyzed the glwd distribution rule of sandstone formation and mudstone formation under different mud specific gravities, as shown in figure 4. (a) (b) figure 4—distribution of the mean values of glwd of the sandstone formation and mudstone formation under different mud specific gravities. figure 4a shows the distribution of the mean glwd of sandstone formation and mudstone formation in dimensions under different mud specific gravities; figure 4b is the dimensionless relationship diagram. as can be seen in the figure, with the increase in mud specific gravity, the geophysical response of glwd gradually increases. however, compared to the influence of potassium ion concentration, the influence of mud specific gravity is relatively small. this can be seen from the fitted r-squared. the r-squared of the mudstone formation and sandstone formation is between 0.22 and 0.25, slightly lower than the fitted value in the case of potassium ion concentration, indicating that the change in mud specific gravity has a relatively weak influence on the geophysical response of glwd. it can be seen from the distribution rule of mudstone and sandstone that the rate of change in the influence of different mud specific gravities on the geophysical response of glwd under different lithologies is the same, indicating that the influence of mud specific gravity on the geophysical response of glwd formations with different lithologies is the same. to better understand the influence of mud specific gravity on the glwd curve, we collected logging data from the 40 development adjustment wells and analyzed the geophysical response distribution of the glwd of 8.5-inch and 12.25-inch borehole sizes under different mud specific gravities, as shown in figure 5. 5 (a) (b) figure 5—glwd mean value distribution of different borehole sizes under different mud specific gravities. figure 5a shows the distribution of the mean glwd in dimensions of different borehole sizes under different mud specific gravities; figure 5b is the dimensionless relationship diagram. as can be seen in the figure, with the increase in mud specific gravity, the geophysical response of glwd gradually increases. the fitted r-squared indicates a significant fitting effect (the fitted r-squared of both 8.5in borehole and 12.25-inch borehole is 0.27). the influence of mud specific gravity on the gamma curve is relatively weak compared to potassium ions. by comparing the influences of mud specific gravity on glwd geophysical response in different boreholes, we can see that the slope of 12.25-inch borehole is high (figure 5 b), the slope of 12.25-inch borehole is 1.3, while that of 8.5-inch borehole is 0.6). this indicates that the gamma value is more susceptible to mud specific gravity in 12.25-inch borehole. the reason is that the larger the radius of a well, the more contributions the mud in the well makes to the logging instrument. based on the statistics of the 55 sets of logging data, we analyzed the influence of four groups of different influence factors on glwd geophysical response. by conducting comparison and analysis, we found that with the rise of potassium ion concentration and mud specific gravity, the glwd geophysical response increases gradually; potassium ions have the most significant influence on gamma; and the bigger the caliper, the greater the influence of potassium ions on glwd geophysical response. building a caliper prediction model by statistical analysis and analysis of regional data, we found that the larger the caliper, the greater the influence of potassium ions on the geophysical response of glwd. based on this study result as well as the existing logging data and geological data for pl block, we built a caliper prediction model. we used the data of two groups of wells selected from 40 development adjustment wells operating in pl block from 2018 to 2019 for modeling. figure 6 is the regional tectonic map of the data from the two groups of wells at layer l50. figure 6a shows the data for the first group of wells, that is, three directional wells g45, g43 and g44 completed at the beginning of 2019. figure 6b shows the data of the second group of wells, that is, j07, j41, and j27. these wells penetrate the formation, with full coverage and complete logging data (including glwd and caliper data), and are representatives of all the development adjustment wells in the block. 6 (a)g45, g44 and g43 wells (b)j07, j41, and j27 wells figure 6—regional tectonic map of the data from the two groups of wells at layer l50. creation of prediction curve based on adjacent well data. to create the prediction curve, we need to rely on the logging data of the target well’s adjacent wells, including glwd curve and caliper curve. here we take three wells (g45, g43 and g44) for example. note that they are all highly-deviated wells, so we first need to make the true vertical depth (tvd) conversion for the data of g45 and g44 wells, that is, the tvd coordinate system rather than the along-hole depth coordinate system is to be used. by interpolation between g45 and g44 wells, the predicted gamma curve and predicted caliper curve of g43 well can be obtained. the calculation eq. 1 to 4 are as follows: ���43' = �1���45 + �2���44,………………………………………..………………………………….(1) ��43' = �1��45 + �2��44,……………………………………………….………………………………(2) �1 = �4345 �4445 = �43−�45 2+ �43−�45 2 �44−�45 2+ �44−�45 2,………………………………………………………………………(3) �2 = 1 − �1,………………………………………………………..…………………………………….(4) where ��� is the caliper, in; �� is gamma, api; �1, �2 are interpolation coefficients, related to geographic location; � is distance between two wells (m); �, � are x and y coordinates of wellhead, m. using the interpolation calculation method, we can get the predicted gamma curve and predicted caliper curve of g43 well (expressed with ��43' and ���43' respectively). figure 7a shows the predicted gamma curve and predicted caliper curve of g43 well at tvd 1300-1600m, and figure 7b shows the predicted gamma curve and predicted caliper curve of j41 well at tvd 1350-1650m. as can be seen in figure 7a, since g45 well and g44 well penetrate the same formation, these gamma curves and caliper curves at tvd show a similar fluctuation rule. it is worth noting that the selected gamma curves of g45 and g44 wells are logging data subject to potassium ion and caliper corrections, which only reflect the formation characteristics, without considering the wellbore influence. therefore, the gamma curve and caliper curve of g43 well predicted on this basis are not influenced by the wellbore. it can be seen from figure 7b that j07 well and j27 well penetrate the same formation, so the gamma curves and the caliper curves in tvd exhibit a similar fluctuation rule. compared with the formation shown in figure 7a, j07 and j27 wells present an obvious difference on their caliper curves (tvd 1580-1650m), this may be associated with the engineering problem encountered in drilling of j07 well. 7 (a) (b) figure 7—prediction of the gamma curve and the caliper curve of the g43 and j41 wells based on the interpolation method. calculation of difference based on measured gamma and predicted gamma. based on the study results above, we can get the predicted gamma curve and predicted caliper curve of g43 well. in actual drilling process, the measured gamma geophysical response of g43 well considers the influence of environmental factors in wellbore, so we calculate the difference between the measured geophysical response and the predicted gamma and obtain a difference gamma curve. figure 8 shows the difference gamma curves obtained based on the difference between the predicted gamma and the measured gamma. figure 8a shows the difference gamma curve and measured caliper curve (tvd 1300-1370m) of the g43 well, and figure 8b shows the difference gamma curve and measured caliper curve (tvd 1350-1420m) of the j41 well. according to the analysis, we can know that difference gamma actually reflects the response of potassium ions in wellbore and caliper to the logging instrument. this response, under a given potassium ion concentration, shall have a certain functional relationship with the caliper. it is easy to see from the comparison of the two wells in figure 8 that there is a correlation between the difference gamma and the measured caliper. 8 (a) (b) figure 8—comparison between the difference curve based on the predicted gamma & measured gamma and the measured caliper. establishment of function relationship between difference gamma and caliper. by statistics, analysis and fitting of the difference gamma curve and measured caliper curve data in above section, we can obtain the scatter fitting relationship between the difference gamma and measured caliper, as shown in figure 9. figure 9a shows the scatter fitting data of difference gamma and measured caliper of g43 well at tvd 13001370m, and figure 9b shows the scatter fitting data of difference gamma and measured caliper of j41 well at tvd 1350-1420m. through comparison between difference gamma curve and caliper curves of 26 wells, it is found that there is linear correlation between them. the function relationship between the difference gamma and the caliper can be obtained by statistics and fitting, which is expressed by eq. 5 and eq. 6. (a) (b) figure 9—scatter fitting relationship between the difference gamma and the measured caliper. 9 ����43 = 0.6872∆���43 + 13.513 (� = 0.5765),………………………….………………………….(5) ����41 = 0.6946∆���41 + 12.911 (� = 0.5635),………………………….…………………………..(6) the scatter fitting relationship between difference gamma and measured caliper is obtained by fitting. from the perspective of fitting results, this method can be used for caliper prediction, and the prediction results have good performance. in pl block, the mathematical model eq.7 can be used to predict the caliper by difference gamma, to understand the conditions of the sidewall, and to provide technical support and a decision-making basis for subsequent drilling and completion operations. ���' = 0.69∆�� + 13.1,…………………………………………………………………………………(7) where ���' is the predicted caliper, in; ∆�� is the difference of gamma ray, api. model verification and analysis. we got a mathematic model (eq. 7) of gamma-based predicted caliper curve by a series of mathematic methods. to verify this model and to perform an analysis of stability and significance, we compared the measured calipers with predicted calipers between two other wells (j04 and j56) in pl block, and the results are shown in table 1. table 1—comparison between the measured and predicted caliper. well name tvd (m) r remarks plg43 1300~1370 0.4931 modelling plj41 1350~1420 0.4421 modelling plj04 1325~1395 0.3901 verification plj56 1330~1400 0.2980 verification as can be seen in the table, this model has certain effects when applied to other wells in the same block, and the high correlation (r 0.30-0.40) between the measured caliper and the predicted caliper indicates that the model is significant and stable. application and decision-making for e59 basic information on the operation of e59. pl oilfield is located in central south of bohai sea, with its structure lying at the northeast end of the middle section of bonan uplift zone and developing on tanlu fault zone. e59 is a highly-deviated well and its maximum well deviation is 68°@2000.49m. the design well depth is 2578.00⊥1554.57m and the actual completed well depth is 2533.00⊥ 1544.50m. spud-in started on june 20, 2019, the second spud-in was completed on october 21, 2019, and the completion operation was finished on october 27, 2019. the main revealed formations include: the pingyuan formation, the minghuazhen formation, the guantao formation and the dongying formation. for more details, refer to table 2. 10 table 2—stratigraphic division datasheet for e59 well. erathem system formation member md (m) tvd (m) elevation (m) cenozoic quaternary pingyuan neogene minghuazhen n2mu 1357.0 903.0 -862.0 n1m1 2288.2 1318.2 -1277.6 guantao n2gu 2473.7 1482.6 -1442.1 n1g1 2818.0▽ 1792.0 -1751.5 paleogene dongying ed completion depth (m) 2818.0 1792.0 -1751.5 kelly bushing (m) 40.5 logging operation design. from the initial depth of the well 311.15mm to elevation -800 m, the lwd is adopted, with log items that include gamma and resistivity; from -800m to the bottom, the lwd is adopted, with log items that include gamma, resistivity, neutron and density. during the completion operation, when the casing was run to 2018m, the normal lowering weight was 52t, but the actual lowering weight was 36t, 30% lower than the normal value, indicating that resistance was encountered. this might be caused by sticking of the upper casing or thrust of the lower casing into the length of the enlargement of the well. in the first case, the discharge can be increased to wash off the cuttings stuck on the casing wall, while in the latter case the casing must be lifted out and then lowered again. considering the timeliness of field drilling operation, the drilling supervisor is required to find out the reason and make the decision promptly. figure 10 shows the geophysical response of e59 well at 2000-2100m(md), from which we can see that at the depth of 2009-2015m, the resistivity is increased to 20-25ω·m, gamma is a bit low, and neutrondensity crossing happens (porosity about 6-12). by analyzing the logging and geochemical data, it is believed that this interval is an oil horizon and therefore will be the main perforation interval in subsequent completion operations. caliper prediction and decision-making on casing operation. first, the predicted gamma curve is created based on the data of adjacent wells, and then the caliper is obtained by interpretation of the mathematical model (eq. 7), as shown in figure 11. as can be seen from the figure, there is a visible difference between predicted gamma and measured gamma at 2009-2015m, while the difference is insignificant in other well intervals. the difference gamma obtained by calculating the difference between measured gamma and predicted gamma also indicates the same phenomenon. meanwhile, the predicted caliper obtained by interpretation of the mathematical model (eq. 7) is obviously enlarged in this depth range. therefore, it can be judged that the enlargement of the well takes place at a depth of 2015 m during the casing running. based on the results of the interpretation, it is suggested that the field operation supervisor lift the casing and then lower it for reinstallation. the results of this study provide a decision-making basis for the field drilling supervision. the casing is lowered to place successfully, demonstrating the effect of this method in field applications. 11 figure 10—field logging and geophysical response of ple59. figure 11—results of the caliper prediction of ple59. conclusions and suggestions 1. with increasing potassium ion concentration and mud specific gravity, the geophysical response of glwd increases gradually; potassium ions have the most significant influence on gamma; and the larger the caliper, the greater the influence of potassium ions on the geophysical response of glwd. 2. the caliper prediction model built based on the scatter fitting function of difference gamma and measured caliper can be applied in pl block. its stability and significance can meet the demand for providing technical support and a decision-making basis for subsequent drilling and completion operations. 3. in-depth mining of glwd geophysical response data is of directive significance to field drilling and completion operations, yet various sources of data need to be utilized for comprehensive analysis. at present, there is no good method that can acquire accurate caliper information indirectly without relying on the caliper logging instrument. conflicts of interest the author(s) declare that they have no conflicting interests. references xu, b., wang, z., li, z., et al. 2019. automatic correction of natural gamma logging data based on environmental influence. journal of oil and gas technology 10(5):99-102. shen, l., wang, z., and qu, x. 2015. influence factors and correction method of gamma logging while drilling. petrochemical industry technology 23(1):108-115. 12 ma, h., zhang, b., kong, f., et al. 2014. application of natural gamma logging tool in gas field development. oilgas field surface engineering 14(12):23-24. cripps, a.c. and mccann, d.m. 2000. the use of the natural gamma log in engineering geological investigation. engineering geology 55(4):313-324. wang, y., liu, b., and jia, c. 2011. study on sidewall stability. the 16th nation exploration engineering (rock & soil drilling and tunneling) technical and academic exchange annual meeting, chengdu, china, 10-12 october. liu, z. 2006. study on inversion method of lwd response and its application. master thesis. southwest petroleum university, chengdu, china. frahm, a.l. and lemke, l.d. 2010. comprehensive glacial sediment characterization and correlation with natural gamma log response to identify hydrostratigraphic units in a rotosonic well core. paper presented at the agu fall meeting, houston, texas, usa, 1-3 december. klaus, l. 2010. environmental corrections to gamma-ray log data: strategies for geophysical logging with geological and technical drilling. journal of applied geophysics 70(1):17-26. abstract introduction influence factors in glwd building a caliper prediction model application and decision-making for e59 conclusions and suggestions conflicts of interest references a sample paper for presentation at anziis 2001 references abdulmohsein, z., bai, b., and neogi, p. 2020. emulsion stability of heavy oil with surfactants and nanoparticles. improv oil gas recover 4. https://doi.org/10.14800/iogr.1177 in the original publication of this article (abdulmohsin et al. 2020), the first author's name zainab abdulmohsin was misspelled. the correct name should have been zainab abdulmohsein. the original article has been corrected. . correction correction to: emulsion stability of heavy oil with surfactants and nanoparticles zainab abdulmohsein, baojun bai, and parthasakha neogi*, missouri university of science and technology, rolla, usa copyright © the authors. this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1215 published online: october 12, 2022. *corresponding author: neogi@mst.edu 1 https://doi.org/10.14800/iogr.1177 mailto:neogi@mst.edu a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.445 received august 3, 2019; revised september 10, 2019; accepted september 18, 2019. *corresponding author: mzx_cq@petrochina.com.cn 1 technology and application on reservoir architecture characterization based on sandbodies spatial orientation zhixin ma*, ji zhang,wen xue,wensheng wang, bin fu, weifeng sun, qianqian fan, and ya li, sulige gas field research center of changqing oilfield company, petrochina, xi’an, china abstract as the high percent of effective sandbody thickness, the braided river reservoir become to an important exploitation area. the shihezi group lower 8th section of sulige gas field is a typical sandy braided river reservoir. strong reservoir heterogeneity is one of the main restriction factor of gas field development, such as su x adding area. referring to the analysis results of modern sedimentary and ancient outcrop configuration, a new reservoir architecture characterize method is presented in this study. the new methods realize river channel sandbody spatial orientation by “changes on bottom of sandbody and microfacies overlay regular pattern”, and realize channel bar sandbody spatial orientation by “logging cycle, silt layer position, and microfacies overlay characteristic”. the reservoir structure analysis on river channel and channel bar were also carried out, and the effective sandbody control effects by reservoir configuration unit were analyzed. the characterization results show: 1) the two main plane combinations in the single channel sandbody of shihezi group 8th section in research are: banded channel which width is 1000~2000m and sheet scale channel which width is 1500~4000m. 2) the main reservoir configuration units include the channel bar, braided river channel and flood plain. and the channel bar is the main reservoir element. 3) the scales of sandbodies are different due to different genetic type. the thickness of channel bar is 3~5m, the width is 250~300m, the length is 500~900m. the width of braided river channel is less than 200m. the deposition pattern presents “alternate channel and bar, wide bar and narrow channel” on flat. 4) 5 levels configuration units control the macro distribution of effective sandbodies, four levels configuration unit is the main control factor, 3 levels configuration unit has little effect on the distribution of effective sandbodies. the proposed method has been successfully used on well location optimization in sulige gas field. it has reference value for the same type of reservoir configuration. introduction since the reservoir configuration analysis method was first proposed by miall in 1985 (miall 1985), the theory was constantly developed and enriched by sedimentary geologists, and quickly became an important means of accurate reservoir characteristics (especially in the late period of oil and gas reservoirs development). reservoir architecture refers to the form, scale, direction and their space stack relationships of different reservoir architecture unit and interlayer (wu 2010; wu et al. 2008, wu et al. 2012, lin et al. 2013). the essence is to study the process of sedimentary environment and the mailto:mzx_cq@petrochina.com.cn 2 relationship of sedimentary products, to systematically reveal the characteristics of sedimentary structure and spatial distribution of three-dimensional space, and to characterize its internal macro heterogeneity (best et al. 2003; lynds and hajek 2006; lunt et al. 2013). reservoir configuration analysis begins with observations of paleo outcrops and modern sediments (miall 1996; robinson and mccabe 1997; liao et al. 1998; ma et al. 2003). however, the underground reservoir configuration is relatively backward. nearly for a decade, with the development of ground penetrating radar, loose surface sedimentation and large tank experiments, it was gradually realized that the dimensional fine dissection of the near-surface sedimentary body (lunt et al. 2013; robinson et al. 1997; liao et al. 1998; ma et al. 2003; lunt et al. 2004) summed up a lot of prototype models (best et al. 2003; lunt et al. 2004; peakall et al. 2007; skellya et al. 2003; ghazi et al. 2009; corbeanu et al. 2001) and empirical formula (leeder 1973; liu and jiao 1996; ma and yang 2000; ma et al. 2008), and established relevant reservoir quantitative geological knowledge. the progress of near-surface sedimentary body configuration greatly contributes to the development of underground reservoir configuration analysis. especially in the dense well pattern area, guided by the reservoir prototype model, reference reservoir quantitative geological knowledge base. the analysis methods of underground reservoir structure were improved, and related research results emerged one after another (wu et al. 2008, wu et al. 2012, lin et al. 2013; ma et al. 2008; zhou et al. 2008; bai et al. 2009; liu et al. 2011; li et al. 2011; zhang et al. 2013). reservoir structure is covered by sedimentary systems, such as meandering river, delta, alluvial fan (lin et al. 2013; jiao et al. 2009; yi et al. 2010; wen et al. 2011; xin 2008). although a lot of experimental research work were carried out and some research results were obtained (best et al. 2003; lynds and hajek 2006; lunt et al. 2013; liao et al. 1998; ma et al. 2003; lunt et al. 2004; peakall et al. 2007; skellya et al. 2003; sun et al. 2014; bai 2010) with the limitation of well pattern, the braided river underground reservoir structure always focus on single well identification of channel bar sand body. it sometimes cannot accurately predict the distribution of channel bar sandbodies on the plane, which reduces the reliability of braided river reservoir configuration. take the shihezi group lower 8th section of sulige gas field as an example, through the multilevel sandbodies spatial orientation, this paper discusses the method of underground braided river reservoir architecture characterization, to deepen the theory of braided river reservoir configuration and guide the well deployment of the adjacent area. geological features the ordos basin is a large multi-cycle craton basin. based on the archean-early proterozoic formation, experienced five sedimentary evolution periods as aulacogen developed on middle-late proterozoic, shallow sea platform developed on early paleozoic, offshore plain developed on late paleozoic, inland lake basin developed on mesozoic, and circumjacent fault depression developed on cenozoic (he et al. 2003). in the period of whole late paleozoic, the ordos basin developed epicontinental sea, seaside lake basin and shallow sea platform (wang et al. 2007). the sedimentary system went through the evolution of tidal flat (lagoon) to barrier island developed on benxi to taiyuan period, lake to delta developed on shanxi to shiqianfeng period (he et al. 2003; wen et al. 2007). sediments have interactive deposit by carbonate rocks, coal seam and terrigenous clastic to terrigenous clastic deposits. according to the present structural configuration of the basin, combined with the nature of basinal basement, the evolution history of the basin, tectonic development and the structural features, the ordos basin is divided into six first-order tectonic units with the yi-shan slope as the main body. sulige gas field is located in inner mongolia autonomous region. the structure belongs to yi-shan slope of the ordos basin, and exploration area is approximately 3.2×104 km2. it is a large lithologic trap gas reservoir which developed in upper paleozoic coal measures hydrocarbon source beds. the research area is located in the north of the sulige gas field, bottom-up developed carboniferous benxi formation and taiyuan formation, permian shanxi formation, shihezi formation and shiqianfeng formation during upper paleozoic. the total sedimentary rock thickness is about 700m. the shihezi formation was divided into eight sections from shihezi 1st section to shihezi 8th section (he et al. 2003; yang et al. 2008). the shihezi 8th section was further divided into two sub-groups as upper shihezi 8th section and lower shihezi 8th section. large and thick braided channel sandbodies of lower shihezi 8th section is the main gas layer 3 (he et al. 2003; wen et al. 2007). the average thickness of sandbodies is 30~40m. the sandbodies are overlaid and spliced by multi-stage channels, and then classified into four groups. the target area has been under development since 2008, working area is 13.0 km2. figure 1 shows a map of the study area. there are 50 gas wells in the area, and average well spacing is 350~500m. the well spacing in the area is the largest in sulige gas field at present. there are sufficient dynamic information and data so it is suitable to carry out reservoir structure research in this area. figure 1—location of the research area. lithologic features. the study area of lower shihezi 8th section is a braided river sedimentary system in the background of seasonal arid climate (chen et al 2008; li and yang 2009), and is the main producing formation. during the depositional period, the tectonic activity was stable and the material supply was sufficient (wang et al 2007), the water was extensive, and the riverstream changed frequently. macroscopic depositional characteristics show “sand pack mud”. lithology mainly composes of medium sandstone to gritstone (li and yang 2009). in addition, mineral composition is mainly composed of quartz and cuttings. quartz content is generally between 45~85%, cuttings content is between 2.0~42.6%, feldspar contents is quite small (wen et al. 2007). figure 2—c-m figure of lower shihezi 8th sandbodies in study area. particle size characteristics. observation of core slice microscope and particle size analysis present that, the lithology of lower shihezi 8th section mainly consists of medium sandstone to gritstone, followed by fine sand, mud, gravel, and silt. moreover, near-provenance sedimentary characteristics are obvious 4 (wen et al. 2007). main particle size of sandbodies is 0.4～1.0 mm. most of particle size is coarse. the probability curve of particle size is mainly two-stage style, the size classification is bad, mainly is composed of saltation population, followed by rolling population (yin et al. 2006). in the c-m figure (figure 2), q-r stage is well developed and p-q stage is not developed. this indicates that although the hydrodynamic conditions in the study area are strong, deposition rate is fast, the sediments classification and transformation was bad. sedimentary structure. sedimentary structure of shihezi 8th section is various (wen et al 2007), developed through cross bedding, tabular cross bedding, and parallel bedding (figure 3). the bottom of sandbodies always present scour surface and partial boulder clay, which reflects strong hydrodynamic conditions. the top of sandbodies constantly present horizontal bedding and ripple cross lamination. figure 3—typical braided river sedimentary structure. multi-level sandbody configuration braided river sand body configuration level division. the study is based on miall’s and wu et al.’s configuration classification scheme (miall 1985; wu et al. 2013). the 0th grade is inner laminated interface, 1st grade is laminated interface, 2nd grade interleaving layer interface, 3rd grade is large reapplication or accretion interface by large bottom interface, 4th grade is equivalent to the top and bottom of the large bottom interface, and the 5th grade is top and bottom of the single channel sandbodies. the 0th grade to 5th grade interfaces belong to the classification of lithological configurations (wu 2010), and the 6th grade interface is single, which represents the beginning or the end of a flood plant. this paper emphasizes the representation of the 4th grade and 5th grade interfaces (single sandbody, single channel) configurationally units distribution. characteristics of configuration units. coring well analysis shows that the study area is mainly developed four kinds of configuration units, including channel bar, braided stream, flood plain, and interchannel. channel bar. the channel bar is a main elements of braided river sediments (yin et al. 2007), formed by sandbodies vertical superposition in several flood events. lithology mainly is composed of medium sandstone to gritstone. well logging curve presents “box” type. both trough cross bedding and tabular cross bedding were developed. braided stream. braided stream is perennial channel of braided river. its lithology mainly is composed of medium to fine sandstone. well logging curve presents a “bell-shape” type, miniature trough cross bedding was developed. the plane forms are interwoven and narrow bands, the profile is top flat and bottom convex. the filling types of braided stream are sand filling, half-sand filling, and mud filling (sun et al. 2014; xing 2014). flood plain. flood plain is distributed at the top of channel. the rocks present gray, sandy brown, brown and black. lithology mainly consists of mud to silty mudstone, mainly develops horizontal bedding. the thickness changes from several centimeters to tens of centimeters and partial absence. the well logging curve shows high gr value. interchannel. the interchannel always develops at the both side of river. the lithology characteristic is mud packed thin sandstone. the stone color, sedimentary structure and logging characteristics are similar as flood plain, and the thickness almost equals to channel sedimentary. 5 interface recognition of single well configuration. interface recognition of single well configuration is the key of reservoir depositional periods division (lin et al. 2013). the lower shihezi 8th section formations are several periods of overlayed composite sandbodies which were crosscut by flush seriously. as a result, it is difficult to identify the configuration interface. fine core observation shows that there is a thin residual muddy compartment, and obvious flush contact relationship with a new period of channel over it, which can be marked as one of the 5th level interface identification. mica clastic vertical occurrence is very common, the hydrodynamic conditions was weakened on the last time of single depositional stage. mica clastic that is hard to deposit in flood period would appear as large numbers, in accordance with the phenomenon. the 5th level configuration interface would be identified and to be recognized as the 4th level interface by the constraint of 5th level. single channel sandbody levels configuration anatomy single channel sandbodies spatial orientation. various methods of channel boundary recognition, such as interchannel deposition method, top sand elevation method (wu 2010; lin et al. 2013; chen et al. 2004), were used in single channel recognition. besides, this study proposed a new method, called “changes on bottom of sandbody and microfacies overlay regular pattern”, to confirm single channel boundary, and to characterize spatial orientation. the basic principles are as follows (figure 4). figure 4—identify single river schematic. single channel sandbodies configuration characteristics. based on precise positioning of space, single channel sandbody can be accurately characterized. the results show that the single channel sandbody of lower shihezi formation 8th section reservoir in sux encryption area has two main plane combinations: banded single channel and sheet scale single channel (figure 5). 6 figure 5—plane configuration unit of single channel sandbody. banded single channel. banded single channel mainly develops in formation 2-1 and 2-2 of lower shihezi 8th section. the single channels are narrow stripes that are isolated and distributed between the river mudstone. this combination is the result of lower horizontal plane, less supply deposition, a single channel lateral migration capacity. the width of banded single channel is 1000~2000m. sheet scale single channel. sheet scale single channel mainly developed in formation 2-3, 2-2, 1-3, 1-2 of lower shihezi 8th section. the single river is in a sheet distribution, and the mudstone between the rivers is not developed. this combination results from higher horizontal plane, enough supply deposition, frequent single channel migration or several single channel intertwining and cutting. the width of sheet scale single channel is 1500~4000m. anatomical profile of single sandbody spatial orientation symbol of channel bar sandbodies. internal channel bar develops mud interlayer (silt layer), vertical positive rhythm is not obvious, sp and gr logging curves are “box” type. braided waterways are mostly bell-shaped, showing obvious positive rhythm, and interlayers are not developed. logging curve morphology. the sedimentation of the channel bar is mainly based on the vertical accretion and downstream accretion. hydrodynamic of upstream face is strong, and weak in negative side water, resulting in the sediment particle size of single accretion layer turning from coarse to fine. because of downstream accretion, accretion layer is developed later and keep moving to downstream. therefore, the particle of upstream face changes a little, the logging curve mainly presents a box style. there is a tendency to thicken up at the retral part, the logging curve mainly presents infundibular. it is possible to estimate the approximate location of channel bar in a single well (figure 6). silt layer development location. modern channel bar of braided river shows that, hydrodynamic of upstream face is strong, sediment particle size is coarse. the silt layer is always developed at the negative side of river and the side with weak hydrodynamic (figure 6). this provides direct evidence to identify the location of channel bar. if a well is drilled to a silt layer, the approximate position can be forecasted (figure 7). figure 6—logging curve morphology. 7 figure 7—silt layer development location. microfacies overlay characteristics. the sedimentation of the channel bar is mainly based on the vertical accretion and downstream accretion. frequent lateral migration of the braided river causes different accretion layer in the lateral of channel bar. individual wells show that the channel sandbodies is overlaid with channel bar sandbodies. this is a key mark to identify the edge of channel bar (figure 8). figure 8—microfacies overlay characteristics. single sandbody configuration characteristics. single sandbody characteristics show that the thickness of channel bar ranges from 3 to 5 m, the width is 250~300 m, the length is 500~900 m. the width of braided river channel is usually less than 200 m. the deposition pattern presents “alternate channel and bar, wide bar and narrow channel” on flat (figure 9). control effect of reservoir architecture on effective sandbodies. five grade interfaces control the effective sandbodies distribution from the macro point of view. considering the drilling situation, nearly all the effective sandbodies are distributed in the channel, partial channel downcutting, or lateral migration connected effective sandbodies that developed in different periods. the 4th grade interface controls the distribution of channel bar and braided river in single channel. the different filling types of braided distributary channel decide the plane heterogeneity of single channel. therefore, the distribution of effective sandbodies is affected. 8 figure 9—silt layer development location. the 4th grade configuration profile shows that most effective sandbodies are distributed in the inter channel bar. and only a few sandbodies are distributed in the channel, which are identified as poor gas reservoirs. the discontinuous siltlayer developed in the 3rd grade of inter channel bar can become an impermeable layer that prevents the fluid from flowing vertically to gas reservoir. the degree of influence relates to thickness and area. if thick and large sandbodies are distributed stably, the effective sandbodies are always in the bottom of channel bar (figure 10). figure 10—control effect of 3rd grade interface. conclusions the new methods were presented to characterize river channel sandbody spatial orientation by “changes on bottom of sandbody and microfacies overlay regular pattern”, and channel bar sandbody spatial orientation by “logging cycle, silt layer position, and microfacies overlay characteristic”. the reservoir structure analysis on river channel and channel bar was carried out. there are two main plane combinations in the single channel sandbody of shihezi group 8th lower section in sux adding area. the banded single channel, as a narrow band surrounded with interchannel mudstone, is 1000~2000m wide. the sheet scale single channel is distributed as a sheet, interchannel mudstone is less developed, and the width of the channel is 1500~4000 m. the thickness of channel bar is usually 3~5m, the width is 250~300 m, the length is 500~900 m. the deposition pattern presents “alternate channel and bar, wide bar and narrow channel” on flat. 5th grade configuration unit controls macro distribution of effective sandbodies, 4th grade configuration unit is the main control factor, 3rd grade configuration unit has little effect on the distribution of effective sandbodies. the method has been successfully applied to optimize well location in sulige gas field, and has reference value to the same type of reservoir configuration. 9 acknowledgement national science and technology major projects "the development demonstration project of a large low permeability lithostratigraphic hydrocarbon 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formation, liuzhong area, karamay oilfield. journal of jilin university (earth science) 40(4): 940-945. zhang, c., yin, t., yu, c., et al. 2013. reservoir architectural analysis of meandering channel sandstone in the delta plain based on the depositional process. sedimentologica sinica 31(4): 653-661. zhou, y., wu, s., yue, d., et al. 2008. recognizing abandoned channel with underground dense well pattern and its application in sabei oilfield. journal of oil and gas technology 30(4): 33-36. zhixin ma is senior engineer of exploration and development of changqing oilfield company. he mainly engaged in fine reservoir description, reservoir configuration characterization, horizontal well geological guidance and eor research of sulige tight sandstone gas reservoir. he holds a master degree in oil and gas field geological engineering from daqing petroleum institute. abstract introduction geological features multi-level sandbody configuration single channel sandbody levels configuration anato anatomical profile of single sandbody conclusions acknowledgement conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1272 received january 6, 2024; revised march 15, 2024; accepted march 22, 2024. *corresponding author: ahmedmoawad625@gmail.com 1 experimental work of nanoparticlesassisted water flooding ahmed moawad ahmed*, egyptian general petroleum corporation, cairo, egypt abstract the nanoparticle is of great importance in enhancing oil extraction. the increasing oil demand pushed scientists to think of new technology to enhance oil recovery from oil reservoirs. the nanoparticle, which reaches a scale of 1-100 nanometers, is an influential element in maximizing oil production. nanoparticles help recover crude oil by several mechanisms such as wettability alteration of the porous media, interfacial tension reduction, disjoining pressure, and mobility ratio reduction. this research introduces the effects of different nanoparticles such as silica, iron oxide, zinc oxide, and mixed nanoparticles on oil recovery. the results showed that nanoflooding improves oil recovery more than conventional water flooding. introduction nanotechnology has the potential to revolutionize the oil industry (krishnamoorti 2006; ahmed et al. 2023). nanotechnology has been tried in exploration, drilling, production, and enhanced oil recovery. nanotechnology appeared in chemical methods used to enhance oil recovery. nanoparticles-assisted surfactants cause releasing of trapped oil in pores and throats. this release happens due to many factors such as reducing interfacial tension (ift) between oil and water, spontaneous emulsion formation, wettability alteration of porous media, and modification of flow character, which ultimately increase oil recovery significantly. the observed reduction in interfacial tension and mobility ratio results from nanoparticles present at the interfacial layers. different types of nanoparticles are used in oil recoveries, such as magnesium oxide, zinc oxide, iron oxide, titanium dioxide, tin dioxide, aluminium oxide, and zirconium oxide. nanoemulsion can be used to enhance oil recovery (odi 2018). nanotechnology has been used to improve surfactant flooding (wu et al. 2017), polymer flooding (giraldo et al. 2017), as well as thermal recovery (greff and babadagli 2013). in drilling operations, nanotechnology improved the rheological properties of drilling mud, reduced filtration loss, and enhanced shale stability (rafati et al. 2018). experimental work in this experimental work, nanoparticles were investigated as nanoagents in eor methods. ten core plugs were used in this experimental work. five core plugs were sandstone core plugs, and the other five were limestone core plugs. routine core analysis was made on the ten core plugs to determine their porosity and permeability. a special core analysis was made on the ten core plugs to determine their wettability. flooding tests were made with formation water on two core plugs and with nanofluids on eight core plugs. results were obtained from tests and presented graphically. core plugs analysis. the cores are all clean from shale. the cores are 100% oil-saturated. the porosity values are shown in table 1. the permeability values are shown in table 2. from amott tests, all plugs are oil-wet. mailto:ahmedmoawad625@gmail.com 2 pvt analysis. the specific gravity of the crude oil used in this experimental work is 0.825=40° api. the viscosity of the crude oil is 2cp at 25°c. table 1—porosity of the core plugs. sandstone limestone sample no porosity (%) sample no porosity (%) 1 18 6 17 2 18 7 19 3 17 8 17 4 18 9 19 5 19 10 18 table 2—permeability of the core plugs. sandstone limestone sample no permeability(md) sample no permeability (md) 1 100 6 99 2 95 7 98 3 98 8 96 4 99 9 97 5 98 10 98 flooding tests. ten core flooding runs were made to investigate the effect of nanoparticles on the oil recovery. five core flooding runs were made in sandstone core plugs, and the other five core flooding runs were made in limestone core plugs. table 3 shows more details about these flooding runs. the flooding apparatus is shown in figure 1. figure 1—schematic diagram of the flooding test setup. 3 table 3—the flooding test runs. no of run fluid injected (nanoparticles/base fluid) lithology 1 only formation water sandstone 2 0.1% wt. silica/formation water sandstone 3 0.1% wt. zinc oxide/formation water sandstone 4 0.1 % wt. iron oxide/formation water sandstone 5 0.05% wt. silica + 0.05% wt. iron oxide/formation water sandstone 6 only formation water limestone 7 0.1% wt. silica/formation water limestone 8 0.1% wt. zinc oxide/formation water limestone 9 0.1 % wt. iron oxide/formation water limestone 10 0.05% wt. silica + 0.05% wt. iron oxide/formation water limestone results and discussion from the conventional water flooding and the nanoflooding tests, nanoflooding has a higher oil recovery factor than water flooding. as seen in figure 2, the recovery factors in sandstone core plugs at the breakthrough for the water flooding (0.7 pv injected), the silica nanoflooding (0.9 pv injected), the iron oxide nanoflooding (0.9 pv injected), the zinc oxide nanoflooding (0.9 pv injected), and the mixed nanoflooding (0.9 pv injected) are 50%, 73%, 74%, 72%, and 69%, respectively. figure 2—the flooding runs in the sandstone core plugs. in figure 3, the recovery factors in the limestone core plugs at the breakthrough for the water flooding (0.5 pv injected), the silica nanoflooding (0.7 pv injected), the iron oxide nanoflooding (0.7 pv injected), the zinc oxide nanoflooding (0.7 pv injected), and the mixed nanoflooding (0.7 pv injected) are 45%, 70%, 69%, and 68%, and 65%, respectively. 4 figure 3—the flooding runs in the limestone core plugs. this high recovery factor occurs due to the mechanisms performed by nanoparticles. mechanisms of the nanoparticles to improve the recovery are the disjoining pressure, interfacial tension reduction, wettability alteration, and mobility ratio reduction (negin et al. 2016). in the disjoining pressure mechanism, the nanoparticles present in the nanofluids tend to form a film that takes the shape of a wedge in contact with the oil phase. this wedge-like film acts to separate the oil droplets from the rock surface. in that way, more oil is recovered than previously possible when using conventional displacing fluids. in the interfacial tension reduction mechanism, the nanoparticles enter between the oil phase and the water phase acting as an agent for reducing the interfacial tension. reduction in interfacial tension increases the capillary number. when the capillary number increases, residual oil saturation decreases. the hydrophilic nanoparticles are mainly used in enhanced oil recovery for strongly oil-wet reservoirs in the wettability alteration mechanism. the primary production mechanism of these nanoparticles is to alter wettability from oil-wet to neutral or water-wet. in the mobility ratio reduction mechanism, nanoparticles increase the viscosity of the displacing fluid dispersed in it. when the viscosity of the displacing fluid increases, its mobility decreases, and the mobility ratio decreases. in recent years, active research efforts have been made on nanoparticles to obtain more precise information on reservoir rock and in-situ fluid properties and the dynamics of displaced and injected fluids. the trends of efforts are summarized in the following three points. 1. addition of nanoparticles in the injected fluid bank, water flooding or eor, and detecting remotely its location and movement through using super magnetic nanoparticles in the flooding bank. the super magnetic nanoparticles will be magnetized and generate an induced magnetic field around them by imposing an external magnetic field from the transmitter well. this induced magnetic field will be observed in the observation well. once observed, the bank's location in the reservoir will be determined (al-shehri et al. 2013; al-ali et al. 2009). 2. nanoparticles added to the injected fluids can detect specific properties of the reservoir rock and fluids. when the nanoparticles are produced, we can retrieve the data. the surface coating on the nanoparticles is designed to change its nature in a specific manner. when the nanoparticles are produced, the changes in their surface coating are investigated from which the desired reservoir property can be deduced (berlin et al. 2011; biederer et al. 2009). 3. using nanoparticles-based sensing devices in reservoir formation for reservoir characterization. the biggest challenge for such applications will be how the tiny, fragile nanosensors can be protected from harsh downhole conditions to collect data properly (bogue 2004; shelley 2008). 5 conclusions nanoflooding is a promising technique for improving oil recovery. it increases oil production, improves sweep and displacement efficiency, and delays breakthroughs. excellent applications have proved that nanoparticles are potential candidates for enhancing oil recovery techniques. from the flooding test, the various types of nanoparticles show a better recovery factor than conventional water flooding. also, nanoflooding delayed the breakthrough of injected fluid. the breakthrough occurred earlier in conventional waterflooding. conflicting interests the author(s) declare that they have no conflicting interests. abbreviations eor: enhanced oil recovery ift: interfacial tension pv: pore volume references ahmed, a.m., salem, a.m., and salem, s.k. 2023. field application of nanoparticles-assisted water flooding. pet. coal 65(1): 255-259. al-ali, z. a., al-buali, m. h., alruwaili, s., et al. 2009. looking deep into the reservoir. oilfield rev. 21(2): 38-47. al-shehri, a.a., ellis, e.s., servin, j.m.f., et al. 2013. illuminating the reservoir: magnetic nanomappers. paper presented at the spe middle east oil and gas show and conference, manama, bahrain, 10-13 march. spe-164461ms. berlin, j. m., yu, j., lu, w., et al. 2011. engineered nanoparticles for hydrocarbon detection in oil-field rocks. paper presented at the spe international symposium on oilfield chemistry, the woodlands, texas, usa, 11-13 april. spe141528-ms biederer, s., knopp, t., sattel, t. f., et al. 2009. magnetization response spectroscopy of superparamagnetic nanoparticles for magnetic particle imaging. j. phys. appl. phys. 42(20): 205007. bogue, r.w. 2004. nanotechnology: what are the prospects for sensors? sensor rev. 24(3): 253-260. giraldo, l.j., giraldo, m.a., llanos s., et al. 2017. the effects of sio2 nanoparticles on the thermal stability and rheological behavior of hydrolyzed polyacrylamide based polymeric solutions. j. pet. sci. eng. 159: 841-852. greff, j. and babadagli, t. 2013. use of nano-metal particles as catalyst under electromagnetic heating for in-situ heavy oil recovery. j. pet. sci. eng. 112: 258-265. krishnamoorti, r. 2006. technology tomorrow: extracting the benefits of nanotechnology for the oil industry. j. petrol. tech. 58(11): 24-26. negin, c., ali s., and xie q. 2016. application of nanotechnology for enhancing oil recovery-a review. petroleum 2(4): 324-333. odi, u. 2018. incorporation of homogenizer in nanoemulsion injection scheme for enhanced oil recovery. improved oil and gas recovery 2. rafati, r., smith, s. r., haddad, a. s., et al. 2018. effect of nanoparticles on the modifications of drilling fluids properties: a review of recent advances. j. pet. sci. eng. 161: 61-76. shelley, s. 2008. nanosensors: evolution, not revolution … yet. chem. eng. progr. 104(6): 8-12. wu, y., chen, w., dai, c., et al. 2017. reducing surfactant adsorption on rock by silica nanoparticles for enhanced oil recovery. j. pet. sci. eng. 153: 283-287. ahmed moawad ahmed is a petroleum engineer at the egyptian general petroleum corporation. ahmed holds a bachelor’s degree in petroleum engineering from the faculty of engineeringcairo university. his main research area is in nanotechnology applications in the petroleum industry. abstract introduction experimental work results and discussion conclusions conflicting interests abbreviations references a sample paper for presentation at anziis 2001 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.437 received july 1, 2019; revised august 11, 2019; accepted august 23, 2019. *corresponding author: dbr@petrochina.com.cn 1 a new production splitting method based on discrimination of injectionproduction relation baorong deng*, jiqun zhang, junhua chang, xinhao li, hua li, and xianing li, research institute of petroleum exploration & development, petrochina, beijing, china abstract the complex mature oilfields in china have been operated for a long history. during their exploration and development, a large amount of diverse production and research data with complicated formats were generated. the gradual penetration of geology research requires more precise reservoir analysis and research. accordingly, it is urgent to make reservoir performance fine analysis for these mature oilfields using efficient and innovative data processing technologies. in this paper, multi-layer water flooding reservoirs were discussed with multi-disciplinary data. through automatic discrimination of injectionproduction relation by computer, vertical and horizontal water flow rates were analyzed quantitatively to diagnose the directions and layers of dominant water flow. then, the productions of production well and water injection well were split by layers to clarify how the water injection affects the performance of production well. compared with conventional methods, the proposed new method is more comprehensive and reasonable in application of data and more scientific and accurate in reservoir performance fine analysis. the software developed on this method has been applied in hundreds of reservoir blocks in daqing, jidong, jilin, liaohe, xinjiang and other oilfields. it is of significant guidance for evaluation on remaining oil potential and preparation of development adjustment plan for mature oil-fields. introduction the production splitting method is critical for the reservoir engineers to figure out the layered injectionproduction amount of each vertical layer of the single well, and it has long been paid attention by the professionals. various splitting methods include early kh value splitting method, numerical simulation method (li et al. 2011), monitoring data restraining method (li et al. 2010), improved formation coefficient method (cao et al. 2014; lan et al. 2012) and so on. however, the production splitting method taking the production well and water injection well as a unified whole and considering multiple layers, multiple directions, artificial intervention and multiple constraints based on the discrimination of injection-production relation has not been reported. by applying various geological, dynamic, monitoring and technological data of the mature oilfields and combining with reservoir experts’ experience, geological achievement, dynamic/static behaviors and monitoring data, the reservoir performance fine analysis method in the use of computer technology was studied in this paper. automatic discrimination of injection-production relation in the single sand body unit by the innovative application of computational geometry discipline was conducted to analyze and evaluate how the well pattern controls the sand body. and then, the well group and layer in which the injected water had an inefficient circulation were found out. based on the discrimination of injectionproduction relation, injection-production flow resistance calculation and water injection rate splitting, this paper presented an innovative production well production splitting technology with multiple constraints and compiled the software system. thus, a reliable research method is provided for clarifying the main mailto:dbr@petrochina.com.cn 2 water production horizon and separate layer oil production of the production well, evaluating the vertical layered production of reserves more scientifically and studying the remaining oil potential distribution. water injection rate splitting technology injection-production relation is the foundation to discuss the water flooding direction, water flow rate, water injection rate and oil production effect. with the gradual penetration of geology research, after the sedimentary micro-facies are subdivided, single sand bodies partly uncontrolled appear in the oil reservoir that was considered being controlled by the well pattern. especially, as to the complex fault block reservoirs, many faults, discontinuous sand bodies and frequent development adjustment measures such as re-perforation or altering layers have made the artificial analysis of injection-production relation over the past years more difficult. intelligent discrimination of injection-production relation by computers is conducted according to the following principles. 1) production wells and water injection wells distributed in different sand bodies are disconnected. 2) water injection wells or production wells drilled in the mudstone area are disconnected. 3) the closed faults or mudstone area occlusions are disconnected. 4) too long water flow path and immobile or weak mobile water flow are caused by sand-body forms. 5) the flow may steer clear of obstacles under suitable conditions. 6) the indirect production wells in line are difficult to connect. 7) two water injection wells on one side of the production well on the same straight line are difficult to be injected. 8) the suitable well spacing and well pattern in the same sand body have flow connections. 9) production wells may connect in multiple directions. 10)a water injection well may connect many production wells under the condition of the proper angle and well spacing. 11)water injection wells and production wells not perforated simultaneously are not corresponding. 12) the flow line cannot cross. figure 1—injection-production relations influenced by single sand body forms, pinchout and faults. 3 figure 2—injection-production relations influenced by well pattern, such as indirect connections and pressure conduction. as shown in figures 1 and 2. it is necessary to determine the injection-production pathway, that is, to discriminate the least resistance path between water injection well and production well. discrimination method of the least resistance path between water injection well and production well by comprehensively applying the data about the reservoir physical property, single sand body spread and forms, fault geometry and sealing capacity, production performance data, water absorption and liquid production profile, perforation and stimulation horizons in oil production and water injection wells, the relative position of the oil and water injection wells and tracer monitoring, the data error was automatically discriminated and the compatibility analysis was made for various information. the least resistance path between water injection well and production well was calculated by applying computational geometry and graphics. the procedures are as follows: 1) the data of static physical properties of geological models such as permeability and thickness field was imported. 2) the visibility graph was constructed. 3) the weighted visibility graph was built according to the static parameter field data describing the characteristics of the reservoir direction. 4) the least resistance path between injection and production wells was calculated by applying the dijkstra algorithm. computational geometry was applied in the visibility graph construction. considering the morphology of non-flow areas such as sand body, fault and mudstone, on the basis of static data field for geological modeling, the center point of each grid was regarded as the vertex in the visibility graph, namely visible point, visible to the four center points (above, below, left and right) at most. if there is a closed fault between the adjacent grids or one of them is located in the non-flow area, it is invisible. according to the above principles, the visibility graph construction of all the visible points is shown in figure 3. its algorithm is described below. a free space cfree is defined, which is composed of two simple disjoint polygons. one polygon is outer boundary, and the other one is inner boundary, namely obstacle, as shown in figure 3a. both outer and inner boundaries of cfree are open sets, and the tangency between microarrayer and outer/inner boundary is acceptable. a starting location a (the location of water injection well (inj) in blue circle) and a termination location b (the location of production well (oil) in red circle) are given, which both belong to cfree. construction algorithm for the visibility graph gvis (cfree ) of cfree and points a and b: algorithm: visiblithgraph (cfree,a,b ) inputs: the inner and outer boundaries of the free space cfree, and the two points (a and b) within the cfree. outputs: visibility graph gvis (cfree, a, b) 4 1) initialize the graph gvis (cfree )=(v, e) to make the set v include the vertexes of both inner and outer boundaries, and points a and b, e = φ; 2) for each vertex v∈v, do w←visiblityvertices (v, cfree); 3) for each vertex w∈w, add the arc (v, w) into e; 4) return gvis (cfree, a, b). the rotary plane sweep method (mark el al. 2007) was applied in the subprocess of visiblity vertices. its inputs include a group of polygons within the cfree and a point v on the plane. all the vertexes visible to v are found out from the vertexes of inner and outer boundaries of the cfree. from the construction algorithm of the visibility graph in figure 3a, the visibility graph gvis (cfree, a, b) is obtained, as shown in figure 3b. the base map of figure 3b is the kh field data sketch map, describing the characteristics of the reservoir direction. water injected flows along the direction with the highest permeability, biggest thickness and pressure difference. based on the visibility graph constructed, the pseudo-resistance among the grids is calculated according to the parameters such as grid permeability and thickness. finally, the shortest path from a to b is calculated by the dijkstra algorithm (reinhard 2013), as shown in figure 3c. (a) (b) 5 (c) figure 3—construction of all the visible points. (a) the sand body where water injection well (inj) and production well (oi)l are located. (b) the unweighted visibility graph of the sand body. (c) the least resistance path between water injection well (inj) and production well (oil). discrimination method for indirect connection wells. the discrimination method for indirect connection wells is complicated. once the direct connections are discriminated depending on the reservoir development characteristics, well pattern distribution mode and injection-production pressure difference, the indirect connections are considered existing if the distance between the indirect connection well and direct connection well and the downhole pressure are both small enough and the permeability and thickness are both big enough, that is, the resistance is below a certain threshold value. the threshold value can be determined according to the liquid volume and pressure of the indirect connection wells. in this paper, by applying geometrical morphology, the indirect connections are discriminated under the constraint of static and dynamic data, as shown in figure 4. to discriminate whether the well o is indirect connection, it is necessary to discriminate whether the wells b, d or c are interfering wells. taking the well b as example, if∠bwo and∠bow are respectively less than a certain threshold value, the well b is indirect connection. figure 4—indirect injection-production connections discrimination. 6 select all the wells and represented by b calculate the resistance between w and o and between w and c (rwo and rwc) all the wells except w and o are inside the wo line? ∠bwo is less than the threshold value �1and ∠bow is less than the threshold value �2? the ratio of rwo/rwc is less than the threshold �3 the well o is an indirect connected well the well o is not a connected well the ratio of rwo/rwc is less than the threshold �3 no no no yes yes yes figure 5—the discrimination flow of indirect connections. after indirect connections are discriminated, the resistance rwo between the wells w and o and the resistance rwb between the wells w and b are calculated by applying the permeability between production well and water injection well, reservoir thick-ness, injection-production pressure difference and others. if the value of rwo/rwb is below a certain threshold value, the well o is indirect connection. the specific discrimination flow is shown in figure 5. dominant water flow discrimination technology calculation of plane percolation resistance between water injection well and production well. by applying the layer data, well location, well trajectory, perforating data, well pattern distribution and treatments of water injection/production wells, the plane percolation resistance between water injection well and production well in a single layer (figure 6), the percolation resistance in injection-production connections in multiple directions in multiple layers (figure 7) and the flow of oil and water between two grids (figure 8) are calculated according to injection-production connections, mechanics of fluids flow and principle of hydroelectricity similarity. figure 6—plane percolation resistance between water injection well and production well in a single layer. 7 figure 7—the percolation resistance in injection-production connections in multiple directions in multiple. layers figure 8—the flow of oil and water between two grids. the total resistance between the wth water injection well and the surrounding connected production wells is as follows, ��� = 1 �=1 � 1 ��,� � ....…………………………………………………………………………….……….(1) the resistance between the wth water injection well and the surrounding connected production wells in the zth layer is as follows, ��,� = 1 �=1 � 1 ��,�,� � ...………………………………………………….………………………………..(2) the resistance between the wth water injection well and the pth production well in the zth layer is as follows, ��,�,� = �� 2���,�ℎ�,� ln �� � +������+ �� 2���,�ℎ�,� ln �� � .……………………………………………………(3) the external resistance between the wth water injection well and the pth production well in the zth layer is as follows, ������ = 1 �=1 � 1 �=1 � 1 ��� �� +����� × 1 2× ���,� ��,� + ���+1,� ��+1,� ℎ�,�+ℎ�+1,� 2 × ���,�+���+1,� 2 × 1 ��,�−��+1,� � � ,.......…………………………………(4) where, w is the number of water injection well; z is the layer number; v is the layer amount; p is the number of production well connected with water injection well in the zth layer; s is the total number of production wells connected with water injection well in the xth layer; μw is water viscosity, mpa.s; μo is oil viscosity, mpa.s; kw,z is the permeability of the wth water injection well in the zth layer, md; hw,z is the effective thickness of wth water injection well in the zth layer, m; re is the outer boundary of the radial flow, m; r is the well radius, m; kp,z is the permeability of the pth production well in the zth layer, m; hp,z is the effective thickness of the pth production well in the zth layer, m; m is the number of simulative grids in the vertical direction of water flow; n is the number of simulative grids from the water injection well to production well; krw is the elative permeability of water phase; kro is the relative permeability of oil phase; dxi,j is the width in the x direction of the grid in the ith row and the jth column, m; ki,j is the permeability of the grid in the ith row and the jth column, md; hi,j is the thickness of the grid in the ith row 8 and the jth column, m; dyi,j is the width in the y direction of the grid in the ith row and the jth column, m; pi,j is the pressure of the grid in the ith row and the jth column, mpa. calculation of water injection flow rate considering treatment and monitoring data. under the constraints of water adsorption profile, layered pressure drop testing data, well logging data in the waterflooded layer and plane comprehensive resistance coefficient, the vertical splitting coefficient is calculated. the relative flow rate of an injection-production unit in the single sand body is as follows, ��,�,� = � × �� ��,�,� ,……………….……………………………………………………………………(5) where, � is the constraint factor considering the treatment and monitoring data, etc; δp is is the pressure difference between water injection well and production well. ��,�,� = ��,�,� �=1 � ��,�,�� ...……………….………..…………………………………………………………(6) the scale coefficient of water injection rate splitting of the wth water injection well in each layer is as follows, ��,� = �=1 � ��,�,�� �=1 � �=1 � ��,�,��� ......……………….…………….……………………………………………..(7) according to the scale coefficients, the water flow in each direction of each layer of injectionproduction unit can be calculated. production splitting technology under the constraint of multiple conditions on the basis of research on injection-production relation mentioned and water injection rate splitting above, this new method deals with layer water cut, with the accordance ratio of indexes of the well only to verify the model precision. the calculation of oil production in each layer is relatively complicated. relevant technical points are given as follows: 1) the comprehensive information system is set up; 2) the injection-production flow connection in each layer is discriminated automatically by computer; 3) water injection rate in each layer is calculated using flow resistance, layered water injection and other data; 4) the flow resistance is corrected using the pressure drop testing data in each layer, and the concept of pressure drop factor is introduced. based on the pressure drop amplitude of water injection well in each layer in 48 hours, the splitting coefficient of water injection rate in each layer is determined and corrected; 5) considering the rise of liquid volume in injection-production unit caused by fracturing, the injection-production flow resistance is reduced in proportion; 6) according to the principle of material balance, the liquid production profile is calculated, and thus liquid-producing capacity of production well in each layer is obtained; 7) the oilfield development rule is analyzed and the recovery percent of layer is constrained; 8) logging data in the water-flooded zone is used to correct the layer water cut; 9) the data of inspection wells are used to correct the saturation of remaining oil and water cut in well layers; 10)according to the de-crease amplitude of water cut in the whole well or the rising amplitude of water cut in the re-perforated water layer after re-perforation, the splitting ratio of water cut and oil production is corrected; 11)with the two-phase (oil-water) percolation theory (ge 2003), the saturation between production well and water injection well is calculated and the water cut in well layers is constrained; 9 12) by the superposition of water cut and oil production in every layer calculated and in contrast with the actual water cut and oil production of the whole well, the higher the coincidence rate and the more accurate the method, the closer the calculation results to actual production. the technology has been applied for thousands of wells in more than 40 reservoir blocks. compared with the water cut of the whole well, more than 80% of the wells have higher fitting rate (figure 9). in comparison with the reservoir numerical simulation results, the trend is similar, as shown in figure 10. by contrast with the water-cut data of the liquid production profile of 88 well layers, the average error is about 3.5% (table 1), suggesting a high precision. figure 9—comparison of calculated and designed water cut of wells. figure 10—recovery of layers calculated by the model and obtained by numerical simulation. table 1—comparison of water cut of layers calculated by the model and production profile. error intervals ≤1% 1~2% 2~4% 4~10% >10% total layer numbers 16 12 29 30 1 88 percentage 18.2 13.6 33 34 1.1 100 accumulative percentage 18.2 31.8 65 99 100 100 applications injection and production corresponding degree over the past years. in the bohai bay area, the structure of complex fault block reservoir is complicated, the sand body is discontinuous and the oil10 bearing area is small. so, it is difficult to improve the injection-production relation of single sand body and build up the effective injection-production system. when the injection-production relation of single sand body is evaluated by considering the distribution characteristics of oil sand body, the geometry of fault block and re-perforating or altering layers, it would spend considerable time to treat the historic data for decades of years if no computer software is available. however, with this technology, together with complete data, the results can be calculated in several minutes. in the compilation of secondary development plan for a reservoir block of dagang oilfield, the injection-production relation was analyzed for hundreds of single sand bodies by applying the technology proposed in this paper, and the perforation corresponding relation was evaluated layer by layer and well by well. figure 11 shows the distribution of injection-production connection ratio. any well group with the ratio of less than 60% should be emphasized. figure 11—distribution of production-injection connection ratio. production splitting in each layer. the production splitting technology has been applied in thousands of wells in order to clarify the reservoir producing status in each layer and remaining reserves of single sand body. figure 12 shows the recovery percent of 290 single sand bodies in a block of dagang oilfield. specifically, 72 single sand bodies are not produced, accounting for 3.8% of the remaining oil; 25 single sand bodies are less produced, representing a recovery percent of less than 5%, and accounting 5.81% of the remaining oil. so, local infill wells can be drilled depending on the vertical superposition. figure 12—recovery percent of 290 single sand bodies in a block of dagang oilfield. conclusions by the reservoir engineers’ random inspection and testing under various oil reservoir geological conditions, such as fault development in complex fault block reservoir, discontinuous sand bodies, small oil-bearing area and the reservoir with long history of production, the injection-production relation discrimination method has been proved with an accuracy over 95%. 11 with full consideration to static geology, production performance and treatments, the production splitting technology under constraints of multi-layer, multi-direction and multi-conditions provides the results better coincident to practical production. it is a reliable research method for quickly clarifying the producing percent of reserves in each layer and the remaining potential of single sand body. conflicts of interest the author(s) declare that they have no conflicting interests. references cao, x., zhang, f., cai, y., et al. 2014. research on a new production split method of thin interbedded sandstone reservoirs. science technology and engineering 14(13):166-171. ge, j. 2003. the modern mechanics of fluids flow in oil reservoir. beijing, china: petroleum industry press. lan, l., liu, r., fu, y., et al. 2012. a new method to cleave production of the separated layers of oil wells. petroleum geology and oilfield development in daqing 31(3):59-62. li, k., yu, g., wang, q., et al. 2011. a new production split method. petroleum geophysics 9(4):19-22. li, c., liu j., li x., et al. 2010. principles and application of production allocation for oil and water injection wells in multilayer commingled development oil reservoir. petroleum geology and oilfield development in daqing 29(1):55-59. mark, d.b., otfried, c., marc, v. k, et al. 2007. computational geometry: algorithms and application. springer. reinhard, d. 2013. graph theory. beijing, china: higher education press. baorong deng is a senior engineer in research institute of petroleum exploration & development, petrochina. baorong deng specializes in production analysis, reservoir simulation and enhance oil recovery. jiqun zhang is a senior engineer in research institute of petroleum exploration & development, petrochina. jiqun zhang specializes in production analysis, reservoir simulation and enhance oil recovery. junhua chang is a senior engineer in research institute of petroleum exploration & development, petrochina. junha chang specializes in production analysis, reservoir simulation and enhance oil recovery. xinhao li is a senior engineer in research institute of petroleum exploration & development, petrochina. xinhao li specializes in production analysis, reservoir simulation and enhance oil recovery. hua li is a senior engineer in research institute of petroleum exploration & development, petrochina. hua li specializes in production analysis, reservoir simulation and enhance oil recovery. xianing li is a senior engineer in research institute of petroleum exploration & development, petrochina. xianing li specializes in production analysis, reservoir simulation and enhance oil recovery. abstract introduction water injection rate splitting technology dominant water flow discrimination technology production splitting technology under the constrai applications conclusions conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.427 received february 25, 2018; revised march 17, 2018; accepted march 24, 2018. *corresponding author: shuailiu15@gmail.com 1 a markov-chain-based method to characterize anomalous diffusion phenomenon in unconventional reservoir shuai liu*, texas a&m university, college station, usa; han li, cgg, houston, usa; and peter p. valkó, texas a&m university, college station, usa abstract the recent success in developing unconventional reservoirs has aroused many new challenges to the theory of reservoir engineering. in this paper, we try to investigate the anomalous diffusion phenomenon caused by the heterogeneity due to the fracture network on the reservoir scale. firstly, we revisit the physical background of the single-phase flow diffusivity equation by discussing the equivalent single particle diffusion. combining the characteristics of single particle diffusion with complex fracture geometry, it is indicated that anomalous diffusion phenomenon will be dominant on the reservoir scale, even for single phase production behavior. then a model based on markov chain is presented to demonstrate the proposed anomalous diffusion by simulating the particle normal diffusion on a geometric graph and then calculating the relation of the mean square displacement vs. time in the embedding euclidean space. based on the simulation results, in consequence, we make discussions on the characteristic size of the heterogeneity due to the fracture network on the reservoir scale, summarize two types of pattern for the anomalous diffusion, and accordingly provide a supportive argument for using the fractional diffusivity equation, in place of the classical one, to model the flow and production behavior in highly fractured unconventional reservoirs. introduction in the last decade, one of the most prominent progresses for the world’s energy industry was undoubtedly the so-called “shale revolution”. the economic development of unconventional reservoirs, such as the shale gas and tight oil, was made possible by the combination of horizontal drilling and hydraulic fracturing. this practice has been motivating more and more interests in the academic community to investigate the nature of fluid flow and production characteristics in porous media with ultra-low permeability and complex fracture system. in turn, academic progress can shed light on the flow mechanism within unconventional reservoirs and improve the understanding and development of these types of plays. recent successful development of unconventional reservoirs, especially shales and tight sands with highly complex fracture systems, yields a bunch of new challenges. many researchers have tried to overcome these challenges by analyzing special phase behavior (nojabaei et al. 2012; luo et al. 2016; jin and firoozabadi 2016; luo et al. 2017) and transport phenomena (riewchotisakul and akkutlu 2016; wu and chen 2016) in nano-size pores, and by considering geomechanics (kim and moridis 2012; yu et al. 2017) such as stress-sensitive permeability. these are all promising avenues, and some informative and inspiring works have been presented or published as has been referred above. on the other hand, despite these progresses, some fundamental concepts and tools for the unconventional reservoir engineering are directly inherited from conventional reservoirs as special situations with ultra-low permeability. generally speaking, in the unconventional reservoir routine methodology used for modelling flow on the reservoir scale and analyzing production is still along the conventional route, which, for the simplest single-phase case, applies the diffusivity equation with some averaged or upscaled parameters. mainly based on the mailto:shuailiu15@gmail.com 2 solutions to the single-phase diffusivity equations, blasingame et al. (1986a, 1986b, 1988, 1989) rigorously derived the rate-decline relation and developed a method to extract the formation properties, such as permeability, drainage area, and hydraulic fracture length by analyzing the flowrate-time data. due to the formation characteristics of unconventional reservoirs, where the traditional pressure transient analysis (pta) becomes infeasible, the rate transient analysis (rta) or production analysis, which has been developed from the above referred works, is the popular way to analyze the reservoir performance. clarkson and pedersen (2010) examined the use of classic rta for analysis of tight oil reservoirs and proposed an integrated rta approach, which can provide reasonable estimates of hydraulic fracture and reservoir properties. as a typical application of rta in the shale reservoirs, belyadi et al. (2015) use this tool to estimate the productivity of marcellus shale wells and identify the most successful completion methods in the investigated play. to take into account the existence of complex fractures in the formations, the dualporosity model (warren and root 1963; kazemi 1969; de swaan 1978) and its variants (abdassah and ershaghi 1986; liu et al. 1987) are widely employed in the study of unconventional reservoirs. bello and wattenbarger (2008) combined the slab matrix transient dual porosity model with rta to study the usage of various shape factor formulations and the effect of matrix geometry on the transient linear response. fuentes-cruz and valko (2015) applied the dual-porosity/dual-permeability model to study the proposed concept of variable matrix-block size and their resulting mathematical model is fundamentally different compared with the standard dual-porosity model due to the interporosity flow. given the ultra-low permeability of the formation matrix and the extensively elongated transient regime, trilinear model (lee and brockenbrough 1983) has been introduced as a simplified but useful “asymptotic” model to study the flow in unconventional reservoirs. ozkan et al. (2009) applied an analytical trilinear solution to describe the performance of the multiple fractured well and concluded that smaller fracture spacing corresponds to better productivity. though it hasn’t aroused wide attention in the community of petroleum engineering, anomalous diffusion has been observed in abundant experiments (adams and gelhar 1992; berkowitz and scher 2001) and wellstudied analytically (metzler et al. 1994; berkowitz and scher 1997) and numerically (zhang et al. 2008; vilaseca et al. 2011) by hydrologists, biologists, and physicists. usually, it is the tracers or the small protein molecules that undertake the anomalous diffusion in a flow field that has very high heterogeneity, such as complex fracture systems or massive large molecular as obstacles. however, since the diffusivity equation describes both the tracers’ diffusion and the flow through porous media, by analogy and similarity the flow through porous media is very likely to show characteristics of anomalous diffusion in highly heterogeneous formations, for example shales. actually, some predecessors in petroleum engineering have done some works on this topic. raghavan (2011) generalized the concepts of classical diffusion by the fractional derivatives to explain features of anomalous diffusion. based on fractional derivatives, he described a nondarcy constitutive equation for the flux. raghavan and chen (2017) replaced by the fractional constitutive flux laws the darcy’s law in their mature dual-porosity model for the multiple fracture horizontal well to obtain the pressure distribution in the drainage region. they provided the asymptotic solutions for the longterm reservoir responses and found that power-law behaviors reflect the heterogeneity in the system. albinali and ozkan (2016a) used anomalous diffusion to represent flow in the naturally fractured region between hydraulic fractures for the transient, single-phase production. based on the sensitivity analyses, they suggested to use this model on a wide range of flow heterogeneity even without the intrinsic details of the formation properties. albinali and ozkan (2016b) discussed the basis of anomalous diffusion and combined this new concept with the dual-porosity model to interpret the flow in the heterogeneous formation. subdiffusion exponents and other coefficients can be extracted from the anomalous diffusion model to help us learn more about the reservoir-rock quality and stimulation efficiency. holy and ozkan (2017) recently developed a 1-d numerical model for the linear, single-phase flow undertaking anomalous diffusion. this work provides the foundation for more general multi-dimensional numerical models in the future. the outline of this paper is listed as follows. in the following section, the physical background of the single-phase flow diffusivity equation is revisited by discussing its equivalent form describing individual fluid particle motion. then, a method is developed by simulating the continuous-time markov chain (ctmc) on a geometric graph to model the single-phase flow in the fracture network, which is embedded 3 in the formation. using the simulation results we can calculate the relation of transferred mean square displacement (msd) vs. time to demonstrate the proposed anomalous diffusion phenomenon. then by the models described above, the simulation results for a highly fractured formation are given in the simulated result section. the plots of msd with respect to time are displayed to show apparently the characteristics of anomalous diffusion with a non-unit slope. some further discussions about the simulation results are provided. as a result, the fractional diffusivity equation is suggested to account for the anomalous transport phenomenon in the highly fractured unconventional reservoirs. revisiting diffusivity equation single-phase flow of slightly compressible fluid in porous media is always the primary and most essential problem for petroleum industry (dake 1983). although it may be called as one of the thoroughly investigated topics in this field, we would like to propose a new perspective for this equation when the porous media has a micro-structure in the form of complex fracture network. for simplicity and without losing generality, we will concentrate on the problem in two dimensions. the assumptions for the discussion and the model in this paper are listed as follows. 1. the fluid is of single phase and slight compressibility. the formation volume factor 𝐵 and viscosity 𝜇 can be considered essentially constant. the total compressibility of fracture rock and matrix rock saturated with the fluid are 𝑐𝑡𝑓 and 𝑐𝑡𝑚, respectively. in addition, only isothermal flow is considered. 2. the formation is horizontal, and its thickness ℎ is constant. its upper and lower boundary is of no flow conditions. 3. the porous media consists of two main parts: the fractures and the matrix. the schematic graph in figure 1a illustrates the domains of our model. • although, in reality, the unconventional reservoir formations have the strong heterogeneity due to fractures in nearly all scales (gale et al. 2014), for the purpose of this work we only take into account the macroscopic fractures (larger than ~10−3 ft). the fracture system consists of natural fracture sets, induced fractures and hydraulic fractures, all of which are interconnected to form a “fracture network” and capable of directly contributing to the flow into the wellbore. the natural fractures and induced fractures have the same formation properties: constant fracture permeability 𝑘𝑓, constant fracture porosity 𝜙𝑓 and constant aperture 𝑏. the hydraulic fractures are assumed to be of planar shape and have infinite conductivity. all the fractures have the same height as the formation thickness and are perpendicular to the horizontal bedding plane. • the matrix is isotropic and homogeneous. this means that we neglect the small-scale fractures, and isolated fractures that have no connections to the interconnected fracture system as mentioned previously. the matrix has constant parameters: permeability 𝑘𝑚, porosity 𝜙𝑚. • based on the nature of the unconventional reservoir that the fractures have pretty much higher permeability than matrix, it is assumed that the fluid initially located in fractures only transports in the fracture system, and that the fluid initially located in the matrix firstly transports slowly through the matrix into the fracture system, after which it continues transporting only in the fracture system. 4. based on the above assumptions, the flow in both domains is dictated by darcy’s law. due to the pretty small size of aperture 𝑏 compared to ℎ we can assume laminar flow in the fracture system. the hydraulic fractures are of uniform spacings, as shown in figure 1b, so that each one is located in the center of its own drainage volume. by the geometric and physical symmetry, we regard the symmetrical element, a quarter of the drainage area for one hydraulic fracture, as our problem domain. as shown in figure 1c, it has the length 𝑙𝑑, the width 𝑤𝑑, and the hydraulic fracture half-length 𝑥𝑓. furthermore, the drainage area’s outer boundaries are of no flow conditions, except for the part of infinite-conductivity fracture that is at constant pressure condition. for simplicity, we also neglect the flow in fractures across the drainage area boundary, if any. 4 (a) (b) (c) figure 1—illustrations of the fracture system and matrix, the drainage area of a hydraulic fracture, and the problem domain. by the above assumptions, the problem has been reduced to a 2-d single phase flow problem with the gravity being neglected. in either the homogeneous and isotropic domains, the matrix or the fracture system, the pressure distribution of slightly compressible flow can be mathematically modeled by the diffusivity equation (eq. 1). 𝑘𝑖 𝜇 ∆𝑝𝑖 = 𝜙𝑖𝑐𝑡𝑖 𝜕𝑝𝑖 𝜕𝑡 ,…………………………………………………………………………….…...……(1) where 𝑖 = 𝑓,𝑚 and 𝑝𝑖 is the pressure in domain 𝑖. since the properties are constant in each domain, eq.1 can be rearranged into the form as shown in eq. 2. 𝑘𝑖 𝜇𝜙𝑖𝑐𝑡𝑖 ∆𝑝𝑖 = 𝜕𝑝𝑖 𝜕𝑡 ...…………………… ……………………………..…………………….……………(2) as a regular step, we wrap up into a single parameter the parameters on the left-hand-side before the laplace operator. in eq. 3 the parameter 𝜂𝑖 is usually called the hydraulic diffusivity coefficient with the unit m2 s⁄ in si unit. obviously, 𝜂𝑖 is also a constant parameter in either the fracture system or the matrix. substituting 𝜂𝑖 back into eq. 1 gives us a result which has the form of the equation dictating the general diffusion process (eq. 4), as shown in eq. 5. 𝜂𝑖 = 𝑘𝑖 𝜇𝜙𝑖𝑐𝑡𝑖 ,……………..……………..………………………..…..…………………………………. (3) 𝐷∆𝐶 = 𝜕𝐶 𝜕𝑡 ,………………………………………………………….…………………………………..(4) horizontal wellbore hydraulic fracture natural fractures & induced fractures drainage area wd ld xf 5 𝜂𝑖∆𝑝𝑖 = 𝜕𝑝𝑖 𝜕𝑡 .…………………………………………………….………………………………………(5) since 𝐷 and 𝜂𝑖 have the same dimension and the above two equations share the same form, there should be some physical analogy between the pressure 𝑝𝑖 and the concentration 𝐶. with the assumption of slightly compressible fluid, the relation between the pressure and density is linear, which means that pressure is equivalent to density in this case. thus, pressure can be taken as some type of “density” or “concentration” for the single-phase fluid particles. in this perspective, eq.5 describes the aggregate behavior of the huge number of fluid particles in the porous media. by the theory of normal diffusion (vlahos 2008), which has been investigated since einstein (1905)’s work on brownian motion, the msd, 〈𝑟2〉, of the fluid particles is related to the time 𝑡 by the diffusivity coefficient 𝐷, as shown in eq. 6. eq. 5 can be derived from eq. 6 (vlahos 2008), which means eq. 5 is only valid for the aggregate behavior of those particles whose msd vs. 𝑡 relationship is dictated by eq. 6. that is, the validity for using eq. 5 for a flow on the domain with a specified scale depends on the validity of eq. 6 for the fluid particles in the same domain. 〈𝑟2〉 ~ 𝑡.………………………………………………………………………………….……………..(6) according to the above analysis, the reason why eq. 5 can be successfully applied to the conventional reservoir’s flow in multiple scales is that the fluid particles moves approximately in a euclidean space due to the relatively homogeneous porous media, and that the average motion of the particles is dictated by eq.6. and for the same reason, eq. 5 is also valid for the flow in some tight sands with very low permeability but no well-developed fracture networks, except for a quite small 𝜂𝑖. however, this isn’t the case for the unconventional reservoirs with complex fracture systems. by the assumptions, all the produced fluid comes directly from the fracture system. and the high production rate during the early period (several months to years) after the beginning of production all comes from the fluid initially located in the fracture system because of the ultra-low matrix permeability. thus, the major fluid flow and the production in this period can be readily modeled by solving eq. 5 with the fracture parameters on the fracture domain, only if the span, shape, and other details of the fracture network are available, which is basically impossible by the current state-of-the-art technology. consequently, we are forced to model the fracture flow based on the combined domains, since we have much more information and confidence to determine the drainage area. using the perspective of diffusing fluid particles, it is obvious that the particles only move in the fracture network instead of the full euclidean space. therefore, although the particle motion is described by eq.6 using the 1-d coordinate attached to the fracture, this relation of msd vs. 𝑡 needs to be transferred to the 2-d coordinate attached to the whole drainage area. this is illustrated in figure 2. in this figure, a particle diffuses from point 1 to point 2 along the yellow path in the fracture. its displacement with respect to the fracture coordinate is 𝑟1 + 𝑟2 + 𝑟3 + 𝑟4, while that with respect to drainage area coordinate is 𝑑, which is much smaller than the previous one. apparently, this transferring should take into account the geometric characteristics of the fracture network, which means the transferred relation of msd vs. 𝑡 will not follow the linear relation as eq.6. according to some prior works (berkowitz and scher 2001; vlahos 2008), it can be intuitively proposed that the modified relation should have the power law form as shown in eq.7. 〈𝑟2〉 ~ 𝑡𝛼.………………………………………………………..…………………..…………………(7) if 𝛼, the diffusivity exponent, doesn’t keep unit, the corresponding process is named as the anomalous diffusion. to demonstrate this phenomenon in highly fractured formation is the main task of the rest of this paper. as a consequence, due to the possible invalidity of eq.6 when 𝛼 isn’t the unit anymore, using eq.5 to model the flow and production based on the whole drainage area may be only a very rough simplification and fails to capture some features of the flow through the unconventional reservoir with complex fracture networks. 6 model based on markov chain to simulate the fluid particle’s motion in the fracture network, which is embedded in a 2-d euclidean space, we take advantage of its normal diffusion. as has been studied in many publications (itô 1974; rogers and willianms 1994), the fluid particles under normal diffusion can be mathematically modeled to have markov property. in more details, denoting the location of a single particle at time 𝑡 as 𝑋(𝑡), we have a continuoustime stochastic process {𝑋(𝑡): 𝑡 ≥ 0}, which is considered to have markov property only if the conditional probability satisfies eq.8 (itô 1974; rogers and willianms 1994). 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖, 𝑋(𝑡𝑛−1) = 𝑖𝑛−1, 𝑋(𝑡𝑛−2) = 𝑖𝑛−2, ⋯ , 𝑋(𝑡1) = 𝑖1 ] = 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖],.....(8) where 0 ≤ 𝑡1 ≤ 𝑡2 ≤ ⋯ ≤ 𝑡𝑛−2 ≤ 𝑡𝑛−1 ≤ 𝑠 ≤ 𝑡 is any non-decreasing sequence of n+1 times and 𝑖1, 𝑖2, ⋯ , 𝑖𝑛−2, 𝑖𝑛−1, 𝑖, 𝑗 are any n+1 states in the state space of markov chain. it means that each step of stochastic “jump” only depends on the current states, and the particle acts as it “forgets” the states it has previously experienced. since in this work the particles only move in the fracture network, the state space of the markov chain only contains the points belonging to the fractures. for simplicity and the limitedness of our computational resources, we only take the endpoints and the intersection points of the fracture segments as the states, as illustrated in figure 3. when a particle occupies a state at a given time, it will “jump” after some “waiting time” at the next step to one of the neighbor states. the target of the “jumping” is chosen randomly according to the probability distribution determined by the diffusivity coefficient, the length, and the aperture of all the fracture segments directly connected to the current state, as shown in eq.9. figure 2—illustration of the displacements with respect to different coordinates. figure 3—illustration of endpoints and intersection points as states. r1 r2r3 r4 d 1 2 1 2 5 74 6 3 7 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖 ] = { 𝜂𝑗𝑏𝑗 𝑙𝑗⁄ ∑ 𝜂𝑘𝑏𝑘 𝑙𝑘⁄𝑘∈𝑁𝑖 , 𝑗 ≠ 𝑖 0, 𝑗 = 𝑖 ,……………………………………………………..(9) where 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖 ] is the probability for jumping from the current state 𝑖 to the neighbor state 𝑗, 𝑁𝑖 is the set of neighbor states of 𝑖, and 𝜂𝑘, 𝑏𝑘 and 𝑙𝑘 are respectively the diffusivity coefficient, aperture and length of the fracture segment connecting 𝑖 and one of its neighbor state 𝑘 . only if this kind of probability distribution is applied will the resulting expectation of the stochastic process hold consistency with the solution of the diffusivity equation. however, the above probability distribution only applies to the states corresponding to regular points, not to those points located on the hydraulic fracture. as stated in the assumptions, the hydraulic fracture has infinite conductivity, which is translated into total absorbing states for the particle stochastic motion. it means that whenever a particle jumps into these states, it will stay there forever and will not jump to other states again. apparently, the probability distribution of these absorbing states is 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖 ] = { 0, 𝑗 ≠ 𝑖 1, 𝑗 = 𝑖 ……………………..………………………..…………….(10) this definition of absorbing state is consistent with the constant pressure condition on the hydraulic fracture boundary. no matter what type the state is, its probability distribution satisfies the normalization condition that ∑ 𝑃[𝑋(𝑡) = 𝑗|𝑋(𝑠) = 𝑖 ]𝑗∈𝑁𝑖 = 1....………………………………………………..…..…………….(11) both definitions in eqs.9 and 10 use only the information of current state 𝑖, which manifests this process as a markov chain. besides the spatial increment, the temporal increment (the “waiting time”) should also keep the markov property, which means that only the “memoryless” poisson distribution should be applied to the temporal increment. while the markov property of time will later be considered implicitly by the kolmogorov forward equation, we state the temporal increment’s poisson distribution here for completeness. by the above concepts, we have implicitly described the fracture network as a graph object, which has the endpoints and the intersection points of the fracture segments as the nodes and the fracture segments between these nodes as edges. this graph is certainly related to the corresponding fracture network, so the graph is classified to be a geometric graph with euclidean coordinates as one of the node attributes and length as one of the edge attributes. besides, another critical attribute for each edge is the weight, which defines the transition rate of the ctmc and is related to the probability distribution previously discussed. the edge weight is naturally defined as 𝜂𝑏 𝑙⁄ . briefly speaking, introducing the graph definition and terminologies explicitly will make our simulation easier to be implemented by programming. so far, we have reduced our problem to a feasible task that a ctmc is to be simulated on a geometric graph object, whose set of nodes are taken as the finite state space, and the weight, 𝜂𝑏 𝑙⁄ , of the edge between node 𝑖 and 𝑗 as the major part of transition rate 𝑞𝑖𝑗. by the kolmogorov forward equation (itô 1974), for the node 𝑖, we have 𝑑𝑃𝑖𝑗(𝑡) 𝑑𝑡 = ∑ 𝑃𝑖𝑘(𝑡)𝑞𝑘𝑗𝑘∈𝑆 ...………………………………….…………………..…………….………(12) in eq.12, 𝑃𝑖𝑗(𝑡) = 𝑃[𝑋(𝑡) = 𝑗|𝑋(0) = 𝑖] is the probability for the particle occurring at node 𝑗 at time 𝑡 after it starts moving from the initial node 𝑖. 𝑞𝑘𝑗 as the transition rate between node 𝑘 and node 𝑗 has the definition as shown in eq.13. 𝑞𝑘𝑗 = { 𝜂𝑗𝑏𝑗 (𝑙𝑗𝑎 2)⁄ , 𝑘 ≠ 𝑗 𝑎𝑛𝑑 𝑗 ∈ 𝑁𝑘 −∑ 𝜂𝑗𝑏𝑗 (𝑙𝑗𝑎 2)⁄𝑗∈𝑁𝑘 , 𝑘 = 𝑗 0, 𝑜𝑡ℎ𝑒𝑟𝑠 ,……………………………………………(13) 8 where 𝑎 is only a characteristic length for the system to make the unit consistent. and 𝑆 is the set of all the nodes in the graph. writing the ordinary differential equation (ode) eq.12 into the matrix form, we have 𝑑�⃑� (𝑡) 𝑑𝑡 = �⃑� (𝑡)𝐐,………………………………………………………………..……………………….(14) where �⃑� (𝑡) is a stochastic vector, and 𝐐 = {𝑞𝑖𝑗} is the transition rate matrix. from graph theory, we know (wikipedia 2017) that for a well-defined weighted graph, each entry of 𝐐 is the opposite of the corresponding entry in the graph’s laplacian matrix, which can be readily obtained. with the help of matrix exponential, the solution of eq.14 can be symbolically expressed as �⃑� (𝑡) = �⃑� (0) exp(𝐐𝑡),………………………………………………………………………………..(15) where �⃑� (0) is the particle’s initial distribution among the nodes. if we temporarily assume that the matrix exponential in eq.15 can be successfully evaluated, we can obtain the probabilities for a particle occurring at each node at any time 𝑡 after it starts to move from node 𝑖. the initial stochastic vector for this case is given by eq.16. �⃑� (0) = [0, 0,⋯ , 0, 1, 0,⋯ , 0] ,………………………………………………….……..………………(16) where 1 is the 𝑖th entry of this vector. these probabilities are equivalent to the particle distribution at time 𝑡 when massive particles all start from 𝑖 to undertake the stochastic process. on the other hand, since it is a geometric graph with euclidean coordinates as node attributes, we can calculate the square of distance between node 𝑖 and all other nodes to obtain a “vector of distance square”, 𝑣 𝑑𝑠, as shown in eq.17. 𝑣 𝑑𝑠 = [𝑑1,𝑖 2 , 𝑑2,𝑖 2 , ⋯ , 𝑑𝑖−1,𝑖 2 , 0, 𝑑𝑖+1,𝑖 2 , ⋯ , 𝑑𝑛,𝑖 2 ] ,………………………………………………………….(17) where 𝑑𝑗,𝑖 is the euclidean distant between node 𝑖 and 𝑗, 𝑑𝑗,𝑖 = [(𝑥𝑖 − 𝑥𝑗) 2 + (𝑦𝑖 − 𝑦𝑗) 2 ] 1 2⁄ . recalling that our main task is to calculate the relation of transferred msd vs. 𝑡 for the formation embedding fracture network (or the euclidean space embedding geometric graph), this task can be done by taking the dot product between �⃑� (𝑡) and 𝑣 𝑑𝑠 as shown in eq.18. 〈𝑟2〉(𝑡) = �⃑� (𝑡) ∙ 𝑣 𝑑𝑠..……………………..…………………………………………….……………(18) theoretically, we have provided the solution to our problem, but in practice the stable evaluation of the matrix exponential is problematic. since usually the longest fractures (~102 ft) are several orders of magnitude longer than the shortest ones (~10-3 ft), the value range of the non-zero entries in the matrix 𝐐 is quite large, which makes 𝐐 a very stiff matrix. some common methods (padé approximation, krylov space methods (moler and van loan 2003)) and packages (expokit (sidje 1998), matrixexp in mathematica (wolfram research, inc. 2017)) for evaluating matrix exponential do not work very well for the cases encountered in this paper. so, we had to resort to numerical methods solving the ode eq.14 directly (basically any “stiff” ode solver can be used). we have used mathematica’s ndsolve function (wolfram research, inc. 2017), which integrates many “stiff” ode solvers into its options, to solve eq.14 numerically for getting �⃑� (𝑡). besides the last step of solving ode, some other packages and algorithms have been used to do some pre-processing work. the 2-d discrete fracture network (dfn) is created using the fracgen; the dfn is processed by a modified python package (splichte 2013) based on the bentley-ottmann algorithm; the graph object is readily created using a python package, networkx (hagberg et al. 2008). simulation results using the described model in the last section, we conduct the simulation to the flow in the fracture networks with different scenarios (table 1): case 0: uses the regular meshes with uniform grid size in both 𝑥 and 𝑦 axis; case 1: uses the fracture network with two orthogonal sets which are randomly generated by fracgen; case 2: also uses the fracture network with two orthogonal sets, but the overall network rotates 45°; 9 case 3: uses the fracture network with two sets having 40° between them, and all the upper domain; case 4: uses a very complex fracture network, which has 4 sets of fractures and is the sample, “mwx4f”, in fracgen. table 1—statistics for the fracture network in various cases. case name max (ft) min (ft) mean (ft) median (ft) number of fractures number of nodes case 0 10 10 10 10 2525 1285 case 1 92.4 1.70e-03 11 7.6 1969 1753 case 2 83.8 1.00e-03 10.5 7.5 1940 1690 case 3 123.7 1.00e-03 13.1 8.5 753 698 case 4 81.6 1.00e-03 10 5.9 2572 2214 the domain of the first 4 cases all have the dimensions of 500 ft ×250 ft coming from the well spacing 1000 ft and fracture spacing 500 ft. and all cases have a hydraulic fracture half-length of 400 ft (𝐼𝑥 = 0.8) which is represented by the blue line on the boundary. since each case contains hundreds and even thousands of nodes, the comprehensive investigation is impossible without the help of some statistical methods, which is out of the scope of this paper. so, we only select 10 nodes randomly in each case to do the simulation on them and to show the relation of msd versus 𝑡. the plots and parameters of the fracture networks, and the results are shown below. case 0. figure 4—map view plot of the fracture network and 10 sampled nodes in case 0. 10 node 34 node 141 node 155 node 181 node 440 node 839 node 844 node 1074 0.10 1 10 100 1000 104 t 1 100 104 msd, ft2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 11 node 1093 node 1126 figure 5—log-log plots of msd vs. time for 10 sampled nodes in case 0. case 1. figure 6—map view plot of the fracture network and 10 sampled nodes in case 1. figure 7—histogram of the fracture length in case 1. 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 12 node 72 node 150 node 236 node 357 node 542 node 801 node 964 node 1104 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 13 node 1526 node 1662 figure 8—log-log plots of msd vs. time for 10 sampled nodes in case 1. case 2. figure 9—map view plot of the fracture network and 10 sampled nodes in case 2. figure 10—histogram of the fracture length in case 2. 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 14 node 139 node 428 node 731 node 965 node 1031 node 1127 node 1194 node 1247 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 0.1 100 105 t 0.001 1 1000 msd, ft2 1 100 104 t 0.1 10 1000 105 msd, ft 2 1 100 104 t 0.1 10 1000 105 msd, ft 2 1 100 104 t 1 100 104 msd, ft2 15 node 1391 node 1650 figure 11—log-log plots of msd vs. time for 10 sampled nodes in case 2. case 3. figure 12—map view plot of the fracture network and 10 sampled nodes in case 3. figure 13—histogram of the fracture length in case 3. 1 100 104 t 1 100 104 msd, ft 2 0.10 1 10 100 1000 104 t 0.10 1 10 100 1000 104 msd, ft2 16 node 7 node 10 node 187 node 225 node 358 node 377 node 471 node 576 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 0.1 100 105 t 0.01 10 104 msd, ft 2 1 100 104 t 0.1 10 1000 105 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 1 100 104 t 1 100 104 msd, ft 2 17 node 678 node 690 figure 14—log-log plots of msd vs. time for 10 sampled nodes in case 3. case 4. figure 15—map view plot of the fracture network and 10 sampled nodes in case 4. figure 16—histogram of the fracture length in case 4. 0.10 1 10 100 1000 104 t 1 100 104 msd, ft 2 0.010 0.100 1 10 t 0.100 10 1000 msd, ft 2 18 node 340 node 488 node 631 node 648 node 1137 node 1152 node 1714 node 1958 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 0.1 10 1000 105 t 0.1 10 1000 105 msd, ft 2 19 node 2128 node 2182 figure 17—log-log plots of msd vs. time for 10 sampled nodes in case 4. discussions of the results when performing the above 5 case studies, for simplicity we assign unit value to the diffusivity coefficient 𝜂𝑗, the aperture 𝑏𝑗, the fracture height ℎ, and the characteristic length 𝑎 and only use 1 𝑙𝑗⁄ as the weight of the edges to construct the weighted graph’s laplacian matrix. since by our assumptions 𝜂𝑗, 𝑏𝑗, ℎ and 𝑎 are all constants, only a constant factor is needed to transfer the “time” 𝑡 in the above plots to the real time, and the phenomena displayed aren’t affected by the values of these parameters as far as they fall into the ranges guaranteeing the basic assumptions of this work. in each of the above plots, besides the resulting relations of msd vs. 𝑡 presented in log-log plot, some dash lines with different colors are added to accommodate our analysis. firstly, the most straight-forward one is the orange dash line, which has exactly the unit slope. because case 0 uses the regular grid to do the simulation, it is exactly the same thing as conducting numerical simulation to the homogeneous reservoirs with the most common spatial discretization. thus, case 0’s result should be expected to show the nature of normal diffusion, as we have discussed in the previous section. it is exactly what we see in case 0’s plots (figure 5). the unit-slope orange line tracks firmly the resulting curve until deviation happens at the late time, when most of the particles have been “locked” in the absorbing nodes and msd levels out. some very small deviations occur at the early or intermediate time of some nodes, node 155, node1074, and node 1126. this is due to the boundary effect of our finite graph on these nodes that are relatively close to the boundaries. then, using case 0 as a reference, we can immediately notice the discrepancies between other cases (figure 8, figure 11, figure 14, and figure 17) and the normal diffusion. although it seems that every node in from case 1 to case 4 has its unique relation due the various local characteristics of the random created dfn, an obvious common phenomenon is that most of the curves deviate from the unitslope orange in quite early time. many of them are concave downwards displaying subdiffusion, with some of them being concave upwards corresponding to superdiffusion. the pair of green dash lines in each plot give us some sense of the scale of heterogeneity. roughly speaking, the average fracture length in all 5 cases is about 10 ft, which corresponds to 100 ft2 for distance square. so, the green line pair shows the point where the msd reaches a value that can be taken as characteristic size of heterogeneity. in case 0 where the fracture segments are all 10 ft long, the slope keeps the unit value before and after 100 ft2 msd is reached due to the totally homogeneous fracture distribution. in other cases, most deviations happen within the range 10 ft2~1000 ft2msd, or 1 ft ~ 10 ft, again roughly speaking. moreover, we can see that each plot has the exact unit-slope section in the very early time when msd is very small. recall that only fractures longer than 10-3 ft are modeled in our work, and the number of fractures with length less than 10-1 ft is very small from all the four histograms. this means that the flow domain with its characteristic dimensions less than the average fracture length can be considered homogeneous to some extent. however, since only 10 nodes have been sampled out of thousands for each case, this point can only be taken as a reasonable suggestion. it should also be noted that this observation has been made while neglecting all other types of heterogeneity. 0.10 1 10 100 1000 104 t 0.10 1 10 100 1000 104 msd, ft 2 0.10 1 10 100 1000 104 t 0.10 1 10 100 1000 104 msd, ft 2 20 although currently we cannot connect the fracture network characteristics (fracture density, fracture length distribution, fracture sets and clusters, and so on) to the properties of the diffusion due to the limited number of sampled nodes, we are capable to summarize some common diffusion patterns when looking at the results from various dfns comprehensively. we have already noted the early time concave period. similarly, the absorbing boundary domination at the late time is quite apparent. from the homogeneous case 0, it is apparent that the absorbing boundary has the effect of greatly leveling out the curve. bearing this in mind, we roughly draw the red straight dash line by hand to try to catch up its average deviating trends in early or intermediate times, and to try to rule out the absorbing boundary effects. so, these handmade trendlines are to some extent secant lines of the resulting curves. consequently, the slope of these trendlines, which is exactly the diffusivity exponent 𝛼 in eq. (7), tells the types of anomalous diffusion in a given range of scale: subdiffusion for 𝛼 < 1 and superdiffusion for 𝛼 > 1 . generally speaking, there are two diffusion patterns for the flow in the fracture network, if the anomalous diffusion does happen. type 1 is that after the early normal diffusion section, the curve directly concaves downward, and the flow begins to undertake subdiffusion until the absorbing boundary dominates. the typical examples for this type are node 964, 1104 in case 1 (figure 8), node 139, 428, 731, 965, 1650 in case 2 (figure 11), node 10, 471 in case 3 (figure 14), and node 1137, 1714, 2128 in case4 (figure 17). type 2 is characterized with a hump-like shape, which means the curve concaves upward to undertake superdiffusion firstly, and then becomes subdiffusion in a larger msd range. the typical examples for this type are node 150, 357, 801 in case 1 (figure 8), node 1031 in case 2 (figure 11), node 7, 377 in case 3 (figure 14), and node 340, 1958, 2182 in case 4 (figure 17). only if the absorbing boundary begins to dominate, the undertaking diffusion is overwhelmingly affected and even totally hidden. these two patterns are kind of intuitive for a flow into hydraulic fractures (the absorbing nodes). we feel that more complex patterns can be expected in some highly heterogeneous formations, possibly alternating subdiffusion and superdiffusion time periods. based on our prior discussions, we now try to answer our major question: is it valid enough to apply the classical diffusivity equation on the reservoir scale to model single-phase flow and to analyze the production? in our opinion, the diffusion pattern classification provides a perspective for the answer. looking back again at case 0, we make a tangential line (the horizontal black dash line) from the final plateau of the curve, and the tangential point and the intersection point with the unite-slope trendline both correspond to a time (the vertical black dash lines). not so surprisingly, we find that in the normal diffusion case, the differences between these two times for different nodes are always around 1 log cycle. so, this can serve as a standard to tell the validity of the averaged model (or homogenization) with the classical diffusivity equation. the type 1 pattern, when only subdiffusion happens, obviously enlarges this time difference to around 1 1 2⁄ or even 2 log cycles, and hence disproves the validity. on the other hand, the superdiffusion and subdiffusion in type 2 pattern counteract with each other to some extent and can lead to the time difference around 1 log cycle, such as node 150 in case 1 (figure 8), node 7, node 377 in case 3 (figure 14), and node 340 in case 4 (figure 17). so, if both type of nodes exist in a situation, we should determine or estimate which type dominates. it would require massive simulation conducted, or some advanced statistical tool employed. however, type 2 pattern can also lead to confusion by substantially shortening the time difference, which displays a superdiffusion on average, like the node 357, 542, 801 in case 1 (figure 8), node 1031 in case 2 (figure 11), node 2181 in case 4 (figure 17). actually, depending on the relation between superdiffusion, subdiffusion and absorbing boundary effects, type 2 pattern can manifest itself as “apparent” superdiffusion, subdiffusion or normal diffusion on average. the above observations provide further supportive argument for using the fractional diffusivity equation for modeling flow in porous media and production behavior in highly fractured unconventional reservoirs. in the end, we can also make some discussions about the common dual-porosity model in the perspective of anomalous diffusions. although the dual-porosity model also bears the two flow domain assumptions (fracture and matrix), it implicitly makes further assumption that the flow particles in the fracture domain undertake the diffusion in a euclidean space. thus, although it considers matrix supplementing fluid into fracture correctly, it still fails to capture the heterogeneity due to the geometry of the fracture network, which may limit the model’s application in highly fractured unconventional reservoirs. 21 conclusions in summary, based on our simulation work and the relevant discussions, we can reach the following conclusions: 1. the physical background of the single-phase diffusivity equation is revisited. combining the characteristics of single particle diffusion with complex fracture geometry, it is indicated that anomalous diffusion phenomenon will be dominant on the reservoir scale, even for single phase production behavior; 2. a markov-chain-based model is presented to model single particle diffusion and it is demonstrated that anomalous diffusion characteristics emerge from considering normal diffusion on a graph that is embedded in a 2-d euclidean space; 3. according to the simulation results, two known types of diffusion pattern (subdiffusion and superdiffusion) may rise from the same graph geometry (possibly alternating in time); 4. the fractional diffusivity equation have advantages in characterizing flow and production in highly fractured unconventional reservoirs. conflicts of interest the author(s) declare that they have no conflicting interests. nomenclature 𝛼 = diffusivity exponent 𝜂 = hydraulic diffusivity coefficient, ft2/sec 𝜇 = viscosity, cp 𝜙 = porosity 𝑎 = characteristic length, ft 𝐵 = formation volume factor, rb/stb 𝑏 = fracture aperture, ft 𝐶 = concentration, mol/ft3 𝑐𝑡 = total compressibility, psi-1 𝐷 = diffusivity coefficient, m2/s 𝑑 = euclidean distance between to nodes in the geometric graph, ft ℎ = formation thickness, ft 𝑘 = permeability, md 𝑙 = fracture length, ft 𝑙𝑑 = length of the problem domain, ft 𝑁𝑖 = the set of the neighbor states of state 𝑖 𝑃 = probability 𝑝 = pressure, psi 𝐐 = transition rate matrix 𝑞 = transition rate, 1/sec 𝑟 = partical displacement, ft 𝑆 = the set of all the nodes in a graph 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warren, j. e. and root, p. j. 1963. the behavior of naturally fractured reservoirs. spe j 3(3): 245-255. spe-426pa. wikipedia. 2017. transition rate matrix. https://en.wikipedia.org. accessed december 18, 2017. wu, k. and chen, z. 2016. real gas transport through complex nanopores of shale gas reservoirs. paper spe180086-ms presented at the spe europe featured at 78th eage conference and exhibition, vienna, austria, 30 may-2 june. yu, w., xu, y., weijermars, r., et al. 2017. impact of well interference on shale oil production performance: a numerical model for analyzing pressure response of fracture hits with complex geometries. paper presented at the spe hydraulic fracturing technology conference and exhibition, the woodlands, texas, 24–26 january. spe-184825-ms. zhang, y., meerschaert, m.m., and baeumer, b. 2008. particle tracking for time-fractional diffusion. physical review e 78(3): 36-42. shuai liu is a phd-degree candidate in the department of petroleum engineering at texas a&m university. his research is about the fracture design and optimization in unconventional reservoirs. liu holds a master’s and bachelor’s degree in petroleum engineering from china university of petroleum, beijing. han li is a seismic imaging geophysicist working at cgg in houston, texas. he got his ph.d degree in petroleum engineering department at texas a&m university in 2017. he co-authored more than 12 articles and conference papers. his expertise is hydraulic fracturing, rock mechanics, numerical simulation and geophysics. https://github.com/splichte/lsi https://en.wikipedia.org/w/index.php?title=transition_rate_matrix&oldid=815062240 24 peter p. valkó is the holder of the r. whiting chair in petroleum engineering at texas a&m university. he holds b.s. and m.s. degrees from veszprém university, hungary, and ph.d. degree from the institute of catalysis, novosibirsk, russia. previously he taught at academic institutions in austria and hungary and worked for the hungarian oil company (mol). his research interests include hydraulic fracturing, performance of stimulated wells and numerical inversion methods. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1219 received july 08, 2022; revised august 12, 2022; accepted september 29, 2022. *corresponding author: weirong.li@xsyu.edu.cn 1 minimum miscibility pressure prediction method based on pso-gbdt model yawen he,weirong li*, shihao qian, xi’an shiyou university, xi’an, china abstract with the development of eor technology, co2 flooding was a very promising method to improve the recovery of conventional and unconventional oil reservoirs. mmp (minimum miscibility pressure ) was one of the important parameters of the co2 flooding, and the use of an artificial intelligence algorithm can accurately predict the mmp, which was important to evaluate the effect of co2 flooding development in the reservoir. this work presents methods to automatically find optimal parameter settings for machine learning model by using an evolutionary algorithm. in this paper, 195 sets of experimental data of mmp were collected and screened from a large amount of literature for model establish, and sensitivity analysis was performed with the pearson's method for feature selection. then, five machine learning algorithms were used for regression and comparison. finally, a particle swarm optimization algorithm was used to optimize the parameters of the machine learning model with best performance. the accuracy of the training set obtained by the hybrid model was 99.9% and the accuracy of the test set was 97.6%. it indicated that the hybrid model are valid and accurate, and it can be used for mmp prediction in both laboratory and actual field. introduction co2 flooding is considered to be one of the most effective eor methods, particularly in developing light oil reservoirs. depending on the injection pressure, there are three classification of co2 flooding, including miscible gas injection, partial miscible gas injection, and immiscible gas injection. the displacement efficiency of reservoir oil by co2 flooding is highly pressure dependent and miscible displacement is only achieved at pressures greater than a certain minimum pressure, termed the minimum miscibility pressure (mmp). the mmp is defined as the lowest pressure for which a given injected gas composition can develop miscibility through a multi-contact process with a specific reservoir at reservoir temperature. mmp is completely independent of reservoir heterogeneity, but it is a strong function of oil composition, composition of the injected gas, and reservoir temperature. the methods used to predict the mmp under gas injection, miscible gas injection, or a dry gas cycling scheme, include lab tests, empirical correlations, equation of state (eos) methods, and data-driven approaches. specific lab test used to determine mmp include the swelling test, slim-tube test, rising bubble test, core flood, and other tests. yellig and metcalfe (1980) first proposed the experimental method to determine the co2-crude oil mmp through a thin tube. in the experiments, co2was injected at a specific rate into a thin tube at different pressures to obtain a recovery-pressure relationship curve to determine the mmp. the rising bubble apparatus method (rba) was proposed to determine mmp, in which an oil sample of a certain height is injected into a vertically placed visible high-pressure glass tube, followed by the injection of gas from the bottom of the glass tube at a constant rate, and mmp was determined from the shape of the bubbles and the distance they travel. harmon and grigg (1988) proposed a experiment to directly measure the relationship between the density and pressure of the injected rich gas phase, the mmp of the gas and crude oil miscible phase was determined by using the gas-oil dissolution characteristics. 2 the empirical correlations are a simple and fast means to determine mmp. various widely used correlations are outlined as follows. orr and silva (1987) proposed an empirical formula to determine the mmp for pure co2 and impure co2/crude oil system. the evp correlation presented by orr and jensen (1986) can determine the mmp for low-temperature reservoirs (t<120°ϝ). yellig and metcalfe (1980) proposed a correlation to forecast the co2 mmp with the temperature as the only correlating parameter from their experimental study. alston et al. (1985) derived an empirical correlation to estimate the mmp for pure or impure co2/crude oil systems. cronquist (1978) proposed an empirical formula to characterizes mmp as a function of reservoir temperature, molecular weight of the oil pentanes-plus fraction, and mole percentage of methane and nitrogen. the eos methods were established based on the theory of phase equilibrium of the system and was mainly used to map the relationship between the phase behavior of the co2 and crude oil system and the miscible function, and thus to obtain mmp for the system (yellig and metcalfe 1980; holm 1987; mungan 1981; cronquist 1978). the existing eos used to calculate mmp were the peng-robinson eos (pr-eos) (silva and orr 1987; orr and silva 1987; alston et al. 1985), nasrifar-moshfeghian eos (nmeos) (nasrifar and moshfeghian 2001), and the improved statistical fluid theory eos (ssaft-eos) (zhao et al. 2006). the eos method mainly uses phase simulation technique to investigate the influence of injected gas on the properties of crude oil. the parameters of eos were tuned by fitting the pvt experimental data to establish a phase model that conforms to the real fluid, and mmp of the oil and gas system is calculated by simulating the multi-stage contact experiment process (al-ajmim et al. 2011). the eos method can establish a phase model that fits the flow state characteristics of oil and gas multiphase fluids, so it can accurately characterize the phase behavior of real reservoir fluids and estimate the physical parameters. the lab measurements have a high accuracy, but it is very time consuming and expensive. the empirical correlations obtained under specific experimental conditions are often limited by failure to satisfy requirements. eos methods usually require a large amount of preliminary experimental data to fit the pvt parameters. recently, artificial intelligence methods have become essential techniques for mmp prediction. they learn high-level features of pvt data using structures composed of several nonlinear transformations to classify large and complex data. the significant advantages of artificial intelligence methods are the high prediction accuracy and the ability to process large amounts of data in parallel. with the development of artificial intelligence techniques, researchers can build and apply the required models in different fields. table 1 shows the research related to machine learning algorithms for mmp prediction. table 1--related works on machine learning based-mmp prediction model. ref. data model optimization algorithm output input parameters mousavi et al. 2008 44 lssvm pure and impure co2 mmp 5 chen et al. 2014 85 ann ga pure and impure co2 mmp 10 choubineh et al. 2019 251 ann mmp of different injected gas and crude oil dong et al. 2019 ann l2 regularization、 dropout mmp saeedi and soleimani 2020 144 ann tlbo、pso pure and impure co2mmp 8 tian et al. 2020 152 bp abc、da pure and impure co2 mmp 5 zhang et al. 2020 170 bp、rf、svm impure co2 mmp 6 (lssvm: least squares support vector machines; bp: back propagation; rf: random forest; svm: support vector machines; tlbo: teaching-learning-based optimization; abc: artificial bee colony; da: dragonfly algorithm) the motivation of this work is to use an optimization algorithm to automatically learn an efficient architecture and best set of hyperparameters of machine learning algorithms without much human intervention. it is difficult for human experts to select the parameters of machine learning algorithms before applying it to solve any real-world problem. it usually demands human expertise and intensive 3 efforts to conduct experiments on many possible configurations of algorithms parameters to finalize one with relatively better performance. researchers have developed hybrid versions of machine learning models for the optimization of parameter selection. particle swarm optimization (pso) is the most preferred selection of scholars to solve optimization problem as it has fewer hyperparameters, a simpler expression, and easy computation. based on previous studies, this paper introduces the machine learning algorithm to establish the mmp prediction model, and uses the pso algorithm to optimize ml algorithm with the best performance to establish the mmp prediction model. the rest of the paper is structured as follows: section 2 explains the proposed pso-based gbdt model architecture; section 3 briefly presents data collected, analyzes the correlation between each parameter and mmp; section 4 presents experimental results and discuss the performance in terms of accuracy; chapter 5 concludes the research of this paper. the proposed method gradient boosted decision trees (gbdt). gbdt was an ensemble of gradient boosting and decision trees. the algorithm classifies or regresses the data by using an additive model (a linear combination of basis functions) and by continuously reducing the residuals generated by the training process. gbdt is calculated through multiple rounds of iterations, and each iteration generates a weak classifier. each classifier is trained based on the gradient of the previous classifier (if the loss function is a squared loss function, the gradient is the residual value). the requirements for weak classifiers are generally simple enough and have low variances and high biases. in the training process reducing the deviation continuously improves the accuracy of the final classifier. the final total classifier is obtained by weighting and summing the weak classifiers obtained from each round of training. the general steps of gbdt are shown in figure 1. for each category, a regression tree is trained first, and the residuals are calculated for each category separately and repeated multiple calculations, and the final model is obtained. when predicting, the category with the highest probability is the corresponding category. figure 1—gbdt algorithm training process diagram. particle swarm optimization. pso was an evolutionary computation technique from the study of bird predation behavior. it searches the optimal solution through collaboration and information sharing among individuals in the group. pso designed massless particle to simulate the birds in the birds' swarm. the particle has only two attributes: speed and position. each particle individually searches for the optimal solution in the search space, which is recorded as the current individual extreme and shares the individual extreme with the other particles in the whole swarm. all the particles in the swarm adjust their velocity and position according to the current individual extreme they find and the current global optimal solution shared by the whole swarm. the process of pso algorithm is illustrated in figure 2 as follows. 4 figure 2—pso algorithm flowchart. experiments data collection and pre-processing. to establish a highly reliable intelligent model, factors related to reservoir temperature (t) and relative molar fractions (mol%) of co2, n2, ch4, and c2-cn were collected as relevant parameters affecting the mmp. this paper collects 395 data from a large number of literature (lai et al. 2017; cardenas et al. 1984; eakin and mitch 1988; graue and zana 1981; kanatbayev et al. 2015; spence and watkins 1980; harmon and reid 1988; thakur et al. 1984; zhang et al. 2016; al-ajmi et al. 2009; glasø 1985; dicharry et al. 1973; henry and robert 1983; khan et al. 1992) including laboratory measurement data and numerical simulation data. 195 sets of experimental data were obtained after sorting and screening for machine learning. as shown in figure 3, the temperature, t , ranges mainly between 50 and 100°c; the molar fraction of co2 mainly concentrates between 0 and 25%; the molar fraction of n2 is mainly from 0 to 10%; the component molar fraction of c1 mainly concentrates between 0 and 60%; the component molar fraction of c2~c5 distributes between 0 and 10%; the component molar fraction of c6 ranges from 0 to 5%; the molar fractions of c7+ ranges between 0 and 75%; mmp values mainly concentrates between 10 and 40 mpa. correlation analysis. affected by the diversity of crude oil components, it is necessary to analyze the correlation between different components and mmp. the interaction between the various components also has a certain effect on mmp. temperature and molar percentages of each component were used as the influencing factors to predict mmp. pearson's method was used to characterize the correlation between each component and mmp. as shown in figure 4, the factors with the greatest influence on mmp was the reservoir temperature, followed by the molar fraction of the carbon component. the molar fractions of co2 and n2 have little influence on mmp. 5 figure 3—input parameter distribution. figure 4—schematic diagram of group correlation analysis. 6 result and discussion the selection of proper hyperparameters of a gbdt model is very time-consuming process when it is to be decided on a trial-and-error basis. thus, it is required to develop an automated approach which can reach to the best gbdt model with minimal human expertise and efforts. the proposed work uses the random but guided nature of pso to find the best gbdt model. it optimizes its hyperparameters on a given dataset in predefined search-space. after data pre-processing and correlation analysis, ten parameters, including t, the molar fraction of co2, n2, c1, c2, c3, c4, c5, c6, and c7+ were used as inputs of the machine learning model, and the corresponding mmp was used as output for model training. to ensure the coverage of the training and test sets as large as possible and without overlap, the entire database was randomly divided into two groups: the training set and the test set. the training set consists of 165 data points, and the test set with 30 data points was used for model validation. five machine learning models are established for comparison, including lr, rr, rf, mlp, and gbdt.figure 5 shows the predicted results obtained by the five models. the horizontal coordinates in figure 5 are the actual values and the vertical coordinates are the predicted mmp values. it shows that the gbdt model has the best performance, followed by random forest. the linear regression, ridge regression, and multilayer perceptron have poor performance. figure 5—performance comparison based on predicted and actual dataset. 7 table 2 shows the accuracy of the five machine-learning models for mmp prediction. the result indicates that gbdt model has an accuracy of 98.5% and 93.7% in the training and test set, which outperforms the accuracy overwhelmingly to the other models. table 2—current status of machine learning prediction mmp research. machine learning model accuracy train set test set linear regression 47.7% 67.0% ridge regression 47.8% 66.6% gradient boosting decision tree, 98.5% 93.7% random forest 95.1% 88.6% mlp 99.3% 65.2% swarm optimization is performed by encoding hyperparameters of gbdt into particles. the fitness function represents the accuracy of the gbdt and has been passed on for generations. the fitness values are estimated over 100 generations to optimize mmp prediction. four important parameters affecting the optimization of pso were clarified. the pso algorithm mainly optimizes four parameters: n-estimators, learning rate, max-depth, and alpha. the number of n-estimators is the number of decision trees, which is the amount of data evaluation. it has a monotonic effect on the accuracy of the model. the larger the nestimators, the better the model. however, the accuracy of the model does not increase after the nestimators reach a certain level. the optimal value of n-estimators is 413. and the value of the learning rate needs to be set within a certain range. high learning rate will lead to unstable learning. too small learning rate increases the training time. the minimum miscibility pressure value of the learning rate is 0.83. the maximum parameter value for the maximum depth decision tree can be applied at high latitudes and low sample sizes. it is very effective to decide whether to increase the depth according to the result effect. alpha is the weight of the l1 regularization term and can be used to speed up the computation in the case of high dimensionality. the optimal value of alpha is 0.50. for the experiments now on, we split the dataset into 60% for training and 40% for evaluation. table 3 shows the range and optimal value of the four hyperparameters of pso algorithm used in the experiment. table 3—the hyperparameters of pso used in the experiment. n-estimators learning rate max-depth alpha default value 100 1 10 0.9 value ranges 10-1000 0.1-1 1-10 0.5-0.95 optimal values 413 0.83 5 0.50 figure 6 visualizes the performance of the pso-gbdt model on training model. the curve is generated by plotting the prediction mmp against the actual mmp at various combination of input setting. experiments show that the pso optimizes the gbdt model well for mmp prediction. after the optimization, the pso-gbdt model achieved 99.9% of accuracy in the training set and 97.6% of accuracy in the test set. the proposed hybrid model confirms to achieve a better performance. the accuracy of the hybrid model is improved by 1.4% and 3.9% for the training and test set, respectively. 8 figure 6—performance of pso-gbdt on training model . conclusions hyperparameter fine tuning has been an obstacle for obtaining a satisfying machine learning model due to the high cost of its trial-and-error process. to tackle this problem, we should speed up the searching efficiency as well as reduce the computation cost of fitness evaluation. we proposed a machine learning model optimized by pso for efficient mmp prediction. to search for the optimal structure of machine learning model, we performed swarm optimization by encoding hyperparameters into particles. main conclusions obtained by this work are as follows: 1. temperature has the greatest influence on the mmp, followed by the molar fraction of carbon components. in contrast, the molar fractions of co2 and n2 components have little effect on mmp. 2. after comparing the mmp prediction models established by the five algorithms, the comparison of accuracy shows that the gbdt model has the best performance, with 98.5% accuracy in the training set and 93.7% accuracy in the test set. 3. with combining pso algorithm, the pso-gbdt model was established. the accuracy of the training set is 99.9 %, and the accuracy of the test set is 97.6 %. the hybrid pso-gbdt prediction model has improved the accuracy of both the training set and the test set, making the mmp prediction more accurate. conflicts of interest the author(s) declare that they have no conflicting interests. references al-ajmi, m., alomair, o., and adel e. 2009. planning miscibility tests and gas injection projects for four major kuwaiti reservoirs. paper presented at the kuwait international petroleum conference and 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presented at the spe annual technical conference and exhibition, dallas, texas, 21-24 september. thakur, g.c., lin, c.j., and patel, y.r. 1984. co2 minitest, little knife field, nd: a case history. paper presented at the spe enhanced oil recovery symposium, tulsa, oklahoma, 19-21 april. tian, y., ju, b., yang, y., et al. 2020. estimation of minimum miscibility pressure during co2 flooding in hydrocarbon reservoirs using an optimized neural network. energy exploration & exploitation 38(6): 24852506. yellig, w.f. and metcalfe, r.s. 1980. determination and prediction of co2 minimum miscibility pressures. journal of petroleum technology 32(1): 160-168. zhang, j., zhang, x., and dong, s. 2020. estimation of crude oil minimum miscibility pressure during co2 flooding: a comparative study of random forest, support vector machine, and back propagation neural network. 2020 ieee 5th information technology and mechatronics engineering conference (itoec). zhang, k., seetahal, s., alexander, d., et al. 2016. correlation for co2 minimum miscibility pressure in tight oil reservoirs. paper presented at the spe trinidad and tobago section energy resources conference, port of spain, trinidad and tobago, 4-6 june. zhao, g.b., adidharma, h., towler, b., et al. 2006. minimum miscibility pressure prediction using statistical associating fluid theory: twoand three-phase systems. paper presented at the spe annual technical conference and exhibition, san antonio, texas, usa, 24-26 september. 10 yawen he, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focused her research in areas involving reservoir simulation, well testing, and production analysis. weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. he research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. li holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. shihao qian, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. he holds a bs degree in petroleum engineering from xi’an shiyou university. abstract introduction the proposed method experiments result and discussion conclusions conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1284 received march 29, 2024; revised july 14, 2024; accepted april 19, 2024. *corresponding author: jude.odo@futo.edu.ng 1 application of proxy models for estimation of cumulative recovery volume from a heavy oil reservoir jude emeka odo*, mike obi onyekonwu, sunday sunday ikiensikimama, university of port harcourt, rivers state, nigeria; chidinma uzoamaka uzoho, laser engineering and consultants limited, rivers state, nigeria; praise udochukwu ekeopara, federal university of technology, owerri, nigeria abstract steam flooding as a popular method for heavy oil recovery is associated with high cost and uncertainty issues. these issues are usually analyzed through various simulations and experiments which are usually time consuming and computationally expensive. hence, in this study a response surface model as proxy model was developed to estimate the cumulative recovery volume (crv) from a heterogeneous reservoir undergoing a steam flooding process. a five inverted spot steam flooding pattern for the heavy oil reservoir was developed, followed by a box-behnken experimental design considering steam and reservoir parameters, was used for data generation. hence, with steam injection rates, steam temperature, steam quality, bottom-hole flowing pressures of the producer wells as the input parameters, a reduced quadratic response surface model was developed to predict the crv. with the developed model as the objective function, the maximization of the crv was achieved while determining the optimal values for the parameters used. the study proved successful as the adjusted and predicted r2 values were recorded as 97.59% and 95.85%, respectively. also, up to 19% increase in crv was achieved after the optimization process. this research, therefore, demonstrates the feasibility of using proxy models to analyse and estimate crv of a steam flooding reservoir while benefiting from the computational advantages they provide. this approach has potential applications in the oil and gas industry, as it can help reduce uncertainty and the associated high costs of heavy oil recovery. introduction there is an increasing demand for fossil energy in the world as human population and mechanization increases (al adasani and bai 2011). according to the international energy agency (iea) forecast for 2008-2035 outlook, there will be a primary energy demand rate of around 300 mmboe/d and crude oil is predicted to escalate to almost 100 mmboe/d by 2035 (evans et al. 2021). this has therefore fostered the need for the exploration and exploitation of various unconventional energy sources. the extraction of crude oil from the subsurface generally follows three stages, namely, the primary, secondary and enhanced oil recovery (tertiary) stages. sponsored by the natural drive mechanism of the reservoir, the oil is being produced in the primary recovery stage, and this usually results to roughly 10% of oil supposed to be produced from the formation. in secondary recovery, specialized fluids are injected into the reservoir, through a displacing technique, can extract 20-40% of original oil in place. then the last production stage involving the production of heavy crude oil unlike primary and secondary uses specialized techniques for 30%-60% of heavy oil production (alawode and falode 2021; muzzafaruddin 2019; mokheimer et al. 2019). mailto:jude.odo@futo.edu.ng improved oil and gas recovery 2 one of the most popular and efficient ways of enhanced oil recovery is the thermal recovery method (hama et al. 2014). the idea here is that heat is used to increase the temperature of the formation thereby lowering the viscosity of the heavy oil contained in this formation, permitting the oil to easily flow towards the production well. most times this method can involve different steam injection techniques (chaalal 2018). thermal recovery method can involve any of these techniques, including steam flooding, steam assisted gravity drainage (sagd), in-situ combustion, cyclic steam injection etc. amongst these techniques is the steam flooding thermal eor method, which is being investigated in this research. steam flooding is a type of thermal eor method that uses an injection-to-production configuration for heavy oil production. steam is pumped into the reservoir from the injector well(s), as shown in figure 1, the pumped steam heats up the formation around the wellbore, eventually forming a steam zone that grows with continuous steam injection while reducing formation fluid viscosity and increasing oil mobility. figure 1—a typical illustration of a steam flooding process (modified frommokheimer et al. 2019). however, while eor methods especially the thermal techniques have proven to be efficient, initial assessment of the feasibility of the chosen technique must be ascertained before field scale application (matthew et al. 2023). the feasibility study must consider the risk, economic viability (realizable oil volume by the process) and optimal parameters for optimal production from such reservoirs. the industry, on this regard, has always relied on building and evaluating reservoir numerical simulation model to carry out these studies. however, the complexity of these numerical simulations makes conducting a full experimental run timeconsuming. additionally, there are significant storage constraints, and often, the simulations lack the flexibility needed to perform sensitivity studies. these studies are essential for assessing the impact of one parameter on another and identifying optimal parameters for achieving optimal production (ma and leung 2020; yu et al. 2021). to mitigate these gaps, an innovative approach, known as proxy models have proven to be successful and have been utilized in providing excellent solutions. the proxy model, also known as the surrogate model, is simply a representation of a complex numerical simulation that is useful in higher levels of reservoir study such as uncertainty analysis, risk analysis, and production optimization (bahrami et al. 2022; silva et al. 2020). this approach has since been applied in various areas with significant results. aboaba et al. (2020) implemented smart proxy models in in computational fluid dynamics (cfd) simulation and thereby reduced the computational cost that would have been associated with the cfd simulations. similarly, by leveraging an optimized least-squares support vector machine (lssvm) as an adaptive proxy model, qiao et al. (2022) were able to handle efficiently production optimization problems. while surrogate models have been applied in these aforementioned areas, yu et al. (2021) leveraged artificial neural networks as a suitable data-driven proxy model for forecasting the cumulative oil production during a steam-assisted gravity drainage process. while, matthew et al. (2023) combined proxy models and nsga-ii (non-dominated sorting genetic algorithm ii) to improved oil and gas recovery 3 determine the optimal values for water injection rates and half-cycle lengths to maximize the oil recovery and co2 stored in the reservoir. these various applications of proxy models therefore make the use of proxy models suitable for application for problems having similar challenging constraints. hence in this study, a quadratic response surface proxy model was developed to estimate the cumulative recovery volume from a heterogeneous heavy oil reservoir undergoing a steam flooding process. with the developed model, further investigative studies provided optimal values for the selected parameters, including steam injection rates, steam temperature, steam quality, bottom-hole flowing pressure to maximize production from this process. several areas covered in this study can be summarized as follows. 1. the complex numerical simulation to model a steam flooding pattern with five inverted spots for a heavy oil reservoir was first developed. 2. the study utilized a box-behnken experimental design, considering steam injection rates, steam temperature, steam quality, and bottom-hole flowing pressure of the producing wells. 3. after creating and validating the proxy model, further uncertainty studies were conducted to evaluate the behaviour of input parameters and optimize the objective function. the paper comprises multiple sections. section 1 provides an overview of the background and research objectives. section 2 outlines the materials and methods employed to attain these objectives. section 3 is dedicated to presenting the results and discussing the comprehensive findings of the study. the final section encompasses the conclusions and recommendations derived from our research. materials and methods steam flooding reservoir simulation model. in proxy model design, defining the actual complex system of interest must first be accomplished. this system otherwise referred (aboaba et al. 2020), involves a space and time simulation usually generated with a simulator with defined input and output sections. hence, in this study a reservoir simulation was developed for a five inverted spot steam flooding pattern for 10 years time step, using eclipse 2019 edition. the developed heterogeneous mode with dimensions of 2500×2000× 2500 (ft), has a porosity of 30%, with varying permeabilities ranging from 500,000 to 1000,000 md across the formations. the model is made up of a single injector well located at the center, from which steam is pumped in and four producer wells as can be depicted in figure 2. however, it is worthy to note that all the reservoir, well configuration and pvt data were obtained from spe 2 model (spe 2010), with slight modifications to our study. (a) 2d steam drive reservoir model (b) 3d steam drive reservoir model figure 2—steam flooding reservoir simulation model. improved oil and gas recovery 4 data generation. in building a proxy model, data is of uttermost importance as the algorithm will leverage on it to produce a suitable proxy model. hence, the data generation for this study took several steps which are summarized as seen in figure 3. firstly, a box-behnken experimental design was utilized to develop experimental runs considering various reservoir and steam flooding parameters. box-behnken design (bbd) is a type of design pattern for response surface modelling specifically for fitting a second-order (quadratic) model. figure 3—steps for generating data for proxy model development. bbd proves beneficial as it eliminates the need to test points at the extremes of the cubic region resulting from two-level factorial combinations. this is particularly advantageous, given that such points are either prohibitively expensive or impossible to test due to physical constraints in experimentation (ahmad et al. 2020; ferreira et al. 2007). next, with the generated experimental runs fed into the reservoir model, the output was then collected for each row or experimental run. while this process may seem time consuming, a python automation script was developed to handle this process within few minutes. table 1 shows the various controllable reservoir parameters considered for the model development. table 1—reservoir and steam flooding parameters for proxy model development. s/n parameters identifiers units min max 1. bottom-hole pressure for well 1 x1 psi 500 2000 2. bottom-hole pressure for well 2 x2 psi 500 2000 3. bottom-hole pressure for well 3 x3 psi 500 2000 4. bottom-hole pressure for well 4 x4 psi 500 2000 5. steam injection rate x5 cc/day 1000 10000 6. steam quality x6 0.1 1 7. steam temperature x7 ºc 100 200 proxy model. a quadratic proxy model serves as a pivotal tool in approximating complex relationships between variables within a system. in this study, the quadratic proxy model was constructed using designexpert-13 software, a robust statistical tool known for its capabilities in experimental design and analysis. generally, quadratic equation takes the general form as, improved oil and gas recovery 5 � � = ��2 + �� + � ,.......................................................................................................................................................(1) where �, �, and � are coefficients, and � represents the independent variable. this equation encapsulates a nonlinear relationship wherein the variable � is squared, thus allowing for the representation of curvature in the relationship between variables. the quadratic model was selected as the proxy model in this study because of both its performance, simplicity and interpretability. additionally, quadratic model provides flexibility by accommodating curvature and nonlinearity in the data, allowing for the representation of complex relationships and often yields accurate predictions within the range of observed data points, making it valuable for interpolation tasks (shacham et al. 2007). objective function. an objective function serves as a cornerstone in optimization tasks, encapsulating the desired outcome or criteria to be maximized or minimized. in our study, the objective function encapsulates the fundamental goals or performance metrics that we aim to optimize. maximizing the objective function is crucial as it enables us to enhance specific aspects of the system under investigation, leading to improved efficiency, performance, or effectiveness. by maximizing the objective function, we seek to achieve the optimal configuration or set of parameters that yield the most desirable outcomes (bhaskar et al. 2017; minhas et al. 2021). in cases where the goal is to maximize the objective function, hence, the general equation for such optimization process can be expressed in the equation below; � = max � �1, �2, …, �� ,..............................................................................................................................(2) where y represent the output value from the optimization process, while � x1, x2, …, xn , represents the objective function to be maximized while x1, x2, …, xn represents the variables or parameters under consideration within the system. similarly, in our case study, the proxy model developed for the estimation of the cumulative volume of oil recoverable from the steam flooding process becomes the objective function to be maximized, while determining the optimal parameters for the reservoir parameters. results and discussions proxy model result and interpretation. proxy models in reservoir engineering are known for their usefulness in approximating relationships within complex reservoir simulation models. in this research, the developed model is a reduced quadratic model which is defined as thus, log10 ��� = 0.0688692�62 + 2.56296 × 10−9�52 − 9.9533 × 10−9�42 − 6.33966 × 10−9�12 − 2.61898 × 10−6�5�6 + 1.58417 × 10−9�4�5 + 1.744 × 10−9�3�5 − 3.90065 × 10−5�7 − 0.0831905�6 − 4.30134 × 10−5�5 + 1.37941 × 10−5�4 − 1.2208 × 10−5�3 + 1.41117 × 10−5�1 + 7.02342............................................................................................................................................................(3) from eq. 3, we can observe that the output is in logarithmic values, hence to obtain the actual values, we need to take exponential of both sides, thereby resulting to a final model as shown in eq. 4, ��� = � log10 ��� ............................................................................................................................................(4) hence, by providing the combination of reservoir and steam flooding parameters, such as the bottom-hole well pressure, steam temperature, and the steam quality values for eq. 4, the cumulative recoverable volume can be accurately estimated. statistical evaluation of developed model. the anova table, as shown in table 2 presents a rigorous examination of the model's performance and the individual predictors. the overall model exhibits remarkable significance (p<0.0001), signifying that it effectively predicts the variable. the high r² value of 0.9816 further improved oil and gas recovery 6 reinforces this, indicating that approximately 98% of the variance in the dependent variable can be attributed to our model. moreover, the r² score is in reasonable agreement with the adjusted r2, that is the difference is less than 0.2. from the table also, its worthy to note that the alphabets a, c, d, e, f and g represent x1, x3, x4, x5, x6 and x7, respectively. hence, among the predictors, a, e, f, e², and f² emerged as key contributors due to their substantial f-values and low p-values (p<0.0001). these variables significantly enhance our model's predictive power. however, it is essential to consider that c, d, and g exhibit p-values greater than 0.05, rendering them statistically insignificant at the 95% confidence level selected in this study. table 2—analysis of variance (anova) for crv. source sum of squares df mean square f-value p-value model 0.1141 13 0.0088 172.30 < 0.0001 significant a-x1 0.0000 1 0.0000 0.8001 0.3762 c-x3 0.0001 1 0.0001 1.81 0.1853 d-x4 0.0001 1 0.0001 1.50 0.2280 e-x5 0.0712 1 0.0712 1397.20 < 0.0001 f-x6 0.0023 1 0.0023 45.51 < 0.0001 g-x7 0.0001 1 0.0001 1.79 0.1879 ce 0.0003 1 0.0003 5.44 0.0245 de 0.0002 1 0.0002 4.49 0.0401 ef 0.0002 1 0.0002 4.42 0.0416 a² 0.0002 1 0.0002 3.00 0.0908 d² 0.0004 1 0.0004 7.38 0.0095 e² 0.0323 1 0.0323 634.59 < 0.0001 f² 0.0023 1 0.0023 45.82 < 0.0001 residual 0.0021 42 0.0001 cor total 0.1162 55 sd=0.0071 mean=6.87 *cv%=0.1039 press=0.0048 r2=0.9816 adj r2=0.9759 adeq. precision=39.0244 * cv is coefficient of variation and press is predicted residual error of sum of squares. improved oil and gas recovery 7 figure 4—(a) plot of actual vs. predicted response of surface; (b) normal probability plot to residuals of crv data; (c) the plot of residuals vs. predicted response of crv data; (d) the plot of residuals vs. run of crv data. figure 4(a) compares the predicted and actual values of crv (mm.bbl) and hence, it can be observed that the data points are scattered around the diagonal line, which represents good prediction with approximately 98% accuracy. points close to the diagonal line indicate accurate predictions, while deviations from the line specifically in red and green colors account for the 2% error in prediction. additionally, the normal probability plot as shown in figure 4(b) indicates that the residuals follow a normal distribution, thus follow the straight line and “s-shaped” curve, suggests that the transformation of the response will provide a better analysis. figure 4(c), however, presents the plot of the residuals versus the ascending predicted response values, which is a random scatter depicting expanding variance, suggesting need for response transformation. lastly, figure 4(d) shows the plot of the residuals versus the experimental run order. the scatter of residuals appears random and is evenly distributed around the mean residual value. this suggests that the residuals are not influenced by the order in which the runs were conducted, indicating their independence from the run sequence. sensitivity analysis. in an attempt to study the effect of the factors (reservoir and steam flooding parameters) considered in this study, a sensitivity study was carried out using the perturbation functionality of the design expert software. the effect of these factors on our response, the cumulative recoverable volume can be seen in figure 5. improved oil and gas recovery 8 figure 5—the effect of these factors on our response surface. as can be observed from figure 5, as the deviation from the reference point increases, crv sharply decreases, this shows that factor e (steam injection rate) plays a critical role in reducing crv and hence, determining its optimal parameter can lead to significant improvements in crv. however, factors a (bhp well_1), c (bhp well_3), and g (steam temperature) can be observed to have exhibited minimal influence as they have relatively flat lines near the reference point, hence, changes in factors a, c, and g have minimal impact on crv. additionally, while factors f (steam quality) and d (bhp well_4) may not be as impactful as factor e, optimizing f and d may contribute positively to crv as they show slight inclines, indicating positive correlations with crv. optimization analysis. the numerical optimization algorithm adopted in this research follows the hill climbing technique. firstly, the objective function (desirability function) is set to ranges from zero to outside of the limits to one at the goal. by leveraging a penalty function, a set of random points based on defined constraints are checked to see if there is a more desirable solution. based on this approach, the solution highlighting the top 5 optimization results is shown in table 3. table 3—top 5 optimization results. number x1 x2 x3 x4 x5 x6 x7 optimized crv desirability 1 1250 0 1250 500 1000 0.1 150 9313994.303 0.959 2 1250 0 1250 500 1000 1 150 9121955.466 0.946 3 648.822 0 747.588 665.041 1418.562 0.108 114.617 9120851.876 0.946 4 1250 0 1250 2000 1000 0.1 150 9013188.917 0.938 5 500 0 500 1250 1000 0.55 150 9009920.854 0.938 improved oil and gas recovery 9 from table 3, it can be observed that the feature b was set to zero, since it was not part of the objective function. from the result also, it can be observed that the highest cumulative recoverable volume 9,313,994.303 bbl which is approximately 19% increase as compared to the average cumulative recoverable volume from the reservoir experimental results. conclusions and recommendations in this study, we developed a quadratic response surface proxy model to estimate the cumulative recovery volume (crv) from a heterogeneous heavy oil reservoir undergoing steam flooding. through rigorous numerical simulations and experimentation, we addressed the challenges associated with high costs and uncertainty in heavy oil recovery processes. our findings demonstrate the feasibility and effectiveness of using proxy models to analyse and optimize steam flooding operations, thereby potentially reducing costs and improving recovery rates in the oil and gas industry. the development of the proxy model involved the creation of a complex numerical simulation to model a steam flooding pattern with five inverted spots for the heavy oil reservoir. utilizing a box-behnken experimental design, we considered key parameters such as steam injection rates, steam temperature, steam quality, and bottomhole flowing pressure of the producing wells. the resulting proxy model, validated with high adjusted and predicted r2 values, successfully predicted crv with remarkable accuracy. through further sensitivity studies, we evaluated the behaviour of input parameters and optimized the objective function to maximize production from the steam flooding process. our results indicate that steam injection rate, steam quality and bottomhole pressure for well_4 played critical role in crv determination, while bhp well_1, bhp well_3, and steam temperature exhibited minimal influence. following the optimization process, we observed a substantial crv increase of up to 19%, highlighting the potential of our approach to enhance recovery outcomes. based on the outcomes of our study, we offer the following recommendations for future research and practical applications:  further research could focus on refining the proxy model by incorporating additional parameters and considering more complex reservoir conditions. this could improve the accuracy of predictions and optimize steam flooding operations even further.  our findings suggest that the developed proxy model has practical applications in the oil and gas industry. field trials and implementation studies could be conducted to validate the effectiveness of the model in real-world heavy oil reservoirs.  evaluating the cost-effectiveness of implementing the proxy model compared to traditional simulation methods is essential. cost-benefit analyses could provide stakeholders with valuable insights into the economic feasibility of adopting proxy models for reservoir optimization. this research work contributes to the ongoing efforts to improve heavy oil recovery techniques by offering a practical and efficient approach for estimating crv in steam flooding operations. by leveraging proxy models, we can mitigate uncertainty and optimize production processes, ultimately driving efficiency and reducing costs in the oil and gas industry. conflicting interests the author(s) declare that they have no conflicting interests. references aboaba, m., martinez, y., mohaghegh, s., et al. 2020. smart proxy modeling application of artificial intelligence & machine learning in computational fluid dynamics. report, contract no. netl-wvu-07-22-2020, us doe, washington, dc. improved oil and gas recovery 10 ahmad, a., rehman, m. u., wali, a. f., et al. 2020. box – behnken response surface design of polysaccharide extraction from rhododendron arboreum and the evaluation of its antioxidant potential.molecules 25(17):1-12. al adasani, a. and bai, b. 2011. analysis of eor projects and updated screening criteria. journal of petroleum science and engineering 79(1): 10-24. alawode, a. j. and falode, o. a. 2021. enhanced oil recovery practices: global trend, nigeria ’ s present status, prospects and challenges. current journal of applied science and technology 40(8):79-92. bahrami, p., moghaddam, f. s., and james, l. a. 2022. a review of proxy modeling highlighting applications for reservoir engineering. energies 15(4):5247-5265. reddy, b. a. v., yusop, z., jaafar, j., et al. 2017. simulation of a conventional water treatment plant for the minimization of new emerging pollutants in drinking water sources: process optimization using response surface methodology. rsc advances 7(19): 11550-11560. chaalal, o. 2018. innovation in enhanced oil recovery. recent advances in petrochemical science 5(2): 1-15. evans, o. e., onyekonwu, m., and ajienka, j. 2021. recovery of nigerian heavy oil: application of steam flooding. journal of energy research and reviews 5(4):21-38. ferreira, s. l. c., bruns, r. e., ferreira, h. s., et al. 2007. box-behnken design: an alternative for the optimization of analytical methods. analytica chimica acta 597:179-186. hama, m. q., wei, m., saleh, l. d., et al. 2014. updated screening criteria for steam flooding based on oil field projects data. paper presented at the spe heavy oil conference canada, alberta, calgary, 10-13 june. spe-170031ms. ma, z. and leung, j. y. 2020. a knowledge-based heterogeneity characterization framework for 3d steam-assisted gravity drainage 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(2019). enhanced oil recovery. international journal of petroleum and petrochemical engineering 5(4):10-13. minhas, n., thakur, a., mehlwal, s., et al. 2021. multi-variable optimization of the shot blasting of additively manufactured alsi10mg plates for surface roughness using response surface methodology. arabian journal for science and engineering 46(12): 11671-11685. mokheimer, e. m. a., hamdy, m., abubakar, z., et al. 2019. a comprehensive review of thermal enhanced oil recovery: techniques evaluation. journal of energy resources technology 141(3):25-45. qiao, l., wang, h., lu, s., et al. 2022. novel self-adaptive shale gas production proxy model and its practical application. acs omega 7(10): 8294-8305. shacham, m., brauner, n., and shore, h. 2007. a new procedure to identify linear and quadratic regression models based on signal-to-noise-ratio indicators.mathematical and computer modelling 46(1): 235-250. silva, l. m. da, avansi, g. d., and schiozer, d. j. 2020. development of proxy models for petroleum reservoir simulation: a systematic literature review and state-of-the-art. international journal of advanced engineering research and science 7(10):36-62. spe. 2010. spe comparative solution project-model 2. https://www.spe.org/web/csp/datasets/set02.htm (accessed 1 march 2024). yu, y., liu, s., liu, y., et al. 2021. data-driven proxy model for forecasting of cumulative oil production during the steam-assisted gravity drainage process. acs omega 6(17): 11497-11509. jude emeka odo, spe, is a lecturer and researcher in petroleum engineering at the federal university of technology owerri, where he has worked for 10 years. his research interests are in reservoir engineering, enhanced oil recovery, production optimization, and proxy modeling. he holds a beng. degree in petroleum engineering from the federal university of technology owerri, an msc degree in petroleum engineering from the university of abeerdeen. he is currently in the final stages of obtaining a phd in petroleum engineering at federal university of technology owerri. mike onyekonwu, spe, is a professor of petroleum and gas engineering at the university of portharcourt, where he has worked as faculty for 40 years and a consultant for the oil and gas industry. his research interests are in reservoir engineering, alkaline, surfactants and polymers for enhanced oil recovery, pvt https://www.spe.org/web/csp/datasets/set02.htm improved oil and gas recovery 11 analysis, and reservoir management. he holds a bsc. (first class) degree in petroleum engineering from university of ibadan nigeria, an msc and phd degrees in petroleum engineering both from stanford university california. sunday sunday ikiensikimama, spe, is a professor of petroleum and gas engineering at the university of portharcourt, where he worked as faculty for 30 years. his research interests are in pvt analysis, enhanced oil recovery, flow assurance, petroleum economics, and risk management. he has a bachelor of engineering degree in chemical engineering, master’s degrees both in chemical engineering and petroleum engineering from the university of port harcourt. he holds a phd in chemical engineering with specialization in pvt analysis from the university of lagos. chidinma uzoamaka uzoho, spe, is the lab manager at laser engineering ltd involved in collaborative research with the university of portharcourt. her research interest is in enhanced oil recovery, core analysis, gas to power technologies, and utilization of agrowaste in enhanced oil recovery. she holds a beng. degree in chemical engineering, an meng degree in gas engineering, and a phd in petroleum engineering all from the university of portharcourt. praise udochukwu ekeopara, spe, is a graduate petroleum engineer from the federal university of technology owerri. his research interests is in enhanced oil recovery, production optimization, and machine learning. he holds a beng degree in petroleum engineering from the federal university of technology, owerri. abstract introduction materials and methods results and discussions conclusions and recommendations conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1212 received august 2, 2022; revised october 26, 2022; accepted december 22, 2022. *corresponding author: shidacunliang@126.com 1 a new method for quantitative description of dominant channels in high water-cut stage cunliang chen*, wei zhang, baolin yue, and bin liu, tianjin branch of cnooc ltd., tianjin, china abstract the development of the dominant channel seriously affects the water-flooding effect of the oil field and leads to a decrease in the recovery. how to effectively describe the dominant channel is an urgent problem to further improve the recovery rate of water-flooding in high water cut oilfields. therefore, the quantitative calculation of the dominant channel’s parameters was carried out by using the seepage theory and mathematical models in this study. the reservoir that developed the dominant channel was regarded as the parallel of the normal reservoir and the dominant channel. the ineffective water injection was calculated from the ineffective circulating water model. according to the principle of equivalence, the ineffective water production of the oil well and the water production of the normal reservoir were calculated. then the parameters of the dominant channel were quantitatively described by the volume analogy and the carman-kozeny formula. the interwell connectivity model was used to calculate the parameters of the dominant channel in the well group. the results showed a good agreement with the actual offshore oilfield situation, and the effectiveness of the method was verified. introduction at present, most oil fields in china have entered a period of high water cut, and long-term water injection development has led to the development of dominant channels in the reservoir (moreno 2013; fattahpour et al. 2012; mamghaderi and pourafshary 2013). the development of dominant channels has led to a large amount of injected water being directly produced by oil production wells, leading to ineffective circulation, exacerbating inter-layer contradictions, resulting in uneven displacement and poor development effects (he et al. 2000; feng et al. 2009; lerlertpakdee et al. 2014). therefore, how to effectively describe the dominant channels quantitatively is a problem to be solved urgently in order to further improve the water flood recovery factor in oilfields with high water cut. at present, the qualitative identification methods of dominant channels are relatively mature (wang et al. 2013; jin 2009; yu et al. 2009; han et al. 2006;wang et al. 2003). it is still difficult to use reservoir engineering methods to quantitatively calculate dominant channels, but many researchers have tried. zeng et al. (2002) proposed the reservoir engineering method of quantitative calculation of the superior channel earlier, but the calculation result has a larger error, but the volume analog formula proposed by him is widely used. peng et al. (2007) used the fuzzy comprehensive evaluation method to quantitatively describe the advantage channel, but the essence is still qualitative judgment, and the specific parameters of the advantage channel cannot be given. liu et al. (2012) conducted a quantitative study using phase-controlled stochastic modeling on the basis of fuzzy comprehensive evaluation. li et al. (2011) and chen et al. (2015) respectively used intelligent training algorithms to study the quantitative calculation of dominant channels, but the method requires a large amount of well-logging data and the scope of application is relatively small. yang et al. (2013) and liu et al. (2003) used the tube flow model to estimate the parameters of the dominant channel. feng et al. (2011) and chen et al. (2013) respectively 2 proposed the method of quantitatively describing the dominant channel using excess water-fuzzy comprehensive evaluation method and excess water-well connection method, but the use of the volume analog formula proposed by zeng is not standardized. liu et al. (2017) proposed a quantitative method based on the theory of mass transfer and diffusion. ding et al. (2013) and wang et al. (2016) respectively carried out quantitative calculation studies of the dominant channel considering the high-speed non-darcy case. in this paper, the seepage index was 0.5 (turbulent state), but it was derived using the laminar flow mode.therefore, on the basis of previous researches, the seepage theory and mathematical methods are carried out to calculate the parameters of the dominant channel, and provided theoretical support for the quantitative identification and governance of the dominant channel. methodology quantitative description of one injection one production advantage channel. in order to ensure the rationality of the calculation, the following assumptions are made: the reservoir is macroscopically homogeneous; after the formation of the dominant channel, the original reservoir as the dominant channel forms parallel connection with the normal reservoir, as shown in figure 1; only residual oil is left in the dominant channel, only producing water, and still obeying darcy's law; the normal reservoir produces oil and water. figure 1--diagram of dominant channel model. in reference, the calculation method of invalid circulating water is proposed, but due to the large calculation error, it is seldom used. based on the percolation theory, the author puts forward the calculation method of the invalid circulating water, that is, the water injected by the actual water injection volume is more than the theoretical water injection volume is the invalid circulating water, which is directly produced by the production well, and the calculation formula is shown in eq.1. wzx wzs wzlq q q  ,....................................................................................................................................................(1) rw wzl i w w w 2 1 ln kk h p q r b r     ,................................................................................................................................................(2) where, qwzx is the invalid circulating water volume, cm3/s; qwzs is the actual water injection volume, cm3/s; qwzl is the theoretical water injection volume, cm3/s; krw is the relative permeability of water phase, the general value within the control radius of water injection well is 1.0; k is the original permeability of reservoir, 10-3μm2; h is the effective thickness of reservoir, cm; δp is the injection pressure difference, mpa; μw is the viscosity of injected water, mpa·s; ri is the control radius of water injection well, m; rw is the radius of water injection well, m; bw is the volume coefficient of water, f. since the invalid circulating water is directly produced by the production well, according to the principle of equivalence, the water quantity produced by the dominant channel of the production well is normal reservoir dominant channel 3 wsd wzxq q ,..............................................................................................................................................................................(3) where, qwsd is the water yield of the dominant channel, cm3/s. according to the volume analogy formula, the volume of the dominant channel can be determined as d dl sl v q v q  ,....................................................................................................................................................................................(4) where, vd is the volume of the dominant channel, cm3; v is the pore volume of the injection production direction, cm3; qdl is the theoretical water production when the dominant channel is the normal reservoir, cm3/s; qsl is the theoretical water production of the production well when the dominant channel is not formed, cm3/s. in the application of eq. 4, some papers mistakenly use the invalid circulating water volume as the dominant channel when it is the theoretical water production of normal reservoir, resulting in the increase of calculation error. therefore, the author puts forward the following calculation methods. after the formation of dominant channel, the water production of normal reservoir is as follows wsc wss wsdq q q  ,..................................................................................................................................................................(5) where, qwsc is the water production of normal reservoir after the formation of dominant channel, cm3/s; qwss is the water production of production well, cm3/s. after the formation of the dominant channel, the oil production is part of the normal reservoir, so the water cut of the normal reservoir can be expressed as wsc wc wsc osc q f q q   ,...................................................................................................................................................................(6) where fwc is the water content of the normal reservoir, f; qosc is the oil production of the normal reservoir after the formation of the dominant channel, cm3/s. according to the relative permeability curve, the relative permeability of some water phases of normal reservoir is calculated, and then the theoretical water production of oil well without forming dominant channel is calculated, as shown in eq. 7. rw wsl i w w w 2 1 ln kk h p q r b r     ,......................................................................................................................................................(7) where qwsl is the theoretical water production, cm3/s. then the theoretical water production when the dominant channel is a normal reservoir is calculated, as shown in eq.8. wsl wscdlq q q  ,.....................................................................................................................................................................(8) then, the volume of the dominant channel can be calculated by substituting eq. 4. considering the dominant channel as one-dimensional flow, the permeability of the dominant channel is calculated according to the volume of the dominant channel and the deformation formula of linear flow. 2 wsd w d d q l k av p    ,.................................................................................................................................................................(9) where kd is the permeability of the dominant channel, 10-3μm2; l is the well spacing, m; a is the conversion coefficient, f. using carman kozeny formula to calculate the roar radius of the dominant channel. 2 d d 8k r    ,.................................................................................................................................................................(10) where, rd is the dominant channel radius, μm; δ is the tortuosity, with the value of 1.5-5.5; ϕ is the porosity, f. 4 quantitative description of dominant channels in the well cluster there are many production wells in the water injection well group, and the production wells may be affected by many water injection wells. therefore, the key to describe the dominant channel in the well group is the production split in each direction of injection and production. in this paper, the split production calculation is based on the inter well connectivity model, which overcomes the shortcomings of traditional split methods that rely too much on subjective judgment. the inter well connectivity model (chen et al. 2018; yousef et al. 2006; chen 2020) is a dynamic inversion method developed in recent years. it can use injection production data to quantitatively calculate the dynamic connectivity between wells in a reservoir. it overcomes the shortcomings of the traditional method (deng et al. 2003; liao and wang 2002; feng et al. 2014) such as complex operation, production impact, and expensive cost, so it is widely used in oilfield production. in reference, a new connectivity calculation model with clear physical meaning is proposed, and its calculation formula is shown in eq. 11.      l l0 1 jn j j ij i i q t q t f q t    ,.............................................................................................................................(11) where, j is the serial number of production well; ql j(t) is the daily underground liquid production of production well j, m3/d; ql0 j(t) is the daily liquid production contributed by non water injection of production well j, m3/d; i is the serial number of water injection well; nj is the number of water injection wells corresponding to production well j; fij is the connection coefficient between water injection well i and production well j; qi(t) is the daily water injection volume of water injection well i, m3/d. the injection production connection coefficient is the proportion coefficient of the injected water flow from the injection well to the production well to the total water injection of the injection well, which can be used to split the ineffective circulating water. the dominant channel is not developed in all injection production directions of the well group, so it is stipulated here that the average value of injection production connectivity coefficient fij greater than that of all injection production connectivity coefficients in the well group is regarded as the dominant channel. therefore, the connection coefficient of injection and production in the direction of developing dominant channel is normalized again, and the invalid circulating water is divided into various directions. g 1 = i ij ij n ij j f f f   ,....................................................................................................................................................(12)      wsd wzx g wzxijij ij i q q f q  ,.......................................................................................................................(13) where ni is the number of oil production wells corresponding to water injection well i; (qwsd)ij is the water production of the dominant channel between water injection well i and oil production well j, cm3/s; (qwzx)ij is invalid circulating water volume between water injection well i and oil production well j , cm3/s; fgij is the normalized connection coefficient between water injection well i and oil production well j, f; (qwzx)i is the total invalid circulating water in water injection well i, cm3/s. in addition, according to the injection-production connection coefficient, the amount of water injection to the oil production well can be calculated, and the water production of the same oil production well in all directions can be split according to this water injection quantity.    wss wss 1 j ij i i nij j ij i i f i q q f i     ,..................................................................................................................................(14) where (qwss)ij is the actual water production in the direction of water injection well i and oil production well j, cm3/s; nj is the number of water injection wells related to oil production well j; (qwss)j is the actual production of oil production well j , cm3/s. 5 after obtaining the invalid circulating water volume and the actual water production volume in all directions, the calculation is carried out according to the method of quantitative description of the one-in-one-dominant advantage channel. application an offshore oil field is located in the lower liaohe depression of the liaodong bay and the middle section of the liaoxi low uplift, and is a lacustrine delta deposit. the average permeability of the oil field is 1100×10-3μm2, and the porosity is 0.30, which is a typical medium-high porosity reservoir. it has been more than 20 years since it was put into development. at present, the recovery degree is 29.6%, and the comprehensive water cut is 80.2%. it is in a high water cut stage. it is of great significance to carry out the identification of superior channels and quantitative description to guide the remaining oil potential. take a block as an example for calculation. the production wells in this block have fast water seepage rate, rapid increase in water content, poor water flooding development effect, and obvious development of dominant channels. using the production data of this block, the dominant channels in each well group were identified and quantitatively described, as shown in table 1. the test results show that there are well-developed channels between wells h3 and h4, h6 and h5, h6 and h7, h9 and h8, which is very consistent with the on-site understanding. in addition, the h6 well group carried out tracer test and calculated the permeability of the dominant channel using tracer data inversion. the calculation results are basically consistent with the method in this paper, and the reliability of the method is verified again. through quantitative calculation, it can be seen that the permeability of the dominant channel in this block is basically above 4000×10-3μm2, and the average radius of the dominant channel is above 35 μm. reagents with larger particle size of the plugging agent should be used to adjust the water drive structure. table 1--preponderant channel recognition and description results of blocks. injection well production well connectivity recognition result invalid circulating water volume m3/d permeability of dominant channels 10-3μm2 mean radius of the dominant channel μm tracer explained permeability 10-3μm2 h3 h4 0.60 √ 62 4856 39.83 h7 0.35 × h6 h4 0.18 × h5 0.29 √ 38 3965 35.99 4233 h7 0.36 √ 47 5661 43.00 5916 h8 0.17 × h9 h7 0.21 × h8 0.40 √ 46 5329 41.72 h10 0.20 × h11 0.18 × aiming at the three well groups developed in the dominant channel, the appropriate displacement control agent is selected according to the pore radius of the dominant channel of the well group for profile control. after the profile control and flooding, each well group has significant oil increasing effect. the whole block increases oil daily by about 60 m3, and the water cut decreases by up to 10% (figure 2). 6 figure 2--production dynamic curve of block h. conclusions regarding the reservoir with developed dominant channel as the parallel of normal reservoir and dominant channel, a calculation method to quantitatively describe the dominant channel between injection and production wells was established by the invalid circulating water model, volume analog formula and carman-kozeny formula. on this basis, the quantitative description of the dominant channels in the well group was realized based on the inter-well connectivity model. the field application results verified the effectiveness of the method, which has important technical guiding significance for the further improvement of water flood recovery in oilfields with high water cut. conflicting interests the author(s) declare that they have no conflicting interests. references chen, c. 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macroscopic throats forming mechanism of unsolidated sand-reservior and their identyfying method. jounal of basic science and engineering 10: 268-276. cunliang chen is a reservoir engineer of tianjin branch of cnooc ltd. he has focused his research in oil and gas field development engineering. chen graduated from china university of petroleum (east china) with a master's degree. wei zhang is a reservoir engineer of tianjin branch of cnooc ltd. he specializes in oil and gas field development engineering. zhang holds the ms degree from china university of petroleum (east china). baolin yue is a reservoir engineer of tianjin branch of cnooc ltd. he has focused his research in oil and gas field development engineering. yue graduated from china university of petroleum (east china) with a master's degree. bin liu is a reservoir engineer of tianjin branch of cnooc ltd. he specializes in oil and gas field development engineering. liu graduated from northeast petroleum university with a master's degree. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1204 received june 2, 2022; revised september 14, 2022; accepted november 14, 2022. *corresponding author: monthepp@chevron.com 1 a machine learning based approach to automate stratigraphic correlation through marker determination monthep parimontonsakul, somwipa lotongkum, and khunalai mularlee, chevron thailand exploration and production, ltd., bangkok, thailand summary stratigraphic correlation is well recognized as one of the essential processes, providing information regarding stratigraphic and compartmentalization in a reservoir. it becomes a starting point for subsurface evaluation processes ranging from reservoir characteristics to reserves and resources estimation and economic evaluation. it has always been a focus area in numerous traditional and modern research. several practices approach stratigraphic correlation, including direct tracing from outcrop, relating geological markers, and comparing the organism characteristics. this work focuses only on one of the traditional work processes, utilizing geological markers to identify stratigraphic correlation. this work primarily studies the potential adoption of data analytics and machine learning in identifying geological markers and connecting them to derive stratigraphic correlation. well logging information is the primary data source to interpret geological markers. determining markers was previously done based on the specific well-log characteristics that are rare and uniquely identified in the geological area. it usually takes tremendous effort to find a particular marker from well logging information, especially when many wells scale up the works. deriving computer-assisted technology with machine learning becomes a key enabler in accelerating and enhancing the business process. the machine learning assisted system has been trained with the entire geoscientists’ marker interpretations. the system consists of two connected machine-learning models. the first model, designed as a multi-class classification, identifies the geological markers using well-logging information. the first model’s predicted markers are then fed as an input to the second model, designed as a binary classification. it analyzes the relationship between markers in the same wellbore. subsequently, the predicted markers resulting from two connected models are linked between two or more wells in the same region to create the stratigraphic correlation. aiming to determine the practicality and potential adoption from one to another, this study implements the same model concept with two different sets of data, two fields in the gulf of thailand. the system has been proven successful in model development and deployment and has achieved nearly human performance levels. introduction in recent decades, the new asset class, unconventional resources, has been developed to fulfill an increasing need in energy demand. several activities have been executed in the energy industry, including exploring new oil and gas areas, delineating the additional reservoirs in an existing field, and developing new wells to optimize field production. these activities lead to a significant increase in the amount of data and effort to complete all tasks in the limited time. stratigraphic correlation is one of the essential processes ranging from an exploration phase to asset development. it provides information regarding stratigraphic and compartmentalization in a reservoir (howell 1983; olea and davis 1986; waterman and raymond 1987; bakke and griffiths 1989; fang et al. 1992; luthi and bryant 1997). 2 stratigraphic correlation is one of the focus areas in numerous traditional and modern research. rudman and lankston (1973), mann and dowell jr (1978) identified a stratigraphic correlation, also called correlation, using the cross-correlation technique. smith and waterman (1980), anderson and gaby (1983), howell(1983), waterman and raymond (1987), fang et al. (1992), edwards et al. (2018), behdad (2019), and le et al. (2019) determined a similarity between two well-log sequences using the dynamic time warping, also called dynamic waveform matching technique. zimmermann et al. (2018), brazell et al. (2019), bakdi et al. (2020), tokpanov et al. (2020), and parimontonsakul (2021) focused on applying machine learning models in stratigraphic correlation identification. this work aims to address the correlation tasks through the geoscientists’ and data analytics’lens, synchronizing with the business workflow related to the stratigraphic correlation. this work presents the use of data analytics and machine learning models to assist or automate the stratigraphic correlation tasks. it focuses only on the traditional work process using a geological marker and explores the potential adoption of data analytic and machine learning models to enhance the process. the same model concept is applied to two fields in the gulf of thailand to determine the practicality and potential adoption from one to another. as a result, the models nearly achieve human performance, supporting the idea of integrating the data analytic workflow into the business workflow. the model results also emphasize the importance of a thorough understanding of the work process through the successful implementation of two models connected in series to improve the model performance. in addition, the two connected models may not easily achieve without the ability to adjust or tweak the model setup, emphasizing the significance of data analytic understanding. stratigraphic correlation several kinds of information are required to identify stratigraphic correlation. for example, a similarity in the fossil content can be interpreted as correlative since it presents the same organism characteristics, which infer the same age of the rock units. a similarity in the unique lithology sequences can also be interpreted as correlative since it derives a distinct lithology sequence in the geological area. given the above examples, this study elaborates that geologists can derive a stratigraphic correlation through geological information: a similarity or specific characteristics between that information, such as lithology, organisms, and a geological period. well logging is one of the primary data acquisition processes, providing lithology information, petroleum reservoirs, and petrophysical properties. this information is sufficient to imply a stratigraphic correlation. one of the traditional interpretations that geoscientists usually start with is a marker. a marker, also called a geological marker or horizon, is defined as a rare and uniquely identified lithology sequence that one can map over a geological area (neuendorf et al. 2011). connecting the same marker exposed in several wells can imply a stratigraphic correlation because it provides the connection of the unique lithology sequence in the area. however, the correlation interpretation does not guarantee that those correlative reservoirs always have pressure communication since several unknown factors can contribute to compartmentalization, such as fault and unconformity (parimontonsakul 2021). as geologists can use well-logging information to interpret a marker, this study proposes that the same process can be assisted by a data analytic process such as machine learning or any computational process. if geologists’ marker interpretation is available, the classification model can be implemented using well-logging information as independent variables or features and labeled marker information as the target predicted values. a clustering model can execute when the only available information is the well-logging data, implying that the machine learning model will provide the group of well-logging patterns, aka pseudo markers (parimontonsakul, 2021). this study focuses only on the classification model where geologists’ marker interpretation is available in this work. this study applies the work process to two fields in the gulf of thailand to determine the use case and application in the actual field data. two areas are selected as it provides the evidence to demonstrate the applicability of the workflow to other fields. 3 analytical problem formulation as previously mentioned, marker identification is an essential process in stratigraphic correlation. this section elaborates on the analytical problem formulation and the model implication. this study intends to focus on only one analytical formulation, convolutional neural network, to demonstrate the implementation of the work process in the actual field data. convolutional neural network (cnn) model has become predominant in the image recognition and computer vision research areas, including several architectures aiming to achieve higher accuracy and more efficient calculations (krizhevsky et al. 2012; krizhevsky et al. 2017; wang et al. 2020; parimontonsakul 2021). due to the limited computational capability, this study employs one of the simplest and the most efficient architectures, mobilenets, to identify the markers. parimontonsakul (2021) proposes one transformation of well-logging information to the image approach. the primary concept is that one column vector represents one section of a well-log sequence, while well-log interval and compression factors, implying zoom-in and out of an image, are added to the well-log sequence. this process creates additional column vectors to the same well log series. he initially proposes to apply eight factors to the same well log sequence, resulting in eight vectors of an image, defined as a pad. the same process is used in other well-log sequences to create the complete image. applying the same concept, this study can make several well-logging images by changing the well-log interval and compression factors, as illustrated in figure 1. the well-log series from left to right are the gamma-ray log, resistivity log, neutron log, and density log in the sandstone scale. the transformation of a well-log to an image is demonstrated. figure 2 presents the mobilenets architecture. the transformed well log image is set up as an input layer in the cnn model, while the output layer is the geoscientists’ marker interpretations. since there is more than one marker in an output layer, the problem is set up as a multi-class classification problem. as the reader is aware that the transformed image consists of only a well log sequence, there is no additional information regarding well location, well depth, or any other information useful in identifying the geological marker. this study introduces two approaches to resolve the concern. the first approach is to create a placeholder column vector in the image as a place to input supplemental information such as well location and well depth. this method provides the simplest solution since it does not require any adjustment to the mobilenets architecture. the second approach is to include additional data input connecting directly to the fully connected layer. in this case, the modified mobilenets architecture needs to be constructed to add extra information to the cnn model. the two approaches are illustrated in figure 3. in this work, the first approach is applied for simplicity in model creation, but this does not imply that the first approach is the best. as a result, this study proposes the modified mobilenets architecture as demonstrated in table 1. this study addresses this issue by creating an additional machine learning model that explores the probability of correctness in the marker prediction given the nearby marker prediction information. this process can be viewed simply as the nearby marker prediction should be similar, or if the marker is alphabetically sorted from shallow to deep, the nearby marker prediction will also be alphabetically sorted in the same manner. there are several techniques to formulate this kind of model. one of the approaches is to formulate it as a classification problem, where independent variables are the predicted markers from the cnn model, including predicted marker depth and other mathematical aggregation such as min, mean, mode, and a max of the numerical values, and the correctness of the marker prediction given the depth threshold as the target predicted values. 4 figure 1—the well log images for mobilenets (parimontonsakul 2021). figure 2—the mobilenets architecture (parimontonsakul 2021). in p u t la y e r d e p t h w ise se pa r a b le c o n v o lu t io n f u lly c o n n e c t e d la y e r 1024 o u t p u t la y e r c o n v o lu t io n d e p t h w ise c o n v o lu t io n p o in t w ise c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n g lo b a l a v e r a g e p o o lin g f u lly c o n n e c t e d 5 (a) (b) figure 3—the modified mobilenets architecture alternative for additional data input (modified from parimontonsakul 2021). (a) the modified mobilenets architecture added additional column vector; (b) the modified mobilenets architecture added additional data input to fully connected layer. metrics this section discusses the metrics to validate the model performance. this study presents metrics for the 3-class classification problem, as illustrated in table 2; however, the same formula can apply to the multi-class classification problem. the precision is the number of correctly classified divided by all predicted values with the same condition, while the recall is the number of correctly classified divided by all true values with the same condition. f1-score is another metric usually applied in classification problems. it can be written as a harmonic means of precision and recall. the mathematical expressions of precision, recall, and f1-score are shown in eqs. 1 to 3 (sokolova and lapalme 2009). in this work, the model prediction performance in each marker is measured by f1-score, while the macro average of the f1-score measures the overall model prediction performance. in p u t la y e r d e p t h w ise se pa r a b le c o n v o lu t io n f u lly c o n n e c t e d la y e r 1024 o u t p u t la y e r c o n v o lu t io n d e p t h w ise c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n g lo b a l a v e r a g e p o o lin g f u lly c o n n e c t e d w e ll lo c a t io n w e ll d e p t h + in p u t la y e r d e p t h w ise se pa r a b le c o n v o lu t io n f u lly c o n n e c t e d la y e r 1024 o u t p u t la y e r c o n v o lu t io n d e p t h w ise c o n v o lu t io n p o in t w ise c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n d e p t h w ise se pa r a b le c o n v o lu t io n g lo b a l a v e r a g e p o o lin g f u lly c o n n e c t e d w e ll lo c a t io n w e ll d e p t h 6 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝑖 = 𝑡𝑝𝑖 𝑡𝑝𝑖+∑ 𝑓𝑝𝑖𝑗𝑗 ,.....................................................................................................................................(1) 𝑅𝑒𝑐𝑎𝑙𝑙𝑖 = 𝑡𝑝𝑖 𝑡𝑝𝑖+∑ 𝑓𝑛𝑖𝑗𝑗 ,...........................................................................................................................................(2) 𝐹1-𝑠𝑐𝑜𝑟𝑒𝑖 = 2×𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝑖×𝑅𝑒𝑐𝑎𝑙𝑙𝑖 𝑃𝑟𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝑖+𝑅𝑒𝑐𝑎𝑙𝑙𝑖 ..........................................................................................................................(3) table 1—the proposed modified mobilenets architecture. layer type output shape input input layer (512, 36, 1) scal_input scaled input layer (256, 32, 1) conv1 conv2d (128, 16, 32) conv1_bn batchnormalization (128, 16, 32) conv1_relu relu (128, 16, 32) conv_dw_1 depthwiseconv2d – batchnormalization relu (128, 16, 32) conv_pw_1 conv2d – batchnormalization relu (128, 16, 64) conv_dw_2 depthwiseconv2d – batchnormalization relu (64, 8, 64) conv_pw_2 conv2d – batchnormalization relu (64, 8, 128) … … … conv_dw_13 depthwiseconv2d – batchnormalization relu (8, 1, 1024) conv_pw_13 conv2d – batchnormalization relu (8, 1, 1024) avg_pool globalaveragepooling2d (1024) fc fullyconnected (1024, 14) output output layer (14) table 2—the 3-class classification problem confusion matrix. true condition condition a condition b condition c predicted condition condition a 𝑡𝑝𝑎 𝑓𝑝𝑎𝑏 = 𝑓𝑛𝑏𝑎 𝑓𝑝𝑎𝑐 = 𝑓𝑛𝑐𝑎 condition b 𝑓𝑝𝑏𝑎 = 𝑓𝑛𝑎𝑏 𝑡𝑝𝑏 𝑓𝑝𝑏𝑐 = 𝑓𝑛𝑐𝑏 condition c 𝑓𝑝𝑐𝑎 = 𝑓𝑛𝑎𝑐 𝑓𝑝𝑐𝑏 = 𝑓𝑛𝑏𝑐 𝑡𝑝𝑐 model development and deployment figures 4 and 5 demonstrate two processes in model development and deployment for each model. the first process focuses on the first model, identifying the geological markers, development and deployment, while the second process focuses on the second model, analyzing the relationship between markers in the same wellbore, development, and deployment. 7 during the first model development, called as marker prediction model, the marker and non-marker data are required as input to the model. the imbalanced dataset from significantly different amounts of data between marker and non-marker needs to be addressed. this work applies the simple sampling approach to reduce the non-marker data to reduce the imbalanced dataset and control the computational time and memory to stay within the acceptable range. during the marker prediction model deployment, each interval of the well-log sequence is evaluated with the trained machine learning model defined in the previous step. the step size between each evaluation is a major concern. if the step size is too small, the number of function evaluations will be high, leading to higher computational time and vice versa. in addition, if the step size is too big, it also negatively impacts the model performance of the second process, implying that the second process will be less accurate. this study does not recommend any concrete solutions that always demonstrate the best step size and suggest further study in this area as needed. in the second model, named the marker association model, development and deployment process are straightforward as there is no other process before the model deployment, as demonstrated in the marker prediction model. two fields in the gulf of thailand, classified as fluvial depositional environments, are evaluated (table 3). geoscientists can identify the geological markers in both fields as the initial set of data to perform the correlation tasks. however, the markers identified by each area are not the same. since each location may have a different set of marker interpretations and originations, this study intends to develop and deploy the model in its area to honor its data distribution. field a and field b are trained and validated separately with the same model concept to demonstrate that the same process can apply in other locations without any adjustment. less than half of the field data have been trained due to limited computational performance, while the models have been tested in all remaining data. figure 4—the training and testing dataset definition. w e ll -01 a b c d t r a in in g d a t a se t t e st in g d a t a se t … st e p size 8 figure 5—the two connected models architecture. table 3—the validated metrics of the mobilenets model in two field in the gulf of thailand. field a field b marker precision recall f1-score precision recall f1-score c 0.9240 0.9356 0.9298 0.9412 0.9287 0.9349 d 0.9392 0.9727 0.9557 0.9276 0.9899 0.9578 e 0.9118 0.9602 0.9354 0.9225 0.9551 0.9385 f 0.9544 0.9458 0.9501 0.9364 0.9346 0.9355 g 0.9298 0.9620 0.9456 0.9233 0.9736 0.9478 h 0.9484 0.9682 0.9582 0.9365 0.9669 0.9514 i 0.9632 0.9458 0.9545 0.9810 0.9513 0.9659 j 0.9332 0.9508 0.9419 0.9159 0.9656 0.9401 k 0.9159 0.9619 0.9384 0.9099 0.9647 0.9365 l 0.9212 0.9509 0.9358 0.9037 0.9494 0.9260 m 0.8370 0.9743 0.9004 0.8477 0.9905 0.9136 n 0.9013 0.9211 0.9111 0.8826 0.9259 0.9037 o 0.9600 0.9796 0.9697 0.9506 0.9647 0.9576 na 0.8162 0.7218 0.7661 0.7963 0.7176 0.7549 macro avg 0.9183 0.9393 0.9280 0.9125 0.9413 0.9267 m a t h e m a t ic a l a g g r e g a t io n t r a in in g d a t a se t t e st in g d a t a se t t r a in e d f ir st m o d e l p r e d ic t e d m a r k e r a s t e st in g d a t a se t t r a in e d se c o n d m o d e l p r e d ic t e d m a r k e r c o r r e c t n e ss p r e d ic t e d m a r k e r a s t r a in in g d a t a se t f ir st m o d e l se c o n d m o d e l 9 discussion the marker prediction models, the cnn models, yield an incredible performance. the trained model in fields a and b in the gulf of thailand presents comparable performance. the f1-score metric reaches up to 0.95 in most markers except the markers l, m, n, o, and na in field a and field b. this result demonstrates that the same model concept can be applied in other fields without further adjustment, emphasizing that only the training data of the target field is required to implement the same model concept in other areas. the trained and validated loss function evaluation is demonstrated in figure 6. figure 6—the loss function evaluation in trained and validated data set in field a. figure 7 demonstrates that applying the marker prediction model alone in the deployment phase confirms the correlation chaos without the marker association model, as presented as the solid light blue line. integrating the marker association model deems necessary as it significantly reduces the number of incorrect correlation identifications, as demonstrated by the solid blue line. it also indicates that the marker association model is important in the process as long as the marker prediction model’s precision scores do not reach the perfect score. the marker association model will complement and help reduce the marker prediction model’s error. it also hypothesizes further optimization in the marker prediction model to provide a higher recall score so that the model tended to interpret more markers and applied the marker association model to remove the incorrectly predicted markers. however, this optimization idea has not been tested yet. 0 0.5 1 1.5 2 0 10 20 30 40 50 60 70 l o s s iteration loss evaluation for marker prediction model in field a trained loss validated loss 10 (a) (b) figure 7—the stratigraphic correlation results from the models, the solid light blue line represents the results from the marker prediction model, the solid blue line represents the results from the marker association model. (a)the stratigraphic correlation results from the marker prediction model, elaborating few incorrect correlation identifications from connecting identical markers;(b)the stratigraphic correlation results from the marker prediction and marker association model, presenting an improved correlation identifications by complementing the error from marker prediction model. 11 conclusions this work introduces a significant step toward the automated stratigraphic correlation using machine learning models in the marker horizon determination problem. the cnn model has been proven successful in identifying the marker horizon in two fields in the gulf of thailand. the model performs as it designs and nearly achieves human performance. however, the cnn model alone does not perform as well as it establishes during the model deployment phase. this concern has been proven and the additional machine learning models are connected in series to improve the model performance. the model results highlight a significant improvement in automated stratigraphic correlations. additionally, the model concept is proven to deploy in two fields in the gulf of thailand without further adjustment, emphasizing the potential adoption of the model concept from one area to another. given the model concept adoption, the rapid growth in digital transformation applying machine learning and other data analytics in the business workflow will not be a far future. this study concludes that data analytics can integrate with the business process to improve accuracy in stratigraphic correlation and assist geoscientists throughout the process. a thorough understanding of stratigraphic correlation and data analytics empowered by machine learning models is non-trivial and demonstrates a step toward a fully automated system. nomenclature cnn = convolutional neural network fn = false negative fp = false positive tp = true positive acknowledgments the authors would like to acknowledge saran boonchirdchoo and juntra wanwises for their efforts in data gathering and explaining the data structure. the authors also would like to express pleasure to nualjun kitvarayut for continuous support in the research topic. conflicting interests the author(s) declare that they have no conflicting interests. references anderson, k.r. and gaby, j.e. 1983. dynamic waveform matching. information sciences 31(3), 221-242. bakdi, s., kannan, n., reddy masini, s., et al. 2020. automated well correlation using machine learning and facial recognition techniques. paper presented at the abu dhabi international petroleum exhibition & conference, 9-12 november. spe-203301-ms. bakke, s. and griffiths, c.m. 1989. interactive quantitative matching of stratigraphic sequences of numerical lithostates based on gene-typing techniques. in correlation in hydrocarbon exploration, ed. collinson, j.d, chap. 5, 61-76. dordrecht: springer. behdad, a. 2019. a step toward the practical stratigraphic automatic correlation of well logs using 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cambridge, massachusetts. rudman, a. j. and lankston, r.w. 1973. stratigraphic correlation of well logs by computer techniques. aapg bulletin 57(3): 577-588. smith, t. f. and waterman, m.s. 1980. new stratigraphic correlation techniques. the journal of geology 88(4): 451-457. sokolova, m. and lapalme, g. 2009. a systematic analysis of performance measures for classification tasks. information processing & management 45(4): 427-437. tokpanov, y., smith, j., ma, z., et al. 2020. deep-learning-based automated stratigraphic correlation. paper presented at the spe annual technical conference and exhibition, 26-29 october. spe-201459-ms. wang, w., li, y., zou, t., et al. 2020. a novel image classification approach via dense-mobilenet models. mobile information systems 20:1-8 waterman, m.s. and raymond, r. 1987. the match game: new stratigraphic correlation algorithms. mathematical geology 19(2): 109-127. zimmermann, t., liang, l., and zeroug, s. 2018. machine-learning-based automatic well-log depth matching. petrophysics 59(6): 863-872. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1252 received march 12, 2023; revised may 24, 2023; accepted june 28, 2023. * corresponding author: liucheng14@cnooc.com.cn 1 pore-scale imaging of oil-brine movement during waterflooding with wettability alteration from tight sandstone cheng liu*, yanjun yin, ruiting bai, cnooc enertech-drilling and production company, tianjin, china; dengke liu, xi’an jiaotong university, xi’an, china abstract to clarify the impact of salinity waterflooding on oil displacement efficiency and the microscopic mechanism, we have used micro-ct, nuclear magnetic resonance, high-pressure mercury injection, and other means to conduct an experimental analysis of salinity waterflooding. the results show that imbibition has little contribution to oil displacement efficiency, and the change in wettability is the main microscopic mechanism of low salinity waterflooding. however, the presence of corner flow can lead to a large amount of dropwise residual oil distribution, affecting the waterflooding effect, and seriously restricting oil recovery. when a strong hydrophilic phenomenon existed, pore size is no longer a key control factor for oil displacement efficiency. this study provides a theoretical reference for the influencing factors of different displacement methods on oil displacement efficiency. introduction the alteration of wettability is the most common reservoir property change in the secondary and tertiary oil recovery processes such as water flooding, chemical flooding and biological flooding (sun et al. 2017; druetta et al. 2019; fani et al. 2022). clarifying the change trend of wettability before and after water flooding can effectively predict water flooding efficiency. previous studies believe that the increase of water wetness will significantly improve the oil displacement efficiency, while the understanding of the effect of the change of interface properties on oil recovery is different (awolayo et al. 2016; dordzie and dejam 2021). besides, to our knowledge, this conclusion is just an assumption and has not been rigorously manifested, nor has pore-scale direct analytical evidence supporting this finding. meanwhile, capillary force is still dominant at the pore scale, wettability alteration due to clay migration may provide additional connectivity at some regions of the pore space, resulting in the evolution of fluid flow path and may improve the ultimate recovery rate (rücker et al. 2015). therefore, it is vital for the researchers to do some investigation on the pore-scale imaging of the waterflooding and the analysis of the relevant microscopic flow path change. to test the conjecture, microscale spontaneous imbibition and waterflooding tests need to be done, and the resultant change in the pore network and wettability can be used to explain the fluid flow path evolution under different conditions. techniques such as scanning electron microscopy (sem) and microfluidic chips have been mailto:liucheng14@cnooc.com.cn 2 applied to observe this change (sameni et al. 2015; song and kovscek 2015; amirian et al. 2019). however, it is hard for sem technique to provide the same field of view during spontaneous imbibition and waterflooding, and microfluidics lack real sandstones properties. the state-of-art x-ray micro-ct could provide images which has enable the brine and oil inside the pore space to be segmented at high resolution in the sandstones and shale (mayo et al. 2015). indeed, some studies have successfully imaged different kinds of fluid with the help of ct (liu et al. 2017). furthermore, the impact of wettability alteration on fluid flow evolution and concomitant wettability alteration have not hitherto been quantified directly at the pore scale. here, we design a new micro-ct image analysis workflow where we proposed a test protocol in which brine with different salinity are injected at varies degree of flooding rate during unsteady-state core imbibition-flooding experiments. we determine the wettability alteration after waterflooding with different brine salinity. based on a workflow of spontaneous imbibition and waterflooding processes, the influencing factors of wettability alteration were investigated. moreover, the underlying mechanisms of wettability alteration at pore-scale were analyzed. methodology materials. we used a tight sandstone sample from c7 formation in ordos basin, china. the sample was first cleaned to remove the oil by a mixture of ethanol and benzene (3:1)，then it was dried at atmospheric pressure and 60 ℃ temperature. before the ct scanning, a contact angle measurement was performed in the original rock to determine the wettability. the fluid mixed with deionized water and 2.5 wt% nai was used as the brine to increase the reflection signal. different concentrations of brine (sodium chloride, nacl) functioned as the aqueous phases. the crude oil was selected from ordos basin in china, then mixed with aviation kerosene (20 wt%) to make its viscosity meet the in-situ situations in the reservoirs. apart from aviation kerosene, 20 wt% iododecane was added to improve x-ray contrast. hence, two types of fluids were used during the tests: brine with different salinity and doped-oil. experimental procedures. the imbibition and waterflooding test were conducted in a hassler type flow cell manufactured by vinci technologies, and the cell was made of carbon fiber epoxy to pre-serve the x-ray signal (lebedev et al. 2017). zeiss xradia 610 versa micro-ct instrument was used for high-resolution imaging, with 85 kev energy, 5.305 μm voxel size, 2s exposure time for each slice, and 518 projections with 513×515×370 voxels. the detailed experimental processes with different conditions are as follows: 1. dry condition: place the specimen inside the cell, and vacuum the system. after 6 h, a ct scan was performed. 2. saturation condition: the specimen was saturated with high-salinity brine, and the fluid flow rate was 1 ml/min. when the pressure between the inlet and outlet were remain the same, turned down the pump and conducted ct scanning for the specimen. 3. drainage condition: set the flow rate at 0.01 ml/min, and injected the mixed crude oil into the specimen. like the above step, a ct scan was performed when the differential pressure was inexistent. 4. spontaneous imbibition condition: set the flow rate at 0.01 ml/min, and injected the high salinity brine into the specimen. the apparent brine permeability was calculated by the data from inlet and outlet pressure. when the differential pressure vanished, we acquired the image. 5. high salinity brine waterflooding condition: flow the low salinity brine at 0.5 ml/min, and measured the differential pressure to determine the end time. the apparent permeability was calculated and the image was captured. 6. low salinity brine waterflooding condition: performed the low salinity brine water-flood with an injection rate of 0.5 ml/min, measured the apparent permeability, and took an image. after this step, another brine with lower salinity was injected into the specimens, and those mentioned parameters were also determined. 3 figure 1 demonstrates the workflow of the experiments. figure 1—flowchart to demonstrate the experimental processes. results phases behavior before spontaneous imbibition. as seen in figure 2, the greyscale value for vacuumed pores was much lower than the value for minerals, and the first one nearly remains the same, while the latter one has a range of distribution, indicating different kinds of minerals, such as detrital grains and clay. clay minerals are loosely distributed in pore spaces; therefore, the relatively dark areas (low greyscale value) in the pores or encircle the grains are identified as clays (aksu et al. 2015; kamal et al. 2019). after saturation, almost all pores are filled with brine, indicating that the overall connectivity of the sample is strong (figure 2b). after drainage, the fluid in a single pore is almost single-phase, such as full of brine or crude oil, just a small number of single pores coexist with two kinds of fluids (figure 2c). it is worth noting that the pores enriched by clay minerals are almost full of oil phase after drainage. since clay minerals are usually hydrophilic (kooli et al. 2014), it also proves that the sample has good overall connectivity. (a) dry sample (b) after brine saturation (c) after drainage figure 2—grayscale and phase-segmented ct images for 2d slices during different steps before spontaneous imbibition. phases behavior after spontaneous imbibition and waterflooding. figure 3 shows the distribution of oil and brine after spontaneous imbibition. spontaneous imbibition has little impact on the overall recovery (figure 3). it can only be seen that the integral rate of brine phase in some small holes increases, indicating that spontaneous imbibition in hydrophilic rocks mainly improves recovery by thickening the water film. however, because the core is relatively dense and the connectivity is relatively poor, the overall effect on improving recovery is small. 4 (a) after spontaneous imbibition (b) after high salinity brine waterflooding (c) after low salinity brine waterflooding figure 3—grayscale and phase-segmented ct images for 2d slices during different steps after spontaneous imbibition and waterflooding. figure segmentation. according to the helium porosity data, the gray value division interval is determined, and then the proportion of pores brines, and oil in different stages is obtained by image segmentation. figure 4a-c represents the phase-segmented ct images for dry, after saturation, and after drainage conditions, respectively. (a) dry sample (b) after brine saturation (c) after drainage (d) after spontaneous imbibition (e) after high salinity brine waterflooding (f) after low salinity brine waterflooding figure 4—the segmented phase volume fractions of different stages in each slice: from the inlet 0 to the end (white, blue, and pink represent pores, brine, and oil, respectively). discussion due to the complex pore structure of rock samples, the influence of gravity on oil dis-placement efficiency can be almost ignored in the spontaneous imbibition stage, so the difference in wettability directly causes the difference in 5 oil displacement efficiency (xu et al. 2019). the ct results of four samples show the degree of hydrophilicity of rock samples and the oil displacement efficiency at the spontaneous imbibition and waterflooding stages. the impact of wettability alteration on waterflooding mode. the existence of corner flow is the main reason for the waterflooding mode alteration (watson and weinstein 1971). as shown in figure 5, the clastic particles of the rock samples in the study area are mainly sub-angular and sub-rounded, with roundness generally less than 0.8 (krumbein calculation method) (krumbein 1941), which has the formation conditions of corner flow. the average round-ness of the four samples is between 0.6-0.8, so the two-dimensional model of a pore channel can be equivalent to a plane with an angle of 100 ° (90 ° is completely corner, 180 ° is completely spherical). figure 5—casting thin sections and sem images in the research area. the numbers represent the roundness of the circled pores. (a), (e) sample 1. (b), (f) sample 2. (c), (g) sample 3. (d), (h) sample 4. as shown in figure 6, under the condition of spontaneous imbibition stages, the penetration rate of the front end of corner flow is related to the particle-particle angle and the degree of hydrophilic: the smaller the angle, the higher the degree of hydrophilic, the higher the penetration rate. when the contact angle is less than 50 °, due to the existence of corner flow, the water film will advance in a completely spontaneous imbibition mode, which will lead to the displacement velocity at the edge of the channel is far greater than that at the center of the hole, resulting in the continuous formation of oil in water, and the single hole oil displacement efficiency is reduced. although the swept area is increased, the overall recovery factor is low. when the contact angle is greater than 50 °, the corner flow cannot be formed, and the water film steadily advances the front end of the water drive in a semi-arc shape. the overall oil displacement efficiency is high, so the recovery factor is high. this result shows that reducing wettability too much will lead to a large amount of corner flow, and a large amount of filamentous residual oil will be formed in the reservoir, which only increases the swept area and seriously restricts the single-hole oil displacement efficiency and a negative impact on oil recovery. 6 figure 6—fluid movement behavior concerning corner flow and pore-throat-shaped angle waterflooding recovery trend evolution. the recovery rate at different stages also shows an interesting trend (figure 7). although the spontaneous imbibition oil displacement efficiency of sample 1 is the highest, the improvement in the subsequent waterflooding stage is not obvious. this trend means that the starting pressure of dropwise residual oil is far greater than that of flaky residual oil, and a large amount of residual oil caused by water film penetration in the early stage is difficult to produce even if the viscosity displacement is increased. therefore, we should not pursue imbibition development excessively for reservoirs with high hydrophilic, and we need to configure relatively high displacement power to maximize the efficiency of reservoir development. figure 7—oil displacement efficiency of different stages the impact of wettability alteration on waterflooding recovery. as figure 8 shows, we used rock cores to measure the wettability, and the results showed that the contact angle gradually increased from no. 1 to no. 4 samples, indicating that the degree of hydrophilic became weaker. however, due to the pore boundary angle condition, as shown in figure 7, the waterflooding efficiency of the no. 1 sample is the lowest. that is, too strong hydrophilic will lead to too much residual oil due to corner flow. figure 8—contact angle measurement for (a) sample 1, (b) sample 2, (c) sample 3, and (d) sample 4. 7 by extracting the oil phase in the pore space, we found that the residual oil in sample 1 was indeed more than that in other samples (figure 9), which showed that strong water film displacement would lead to a fast penetration rate, resulting in too much residual oil in the form of dots, affecting the waterflooding recovery. (a) sample 1 (b) sample 2 (c) sample 3 (d) sample 4 figure 9—residual oil distributions for different samples effect of pore structures on oil displacement efficiency. using the combined method of nuclear magnetic resonance and high-pressure mercury injection, the factors affecting the pore structure of the mainstream zone of water-flooding are explored. in this study, we compared the samples after oil saturation and waterflooding with low salinity to obtain a waterflooding space. the space that accounts for 80 % of the waterflooding space is defined as the mainstream waterflooding zone, which is coupled with the pore size distribution to calculate the average pore size of the mainstream waterflooding space. as shown in figure 10, sample 2 has the largest dis-placement zone, which means the highest oil displacement efficiency. sample 1 has the largest average pore size in the mainstream displacement zone, sample 3 is in the middle, and sample 4 has almost no displacement zone. this result corresponds to the previous research results, indicating that pore size is not a decisive factor in determining water-flooding efficiency. excessive water wettability can easily lead to leading edge protrusion, and even large pore sizes cannot offset the dotted residual oil distribution caused by corner flow. conclusions capillary imbibition and viscous displacement are the main driving forces during waterflooding, and understanding them can help to formulate waterflooding plans. in this study, ct and other means were used to carry out spontaneous imbibition and salinity waterflooding experiments, and the following conclusions were obtained: 1. spontaneous imbibition has little impact on oil displacement efficiency. water flooding can significantly improve oil displacement efficiency, but due to pressure drop constraints, its spread is severely limited. low salinity water can further improve oil recovery. 2. changes in wettability are the key microscopic mechanism for improving oil dis-placement efficiency, corner flow seriously affects displacement efficiency. 3. the excessive hydrophilic condition can lead to severe corner flow. under this premise, the pore size cannot directly control the displacement efficiency. severe corner flow can cause leading edge protrusion, leading to the widespread distribution of drop-shaped residual oil, seriously restricting the improvement of displacement efficiency in the later stage. 8 (a) (b) (c) (d) figure 10—pore size and waterflooding zone combined with nuclear magnetic resonance and high-pressure mercury injection. references aksu, i., bazilevskaya, e., and karpyn, z. 2015. swelling of clay minerals in unconsolidated porous media and its impact on permeability. georesj 7:1-13. amirian, t., haghighi, m., sun, c., et al. 2019. geochemical modeling and microfluidic experiments to analyze impact of clay type and cations on low-salinity water flooding. energy & fuels 33(4): 2888-2896. 9 awolayo, a., sarma, h., alsumaiti, a. 2016. an experimental investigation into the impact of sulfate ions in smart water to improve oil recovery in carbonate reservoirs. transport in porous media 111: 649-668. dordzie, g. and dejam, m. 2021. enhanced oil recovery from fractured carbonate reservoirs using nanoparticles with low salinity water and surfactant: a review on experimental and simulation studies. advances in colloid and interface science 293:102449. druetta, p., raffa, p., picchioni, f. 2019. chemical enhanced oil recovery and the role of chemical product design. applied energy 252:113480. fani, m., pourafshary, p., mostaghimi, p., et al. 2022. application of microfluidics in chemical enhanced oil recovery: a review. fuel 315:123225. kamal, m.s., mahmoud, m., hanfi, m., et al. 2019. clay minerals damage quantification in sandstone rocks using core flooding and nmr. journal of petroleum exploration and production technology 9:593-603. kooli, f., yan, l., tan, s., et al. 2014. organoclays from alkaline-treated acid-activated clays: properties and thermal stability. journal of thermal analysis and calorimetry 115:1465-75. krumbein, w.c. 1941. measurement and geological significance of shape and roundness of sedimentary particles. journal of sedimentary research 11(2):64-72. lebedev, m., zhang, y., sarmadivaleh, m., et al. 2017. carbon geosequestration in limestone: pore-scale dissolution and geomechanical weakening. international journal of greenhouse gas control 66:106-19. liu, z., yang, y., yao, j., et al. 2017. pore-scale remaining oil distribution under different pore volume water injection based on ct technology. advances in geo-energy research 1(3):171-181. mayo, s., josh, m., nesterets, y., et al. 2015. quantitative micro-porosity characterization using synchrotron micro-ct and xenon k-edge subtraction in sandstones, carbonates, shales and coal. fuel 154:167-73. rücker, m., berg, s., armstrong, r., et al. 2015. from connected pathway flow to ganglion dynamics. geophysical research letters 42(10):3888-3894. sameni, a., pourafshary, p., ghanbarzadeh, m., et al. 2015. effect of nanoparticles on clay swelling and migration. egyptian journal of petroleum 24(4):429-437. song, w. and kovscek, a.r. 2015. functionalization of micromodels with kaolinite for investigation of low salinity oil-recovery processes. lab on a chip 15(16):3314-25. sun, x., zhang, y., chen, g., et al. 2017. application of nanoparticles in enhanced oil recovery: a critical review of recent progress. energies 10(3):345-352. watson, r.d. and weinstein, l.m. 1971. a study of hypersonic corner flow interactions. aiaa journal 9(7):1280-1286. xu, d., bai, b., wu, h., et al. 2019. mechanisms of imbibition enhanced oil recovery in low permeability reservoirs: effect of ift reduction and wettability alteration. fuel 244:110-119. cheng liu is a senior engineer in cnooc enertech-drilling & production co. his research interests include unconventional oil and gas reservoir core analysis experiment and seepage experiment. liu holds a master's degree in engineering from china university of mining and technology. yanjun yin is a senior reservoir engineer in cnooc. his research interests include reservoir development plan, reservoir simulation. yin holds a bachelor’s degree from northeast petroleum university, china, a master’s degree from china university of petroleum, beijing. ruiting bao is a reservoir engineer in cnooc. her research interests include unconventional resources， comprehensive treatment of old oil fields. bai holds a master ’ s degree in petroleum engineering from xi ’ an shiyou university and a phd degree in petroleum engineering from china university of geosciences, beijing. 10 dengke liu is a associate professor in the school of human settlements and civil engineering at xi'an jiaotong university. his research interests include unconventional resources' pore structures and fluid flow behavior. liu holds a bachelor's degree in geology from northwest university, china, and a phd degree in mineral prospecting and exploration from northwest university, china and university of alberta. abstract introduction methodology results discussion conclusions references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1229 received january 2, 2023; revised february 04, 2023; accepted february 11, 2023. * corresponding author: mfsnosy@yahoo.com 1 role of the low salinity condensate water during steam injection in carbonate reservoirs mohamed fouad snosy*, general petroleum company, cairo, egypt; mahmoud abu el-ela, cairo university, cairo, egypt; ahmed el-banbi, the american university in cairo, cairo, egypt; and helmy sayyouh,cairo university, cairo, egypt abstract numerous laboratory and pilot tests have verified low salinity waterflooding (lswf) as a promising enhanced oil recovery (eor) method in carbonate reservoirs. the multi-ion exchange (mie) and anhydrite dissolution mechanisms are widely accepted mechanisms for the lswf. this study investigates the effects of the low salinity condensed water (lscw) and anhydrite dissolution on oil recovery during steam injection in carbonate reservoirs. the work has been verified using actual laboratory and production data of an existing cyclic steam injection project in carbonate reservoir. several core samples were extracted from the reservoir under study. the wettability index of two cores was measured. the first core was taken from well-01 before starting any steam injection in its area. however, the second core was extracted from well-02, which was drilled in the area affected by steam injection. the analysis of the production data of the 9 oil wells was performed to study the effect of anhydrite percentage on oil recovery. the analysis showed that the lscw could alter wettability in the direction of water wet. the analysis also concluded that although the anhydrite dissolution caused alteration of wettability, the increase of anhydrite percentage could cause a reduction in reservoir quality and oil production. introduction the lswf is defined as waterflooding technique that decreases the total dissolved salts (tds) of the injected water and/or modifies the injected water ionic content. the first core flooding experiment in the carbonate reservoir was conducted by bagci et al. (2001), who documented higher oil recovery up to 18.8% by changing the injected water composition to 2% kcl plus 2% nacl brine mixture. furthermore, diluted sea water injection in carbonate plugs showed additional oil recovery up to 11% in several experiments performed by shariatpanahi et al. (2011), fathi et al. (2010), and zekri et al. (2019). the mechanism of the lswf in carbonate reservoirs is still debatable. the proposed mechanisms include fine migration, multi-component ion exchange (mie), calcite dissolution, interfacial tension (ift) reduction, double-layer expansion, anhydrite dissolution, salting-in, water micro-dispersion, osmosis pressure effect, and surface roughness (snosy et al. 2021). it should be highlighted that the mie mechanism is widely accepted as the main controller for the performance of the carbonates' lswf projects. the carbonate reservoir's mie mechanism was supposed to be anion exchange and not cation exchange like sandstone reservoirs. the mechanism is attributed to the adsorption of potential determining ion (pdi) so42-, ca2+ and/or mg2+ onto the rock surface (snosy et al. 2022a). the mie evidence of the lswf in the carbonate mailto:mfsnosy@yahoo.com 2 reservoirs was proposed by austad et al. (2005). then, this mechanism was accepted by strand et al. (2008a), ligthelm et al. (2009), zhang and austad (2006), puntervold (2008), and myint and firoozabadi (2015). they demonstrated that the incremental oil recovery of sea water injection in carbonates is attributed to the high sulfate concentration. moreover, austad et al. (2011) and pu et al. (2008) proposed that the anhydrite dissolution in the carbonates is a method of generating in-situ so42which is thought to act as a catalyst in the wettability alteration process. furthermore, al-saedi et al. (2019) investigated the effect of the condensed steam (low salinity water) during steam injection in sandstone reservoirs. they reported that the wettability was altered towards more water-wet when the steam was turned into low saline (ls) water. in addition, they reported that the lscw could act as a wettability modifier only without reducing the oil viscosity. moreover, there are no available studies for investigating the effect of condensed water during steam injection in carbonate reservoirs. therefore, this work was performed to study the effect of lscw and anhydrite dissolution in carbonate reservoirs using laboratory and field data of an existing cyclic steam injection project. reservoir description the reservoir under study is made up of dolomite, anhydrite nodules, shell fragments, and argillaceous materials. the dolomite is tannish gray, dark gray, light brown, brown, tannish brown, medium-hard to very hard, fine – cryptocrystalline, anhidrotic in parts, sandy in parts, glauconitic at rare parts, and vuggy in parts. while, the anhydrite is off white, milky white, white, light brown, colorless, medium-hard to hard, fine – cryptocrystalline translucent opaque, with sucrose texture in parts. the reservoir contains heavy oil accumulations and could not produce cold production. it has been producing under cyclic steam stimulation. most of the trials performed to produce this zone as cold production were failed until the first cyclic steam trail was made. the formation contains extra heavy oil with 12-15 oapi and viscosity of 4000 cp at standard conditions, 10% h2s, 10% co2, and 15% asphaltene contents. the geochemical analysis and studies indicated that the biodegradation is due to bacterial action. table 1 summarizes the reservoir's average properties. table 1—average reservoir properties parameters value estimated original oil in place 1.1 × 109stb reservoir average depth 850-1000 ft average initial water saturation 30% average porosity 35% average reservoir permeability 10-35 md initial reservoir pressure 500 psi initial reservoir temperature 100 of oil viscosity at standard conditions 4000 cp oil gravity 10-12 oapi 3 results and discussion effect of lscw on the wettability. two cores from two wells were used to study the effect of lscw. the two cores have the same rock compositions: dolomite, anhydrite nodules, shell fragments, and argillaceous materials. the first core was taken from well-01 before starting any steam injection in its area. however, the second core was taken from well-02, which was drilled in the area affected by steam injection. amott wettability index for several core samples from the two wells (well-01 and well-02) was measured as shown in table 2. the core samples of well-01 reported amott wettability index ranges from -0.10 to 0.51 with an average value of -0.29. these values reveal that the core samples have oil to neutral wettability index. while the core samples of well-02 reported amott wettability index ranges from -0.11 to -0.26 with an average value of -0.15. these values reveal that the core samples have a neutral wettability index. table 2—amott wettability index for core samples of well-01 and well-02 well-01 well-02 sample amott wettability index sample amott wettability index a-2 -0.51 oil wet b-1 -0.26 neutral a-3 -0.10 neutral b-2 -0.12 neutral a-4 -0.23 neutral b-3 -0.11 neutral a-5 -0.20 neutral b-4 -0.12 neutral a-6 -0.25 neutral a-7 -0.39 oil wet a-8 -0.34 oil wet these results reveal that the lscw alters the rock wettability from oil-neutral wet to neutral wet. the average amott index changed from an average of -0.28 in well-01, which had no effect of steam, to -0.15 average in well-02, which has an effect of steam injection. it should be highlighted that these results are consistent with those obtained by hjelmeland and larrondo (1986), wang and gupta (1995), punase et al. (2014), and rao (1999). they reported that carbonate became water-wet with temperature increase. furthermore, the results of this study agree with those of blevins et al. (1984), who suggested that the rock wettability of the qarn alam field in oman became more water-wet with an increase in temperature. it should be highlighted that the alteration of wettability was attributed to the presence of lscw in carbonate reservoirs. this can be clarified as a result of two mechanisms which were proposed to study the effects of sulfate anion in carbonates: anhydrite dissolution and mie mechanisms. for the anhydrite dissolution mechanism, worden and smalley (1996) documented that anhydrite and hydrocarbons were reacted together, in carbonate reservoirs of hotter than 140°c, to produce calcite and h2s. it should be stated that the sharp increase of h2s in produced oil in the current study after steam injection in all wells up to 10% was a strong evidence for anhydrite dissolution. austad et al. (2011) stated that the anhydrite (caso4) dissolution generates in-situ so42ions which act as a catalyst agent in the wettability alteration process. the mie mechanism was attributed to the adsorption of potential determining ion (pdi) so42-, ca2+ and/or mg2+ onto the rock surface. adsorption of so42decreases the positive charge density on the rock surface. it minimizes electrostatic repulsive force and causes co-adsorption of ca2+ and mg2+ on the rock surface. ca2+ reaction with carboxylic acid groups breaks the attractive interactions between the oil and rock interface, which changes rock surface into more water wet (snosy et al. 2022b). furthermore, fathi et al. (2010) proposed that the high temperature (above 90 oc) could cause substitution of ca2+ ions on the carbonate surface by mg2+ ions from the injected water. therefore, the displaced ca2+ ions bond to carboxylic acid molecules and cause absorption of them in the form of calcium-carboxylate 4 complexes. thereby further improving oil recovery is achieved. moreover, strand et al. (2008b) and hognesen et al. (2005) concluded that sulfates could act as a catalyst at high temperature and below a certain concentration (1.0 g/l and 2.31 g/l, respectively). that will cause a decrease in ift and alteration of wettability to more water wet. effect of anhydrite on the oil recovery. the oil production data of 9 wells were collected. the 9 wells have almost the same reservoir characteristics and same completion strategy. the wells were cased hole wells, drilled in the same period, and showed encouraging production behavior. these 9 wells are selected because they have less heterogeneity and minor natural fracture. it is believed that the oil production from the wells has occurred through matrix dominant with minor natural fracture. the anhydrite percentage varies significantly in the selected wells as it ranges from 2% up to 10%. table 3 shows the rock properties, anhydrite percentage, fracture density, and well production data in the selected wells. figure 1 presents the relationship between the anhydrite percentage and the oil production rate before and after acidizing and steam injection in the selected wells. the acid stimulation was performed to remove skin damage after drilling and open channels for steam injection. however, figure 2 represents the relationship between the anhydrite percentage and (1) the 5 years cumulative oil production, and (2) 5 years cumulative oil production per net pay thickness. figures 1 and 2 document that increasing of the anhydrite content in the reservoir causes reduction of the oil recovery as a result of reservoir quality decrease. it is obviously clear that the anhydrite amount in the reservoir has a negative impact on the oil production rate. the oil wells which are located in reservoir area of high anhydrite percentage show less oil production rate and less cumulative oil production. it is concluded that the anhydrite dissolution causes alteration of wettability. however, the increase of the anhydrite percentage could cause a reduction in the reservoir quality and oil production. table 3—average properties of the selected wells well* net thickness, ft anhydrite content, % φ, % swi, % fracture density /ft cold oil prod. rate, stb/d 5 years cum. oil, stb (5 years cum. oil / thickness) stb/ft w-02 81 2% 27 40 0.04 25 64,295 794 w-03 102 5% 23 37 0.16 13 48,363 474 w-04 107.5 10% 24 36 0.16 15 49,663 462 w-05 112 5% 29 40 0.03 13 63,763 569 w-06 123 11% 25 35 0.13 4 44,025 358 w-07 112 4% 26 40 0.06 15 61,971 553 w-08 120 8% 25 35 0.13 6 37,843 315 w-09 118 6% 26 37 0.17 25 53,053 450 w-10 112 4% 26 37 0.06 25 56,755 507 * well-02, well-03,..well-10 are drilled at the same time and completed with the same strategy. however, well-01 was drilled earlier and completed with different technique (open hole section) so it is not included in this analysis. 5 figure 1—relationship between the anhydrite content and the oil production rate before and after acid and steam injection for the selected oil wells. figure 2—relationship between the anhydrite content and the oil production data of the selected wells. 6 conclusions 1. the wettability index measurements for several core samples indicate that the rock wettability may be alerted after steam injection to the direction of water wet. 2. the alteration of wettability is attributed to the presence of low salinity condensed water after. 3. the multi-component ion exchange mechanism may be the primary mechanism of wettability alteration due to lscw. 4. the anhydrite dissolution in the reservoir under study may help in wettability alteration. 5. although the anhydrite dissolution causes alteration of wettability, increasing anhydrite percentage reduces the reservoir quality and oil production. conflicting interests the author(s) declare that they have no conflicting interests. nomenclature api = american petroleum institute oil gravity cum. = cumulative production eor = enhanced oil recovery φ = porosity, fraction ls = low salinity water lscw = low salinity condensed water lswf = low salinity water flooding mie = multi-component ion exchange ooip = original oil in place pdi = potential determining ion swi = initial water saturation, fraction tds = total dissolved salts references al-saedi, h.n., al-bazzaz, w., and flori, r.e. 2019. is steamflooding a form of low salinity waterflooding? paper presented at the spe middle east oil and gas show and conference, manama, bahrain, 15-18 march. spe-194820ms. austad, t., shariatpanahi, s., strand, s., et al. 2011. conditions for a low-salinity enhanced oil recovery (eor) effect in carbonate oil reservoirs. energy fuels 26:569-575. austad, t., strand, s., høgnesen, e.j., et al. 2005. seawater as ior fluid in fractured chalk. paper presented at spe international symposium on oilfield chemistry. the woodlands, texas, usa, 2-4 february. spe-93000-ms. bagci, s., kok, m.v., and turksoy, u. 2001. effect of brine composition on oil recovery by waterflooding. petroleum science and technology 19(3): 359-372. blevins, t.r., duerksen, j.h., and ault, j.w. 1984. light-oil steam flooding an emerging technology. journal of petroleum technology 36(7): 1-15. spe-10928-pa. carlberg, b.l. 1973. solubility of calcium sulfate in brine. paper presented at the spe oilfield chemistry symposium, denver, colorado, usa, 24-25 may. spe-4353-ms. fathi, s.j., austad, t., and strand, s. 2010. "smart water" as a wettability modifier in chalk: the effect of salinity and ionic composition. energy and fuels 24(4): 2514-2519. hjelmeland, o.s. and larrondo, l.e. 1986. experimental investigation of the effects of temperature, pressure, and crude oil composition on interfacial properties. spe reservoir engineering 1(4):321-328. spe-12124-pa. 7 hognesen, e.j., strand, s., and austad, t. 2005. waterflooding of preferential oil-wet carbonates: oil recovery related to reservoir temperature and brine composition. paper presented at the spe europec/eage annual conference, madrid, spain, june 13-16. spe-94166-ms. ligthelm, d., gronsveld, j., hofman, j., et al. 2009. novel waterflooding strategy by manipulation of injection brine composition. paper presented at the spe europec/eage conference and exhibition. amsterdam, the netherlands, 8-11 june. spe-119835-ms. myint, p.c. and firoozabadi, a. 2015. thin liquid films in improved oil recovery from low-salinity brine. curr. opin. colloid interface sci. 20:105-114. pu, h., xie, x., yin, p., et al. 2008. application of coalbed methane water to oil recovery from tensleep sandstone by low salinity waterflooding. paper presented at the spe improved oil recovery symposium, tulsa, oklahoma, usa, 20-23 april. spe-113410-ms. punase, a., zou, a., and elputranto, r. 2014. how do thermal recovery methods affect wettability alteration? journal of petroleum engineering 2014(3):1-15. puntervold, t. 2008. waterflooding of carbonate reservoirs: eor by wettability alteration. ph.d. thesis, university of stavanger, stavanger, norway. rao, d.n. 1999. wettability effects in thermal recovery operations. spe reservoir evaluation & engineering 2(5):420-430. spe-57897-pa. shariatpanahi, s.f., strand, s., and austad, t. 2011. initial wetting properties of carbonate oil reservoirs: effect of the temperature and presence of sulfate in formation water. energy and fuels 25(7):3021-3028. snosy, m. f., abu el ela, m., el-banbi, a., et al. 2022a. impact of the injected water salinity on oil recovery from sandstone formations: application in an egyptian oil reservoir. petroleum 8(1): 53-65. snosy, m. f., abu el ela, m., el-banbi, a., et al. 2022b. role of the injected water salinity and ion concentrations on the oil recovery in carbonate reservoirs. petroleum research 7(3): 394-400. snosy, m.f., abu el ela, m., el-banbi, a., et al. 2021. comprehensive investigation of low salinity waterflooding in carbonate reservoirs. journal of petroleum exploration and production technology 12:701-724. strand, s., austad, t., puntervold, t., et al. 2008a. "smart water" for oil recovery from fractured limestone: a preliminary study. energy and fuels 22(5):3126-3133. strand, s., puntervold, t., austad, t. 2008b. effect of temperature on enhanced oil recovery from mixed wet chalk cores by spontaneous imbibition and forced displacement using seawater. energy and fuel 22(5):3222-3225. wang, w. and gupta, a. 1995. investigation of the effect of temperature and pressure on wettability using modified pendant drop method. paper presented at the spe annual technical conference and exhibition, dallas, texas, usa, 22-25 october. spe-30544-ms. worden, r. h. and smalley, p. c. 1996. h2s-producing reactions in deep carbonate gas reservoirs: khuff formation, abu dhabi. chemical geology 133(4):157-171. zekri, a.y., harahap, b.a., al-attar, h.h., et al. 2019. effectiveness of oil displacement by sequential low-salinity waterflooding in low-permeability fractured and non-fractured chalky limestone cores. journal of petroleum exploration and production technology 9(1):271-280. zhang, p. and austad, t. 2006. wettability and oil recovery from carbonates: effects of temperature and potential determining ions. colloids and surfaces a: physicochemical and engineering aspects 279(1): 179-187. mohamed snosy is a senior reservoir engineer in general petroleum company in egypt. he has more than 14 years of diversified international experience in reservoir engineering and reservoir simulation. he has extensive experience in oil, gas, sandstone, and carbonate reservoirs (natural flow, artificial lift, naturally fractured reservoirs, secondary recovery, and thermal oil recovery). furthermore, he holds his ph.d. degrees in petroleum engineering from cairo university in egypt. mahmoud abu el-ela is a professor of petroleum engineering at cairo university. he is also managing director for the mining studies & research center (msrc) at the faculty of engineering, cairo university. since 1997, he has been a technical consultant in petroleum engineering for several national and international companies (khalda petroleum company “jv between egpc and apache”, worley, etc.). abu el ela holds a b.sc. and m.sc. in petroleum engineering from cairo university, and a ph.d. from curtin university of technology, australia. abu el ela’s current interests include fields development planning, reservoir management, production optimization, and enhanced oil recovery along with gas conditioning & processing. he has supervised several m.sc. and ph.d. thesis and published more than 50 technical papers in specialized international journals and conference proceedings. also, he is reviewer for many journals. 8 abu el ela is an spe member, and currently he is the faculty advisor for the spe student chapter at cairo university. ahmed el-banbi is a professor of petroleum engineering and chair of the petroleum engineering department at the american university in cairo. he previously worked for cairo university. prior to that, elbanbi worked for schlumberger, where he held a variety of technical and managerial positions in five countries. he has considerable experience in managing multidisciplinary teams and performing integrated reservoir studies. el-banbi authored or coauthored one book, two book chapters, and more than 90 journal and conference papers, and holds one us patent. he holds bs and ms degrees from cairo university, and ms and phd degrees from texas a&m university; all in petroleum engineering. el-banbi has been a member of numerous spe committees, was the program chair for the 2015 spe north africa technical conference and exhibition and a reviewer for many journals. helmy sayyouh obtained his b.sc. and ms. degrees in petroleum engineering from cairo university in 1970 and 1974 respectively and ph.d. from penn state university, usa in 1979 and became an assistant professor of reservoir engineering. he rose to the rank of associate professor in 1984 and full professor in 1989. he was the chairman of the department of mining, petroleum and metallurgical engineering, faculty of engineering at cairo university from 2005 to 2008. presently, he is the professor of petroleum reservoir engineering. since 1986, he had been a consultant engineer in the areas of petroleum reservoir engineering, enhanced oil recovery, reservoir simulation and natural gas engineering. he was an active member in the egyptian high production committee (egpc) from 1995 to 2001 with the objective of proposing and evaluating means of maximizing recovery and optimizing production from egyptian fields, and identifying and solving common problems faced by oil companies. dr. sayyouh is a member of spe of aime, egyptian society of engineering professions, and new york academy of science. dr. sayyouh supervised more than 60 m.sc. and ph.d. thesis and published over 150 technical papers in specialized international journals and conference proceedings all over the world. abstract introduction reservoir description results and discussion conclusions conflicting interests nomenclature references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1286 received may 17, 2024; revised july 1, 2024; accepted august 14, 2024. *corresponding author: modibbo.edu@gmail.com 1 study to investigate the potential of coalbed methane (cbm) in nigeria ibrahim modibbo ahmed* and saleem qadir tunio, cyprus international university, nicosia, north cyprus abstract the increasing global demand for energy has led to a heightened interest in unconventional hydrocarbons, including coalbed methane (cbm), a type of natural gas found in coal deposits. this research explores the viability of utilizing cbm in nigeria, focusing on four key basins, including okpara, onyeama, okaba, and owukpa basin. key coal quality parameters, such as coal rank, depth, moisture content, ash content, and volatile matter, were analyzed and compared to data from prominent coal basins in the united states, indonesia, china, india, australia, and canada. the findings indicate that nigerian coal is predominantly sub-bituminous, with an average moisture content of 10.95% by weight and is located at relatively shallow depths. these characteristics suggest that nigeria has significant potential for cbm production, positioning it as a promising alternative energy source for the country. introduction as conventional oil and natural gas supplies continue to decline globally, the need to explore unconventional energy sources has become increasingly urgent. innovations in the petroleum industry have necessitated the development of new methods to exploit “unconventional” oil and gas reservoirs, which were previously untapped. according to the international energy agency's 2011 world energy outlook, unconventional hydrocarbons are those that cannot be extracted in their natural state from a conventional production well without the use of heating or dilution (wolfson 2023). these resources include coalbed methane (cbm), shale gas, shale oil, tight gas, tight oil, coal seams, tar sands, and gas hydrates, all of which require advanced energy and technology to extract. geologically, unconventional hydrocarbons are solid, liquid, or gaseous hydrocarbons that originated from organic compounds in source rocks over geological time and may have undergone changes, especially in the case of solid particles and extra-heavy liquids (chew 2013). coalbed methane (cbm) is a type of natural gas primarily composed of methane, found within coal seams. many countries possess cbm reserves, but the united states, canada, australia, china, and india are the primary producers. according to the u.s. energy information administration (energy information administration 2023), the united states has approximately 11,878 billion cubic feet of proven cbm reserves, leading the global market. the profitability of cbm projects in the u.s. is influenced by various factors such as seam thickness, gas content, methane content, coal rank, and permeability (green et al. 2019). nigeria, with over 2 billion metric tons of coal reserves, including 650 million tons of proven reserves (bureau of public enterprises 2006), has significant cbm potential. despite this, nigeria's cbm resources remain largely undeveloped due to insufficient research into cbm's potential and the lack of development techniques to optimize its production. nigeria's electricity sector also faces challenges; the country generates between 2,687 and 4,200 megawatts of power, far below the peak demand of 12,800 megawatts. 86% of nigeria's electricity is currently generated from fossil fuels, particularly natural gas (barka and nur 2023). the mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 decline in crude oil and natural gas production threatens the country's natural gas supply, which is crucial for power generation. cbm, as a clean source of natural gas, offers a viable alternative to replace natural gas as an energy source. this research aims to evaluate the potential of coalbed methane (cbm) development in nigeria by analyzing the physical properties of coal. the study is divided into two parts: the first part investigates the potential of cbm in nigeria by examining coal quality parameters such as ash content, moisture content, and volatile matter. the second part compares the quality of nigeria's coal with that of other cbm-producing countries, including the united states, china, india, and indonesia. literature review coal characterization. coal characteristics are determined through various methodologies and analytical tools that identify both the physical and chemical properties of coal. the two primary methods used for determining coal quality are proximate analysis and ultimate analysis. proximate analysis: this method estimates key parameters such as calorific value, volatile matter, fixed carbon, and moisture content in coal (ozbayoglu 2018). ultimate analysis: this method independently identifies the elemental composition of coal, including carbon, hydrogen, nitrogen, sulfur, and oxygen. the results are often presented as percentages (sgs corp 2022). coal is categorized into four distinct ranks based on its characteristics: anthracite, sub-bituminous, bituminous, and lignite, with lignite being the lowest grade, as shown in table 1. the ranking of coal is primarily determined by two factors: the amount of thermal energy it can provide and the types and concentrations of carbon it contains. the quality of a coal deposit is influenced by the amount of pressure and heat it has been subjected to over time (energy information administration 2022). table 1—coal rank system (adapted from greb et al. 2017). global coalbed methane reserves. as technology advances, the global demand for energy resources, particularly crude oil, continues to rise. over the past decade, coalbed methane (cbm), an unconventional resource, has emerged as a viable alternative to meet the increasing energy needs within the global energy mix. improved oil and gas recovery 3 this growth in demand is driven by the expanding global economy and population, which require a consistent and reliable energy supply (ritchie et al. 2020). the largest cbm reserves are located in countries such as russia, the united states, china, canada, australia, indonesia, poland, germany, and france (mastalerz 2014). specifically, the united states, canada, china, australia, and russia hold the most significant cbm reserves (liu et al. 2023). the estimated global cbm reserves exceed 229 trillion cubic meters, presenting promising development prospects for this unconventional natural gas resource (zhang et al. 2021). australia has been actively involved in cbm extraction and is well-known for having significant reserves of cbm, which are expected to be between 8.3 to 14.3 trillion cubic meters (liu et al. 2023). the nation's emphasis on using cbm as a fuel source is consistent with its dedication to more environmentally friendly energy options (martin et al. 2021). furthermore, canada has been acknowledged for its involvement in the production of cbm, which adds to the country's energy portfolio (cho et al. 2016). cbm extraction in china saw its initial investigation in the 1980s (yang 1987) and the country's first commercial production from a cbm well did not begin until 2003 (qin 2006). china has made notable strides in improving cbm production techniques. drilling cost reductions and enhanced single-well output have resulted from innovations in completion technology, reservoir reconstruction, and drilling techniques (lu et al. 2021). more than 90% of china's cbm production comes from high-rank coal, making it an essential component of the country's cbm production (liu et al. 2023). due to its substantial cbm reserves, the nation plays a significant role in the worldwide cbm industry (xia et al. 2019). globally, coal remains the primary source of electricity generation on almost every continent, providing a reliable and secure supply of electricity to both industrialized and developing countries (world coal association 2012). the properties of coal, such as ash content, moisture, fixed carbon percentage, sulfur content, tar and light oil percentage, etc., must be considered to optimize energy production efficiency. coal reserve in nigeria. in nigeria, significant coal deposits are found across the country, particularly from the southern to the northeastern regions, where there are primarily four coal mines. the coal characteristics in each of these basins may vary, influencing their suitability for different energy production methods. nigeria is estimated to have 2.5 gigatons (gt) of proven coal reserves. approximately 90% of these deposits are composed of sub-bituminous and bituminous coals, with the remaining 10% being lignite. these coal deposits are located in the lower, middle, and upper benue troughs. lignite and sub-bituminous coals are predominant in the lower and upper troughs, while high-volatile bituminous coals are more common in the middle trough. significant coal sites include lafia-obi in the middle trough, and the onyeama and okaba mines in the lower trough (oboirien et al. 2018). nigeria is home to over 23 coal mines (oboirien et al. 2018). according to the nigerian coal corporation, four underground mines—okpara and onyeama in enugu state, okaba in kogi state, and owukpa in benue state—are currently producing coal. additionally, there are 13 untapped coal reserves. nigeria's primary coal reserves are found in the cretaceous anambra basin to benue basin of bakina and okigwe city of imo state. the coal in this area is mostly found at the lower to upper grade of coal type (adedosu et al. 2007). the enugu coalfield, particularly the okpara and onyeama underground mines, is abundant in coal. these basins are part of the eastern extension of the cretaceous sedimentary basin (synclinorium). the onyeama seam, for instance, is located where the asata river cuts through the enugu escarpment (adedosu et al. 2010). orukpa and okaba, both surface mines, are located in the north-central states of benue and kogi (olaleye et al. 2009). the basic components of okaba coal and shale are more abundant than global averages, although the trace amounts of heavy metals are well below coal quality standards. okaba coal has an average moisture content of 12.51%, an ash content of 11.48%, and a volatile matter content of 47.49% (fatoye et al. 2012). improved oil and gas recovery 4 methodology study area. this study primarily focuses on four of nigeria's cbm basins: okpara, onyeama, okaba, and owukpa. all of these basins are located along or near the river benue channel. the okpara and onyeama basins, which show significant potential, are located in enugu state in southeastern nigeria, covering an area of over 667,000 acres. figure 1 provides a location map showing these basins, extending from the bida basin to the lower and upper benue trough basin. the okaba basin is situated in kogi, near lokoja, as marked on the figure 1. figure 1—coalbed methane producing fields in nigeria (modified from akinyemi et al. 2022). data collection. quantitative data on coal attributes and quality have been sourced from the nigerian coal corporation (ncc), which is responsible for coal exploration and quality testing throughout the country. according to ncc data, there are currently four active coal mines in nigeria, as detailed in table 2. for this study, the collected coal data encompasses coal rank, seam depth, recoverable reserves, moisture content, volatile matter, ash content, and gas content. table 2—list of four cbm basins in nigeria. no. basins location(state) status 1 okpara enugu mining by excavating 2 onyeama enugu mining 3 okaba kogi operating coal mine 4 owukpa benue mining improved oil and gas recovery 5 data analysis. the proximate analysis method was employed to assess the ash content, moisture content, calorific value, and volatile matter of the coal samples. for this analysis, 1 gram of each coal sample, passed through a 212 µm sieve, was used. moisture content was determined using a labcon air oven in accordance with the south african national standards (sans) 5925:2007. volatile matter was analyzed using a volatile furnace based on iso 562:1998. ash content was evaluated with a lenton programmable furnace, following iso 1171:1997 guidelines (taylor et al. 1998). fixed carbon content in the coal was calculated using the appropriate formula as eq. 1, fixed carbon (%) =100 – moisture (%) – ash (%) volatile matter (%)........................................................(1) porosity is determined through core analysis. initially, the bulk and grain densities are measured, and porosity is then calculated by dividing the pore volume by the bulk volume. with all necessary data collected and assumptions established, a comparative data analysis technique was used in this study. this approach involved examining cbm data from nigeria and comparing it with data from cbm-producing countries such as the u.s., china, indonesia, india, australia, and canada. the gas-proven results were calculated by multiplying the gas reserves (in million tons) by the gas content (cubic feet per ton). gas content (cubic feet)=proven reserve (tons) * gas content (cubic feet/ton)..............................................(2) results and discussions the coal deposits in nigeria are characterized by shallow depths, sub-bituminous rank, low ash content, and high volatile matter. as summarized in table 3, coal from the four basins analyzed is classified as subbituminous coal, which is a low-rank coal type, according to the united states geological survey (u.s. geological survey 2017). sub-bituminous coal, often gray-black or dark brown, represents an intermediate stage between lignite and higher-quality bituminous coal. it is widely used in power plants for steam generation and can also be liquefied to produce petroleum and natural gas (energy education 2008). table 3—coal quality of four nigeria`s basins. quality parameter locations okapara onyeama okaba owukpa average proven reserve(mt) 24 40 73 57 coal rank sub-bituminous sub-bituminous sub-bituminous sub-bituminous sub-bituminous depth (m) 180 100.2 100 100 120.05 moisture (%) 7.5 12.61 15.4 8.3 10.95 ash (%) 8.4 3.67 7.3 8.6 6.99 volatile matter 38.26 36.64 36.4 38.6 37.48 gas content (scf/ton) 312.14 312.14 312.14 312.14 312.14 the coal seams in nigeria generally lie at shallow depths, around 100 meters, except for the okapara basin in enugu, where the formation reaches a depth of 180 meters. the average moisture content is 10.95%, while ash content varies from 3.67% to 8.6% in the owukpa basin, with an overall average of 6.99%. the gas content of these cbm basins suggests significant potential for coal-bed methane production. mature coals, which are deeper and older, typically have higher carbon content and lower moisture and volatile materials. this results in increased carbon dioxide (co2) production during combustion or gasification, with fewer volatile gases such as methane and hydrogen. high ash content can lead to increased slagging and fouling in gasifiers, reducing gas production efficiency and increasing maintenance requirements. additionally, inorganic chemicals in ash may react with gas-forming compounds, potentially altering the gas composition. high moisture content in gas can produce water vapor, which may dilute the desired gas products. improved oil and gas recovery 6 nigeria's coal shows considerable potential for combustion processes which involve the burning of coal to release thermal energy which can be used to generate electricity, heat, or other industrial process, as it contains a high concentration of volatile matter, which facilitates gas generation, including flammable gases like methane, hydrogen, and carbon monoxide. the specific gas products can vary based on the volatile matter composition and the conditions of gasification or combustion. for example, methane tends to be the primary gas at lower temperatures, while higher temperatures may favor the production of carbon monoxide and hydrogen. table 4 provides a summary of the reservoir characteristics. the reservoir's porosity of 1.9% is considered low for a coal-bed methane (cbm) reservoir. typically, a porosity greater than 5-10% is preferred, as it enhances the storage capacity for methane. however, it is worth noting that even reservoirs with lower porosity can still be productive, as several cbm reservoirs with similar characteristics have successfully generated gas. permeability of 45 millidarcies is considered moderate to good for coal beds. while methane flow through coal seams is generally more efficient at higher permeability levels, significant gas production can still occur at lower permeability values. the coal seam thickness of 1.7 meters, though not very substantial, can be viable for extraction if the porosity and permeability are adequate. thicker coal seams typically offer more storage capacity for gas, which can lead to higher production rates. table 4—average reservoir data. coal thickness (m) 1.7 porosity (%) 1.9 permeability (md) 45 density (g/m3) 1.4 specific gravity 1.33 coalbed methane (cbm) reserve. the cbm reserves across these four basins have been evaluated based on an average gas content of 312.14 standard cubic feet per ton of coal. figure 2 provides a graphical representation of the gas reserves in each of these basins. figure 2—estimated gas proven reserve. improved oil and gas recovery 7 depths of the seams. the coal seams in the owukpa, okaba, and onyeama fields are approximately 100 meters deep, close to the surface, while the okpara basin features coal seams at a depth of 180 meters. compared to other cbm basins globally, the shallow depth of nigerian coal suggests that it can be readily extracted through pit mining. figure 3 shows a comparison of the seam depths of nigeria's cbm basins with those of cbm basins worldwide. figure 3—comparison of seams depth. moisture content analysis. in comparison to the other four nigerian basins, as illustrated in figure 4, okpara coal exhibits the lowest moisture content. the highest moisture content is observed in coal from the united states, whereas coal from china has a relatively low moisture level of 1.02%. nigerian coal averages 10.95% moisture, which is similar to that of australian coal. this low moisture content enhances power plant efficiency and reduces coal transportation costs, indicating that nigeria's coal holds significant potential for power generation. figure 4—comparison of moisture content. improved oil and gas recovery 8 ash content. coal from the onyeama field is noted for its low ash content compared to other analyzed basins, while coal from india shows a higher ash value. the average ash concentration in nigerian coal is 6.99%, which is comparable to that of the powder river basin in the united states. these figures are considered favorable since coal with high ash content can lead to environmental pollution (air, water, and land) and reduce the efficiency of combustion boilers used for power generation. indian coal, with its high ash content, poses environmental challenges and is less suitable for use in power sectors. as shown in figure 5, coal from nigeria and the united states is relatively pure in comparison. figure 5—result of ash content. figure 6—volatile matter comparison analysis. volatile matter. the four nigerian basins exhibit high concentrations of volatile matter (vm), averaging 33.82%, surpassing those of all other basins except the powder river basin in the united states. chinese coal, in contrast, has the lowest volatile matter concentration. the elevated volatile matter content in nigerian coal requires moderate temperatures for effective combustion of the coal dust. figure 6 illustrates the volatile matter levels in the nigerian basins and compares them with those in other cbm-producing countries. additionally, improved oil and gas recovery 9 the high volatile matter content suggests that nigeria's coal rank is low and of average grade, as lower volatile matter typically indicates higher coal rank. conclusions the study estimates the proven coalbed methane (cbm) reserves in the four nigerian basins at 194 million tons of coal, which translates to approximately 60 trillion cubic feet (tcf) of cbm, given a gas content of 312.14 scf/ton. the coal in these basins is classified as sub-bituminous, indicating a lower grade. the average moisture content across these basins is 10.95%, which is comparable to that of australian coal. among the analyzed basins, the onyeama coal field is noted for its low ash content, whereas coal from india shows higher ash values. the nigerian coals are identified as sub-bituminous, with shallow deposits 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of coal? 2017. u.s. geological survey. https://www.usgs.gov/faqs/what-are-types-coal (accessed 24 december 2022). wolfson, r. 2023. energy, environment, and climate, 4th edition. new york, ny, u.s.a.: w.w. norton inc. xia, l., yin, y., yu, x., et al. 2019. an approach to grading coalbed methane resources in china for the purpose of implementing a differential production subsidy. petroleum science 16(2): 447-457. yang, l. 1987. national coal mine gas geological map of china. xi'an, shaanxi science and technology press 12(3):248-257 (in chinese). zhang, l., kang, t., kang, j., et al. 2021. response of molecular structures and methane adsorption behaviors in coals subjected to cyclical microwave exposure. acs omega 6(47): 31566-31577. ibrahim modibbo ahmed is a petroleum engineer who currently serves as a research assistant at cyprus international university, north cyprus. his research interests are coal bed methane (cbm), enhanced oil recovery (eor), and biogas. he holds a bsc and msc in petroleum and natural gas engineering from cyprus international university and is currently pursuing a phd in energy systems engineering at cyprus international university. dr. saleem qadir tunio is an experienced academician and researcher in the field of petroleum engineering with phd in petroleum engineering from the university of technology petonas (utp) malaysia with master's degree in petroleum engineering from the university of adelaide, australia, and bachelor's in petroleum and natural gas engineering from mehran university of engineering and technology pakistan. his overall experience is related to teaching and research for more than 17 years in countries like (pakistan, malaysia and cyprus) which includes teaching petroleum engineering courses both at undergraduate and postgraduate levels and supervising research projects/thesis. his research is related to unconventional hydrocarbons, formation evaluation and enhanced hydrocarbons recovery. https://www.bpe.gov.ng/nigerian-coal-corporation/ https://www.bpe.gov.ng/nigerian-coal-corporation/ https://en-us/services/proximate-and-ultimate-analysis https://www.usgs.gov/faqs/what-are-types-coal abstract introduction literature review methodology results and discussions conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1205 received may 10, 2022; revised june 20, 2022; accepted june 27, 2022. * corresponding author: maicaolan@hcmut.edu.vn 1 a comparative study on different machine learning algorithms for petroleum production forecasting lan mai-cao*, ho chi minh city university of technology (hcmut), ho chi minh city, vietnam and hoa truong-khac, petrovietnam exploration & production corporation – integrated technical center (pvep-itc), ho chi minh city, vietnam abstract in the recent years, machine learning and its subset, deep learning, have been quickly developed and applied with great success in various areas of petroleum engineering. different machine learning algorithms for petroleum production forecast are studied in this work for efficiency comparison purpose. historical production data from an oil well currently producing in the oilfield x, southern vietnam has been first preprocessed to construct eight different predictive models for production forecast on the oil well under consideration. the algorithms under consideration in this work are: (1) the classical machine learning algorithms, including random forest, gradient boosting, k-nearest neighbor, support vector regression; and (2) the deep learning algorithms, including multilayer perceptron, convolutional neural network, long short-term memory, and gated recurrent unit. the results from this comparative study show that in spite of their simplicity, some classical machine learning algorithms, especially the support vector regression shows its high efficiency in performing the prediction tests. in addition, it can be found from this work that preprocessing of the historical production data is crucial to the success of the application of artificial neural networks to production forecasting. introduction production forecast is an important task to perform economic evaluation and production optimization for oil and gas reservoirs. one of the most popular methods for production forecasting is decline curve analysis (dca) thanks to its simplicity with the empirical observation of production decline and the basic assumption about the preserved trend of the rate decline curve in the future (arps 1945). since the physics associated with the hydrocarbon recovery process are not fully captured by dca, prediction results of the method are usually not robust (satter and iqbal 2016). a more comprehensive approach to oil and gas production prediction is reservoir simulation. although this approach yields more reliable prediction results, it requires much more data and effort as well as advanced domain knowledge for a valid reservoir model (islam et al. 2016). with the rapid development of computing technology and data analytics, machine learning (ml) and its special subset, deep learning (dl), have emerged as an advancement of data-driven approach based on artificial intelligence (yucel et al 2020). in principle, the ml approach is well suited for problems which require advanced domain knowledge that is hard to gain but for which plenty of observed data is available. in recent years, various ml and dl applications have been applied with great success in different areas of mailto:maicaolan@hcmut.edu.vn 2 petroleum engineering such as oil production optimization (shirangi 2012), drilling hydraulics prediction and optimization (wang and saeed 2015), ann-based screening tool for co2 injection in naturally fractured reservoirs (hamam and ertekin 2018), interpretation of flow-rate, pressure and temperature data (tian and horne 2019), monitoring oi production rate (khan et al. 2019), reservoir characterization and modeling (lan and le 2019; lan and hoa 2021), enhancement of production forecast (doan and vo 2021), to name just a few. the objective of this work is to examine the ability of different machine learning algorithms to predict oil and gas production from historical data of a well currently producing oil from the field x (due to the operator’s requirements, the real name of the field of interest is not shared) in southern vietnam. in particular, four classical machine learning algorithms, including random forest (rf), gradient boosting (gb), k-nearest neighbor (k-nn), and support vector regression (svr) together with four advanced models, namely multilayer perceptron (mlp), convolutional neural network (cnn), recurrent neural network (rnn), long short-term memory (lstm), and gated recurrent unit (gru) have been studied for efficiency comparison. the remaining parts of this paper is organized as follows. section 2 briefly presents the background and workflow to implement machine learning algorithms for petroleum production forecasting. section 3 presents and discusses the results from this comparative study. section 4 summarizes the main points of this study along with some concluding remarks on the performance of the different algorithms under consideration. methodology this section briefly presents the background of the machine learning algorithms used in this work. the classical ml algorithms under consideration include:  k-nearest neighbors, k-nn (cover and hart 1967)  random forest, rf (breiman 2001)  gradient boosting, gb (friedman 2001)  support vector regression, svr (drucker et al. 1997) the more advanced algorithms associated with the following deep neural networks are also studied in this work:  multilayer perceptron, mlp (cheng and titterington 1994)  convolutional neural network, cnn (lecun 1989)  long short-term memory, lstm (hochreiter and schmidhuber 1997)  gated recurrent unit, gru (chung et al. 2014) the workflow for our comparative study on aforementioned algorithms in this study consists of the following steps: step 1: data preparation  outlier detection: this task is to properly detect and handle outliers to ensure that our data is statistically significant.  data scaling: all data values are scaled into the fixed range to prevent the learning algorithms from being biased to greater magnitudes of the data, especially in those algorithms that leverage similarities between samples such as k-nn, svr, etc. …  cross validation: the main concern in regression is the ability of the trained model to perform on unseen data. for a valid performance evaluation, the dataset is splitted into training, validating and testing subsets. in addition, the testing set is not used for model construction.  autoregression modeling: for time series data, the future value of a variable, yt , can be predicted using a linear combination of its past values as follows (paolella 2019). yt = β0 + β1yt−1 + β2yt−2 +⋯+ βpyt−p + ϵt ,.................................................................................(1) where βi (i=0, 1, 2 ... p) are regression constants, yt−p is the value of y at time (t-p) in the past, and ϵt is the noise. 3 step 2: model construction in this step, several classical ml and dl networks are constructed with the training dataset through which the model parameters are tuned to minimize the loss functions. the validation set is used to adjust the hyperparameters of the network during the training process. step 3: model testing the trained models are tested in this step with the blind test dataset for performance evaluation. different performance metrics are calculated including the mean squared error (mse), mean absolute error (mae). results and discussion three test cases have been performed with different classical machine learning and deep learning algorithms in this work. the objective of these test cases is to examine the performance efficiency of those algorithms in production forecasting on an oil well currently producing from the oilfield x in southern vietnam. the historical production data includes the flow rates of oil, gas, water and the bottom-hole pressures collected at more than a thousand points in time. test case 1: four classical machine learning algorithms including k-nn, rf, gb, svr have been studied in this test case. all models have one single output which is the bottom-hole pressure difference between a particular time of interest and the initial time (δ�) . as can be seen from figure 1, all models fit quite well with the training dataset (the left figure). for the test dataset, however, some algorithms including rf and gb provide the predicted values with high deviation from the measured data (the right figure). among the others, svr yields excellent results that match very well with the observed data throughout the full time range of interest. especially, svr shows its ability to capture stiff changes of pressure occurring in the middle of the testing period. figure 1—the results in the full time range (left) ;the results in the test dataset interval (right). the vertical dash line represents the time where the dataset is splitted into 2 subsets: the training dataset is located to the left of the line whereas the test dataset is located to its right. 4 (a) rf (b) gb (c) k-nn (d) svr figure 2—cross plots of the bottom-hole pressure from the four classical ml algorithms (test case 1). (a) random forest; (b) gradient boosting; (c) k-nearest neighbor; (d) support vector regression. the cross plots in figure 2 show how the predicted bottom-hole pressures deviate from between the measured and predicted values. as can be seen from the figure, the four algorithms under consideration yield very good match with the training dataset. the performance metrics of the four classical ml algorithms are shown in table 1 for test case 1. as can be seen from table 1, all algorithms yield quite good performance metrics, and the svr algorithm shows its superior with the highest r2 and lowest errors. table 1—performance metrics of the four classical ml algorithms (test case 1) algorithm/model mse (psia) mae (psia) r2 random forest (rf) 3894.56 40.11 0.87 gradient boosting (gb) 4500.84 44.68 0.85 k-nearest neighbor (k-nn) 2612.07 37.13 0.91 support vector regression (svr) 1194.33 15.84 0.96 5 test case 2: the objective of this test case is to check the model ability to perform time-series forecast with multiple network outputs. the same classical machine learning algorithms, i.e. rf, gb, k-nn, svr have been studied in this test case with the two outputs which are the bottom-hole pressure and oil rate. compared to the single output case, good matches can also be observed in this test case with the training dataset whereas further deviation from the measured data can be noticed, especially with the predicted oil rate. figure 3 show that among the others, the svr again is the most efficient algorithm for time-series forecasting. while the other algorithms tend to yield big errors at some points in time when high peaks occur, svr shows its ability to capture stiff changes in bottom-hole pressure and oil rate. figure 3—test case 2 with classical ml algorithms. �p vs time full dataset (top left); �p vs time test dataset (top right); oil rate vs time – full dataset (bottom left); oil rate vs time – test dataset (bottom right). it can be seen from figure 3 that the predicted values by the models with multiple outputs are not as good as those having single output. since the loss function is formulated as the weighted average of the component losses, the loss function evaluation can be adjusted with the weight values. in principle, small weight is used for data with high uncertainty. since the bottom-hole pressure is measured by a permanent downhole gauge with high reliability in our case, its weight is greater than that of the oil rate. test case 3: four deep learning models including multilayer perceptron (mlp), convolutional neural network (cnn), long short-term memory (lstm) and gated recurrent unit (gru) have been studied in this test case. all models have two outputs, the bottom-hole pressure difference ( δ�) and the oil rate of the well under consideration. as can be seen from figure 4, the predicted values are in good agreement with the measured data for most of the cases in a global sense. for the test dataset, however, deviations of the predicted values from the measured data are observed. in this test case, the predicted pressures are not much different among the four deep neural network models. on the other hand, greater oil rate differences between the models are observed. 6 it should be noted from figure 4 that the deep neural networks studied in this test case do not show their ability to capture stiff changes, such as the two peaks in the pressure profile (the top-right figure) and some drop down in the oil rate profile (the bottom-right figure). figure 4—test case 3 with deep learning algorithms: �p vs time full dataset (top left); �p vs time test dataset (top right); oil rate vs time – full dataset (bottom left); oil rate vs time – test dataset (bottom right). table 2—performance metrics for the four deep neural networks (test case 3) algorithm/model mse (psia) mae (psia) r2 multilayer perceptron (mlp) 2064.24 25.93 0.93 convolutional neural network (cnn) 3620.19 41.63 0.88 long short-term memory (lstm) 2914.20 33.21 0.90 gated recurrent unit (gru) 2481.41 37.29 0.92 conclusions this paper reports a comparative study on different machine learning algorithms for petroleum production forecasting. in particular, four classical machine learning models (k-nearest neighbor, random forest, gradient boosting, support vector regression) and four deep neural networks (multilayer perceptron, convolutional neural network, long short-term memory, and gated recurrent unit) have been studied for their ability to perform prediction on a time-series data. the results from this work show that unlike in image processing, voice recognition or object detection where complicated deep neural networks proved to be highly powerful, the classical machine learning approach with the support machine regression is computationally efficient with good performance metrics and short computation time in all test cases performed in this work for petroleum production forecasting from historical production data of the oil well of interest. 7 acknowledgement we would like to thank ho chi minh city university of technology (hcmut), vnu-hcm for the support of time and facilities for this study. conflicting interests the authors declare that they have no conflicting interests. nomenclature cnn: convolutional neural network dca: decline curve analysis dl: deep learning gb: gradient boosting gru: gated recurrent unit k-nn: k-nearest neighbor lstm: long short-term memory ml: machine learning rf: random forest rnn: recurrent neural network svr: support vector regression references arps, j.j. 1945. analysis of decline curves. transactions of the aime 160(1): 228–247. breiman, l. 2001. random forests.machine learning 45(1): 5–32. cheng, b. and titterington, d.m. 1994. neural networks: a review from a statistical perspective. statistical science 9(1): 2–54. chung, j., gulcehre, c., cho, k., et al. 2014. empirical evaluation of gated recurrent neural networks on sequence modeling. arxiv preprint: 1–9. cover, t.m. 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intelligence and machine learning applications in civil, mechanical, and industrial engineering, ed. bekdas, g., nigdeli, s.m., and yucel m., chap. 1, 1-12. hershey, pennsylvania, usa: igi global. mai-cao lan received b.e. degree (1991) in mechanical engineering from hcmut, vietnam, m.e. degree (1998) in systems engineering from royal melbourne institute of technology, australia, and ph.d. degree (2009) in computational mechanics from the university of southern queensland, australia. currently, dr. lan is the head of the department of drilling & production engineering, faculty of geology and petroleum engineering, ho chi minh city university of technology, vietnam. his current research mainly focuses on enhanced/improved oil recovery (eor/ior), integrated production modeling, flow assurance and machine learning applications in petroleum industry. truong-khac hoa graduated with a bachelor's degree from the university of natural sciences, ho chi minh city, majoring in applied mathematics in 2002. completed the master's program at ho chi minh city university of technology, majoring in petroleum engineering in july 2019. msc. truong khac hoa is currently working at the integrated technical center of petrovietnam exploration & production corporation pvep. abstract introduction methodology results and discussion conclusions acknowledgement conflicting interests nomenclature references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1256 received september 14, 2023; revised november 20, 2023; accepted december 16, 2023. *corresponding author: osamaajaz99@gmail.com 1 coalbed methane potential of pakistan-a review osama ajaz*, lmk resources pakistan (pvt) limited, karachi, pakistan; saleem qadir tunio, cyrpus international university,nicosia, north cyprus; darya khan bhutto, najeeb anjum soomro, and bilal shams, dawood university of engineering and technology, karachi, pakistan abstract the continuous decrease in gas reserves and increase in natural gas demand forces pakistan to explore new reserves. coalfields in the country offer potential availability of gas reserves in the form of coalbed methane (cbm). these coalfields can accommodate gas demand of the country in long-terms. cbm is a clean energy source and shows a complex storage mechanism as compared to conventional gas reserves. hence, modern techniques are required for its exploitation. this paper provides a review and analysis of literature for cbm and co2-ecbm production from the largest coalfield. based on available data, similarity among different coalfields assist in calculating potentiality of cbm. the study investigates production potential of cbm and co2-ecbm in thar coalfields. the co2 injection can enhance cbm production, and a significant amount of co2 can be stored because of process. being largest coal reserves in the country, the investigation concludes that thar coalfield can accommodate the country’s gas demand. this study proposes technical recommendations for practical implications of large-scale development of cbm and co2-ecbm subjected to the in-depth calculation of gas adsorption, gas content, and optimum depth for co2 injection. introduction oil and coal, being major energy contributors for decades, indicate their reliable energy sources (eia 2015). lower emissions give natural gas an edge over oil. since the last few decades, there has been no significant gas discovery found in pakistan. hence, the reserves are declining over time. in recent times, the country is facing a shortage of gas supply, which becomes worst during winter. the southern part has been faced with gas shortage despite the presence of huge coal reserves in the region. these coalfields can be the potential source to reduce the imbalance between gas supply and its demand, in terms of coalbed methane (cbm). coal bed methane (cbm) contributes around 6% to 9% of natural gas production around the world (eia 2016). the coalification process generates cbm, which remains trapped in the coal matrix. cbm consists mainly of methane (i.e., > 90%). when coal does not anticipate the release of methane following dewatering, co2 and/or n2 are injected to enhance production of methane, and this process is called enhanced coal bed methane recovery (ecbm). ecbm appears to be an economical coalbed methane production procedure. it offers the ability of environmental mitigation by sequestrating a considerable amount of co2 in coalbed. a few studies have addressed cbm and ecbm recovery from the thar coalfields of pakistan. thar coalfield has importance for being the largest coal reserve in the country. the literature studies estimated the potential recovery of billions of cubic feet of natural gas from thar coalfields. however, cbm and ecbm recovery are not discussed as distinct features of recovery in the literature. this study provides a review of the literature, and the ability of thar coal reserves to meet gas demand using cbm and ecbm mechanisms for the country based on available data. 2 coalbed methane in cbm, gas is adsorbed onto coal surface, which makes it different from conventional natural gas in terms of occurrence. this feature allows coal surface area to accommodate greater volumes of gas, in comparison to equivalent conventional reservoirs. the gas is held within the coal matrix and fractures surrounding it. this gas tends to flow away from the coal surface, water presence restricts this movement of gas. due to this, gas remains trapped between the water and coal matrix as shown in figure 1. cbm sites vary in properties depending on geological history, burial depth, coal type, and gas content. hence, the geometrical structure across the coal matrix and the arrangement of cleats (natural fractures) were found to be dissimilar. all these properties combined for the projection of the estimated ultimate recovery of gas. coalbed matrix natural gas is held in contact with coal through high water pressure water in cleats and fractures figure 1—coalbed matrix illustrating gas surrounding the coal bounded by water and rock. gas trapping mechanism. dual or two porosity are mostly found in coals: macro-porosity and micro-porosity, where the average porosity of matrix is less than 1% (gunter et al. 1997). coals of the thar field show dual nature of porosity, with presence of cleats (siddiqui et al. 2011). whereas, micro-porosity determines matrix porosity. therefore, gas could show presence in the following possible ways: a. adsorbed condition (gas is adsorbed on the surface of the coal matrix) b. free gas (when gas is present in the micro-pores and macro-pores) c. mixture form (when gas is dissolved in the water present in coal matrix) adsorbed state of gas shares higher fractions of storage, this leaves dissolved or free gas to share less amount for storage. production scenario. conventional reservoir starts producing by simply drilling a wellbore to the target zone. in contrast, penetrating coal seam does not cause cbm to flow out of the well. the natural pressure of the system must be decreased using either means, in order to encourage gas to flow. cbm is conventionally produced by reversing the physical adsorption process. this is done by means of reducing the partial pressure of adsorbed material into coal mass (metcalfe et al. 1991). as shown in figure 2, the typical stages of production for cbm wells are (godec et al. 2014): a) dewatering stage: cbm wells produce water initially. this water production is higher in the beginning, which decreases when pressure depression accelerates gas desorption. the gas desorbs and becomes part of producing fluid. the production of gas increases with the decrease in water production. b) stable production stage: gas production reaches the maximum while water production moves to its minimum value. after this stage, gas production decreases slowly. c) decline stage: water production is negligible during this stage, whereas gas production continuously declines. eventually, a stage comes when gas is uneconomical to produce. 3 figure 2—volumes of methane and water during stages of cbm production (reproduced from rice 2000). in conventional gas reservoirs, decreasing pressure causes gas to expand. however, in cbm reservoir threshold value of pressure is needed to initiate desorption. the cleat system remains saturated with water until the initial reservoir pressure is higher than the desorption pressure (sloss 2015). this condition is undersaturated. during water production, no gas is produced under this condition. during water production, a stage comes when pressure declines and reaches to desorption point, where the gas production starts, as shown in figure 3. the gas follows the darcy flow through the cleat network to the wellbore (sloss 2015). the coal releases ch4 in three main stages: a) desorption of the gas from the internal micropores on the surface of the coal. b) diffusion of the gas through the matrix of the coal c) the fluid flow of the gas through the fracture network within the seam to the production well. the good orientation type depends upon coal rank. vertical wells are recommended for lowerrank coal, whereas high-rank coals are produced through horizontal wells (godec et al. 2014). hence, vertical wells are recommended for cbm production from thar coalfield. water gas ch4 h2o 1st stage 2nd stage figure 3—vertical well showing stages of cbm production. similitude among cbm coalfields coalfields show their presence in almost every region of the country. however, thar coalfield, having lignite reserves, shares higher deposits than the rest. besides this, lakhra and sondha-jerruk show a significant amount of coal as well (report). these coal deposits are included in the study based on their presence of greater amounts and availability of data. the data available in table 1 shows the properties of tharcoal and other coalfields in the world. the data is analyzed to draw an analogy with deposits in other countries. the limited available data on the world’s 4 developing cbm fields are used to draw an analogy and project the potential of the thar coal field for producing gas. table 1—similitude among pakistan’s largest coalfields with world’s cbm coalfields. country pakistan (talapatra and karim 2020) india (altowilib et al. 2020) china (zhou 2013) malaysia (rao and phadke 2017) indonesia (ranathun ga et al. 2014) australia (clarkson and bustin 2011) brazil (sinayuc et al. 2011) united states (primer 2009) project thar coalfield lakhra sondhajerruk jharia, jharkhand guhanshan sarawak south sumatra basin sydney basin paran basin illinois wyoming ash content, % 2.9011.50 4.3049.00 2.7052.00 9.01 7.99 20 5.2 35.5 41.99 17.4 6.6 moisture content, % 29.6055.50 9.7038.10 9.0048.00 1.4 2.68 2.74 10 0.9 0.93 3.1 23.8 fixed carbon, % 14.2034.00 9.8038.20 8.9058.80 60.7 93.2 n/a n/a 42 29.91 n/a n/a depth, m 120-200 80-450 1-85 450 m500 m 530 (avg.) n/a 516.3 (avg.) n/a 620 (avg) n/a n/a gas content m3/t n/a n/a n/a n/a n/a n/a 51.6 12.9 2.18 n/a n/a recoverable gas, bcm 25.35 n/a n/a n/a 31.2 n/a n/a n/a n/a n/a n/a ash content. methane adsorption capacity is correlated with ash content. increasing ash content reduces the adsorption capacity of methane. however, a higher range of ash content seems to decrease adsorption capacity (feng et al. 2014). considering this phenomenon, the adsorption of gas in tharcoals would be less than that of lakhra and sondhajherruk. furthermore, ash content of thar coalfield shows similarity with jharia coal deposits, shown in figure 4. figure 4—ash content of different coalfields. 5 moisture content. for accurate calculation of gas production and recovery, the moisture content effect is incorporated in different directions of reservoir properties. sorption rate, gas diffusivity, and gas adsorption decrease with an increase in moisture content (cao et al. 2020). this is because water molecules occupy large spaces, leaving less volume for gas residence (pan et al. 2010; li and zhang 2014). the higher moisture content implies lower gas residence in coal seams (talapatra and karim 2020). even though higher moisture contents (figure 5) in coals of thar indicate lower gas storage in the spaces. thar coal has the advantage of more gas storage due to its great amount as compared to the other regional deposits. figure 5—moisture content of different coalfields. fixed carbon. carbon and energy content decides coal ranks. the lower coal ranks have lower carbon contents (tunio and ismail 2014) . coals in thar, being lignite, have lower carbon content. paran basins show similarity with thar coalfields in terms of carbon content (figure 6). gas content in paran basin is lower as compared to others in table 1, whereas gas content in coals of thar is still to be determined. figure 6—carbon content of different coalfields. enhanced coal bed methane (ecbm) recovery the reservoir pressure method can recover around 50% of gas-in-place (gale et al. 2001). this method is simple but inefficient. hence, a considerable amount of gas is left behind, which cannot be recovered by 6 the depletion method. the remaining gas can be recovered by displacement desorption, in which another gas having a higher adsorption capacity is injected. the injected gas displaces the gas in the coal seam. any such method used to recover ch4 is regarded as ecbm, shown infigure 7. several recovery agents such as n2, co2, and flue gas are used for this purpose. however, co2 has gathered attention due to its sequestration ability and promising environmental mitigating effect. co2 shows a greater affinity to coal than ch4. early laboratory measurements concluded that coals can absorb twice as much co2 as methane by volume. how recent research on coals of different ranks in the united states claimed this ratio could be as high as 10:1 in low coal ranks (stanton et al. 2001). therefore, there is a large potential for co2 storage in unmineable coal seams of the world. since thar coalfield has low-rank coal so it offers higher co2 storage against ch4 production. co2 injection in coal seams causes a reduction in strength and permeability. this reduction in strength affects ecbm and the long-term safety of co2 sequestration, as co2 may migrate back to the atmosphere after sometime of injection. this makes it a great challenge to produce methane against the best bargain of co2 storage. however, hydraulic fracturing can increase seam permeability so that co2 can provide maximum penetration in the formation. injection wellco2 ch4 production well co2 ch4 figure 7—vertical well showing co2-ecbm recovery. coal seams should be deep enough to ensure enough reservoir pressure. this parameter serves as a key control on the amount of gas adsorbed to coal. the permeability decreases with an increase in depth. hence, the effective optimal depth window for co2-ecbm is between 300 and 1500m (laenen et al. 2005). since the depth of tharcoals ranges from 120-200m, it could offer less efficiency. figure 8—measured ch4, n2 and co2 langmuir isotherms (data source: sinayuc et al. 2011). 7 experiment test showing the adsorption of co2 is twice that of methane, shown in figure 8. this makes co2 displace methane efficiently and remain stored in a coalbed (sinayuc et al. 2011). geology is also one of the most important parameters to be considered to store co2. the bara formation of the thar area containing coal seems to provide a good geology structure for co2 storage, but more study is required in this regard. effect of rank on ecbm. thar coalfield can offer around 20% efficiency due to the presence of lignite reserves, shown in figure 9. however, a great amount of gas storage in a coal seam is a function of its adsorption capacity, and other geological factors: stratigraphy, structural geology, and hydrology. whereas coal sorption capacity is a function of pressure, temperature, the permeability of the coal seam, rank, moisture content, surface area, and macerals composition of coal. figure 9—ecbm percentage recovery against each coal rank (data source: godec et al. 2014). co2-ecbm projects. four co2-ecbm field projects have been completed in china (zhou et al. 2013), three in the qinshui basin and one at the eastern margin of the ordos basin. being environmentally friendly in nature, cbm is being exploited across many parts of the world. table 2 shows injecting amount of co2 at various location of the world. table 2—co2-ecbm projects around the world (leung et al. 2014). project name location year co2 inj. rate (mt/yr) san juan basin new mexico, usa 1996 0.1 fenn big valley alberta, canada 1998 0.02 recopol poland 2003 0.0004 qinshui basin china 2003 0.01 yubari japan 2004 0.004 permian basin texas, usa 2005 0.3 pamham dome/uinta basin utah, usa 2005 0.9 hokkaido japan 2015 0.01 thar coal potential and gas demand the rapid decline in gas reserves leaves pakistan facing a shortage of energy. in recent years, natural gas demand has risen to 6 bcfd across the country, with a supply of 4 bcfd (pakistan ’s inevitable demand for energy 2018). this shortage becomes worst during the winter season when a rise in demand is observed. the 8 cbm or ecbm from thar coalfield can accommodate regional demand and beyond. since thar coal seams have lignite coal so it offers suitability for co2 sequestration along with ch4 production. lignite coals contribute to 99.7% of coal reserves in pakistan, as shown in figure 10, table 3 in appendix-ishows the distribution of types of coal reserves in the country. the country has lignite reserves in great amounts that could accommodate methane gas even with lower gas content per ton. figure 10—coal type reserves in pakistan. figure 11 shows a simulation of the production capacity of a different block at thar coalfield (zahid 2018). the studies discussed are based on a limited amount of data available. however, detailed data and studies can further estimate the amount of ch4 production and co2 storage in thar coalfields. block 1 appears to be the most promising candidate for cbm and ecbm production. further detailed data could indicate right candidate block for the long-term. figure 11—simulation ch4 production capacity for each block of thar coalfield (data sources: zahid 2018). 9 conclusion and suggestions cbm is promising unconventional reserves held in an absorbed state. many factors contribute to its large-scale production. the study evaluated cbm and ecbm from potential coalfields in pakistan and conclude following findings: 1. properties of coals present in thar, lakhra, and sonda jherruk show the potential of cbm presence. thar coalfield, being great in quantity, gathered preference for studies present in literature. 2. the high amount of moisture present in thar coals implies a long dewatering time before cbm development for production. 3. gas content and gas adsorption need to be studied to calculate the exact recoverable methane. 4. after cbm recovery, co2-assisted cbm production could be calculated. more studies need to be carried out for enhanced methane recovery and sorption behavior of coal. 5. lignite reserves have lower exchange efficiency for co2 and ch4, hence co2 injection offer co2 sequestration as well. open pit mining in thar coalfield causes methane emissions directly into the atmosphere. this gas could accommodate areas suffering from energy shortages. whereas the pilot project can reflect its wide-scale applicability to meet domestic gas needs. since the administrative proposition is beyond the scope of this study. therefore, the technical implication of cbm production from thar coalfield is as under: 1. gas adsorption capacity at different depths and seams is to be determined. 2. the average volume of gas content per ton in coals of thar is still to be determined. 3. the product of coal seam available and gas content will simulate cbm reserves in an absorbed state. 4. the deposition depth of coal is shallower than the optimal depth for co2-ecbm. hence, maximum efficient depth for thar coalfield is to be carried out for safe storage of co2. conflicting interests the author(s) declare that they have no conflicting interests. references altowilib, a., alsaihati, a., alhamood, h., et al. 2020. reserves estimation for coalbed methane reservoirs: a review. sustainability 12(24): 10621. cao, y., chen, w., yuan, y., et al. 2020. experimental study of coalbed methane thermal recovery. energy science & engineering 8(5): 1857-1867. clarkson, c. r., and bustin, r. m. 2011. coalbed methane: current field-based evaluation methods. spe reservoir evaluation & engineering 14(1):60-75. eia. 2015. annual coal reports. u.s. energy information agency, washington, dc. eia. 2016. annual coal reports. u.s. energy information agency, washington, dc. feng, y., yang, w., and chu, w. 2014. contribution of ash content related to methane adsorption behaviors of bituminous coals. international journal of chemical engineering 14:956543. gale, j. and freund, p. 2001. coalbed methane enhancement with co2 sequestration worldwide potential. environmental geosciences 8(3): 210-217. godec, m., koperna, g., and gale, j. 2014. co2-ecbm: a review of its status and global potential. energy procedia 63:5858-5869. gunter, w. d., gentzis, t., rottenfusser, b. a., et al. 1997. deep coalbed methane in alberta, canada: a fuel resource with the potential of zero greenhouse gas emissions. energy conversion and management 38: 217-222. laenen, b. and hildenbrand, a. 2005. development of an empirical model to assess the co2-ecbm potential of a poorly explored basin. in proceedings of the 4th annual conference on carbon capture and sequestration, alexandria, 2-5 may. leung, d. y., caramanna, g., and maroto-valer, m. m. 2014. an overview of current status of carbon dioxide capture and storage technologies. renewable and sustainable energy reviews 39: 426-443. li, x. and fang, z.m. 2014. current status and technical challenges of co2 storage in coal seams and enhanced coalbed methane recovery: an overview. international journal of coal science & technology 1: 93-102. 10 metcalfe, r. s., yee, d., seidle, j. p., et al. 1991. review of research efforts in coalbed methane recovery. paper presented at the spe asia-pacific conference, perth, australia, 4-7 november. spe-23025-ms. pakistan’s inevitable demand for energy. 2018. https://mettisglobal.news/pakistans-inevitable-demand-for-energy-mgopinion/ (accessed 12 november 2021). pan, z., connell, l. d., camilleri, m., et al. 2010. effects of matrix moisture on gas diffusion and flow in coal. fuel 89(11): 3207-3217. coal mine methane recovery: a primer. 2019. u.s. environmental protection agency (usepa), usa. ranathunga, a. s., perera, m. s. a., and ranjith, p. g. 2014. deep coal seams as a greener energy source: a review. journal of geophysics and engineering 11(6): 063001. rao, a. b. and phadke, p. c. 2017. co2 capture and storage in coal gasification projects. earth and environmental science 76(1): 012011. rice, c.a. 2000. water produced with coal-bed methane. us geological survey fact sheet, fs-156-00, washington, d.c. siddiqui, i., solangi, s. h., samoon, m. k., et al., 2011. preliminary studies of cleat fractures and matrix porosity in lakhra and thar coals, sindh, pakistan. journal of himalayan earth sciences 44(2): 25-32. sinayuc, c., shi, j. q., imrie, c. e., et al. 2011. implementation of horizontal well cbm/ecbm technology and the assessment of effective co2 storage capacity in a scottish coalfield. energy procedia 4:2150-2156. sloss, l. l. 2015. potential for enhanced coalbed methane recovery. iea clean coal centre, london, united kingdom. stanton, r. w., flores, r. m., warwick, p. d., et al. 2001. coal bed sequestration of carbon dioxide. paper presented in the 1st national conference on carbon sequestration, washington, usa, 14-17 may. talapatra, a. and karim, m. m. 2020. the influence of moisture content on coal deformation and coal permeability during coalbed methane (cbm) production in wet reservoirs. journal of petroleum exploration and production technology 10:1907-1920. tunio, s. q. and ismail, m. s. 2014. effect of coal rank and porosity on the optimization of ecbm recovery. asian j appl sci 7(3): 158-168. zahid, u. 2018. application case study of enhanced coal bed methane recovery process in thar coal fields. environmental progress & sustainable energy 37(2): 900-911. zhou, f., hussain, f., guo, z., et al., 2013. adsorption/desorption characteristics for methane, nitrogen and carbon dioxide of coal samples from southeast qinshui basin, china. energy exploration & exploitation 31(4): 645-665. osama ajaz is working under the capacity of petroleum engineer with lmk resources pakistan (pvt) limited. he holds b.e and m.s. in petroleum engineering. his research areas include artificial lifting methods, enhanced oil & gas recovery, and engineering aspects of carbon storage. saleem qadir tunio is serving as assistant professor at faculty of engineering, cyprus international university. he obtained his b.e in petroleum and natural gas from mehran university of engineering and technology and m.s in petroleum engineering from the university of adelaide, australia and holds ph.d. in petroleum engineering from universiti teknologi petronas (utp), malaysia. he has expertise in the areas of unconventional hydrocarbons and enhanced hydrocarbons recovery. darya khan bhutto is working as assistant professor at department of petroleum and gas engineering, dawood university of engineering and technology, pakistan. he obtained his b.e in petroleum and natural gas from mehran university of engineering and technology and m.s in oil gas well engineering from china university of petroleum (east china). he has expertise in the areas of enhanced oil recovery, unconventional reservoirs, drilling engineering, wettability alteration, petrophysics. he is a member of society of petroleum engineers international and pakistan engineering council. najeeb anjum soomro is working as assistant professor at department of petroleum and gas engineering, dawood university of engineering and technology, pakistan. he obtained his b.e in petroleum and natural gas from mehran university of engineering and technology in 2008 and m.s in oil gas well engineering from china university of petroleum (east china). he has expertise in the areas of enhanced oil recovery, unconventional reservoirs, hydraulic fracturing, well completion integrity. he is a member of society of petroleum engineers international and pakistan engineering council. https://mettisglobal.news/pakistans-inevitable-demand-for-energy-mg-opinion/ https://mettisglobal.news/pakistans-inevitable-demand-for-energy-mg-opinion/ 11 bilal shams is working as assistant professor at department of petroleum and gas engineering, dawood university of engineering and technology, pakistan. he obtained his b.e in petroleum and natural gas from mehran university of engineering and technology, m.e in petroleum engineering from mehran university of engineering and technology and completed his phd in oil gas field development engineering from china university of petroleum (east china). he has expertise in the areas of modelling in multiphase flow/porous media, production optimization and reservoir management. he is a member of society of petroleum engineers international and pakistan engineering council. abstract introduction coalbed methane similitude among cbm coalfields enhanced coal bed methane (ecbm) recovery thar coal potential and gas demand conclusion and suggestions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1251 received july 7, 2023; revised august 20, 2023; accepted september 7, 2023. *corresponding author: mostafashajari@gmail.com 1 stimulation of low pressure carbonates reservoirs with a triphase emulsified acid system "3pea" of southern iran -case studies mostafa shajari* and hamed malhani, national iranian south oil company, ahvaz, iran abstract matrix acidizing tries to enhance oil wells productivity as one of the main kind of well stimulation techniques in petroleum industry. this method of acidization is being implemented by stepwise injection of high rate stimulation fluids through the wellhead into the target zone of reservoir rock. acid penetration depth and consequently the treated radius are the key factors to reach the maximum effectiveness of stimulation operations on production improvement and it can be optimized by an exact design of: fluid type, stimulation fluid volume, job stages and operating pressure. based on recorded data and job reports, recent conventional matrix acidizing jobs had low effect on improving oil production rate in some old iranian oil fields, especially depleted with low reservoir pressure ones. firstly a possible reason of this problem was assessed as shallow acid penetration radius and insufficient treated area around the wellbore and well testing data confirmed this probability. depth of damaged zone and acid penetration directly related on the porosity type, permeability, lithology, injection rate and production history of matrix acidizing candidate wells. in this study, successful application of a new kind emulsified acid system is evaluated in a low pressure, carbonates reservoirs in south of iran. application of nitrogen in stimulation treatments has gained wide acceptances in recent years. the applied triphase emulsified acid increases stimulated radius of near wellbore area by retardation the reactivity of acid system by adding a gaseous phase to emulsion of hcl and gasoil. use of this acid system made it possible to achieve a 137% greater well productivity than traditional systems, in this study. introduction a common concern in all matrix acidizing operations is the job effect on oil production rate. this purpose is achieved by reducing the pressure draw down and increasing the down hole pressure with passing the damaged zone of near wellbore area (chang et al. 2008;letichevskiy et al. 2017; alvarez et al. 2000). different kinds of retarded acids have been used in matrix acidizing operations to enlarge the treated zone of near wellbore area so far. some of famous retarded acid types are: emulsified acid, gelled acid, hybrid acid system, organic acid, chemically retarded acid & gldas (moid et al. 2020; li et al. 2008; shuchart et al. 2009). the mentioned retarded system acids have been used in recent years in field "m" (an iranian southern oil field) but desired results was not achieved; in other words an acceptable and stable production raise was not observed by matrix acidizing in candidate wells of field-m and made it necessary to revise job designs. 2 applying foam or gaseous phase in stimulation fluids seems to help stimulation designers solving the issue based on literature and experimental studies (alvarez et al. 2022). foam has different applications in acidizing operations. some of its main usages are: controlling fluid-loss, as a diverting agent, lifting fluid and foamed acid (economides and nolte 1989; parlar et al. 1995). one of the main retarded acids is the emulsified composition of hcl and gasoil by various percentages. but mixture of these two phases could not solve the issue to stimulate farther radius around the wellbore. a triphase emulsified acid system is made by adding a gaseous phase of nitrogen (n2) to the mentioned emulsion (economides and nolte 1989). adding this phase reduces the reactivity of the acid system based on the laboratory tests. it seems that nitrogen agitate reservoir rock merely by reducing contact area of triphase acid and rock (liu et al. 2022; parlar et al. 1995). the recommended composition of triphase emulsified acid system in recent studies are: 50% hcl (15% concentration), 25% gasoil + 25% n2. liquid volumes are pumped as a wide range of 150 to 500 gal/ft (in this paper triphase emulsified acid is abbreviated as "3pea"). the desirable flow characteristics of emulsified foam acid enhances the fluid movement in porous media, it happens by rapid expansion of gaseous phase of acid and pushing the liquid phase to deeper radii. also, recovery of acid and flowing well back are annoying parts of acidizing jobs in low pressure reservoirs; and hereby foam conveniences cleaning and flow back by expansion and lightening the well column (hung et al.1989; abou-sayed et al. 2007). the surveyed parameters to evaluate acidizing operations performance in this study are: q (production rate of oil), pwf (flowing wellhead pressure), pdh (downhole/sand face pressure) and s (skin factor). these parameters have been followed up and compared before and after the acid jobs. case studies field characteristics: field-m is located in southwest of iran and the first well was drilled 40 years ago in the field. reservoir pressure has been declined to less than 60% of its initial pressure and critical condition is faced to exploit producing wells of the field. field-m is divided to 8 sectors but the general characteristics do not show a sharp variation through the sectors. in this article the performance of 3 acidizing scenarios have been compared in 15 producing oil wells (5 wells by each scenario) and we tried to choose similar case studies for all 3 scenarios to make it possible having a fair and reliable assessment. all candidate wells of matrix acidizing were completed cased hole with perforated interval less than 50 ft, to make it possible to perform a single stage acidizing without diverting agent. the summary of general information of candidate wells are as follow: well no. 1: located in sector 2 of the field. its drilling had been finished 11 years ago and had a continuous production of oil about 500 bpd till last year and dead last year. the perforated interval is 45 ft. completed in mixed lithology of carbonate (55% dolomite & 45% limestone). the last injectivity of well was reported 8 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 2: located in sector 5 of the field. its drilling had been finished 23 years ago and had a periodic production of oil between 0 500 bpd in recent years. the perforated interval is 34 ft. completed in mixed lithology of carbonate (30% dolomite & 70% limestone). the last injectivity of well was reported 10.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 3: located in sector 3 of the field. its drilling had been finished 2 years ago and did not produce oil till now. the perforated interval is 38 ft. completed in mixed lithology of carbonate (35% dolomite & 65% limestone). the last injectivity of well was reported 4 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 4: located in sector 1 of the field. its drilling had been finished 8 years ago and had a periodic production of oil between 0 500 bpd in recent years. the perforated interval is 43 ft. completed in mixed lithology of carbonate (40% dolomite & 60% limestone). the last injectivity of well was reported 7.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 5: located in sector 8 of the field. its drilling had been finished 9 years ago and had a continuous production of oil about 400 bpd in recent years. the perforated interval is 29 ft. completed in pure lithology of 3 limestone. the last injectivity of well was reported 9.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 6: located in sector 1 of the field. its drilling had been finished 11 years ago and had a continuous production of oil about 300 bpd till last year and dead last year. the perforated interval is 26 ft. completed in mixed lithology of carbonate (50% dolomite & 50% limestone). the last injectivity of well was reported 6 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 7: located in sector 8 of the field. its drilling had been finished 16 years ago and had a periodic production of oil between 0 500 bpd in recent years. the perforated interval is 38 ft. completed in mixed lithology of carbonate (15% dolomite & 85% limestone). the last injectivity of well was reported 10 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 8: located in sector 2 of the field. its drilling had been finished 3 years ago and did not produce oil till now. the perforated interval is 43 ft. completed in pure lithology of limestone. the last injectivity of well was reported 5.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 9: located in sector 5 of the field. its drilling had been finished 7 years ago and had a continuous production of oil about 500 bpd in recent years. the perforated interval is 47 ft. completed in pure lithology of dolomite. the last injectivity of well was reported 6.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 10: located in sector 3 of the field. its drilling had been finished 11 years ago and had a continuous production of oil about 400 bpd in recent years. the perforated interval is 41 ft. completed in pure lithology of limestone. the last injectivity of well was reported 8.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 11: located in sector 5 of the field. its drilling had been finished 28 years ago and after changing the production interval, it did not produce oil in recent years. the perforated interval is 44 ft. completed in mixed lithology of carbonate (45% dolomite & 55% limestone). the last injectivity of well was reported 5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 12: located in sector 3 of the field. its drilling had been finished 2 years ago and did not produce oil till now. the perforated interval is 49 ft. completed in pure lithology of limestone. the last injectivity of well was reported 7 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 13: located in sector 8 of the field. its drilling had been finished 9 years ago and had a periodic production of oil between 0 500 bpd in recent years. the perforated interval is 40 ft. completed in mixed lithology of carbonate (25% dolomite & 75% limestone). the last injectivity of well was reported 6 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 14: located in sector 1 of the field. its drilling had been finished 15 years ago and had a continuous production of oil about 400 bpd in recent years. the perforated interval is 37 ft. completed in pure lithology of dolomite. the last injectivity of well was reported 3.5 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. well no. 15: located in sector 2 of the field. its drilling had been finished 6 years ago and had a continuous production of oil about 500 bpd till now, but the pwf has been declined recently. the perforated interval is 40 ft. completed in mixed lithology of carbonate (40% dolomite & 60% limestone). the last injectivity of well was reported 9 bbl per minute (by maximum injection pressure of 1500 to 2000 psi) before matrix acidizing. acidizing job design the first 5 wells (well no.1 to 5) have been acidized with conventional acid systems, the next 5 wells (well no.6 – 10) were designed by low volume 3pea and the last ones (well no.11 to 15) were done by high volume 3pea. conventionally the main acid stage is designed as hcl 28% (or hcl 15%) and hybrid acid (70% hcl 15% + 30% acetic acid) or emulsified acid (70% hcl 15% + 30% gasoil) with total volume 150 to 200 us gal/ft for this stage. also displacing stage contained water and gasoil in previous designs. the 3pea jobs have been designed in 4 stages: 1. pre-flush: carrier fluid of water with the mixture of surface tension reducing agent and mutual solving agent as its additives (karimi et al. 2018). 4 2. main acid: this stage contains two main parts; at first the strong acid of hcl 28% is injected to remove near wellbore damages by volume of 80 to 150 us gal/ft and then the three phase emulsified acid (3pea) is injected to create wormhole in farther distances and increase the stimulated radius (hoefner and fogler 1987). the volume of this section is as twice as the previous hcl acid. in first 5 jobs we used hcl 28% with volume 80 to 100 us gal/ft and 3pea with volume 160 to 200 us gal/ft, that we named it low volume 3pea in this article; and then by revising job designs, the acid volumes increased to 130 to 150 us gal/ft for hcl 28% and 260 to 300 us gal/ft for 3pea, and it is named high volume 3pea. 3. post-flush: carrier fluid of water with additive of surface tension reducing agent (al-rekabi et al. 2020). 4. displacing fluid: this stage is used to push the job design fluids to the formation (ma et al. 2022). and contains two parts, here. firstly gasoil is being injected as equivalent volume 20% of well column and finally the sub-stage of foam with quality of 65 to 70% is injected as same volume of well column. operation results it should be mentioned that the first jobs of new acid system was done with hcl 28% volume of 80-100 us gal/ft and 3pea volume of 160-200 us gal/ft in main acid stage. but based on previous researches and regarding the new acid system job results (especially skin reduction amount and pressure drop), it was decided to revise the acid volumes by increasing hcl 28% to 130-150 us gal/ft and 3pea to 260-300 us gal/ft. one sample of job injection data for each mentioned designs is shown in figures 1 to 3. first graph refers to the conventional acid system and an ordered general trend can be observed through the injection period. the second and third graphs belong to low volume 3pea and high volume 3pea acid systems respectively and the fluctuations could be due to existence of gaseous phase in 3pea. figure 1—sample of job injection data for conventional acid system. 5 figure 2—sample of job injection data for low volume 3pea system. figure 3—sample of job injection data for high volume 3pea system. table 1 shows the average skin factor measured in candidate wells of matrix acidizing. it can be seen an average skin factor reduction of -4.6 by conventional acidizing, whereas this parameter is improved in acidizing with low volume “3pea” by 45% and high volume “3pea” enhances the parameter by 78%. so a clear improvement can be observed in “3pea” acid system usage for the matrix acidizing candidate wells of field-m. 6 table 1—the average skin factor of matrix acidizing candidate wells. acid type pre-operation average skin factor post-operation average skin factor skin reduction due to acidizing operation conventional acid systems 6.1 1.5 4.6 low volume "3pea" 5.5 -1.2 6.7 high volume "3pea" 6.3 -1.9 8.2 production rate. all post-operation rates have been monitored for 6 months after acidizing operation and the final acceptable rate has been validated if it was stable through last 2 months. system acids used in conventional design: hybrid acid (mixture of hcl and organic acids), emulsified acid (hcl emulsion in gasoil), hcl 15% and hcl 28%. conventional acid system job results. table 2 and figure 4 show the amount of pre-operation and postoperation rate of acidizing jobs with conventional acid system. data shows the 59% increase of oil production rate (and average rate rise per job of 160 (bbl/day)) by conventional acidizing. this amount is very close to matrix acidizing results of recent 10 years in field-m which is 52% increase of oil production rate (and average rate rise per job of 145 (bbl/day)). so a key reasons of necessities to acidizing design revisions was low production improvement of matrix stimulation jobs. table 2—pre-operation and post-operation rate of acidizing jobs with conventional acid system. post-operation rate (bbl/day)pre-operation rate (bbl/day)well no. 5005001 5002002 003 2502504 9004005 21501350total rate total production increase: 800 (bbl/day) average of rate rise per job: 160 (bbl/day) figure 4—changes of oil rate in acidizing jobs candidate wells with conventional acid system. 7 low volume 3pea job results. the first jobs of "3pea" have been done with this composition: 50% hcl (15% concentration), 25% gasoil + 25% n2 with total fluid volume of about 250 us gal/ft. a job success rate achieved by this method was about 40% and average increase of 270 bbl/day production rate per job. table 3 and figure 5 pre-operation and post-operation rate of acidizing jobs candidate wells with low volume 3pea system. these results confirm the improvement of stimulation jobs with this acid type with respect to the conventional one by 68% increase in production rate, due to its deeper effect on target zones. but we decided to design 3pea acidizing jobs with higher volumes to evaluate the its performance in next jobs. table 3—pre-operation and post-operation rate of acidizing jobs candidate wells with low volume 3pea system. post-operation rate (bbl/day)pre-operation rate (bbl/day)well no. 25006 5002507 008 10005009 75040010 25001150total rate: total production increased: 1350 (bbl/day) average of rate increased per job: 270 (bbl/day) figure 5—changes of oil rate in acidizing jobs candidate wells with low volume 3pea system. high volume 3pea job results. next jobs were designed with higher ratio of gaseous phase and higher volume: 40% hcl (15% concentration), 20% gasoil + 40% n2 with total fluid volume of about 400 us gal/ft. a job success rate achieved by this method was about 65% and average increase of 380 bbl/day production rate per job. table 4 and figure 6 pre-operation and post-operation rate of acidizing jobs candidate wells with high volume 3pea system. the total acid volume has been doubled and the amount of production rate is increased 40% due to acidizing by high volume 3pea system with respect to the low volume 3pea. this result show the positive effect of n2 gaseous phase to push acid phase more and make deeper penetration radios around the wellbore. 8 table 4—pre-operation and post-operation rate of acidizing jobs candidate wells with high volume 3pea system. post-operation rate (bbl/day)pre-operation rate (bbl/day)well no. 1000011 0012 60030013 100040014 50050015 31001200total rate: total production increased: 1900 (bbl/day) average of rate increased per job: 380 (bbl/day) figure 6—changes of oil rate in acidizing jobs candidate wells with high volume 3pea system. pressure. changes of pre-operation and post-operation pressure of acidizing jobs candidate wells are discussed. well flow pressure and down hole pressure are two nodes parameters to evaluate the effect of acidizing jobs on well performance; where ever the amount of down hole pressure is more crucial in technical analysis because it presents the pure effect of stimulation job on flow conditions without the effect of well column or well completion design on it. so we consider this parameter here to evaluate the effect of different acid systems. table 5—preand post-operation pressure of acidizing jobs candidate wells with conventional acid system. δpwellheadpwf2pwf1δpsandfacepdh2pdh1well no. 7531524045129012451 140350210165135011852 0000003 2031029045120511604 2405102701105245013455 total wellhead pressure increased: 475total downhole pressure increased: 1360 average of wellhead pressure increased per job: 95average of downhole pressure increased per job: 272 * the unit of all parameters in this table is "psi" 9 table 6—pre-operation and post-operation pressure of acidizing jobs candidate wells with low volume 3pea system. δpwellheadpwf2pwf1δpsandfacepdh2pdh1well no. 29529501370137006 100330230560171011507 0000008 310575265895234514509 1604302705051890138510 total wellhead pressure increase: 865total downhole pressure increase: 3330 average of wellhead pressure increased per job: 173average of downhole pressure increased per job: 666 * the unit of all parameters in this table is "psi" table 7—preand post-operation pressure of acidizing jobs candidate wells with high volume 3pea system. δpwellheadpwf2pwf1δpsandfacepdh2pdh1well no. 545545025102510011 00000012 1653852204901780129013 28552023511102470136014 70320250501365131515 total wellhead pressure increased: 1065total downhole pressure increased: 4160 average of wellhead pressure increased per job: 213average of downhole pressure increased per job: 832 * the unit of all parameters in this table is "psi" changes of pre-operation and post-operation pressure of acidizing jobs candidate wells is presented in tables 5 to 7. down hole pressure data shows the improvement of stimulation jobs with low volume 3pea system with respect to the conventional acid type by 140% increase (tables 5 and 6); also we can see 80% rise in it by high volume 3pea system with respect to the low volume 3pea system (tables 6 and 7). pressure analysis in wellhead and downhole of the candidate wells confirms the previous results of production rate and skin factor analysis (figures 7 and 8). figure 7—changes of flowing wellhead pressure by acidizing jobs with different acid system. 10 figure 8—changes of flowing down hole pressure by acidizing jobs with different acid system. conclusions acidizing job results confirm the effectiveness of triphase emulsified acid (3pea) in carbonate reservoirs especially depleted ones with low damage radius around the well bore. different indices have shown improvement of job performance by using 3pea. it can be recommended the main acid stage with two substages; firstly an strong 28% hcl to make ready the path fluid and secondary 3pea with optimum acid volume of about 150 us gal/ft for hcl 28% and 300 us gal/ft for 3pea. we achieved more than 100% increase in production rate and flowing pressure and about 80% higher reduction amount of skin factor by this acid system. the current experience recommends 3pea application in the wells with perforated interval shorter than 50 ft and in a single stage job. next surveys can be done to evaluate the effect of 3pea in longer intervals with an optimum diverter. acknowledgements the authors would like to thank mr. mohammad hossein ghazal the head of petroleum engineering department of nisoc for his kind supports. our thanks are extended to the members of nisoc stimulation section who participated in the acidizing operations: mr. mohsen shariati, mohammad ramezani, ehsan ganjiazad, ahmad mohammadi, iman abaeifar, hooman banashoushtari. references economides, m.j. and nolte, k.g. 1989. reservoir stimulation, 2nd edition. englewood cliffs, new jersey: prentice hall. alvarez, j., alarcon, x., tellez, j., et al. 2022. implementing a new foam-acid technology for matrix stimulation of challenging low pressure, naturally fractured carbonates reservoirs: case studies, northern iraq. paper presented at the international petroleum technology conference, riyadh, saudi arabia, 12-15 february. iptc-22603-ms. chang, f. f., nasr-el-din, h. a., lindvig, t., et al. 2008. matrix acidizing of carbonate reservoirs using organic acids and mixture of hcl and organic acids. paper presented at the spe annual technical conference and exhibition, denver, colorado, 21-24 september. spe-116601-ms. letichevskiy, a., nikitin, a., parfenov, a., et al. 2017. foam acid treatment-the key to stimulation of carbonate reservoirs in depleted oil fields of the samara region. paper presented at the spe russian petroleum technology conference, moscow, russia, 11-13 october. spe-187844-ms. parlar, m., parris, m. d., and jasinski, r. j., et al. 1995. an experimental study of foam flow through berea sandstone with applications to foam diversion in matrix acidizing. paper presented at the spe western regional meeting, bakersfield, california, 8-10 march. spe-29678-ms. li, s., li, z., and r. lin, 2008. mathematical models for foam-diverted acidizing and their applications. petroleum science 5(2): 145-152. 11 shuchart, c.e., jackson, s., mendez-santiagoet, j., et al. 2009. effective stimulation of very thick, layered carbonate reservoirs without the use of mechanical isolation. paper presented at the international petroleum technology conference, doha, qatar, 7-9 december. iptc-13621-ms. liu, p., barakat, a.k., kalabayev, r., et al. 2022. combination of co2 foam and fit-for-purpose fluids during acid fracturing revive potential of a jurassic well in a depleted, high-temperature carbonate reservoir in north kuwait. paper presented at the adipec, abu dhabi, uae, 31 october-3 november. spe-211387-ms. moid, f., rodoplu, r., nutaifi, a.m., et al. 2020. acid stimulation improvement with the use of new particulate base diverter to improve zonal coverage in hpht carbonate reservoirs. paper presented at the international petroleum technology conference, dhahran, kingdom of saudi arabia, 13-15 january. iptc-20154-abstract. alvarez, j.m., h. rivas, and g. navarro. 2000. an optimal foam quality for diversion in matrix-acidizing projects. paper presented at the spe international symposium on formation damage control, lafayette, louisiana, usa, 23-24 february. spe-58711-ms. hung, k., a. hill, and k. sepehrnoori. 1989. a mechanistic model of wormhole growth in carbonate matrix acidizing and acid fracturing. journal of petroleum technology 41(1): 59-66. abou-sayed, i., shuchart, c.e., choi, n.h., et al. 2007. well stimulation technology for thick, middle east carbonate reservoirs. paper presented at the international petroleum technology conference, dubai, u.a.e., 4-6 december. iptc-11660-ms. karimi, m., shirazi, m.m., and ayatollahi, s. 2018. investigating the effects of rock and fluid properties in iranian carbonate matrix acidizing during pre-flush stage. journal of petroleum science and engineering 166:121-130. hoefner, m.l. and fogler, h.s. 1987. role of acid diffusion in matrix acidizing of carbonates. journal of petroleum technology 39(2):203-208. al-rekabi, m.a., aktebanee, a., ai-ghaffari, a.s., et al. 2020. carbonate matrix acidizing efficiency from acidizing induced skin point of view: case study in majnoon oilfield. paper presented at the international petroleum technology conference, dhahran, kingdom of saudi arabia, 13-15 january. iptc-20006-ms. ma, g., chen, y., wang, h., et al. 2022. numerical analysis of two-phase acidizing in fractured carbonate rocks. journal of natural gas science and engineering 103(7):104-116. abstract introduction case studies acidizing job design operation results conclusions acknowledgements references a sample paper for presentation at anziis 2001 correction correction to: application of numerical well testing in strong anisotropic sandstone gas field yanyan sun*, jiwu fan, zhenping xu, and zhichao li, changqing oilfield, petrochina, xi’an, china in the original publication of this article (sun et al. 2020), the second author's name jiu fan was misspelled. the correct name should have been jiwu fan. the original article has been corrected. references sun, y., fan, j., xu, z. et al. 2020. application of numerical well testing in strong anisotropic sandstone gas field. improv oil gas recover 4. https://doi.org/10.14800/iogr.457. copyright © the authors. this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1214 published online: october 21, 2021. *corresponding author: 278142801@qq.com 1 https://doi.org/10.14800/iogr.457 mailto:278142801@qq.com copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1299 received august 7, 2024; revised august 14, 2024; accepted august 21, 2024. *corresponding author: amoniogolo@yahoo.com 1 gas cap size in thin oil rims: effect on oil recovery efficiency victor molokwu, harriot-watt university, edinburg, uk;naomi amoni ogolo*, and mike onyekonwu, university of port harcourt, rivers state, nigeria abstract oil recovery efficiency from thin oil rims is generally low due to various contributing factors. the influence of gas cap size on oil recovery is particularly critical, as the gas cap drive mechanism can become predominant, significantly impacting the oil recovery factor, especially in the presence of a large gas cap. while a water drive mechanism is typically considered optimal for oil displacement in petroleum reservoirs, its effectiveness in thin oil rims is contingent on not displacing oil into the gas zone. this simulation study investigates the impact of gas cap size on oil recovery efficiency under the influence of both strong and weak aquifers, utilizing data from a thin oil rim in the niger delta. the study simulates four scenarios: a strong aquifer with a large gas cap, a weak aquifer with a large gas cap, a strong aquifer with a small gas cap, and a weak aquifer with a small gas cap. the results indicate that oil recovery efficiency ranges from 29% to 31% in scenarios with large gas caps, whereas scenarios with small gas caps achieve recovery efficiencies between 49% and 62%. these findings suggest that large gas caps in thin oil rims constrain oil recovery, regardless of aquifer strength. consequently, the study supports a field development strategy that prioritizes the extraction of gas from large gas caps in thin oil rims prior to oil production. introduction there is typically only one opportunity to optimize the development of a real-life petroleum reservoir. when errors occur during the development phase, often due to an incomplete understanding of the reservoir system, they are not only costly to rectify but also challenging to reverse. however, reservoir simulation allows for the creation and examination of multiple scenarios, highlighting the importance of conducting comprehensive simulation studies, particularly when dealing with complex situations such as production from thin oil rims. these studies are crucial for determining the most effective exploitation techniques for each specific scenario, thereby preventing resource wastage during development and maximizing oil recovery efficiency. additionally, simulation provides a deeper understanding of the unique characteristics of each reservoir, which in turn leads to more informed production strategies. oil production from thin oil rims with large gas caps and strong aquifers presents significant challenges to the petroleum industry, primarily due to low oil recovery efficiencies and other associated issues. the difficulties posed by large gas caps in thin oil rims have been extensively discussed in the literature (olabode et al. 2023; peter 2019). water is an effective agent for oil displacement in petroleum reservoirs; however, in thin oil rims under strong water drive conditions, early water breakthrough often occurs, leading to substantial volumes of produced water. this can shift portions of the oil zone into the gas cap, further reducing the volume of recoverable oil. therefore, it is imperative to investigate the influence of a large gas cap on oil recovery efficiency in the context of both strong and weak aquifers within thin oil rims. understanding these mechanisms is crucial for devising a strategic production technique that maximizes oil recovery efficiency. mailto:amoniogolo@yahoo.com improved oil and gas recovery 2 under the gas cap drive mechanism, one of the primary assumptions is minimal or negligible water production (ahmed 2006). however, this assumption does not hold for thin oil rims with strong underlying aquifers. in such scenarios, water coning occurs early in the reservoir’s life due to the thinness of the pay zone, making well placement a critical issue. this has led to recommendations such as the use of horizontal wells for oil recovery from thin oil rim reservoirs (akpabio et al. 2013; aladeitan et al. 2016; yang et al. 2013). research indicates that in thin oil rims with large gas caps, oil recovery increases with horizontal permeability and decreases with higher oil production rates and longer horizontal wells (agi et al. 2017). another study on thin oil rims with large gas caps concluded that it is preferable to place horizontal wells below the oil-water contact, whereas for reservoirs with small gas caps and strong aquifers, horizontal wells should be placed above the gasoil contact (iyare et al. 2012). various methods for effectively exploiting thin oil rims have been proposed (uwaga and lawal 2006; billiter et al. 1998; billiter et al. 1999; chan et al. 2011; wojtanowicz 2006; razak et al. 2011; olabode 2020). this study aims to evaluate the effect of gas cap size on oil recovery efficiency in the presence and absence of a strong water drive, using vertical wells in thin oil rims. statement of theory and definitions reservoir performance, particularly in terms of oil recovery, is largely determined by the dominant drive mechanism operating within the reservoir. these drive mechanisms include water drive, gravity drainage, rock and liquid expansion, depletion (solution gas) drive, gas cap drive, and combination drive mechanisms. this study investigates the impact of gas cap size on oil recovery efficiency, with the expectation that the gas cap drive mechanism will dominate in reservoirs with large gas caps, significantly influencing oil recovery. in reservoirs with strong aquifers, the water drive mechanism also plays a critical role, with oil recovery efficiencies ranging from 35% to 75% (ahmed 2006). given that some thin oil rims with gas caps are underlain by aquifers, it is essential to conduct simulation studies to assess how gas cap size affects oil recovery efficiency in the presence of both strong and weak underlying aquifers. oil recovery efficiency is a critical parameter that determines the economic viability of an oil reservoir and justifies the investments made in production. therefore, it is imperative to investigate any factors influencing this parameter during production to facilitate the implementation of an effective reservoir management strategy. the reservoir drive mechanism is a key factor in this regard, and this paper focuses on the gas cap drive in the context of water drive within thin oil rims. under the gas cap drive mechanism, the energy available for oil production is primarily derived from the expansion of the gas cap and the solution gas, resulting in oil recovery efficiencies ranging from 20% to 40% (ahmed 2006). this study specifically examines oil recovery efficiency in thin oil rims with varying gas cap sizes, considering both strong and weak aquifer strengths. description and application of equipment and processes the primary objective of this study is to examine the variation in oil recovery in a thin oil rim under different gas cap sizes—specifically, large and small gas caps—while considering the influence of both strong and weak aquifer strengths. the investigation was conducted through numerical simulation using the eclipse. the reservoir model, constructed using data from a thin oil rim in the niger delta, is depicted in figure 1. the fundamental rock and fluid properties, prior to any necessary modifications, are detailed in table 1. improved oil and gas recovery 3 figure 1—a view of the thin oil rim model. table 1—reservoir rock and fluid properties. rock and fluid property property value average reservoir properties depth, ft 10421 porosity (�) 0.23 permeability (�), md 1292 reservoir thickness, ft 45 net to gross 0.81 initial reservoir pressure (��), psia 4540 initial water saturation (���) 0.15 formation water compressibility (��), psi-1 2.986×10-6 rock compressibility (��), psi-1 1.1767×10-6 initial fluid properties viscosity ( ��� ), cp 0.42110 formation volume factor (���), rb/stb 1.512 saturation pressure (��), psia 4540 instantaneous gor, scf/stb 963.5 average aquifer properties porosity (��) 0.24 permeability ( ��), md 1292 thickness, ft 70 inner radius ( ��), ft 5604 in this study, four scenarios were simulated at six different oil production flow rates over a 40-year period, spanning from 1968 to 2008. the production flow rates applied were 2,000, 4,000, 6,000, 8,000, 10,000, and 12,000 stb/day. however, oil recovery comparisons were primarily focused on the flow rates of 2,000 and improved oil and gas recovery 4 12,000 stb/day across the four scenarios under consideration. the analysis of results concentrated on the cumulative volume of recovered oil and the oil recovery efficiency achieved in the four simulated cases. the four scenarios considered in this study include: (1) a strong aquifer with a large gas cap (sa&lgc); 2) a weak aquifer with a large gas cap (wa&lgc); 3) a strong aquifer with a small gas cap (sa&sgc); and (4) a weak aquifer with a small gas cap (wa&sgc). these scenarios represent various reservoir drive mechanisms, including those dominated by water drive and gas cap drive, exclusively gas cap drive, exclusively water drive, and a case where neither drive mechanism is predominant. for all wells and cases, a minimum bottom-hole pressure constraint of 1,000 psia was maintained. the aquifer strength was varied by adjusting the permeability, with a factor of 0.01 applied for a weak aquifer and a tenfold increase from the base permeability value for a strong aquifer. the gas cap size was modified using pore volume multipliers for grid block cells around the initial gas-oil contact. for large gas caps, the pore volumes of cells 50 feet above the initial gas-oil contact were multiplied by a factor of 100, whereas for small gas caps, this factor was set at 0.01. presentation of data and results the detailed results of the simulation study for the four cases under consideration are presented and analyzed. figures 2 and 3 depict the oil production rate profiles for scenarios initiated at 2,000 and 12,000 stb/day, respectively. the results indicate that scenarios with small gas caps sustained slightly higher production rates over time compared to those with large gas caps. additionally, it was observed that the production rate declined more rapidly at the higher rate of 12,000 stb/day than at 2,000 stb/day. figure 2—oil production of the four scenarios at 2,000 stb/d. improved oil and gas recovery 5 figure 3—oil production of the four scenarios at 12,000 stb/d. figures 4 and 5 illustrate the cumulative oil production over time for scenarios with production rates of 2,000 and 12,000 stb/day, respectively. the results indicate that scenarios with small gas caps achieve higher cumulative oil recovery volumes compared to those with large gas caps. notably, the outcomes for the two scenarios with large gas caps are similar, despite one having a stronger aquifer strength than the other. this suggests that, in this study, the impact of a large gas cap on oil recovery is more significant than the influence of a strong water drive in thin oil rims. furthermore, it is observed that the differences in oil recovery between the four scenarios are more pronounced at the higher production rate of 12,000 stb/day (figure 5) compared to 2,000 stb/day (figure 4). figure 4—cumulative oil production of the four scenarios at 2,000 stb/d. improved oil and gas recovery 6 figure 5— cumulative oil production of the four scenarios at 12,000 stb/d. figure 6 presents the oil recovery efficiencies for the four scenarios at production rates of 2,000 and 12,000 stb/day. the data clearly indicate that oil recovery efficiencies are higher in scenarios with small gas caps. specifically, at production rates of 12,000 and 2,000 stb/day, the recovery efficiencies for strong aquifers with small gas caps are 61.5% and 57.6%, respectively. for weak aquifers with small gas caps, the recovery efficiencies are 49.9% and 49.8%, respectively. the presence of a strong aquifer appears to significantly contribute to the higher oil recovery factor, as the small gas cap has a minimal impact on oil recovery. in contrast, for scenarios involving large gas caps, the oil recovery efficiencies at 12,000 and 2,000 stb/day for strong aquifers are 30.6% and 30.9%, respectively, while for weak aquifers, the efficiencies are 29.5% and 30.9%, respectively. notably, higher oil recovery efficiencies are observed at 12,000 stb/day for scenarios with small gas caps, whereas higher efficiencies for large gas caps are observed at 2,000 stb/day. this suggests that the effect of production rate on oil recovery efficiency varies with the size of the gas cap. therefore, further research is necessary to explore the impact of production rate on oil recovery efficiency in these scenarios. figure 6—oil recovery of the four scenarios at 2000stb/d and 12000stb/d. improved oil and gas recovery 7 the oil recovery efficiencies for production rates of 4,000, 6,000, 8,000, and 10,000 stb/day were also derived from the simulation study, with a more comprehensive result presented in figure 7. for scenarios involving large gas caps, the presence of a strong aquifer consistently resulted in slightly higher oil recovery efficiencies across all flow rates compared to scenarios with weak aquifers. in contrast, for scenarios with small gas caps, the oil recovery efficiencies were significantly higher in the presence of strong aquifers compared to weak aquifers. this trend aligns with expectations, as water drive is effective in displacing oil from petroleum reservoirs, with strong water drives providing better sweep efficiency. specifically, the cases with a strong aquifer and small gas cap (sa&sgc) exemplify the water drive mechanism in operation, with minimal influence from the gas cap drive. these scenarios yielded oil recovery factors ranging from 57% to 62%, which is consistent with the expected recovery efficiencies of 35% to 75% for water drive reservoirs (ahmed 2006). figure 7—results of oil recovery efficiency for the four scenarios at different production rates. in scenarios involving weak aquifers with small gas caps, neither the water drive nor the gas cap drive mechanism is dominant, resulting in an oil recovery efficiency of approximately 49%. this situation allows other drive mechanisms, such as gravity drainage, solution gas drive, and combination drive, to influence the oil recovery efficiency. however, for this study, it is important to note that in both scenarios with a strong aquifer and small gas cap (sa&sgc) and a weak aquifer with a small gas cap (wa&sgc), the influence of a large gas cap and its associated drive mechanism were absent, leading to higher oil recovery efficiencies. this indicates that the presence of large gas caps in thin oil rims restricts oil recovery efficiency, which is highly undesirable. the oil recovery efficiencies for scenarios with large gas caps ranged from 29% to 31%, which aligns with the expected range of 20% to 40% for gas cap drive mechanisms (ahmed 2006). improving oil recovery efficiency is a primary objective in the petroleum industry, necessitating the adoption of optimal production strategies to achieve this goal. overall, the results demonstrate that the presence of a large gas cap in thin oil rims significantly reduces oil recovery efficiency, regardless of production rate and aquifer strength. oil recovery efficiencies are notably higher in thin oil rims with small gas caps compared to those with large gas caps. one possible explanation for the reduced efficiency in thin oil rims with a large gas cap and a strong aquifer is oil smearing, where the gas-oil contact shifts upward into the gas zone, potentially pushing part of the oil zone into the gas zone and thereby trapping and losing recoverable oil. the scenario with a weak aquifer and a large gas cap (wa&lgc) represents a typical gas cap drive mechanism, with an expected oil recovery efficiency of 20% to 40% (ahmed 2006). therefore, a recommended improved oil and gas recovery 8 strategy for oil production from thin oil rims with large gas caps is to first produce the gas to reduce the gas cap size and minimize its impact on oil recovery efficiency before subsequently producing the oil. this production approach, supported by various studies, is validated by the results of this simulation study but is applicable specifically to cases with large gas caps and not to those with small gas caps. conclusions the conclusions derived from this study are as follows: 1. the presence of a strong water drive in thin oil rims with large gas caps does not necessarily enhance oil recovery efficiency. this is due to the risk of oil smearing, which can lead to a substantial loss of recoverable oil. 2. large gas caps in thin oil rims significantly limit oil recovery efficiency. to mitigate the impact of the gas cap drive mechanism on oil recovery, it is recommended to first produce the gas before extracting the oil. 3. thin oil rims with small gas caps yield better oil recovery efficiencies compared to those with large gas caps. additionally, a strong water drive in thin oil rims with small gas caps markedly improves oil recovery efficiency. recommendation for thin oil rims with large gas caps, producing the gas first before producing the oil is recommended in order to improve oil recovery efficiency. acknowledgement we thank laser engineering and resources consultants limited for providing us with data from a thin oil rim reservoir that was used in this work. conflicting interests the author(s) declare that they have no conflicting interests. references agi, a., junin, r., jeffrey, g., et al. 2017. exploitation of thin oil rims with large associated gas cap. international journal of petroleum engineering 3(1):14-48. ahmed, t. 2006. reservoir engineering handbook, third edition. houston: gulf professional publishing. akpabio, j. u., akpanikka, o. i., and isemin, i. a. 2013. horizontal well performance in thin oil rim reservoirs. international journal of engineering sciences and research technology 2(2) :219-225. aladeitan, y. m. and akinyede, o. m. 2016. optimization of oil rim development by improved well design. journal of scientific and engineering research 2(2):169-174. billiter, t. c. and dandona a. k. 1998. breaking of a paradigm: simultaneous production of gas cap and oil column. paper presented at the spe annual technical conference and exhibition, new orleans, louisiana, usa, 1-3 september. spe-49083-ms. billiter, t. c. and dandona, a. k. 1999. simultaneous production of gas cap and oil column with water injection at the gas/oil contact. spe reservoir evaluation and engineering 2(5): 412-419. spe-57640-pa. chan, k. s., kifi, a. m., and darman, n. 2011. breaking oil recovery limit in malaysian thin oil rim reservoirs: water injection optimization. paper presented by international petroleum technology conference, bangkok, thailand, 1-8 november. iptc-14157-ms. iyare, u. and marcelle-de silva, j. k. 2012. effect of gas cap and aquifer strength on optimal well location for thin improved oil and gas recovery 9 oil rim reservoir. paper presented at the spe energy conference and exhibition, trinidad, 11-13 june. spe-158544ms. olabode, o. 2020. effect of water and gas injection schemes on synthetic oil rim models. journal of petroleum exploration and production technology 10(1):1343-1358. olabode, o., adewunmi, p., uzodinma, o., et al. 2023. simultaneous studies on optimizing oil productivity in oil rim reservoirs under gas cap blow down production strategy. petroleum 9(3): 373 389. peter, o., onyekonwu, m., and ubani, c. e. 2019. exploitation of thin oil rim with large gas cap, a critical review. paper presented at the spe nigeria annual international conference, lagos, nigeria, 3-5 august. spe-198724-ms. yang, q., tong, k., ge, l., et al. 2013. development strategy research and practice on reservoir with big gas cap and narrow oil rim in bohai bay. advances in petroleum exploration and development 5(2): 62-68. razak, e. a., chan, k. s., and darman, n. 2011. breaking oil recovery limit in malaysian thin oil rim reservoirs: enhanced oil recovery by gas and water injection. paper presented at the spe asia pacific enhanced oil recovery conference, kuala lumpur, malaysia, 1-5 july. spe-143736-ms uwaga, a. o. and lawal, k. a. 2006. concurrent gas cap and oil-rim production: the swing gas option. paper presented at the spe nigeria annual international conference and exhibition, lagos, abuja, nigeria, 1-13 july. spe105985-ms wojtanowicz, a. k. 2006. down hole water sink technology for water coning control in wells. wiertnitwo nafta gaz 23(1): 575-586. victor molokwu has a b. eng. in petroleum engineering from the university of benin in nigeria, and a master of science degree in petroleum engineering and project development from the institute of petroleum studies, university of port harcourt in nigeria. he is a ph.d candidate in the institute of geoengineering, heriot watt university, edinburgh, united kingdom. molokwu has several years of experience in reservoir development studies. his research interests include physics-based deep learning, numerical methods, reservoir simulation, well test analysis and production data analysis. naomi amoni ogolo is a petroleum engineer with area of specialization in reservoir engineering. she holds a post graduate diploma in petroleum technology and gas engineering, a master of engineering in petroleum and gas engineering and a ph.d in petroleum engineering, all from the university of port harcourt. she is a member of several professional organizations including society of petroleum engineers (spe). as at the time this study was conducted, she was a research fellow in institute of petroleum studies, university of port harcourt. dr. ogolo’s areas of interest include improved oil and gas recovery from petroleum reservoirs, flow assurance and natural gas hydrates. she is also interested in environmental recovery and preservation especially from oil and gas industrial activities. mike onyekonwu is a professor in petroleum engineering of university of port harcourt and a seasoned professional in reservoir engineering. he has served in various capacities in university of port harcourt, as well as in various national and international bodies. as at the time this work was carried out, he was the director of institute of petroleum studies, university of port harcourt. he is the managing consultant of laser engineering and resources consultant limited. prof. onyekonwu obtained a first class degree in petroleum engineering from university of ibadan in nigeria. he has a master’s degree and ph.d in petroleum engineering from stanford university, california, usa. he is a member of several professional organizations including society of petroleum engineers (spe). he has published more than one hundred conference and journal articles and four books. he is interested in proffering solution to problems that plague the oil and gas industry and takes delight in mentoring young ones. abstract introduction statement of theory and definitions description and application of equipment and proce presentation of data and results conclusions recommendation acknowledgement conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1198 received october 18, 2021; revised november 26, 2021; accepted december 28, 2021. *corresponding author: yuangw1983@sina.com 1 the phase behavior study of air-foam flooding in changqing ultra-low permeability reservoirs guowei yuan*, yangnan shangguan, min wang, jie zhang, and zhaofeng du, changqing oilfield company, petrochina, xi'an, china abstract for phase change characteristics of air foam flooding in changqing ultra-low permeability reservoirs, experiments were performed with the air and the gas-phase oxidation of p-x diagram under reservoir conditions using the pvt high pressure physical device and gas chromatograph. the phase behavior of crude oil and air bubbles after multiple contacts was determined by pvt simulation and the phase equilibrium model. the critical temperature and critical pressure of crude oil were determined to be 424.4℃ and 9.85mpa. results show gas dissolved in crude oil after oxidation was strong in the air under the same pressure. because the foam system and crude oil emulsification during contact have produced multiple contact oxidation, the effect was less than that in air and oil, resulting in a relatively small oxidation of c2-c6, while the oxidation of c7-c16 was relatively more. furthermore, the trend of gas phase composition approaching c2-c6 was relatively slow, while oil phase composition was closer to c7+, due to the increase in the c7-c16 component. the study provides important insight for miscible flooding and non-miscible flooding applications, as well as for gas injection project design. introduction air-foam flooding has been proven to be a very promising technology to enhance oil recovery (eor). in the air-foam flooding process, the study of phase behavior is very important for the gas injection process. when there are multiphase flow, interphase mass transfer and heat transfer will co-exist in the oil-gas system. when the gas is injected, the physical and chemical properties of the fluid, such as viscosity, density, volume coefficient, interfacial tension, bubble point pressure, and gas-liquid components and composition, will change (wang et al. 2008; yan et al. 2008; guo et al. 2003). therefore, a quantitative description of the phase change in the air / air foam flooding process is essential to understand the latest changes in reservoir fluid parameters, which is also an important basis for studying the mechanism of miscible and immiscible flooding, and for gas injection engineering design (zhang et al. 2009; li and zhang 2001). guo et al. (2000) had measured the pvt of crude oil after different amounts of co2 were injected into the oil system at reservoir temperature, using the high-pressure phase equilibrium experiment device. the results showed that different composition of oil sample had a great influence on the phase behavior of co2 injection. in the process of air-foam flooding, the phase behavior of air, foam, and crude oil has not been studied and reported yet. therefore, this study aimed to quantify the phase behavior of air and foam on crude oil under different conditions through experiments. 2 the study area is in the wuliwan district of jing'an oilfield. the producing formation was the chang 6 oil formation of triassic. the initial driving mechanism was a dissolved gas drive. the main properties of the reservoir are shown in table 1. the pressure difference between reservoir and saturation pressure is small. the average permeability of the formation is 1.5×10-3μm2. the original gas oil ratio is high. it was a typical low porosity, low permeability, and low viscosity reservoir. table 1—main reservoir properties of the target reservoir. parameter value parameter value reservoir pressure, mpa 12.26 viscosity of surface crude oil, mpa·s 7.69 bubble point pressure, mpa 7.5 viscosity of formation crude oil, mpa·s 2.0 reservoir temperature,℃ 56 specific gravity, g/cm3 0.8559 permeability, 10-3μm2 1.5 porosity, % 8 experiment preparation experimental instruments. to conduct the experiment, the following devices and instruments were chosen:  jegri-pvt analysis system of the dbr company of canada. the main features of the device include the volume of the pvt chamber is 150 ml; pvt chamber is set to overall visibility; test temperature ranges from 30 to 200℃; temperature test accuracy is 0.1℃; test pressure ranges between 0.1 and 70 mpa; pressure test accuracy is 0.007mpa;  american hp-6890 gas chromatograph. temperature control ranges from 0 to 399.0℃; minimum energy detection is 3×10-2g/s; maximum sensitivity is 1×10−12a/mv;  ruska automatic pump. the working pressure ranges between 0 and 70 mpa; working temperature ranges from 0 to 40.0℃; resolution is 0.001ml;  sample preparation device;  intermediate container;  injected air was provided by xianyang yanshan chemical co., ltd. experiment steps. preparation of crude oil. in most previous study, single methane was selected as dissolved gas(liu and zhang 1996; wang et al. 2001; ke et al.1994). to better simulate the properties of crude oil under formation conditions, we prepared associated gas and formation degassed crude oil under the conditions of formation temperature and formation pressure, fully considering the bubble point pressure and original gas-oil ratio. the composition of the oil sample was the same as in reservoir conditions, making the research results more reliable and convincing. 1. the experiment process is shown in figure 1. 500 ml of degassed crude oil was injected into the sample preparation container. the associated gas volume required was calculated according to the original producing gas-oil ratio and the bubble point pressure (7.5mpa). the associated gas at the separator temperature was transferred into the piston type high-pressure vessel by the gas booster pump, and was pressurized to the sample preparation pressure. after the oil and gas samples were injected into the sample preparation device, they were heated to the formation temperature and stirred to form the crude oil samples that were not degassed. 2. the gas-bearing crude oil in the sample preparation device was fully stirred for six hours under the formation conditions, and then was flashed to the atmosphere for single degassing experiment. as a result, the composition of the oil and gas phase after degassing, the flash gas-oil ratio, and the density of the degassed crude oil were determined. 3 figure 1—pvt experimental flow chart. pvt properties of crude oil. a certain volume of formation crude oil (40ml) was transferred into dbrpvt cylinder under reservoir condition. the following steps were conducted: 1. adjusting pvt cylinder to experiment required temperature, depressurizing from a relatively high pressure (20mpa) step by step, waiting for the crude oil to stabilize for half an hour after each depressurization, and then recording the expansion volume of the crude oil; 2. when the pressure dropped below the bubble point pressure, recording the total volume of oil and gas expansion; 3. changing the experimental temperature, and repeat steps 1 and 2. phase diagram and phase state characteristics under reservoir conditions. a certain volume of formation crude oil (40ml) was transferred into dbr-pvt cylinder under reservoir condition. the following test was performed: 1. calculating the volume of gas that was added to the oil system at each time according to the percentage of air (oxidized gas) and crude oil (6%, 12%, 18%, 24%, 30%, 36%, 42%, etc.) 2. according to the calculated volume of gas, air (oxidized gas) to the pvt cylinder in turn, and then the air was pressurized and stirred until it dissolved. when the gas completely dissolved to saturation, measuring the bubble point pressure and crude oil expansion volume. 3. according to the calculated volume (the volume ratio of oilgas-foam system is 2:2:1), 40ml crude oil and 40ml air (note: the volume of gas was the volume under the reservoir condition) and 20ml foam system were injected into the pvt cylinder respectively; measuring the gas phase composition and oil phase composition after 6-8 hours of reaction, and then the ternary phase diagram were determined. experimental results and analysis p-v diagram of crude oil. through the composition test of oil samples, the results show that its composition and physical properties were consistent with the formation oil in the study area and were consistent with the experimental oil. the relationship between relative volume and pressure was studied at 46℃, 56℃ and 66℃. the results are shown in figure 2. the relative volume of crude oil refers to the ratio of oil-gas volume under the same temperature but different pressures to crude oil volume at bubble point pressure. with a gradually decreasing of pressure, the volume of crude oil increased, indicating an expansion performance. at the same time, it can be seen that there were obvious inflexion points in the three curves in the figure. when the pressure dropped to a certain level, the dissolved gas in the crude oil gradually separated, resulting in an obvious increase of oil-gas volume, and the corresponding pressure at this inflexion point was the bubble point pressure at current temperature. the bubble point pressure of crude oil at 46℃ and 66℃ was 7.2 mpa and 8.0 mpa, while that at reservoir temperature was 7.5 mpa (table 2). as the temperature 4 increased, the bubble point pressure increased. at the same time, it can be seen from the figure that the higher the temperature, the greater the volume of crude oil increased when the same pressure value was reduced, indicating that the higher the temperature, the higher the expansion performance of the crude oil under the reservoir conditions. figure 2—p-v diagram of crude oil at different temperatures. table 2—bubble point pressure of crude oil at different temperatures. temperature (℃) 46.0 56.0 66.0 bubble point pressure (mpa) 7.2 7.5 8.0 p-t diagram of crude oil. the bubble point pressure of crude oil under different temperature conditions is measured by experiments, and then the measured bubble point pressure was used in the pvt numerical simulation software (pvtsim20) to get the p-t relation diagram of crude oil under reservoir conditions (figure 3). the bubble point pressures at 36℃, 46℃, 56℃, 66℃ and 76℃ were measured. the phase equilibrium model was used to predict the p-t phase diagram of crude oil. as a result, the critical temperature of crude oil was determined to be 424.4 ℃, and the critical pressure was 9.85mpa (figure 3). figure 3—p-t simulation of crude oil. p-x diagram and phase state characteristics under reservoir conditions. the bubble point pressures of air injected at different concentrations and oxidized gas were investigated. the phase diagram of the bubble point pressure (expansion coefficient)-air (oxidized gas) composition was drawn and given as figures 4 and 5. 5 figure 4—p-x phase diagram of air and oxidized gas with crude oil. figure 5—relationship between the expansion coefficient of the crude oil and the volume of gas injection. whether the injected gas is air or oxidized gas, with increasing concentration, the bubble point pressure of crude oil increased, and the rate of increase was relatively stable. it means that the formation pressure continuously increased with the supply of reservoir energy in the gas injection; the injected gas can be partially dissolved in the crude oil, causing the volume of crude oil to expand. the greater the amount of dissolution, the larger the expansion volume. the increase of the elastic potential energy of crude oil was beneficial to the development of crude oil. at the same pressure, the ability of the oxidized gas dissolved in the crude oil was stronger than that in the air, because the methane was the main composition in the oxidized gas. the oxidized gas also contained 2.52% of carbon dioxide and 11.84% of c2-c6. the solubility of these gases in the crude oil was stronger than that in the nitrogen. the ternary phase of multiple air bubble contact. in the air multiple contact experiment, the contents of co2, methane, and c2-c6 in the gas phase increase with the increase of contact times under the reservoir temperature and pressure (figure 6). however, due to the low-temperature oxidation reaction between crude oil and oxygen, the medium and heavy components of the crude oil split and the components of the gasliquid phase tended to be closer, which is conducive to the oil displacement. in the air foam multiple contact experiment, due to the emulsification of the foam system and crude oil in the contact process, its oxidation effect was less than that of the air and crude oil multiple contact (figure 7). the c2-c6 produced by oxidation was relatively less, while the c7-c16 was relatively more, so the composition of gas phase tended to approach c2-c6 is relatively slow. however, the oil phase composition is closer to c7+, due to the increase of c7-c16 component. thus, it is more difficult to miscible than multiple air contact. figure 6—ternary phase diagram after multiple contact of air and crude oil. figure 7—ternary phase diagram after multiple contact of air bubble and crude oil. 6 conclusions 1. according to the physical properties of the crude oil under the reservoir conditions, the simulated oil is configured in the lab. through the test, the composition of the simulated oil simulate the reservoir state, and the research results were close to the actual development situation. 2. through pvt experiment, the critical temperature and critical pressure of oil sample determined to be 424.4℃ and 9.85mpa, respectively. 3. the p-x phase diagrams of air and oxidized gas injected under reservoir conditions were studied. with increasing concentration, the bubble point pressure of crude oil continuously increased and the rate of increase was relatively stable. 4. in the process of gas injection, the formation pressure was increased continuously by the supply of reservoir energy. the injected gas can be partially dissolved in the crude oil, making the volume of the crude oil expand. the higher the dissolved volume, the larger the expansion volume and the higher the elastic potential energy of the crude oil, which is conducive to the exploitation of crude oil. 5. under the same pressure, the ability of gas dissolved in crude oil after oxidation was stronger than that in air. as a result of the emulsification between the foam system and the crude oil in the contact process, its oxidation effect was less than that in the air and the crude oil multiple contact. c2-c6 produced by oxidation was relatively less, while c7-c16 was relatively more. therefore, the trend of the gas phase approaching c2-c6 was relatively slow. however, the oil phase composition was closer to c7+, due to the increase in the c7-c16 component. it is more difficult to miscible than multiple air contact. conflicts of interest the author(s) declare that they have no conflicting interests. reference wang, j., li, n., sun, h., et al. 2008. experimental study on enhanced oil recovery by air foam flooding in heterogeneous reservoirs. petroleum drilling techniques 36(2): 4-6. yan, f., yang, x., and zhang, j. 2008. analysis of the effect of air-foam flooding on the recovery efficiency of the ultra-low permeability oilfield. academic journal center of yan’an university (edition of natural science) 27(4): 58-60. guo, w., liao, g., shao, z., et al. 2003. gas injection enhanced recovery technology. beijing: petroleum industry press. zhang, l., dong, l., zhang, k., et al. 2009. experimental study of air-foam flooding technology in maling oilfield. xinjiang geology 27(1): 85-88. li, s. and zhang, z. 2001. gas injection to improve oil recovery. chengdu: sichuan science and technology press. guo, x., yan, w., and ma, q. 2000. experimental determination and calculation of phase behavior of fluid-co2 system in oil and gas reservoir. journal of china university of petroleum (edition of natural science) 24(3): 12-15. liu, z. and min, j.1996. application of foam flooding in shengli oilfield. oil and gas recovery technology 3(3): 23-29. wang, s., lin, r., and mei, b. 2001. a preliminary study on the types of non-hydrocarbon compounds in liaohe heavy oil. acta petrolei sinica 22(1):36-40. ke, j., han, b., yan, h., et al. 1994. correlation and calculation of gas solubility in heavy oil of karamay 9 area. acta petrolei sinica 15(3): 91-94. abstract introduction experiment preparation experimental results and analysis conclusions conflicts of interest reference copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1250 received june 1, 2023; revised july 1, 2023; accepted july 17, 2023. *corresponding author: osamaajaz99@gmail.com 1 experimental study on gas injection for ultra deep and high-pressure fracturedvuggy carbonate oil reservoirs hasan butt, china university of petroleum (east china), qingdao, china; and osama ajaz*, lmk resources pakistan (pvt) limited, karachi, pakistan abstract in the development of ultra-deep fractured-vuggy carbonate reservoirs, normally only few wells were drilled and hydraulically fractured to create channels connecting the large vugs. production decline at early stages due to rapid pressure decline appears to be the main problem, and water and gas injection via huff-and-puff mode can be applied to maintain oil production. for the targeted reservoir (6,000-7,500 meter depth) in the northwest china, nitrogen injection has shown good ior (improved oil recovery) response. in this study, injection of co2 and methane rich natural gas with different injection-production modes was studied in the laboratory. the laboratory techniques are using a specially designed experimental set-up with multiple cavities connected by small channels to simulate the fractured-vuggy carbonate reservoir. the physical model was designed based on the characteristics of the fractured-vuggy carbonate reservoir and similarity theory, to investigate the influencing factors and the mechanisms of oil recovery of gas injection. gas huff-and-puff experiments were conducted using three different injection-production modes, including vertical model with injection well at top and production well at the bottom, vertical model with injection and production wells at the bottom, and horizontal model with injection and production wells at the same end, under pressure up to 65 mpa. the minimum miscible pressure (mmp) of co2 and natural gas with the crude oil were measured through a slim-tube test. the effects of gravity stabilization and miscibility on oil production were analyzed. the experimental results show that the mmp of co2 of the targeted oil is 30.1 mpa, and over mmp of 47.6 mpa for the methane-rich natural gas, and the ior performance of the methane-rich natural gas is better than that of co2 at ultra-high pressure conditions. it indicates that the action of gravity stabilized oil displacement can be the most important mechanism in the development of high pressure fractured-vuggy reservoirs for gas injection, overshadowing the miscibility effect of co2 for high pressure applications. the results of the study can provide important guidelines for designing gas injection process in ultrahigh pressure fractured-vuggy carbonate reservoirs. introduction many ordovician type and naturally fractured-vuggy carbonate reservoirs have been explored, such as in the tahe oilfield of northwest china, which are buried deeply (6000-7500 m) and with ultra high-pressure (60-75 mpa). the permeability of the reservoir rock matrix is extremely low, ranging from 0.1 to 1 md, and oil and gas are stored in natural fractures and small and large vugs (du et al. 2011; xu et al. 2010; zheng et al. 2010). hydraulic fracturing has been applied to create connections among the vugs and production wells, natural and man-made fractures (up to millimeter size opening) and vugs (up to meter size diameter) are the main flow channels of fluids and primary hydrocarbon storage spaces respectively (chen et al. 2005; corbett et al. 2010; yousef et al. 2014). in the early stage of oil production, the fractured-vuggy carbonate reservoirs of tahe oilfield mainly depended on natural energy for exploitation (camacho-velazquez et al. 2002; chen et al. 2005). later, the mode of artificial 2 water injection was implemented to supplement the energy for production. due to the extremely high heterogeneity of the reservoirs and incomplete well pattern, the effect of water injection gradually becomes minor and negligible with the increase of water injection cycle (li et al. 2013; pratap et al. 1997; rivas-gomez et al. 2001; rong et al. 2016). there is a lot of remaining oil still in the reservoir after water injection (jing et al. 2012; rezaei et al. 2013; wang et al. 2016). the production of this remaining oil is a major challenge in the development process, and there is need to explore new enhance oil recovery methods (farhadinia et al. 2011; shakiba et al. 2016), including gas injection, and nitrogen injection has shown good ior (improved oil recovery) response (su et al. 2017a yuan et al. 2015; yue et al. 2018). in recent years, many researchers have designed and built physical experimental models to simulate the fractured-cavity carbonate reservoir in order to reveal the mechanism and influencing factors of water and gas injection for enhanced oil recovery. most of the studies were conducted by generating specific physical models which were usually in regular structure or fixed special distribution (cruz-hernandez et al. 2001; li et al. 2008; li et al. 2009; wang et al. 2011). however, the distribution and connection of fractures and caves (or vugs) could not reflect correctly by these simple physical models (su et al. 2017b). in this study, the buried depth of the target fractured-vuggy reservoir in tahe oilfield is between 5,210-6,020 m, in which a lot of large vugs have been identified by various geological, geophysics and well logging techniques (tian et al. 2019). based on the characteristics of the fractured-vuggy reservoir and the similarity theory, an experimental model with multiple cavities connected by small channels is innovatively designed and built to simulate the fractured-vuggy reservoir. co2 and natural gas huff-and-puff experiments were conducted under the reservoir conditions with different injection-production modes. pvt and mmp experiments were also performed to facilitate the ior mechanism analysis with different types of injection gas in terms of miscibility, gas driving, and gravity stabilization effects. experimental arrangements materials. the average surface density and viscosity of the oil in targeted reservoir are 0.8744 g/cm3 and 13.83 mpa.s, respectively, which is a light-medium conventional crude oil with medium sulfur and high wax content. the oil sample used in the experiment was prepared by dead oil and natural gas in the laboratory according to a gas-oil ratio of 66 m3/m3. the basic physical parameters of the crude oil are shown in table 1. table 1—the basic physical properties of simulated oil parameters value formation temperature, °c 130 formation pressure, mpa 40-65 saturation pressure (pb), mpa 16.5 formation oil volume factor (bo@130 °c, 40 mpa) 1.14 solution gas-oil ratio (gor), m3/t 63-73 formation oil density, g/cm3 0.848 surface oil density (@ 20 °c, 0.101mpa), g/cm3 0. 91 surface oil viscosity (@20 °c, 0. 101 mpa), mpa·s 78. 47 formation oil density at saturation pressure (@130 °c), g/cm3 0. 827 formation oil viscosity at saturation pressure (@130 °c), mpa·s 2. 654 the gases used for injection include co2 (purity 99.9%) and a natural gas (c1-93.30%, c2-4.94%, c3-1.34%, and co2-0.4%), which were prepared and supplied by qingdao tianyuan gas company. the water sample was 3 prepared according to the analysis results of formation water with a salinity of 15×104 ppm. the crude oil components and related physical properties under experimental conditions are listed in tables 1 and 2. co2 and natural gas mmp experiments. mmp is the threshold pressure at which gas and oil achieve miscibility in-situ at a constant temperature. it is an important parameter for designing miscible displacement and predicting miscible state. the main parameters affecting miscibility are the injection gas composition, reservoir fluid composition, and reservoir temperature. slim-tube test is the widely accepted experimental technique for determining mmp in the petroleum industry. experiments were carried out using a conventional high-pressure pvt analyzer to test the physical properties of the reservoir crude oil (the maximum working pressure of the equipment was 70 mpa and the temperature was 150°c). the flow chart of the slim tube test device is based on the conventional standard experimental procedure, as shown in figure 1. the main parameters of the slim tube test device is shown in table 2. 1. displacement pump, 2. formation oil, 3. injection gas, 4. slim tube model, 5. observation window, 6. back pressure valve, 7. thermostat box, 8. separation bottle, 9. gas meter figure 1—the schematic diagram of slim displacement experiment apparatus. table 2—the parameters of the slim tube model. main parameter value temperature resistance, °c 180 pressure resistance, mpa 70 length, m 12 inner diameter, mm 14 filler glass beads, mesh 80 mesh, 120 mesh (each 50%) pore volume, cm3 65 porosity, % 51.73 permeability, d 5 firstly, the mmp of crude oil was predicted by commercial simulation software, according to crude oil composition and reservoir temperature. on the basis of predicted mmp values, five displacement pressure points were set appropriately above and below the miscible pressure, and then slim tube miscibility pressure test was carried out. a certain amount of petroleum ether was injected into the slim tube for cleaning and dried with nitrogen, and then saturated with the oil sample. co2 and natural gas was injected at a rate of 0.3 ml/min to 4 displace the crude oil. the volume of the crude oil was measured during the displacement process, and the gas injection was stopped until 1.2 pore volume gas injected or no longer oil produced. according to the software predicted results of mmp, the slim tube test for two types of gases (co2/natural gas) under 5 different displacement pressures were carried out separately. the experimental temperature was held constant at 130 °c. it is generally believed that when the ultimate recovery is greater than 90%, the displacement pressure is the minimum miscible pressure of the gas and crude oil. the results of the mmp experiment can be seen in figures 2 and 3. according to the miscibility determination criterion of the slim tube experiment, it was determined that the mmp of co2 and formation oil is 30.1 mpa, and the mmp of natural gas and formation oil is 47.6 mpa. co2 obtains miscibility more easily than natural gas under reservoir condition. figure 2—result of the slim tube test for determining co2 mmp. figure 3—result of the slim tube test for determining natural gas mmp. the fractured-cavity models and experimental set-up. the physical simulation experiment is an important research method for optimizing the gas injection parameters, injection medium, and evaluating the effects of gas injection. following parameters are taken into consideration for experimental study. similarity criteria. a fractured-cavity physical model was designed based on the fracture-vuggy reservoir characteristics and similarity theory, and an experimental study was conducted. the experimental model 5 construction is according to similar criterion to define the experimental conditions and the characteristics of the model, creating the more significant experimental model results to the actual fracture-vuggy reservoir. considering the vug is the main storage space in fractured-vuggy reservoirs, in the process of experimental model design, it is not necessary to satisfy multiple similar criterions at the same time. the similar criterion design is emphasis on the fluid flow in the vug (haibo et al. 2014). at this point, the viscous force shows negligible effect, while the gravity differentiation plays a vital role due to the smaller seepage area of fractured-vuggy reservoirs. hence, the similar design is mainly based on the relation between gravity and pressure, oil production rate, and injection flow rate (su et al. 2017b). according to similar theory, when the similarity coefficient is 1, the field parameters and model parameters are similar. the similarity coefficient can be calculated by the ratio of field parameters to model parameters. to ensure the rationality of the model, the geometric similarity, kinematic similarity, and dynamic similarity analysis of the model were carried out by dimensional analysis, see table 3. table 3—similarity criteria group of fracture cavity type reservoir. kinematic similarity dynamic similarity geometric similarity 𝜋1 = 𝑄/𝜌𝑣𝐿2 𝜋3 = 𝑝/𝜌𝑣2 𝜋6 = 𝑉𝑣𝑢𝑔/𝐿 3 𝜋2 = 𝑡𝑣/𝐿 𝜋4 = 𝑔𝐿/𝑣2 𝜋7 = 𝐾𝑓/𝐿 2 𝜋5 = 𝜇/𝜌𝑣𝐿 𝜋8 = 𝑟𝑤/𝐿 𝜋9 = 𝑥𝑓/𝐿 𝜋10 = 𝜑𝑣 𝜋11 = 𝜑𝑓 the characteristic parameters of the fracture-cavity model mainly consider the filling of the gravel in the cave, and the number of fractures connecting caves. we have regrouped main similarity criterions to meet the need of experimental research, see table 4, which can reflect the fractured-vuggy reservoir characteristics. table 4—similarity criterion group of the physical model and stimulation experiment. serial number similarity criterion physical meaning source satisfaction condition 1 𝑉𝑣𝑢𝑔/𝐾𝑓𝑥𝑓 ratio of cavity volume to fracture conductivity 𝜋6/𝜋7𝜋9 geometric similarity 2 𝑄𝑡/(𝜑𝑣 +𝜑𝑓)𝜌𝐿 3 injection rate 𝜋1𝜋2/(𝜋10 + 𝜋11) kinematic similarity 3 𝑝/𝜌𝑔𝐿 injection pressure / gravity 𝜋3/𝜋4 dynamic similarity 4 𝜇/𝜌𝑣𝐿 viscous force / inertial force 𝜋5 dynamic similarity 5 𝑣2/𝑔𝐿 inertial force / gravity 1/𝜋4 dynamic similarity 6 according to the similarity criteria of physical model huff-and-puff experiment, the main parameters of simulation were determined by actual reservoir parameters, as shown in table 5. table 5—physical model parameter values. parameters fracture aperture, mm fracture permeability, 𝜇𝑚2 cavern volume, 𝑚3 cavern diameter, m flow time, d filling degree, % injection rate, m3/d actual reservoir 0.1-5.0 1-106 0.004-10000 0.2-30 1-10 0-100 30-150 physical model 3 2-20 0.0006-0.002 0.0765 0.05-0.5 100 0.1-0.5* similarity coefficient 1-1.6 0.05-5×105 0.50-2×106 2.6-392 2-200 0-1 200-2×105 *the unit is ml/min designing and description of multiple-cavity model.to investigate the mechanism of co2 and natural gas huff-and-puff, a physical model with multiple cavities connected by small channels was designed by using the similarity theory. inside the model, two metal pistons were used to separate the high-pressure vessel into three cavities (simulated karst caves), each piston had three holes which connected the chambers (simulated fractures) as shown in figure 4, and the chambers were filled with carbonate fragments (stones), as shown in figure 5. figure 4—different injection-production well modes in co2/natural gas huff-and-puff experiment. vertical model: top injection and bottom production horizontal model: same side injection and production injection end (production end) injection end (production end) production end injection end vertical model: bottom injection and production 7 figure 5—experimental model tube and carbonate stone fillings. the main design parameters of the model are as follows: the inner height is 40 cm, the inner diameter is 7.65 cm, the effective height is 27.5 cm (except the thickness of the piston), the diameter of connecting hole of the piston is 3 mm, the model is filled with carbonate rock fragments of 0.5-1.0 cm, the pressure is 70 mpa, and the temperature is 150 °c. the model can be adjusted to any angle of injection and production according to simulation requirements under experimental conditions. the schematic flow chart of the experimental device is mainly composed of physical model system, displacement system, temperature control system, back-pressure control system, data monitoring system, metering system and a number of pipelines and valves, as shown in figure 6. 1. displacement pump; 2. formation oil container; 3. co2/ natural gas container; 4. brine container; 5. rotatable fracture-cave sand filled model; 6. thermostatic oven; 7. pressure sensor; 8. observation window; 9. back pressure valve; 10.separation bottle; 11.sampling port; 12. gas meter. figure 6—the schematic diagram of co2 /natural gas huff-and-puff experimental apparatus. experimental procedures. the experimental process in multiple fracture-cavity model include seven steps: (1) experimental model approach: the fracture-cavity model was filled with carbonate rock pieces, and placed vertically/horizontally into the thermostatic displacement device. (2) water injection: the water was injected from the bottom of the model to measure the porosity, and the model pressure was controlled to 18 mpa. 8 (3) oil injection: the oil was injected from the topside of the model to displace the saturated water until no more water flow from the outlet end, and then the irreducible water as well as initial oil saturation was measured. the temperature of the experimental model was kept constant at 130 °c, and pressure was controlled to 18 mpa. (4) gas injection: the co2/natural gas was injected into the model until it reaches the required pressure of 65 mpa. (5) soaking: the model temperature was maintained at formation temperature (130 °c), and injection valve was closed to allow the injected gas to soak and stabilized the pressure inside the model. (6) oil production: the outlet valve was opened to produce oil and gas under back pressure control. the volume of the produced gas/oil and the pressure difference at that point were measured and when the pressure reached to 18 mpa, production was stopped. (7) second huff-and-puff cycle: during the second cycle of huff-and-puff, the gas was re-injected into the model to the same pressure value (65 mpa), and the above experimental process was repeated until the ultimate huff-and-puff cycle reached. total 6 cycles of co2 and natural gas huff-and-puff for vertical model with injection and production wells at the bottom and horizontal model with injection and production wells at the same end, and 1 cycle for vertical model with injection well at top and production well at the bottom were carried out. the experimental results were compared and analyzed to select the optimal injection gas and injection-production well mode. related data and estimations (for example, ooip, swi, and pore volume) for each experiment are presented in table 6. table 6—the experimental conditions of the gas injection huff-and-puff and preliminary calculations. model measurement parameters value model measurement parameters value pore volume, ml 675 temperature, ° c 130 saturated oil volume, ml 606 gas injection pressure interval, mpa 18-65 porosity, % 53.43 gas injection rate, ml.min-1 0.1 oil saturation, % 89.78 soaking time, min to stable pressure experimental results and discussions co2 huff-and-puff under different injection-production modes. the main eor mechanisms of co2 huffand-puff are: a) oil swelling; b) hydrocarbon extraction by co2; c) viscosity reduction; d) solution gas drive. for co2 injection experiments, six huff-and-puff cycles for bottom injection and production, and horizontal sameend injection and production were carried out. the recovery factor (rf) for each set of huff-and-puff experiment was defined as the cumulative oil production divided by the ooip (original oil in places) corresponding to that particular experiment. the incremental recovery factor for each cycle was defined as the produced oil for that specific cycle divided by the ooip. the experimental results of six cycles of co2 bottom injection and production, and horizontal same-end injection and production in terms of incremental recovery factor and oil exchange rate are compared in figures 7 and 8. it was inferred that the effect of bottom injection and production was similar to that of horizontal same-end injection and production. 9 figure 7—incremental recovery factor of co2 and natural gas huff-and-puff experiment in horizontal model with injection and production at the same end. figure 8—recovery factor of co2 and natural gas huff-and-puff experiment in horizontal model with injection and production at the same end. according to the co2 and oil mmp analysis, co2 was miscible with crude oil under experimental conditions. the solubility and swelling coefficient of co2 in crude oil was high, whereas the density of co2 was close to crude oil under high pressure conditions. the migration and diffusion rate of co2 in crude oil was low because most of the injected co2 accumulated at the injection-end or in the cavity near the injection-end. it was difficult to move or flow towards the upper part or other “karst cavities” connected through fractures and developed the mechanism of gravity stabilized oil displacement. the production mechanism for bottom injection and production, and horizontal same-end injection and production was mainly relied on elastic energy produced by oil swelling. most of the injected co2 produced along with crude oil, resulted in faster energy release, and hence lower oil exchange ratio and overall oil production. it was observed that the water was also produced during production process of bottom injection and production well mode. during the soaking period, the water moved to the bottom of the model due to gravity difference. for top injection and bottom production well mode, one cycle of co2 huff-and-puff was carried out. during the injection period, the injected co2 was completely dissolved in crude oil at high pressures, and swelling elastic energy caused oil to flow towards production well, as shown in figure 9. but when the pressure decreased less than mmp of co2 and oil (30.1 mpa), the gas separated from the crude oil, and moved to the upper part showing gravity stable displacement effect, resulted in increased oil production and exchange ratio. 10 figure 9—incremental recovery factor of co2 and natural gas huff-and-puff experiment in vertical model with injection and production at the bottom of the model. for natural gas injection experiments, six cycles of huff-and-puff for bottom injection and production, and horizontal same-end injection and production were carried out. the rf obtained by co2 and natural gas huffand-puff are shown in figure 10. figure 10—recovery factor of co2 and natural gas huff-and-puff experiment in vertical model with injection and production at the bottom of the model the experimental results of natural gas indicate that the bottom injection and production well mode has better effect than horizontal same-end injection and production well mode. the production mechanism for horizontal same-end injection and production was mainly depended on liberation of elastic energy. during the injection process, natural gas was accumulated near the injection-end resulted in increasing internal pressure of the model. at early stages of production, when the pressure was high (50-65 mpa), natural gas was miscible with crude oil and considerable amount of gas was produced with oil. due to which oil exchange ratio and the recovery rate maintained a linear trend. however, at the lower pressure range (<50 mpa), the natural gas separated from the oil and migrated to the upper part of the cavity near injection-end. the placement of the model in horizontal direction leads to the natural gas accumulation close to the production end which causes gas channeling effect. after the gas breakthrough, the oil exchange ratio and recovery rate decreased sharply. for bottom injection and production well mode, natural gas was in near miscible or immiscible state with crude oil at high pressure conditions. since the density of natural gas was much less than the density of crude oil and the mass transfer of natural gas was faster in crude oil. hence, natural gas migrated to the upper part of the model during the process of injection and well soaking. during preliminary stage, oil production was mainly based on 11 liberation of elastic energy produced due to oil swelling. as the model pressure decreased below mmp of natural gas and crude oil (47.6 mpa), the gas separated from crude oil and moved to the upper part of the model and formed the gas cap drive effect, resulted in a significant increase in oil production. the comparison of comprehensive experimental results by co2 and natural gas are shown in table 7. the experimental results indicate that the top injection and bottom production mode has better effect than the other two modes. table 7—the effect comparison for co2 and natural gas huff-and-puff under different injection-production patterns. horizontal model-same end injection production vertical model-lower injection lower production co2 huff-and-puff natural gas huff-andpuff co2 huff-and-puff natural gas huff-and-puff average one-cycle oil production, ml 24.60 27.47 28.82 72.52 average one-cycle oil exchange rate, g/g 0.198 0.348 0.212 0.961 average single cycle recovery, % 4.06 4.53 4.75 11.97 ultimate recovery factor, % 24.36 27.20 28.53 71.80 conclusions in this study, the performance of co2 and natural gas huff-and-puff in deep and high pressure fractured-vuggy carbonate reservoirs was investigated. a specially designed physical model with multiple fractured-cavity has been used to simulate the oil displacement and fluid flow process in different injection-production modes. the following conclusions can be drawn. 1. the slim tube experiment shows that co2 and the methane rich natural gas both can achieve miscible state with the oil under the reservoir conditions of the targeted block in tahe oilfield. the mmp for co2 is 30.1 mpa, and 47.6 mpa for the natural gas, so the capacity of miscibility of co2 is much higher than that of the natural gas, in which co2 has very high solubility in oil that can make the produced fluid containing more co2 than oil, reducing the gas/oil exchange ratio and economics 2. the experimental results indicate that, when the multi-cavity model was in vertical position, gas injection can significantly improve oil recovery in the ultra-high pressure fractured-vuggy reservoirs, and top gas injection and bottom production (either using co2 or natural gas) has better ior response than the huffand-puff process with injection-production at the bottom end, and much better than that when the model was in horizontal position and injection-production at the same ends. that indicates that gravity stabilization is important for the high-pressure fractured-vuggy reservoir. 3. for the huff-and-puff process and when the vugs are vertically located, the ior performance of methane rich natural gas is much better than that of co2 at ultra high pressure conditions that mean gravity stabilization can overshadow the miscibility effect that can prevail at low pressure conditions. 4. for the targeted fractured-vuggy reservoir at ultra high pressure conditions, gas injection with lean gases (such as, nitrogen, methane, and methane rich natural gas) in a huff-and-puff mode is recommended for a gravity stabilized operation and for pressure maintenance, and co2 is not a suitable injectant at this high pressure condition. 12 nomenclatures ior = improve oil recovery mmp = minimum miscibility pressure hseip = horizontal same-end injection and production vbibp = vertical bottom injection and bottom production vtibp = vertical top injection and bottom production conflicting interests the author(s) declare that they have no conflicting interests. references camacho-velazquez, r., vasquez-cruz, m., castrejon-aivar, r., et al. 2002. pressure transient and decline curve 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carbonate reservoir. journal of petroleum science and engineering 129: 15-22. yue, p., xie, z., huang, s., et al., 2018. the application of n2 huff and puff for ior in fracture-vuggy carbonate reservoir. fuel 234: 1507-1517. zheng, s., li, y., and zhang, h. 2010. fracture-cavity network model for fracture cavity carbonate reservoir (in chinese). journal of china university of petroleum (edition of natural science) 34(3): 72-75. hasan butt is a ph.d. candidate at china university of petroleum (eastchina). he holds m.sc. in geology from karachi university. his research areas include artificial lifting methods, enhanced oil & gas recovery. osama ajaz is working under the capacity of petroleum engineer with lmk resources pakistan (pvt) limited. he holds b.e and m.s. in petroleum engineering. his research areas include artificial lifting methods, enhanced oil and gas recovery, and engineering aspects of carbon storage. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1268 received february 2, 2024; revised april 14, 2024; accepted may 22, 2024. *corresponding author: mouhannad2019@gmail.com 1 revitalizing heavy oil production: a strategic transition from sucker rod pumps to progressive cavity pumps mouhannad hamdan al ibrahim*，al baath university, homs, syria abstract this research highlights the critical importance of the oil industry as a vital cornerstone of the global economy. it emphasizes the need for continuous improvements and innovation in oil production techniques to meet the increasing global energy demands. oil is a key resource that fuels various industries, and its extraction and production require continuous refinement of processes. pumps play a crucial role in oil production processes, making it essential to explore recent developments in pump technology, with a specific focus on progressive cavity pumps. these pumps represent a highly advanced and forward-thinking innovation that is gaining prominence in the oil and gas sector. the study compares progressive cavity pumps with traditional sucker rod pumps used in the tishreen field where harsh conditions exist, such as heavy oil of 14 api with unconsolidated sand formation, using pipesim. the research findings unequivocally demonstrate that progressive cavity pumps outperform traditional sucker rod pumps both in terms of performance and economic efficiency. progressive cavity pumps stand out because of their remarkable ability to effectively address challenges, such as managing high water-cut ratios and operating under low reservoir pressures while achieving greater efficiency at different production rates. however, the significance of progressive cavity pumps extends beyond superior performance. the study highlights the substantial economic benefits that arise from adopting these pumps. replacing conventional sucker rod pumps with progressive cavity pumps has been shown to yield significant cost savings while also enhancing profitability within the oil production process. introduction after well construction operations reach their final stages, production engineers assume responsibility for producing fluids. at the beginning of production, the reservoir pressure is sufficient to push the fluids from the formation to the surface using one of the drive mechanisms (water drive, gas drive, gravity drive, et al.), and then the fluids reach the separators to carry out the treatment operations for the produced oil. after a period of fluid production, the reservoir pressure begins to decrease to values at which it is not possible to push fluids to the surface. to improve the oil production process, one of the artificial lifting methods is used, including lifting using sucker rod pumps, progressive cavity pumps, submersible electric pumps, and gas lift, as these methods provide sufficient support to help convey fluids to the surface (merey 2020; takacs 2015). the working mechanism of these methods varies, as some rely on rotational movement to transport fluids, and others dependent on the up and down movement of the pump piston or focus on injecting gas into the tubing to reduce the weight of the liquid column and raised it to the surface (fozao et al. 2015). in addition, each method of artificial lifting has pros and cons and conditions for applying this method. choosing the appropriate lifting method for any well depends on several points, including depth and type of reservoir, pressure and temperature of the reservoir, gor, wc%, viscosity and density of oil, and other important factors (takacs 2015). this study improved oil and gas recovery 2 will address applying progressive cavity pumps instead of sucker rod pumps used in the tishreen oil field in terms of performance and the economic aspect of the replacement process. therefore, it is necessary to think carefully before choosing the appropriate lifting method to avoid repeated maintenance and repair operations and the additional economic cost resulting from the periodicity of these operations and the cost of lost production during shut shutdown of the well. heavy oil with high viscosity represents the main problem that obstructs production operations, which requires special methods to deal with this oil and increase its production rate including thermal heating of wells, injecting fluids into the wells to reduce the viscosity of the oil, and other methods used to overcome this problem (kantar et al. 1985). the burdens of the heavy oil production process and the economic cost associated with it increase when heavy oil is extracted from unconsolidated sand reservoirs, as the production of sand leads to its accumulation within the production pipes and the bottom of the well, thus causing damage to the subsurface equipment installed inside the wells. this then requires replacing this equipment and carrying out operations of wells washing to get rid of this sand that causes these damages and obstructions to flow and carrying out previous maintenance and repair operations requires a rig to raise the production string and replace the equipment, thus adding more economic burdens (marchan et al. 2014; del pino et al. 2020). these problems and challenges require more research and studies in an attempt to overcome them. therefore, in this study, we will simulate several scenarios to confront these challenges and work to mitigate their severity using the pipesim program to conduct the simulation process and show the results. sucker rod pump. about 85% of artificially lift wells in the united states are constructed with sucker rod pumping systems, which are the most common and ancient type of artificial lift for oil wells. this domination reaches parts of canada and south america. sucker rod pumps are the main source of power for wells, which make up around 80% of all oil wells. these figures, which reflect onshore activities and go back to about 1980, still highlight the rod pumping industry’s continued dominance (fozao et al. 2015). sucker rod pumping systems are advised for new, low-volume wells because of their mechanical simplicity and the familiarity of the operational staff with them. rod pumps are frequently easier for new employees to operate than other forms of artificial lift. these types of systems have the extra benefit of having a high value for repair and operating efficiency throughout a wide range of well-producing properties (brown 1984; moreno and garriz 2020). the american petroleum institute’s standards were followed in the manufacturing of sucker rod pumping system components, guaranteeing reliability and compatibility among manufacturers. but for a longer equipment life, the system needs extensive corrosion protection because of ongoing fatigue, especially on the sucker rod string, pump components, and unanchored tubing. even while sucker rod pumping methods may not be compatible with wells that have severe dog-leg, they are not very good at lifting sand, and paraffin and scale can cause problems (del pino et al. 2020). a poor capacity for gas-liquid separation in the tubing-casing annulus might cause inefficient operation and concerns with gas lock. even with possible inconveniences, shortcomings like leakage from the polished rod stuffing box in a beam pumping system may be minimized with careful design and operating considerations. it is essential to make sure the system is scaled according to well productivity and to minimize over-pumping without pump-off control (poc) to prevent mechanical damage and guarantee effective pump performance (kaplan and duygu 2014). major components. figure 1 illustrates the major components in the sucker rod pumping systems, including 1) the prime mover, which provides power to the system; 2)the gear reducer, which reduces the speed of the prime mover to a suitable pumping speed; 3)the pumping unit, which translates the rotating motion of the gear reducer and prime mover into a reciprocating motion; 4)the sucker rod string, which is located inside the production tubing, and which transmits the reciprocating motion of the pumping unit to the subsurface pump; and 5) the subsurface pump. improved oil and gas recovery 3 figure 1—sucker rod components and mechanism of work (di tullio and marfella 2018). the traveling valve is open on the right side of the picture during the downstroke of the plunger allowing fluid above the standing valve to rise. the traveling valve closes when the plunger hits the bottom of its stroke and starts to rise on the lift side. the working barrel's capacity increases as a result of the plunger lifting the fluid above it. when the pressure in the working barrel drops as a result of this upstroke movement and falls below the pressure going through the bottom hole, the standing valve opens. formation fluids can now go higher as a result. during the whole cycle, the plunger lifts wellbore fluids up to one complete stroke length each time it moves higher. advantages and limitations. the advantages of the sucker rod pumps include 1) ease of operation: it is easily operated by engineers and technicians; 2) versatility: it is effective in various conditions, including heavy oil and sand-laden environments but with some constraints; 3) surface accessibility: many components are located on the surface, facilitating maintenance and component replacement; 4) suitability for deviated wells: it can be used in deviated wells with the right components and assembly; 5) diverse types: it offers over three different types, providing a wide range of options and adaptability. the limitations include 1) pumping rods interruptions: frequent interruptions due to expansion and contraction forces during the up-and-down strokes caused by oil viscosity and liquid column weight; 2) lower production rate: relatively low production rates compared to other methods; 3) gas-lock possibility susceptibility to gas-lock phenomenon (allison et al. 2018); 4) high installation costs installation operations can be expensive.; 6) lengthy maintenance and repair time maintenance and repair operations require a relatively long duration. improved oil and gas recovery 4 progressive cavity pump. the progressive cavity pump (pcp) was developed in 1932 by rené moineau and robert bienaimé, and it has since revolutionized the oil production industry (klein 2002). the pcp is distinguished by its distinct positive displacement mechanism, which is the result of clever engineering and has helped it advance oil extraction technology. the two primary parts of the pcp are the double internal helical elastomer-lined stator and the helical rotor (figure 2). made of sturdy steel, the helical rotor revolves inside the stator coated with elastomers, generating a dynamic system of increasing cavities. this complex relationship between the rotor and stator is the basis of the pcp's operating concept (delpassand 1997). the helical shape makes it easier for cavities to develop between the two parts when the rotor rotates within the stator. these voids function as separate pockets that gradually fill with liquid. in particular, heavy and viscous oils may be easily lifted and transported to the surface by the pcp thanks to its coordinated rotation and cavity creation. the pcp is unique among pumping systems in that it uses a positive displacement mechanism, which makes it particularly useful for extracting unconventional oil deposits (alfaqih et al. 2017). the introduction of the pcp solved the problems of conventional pumping techniques in difficult reservoirs, which resulted in a paradigm change in the oil and gas sector. it is a vital instrument for increasing production rates and cutting operating expenses because of its versatility in handling different well conditions and fluids with a high solid content. one essential part of the pcp that improves its efficiency and flexibility is the elastomer-lined stator. because of their adaptability and durability, elastomers produce a sealing effect that keeps fluid from slipping and guarantees a good lift as the pump rotates (enríquez-méndez et al. 2015). this functionality is especially helpful in situations when conventional pumping systems could malfunction, including when removing abrasive or heavy fluids. figure 2—surface and downhole assemblies of pc pump (mills and gaymard 2007). advantages and limitations. pcp systems present cost savings, offering the same pump capacity at a lower capital cost compared to traditional pumps. they excel in conditions where other artificial lift systems struggle, especially when dealing with heavy oil (lehman 2004). there’s no need for expensive foundations, and their construction is straightforward and adaptable to various wellhead configurations. installation is both fast and dependable, reducing rig mobilization expenses. pcps deliver cost-effective operations with extended lifespans and lower power consumption and maintenance demands compared to alternative artificial lift systems. the impressive volumetric and mechanical efficiency of pcp systems enhances field production while reducing improved oil and gas recovery 5 energy requirements (klein 2002). table 1 summarized and compared the advantages and disadvantages between sucker rod and progressive cavity pumps. table 1—comparison between sucker rod and progressive cavity pump. sucker rod pump (srp) progressive cavity pump (pcp) advantage disadvantage advantage disadvantage simple design deviated wells low cost deviated wells easy installation high solid content high viscous fluids sensitivity to fluid environment low-pressure wells limited production rate large concentration of solids limited production rate high temperature and high viscous oil gassy wells toleration of free gas limited temperature widely availability in different sizes depth limitation no valve problems depth limitation flexible paraffin problems high efficiency corrosion handling tishreen field the tishreen field in syria was operated by the syrian petroleum company (spc) and is located approximately 65 km southeast of deir ezzor city (figure 3). it is a significant accumulation of heavy oil containing 50 wells, of which 41 are presently producing oil with an average of 14 ° api. the field employs a water drive production mechanism, and a decline analysis conducted in multiple areas of the field indicates that the average annual decline rate is approximately 6%. the reservoir is made up of unconsolidated sand, which forms permeable networks for the transportation of fluids from the reservoir to the well. however, the production of water has increased lately, and some wells have up to 92% water content. therefore, spc has taken measures such as conducting cement plugs and changing perforation locations to prevent water from creeping towards the wells. the high-water content, high sand content, and high oil viscosity are the main issues facing the tishreen oil field, causing a decrease in oil production and maintenance and work-over operations. these problems are due to the production of large quantities of water and the failure of surface units, such as engine burnout and gear problems. moreover, subsurface units face problems like the piston becoming stuck due to the presence of sand. in 2011, spc started a project to replace sucker rod pumps with the installation of progressing cavity pumps. unfortunately, the project stopped, so an experimental study will be conducted to replace the srp with pcp. problem statement. sucker rod pumping (srp) was employed at the tishreen oil field to produce hydrocarbon storage, which is primarily composed of sand. the sand created results in issues and malfunctions with the sucker rod pump, necessitating frequent replacements with new pumps throughout the year. to make the production more economically viable, this study aims to raise the rate of oil production by substituting a sucker rod pump with a progressive cavity pump and to decrease the quantity of sand that enters the pump by employing a gravel pack. the objectives of this study consist of the following sub-objectives, 1) to compare the efficiency of the sucker rod pump with the pc pump with/without the gravel pack, 2) to estimate pc pump efficiency at pressure drops and different water cuts and high speed; 3) to conduct an economical comparison between srp/pcp. improved oil and gas recovery 6 figure 3—structural map of tishreen field with the location of the wells. case study the change from conventional srp systems to pcp artificial systems represented a revolutionary change in oil production in colombia’s teca and nare oil fields. pcp technology was used because of the difficulties in handling heavy crude oil (12 api), high viscosity (12000 cp), and a production rate of 250 bbl/day. additionally, the inherent problems of sand sticking and rod failures in srp structures were the main contributing factors. the change greatly increased operating efficiency, especially when it came to handling the challenges brought on by the crude oil’s high viscosity. the switch to pcp systems not only improved oil extraction but also resulted in significant cost savings by lowering energy usage and well downtime. in these locations, pcp systems showed extraordinary adaptation to the unique viscosity properties of the oil, exhibiting a noteworthy 78-88% energy reduction over the preceding srp (ramirez et al. 2007). tables 2 and 3 provide essential parameters, including those related to reservoir characteristics, equipment specifications, and production rates, among others, illustrating the comprehensive nature of the data and offering valuable insights into the field's operational dynamics, including reservoir temperature (158 ℉), oil viscosity (100 cp), reservoir thickness (150 ft), casing size (7 inches), tubing size (4 ½ inches), and production rates (288 bbl/d for liquid and 204 bbl/d for oil with sucker rod pump), contribute crucial insights for understanding and addressing these challenges. by leveraging this data and optimizing production techniques, spc aims to enhance the long-term productivity and sustainability of the tishreen oil field. improved oil and gas recovery 7 table 2—data of tishreen field. parameters value reservoir pressure 2000 psi oil viscosity@ reservoir temp 100 cp reservoir temperature 158 ℉ oil gravity 14 api water cut 29 % gas-oil ratio 0 reservoir thickness 150 ft borehole diameter 8.5 in reservoir permeability 300 md drainage radius 1500 ft table 3—data of tishreen-well 3. parameters value casing length 4888 ft tubing length 3280 ft casing size 7 inches tubing size 4 ½ inches perforation 3930 ft liquid pro/srp 288 bbl/d oil pro/srp 204 bbl/d pcp type 42 k 1200 rpm 150-300 pipesim program. for modeling and simulating multiphase flow in oil and gas production systems, schlumberger released a commercial software, pipesim, a flexible piece of software. it carries out duties such as fluid flow simulation, analysis of pressure drops, forecasting the formation of hydrates and wax, production system optimization, well performance evaluation, and flow assurance concerns resolution. engineers may maximize hydrocarbon recovery and reduce operational expenses by using pipesim to assist them in making informed decisions about the design and use of production systems. for the oil and gas sector, it is a useful instrument to guarantee reliable and effective production operations. pipesim is utilized in this case study to perform nodal analysis profiles, (pressure/temperature) profiles, and model pc pump efficiency with and without gravel pack mechanism. result analysis simulation of pcps. modeling wells in pipesim involves a comprehensive series of stages. within these stages, crucial factors were considered. these encompass identifying the well type (production or injection), determining well deviation, specifying depths and dimensions of casing and tubing, taking into account formation temperature, reservoir pressure, and downhole equipment such additionally, perforation places, fluid properties, surface equipment, including chokes. improved oil and gas recovery 8 in this study, the 42 k 1200 progressive cavity pump was selected (figure 4). this choice was made because it meets the requirements of our wells. after inputting parameters and designing the wells, we perform a nodal analysis for the well to assess its condition and pre-existing issues. figure 4—progressive cavity pump simulation using pipesim. in the oil and gas sector, nodal analysis is an essential and modern method that enables engineers to accurately evaluate pressure decreases at different nodes in the production system. it is possible to accurately compute pressure differences from the bottom hole to surface separation units by altering factors like as pipe diameter, pressure, and temperature (mahmud and abdullah 2017). this optimizes the production from current wells cost-effectively and efficiently. the intersection of the inflow performance (ipr) and outflow performance (opr) curves (figure 5), which aim to maximize hydrocarbon output while reducing operating expenses within budgetary limitations, was where conclusions regarding petroleum production was based (hashmet et al. 2012). traditional nodal analysis, however, has drawbacks since it is static and ignores timedependent variables and inflow performance relationship (ipr) models in shale gas wells. furthermore, multiwell interference was ignored. analytical and numerical models were being developed to solve these problems (zhou et al. 2016). finding a location in the production well, segmenting the system, and figuring out pressures in both directions are all steps in the nodal analysis procedure (shah and hossain 2015). improved oil and gas recovery 9 figure 5—intersection of ipr and vlp (igwilo et al. 2018). enhancing oil production processes is crucial for the oil and gas industry to reduce operational and maintenance costs while increasing overall oil production, ensuring profitability and meeting global market demands. to maximize these improvements, effective planning is essential to ensure efficiency and costeffectiveness. data analysis plays a key role in identifying areas for enhancement, requiring swift implementation of necessary changes. staying updated with the latest technologies is equally vital to maintain peak efficiency. finally, the implementation of oil production improvements should be carried out diligently, with adequate time and attention devoted to execution (shah and hossain 2015). optimizing oil and gas production from a wellbore involves meticulous consideration of various parameters such as tubing diameter, wellhead pressure, choke type and size, surrounding area density, and perforation configuration (igwilo et al. 2018). figure 6—nodal analysis (operation point). when comparing pressure and flow rate, two curves will be plotted (figure 6). the point where these curves intersect will meet two criteria: 1) the flow into the node will be equal to the flow out of it, and 2) there will only be one pressure present at the node. this is because the pressure drop in any component varies with the flow rate. the node in the bottom hole has been selected to measure the pressure in this instance. a lower pressure in the bottom hole will result in a higher efficiency of the pc pump (table 4). improved oil and gas recovery 10 table 4—oil production rate using pcp without gravel pack. simulation of pcps with gravel pack. the gravel pack technique is extensively utilized for sand-control purposes. it allows only very small particles to pass through, while simultaneously stabilizing the borehole and filtering out sand from the liquid (table 5). by making full use of gravel packs and pre-packed wire-wrapped sand screens, sand control can be optimized, thereby maximizing productivity (figure 7). table 5—properties of a gravel pack. permeability 120000 md screen diameter 4 in tunnel 10 in figure 7—simulation pcp with gravel pack. item liquid production, bbl/day pressure at na oil production, bbl/day efficiency, % speed = 150 rpm 348 894 247 74 improved oil and gas recovery 11 figure 8—nodal analysis (ipr versus vlp). figure 9—nodal analysis profile. when the inflow reservoir pressure increases, the flow rate will also increase accordingly (figure 8). the pressure and temperature are directly proportional, meaning that their ratio remains constant. elevation is closely associated with temperature and pressure (figure 9). higher temperatures can negatively impact the stator and elastomer’s performance and reduce the efficiency of the pc pump. table 6—oil production rate at pcp with gravel pack. item liquid production, bbl/day pressure at na oil production, bbl/day efficiency % speed = 150 rpm 347 888 246 73.4 table 6 at a pump speed of 150 rpm, the system achieves a liquid production rate of 347 bbl/day, an oil production rate of 246 bbl/day, with a pressure at the nozzle of 888 units, and an efficiency of 73.4%. these values provide insights into the performance and productivity of the pumping system under specific operating conditions. it was observed that there were only slight changes in the flow rates and efficiency of the well without a gravel pack as compared to the well with a gravel pack. it was observed that there were only slight changes in the flow rates and efficiency of the well without a gravel pack as compared to the well with a gravel pack (table 7). however, it is necessary to use a gravel pack to limit the amount of sand produced with oil. improved oil and gas recovery 12 this helps in reducing the damage caused by sand accumulation inside the tubing and ultimately results in reduced maintenance costs and work-over operations. such operations could include replacing subsurface equipment or performing well-washing operations to reduce the sand content. table 7—compare the production rate of srp/pcp. srp pcp with gravel pack liquid, stb/d oil, stb/d liquid, stb/d oil, stb/d 288 204 347 246 pressure and temperature with gravel pack results (permeability sensitive).increased permeability of gravel packing directly impacts flow rate. as permeability increases, the efficiency of pcp operation also increases (figure 10). figure 10—oil production and efficiency at different permeability of the gravel pack. table 8—efficiency with the permeability of gravel pack. gp permeability, md 20000 40000 60000 80000 100000 120000 oil flow rate, stb/d 244.8 246.5 246.1 246.5 246.8 247 efficiency, % 73.8 74.2 74.3 74.4 74.5 75 sensitive of the water cut. the results of simulations of production rates at different water cuts showed a significant superiority of progressive cavity units against sucker rod units, which showed a significant decrease in the production rate with an increase in the water cut (figure 11). this can be explained by the high efficiency of the progressive cavity pumps in dealing with high water rates and the great ability of these pumps to maintain the production system is stable and does not suffer from the turbulent flow that causes the production group to vibrate and thus go out of service over time as a result of interruptions in the pumping rods (figure 12). improved oil and gas recovery 13 figure 11—nodal analysis (water cut sensitive). figure 12—oil production of srp/pcp at water cut. pressure drops sensitive of pcp. the production rates of different water cuts were simulated and it was found that progressive cavity units were significantly better than sucker rod units. sucker rod units showed a considerable decrease in production rate as the water cut increased (figure 13). this can be attributed to the high efficiency of progressive cavity pumps in dealing with high water rates and their great ability to maintain a stable production system (figure 14). they do not suffer from turbulent flow, which causes the production group to vibrate and eventually go out of service due to interruptions in the pumping rods. improved oil and gas recovery 14 figure 13—nodal analysis (pressure drop sensitive). figure 14—oil production rates of pcp at pressure drops. speed sensitive of pcp. it has been observed that by utilizing gravel packs with pump speed as sensitive data, the flow rate and efficiency increase from 50 rpm to 250 rpm. however, above a certain speed, the flow rate and pcp efficiency decrease, indicating that the system is in ill condition (figure 15). additionally, increasing the rotation speed of the pcp from 50 rpm to 300 rpm results in an increase in production rate from 90 bbl to 450 bbl (figure 16). however, this increase in production rate is accompanied by a decrease in efficiency from 81.77% to 67.89% at a rotation speed of 300 rpm (figure 17 and table 9). it should be noted that 300 rpm is considered one of the prohibited speeds that must not be applied, as illustrated in figure 18. improved oil and gas recovery 15 figure 15—nodal analysis (speed profile). figure 16—p/t profile at different speeds of pcp . figure 17—liquid production versus pcp efficiency. improved oil and gas recovery 16 table 9—production of pcp at a different speed. speed, rpm system dp, psi liquid, stb/d oil, stb/d water, stb/d efficiency, % 50 rpm 1799.024 127.187 90.30278 36.88423 81.77261 100 rpm 1800.04 246.4408 174.973 71.46783 79.17566 150 rpm 1799.732 355.5015 252.4061 103.0954 76.0468 200 rpm 1800.144 457.1599 324.5835 132.5764 73.42209 250 rpm 1799.868 554.8185 393.9211 160.8974 71.27541 300 rpm (ill-conditioned ) 1693.902 634.5778 450.5502 184.0276 67.89398 figure 18—nodal analysis (ill condition). in this well, it is impossible to use the progressive cavity pump at a speed of 300 rpm, as this speed exceeds the pump’s performance square (yellow square) at the lower and right sides, which represents the permissible limit for fluid withdrawal. applying this value of speed accelerates the process of the production system getting out of stability as a result of the vibrations accompanying the rotation process. thus, interruptions occur in the pumping rods. economic evaluation the decision-making process of introducing new technologies into the oil and gas business revolves around economic appraisal. the primary goal of calculating possible financial savings entails a thorough analysis comparing the outcomes obtained using the new technology to those obtained using the previous approach. this assessment procedure takes into account several significant factors as follows, each of which contributes to a comprehensive evaluation of the technology's economic viability and overall cost-effectiveness. 1. fixed capital expenses: this category includes both surfaceand underground-based assets that were purchased as original investments. the initial outlay of fixed capital expenses is necessary for establishing the new technology. 2. installation expenses: the process of putting new technology into use frequently has accompanying installation costs. these expenses are required to incorporate the technology into the current operational or infrastructure architecture. improved oil and gas recovery 17 3. operational expenses: there are ongoing operational costs to take into account after the device is installed. these costs cover everything needed to run and maintain the technology daily, including labor, supplies, and regular servicing. 4. costs of energy: energy consumption is a crucial factor in the oil and gas sector. for a thorough economic analysis, it is essential to examine the new technology's energy needs and associated expenses. 5. number of wells: the number of wells to which the new technology will be applied must be determined. the overall economic impact is directly influenced by the implementation's scale. 6. production rate: a crucial factor is the production rate of the involved wells. economic evaluation requires an understanding of how technology impacts daily production rates and, in turn, the revenue earned. 7. costs for maintenance and make-goods: the operating costs also include ongoing maintenance and potential work-over procedures. these expenses play a crucial role in the economic evaluation since they affect the technology's long-term viability and profitability. however, before implementing new technology in the oil and gas industry, completing a full economic review while taking these crucial factors into account is essential. decision-makers can use it to evaluate the technology's prospective economic benefits, cost savings, and general viability, ensuring that investments are made properly and that the sector continues to develop effectively and sustainably. equipment and operating requirements. the economic feasibility study covers ten years and involves ten wells with a production rate of 5000 barrels per day (bbl/day) of oil, and the cost represent approximately values and estimated in dollars (table 10). table 10—cost of the equipment and operating requirements. capital costs pcp, $ srp, $ savings, $ savings, % equipment description capital investment 60,000 124,000 64,000 51.60 installation costs 11,375 34,125 22,750 66.67 total,$ 86,750 operation cost power consumption 43,362 56,370 13,008 23.1 gas locking 0 1,896 1,896 100 preventative maintenance 614 3,148 2,534 80.5 yearly total 43,976 61,414 17,438 28.4 10-year total 439,760 614,140 174,380 28.4 total savings * $104,188 39.9 total savings** $261,130 10 total savings*** $2,611,300 *after 1-year operation;**in a 10-year life cycle of the well. assuming no equipment changes; ***assuming that there are 10 wells. improved oil and gas recovery 18 table 11—cost details of srp/pcp. comments pcp srp savings capital investment includes the drive head, motor, vfd, and pump. excludes rods and tubing. includes the pump jack, pad, piles, and downhole pump. excludes rods and tubing. installation costs installation time of the pcp system is 1 day. the cost of lost production at the volume is $11,375 per day. the average installation time is 3 days (1-day pad piles, 1-day jack install, 1-day pump install) 1-2 days power consumption annual power consumption: 481,800 kwh @$0.09/kwh. assuming 100% uptime of equipment. annual power consumption: 626,340 kwh @$0.09/kwh. assuming 100% uptime of equipment. 144,540 kwh gas locking 0 hrs. the pcp will not gas lock as the gas is free to pas s through the pump. 2x/year @ 2hr each. the amount of time it will take to put the well on tap, remove all gas built up in the pump, and take the well off tap. the cost of lost production is $474/hour of downtime. (* a well with excessive gas will need more.) 4 hours per year preventative maintenance oil change & grease oil change & grease 1 hr. labor*, $125/hr. $474 lost production * labor rates vary 1 hr. labour including a vac truck, $200/hr. $474 lost production. 1 hour 1.5 gallons of oil@ $10/gallon* *prices of oil may vary 750 gallons of oil @ $10/gallon. 178.5 gallons maintenance and work-over costs. these maintenance and repair costs need to be considered in the overall economic evaluation of the project. from table 12, it is evident that covering 40% of the costs for srp enabled the implementation of pcp in the tishreen field, achieving equivalent production rates. furthermore, it took only 158 days to recover the total costs for the progressive cavity pumps. table 12—maintenance and workover costs. item pcp, $ srp, $ saving, $ saving, % equipment and operation 1,153,510 2,195,390 1,041,880 47.45 work-over cost 49,350,000 82,250,000 32,900,000 86.4 cost of lost production 7,770,000 12,950,000 5,180,000 13.6 total 58,273,510 97,395,390 39,121,880 40.17 improved oil and gas recovery 19 the period required to recover costs. pcp systems have a faster cost recovery time of 158 days, compared to srp systems which require 264 days for cost recovery (figure 19). the total costs encompass the sum of expenses associated with equipment, operating requirements, maintenance, and repair operations. table 13 and figure 20 provide a comprehensive overview of the financial aspects involved in the project evaluation . figure 19—time required to recovery the cost. table 13—saving costs analysis. item saving, $ saving, % equipment and operation 1,041,880 2.7 work-over cost 32,900,000 84 cost of lost production 5,180,000 13.3 total 39,121,880 figure 20—saving details. improved oil and gas recovery 20 conclusions the investigation in tishreen was aimed at analyzing the performance of a pcp and improving it against sand effect and premature failure. to achieve this, pipesim software was used to compare the effectiveness of the pump with and without a gravel pack. the study concludes that gravel packs can help preserve pc pump efficiency and prevent premature failure. based on previous results, here are the conclusions about switching from srp to pcp: 1. the use of gravel packs did not significantly affect the flow rates and efficiencies of pcp. 2. at high speed, there were some ill conditions with the use of a pcp with gravel pack at speed sensitives. 3. pcp systems have a faster cost recovery time of 158 days, compared to srp systems which require 264 days for cost recovery. 4. pcp systems offer cost savings right from the start, with lower capital costs for equipment and installation compared to srp systems. acknowledgments the authors would like to thank syrian petroleum company which provides experimental data. conflicting interests the authors declare that they have no conflicting interests. references alfaqih, m. r., ariwibowo, a., and juliana, c. t. 2017. performance analysis for progressive cavity pumps production scenario in sandy and heavy oil wells. paper presented at the spe middle east artificial lift conference and exhibition, manama, kingdom of bahrain, 16-19 november. spe-184188-ms. allison, a. p., leal, c. f., and boland, m. r. 2018. solving gas interference issues with sucker rod pumps in the permian basin. paper presented at the spe artificial lift conference and exhibition-americas, the woodlands, texas, usa. 28-30 august. spe-190936-ms. brown, k. e. 1984. the technology of artificial lift methods, volume 4. del pino, j., garzon, d., nuñez, w., et al. 2020. sucker rod pump downhole valve selection for wells with high sand production: laboratory test results. spe artificial lift conference and exhibition-americas, virtual, 10-12 november. spe-201156-ms. delpassand, m. s. 1997. progressing cavity (pc) pump design optimization for abrasive applications. paper presented at the spe production operations symposium, oklahoma city, 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to gas in progressive cavity pumps in boscan field to improve run life. paper presented at the spe latin american and caribbean petroleum engineering conference. spe-169414-ms. merey, ş. 2020. comparison of sucker rod pump and progressive cavity pump performances in batı raman heavy oil field of turkey. celal bayar university journal of science 16(2):191-199. mills, r. a. r. and gaymard, r. 2007. new applications for wellbore progressing cavity pumps. spe-35541-ms. moreno, g. a. and garriz, a. e. 2020. sucker rod string dynamics in deviated wells. journal of petroleum science and engineering 184: 106534. ramirez, j., abril, w., vargas, l., et al. 2007. saving energy in heavy-oil fields in colombia with progressive cavity pumps. paper presented at the spe latin american and caribbean petroleum engineering conference, buenos aires, argentina, 15-17 april. spe-108083-ms. shah, m. s. and hossain, h. m. z. 2015. evaluation of natural gas production optimization in the kailashtila gas field in bangladesh using the decline curve analysis method. bangladesh journal of scientific and industrial research 50(1): 29-38. takacs, g. 2015. sucker-rod pumping handbook: production engineering fundamentals and long-stroke rod pumping. houston: gulf professional publishing. zhou, w., banerjee, r., and proano, e. 2016. nodal analysis for unconventional reservoirs—principles and application. spe journal 21(1): 245-255. mouhannad al ibrahim holds a bachelor's degree in petroleum engineering. he is an engineer at the syrian petroleum company (spc) with expertise in production optimization, well performance analysis, artificial lift systems, and reservoir engineering. currently, he is pursuing a master’s degree in oil and gas field development engineering at al baath university of chemical and petroleum engineering, he is dedicated to advancing his knowledge and skills in the energy sector with a focus on enhancing production efficiency and reservoir management. abstract introduction tishreen field case study result analysis economic evaluation conclusions acknowledgments conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1267 received december 1, 2023; revised january 31, 2024; accepted february 21, 2024. *corresponding author: ahmedelswisy22@gmail.com 1 prediction of brine hydrate formation temperature using ann-based model ahmed elswisy*, belayim petroleum company, cairo, egypt; mohsen elnoby, future university in egypt, new cairo, egypt; adel salem, suez university, suez, egypt abstract this study aims to leverage artificial neural networks (ann) for predicting the hydrate formation temperature (hft) of brines commonly employed in completion, workover, and well intervention operations. to achieve this goal, this study constructed a robust ann model incorporating inputs such as the brine salts components' weight, gas specific gravity, pressure, and percentages of impurity gases (n2, h2s, co2). to achieve highly accurate forecasts for hydrate formation temperatures in both monovalent and divalent brines, a comprehensive real dataset with a wide range of variations was utilized. optimization processes were then conducted to identify the optimal configuration for the ann structure. this included optimization of the training function and determining the appropriate number of hidden neurons, among other factors. the resulting ann models proposed in this study provide a correlation that can be directly utilized to estimate the hydrate formation temperature. introduction completion fluid. completion fluid is pumped downhole to perform operations after the initial drilling of a well. clear brine, as a completion fluid, is used to kill the well and remains in the wellbore until the new completion string is installed. it can also be used as a packer fluid, or as workover fluid for a remedial operation in the well. using brine at hplt (high pressure and low temperature) environment, which is available at deepwater environment, may arise troubles like hydrate formation (figure 1)(bellarby 2009). figure 1—gas hydrates plugs (crumpton 2018). hydrate. gas hydrates are called clathrates which consist of two different molecules that are mechanically connected but not chemically bonded. water, by hydrogen bonding, forms cage that is physically entraping gas molecules normally that is smaller than n-pentane. methane, ethane, propane, butanes, co2, n2, and h2s. they 2 are a solid structure of gas and water that closely resemble dirty ice or snow. it is discovered in 1810 by sir humphrey davy (sloan 2010). gas hydrates have the potential to obstruct the tubing of the well, christmas tree, and flowlines. it is crucial to exercise meticulous care to proactively prevent their formation by addressing potential causes and implementing remedial actions as needed (zahedi et al. 2009). for deep and ultra-deep water wells, pressure could reach 10,000 psi and temperatures at seabed/mudline could be 35°f. these p-t conditions can activate the formation of the hydrates. hydrates formation. formation of hydrates necessitates relatively low temperatures, high pressures, water and low-molecular weight gases, such as methane, ethane, propane, i-butane, n-butane, co2, h2s, and nitrogen. when water mixed with low molecular weight gases with enough conditions of relatively low temperature and high pressure, hydrates is formed. the formed clatherates are a solid/rigid network of water molecules that cage in gas molecules of another substance (figure 2). the most common gas could form hydrates is methane (ch4) (bellarby 2009). figure 2—lattice crystal of hydrate (bellarby 2009). as shown in figure 3, it is a hydrates stability curve for a typical gas composition. it is inevitable that, with temperature reduction and pressure increase, the conditions are more suitable to form hydrates (crumpton 2018). figure 3—example of hydrate stability curve. 3 hydrates stability also depends on water salinity and the type of salt in the brine/electrolyte which forms the hydrates. the hydrate disassociation curves are shown in figure 4 . one is for typical hydrocarbon gas mixed with pure water, and another is for formation water (50,000 ppm total solids) . figure 4—example of hydrate stability curve (data source: bellarby 2009). as shown in figure 5, the hydrate stability curves for two monovalent brines are different from each other, due to different salt types. in figure 6, for the same gas composition and salt types, the hydrate stability curve is different from each other due to different salt concentration. figure 5—hydrate stability curve for two monovalent brines (data source: sloan 2006). figure 6—hydrate stability curve for three divalent brines (data source: sloan 2006). 0 2 4 6 8 10 260 265 270 275 280 285 p re ss u re , m p a temperature, k hydrate stability curve 3% nacl 15% nacl, 8% kcl 0 50 100 150 200 280 285 290 295 300 305 310 315 p re ss u re , m p a temperature, k hydrate stability curve 5% cacl2 4 hydrate formation temperature calculation. experimental measurements. experimental measurements stand out as the most reliable and accurate method for determining hydrate formation temperature (hft). numerous scientists have conducted experiments encompassing various gas types and conditions to estimate hft. ng and robinson (1985), for instance, delved into hydrate formation conditions for pure gases in the presence of solutions containing up to 20 wt% methanol. bishnoi and dholabhai (1993) reported data on hydrate formation conditions in electrolyte solutions, glycol, and methanol. subsequently, talaghat (2009) conducted laboratory studies to measure the rate of hydrate formation for pure gases in the presence of hydrate inhibitors. ameripour (2009) made significant contributions by developing correlations to estimate hydrate formation pressure or temperature for different gas hydrates, both with and without inhibitors. this involved utilizing variables for regression and developing correlations, taking into account factors such as gas specific gravity, pseudo-reduced temperature and pressure, water vapor pressure, and liquid water viscosity. visual basic programming was employed to create these correlations. in a different study, marinakis and varotsis (2013) investigated the effects of aqueous phase salinity for two gas mixtures at varying salinity levels. k-value method. this method uses the vapour-solid equilibrium constants for predicting conditions of hydrate formation. ∑ 𝑦𝑖 𝑘𝑣𝑠,𝑖 = 1𝑁 𝑖=1 ......................................................................................................................................................(1) gas gravity method. the gas gravity plot developed by katz (1945) was a relation between the hydrate formation pressure and temperature with the specific gravity of natural gases. empirical correlations to calculate hydrate formation conditions by gas gravity are hammerschmidt (1936), berge (1986), kobayashi et al. (1987), motiee (1991), and ghiasi (2012) correlations. hammerschmidt (1936) developed his hydrate temperature formation, where α and β are constant. 𝑇 = 𝛼𝑃𝛽.............................................................................................................................................................(2) ghiasi (2012) proposed the following equation to 𝑇 = 𝐴0 + 𝐴1 × 𝑀 + 𝐴2 × 𝑀2 + 𝐴3 × 𝐿𝑛(𝑃) + 𝐴4 × (𝐿𝑛(𝑃)) 2 + 𝐴5 × 𝑀 × 𝐿𝑛(𝑃)....................................(3) holder et al. (1988) proposed a simple relationship to calculate the hydrate formation pressure of pure gases, where gas is expressed in the relationship as coefficients (a and b). 𝑃 = exp (𝑎 + 𝑏 𝑇 ),...............................................................................................................................................(4) thermodynamic models. this method accounts for the interactions between water molecules which form the crystal lattice and gas molecules. many models were proposed based on this method, such as elgibaly and elkamel’s model (1998) and nasrifar et al’s model(1998). javanmardi and moshfeghian (1999) created a thermodynamic model for hydrate formation temperatures calculation of different hydrate in mixtures of common electrolytes (nacl, kcl and cacl2). soft computing techniques. it is the method that does not involve the knowledge of the fundamental principles governing the process, such as artificial intelligence methods. they use the power of the big data for data analysis and interpretation, and models regressed by data training can be used to calculate and predict hydrate formation temperature. heydari et al. (2006) used artificial neural network to predict hydrate formation temperature by using 167 of real data with the range of 32-74 °f for temperature, 50-4200 psia for pressure and 0.554-1 for gas specific gravity. zahedi et al. (2009) used artificial neural networks to propose a model with gas specific gravity and pressure as inputs. khajeh (2009) used adaptive neuro-fuzzy inference system (anfis) to obtain a new regression model. fayazi (2014) used least square support vector machine (lssvm) algorithm to construct the model to forecast hydrate formation temperature. rashid et al. (2014) proposed an approach for methane hydrate formation temperature prediction accurately with the presence of salt, which is already dissolved in the water that will form the hydrate. they used 131 datasets to build a model that predict hydrate formation temperature using least square support vector machine (lssvm) method. the input data for the model are gas specific gravity, hydrate formation pressure, and molality as an expression for salinity, and the output is hydrate formation temperature. the pitfalls of rashid et al’s model was that the developed model was based on data of methane hydrate only and using salt molality without defining salt type. olabisi et al. (2019) built an ann model 5 which was trained using 459 hydrate formation experimental data points from katz’s (1945) chart and wilcox et al. (1941) chart. specific gravity and pressure were chosen as the inputs in the 4-layer network, and hydrate formation temperature was the output. the data points were pressures were from 49 psia to 4000 psia, and gas specific gravity was 0.5539, 0.6, 0.7, 0.8, 0.9 and 1.0. el-hoshoudy et al. (2021) used katz’s (1945) gravity chart to extract (1469) data points of gas hydrate formation pressure, temperature, and specific gravity. also, maekawa (2001) studied the different equilibrium conditions for gas hydrate of methane and ethane mixtures in pure water and 3.0 wt% nacl solution. nasrifir and moshfeghian (2000) presented a model for pure co2 and co2-rich gas hydrate formation conditions prediction in aqueous solutions containing electrolytes and their mixtures. methodology data pre-processing and acquisition. we started by data gathering, filtering, and cleaning. it was performed by removing the illogic and missing values, which is an important step in any ann model to be accurate and successful. data description. in this study, about 200 datasets were collected form real data of monovalent brine and 300 datasets of divalent brine. dataset consist of inputs, including weight percentages of the brine salts components for both monovalent brines (nacl, kcl, nabr) and divalent brines (cacl2, cabr2), gas specific gravity, pressure, and gas impurities percentages (n2, h2s, co2), and the hydrate formation temperature as output. in the case of monovalent brines, a comprehensive statistical analysis was conducted for all data parameters, as outlined in table 1. the data revealed a broad spectrum across these parameters. for example, nacl weight percentage varied from 0% to 15%, kcl weight percentage ranged from 0% to 15%, nabr weight percentage spanned from 0% to 30.6%, pressure fluctuated between 0.27 and 142 mpa, co2 percentage ranged from 0% to 24.9%, h2s percentage exhibited a range from 0 to 17.6%, n2 percentage varied between 0% and 6.8%, and gas specific gravity ranged from 0.55 to 0.9. moreover, the hydrate formation temperature showed a range between 264.4°f and 303.1°f. table 1—statistical analysis of monovalent brines. nacl, % kcl, % nabr, % p, mpa co2, % h2s, % n2, % sp. gr. t,k mean 2.24 2.05 2.86 10.41 3.00 1.83 0.35 0.65 284.07 standard error 0.27 0.29 0.60 1.13 0.46 0.31 0.08 0.01 0.67 median 0.00 0.00 0.00 5.19 0.00 0.00 0.00 0.65 284.20 standard deviation 3.64 3.95 8.22 15.52 6.25 4.13 1.11 0.09 9.19 sample variance 13.24 15.59 67.50 240.79 39.06 17.08 1.22 0.01 84.50 kurtosis 2.23 2.68 5.40 33.60 2.96 6.03 29.02 0.02 -0.96 skewness 1.69 1.96 2.65 4.95 2.01 2.53 5.37 0.88 -0.22 range 15.00 15.00 30.60 142.15 24.90 17.60 6.80 0.34 38.70 minimum 0.00 0.00 0.00 0.27 0.00 0.00 0.00 0.55 264.40 maximum 15.00 15.00 30.60 142.42 24.90 17.60 6.80 0.90 303.10 table 2 presents the results of statistical analysis for all parameters related to divalent brines. the data exhibited a considerable range across various factors. cacl2 weight percentage varied from 0% to 33%, cabr2 weight percentage ranged from 0% to 32%, pressure spanned from 0.27 to 204.58 mpa, co2 percentage showed a range of 0% to 24.9%, h2s percentage had a range of 0% to 17.6%, n2 percentage ranged from 0% to 6.8%, and gas specific gravity varied between 0.55 and 0.9. additionally, the hydrate formation temperature exhibited a range of 282.52°f to 309.75°f. 6 table 2—statistical analysis of divalent brines. cacl2 cabr2 p, mpa co2 h2s n2 gas sp. gr. t,k mean 16.61 10.17 41.51 1.73 0.99 0.15 0.77 282.52 standard error 0.71 0.71 2.80 0.26 0.17 0.05 0.01 0.82 median 27.00 3.00 19.85 0.00 0.00 0.00 0.84 285.75 standard deviation 12.97 13.08 51.42 4.87 3.16 0.83 0.10 15.11 sample variance 168.24 171.11 2644.16 23.69 10.01 0.69 0.01 228.27 kurtosis -1.75 -1.30 1.71 8.70 14.63 59.75 -0.80 -0.50 skewness -0.43 0.80 1.61 3.04 3.75 7.73 -0.88 -0.55 range 33.00 32.00 204.31 24.90 17.60 6.80 0.34 67.21 minimum 0.00 0.00 0.27 0.00 0.00 0.00 0.55 242.54 maximum 33.00 32.00 204.58 24.90 17.60 6.80 0.90 309.75 correlation coefficient. the correlation coefficient is employed to assess the connection between two parameters. it serves as a measure of the influence of each feature or input on the output. when numerous parameters impact the output, it can function as a screening or evaluation tool, helping identify the most impactful parameters and whether their effects are positive or negative. 𝐶𝑜𝑟𝑟𝑒𝑙𝑎𝑡𝑖𝑜𝑛 𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡(𝑥, 𝑦) = σ(𝑥−𝑥𝑎𝑣𝑔)(𝑦−𝑦𝑎𝑣𝑔) √σ(x−xavg)2σ(𝑦−𝑦𝑎𝑣𝑔)2 ,.................................................................................(5) the correlation coefficient plots for different parameters in monovalent and divalent brines are depicted in figures 7 and 8, respectively. figure 7—correlation coefficient of different parameters for monovalent brines. figure 8—correlation coefficient of different parameters for divalent brines. -0.6 -0.4 -0.2 0 0.2 0.4 0.6 nacl kcl nabr p co2 h2s n2 spec grav. c o ef fi ci en t -0.6 -0.4 -0.2 0 0.2 0.4 0.6 cacl2 cabr2 p co2 h2s n2 spec grav c o ef fi ci en t 7 data normalization. to prepare the data for constructing the ann model, it is essential to perform data normalization. this step ensures that all variables are converted to a comparable scale, facilitating a more accurate and efficient learning process. to normalize the data within the range of -1 to 1, the following equation was applied. 𝑥𝑛𝑜𝑟 = 2 ∗ ( 𝑥−𝑥𝑚𝑖𝑛 𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛 ) − 1.............................................................................................................................(6) for monovalent brines: 𝑁𝑎𝐶𝑙 𝑤𝑡%𝑛𝑜𝑟 = 0.1333 ∗ 𝑁𝑎𝐶𝑙 𝑤𝑡% − 1,................................................................................................................(7) 𝐾𝐶𝑙 𝑤𝑡%𝑛𝑜𝑟 = 0.1333 ∗ 𝐾𝐶𝑙 𝑤𝑡% − 1,....................................................................................................................(8) 𝑁𝑎𝐵𝑟 𝑤𝑡%𝑛𝑜𝑟 = 0.0654 ∗ 𝑁𝑎𝐵𝑟 𝑤𝑡% − 1,...............................................................................................................(9) 𝑃𝑛𝑜𝑟 = 0.0141 ∗ 𝑃 − 1.0038,................................................................................................................................(10) 𝐶𝑂2 %𝑛𝑜𝑟 = 0.0803 ∗ 𝐶𝑂2% − 1,.........................................................................................................................(11) 𝐻2𝑆%𝑛𝑜𝑟 = 0.1136 ∗ 𝐻2𝑆% − 1,..........................................................................................................................(12) 𝑁2%𝑛𝑜𝑟 = 0.2941 ∗ 𝑁2% − 1,.............................................................................................................................(13) 𝛾𝑔 𝑛𝑜𝑟 = 5.8116 ∗ 𝛾𝑔 − 4.2064............................................................................................................................(14) when hft is obtained, it will be normalized and to converted to original value by using the expression as follows, 𝐻𝐹𝑇 = 19.35 ∗ 𝐻𝐹𝑇𝑛𝑜𝑟 + 283.75................................................................................................................(15) for divalent brines, the equations used for data normalization are as follows. 𝐶𝑎𝐶𝑙2 𝑤𝑡%𝑛𝑜𝑟 = 0.0606 ∗ 𝐶𝑎𝐶𝑙2 𝑤𝑡% − 1 ,..............................................................................................(16) 𝐶𝑎𝐵𝑟2 𝑤𝑡%𝑛𝑜𝑟 = 0.0625 ∗ 𝐶𝑎𝐵𝑟2 𝑤𝑡% − 1,.............................................................................................(17) 𝑃𝑛𝑜𝑟 = 0.0098 ∗ 𝑃 − 1.0026,.......................................................................................................................(18) 𝐶𝑂2 %𝑛𝑜𝑟 = 0.0803 ∗ 𝐶𝑜2% − 1,................................................................................................................(19) 𝐻2𝑆%𝑛𝑜𝑟 = 0.1136 ∗ 𝐻2𝑠% − 1,.................................................................................................................(20) 𝑁2%𝑛𝑜𝑟 = 0.2941 ∗ 𝑁2% − 1,.....................................................................................................................(21) 𝛾𝑔 𝑛𝑜𝑟 = 5.8116 ∗ 𝛾𝑔 − 4.2064....................................................................................................................(22) when hft is obtained from it will be normalized and to convert it to original value, use expression: 𝐻𝐹𝑇 = 33.606 ∗ 𝐻𝐹𝑇𝑛𝑜𝑟 + 276.14..............................................................................................................(23) artificial neural networks (ann). ann is typically structured with three layers: input, hidden, and output layers. the methodology of ann involves the utilization of weights and biases to establish connections between these layers, influencing the network's performance (figure 9). the objective is to compare the target with the output value, measure the disparity between them, and then adjust weights based on this difference until it reaches an acceptable minimum value. the data undergoes various stages, including training, testing, and validation. in this study, the dataset was partitioned, allocating 70% for training and 30% for testing and validation purposes. 8 figure 9—flowchart of artificial neural network network optimization. the performance of the artificial neural network (ann) of divalent and monovalent brines (figures 10 and 11) will undergo optimization through the adjustment of two key factors: the training function and the number of neurons. various training methods, including the levenberg-marquardt, bayesian regularization, and scaled conjugate gradient methods, will be utilized for data training. the mean square error (mse) will be computed, and the training method or number of neurons associated with the lowest error will be selected for optimal performance. 𝑀𝑆𝐸 = ∑ (𝑋𝑖𝑜−𝑋𝑖𝑝)2𝑛 𝑖=1 𝑛 ........................................................................................................................................(24) figure 10—network configuration for monovalent brines. the inputs for the hidden are calculated from the following expression, 𝑆𝑖, 𝑗 = ∑ (𝑤𝑖, 𝑗 ∗ 𝑥𝑗) + 𝑏𝑖𝑛 𝑖=1 ,..........................................................................................................................(25) where, i represents number of neurons, and j represents number of inputs, xj represents the inputs. the outputs from the hidden layer (according to tan sigmoid activation function) are calculated using, 𝐻𝑖 = 2 1+exp (−2∗𝑆𝑖) − 1.............................................................................................................................(26) to get the final value of pct, the function between output layer and hidden layer is linear and calculated by, 𝑁𝑒𝑡 = ∑ (𝑤2𝑖 ∗ 𝐻𝑖) + 𝑏2𝑛 𝑖=1 ,.........................................................................................................................(27) where w2i is the weight of neuron i at the hidden layer and output layer. 9 figure 11—network configuration for divalent brines. results analysis the correlation between the mse and number of neurons for different training function were analyzed in this section for monovalent and divalent brines, respectively. monovalent brines. the configuration that yielded the smallest mse was with 19 neurons in the hidden layer, using the levenberg-marquardt training function, resulting in an mse of 0.315×10-2. with the bayesian regularization training function, a setup featuring 14 neurons in the hidden layer achieved an mse of 0.0693× 10-2. on the other hand, when using the scaled conjugate gradient training function, 19 neurons in the hidden layer produced an mse of 3.15×10-2 (figure 12). table 3 summarized the weights and biases of the ann model for monovalent brines with 14 neurons. figure 12—mse for various number of neuron by the different training functions for monovalent brines. 10 table 3—weights and biases of ann model for monovalent brines. neuron wi, 1 wi, 2 wi,3 wi,4 wi,5 wi,6 wi,7 wi,8 bi w2,i b2 1 0.442 0.265 -0.334 -0.235 0.243 0.149 -0.199 -0.593 -0.145 0.892 -0.41 2 1.226 1.383 -1.918 0.877 -0.213 -0.247 0.111 0.972 0.806 2.410 3 -0.061 -0.031 0.067 0.393 -1.051 -0.457 -0.064 -0.835 0.127 -1.521 4 -0.065 -0.262 -0.586 8.144 0.381 0.320 0.007 -0.925 8.334 7.163 5 0.330 0.847 0.360 -0.420 -1.079 -1.024 -0.575 4.795 -0.023 -2.392 6 -0.384 -0.094 -0.377 -0.107 0.183 0.154 0.050 -0.058 -0.141 0.672 7 0.086 0.052 -0.036 -0.458 0.984 0.666 0.082 0.868 -0.146 1.584 8 0.043 -1.221 0.529 -2.228 0.141 -0.592 1.381 -0.457 -1.553 2.252 9 0.051 0.259 0.845 0.601 -0.814 -0.508 0.120 3.773 -0.332 -1.926 10 -1.113 -1.037 -0.505 -1.639 0.730 0.469 0.550 -2.986 -0.585 -2.722 11 -0.109 -0.653 -0.753 5.698 1.090 0.745 -0.104 -2.697 5.299 -4.181 12 0.542 -1.335 -0.682 1.528 1.067 -0.885 0.430 -0.750 0.379 -1.698 13 -1.482 -1.001 -0.563 2.794 0.093 0.004 -0.460 -0.696 -0.263 2.280 14 -0.630 0.485 0.111 -2.987 0.463 0.548 0.290 -1.393 -1.651 -1.920 divalent brines. under the levenberg-marquardt training function, employing 18 neurons in the hidden layer resulted in a mse of 0.0237×10-2. meanwhile, with the bayesian regularization training function, utilizing 16 neurons in the hidden layer yielded an impressively low mse of 0.0036×10-2. when employing the scaled conjugate gradient training function, 15 neurons in the hidden layer led to an mse of 1.88×10-2 (figure 13). table 4 summarized the weights and biases of the ann model for divalent brines with 16 neurons. figure 13—mse for number of neuron by different training functions for divalent brines. 11 table 4—weights and biases of ann model for divalent brines. neuron wi,1 wi,2 wi,3 wi,4 wi,5 wi,6 wi,7 bi w2,i b2 1 -1.038 0.748 -1.604 -0.635 0.158 -0.597 2.590 -0.310 2.038 0.963 2 0.350 0.584 -15.123 -2.800 2.605 4.680 0.264 -10.534 -4.151 3 -0.634 -1.389 0.628 -0.118 1.668 -1.767 -4.848 -0.863 2.306 4 -0.834 -1.534 0.808 -1.292 0.552 0.235 -1.415 -0.410 -2.586 5 0.750 -0.045 -9.304 -0.963 2.174 6.270 0.426 -1.461 -6.474 6 -1.384 0.617 -1.516 -1.924 1.065 -0.002 2.083 -0.869 -2.303 7 1.339 -0.297 -9.484 -1.079 1.445 2.819 -0.220 -5.934 5.150 8 -1.591 0.068 6.329 -0.897 -0.513 -0.250 1.303 4.556 2.524 9 0.508 1.768 -3.732 -0.790 1.717 1.441 0.330 -1.284 3.178 10 1.142 -2.781 0.289 -0.554 0.169 0.136 -3.758 -1.801 2.431 11 -0.231 -0.405 8.515 0.402 -1.947 -6.867 -0.435 0.116 -6.637 12 -0.611 0.119 -0.554 -1.188 -1.505 1.447 -0.562 -0.724 3.457 13 -0.713 1.340 0.629 0.533 0.882 -0.148 0.609 0.241 2.448 14 -0.539 -0.282 -1.708 1.374 0.406 -0.684 5.769 -1.168 2.529 15 -0.617 -1.371 1.187 -0.314 1.335 0.086 2.503 -0.352 2.432 16 -0.674 -2.211 3.617 -1.207 -1.515 -1.332 -0.205 -0.044 3.486 upon optimization, it appears that the bayesian regularization training function exhibits the lowest error across both types of brines. specifically, for monovalent brines, a 14-neuron network yields the most accurate match and the lowest mse. in the case of divalent brines, a 16-neuron network demonstrates the best results with the lowest mse. as shown in figures 14 and 15, the predicted hft by ann model showed great agreement with actual hft for both monovalent and divalent brines. consequently, the weights and biases corresponding to these networks were chosen and employed for further investigation. figure 14—predicted hft by ann model vs. actual hft for monovalent brines. 12 figure 15—predicted hft by ann model vs. actual hft for divalent brine. results comparison. the ann models were contrasted with the computed outcomes derived from ameripour's (2009) correlation. the designated specific gas gravity was set at 0.645, and the nabr brine concentration was 20% for monovalent brines. figure 16—hydrate pressure vs. temperature of the two models for monovalent brines. table 5—comparison of error% between the two models for monovalent brines. pressure, mpa t, k t, k (amereripour 2009) er% t, k (ann model) er% 27.85 291.93 297.2729107 -1.830202692 291.6230148 0.105157 27.03 291.43 297.0856811 -1.940665368 291.4691147 -0.01342 21.65 290.98 295.6254951 -1.596499799 290.2123662 0.26381 20.51 290.71 295.2514293 -1.56218544 289.9994762 0.24441 13.65 288.43 292.2078762 -1.309806955 289.3868945 -0.33176 14.41 288.26 292.6366603 -1.518303018 289.5172242 -0.43614 0 5 10 15 20 25 30 286 288 290 292 294 296 298 p re ss u re , m p a temperature, k real data ameripour correlation ann model 13 in the case of divalent brines, the specific gas gravity was determined to be 0.572, with a cacl2 brine concentration of 10%. upon examining figures 16 and 17, it becomes evident that the ann model exhibits a closer alignment with actual data, showcasing a lower error rate (er%). tables 5 and 6 summarized and compared the error between two models for monovalent and divalent brines, respectively. figure 17—hydrate pressure vs. temperature of two models for divalent brines. table 6—comparison of error (%) between two models for divalent brines. p, mpa t, k t, k (amereripour 2009) er% t, k (ann model) er% 0.63 266.7 246.9805032 7.393887068 267.3144 -0.23036 0.88 269.2 256.6640622 4.656737649 269.1893 0.003977 1.14 271.1 263.1862017 2.919143606 270.9729 0.046876 1.44 273.5 268.420014 1.857398887 272.8247 0.246908 1.88 275.4 273.7304152 0.606239951 275.1539 0.089354 2.48 277.4 278.6079655 -0.435459812 277.6289 -0.08251 3.34 279.7 283.2550483 -1.271021911 279.8993 -0.07125 conclusions this study introduces a novel method for predicting and estimating hft values. the newly developed ann hft prediction model demonstrates its robustness when compared to other previously published hft models. the methodology was applied to two distinct types of brines, monovalent and divalent, to enhance accuracy. the optimization strategies employed in each model proved successful in achieving high accuracy levels, with an r value of 0.95 for the monovalent brine model and 0.96 for the divalent brine model in the testing dataset. an additional noteworthy aspect of this study is its potential time-saving benefits in hft estimation, making it particularly valuable for real completion operations, especially in high-pressure, low-temperature (hplt) environments. nomenclature 𝛾 = gas specific gravity; ki = equilibrium constant for component i; yi = mole fraction of each component in the gas on a water free basis; m = molecular weight; 0 1 2 3 4 245 250 255 260 265 270 275 280 285 290 p re ss u re , m p a temperature, k real data ameripour correlaton ann model 14 mse = mean square error. acknowledgments i would like to express my sincere pray to my mentor prof. ahmed gawish who has passed away. conflicting interests the author(s) declare that they have no conflicting interests. references ameripour, s. 2006. prediction of gas-hydrate formation conditions in 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d. l. 1945. prediction of conditions for hydrate formation in natural gases. transactions of the aime, 160(1): 140149. khajeh, a., modarress, h., and razaee, b. 2009. application of adaptive neuro-fuzzy inference system for solubility prediction of carbon dioxide in polymers. expert systems with applications 36(3): 5728-5732 kobayashi, r., song, k.y., and sloan, e.d. 1987. phase behavior of water/hydrocarbon systems. pet. eng. handb. 25:1316. maekawa, t. 2001. equilibrium conditions for gas hydrates of methane and ethane mixtures in pure water and sodium chloride solution. geochemical journal 35(1): 59-66. marinakis, d. and varotsis, n. 2013. solubility measurements of (methane+ ethane+ propane) mixtures in the aqueous phase with gas hydrates under vapour unsaturated conditions. j. chem. thermodyn. 65:100–105. motiee, m. 1991. estimate possibility of hydrates. hydrocarbon processing 70:98-99. nasrifar, k. and moshfeghian, m. 2000. computation of equilibrium hydrate formation temperature for co2 and hydrocarbon gases containing co2 in the presence of an alcohol, electrolytes and their mixtures. journal of petroleum science and engineering 26(4): 143-150. nasrifar, k., moshfeghian, m., and maddox, r. n. 1998. prediction of equilibrium conditions for gas hydrate formation in the mixtures of both electrolytes and alcohol. fluid phase equilibria 146(2): 1-13. ng, h. j. and robinson, d. b. 1985. hydrate formation in systems containing methane, ethane, propane, carbon dioxide or hydrogen sulfide in the presence of methanol. fluid phase equilibria 21(1-2): 145-155. 15 olabisi, o. t., atubokiki, a. j., and babawale, o. 2019. artificial neural network for prediction of hydrate formation temperature. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 5-7 august. spe-198811-ms. rashid, s., fayazi, a., harimi, b., et al. 2014. evolving a robust approach for accurate prediction of methane hydrate formation temperature in the presence of salt inhibitor. journal of natural gas science and engineering 18: 194-204. sloan, e. d. 2010. natural gas hydrates in flow assurance. houston, texas, usa: gulf professional publishing. talaghat m.r. 2009. experimental and theoretical investigation of simple gas hydrate formation with or without presence of kinetic inhibitors in a flow mini-loop apparatus. fluid phase equilibria 279(1): 28-40. wilcox, w. i., carson, d.b, and katz, d. l. 1941. natural gas hydrate. industrial and engineering chemistry 33: 662-669 zahedi, g., karami, z., and yaghoobi, h. 2009. prediction of hydrate formation temperature by both statistical models and artificial neural network approaches. energy conversion and management 50(8): 2052-2059. ahmed elswisy is a petroleum engineer at belayim petroleum company which is a jv petroleum company in egypt, where he has worked for the last 4 years. he also worked at scimitar petroleum company for 6 months and for fue as teaching assistant for a year. his research interests are in drilling, completion and workover. he holds b.s. degree from cairo university, and currently is a m.s. candidate in petroleum engineering of suez university . mohsen elnoby is a professor in the department of petroleum engineering at fue university. he was the chairman of the board and md of petrodara petroleum company for 4 years, the chairman of the board and md of qarun petroleum company for 2 years, the chairman of the board and md of general petroleum company– egypt for 1 year. since 2019, he has been working for fue university as assoc. prof. his research interests are in well completion, workover, and production engineering. he holds b.s. degree from cairo university, and m.s. and ph.d degree from faculty of engineering, suez university, all in petroleum engineering. adel salem is the head of petroleum engineering department at the suez university. he worked as a field petroleum production engineer at qarun petroleum company western desert – egypt for 1 year. since 2008 he has been working for suez university as assoc. prof. and then as a full prof. his research interests are in nanotechnology in eor/ior, drilling fluid, simulation of multiphase flow under steady and transient conditions. he holds b.s. and m.s. from faculty of engineering, suez university, and ph.d from leoben university at austria, all in petroleum engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1227 received december 12, 2022; revised february 4, 2023; accepted march 16, 2023. *corresponding author: shiyuywy@126.com 1 reservoir simulation of co2 sequestration in brine formation yanpeng chen, research institute of petroleum exploration and development, beijing, china; xiaodong huang, xi’an shiyou university, xi’an, shaanxi, china; zhen dong, research institute of petroleum exploration and development, beijing, china; yu shi*, xi’an shiyou university, xi’an, shaanxi, china abstract considering the long-term and slow processes of co2 sequestration in brine formation, it is hard to systematically investigate the underlying mechanisms of co2 sequestration in a saline aquifer with bench-scale experiments. in this work, simulation research of co2 sequestration in a real saline aquifer was proposed and conducted to investigate the effects of co2 injection on the formation and to reveal the mechanisms of co2 sequestration. to be specific, the simulation of co2 sequestration was carried out with both a homogeneous model and a heterogeneous model. the former model aimed to investigate the effect of co2 injection rate on the reservoir conditions and the formation properties. the latter one focused on unveiling the impacts of heterogeneity of formation properties and geological structure, two critical inherent properties of the real saline aquifer, on co2 distribution and trapping. the results show that the distribution of ph was affected by the distance to the injector, geological structure, and heterogeneity of permeability. the lowest ph, which was controlled by the maximum formation pressure and corresponding solubility of co2, can be found in the location of the co2 injector. the porosity changes caused by the reaction with solid minerals in both two models were relatively small after 30 years of co2 injection. meanwhile, the maximum formation pressure was undisputedly located at the co2 injector. then, the formation pressure will gradually decrease with an increase in the distance to the injector satisfying a power function. introduction due to an increase in consumed amounts of fossil fuels, the content of co2 in the atmosphere has risen gradually, which inevitably leads to a serious greenhouse effect on a global scale. how to reduce carbon emissions, while ensuring economic development, has become one of the most important challenges that every country faces. carbon capture and storage (ccs) is a technology that separates, collects, and compresses co2 gas from industrial emissions, and then injects it into places under suitable storage conditions to isolate it from the atmosphere for long-term storage (rashidi et al. 2020). according to the iea report, the contribution of ccs to reducing co2 emissions will increase from 3% in 2020 to 10% in 2030 and a further 19% in 2050, making it one of the most attractive technologies to reduce carbon dioxide emissions (zhao and liu 2019; james 2020; li and qin 2017). ccs mainly includes geological storage, marine storage, mineral storage, ecological storage, and industrial utilization (liu 2017). among them, co2 mailto:shiyuywy@126.com 2 geological sequestration has been of interest to researchers and industries owing to the effectiveness and low cost of reducing co2 emissions. the storage sites mainly include deep saline layers, abandoned oil and gas reservoirs or those under development, and unexploitable coal seams. among them, co2 sequestration in the deep underground saline layer has become the most promising co2 geological sequestration technology due to its advantages, such as a large volume, a long storage time, and wide distribution of storage sites (yang 2010; ma 2010). therefore, it is pragmatic and theoretical importance to investigate the co2 flow behavior and the corresponding effect on the saline aquifer. the following conditions are commonly required for a success co2 sequestration in a saline aquifer (bentham and kirby 2005; zhang et al. 2011; lee et al. 2012; chen and li 2015): (1) a tight cap rock of the saline aquifer, i.e., an impermeable cap rock; (2) a high injectivity of the saline aquifer, i.e., a sufficient capacity to store large. meanwhile, the mechanisms of co2 sequestration in saline aquifer mainly involves four processes: structural sequestration, residual gas sequestration, dissolution sequestration, and mineralization sequestration. these mechanisms, on one hand, improve the sequestration of co2 in the formation. however, on the other hand, it will result in (1) an increased formation pressure, (2) a dynamic formation property (porosity and permeability), and (3) a weakened rock strength (agofacek et al. 2019; veer et al. 2015; al-khdheeawi et al. 2020). all those mechanisms will lead to issues of sealing ability and stability of caprock to some extent because of the reaction between injected co2 and formation minerals as well as the potential migration of co2 in the caprock. to maintain stable and safe storage and avoid a possible and dangerous leakage, a long-term safety sequestration of co2 saline sequestration should be conducted considering that the migration processes of co2 and chemical reaction between co2 and mineral components of rock is actually quite long and slow process (zhang 2018; yu et al. 2015; winkler et al. 2010; agofack et al. 2019). therefore, the numerical simulation is a pragmatic and effective method to assess the above-mentioned long-term co2 storage in saline aquifers, especially, compared with bench-scale experimental research (brantley 2015). in 2011, tosha (2013) conducted a research aiming to examine the effect of injected co2 collected from the refinery on the stability of geological structure of the aquifer via the numerical simulation technique. ma (2013) took the co2 geological sequestration layer in the ordos basin demonstration area as the research object and carried out the numerical simulation of carbon dioxide geological sequestration located in the ordos basin, china. the influence of formation permeability, injection rate, temperature, and cap on formation pressure and mole fraction distribution of co2 were calculated and discussed. in this work, a homogeneous and a heterogeneous simulation model were established to numerically mimic the co2 sequestration during a co2 injection process lasting for 30/40 years. the effects of three factors, including co2 injection rate, amounts of co2 injection, and the heterogeneity of saline aquifer on the co2 storage, were systematically investigated. specifically, three parameters, including ph, porosity, and formation pressure, were calculated and analyzed to examine the influences of the above-mentioned three factors on co2 sequestration. the results show that the changes in porosity were very slight. the geological structure, heterogeneity of permeability, and co2 injection rate imposed a great effect on the formation pressure and ph. numerical simulation model homogeneous model. to investigate the effect of co2 injection on the saline aquifer, a co2 storage mechanism model was established and shown in figure 1a. before the co2 injection simulation, the initial conditions were analyzed according to the actual situation as shown in table 1 (as homogeneous model). the initial formation pressure was 9.6mpa, the initial temperature was 26oc. the porosity and permeability were 0.15 and 2 md, respectively. the salt mass fraction was 0.05. the sizes of x, y and z directions are 10000m, 10000m and 20m, respectively. also, the top layer depth of the formation is 1000m. the total 3 number of grids is 625, the injection well is the origin of the model coordinates, the injection rate is unchanged, and the influence of co2 on the reservoir at different times was observed. heterogeneous model. the geological and physical properties were collected from a saline aquifer located in xinjiang, china. the initial pressure and temperature were 12.5 mpa and 30 oc, respectively. the average porosity was 5.4%. the salt mass fraction was 0.00253 according to the water analysis report. the length and width of the model block were set as 3600m and 4000m. the average formation thickness was around 40m. the average grid sizes of x, y, and z directions were 100m, 100m, and 10m, respectively. a total of 5760 grids (36×40×4) were involved in the model (figure 1b). table 1 also presents the main input parameters for the heterogeneous simulation model. (a) homogeneous (b) heterogeneous figure 1—reservoir model by simulation. table 1—parameters of carbon dioxide-water-rock model parameter homogeneous model heterogeneous model formation thickness, m 20 40 average permeability, md 2 1.4 average porosity 0.15 0.054 coefficient of compressibility, pa-1 4.5×10-10 4.5×10-10pa-1 temperature, ℃ 26 30℃ pressure, mpa 9.6 10mpa salinity, mg/l 0.06 0.00253 results and discussion during the entire simulation process, co2 was injected into the reservoir at a constant rate, 10 tons/d for the homogeneous model and 3, 4, and 5 tons/d for the heterogeneous model. three parameters, including ph, formation pressure, and porosity, strongly related to the safety and effectiveness of co2 sequestration were calculated and analyzed to assess the dynamic effect of co2 injection on the saline aquifer. 4 ph. homogeneous model. the ph value of the near wellbore zone decreased rapidly in the first year, which decreased from 7.88 to 5.73, in the near wellbore region. after that, the decline rate of ph gradually slows (figure 2). to be specific, the ph of near wellbore zone was around 4.91 after a constant-rate co2 injection of 40 years (figure 3). meanwhile, one can find that the area with a decreased ph compared with the original ph gradually expanded with an increase in the amount of injected co2 or injection time (figure 4). the reason is that minimum ph was dominated by the solubility of co2 in the formation water. generally, the higher solubility of co2 in water, the higher ph becomes. in other words, once the maximum solubility reaches under a certain condition (formation pressure and temperature), the ph of the formation fluids will get the smallest value, then be a constant due to the unchanged solubility of co2. noted that the ph (4.90) of 20 years is slightly lower than that (4.91) of 40 years. the difference between the values was caused by the chemical reaction between the h+ and mineral components of rock. 1 year 10 years 20 years 40 years figure 2—the ph 2d distribution of homogeneous model at different times. figure 3—ph of injector at different times. figure 4—sectional ph distribution. 5 heterogeneous model. figure 5 shows the ph distribution at different injection stages (1, 10, 20, and 30 years) with injection rates of 5, 4, and 3 tons/d. compared with the ph distribution of the homogeneous model, the ph distribution of the heterogeneous model looks much more complicated. it seems that the ph distribution does not follow the rules that ph gradually increases with an increase in the distance to the well location. based on figure 5, the lowest ph is mainly found in the upper right part of the model. then, the several red points mean the highest ph in the center part of the model. the mechanisms behind such distribution are that the upper right part of the model is the high part of the geological structure, i.e., a low buried depth. once the scco2 is injected into the formation, the co2 migrates to the higher part of the geological structure with aid of the buoyancy. consequently, the reaction between scco2 and brine taking place in the zone affected by the migration generates h+, and consequently, a low ph value of rock. as shown in figure 6, with co2 injection, the wellhead ph changes significantly and the ph near the wellhead decreases as well. the main reason for the rise of ph value in some areas is that carbonate dissolution consumes more h+ formed by co2 dissolved in water. 1 year 10 years 20 years 30 years (a) 5 tons/d 1 year 10 years 20 years 30 years (b) 4 tons/d 1 year 10 years 20 years 30 years (c) 3 tons/d figure 5—2d ph distribution of heterogeneous model with different injection rates. 6 (a) 5 tons/d (b) 4 tons/d (c) 3 tons/d figure 6—the sectional ph distribution with different injection rates. 7 formation pressure. homogeneous model. the injection of supercritical co2 undoubtedly would increase the formation pressure and disequilibrate the original state, which imposes a certain impact on the stability of the formation. apparently, it will be imperative to quantitatively evaluate the impact of the increased formation pressure considering the potential leakage of injected co2. figure 7 shows the formation pressure distributions with time proceeding at a constant injection rate of 10 tons/d. it can be observed that the reservoir pressure is increased evenly in the horizontal direction from the injection point. firstly, the pressure at the injection point is the highest during the entire process, with a bottom-hole pressure of 13.7 mpa in the first year, an increase of 4.1 mpa from the initial formation pressure. when the injection time has reached 40 years, and the pressure at the injection point has increased to 23.1 mpa, much larger than the initial pressure of 9.6 mpa. secondly, due to an increase in reservoir pressure caused by a continuous co2 injection, a high-pressure area with a peak pressure located at the injector position, and pressure gradually decreased to the initial formation pressure with an increase in the distance to the injector. the relationship between the distance to the wellbore and the formation pressure is depicted in figure 8, which actually can be quantified with a logarithm function. the longer the injection time of co2 is, the larger the high-pressure area becomes. figure 8 also indicates the pressure changes from the wellhead location at different times after co2 injection. as co2 increases, the pressure increases and spreads over a wider area. 1 year 10 years 20 years 40 years figure 7—the formation pressure distributions of homogeneous model at different times. figure 8—the sectional formation pressure distribution (5 tons/d) at different times. heterogeneous model. figure 9 shows the horizontal pressure distributions at different injection stages (1, 10, 20, and 30 years) with a constant injection rate of 5 tons/d. it can be found that the spatial distribution of the heterogeneous model is remarkably different from that of the homogeneous model, although both the maximum formation pressures are in the position of the injector. the possible reason for such a difference is that the spatial distribution of formation pressure in the heterogeneous model is affected not only by the injected co2 but also by the geological structure of the saline aquifer. the formation depth inherently results 8 in different formation pressures and the deviation of pressure distribution between the homogeneous model and the heterogeneous model. in addition, the increment of formation pressure is strongly pertinent to the amount of injected co2. for instance, the pressure at the well position is gradually increased with an increase in co2 injection rate. in other words, a large injection rate of co2 is, a high formation pressure becomes, according to the simulation results of different injection rates of 5, 4, and 3 tons/d (figure 10). 1 year 10 years 20 years 30 years (a) 5 tons/d 1 year 10 years 20 years 30 years (b) 4 tons/d 1 year 10 years 20 years 30 years (c) 3 tons/d figure 9—2d formation pressure of heterogeneous model with an injection rate of (a) 5 tons/d; (b) 4 tons/d and (c) 3 tons/d. (a) 5 tons/d 9 (b) 4 tons/d (c) 5 tons/d figure 10—the sectional formation pressure distribution with co2 injection rates of (a) 5 tons/d; (b) 4 tons/d and (c) 3 tons/d at different times. porosity. homogeneous model. figure 11 shows the dynamic porosity distributions of the homogeneous model with time proceeding. it can be observed that an area with an increased porosity, which surrounds the injector, is formed and gradually enlarged owing to an increase in amounts of injected co2. such changes in porosity have mainly resulted from the chemical reaction between the h+ and minerals, that is to say, the dissolution of minerals in the weak acid formed by the injected co2 and formation water. meanwhile, the spatial distribution of porosity is presented in figure 12. to be specific, the porosity increased from 15% to 15.06% in 40 years, an increase of only about 0.4% compared to the initial value. a minor increase in porosity implies that the reaction of the dissolution of minerals is a gentle and long-term process, which cannot lead to a sharp change in porosity. one can find that the distribution pattern of porosity is similar to that of formation pressure. however, the area with an enlarged porosity is much smaller than that affected by an increased formation pressure, which actually is resulted from the spatial distribution of ph. 10 1 year 10 years 20 years 40 years figure 11—2d porosity distributions of homogeneous model at different times. figure 12—sectional porosity distribution at different times in homogeneous model. heterogeneous model. figure 13 shows the porosity distribution at different injection stages (1, 10, 20, and 30 years) at an injection rate of 5, 4, and 3 tons/d. according to the figures, one can find that the changes in porosity are very unnoticeable at different times. to be specific, porosity of the formation only increased by 0.000014 in 30 years. such a small change in porosity implies that the co2 sequestration caused by mineral carbonation is not the main contributor to co2 trapping in this aquifer. co2 dissolves in water to form a weak acid, leading to carbonate dissolution in the reservoir and an increase in porosity. according to the current simulation (figure 14), this reservoir is less affected by acid dissolution, and its porosity increases only by 0.000014 in 30 years. 1 year 10 years 20 years 30 years (a) 5 tons/d 1 year 10 years 20 years 30 years (b) 4 tons/d 11 1 year 10 years 20 years 30 years (c) 5 tons/d figure 13—2d formation pressure of heterogeneous model with an injection rate of (a) 5 tons/d; (b) 4 tons/d and (c) 3 tons/d. figure 14—sectional porosity distribution at different times in heterogeneous model overlaid each other. conclusions in this work, the numerical simulation was carried out to realize the establishment of the heterogeneous model in the actual situation. the influence of co2 geological sequestration on reservoirs and cap rocks was studied, and the following conclusions are drawn: 1. the whole process of co2 storage changes the original geochemical properties and physical parameters of the reservoir and cap rock, and the co2 injection leads to the continuous increase of the pressure in the formation, which may cause vertical differential deformation of the surface, fault activation, and even earthquake; co2 escape leads to pollution of freshwater aquifers, and a large amount of gas emission endangers human safety and ecological safety nearby. 2. through the simulation, the formation of weak acid after co2 injection causes the ph value of the formation to change, resulting in the increase of reservoir acidity, especially the injection point and the area around the change range is large, and then promotes the co2-water-rock geochemical reaction. the acidity of the formation also leads to the dissolution of minerals and the precipitation of new minerals, and the dissolution is greater than the precipitation in the acidic area, which is also the main reason for the increase in porosity. 3. at present, most of the established numerical models are mean value models and focus on the transport and reaction of co2 in the reservoir. this paper has realized the analysis of the physical changes of the reservoir and cap under different conditions of the actual model. 12 conflicts of interest the author(s) declare that they have no conflicting interests. references al-khdheeawi, e.a., mahdi, d.s, ali, m., et al. 2020. impact of caprock type on geochemical reactivity and mineral trapping efficiency of co2. paper presented at the offshore technology conference asia, kuala lumpur, malaysia, 7-11 november. otc-30094-ms. agofack, n., cerasi, p. , stroisz, a., et al. 2019. sorption of co2 and integrity of a caprock shale. paper presented at the american rock mechanics association symposium, new york, usa, 7 june. bentham, m. and kirby, m.g. 2005. co2 storage in saline aquifers. oil & gas science and technology 60(3):1-10. brantley, d. 2015. 3-d numerical 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petroleum university, daqing, china. ma, j. 2013. study on the transport law of supercritical carbon dioxide under geological storage (in chinese). phd dissertation, tsinghua university, beijing, china. rashidi, m., dabbi, e. p., bakar, z., et al. 2020. a field case study of modelling the environmental fate of leaked co gas in the marine environment for carbon capture and storage ccs. paper presented at the spe asia pacific oil & gas conference and exhibition, virtual,12-15 november. spe-202394-ms. tosha, t. 2013. anumerical simulation study for the distributed ccs. energy procedia, 37: 6010-6017. veer, e., waldmann, s., and fokker, p.a. 2015. a coupled geochemical-transport-geomechanical model to address caprock integrity during long-term co2 storage. paper presented at the 49th u.s. rock mechanics/geomechanics symposium, san francisco, california, 28-30 june. arma-2015-165. winkler, m., abernathy, r., nicolo, m., et al. 2010. the dynamic aspect of formation-storage use for co2 sequestration. paper presented at the spe international conference on co2 capture, storage, and utilization, new orleans, louisiana, usa, 10-14 november. spe-139730-ms. yang, f. 2010. mechanism and geological simulation o carbon dioxide sequestration in saline layer (in chinese). ms thesis, china university of geosciences (beijing), beijing, china. zhao, t. and liu, z. 2019. a novel analysis of carbon capture and storage (ccs) technology adoption: an evolutionary game model between stakeholders. energy 19:189-200. zhang, g., taberner, c., cartwright, l., et al. 2011. injection of supercritical co2 into deep saline carbonate formations: predictions from geochemical modeling. spe journal 16(4):959-967. zhang, j. 2018. study on mechanism of supercritical carbon dioxide-water-rock interaction in tight reservoir (in chinese). ms thesis, southwest petroleum university, chengdu, china. 13 yanpeng chen, received a b.e. from yangtze university and a phd. in geological resources and geological engineering from china university of petroleum (2008). he has been working as an exploration and development geophysicist in research institute of petroleum exploration and development (petrochina) since 2008. his work mainly focused on the development and exploration of coalbed gas and ccs. xiaodong, huang, is a master candidate in oil and gas field development of xi’an shiyou university. his research mainly involves the reservoir simulation and co2 storage in aquifer. zhen dong, received a b.e. and a m.e. in drilling engineering from china university of petroleum in 2010 and 2013, respectively. mr. dong is a senior geological engineer mainly working on the development of coalbed gas and ccus techniques in research institute of petroleum exploration and development (petrochina). yu shi, an associated professor in xi’an shiyou university. previously, shi worked as a reservoir engineer at the research institute of petroleum exploration and development, petrochina. shi holds a phd degree in fluid mechanics from the chinese academy science, and a phd degree in petroleum engineering from the university of regina. shi’s major research focuses on phase behavior, microscale flow behavior in porous media, heat and mass transfer, and formation evaluation. shi is a member of spe. abstract introduction numerical simulation model results and discussion conclusions conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1291 received july 2, 2024; revised august 14, 2024; accepted august 20, 2024. *corresponding author: mahamadaya_184@yahoo.com 1 developing dynamic killing technique for off-bottom killing condition mohamed yossef*, belayim petroleum company, cairo, egypt; adel salem, suez university, suez, egypt and future university in egypt (fue), cairo, egypt abstract dynamic killing is a non-conventional well control technique that employs annular pressure loss in conjunction with hydrostatic pressure to halt well influx. this method is particularly applicable in off-bottom conditions, where the drill bit is away from the well's bottom. off-bottom conditions are common during tripping operations, where surface pressure may not accurately reflect bottom-hole conditions. ignoring the region beneath the drill bit necessitates higher kill rates, which may exceed equipment limits, such as maximum rated surface pressure. in this study, the effect of kill fluid falling below the drill bit was examined in terms of critical influx velocity. a python program was developed to model single-phase and two-phase flow conditions within the drill string, annulus, and below the bit. the focus was on accurately modeling the area below the bit, using three different approaches: static, dynamic zero net liquid holdup (znlh) flow, and countercurrent two-phase flow. two gas influx scenarios were employed to test, verify, and assess these modeling approaches. results indicated that the static znlh approach required the highest kill rate, while the countercurrent two-phase flow approach required the lowest. in terms of bottom-hole pressure, the static znlh approach resulted in the lowest pressures, whereas the countercurrent two-phase flow approach yielded the highest pressures. temperature significantly impacts the properties of the kill fluid, such as density and viscosity, even when water is used. additionally, reducing the kill string depth logarithmically increases the required kill rate. the critical gas velocity, which influences the kill fluid's fall-off at a certain depth, decreases with increasing gas influx rate.this work provides a roadmap for applying dynamic kill techniques in off-bottom conditions, accommodating both low and high gas influx rates. introduction the conventional well control techniques based on the constant bottom hole pressure (bhp) concept in some cases fails to controls well kicks. from well ’s blowout statistics, 25% of blowouts happened due to swabbing effect due to excessive tripping speed while pull out of hole. meanwhile 80% of blowout events happened when the bit position is off-bottom in those cases the dynamic kill technique incorporated (yin et al. 2023). the dynamic kill method, announced by mobil oil corporation and initially presented by blount and soeiinah, was used to control a high-deliverability gas well blowout (400 mmscf/day) in indonesia's arun field, which continued to burn for 89 days. the blowout was controlled within 50 minutes once the killing operation commenced (vallejo-arrieta 2002). mailto:mahamadaya_184@yahoo.com improved oil and gas recovery 2 the dynamic kill technique involves pumping fluid at the surface into the blowout flow path to increase the combined annular pressure loss and hydrostatic pressure along the blowout flow path, surpassing the formation pressure. in some instances, blowouts occur while the drill string remains off-bottom, complicating the wellkilling process as the ability to circulate the kick fluid out is not feasible. limited research has been conducted on off-bottom kills, particularly considering the ability of heavier kill fluid to fall and flow counter-current against the formation fluid, which supports well killing. this paper aims to simulate the off-bottom dynamic kill process for gas well blowouts, highlighting the effect of liquid fall-down on selecting the killing rate. the study incorporates different flow models, including twophase flow models, static zero net liquid holdup, and dynamic zero net liquid holdup, to achieve a more accurate flow model for calculating well-killing requirements. the counter-current flow of killing fluid dropping through the influx fluid was primarily studied by gillespie et al. (1990) for off-bottom dynamic killing conditions. they defined a certain limit at which the kill fluid begins to fall through the gas influx, termed the critical gas velocity. this is defined as the gas velocity at which the liquid begins to fall, considered equal to the relative settling velocity of the largest droplet. the critical gas velocity variables are illustrated in eq. 1 (gillespie et al. 1990). they based the well-killing condition on two variables: the largest droplet diameter in the gas stream and the droplet drag coefficient. ������ = 4� ����(��−��) 3�� �� ,....................................................................................................................................(1) gillespie et al. (1990) used three approaches for droplet size estimation, which produced different critical velocity values, varying widely, with the highest value being almost four times the lowest for the same conditions. a high value for the droplet drag coefficient would lead to a conservative estimate of the critical gas velocity (gillespie et al. 1990; flores-avila et al. 2003). additionally, liquid holdup, which may exist while circulating a fluid, was not considered in their estimation. kouba et al. (1993) employed the critical gas velocity model to estimate formation fluid rates below which a minimum value of liquid holdup would exist. they utilized barnea’s studies, which indicated that liquid holdup is 0.25 during slug flow, 0.75 for bubble flow, and zero for annular flow, to estimate the liquid holdup below the killing string during off-bottom dynamic killing operations. they made several assumptions: no-slip flow between the gas and liquid phases above the injection point, no friction pressure loss below the injection point, and a minimum value of liquid holdup for each flow pattern. these assumptions led to higher required kill rates (kouba et al. 1993; flores-avila et al. 2003). flores-avila et al. (2002) extended the research on the effect of kill fluid falling through the upward-moving formation kick fluid, particularly when the injection point is off-bottom in blowout wells. their study demonstrated that the accumulation of injected kill fluid below the kill string would increase bottom hole pressure and assist in killing the well by using two important concepts. the first concept is the critical gas velocity, which controls the accumulation of kill fluid below the injection point. this was predicted by revising turner's (turner et al. 1969) model of terminal velocity for liquid droplets. the new proposed model considers the flow regime of the continuous phase when evaluating the drag coefficient, suggesting a value of 0.44 instead of the 0.2 proposed by turner et al. (1969). additionally, they incorporated the deviation angle from the vertical, as given by eq. 2 (flores-avila et al. 2003). vscrit = 14.27 σ ρl−ρg kdcos α ρg2 0.25 ,.......................................................................................................................(2) the second concept is the volume of kill fluid that falls and accumulates below the injection point, which can be predicted using the concept of static zero net liquid flow holdup (znlf). improved oil and gas recovery 3 zero net liquid flow hold-up. liquid hold-up is defined as the ratio of the liquid volume in a pipe portion to the total volume of that portion under downhole conditions. conversely, the zero net liquid flow (znlf) holdup expression arises when a portion of a well becomes filled with dropped liquid while gas flows through that well portion, rendering the liquid portion stagnant (flores-avila et al. 2002). typically, slip velocity is the difference between the absolute velocities of the gas and liquid phases. the absolute velocity is defined as the ratio between superficial velocity and its volumetric hold-up, as given in eq. 3. however, under vertical znlf conditions, the liquid is stagnant, resulting in a superficial liquid velocity of zero. thus, znlf is defined by eq. 4 (kanshio 2019): vs = vg − vl = vsg 1−hl − vsl hl ,...........................................................................................................................(3) vg0 = vsg 1−hl0 ,.................................................................................................................................................(4) where, hl0 = 1 − vsg vg0 ,...............................................................................................................................................(5) flores-avila et al. (2002) utilized the experimental results of arpandi et al. (1996), which were conducted for a gas-liquid cylindrical cyclone with multiphase inlet flow and continuous liquid phase withdraw from vessel bottom and gas exit from top as explained in figure 1, to calculate gas slip velocity (eq. 6) and, consequently, the zero net liquid flow (eq. 7). figure 1—gas-liquid cylindrical cyclone (flores-avila et al. 2003). vgo = 1.15 vsg + 0.35 g di(ρl−ρg) 3ρg kd ,...................................................................................................................(6) hl0 = [1 − vsg vg0 ](1 − ld lp ),............................................................................................................................(7) enhanced model in this study, we aimed to develop an enhanced model to account for the effect of liquid fall-off below the kill string. the dynamic kill mathematical model was established to evaluate the killing process in off-bottom scenarios. the model consists of two major components: the reservoir inflow performance model and the wellbore performance model. combining these models provides the actual well blowout deliverability, which serves as the starting point for the modeling process. l d l p improved oil and gas recovery 4 the model divides the well system into four distinct regions, as illustrated in figure 2. region 1 represents the formation, which is the source of the blowout fluid flow. region 2, located in the wellbore, encompasses the section where counter-current two-phase flow occurs, with upward-moving formation fluid and downwardmoving kill fluid, starting from the end of the kill string to the bottom of the well. region 3, also within the wellbore, represents co-current two-phase flow, where both formation and kill fluids move upward through the annulus from the end of the kill string depth to the surface. finally, region 4 is characterized by single-phase flow, with kill fluid moving downward inside the kill string. region 4 single phase flow (kill fluid) into the kill string region 3 two phase flow (formation and kill fluid) through the annular section region 2 two phase flow (formation and kill fluid) from the bottom-hole to the sting depth region 1 producing formation figure 2—off-bottom well blowout system modeling with four regions (vallejo-arrieta 2002). reservoir model (region 1). the reservoir model was constructed using forchheimer ’s equation (eq. 8) for radial gas flow in porous media. this model accounts for high gas velocities near the wellbore by incorporating a non-darcy gas flow term, as described in eq. 11 (ikoku 1980; forchheimer 1901). pr2 − pwf2 = a qsc + b qsc2 ,..............................................................................................................................(8) where, b = 1422 μg zr tr k ℎ [ ln 0.472 re rw ] ,....................................................................................................................(9) a = 3.161∗10−12 β ƴg zr tr ℎ2 1 re − 1 rw ,..............................................................................................................(10) β = 2.33∗1010 kg1.201 ,.................................................................................................................................................(11) wellbore model. the wellbore model is based on the general conservation equation and newton’s second law to derive the general form of the pressure gradient, as shown in eq. 12. this implies that the total pressure loss across the system is the sum of pressure losses due to hydrostatic pressure reduction, friction loss caused by the improved oil and gas recovery 5 shearing force between the fluid and the pipe wall, and pressure loss due to fluid acceleration. the acceleration component is typically negligible due to its minor effect on the total pressure loss value. dp dl total = dp dl elevation + dp dl friction + dp dl acceleration..............................................................(12) to enhance the model's accuracy, the effect of temperature changes was incorporated by using the wellbore temperature model proposed by hassan and kabir, as detailed in eq. 13 (hasan and kabir 2012; hasan and kabir 2018), ���� = ��� + 1−� �−� �� �� (�� ���� − �� ���� �� j g )................................................................................................(13) single phase flow (region 4). in this region, which contains only killing fluid, sea water is used due to the large volume required for the dynamic killing process, making water a practical choice. therefore, the general pressure gradient equation for this region can be expressed as shown in eq. 14 (in field units), dp dl total = ρl 144 + ( ρlfvl 2 772.17 ds )...................................................................................................................(14) concurrent two-phase flow (region 3). this region features concurrent flow, where both kill fluid (water) and reservoir fluid (gas) move in the same direction (upward) through the annulus, from the end of the drill string to the surface. in a two-phase flow scenario, the flow regime transitions through several stages: annular flow, churn flow, slug flow, and ultimately bubble flow as the liquid hold-up reaches its maximum value. to model this flow condition, the mechanistic two-phase flow model presented by hassan and kabir (2007) was employed. this model establishes specific conditions to identify the flow regime. once the flow type is detected, flow parameters are determined from table 1, and the nature of gas bubble rise velocity is selected. at this stage, eq. 15 can be used to calculate the gas void fraction (hg). hg = vsg co vm+v∞ .................................................................................................................................................(15) table 1—flow parameter according flow pattern and type. flow pattern flow parameter, �� gas rise velocity, �∞concurrent upward countercurrent bubble 1.2 2.0 �∞� slug 1.2 1.2 �∞ churn 1.15 1.15 �∞ annular 1.0 1.0 0 for the two-phase flow, mixture fluid parameters are computed based on the volumetric weighted average for the two phases, as illustrated in eqs. 16 through 19. hl = 1 − hg ,...................................................................................................................................................(16) ρm = ρlhl + ρghg ,........................................................................................................................................(17) ρm = ρlhl + ρghg ,........................................................................................................................................(18) µm = µlhl + µghg .........................................................................................................................................(19) countercurrent two-phase flow (region 2). region 2 is crucial in the off-bottom dynamic kill model, as it examines how the area below the kill string affects the required dynamic kill rate. this area is often neglected, but if the kill fluid coming out from the kill string falls down to the bottom of the well in the opposite direction improved oil and gas recovery 6 to the kicked fluid, it will contribute to the well-killing process. if the gas superficial velocity at the end of the kill string is less than the critical velocity, the kill fluid will fall down. to study this region, two different approaches can be utilized. the first approach involves using the twophase mechanistic model for countercurrent flow conditions as presented by hassan and kabir (2007). in this model, since the two-phase flows are in opposite directions, the void fraction equation is applied with a negative sign, as shown in eq. 20. hg = vsg co vm−v∞ ,...............................................................................................................................................(20) the second approach employs the dynamic zero net liquid hold-up (znlh) method to determine the liquid hold-up below the kill string. kolla et al. (2018) conducted laboratory tests to evaluate the dynamic znlh and developed a model that accounts for the fluid properties of both kick and kill fluids, as well as the superficial velocity of the kill fluid. this model is detailed in eqs. 21 through 25 (kolla et al. 2018). vsg∗ 2 + vsl∗ 2 = 1,..............................................................................................................................................(21) vsg∗ = vsg ρg0.5 g d ρl − ρg −0.5 ,...................................................................................................................(22) vsl∗ = vslz2n ρln g d ρl − ρg −n ,.....................................................................................................................(23) n = 25µ g d σ 0.25 ,..........................................................................................................................................(24) hldz = vslz vslz+vsg ............................................................................................................................................(25) model verification. to assess the accuracy of the model, its results were validated against actual well blowout and killing data from indonesia's arun field (kouba et al. 1993) and the case analyzed by gillespie et al. (1990), which involved a potential dynamic kill of a workover well under off-bottom conditions. arun field blowout. for the arun field blowout case, reservoir data and wellbore input data, as detailed in table 2, were used to establish the well flow model. the model output was then compared with the actual data. initially, the data were used to construct the well’s blowout ipr/vlp model, which provided the initial conditions for the well-killing process and resulted in a well blowout rate of 454,000 mmsf/d (figure 3). the same data in table 2 were also used to develop the well ipr/vlp performance curve using commercial software (prosper), yielding a well blowout rate of 473,841 mmsf/d (figure 4 and table 3). table 2—blowout data from mobil oil indonesia's arun field well c-ii-2. input data value reservoir pressure (psia) 7,100 reservoir temperature (°f) 230 gas specific gravity 0.6 casing id (in) 8.535 drillpipe od (in) 5.00 drillpipe id (in) 4.275 pipe roughness (in) 0.0018 measured depth (ft) 10,210 true vertical depth (ft) 9,650 improved oil and gas recovery 7 figure 3—well's blowout rate using ipr/vlp model. figure 4—well's blowout rate using commercial software. table 3—summary of well ipr/vlp performance using commercial software. parameters values units gas rate 473,841 mmscf/day oil rate 0 stb/day water rate 0 stb/day liquid rate 0 stb/day solution node pressure 6672.51 psia dp friction 5947.1 psi dp gravity 710.399 psi secondly, the verification of the well-killing dynamic model was conducted by comparing the model results for the killing rate of arun field well c-ii-2 with the actual well-killing rate data. the model predicted a minimum pumping rate of 84.5 bbl/min with 7216 psi bottom hole flowing pressure compared with reservoir improved oil and gas recovery 8 pressure 7100 psi which explained in figure 5. in practice, the well blowout was effectively controlled when the pumping rate was increased to 85 bbl/min, and reignited when the pumping rate was reduced to 80 bbl/min. figure 5—arun field well c-ii-2 predicted dynamic killing rate. gillespie’s case in workover well. gillespie et al. (1990) analyzed a potential dynamic kill for a workover gas well under off-bottom conditions. the study focused on a gas recycling well within an enhanced oil recovery (eor) project, which was completed with 2-7/8” tubing and snubbed with 1-1/4” coiled tubing to wash sand and dynamically kill the well using a 9.5 lbm/gal sodium chloride (nacl) solution. reservoir data are provided in table 3, and the well schematic is shown in figure 6. figure 6—well completion with kill string (gillespie et al 1990). improved oil and gas recovery 9 table 4—reservoir data (gillespie et al. 1990). parameters values net thickness, ft 110 permeability, md 100 porosity, % 22 water saturation, % 40 temperature, of 172 reservoir pressure, psi 4,700 the reservoir and wellbore data listed in table 4 were used in the model to determine the minimum dynamic kill rate using 9.5 lbm/gal killing fluid with 1-1/4” coiled tubing at a depth of 10,053 ft. the model predicted a killing rate of 0.8 bbl/min, as presented in figure 7, while gillespie reported a range of killing rates between 0.5 and 1.0 bbl/min (gillespie et al. 1990). figure 7—minimum dynamic killing rate in work over well case with 1-1/4” ct at 10053 ft. case studies the primary objective of this study is to evaluate the performance of dynamic well control techniques under off-bottom conditions and to identify their limitations. to achieve this, a computer model was developed using the python programming language to simulate and analyze dynamic killing scenarios for off-bottom gas blowouts. arun field well c-ii-2 case. a critical aspect of the modeling process is the area below the end of the kill string (region 2), which was modeled using three different approaches. for the case study of arun field well c-ii-2, figures 8 through 10 illustrate the well inflow/vlp performance with the end of the kill string positioned at 8,000 ft. the killing rate was maintained at 3,850 gal/min, using water as the killing fluid. the modeling approaches included static znlh (figure 8), dynamic znlh (figure 9), and two-phase flow model (figure 10). the static znlh model resulted in the lowest bottom hole flowing pressure (7,198 psi), whereas the twophase flow model showed the highest bottom hole flowing pressure (7,478 psi) during well-killing operations. not accounting for liquid fall-off led to a higher required killing rate (4,390 gal/min) to halt gas influx. improved oil and gas recovery 10 conversely, when maintaining a fixed bottom hole flowing pressure and performing sensitivity analysis on the killing rate, the static znlh model indicated a higher required killing rate (3,850 gal/min), while the twophase flow model suggested a lower killing rate (3,765 gal/min). figure 8—the predicted off-bottom dynamic killing rate of arun field well c-ii-2 using static znlh. pwf=7356 psi figure 9—the predicted off-bottom dynamic killing rate of arun field well c-ii-2 using dynamic znlh. pwf = 7198 psi improved oil and gas recovery 11 pwf=7478 psi figure 10—the predicted off-bottom dynamic killing rate of arun field well c-ii-2 using two phase flow model. gillespie’s case. figures 11 through 13 illustrate the well inflow/vlp performance for gillespie’s case with the end of the kill string positioned at 2,024 ft. the analysis was conducted at a constant killing rate of 3.7 bbl/min, using water as the killing fluid, and applied static znlh, dynamic znlh, and two-phase flow model. the static znlh model resulted in the lowest bottom hole flowing pressure (4,909 psi), while the two-phase flow model showed the highest bottom-hole flowing pressure (5,393 psi) during the well-killing operation. ignoring liquid fall-off led to a higher killing rate (295 gal/min) required to stop gas influx. conversely, when maintaining a constant bottom-hole flowing pressure and performing sensitivity analysis on the killing rate, the static znlh model indicated a higher required killing rate (155 gal/min), whereas the two-phase flow model suggested a lower killing rate (145 gal/min). figure 11—the predicted off-bottom dynamic killing rate of gillespie’s case using static znlh. pwf = 4909 psi improved oil and gas recovery 12 figure 12—the predicted off-bottom dynamic killing rate of gillespie’s case using dynamic znlh. figure 13—the predicted off-bottom dynamic killing rate of gillespie’s case using using two-phase flow model. results and discussion one of the objectives of the model is to demonstrate the effect of well operating conditions on the killing parameters, and some of the figures generated by the model illustrate this effect. temperature. temperature has a significant effect on the properties of killing fluids. in the first case study (arun field well c-ii-2), despite using water as the killing fluid, its properties changed dramatically with depth due to temperature variations. figures 14 and 15 illustrate the impact of temperature on water density and viscosity. water density decreased from 62.5 pounds of cuber foot (pcf) at surface conditions to 59.5 pcf at downhole conditions, while water viscosity decreased from 1.3 cp at the surface to 0.2 cp at total well depth. these changes in water properties will influence the required killing rate, with the effect being even more pronounced if a non-newtonian fluid were used as the killing fluid. pwf = 5001 psi pwf = 5393psi improved oil and gas recovery 13 figure 14—effect of temperature on water density. figure 15—effect of temperature on water viscosity. figure 16—the effect of killing depth on the required kill rate. improved oil and gas recovery 14 killing depth. it is evident that the depth of the kill string has a crucial effect on the required kill rate. figure 16 illustrates how the depth of the kill string impacts the kill rate in the second case (gillespie’s case). as the depth of the kill string decreases, the required kill rate increases, and follows a logarithmic relationship. gas influx rate. as previously discussed, the key criterion determining whether the kill fluid will fall to the bottom of the well or move upward with the gas influx is the critical gas velocity (vc). if the superficial gas influx velocity (vsg) at the end of the kill string depth exceeds the critical velocity, the kill fluid will fall. figures 17 to 20 illustrate vsg and vc with depth, ranging from the end of the kill string at 2,000 ft to the well’s bottom, under different gas influx rates. at low influx rates, the superficial gas velocity is low, resulting in a larger gap between vsg and vc. as the gas influx rate increases, vsg rises and vc decreases until they approach a certain limit (influx rate). at this point, vsg becomes lower than vc, and the kill fluid will no longer fall but instead will flow upward with the kick fluid to the surface. it is important to note that both velocities decrease with increasing well depth, primarily due to the effect of pressure on gas density. additionally, the critical gas velocity decreases with increasing gas influx rate because the higher bottom hole pressure results in greater gas density and consequently a lower critical velocity. figure 17—vc and vsg with depth at gas influx rate of 1 mmscf/d. figure 18—vc and vsg with depth at gas influx rate of 10 mmscf/d. improved oil and gas recovery 15 figure 19—vc and vsg with depth at gas influx rate of 24 mmscf/d. figure 20—vc and vsg with depth at gas influx rate of 25 mmscf/d. conclusions in this study, three approaches were employed to develop an optimal model for predicting the dynamic kill technique with the kill string positioned off-bottom. given the limited practical efforts to model this killing condition, the results obtained can be generalized for modeling off-bottom dynamic killing in gas blowout wells. the constructed model was validated with actual well killing data, and the following conclusions were drawn: 1. the static zero net liquid hold-up (znlh) model resulted in the lowest bottom hole flowing pressure, indicating a higher kill rate, whereas the two-phase flow model produced the highest bottom hole flowing pressure, reflecting a lower kill rate for well killing operations. 2. temperature significantly impacts the properties of the killing fluid, even when water is used. changes in temperature alter the fluid's density and viscosity, which in turn affects the required killing rate. 3. the required kill rate exhibits an inverse logarithmic relationship with the depth of the kill string. 4. liquid fall-off below the end of the kill string will continue if the superficial gas velocity is lower than the critical gas velocity. as the gas influx rate increases, the superficial gas velocity rises and the critical gas velocity decreases until a certain limit (gas influx rate) is reached, beyond which the liquid fall-off ceases. improved oil and gas recovery 16 5. the critical gas velocity is inversely proportional to the gas influx rate. higher gas influx rates lead to increased bottom hole pressure and higher gas density, resulting in a lower critical gas velocity. 6. both superficial and critical gas velocities decrease with increasing well depth due to the effect of pressure on gas density. recommendation for the future work, i would recommend to modify the model to utilize non-newtonian fluid to be used as killing fluid. nomenclature a = well vertical depth, ft; co = flow parameter, dimensionless; cp = heat capacity, btu lbm−℉ ; dmax = maximum droplet size, ft; di = pipe internal diameter, ft; ds = kill string internal diameter, in; f = moody friction factor, dimensionless; g = gravity acceleration, ft/sec2; gg = geothermal gradient, of/ft; hl = liquid hold-up, fraction; hl0 = liquid hold-up at znlh condition, fraction; hg = gas void fraction, fraction; h = reservoir thickness, ft; j = ft-lbf to btu conversion factor, dimensionless; kd = sphere drag coefficient, dimensionless; k = reservoir permeability, md; l = total well measured depth, ft; ld = piper length with annular flow, ft; lp = pipe length, ft; lr = relaxation distance parameter, ft-1; pr = reservoir pressure, psi; pwf = flowing bottom hole pressure, psi; qsc = gas flow rate at surface condition, scf/day; rw = wellbore radius, ft; re = reservoir radius, ft; t = temperature, r; tann = annular fluid temperature, of; tei = undisturbed formation temperature, of; improved oil and gas recovery 17 greek: vscrit = critical gas velocity, ft/sec; vs = slip velocity, ft/sec; vg = gas velocity, ft/sec; vl = liquid velocity, ft/sec; vsg = superfacial gas velocity, ft/sec; vsl = superfacial liquid velocity, ft/sec; vgo = gas slip velocity at znlh condiction, ft/sec; vm = mixture velocity, ft/sec; v∞ = gas rise velocity, ft/sec; z = gas compressibility factor, dimensionless; σ = gas/liquid interfacial tension, lbm/sec2; α = deviation angle from vertical, degree; μg = gas viscosity, cp; μl = liquid viscosity, cp; μm = mixture viscosity, cp; β = turbulance factor, ft-1; ƴg = gas specific gravity, dimensionless; ρl = density of liquid phase, lb/ft3; ρg = density of continuous gas phase, lb/ft3; ρm = mixture density, lb/ft3; conflicting interests the author(s) declare that they have no conflicting interests. references arpandi, i. a., ashutosh r. j., shoham, o., et al. 1996. hydrodynamics of two-phase flow in gas-liquid cylindrical cyclone separators. spe journal 1: 427-436. flores-avila, f. s., smith, j. r., bourgoyne, a. t., et al. 2002. experimental evaluation of control fluid fallback during off-bottom well control: effect of deviation angle. paper presented at the iadc/spe drilling conference, dallas, texas, usa, 26-28 february. spe-74568-ms. flores-avila, f. s., smith, j. r., bourgoyne, a. t. 2003. new dynamic kill procedure for off-bottom blowout wells considering counter-current flow of kill fluid. paper presented at the spe/iadc middle east drilling technology conference and exhibition, abu dhabi, united arab emirates, 20-23 october. spe-85292-ms. forchheimer, p.1901.wasserbewegung durch boden. zeitschrift der verein deutsher ingenieure 45:1731 gillespie, j. d., morgan, r. f., and perkins, t. k. 1990. study of the potential for an off-bottom dynamic kill of a gas well having an underground blowout. spe drilling engineering 5(3): 215–219. spe-17254-pa. hasan, a. r. and kabir, c.s. 2012. wellbore heat-transfer modeling and applications. journal of petroleum science and engineering 87:127-136. hasan, a. r. and kabir, c.s. 2018. fluid flow and heat transfers in wellbores (second edition). society of petroleum engineers. ikoku, c. u. 1980. natural gas engineering. tulsa: penn well publishing co. https://doi.org/10.2118/74568-ms https://doi.org/10.2118/85292-ms improved oil and gas recovery 18 kolla, s. s., mohan, r. s., and shoham, o. 2018. mechanistic modeling of liquid carry-over for 3-phase flow in glcc© compact separators. paper presented at the asme 5th joint us-european fluids engineering division summer meeting, quebec, canada. 15-20 july. kouba, g. e., macdougall, g. r., and schumacher, b. w. 1993. advancements in dynamic kill calculations for blowout wells. spe drilling and completion 8(3): 189-194. spe-22559-pa. kanshio, s. 2019. an empirical correlation for zero-net liquid flow in gas-liquid compact separator. american journal of chemical engineering 7(3):81-89. turner, r.g., hubbard, m.g., and dukler, a.e. 1969. analysis and prediction of minimum flow rate for the continuous removal of liquid from gas wells. journal of petroleum technology 21(1): 1475-1482 vallejo-arrieta, v. g. 2002. analytical model to control off-bottom blowouts utilizing the concept of simultaneous dynamic seal and bullheading. phd dissertation, louisiana state university, baton rouge, louisiana. yin, b., ren, m., liu, s., et al. 2023. dynamic well killing method based on y-tube principle when the drill bit is offbottom. engineering science and technology, an international journal 41(1): 101385. mohamed yossef, spe, is a senior drilling engineer started working in 2007 with belayim petroleum company (petrobel) in cairo, egypt. he worked as drilling well site leader for saudi aramco from 2018 to 2020 and from 2022 to 2023, and then as senior well site leader in majnoon oil field basra, iraq. he is a certified well control instructor and assessor for both international well control forum (iwcf) and international association of drilling contractors (iadc). mr. yossef has 17 years of drilling operations experience. he specializes in modern water shut off techniques and predicting drilling rate of penetration for hybrid bits. mr. yossef holds b.sc. and m.sc. degree in petroleum engineering from the suez university, egypt. adel salem is a professor of petroleum and mining engineering, suez university. prof. salem holds a phd in petroleum engineering in 2008 from leoben university, austria, and a b.sc. and m. sc. from suez canal university, egypt, all in petroleum engineering. prior to suez university, prof. salem served as a full-time assistant professor at american university in cairo (auc) from 2011 to 2014, and then as an associate professor at petroleum engineering department, future university in egypt from 2014 to 2016. prof. salem has published more than 100 papers in areas such as eor, characterization of formation damage, nanotechnology applications for eor and smart drilling fluids, oil shale, well testing, and radial drilling. developing dynamic killing technique for off-botto abstract introduction enhanced model case studies results and discussion conclusions recommendation nomenclature conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1305 received august 16, 2024; revised august 24, 2024; accepted september 1, 2024. *corresponding author: masud.babayev2022@khazar.org 1 enhancing sagd efficiency: a study on steam quality and injection rate optimization masud babayev* and grigorii penkov, khazar university, baku, azerbaijan; sardar asadov, university of tulsa, oklahoma, usa abstract the production of heavy oil presents a significant challenge due to its high viscosity, which limits natural flow. this study aims to assess the effectiveness of steam assisted gravity drainage (sagd) in enhancing heavy oil recovery by employing a comprehensive numerical simulation model. a commercial compositional simulator was utilized to evaluate the impact of steam quality and injection rate on recovery efficiency, using reservoir properties from oilfield alpha. the results demonstrate that optimizing steam quality is critical, with an increase from 0.6 to 0.8 leading to an improvement in recovery from 43.58% to 46.16%. additionally, higher injection rates were shown to substantially boost oil production, with simulations at 700 bbl/day achieving a final recovery factor of 52.691%. these findings highlight the importance of optimizing both steam quality and injection rates to maximize sagd performance, providing valuable insights for future field applications and the refinement of heavy oil production strategies. introduction global energy demands are increasing rapidly, while conventional resources are depleting. consequently, there is a growing need to tap into unconventional energy resources, which include tight gas/oil, gas/oil shale, coalbed methane, gas hydrates, and heavy oil. extracting hydrocarbons from these subsurface sources requires advanced technological solutions. within the oil sector, a distinction is made between conventional (light) oils and unconventional oils, which include heavy oil, extra-heavy oil, and bitumen. differentiating between these requires laboratory analysis of fluid samples. heavy oils are characterized by higher levels of oxygen, nitrogen, sulfur, and heavier oil fractions compared to light oils (santos et al. 2014). heavy crude oil is a type of reservoir oil with greater viscosity and density than light oil, making it more difficult to flow through reservoirs. it has a higher molecular weight and complex composition. heavy crude oil is defined as any petroleum liquid with a gravity of less than 20°api and a reservoir viscosity ranging from 50 to 5,000 centipoises. although there is some variation in classification, crude oils with viscosities exceeding 10 cp and up to 10,000 cp are also considered heavy. according to the world energy council (2007), heavy oil is defined as having a gravity below 22.3°api or a density above 0.920, while oils with an api gravity of less than 10 ° are classified as extra-heavy. heavy oils are further characterized by high viscosity, specific gravity, asphaltene content, carbon residues, low hydrogen-to-carbon ratios, and elevated levels of sulfur, nitrogen, heavy metals, and acid numbers. these characteristics are typically the result of microbial degradation of conventional light crude oil reservoirs over geological time (wei 2016; çağdaş 2007; luo 2012). mailto:masud.babayev2022@khazar.org improved oil and gas recovery 2 in the oil and gas industry, bitumen from oil sands is occasionally classified as extra-heavy crude oil, even if its api gravity is below 10 ° . however, some experts distinguish bitumen from extra-heavy oil due to differences in the degree of microbial degradation and erosion over extended geological periods. overall, producing heavy oil is generally less challenging than extracting bitumen, primarily due to differences in viscosity. in figure 1, the global distribution of heavy oil reserves and the corresponding production technologies are depicted. canada, the united states, venezuela, and several other nations are among the largest holders of heavy oil reserves worldwide. among the various extraction methods, steamassisted gravity drainage (sagd) stands out as the most commonly employed. this preference is due to its ability to achieve the highest recovery factors, making it the favored method for enhancing oil production from challenging reservoirs. figure 1—distribution of heavy oil around the world (chopra and lines 2008). as the demand for energy continues to rise, heavy oil extraction is becoming an increasingly attractive option. however, heavy oils pose significant challenges due to their higher viscosity compared to light oils, necessitating the use of thermal technologies for efficient reservoir exploitation. thermal methods, which include hot water injection, steam injection or steam drive, steam-assisted gravity drainage (sagd), cyclic steam stimulation, and in-situ combustion, are essential for reducing the viscosity of heavy oils, as viscosity decreases with increasing temperature. steam-assisted gravity drainage (sagd) is a widely used thermal recovery method for extracting bitumen and super-heavy oil. despite its effectiveness, sagd is associated with high costs and significant carbon intensity due to the extensive use of steam. according to nduagu et al. (2017), sagd reservoirs rank among the most expensive to produce worldwide, making the optimization of steam utilization a critical factor for operators. sagd operates by first injecting high-quality steam into the reservoir to mobilize the viscous crude oil between injection and production wells (figure 2). the process involves the formation of a steam chamber as steam is injected from an upper horizontal well, heating the oil, which then drains by gravity into a lower horizontal well along with the steam condensate (singfield 2016; li et al. 2020). common well configurations for sagd include dual-horizontal and vertical-horizontal well patterns. the dual-horizontal well setup typically involves two parallel horizontal wells spaced 4-6 meters apart, with the lower well dedicated to oil production and the upper well used for steam injection (tian and sun 2013; li et al. improved oil and gas recovery 3 2017). in the vertical-horizontal configuration, steam is injected through vertical wells while oil is produced from a lower horizontal well. this setup is advantageous for reservoirs with thick layers of super-heavy oil but is less effective for thin-layer reservoirs due to the limited rise of the steam chamber and constrained gravity drainage. to improve the economic viability of exploiting thin-layer super-heavy oil reservoirs, one strategy involves reducing the vertical distance between the injection and production wells in the dual-horizontal well sagd configuration. li (2014) conducted research on applying sagd in narrow super-heavy oil reservoirs, focusing on increasing the horizontal distance between wells to expand the steam chamber and enhance recovery. figure 2—schematic representation of sagd process (singfield 2016). steam quality, defined as the proportion of steam vapor in a steam-water mixture, plays a critical role in heat transfer and enhancing oil mobility during steam-assisted gravity drainage (sagd) operations. the injection rate, representing the volume of steam injected per unit time, directly influences oil production and the development of the steam chamber. the cumulative steam-oil ratio (csor), which is the total volume of steam injected divided by the total volume of oil produced, serves as a key metric for evaluating the efficiency of steam usage in oil recovery. economically viable csor values typically range from 2 to 10 bbl/bbl (gates and chakrabarty 2006). recent studies have focused on optimizing sagd through various parameters. for instance, swadesi et al. (2020) explored the impact of steam quality and injection rate on cyclic steam stimulation (css) using the cmg stars simulator, highlighting the importance of optimizing these factors to improve steam injection efficiency. however, despite advancements in sagd technology, most research has primarily concentrated on well spacing and its influence on sagd efficiency, leaving a significant gap in understanding how steam quality and injection rate specifically affect sagd performance. addressing these parameters is critical as they are more easily adjusted compared to well patterns, which require extensive geological data. with the development of tools like cmg stars, it is now possible to analyze and optimize sagd processes by varying steam quality and injection rates. this research aims to bridge the existing gap by investigating how modifications in these two factors can enhance the effectiveness and cost-efficiency of heavy oil recovery methods. methodology in this study, the sagd process was applied to a heavy oil reservoir, utilizing a dual-horizontal well configuration. the upper horizontal well was employed for steam injection, while the lower horizontal well facilitated the production of oil and condensed steam. the study focused on varying key parameters, including improved oil and gas recovery 4 well spacing, steam quality, and injection rate. to analyze these variables, the cmg stars reservoir simulator was employed to create and assess a model, providing critical insights into the process. key technical metrics such as the oil recovery factor (rf), the cumulative steam-oil-ratio (csor), and cumulative oil production were used to evaluate the system's performance. the methodology was developed with reference to the cmg stars manual (2021), which guided the simulation process. input parameters relevant to common heavy oils, including rock and fluid properties, were determined. table 1 presents these parameters and values for oilfield alpha. table 1—input parameters and their values for the reservoir simulation model. input parameter value grid type cartesian number of grid blocks 25 × 15× 10 grid block dimensions 1000 ft × 300 ft × 90 ft grid top 1300 ft reference depth 1300 ft owc depth 1380 ft initial pressure 650 psi reservoir temperature 110 f porosity 0.308 or 30,8 % horizontal permeability 1700 md vertical permeability 1400 md initial oil saturation 0.8 or 80 % oil gravity 9.8 api oil viscosity 15780 cp in this model, the absence of a gas phase results in certain parameters exhibiting a linear relationship with pressure. figures 3 and 5 demonstrate this by showing how the formation volume factor of oil (bo), oil density, and oil viscosity vary with changes in pressure. figure 3—variation of oil formation volume factor (bo) with pressure. improved oil and gas recovery 5 figure 4—variation of oil density with pressure. figure 5—variation of oil viscosity with pressure. the primary challenge in heavy oil production is the high viscosity of the oil. thermal methods are employed to reduce viscosity by raising the temperature. since each heavy oil type possesses unique properties, the viscosity-temperature relationship can differ across fields. this variation is depicted in figure 6 for the current model. improved oil and gas recovery 6 figure 6—relationship between oil viscosity and temperature. as previously noted, the absence of a gas phase in this context is significant. figure 7 presents the water-oil relative permeability curves, providing further insight into the fluid flow characteristics and aiding in the refinement of the reservoir model. figure 7—relative permeability curves for water and oil. after defining all input parameters, the cmg stars simulator was employed to create a 3d representation of the conceptual model, as shown in figure 8. this figure illustrates the grid layout and the depth of each layer. improved oil and gas recovery 7 figure 8—3d view of the conceptual reservoir model. for the sagd process, two horizontal wells were drilled with an 18-foot (5.4864 m) spacing, selected as the optimal distance for production. this spacing falls within the commonly cited range of 4-6 meters in the literature. a smaller spacing could result in early water breakthrough due to high vertical permeability. figure 9 provides a cross-sectional view of the setup. table 2 lists the operational parameters required to initiate the simulation. figure 9—cross-sectional view of sagd process. table 2—operational constraints and parameters for wells. recovery method injector constraint producer constraint sagd max bhp-950 psi max stf 400 bbl/day min bhp-500 psi max stw 500 bbl/day results and discussions after the initial simulation run, the calculated reserves are summarized in table 3. this table reflects only the oil and water phases, as there is no gas phase present. improved oil and gas recovery 8 table 3—results of reserves calculation from reservoir simulation. volume unit value gross formation ft3 2.70×107 formation pore ft3 8.316×106 aqueous phase ft3 1.6632×106 oil phase ft3 6.6528×106 gaseous phase ft3 0 the analysis evaluates the effectiveness of sagd operations using two horizontal wells, emphasizing the role of steam quality in optimizing performance. the sensitivity analysis investigates the impact of steam quality at ratios of 0.6, 0.7, and 0.8 on sagd efficiency. figure 10, derived from cmg stars data, compares steam characteristics with the recovery factor (rf). the key parameters assessed include the steam-oil ratio (sor) and the recovery factor. figure 10—effect of steam quality on oil recovery factor as depicted in figure 10, the orange line associated with a steam quality of 0.8 indicates a superior recovery factor, suggesting that higher steam quality corresponds to increased recovery efficiency. conversely, the green line demonstrates the lowest recovery factor. until 2017, both lines exhibit similar trends; however, they diverge thereafter, with the orange line achieving its peak performance. this trend contrasts with the steam-oil ratio, where higher steam quality results in a lower ratio. this behavior is attributed to the enhanced oil production potential at higher steam quality, as illustrated in figure 11. improved oil and gas recovery 9 figure 11—csor for different steam qualities. the final simulation results are summarized in table 4, offering a detailed comparison of the outcomes. after identifying the optimal steam quality of 0.8, the next step is to determine the maximum injection rate. while higher injection rates theoretically enhance production, it is crucial to account for the associated steam consumption. the evaluation includes injecting water at rates of 400, 500, 600, and 700 barrels per day (bbl/day), with steam generation adjusted according to the specified steam quality. figures 12 and 13 compare the versatility of different injection rates, revealing that increased injection generally leads to improved optimization. figure 11 illustrates the recovery factor (rf), showing that the results for 700 bbl/day and 600 bbl/day are quite similar, with only minor differences. this similarity underscores the importance of considering economic factors in the decision-making process. table 4—rf, csor, and cumulative oil production for various steam qualities. steam quality recovery factor, % cum. steam-oil ratio, bbl/bbl cum. oil production, bbl 0.8 46.16 2.003 538457.12 0.7 45.65 2.032 532477.12 0.6 43.58 2.137 508422.03 after identifying the optimal steam quality of 0.8, the next step is to determine the maximum injection rate. while higher injection rates theoretically enhance production, it is crucial to account for the associated steam consumption. the evaluation includes injecting water at rates of 400, 500, 600, and 700 barrels per day (bbl/day), with steam generation adjusted according to the specified steam quality. figures 12 and 13 compare the versatility of different injection rates, revealing that increased injection generally leads to improved optimization. figure 12 illustrates the recovery factor (rf), showing that the results for 700 bbl/day and 600 bbl/day are quite similar, with only minor differences. this similarity underscores the importance of considering economic factors in the decision-making process. improved oil and gas recovery 10 figure 12—impact of injection rates on recovery factor. recovery factor (rf) alone is not a sufficient metric for evaluating economic viability. specifically, the cumulative steam-oil ratio (csor) at an injection rate of 400 bbl/day is not the most economical option. according to gates and chakrabarty (2006), an economically acceptable csor falls within the range of 2 to 10 bbl/bbl. during the 2015-2017 period, higher csor values were observed due to the initial kick-off phase; however, all rates eventually decreased below this threshold. the 700 bbl/day injection rate maintains a stable csor similar to that of the 600 bbl/day rate but achieves a lower ratio compared to the latter. thus, in terms of balancing economic viability and recovery efficiency, the 700 bbl/day rate is preferable over the 600 bbl/day rate. for a detailed comparison of csor at different injection rates, refer to figure 13. figure 13—csor for various injection rates. table 5 outlines the sensitivity of sagd operations to variations in both steam quality and injection rate. in the initial scenario, with a steam quality of 0.6 and an injection rate of 400 bbl/day, the recovery factor (rf) was 46.159%. however, as both steam quality and injection rate were increased, the recovery improved significantly, with the rf rising to 52.691% in the subsequent scenario. while further increases in the injection rate could potentially enhance recovery, it is important to note that under an injection pressure of 950 psi, the improved oil and gas recovery 11 maximum injection rate achieved was 700 bbl/day. the 950 psi injection pressure is a critical parameter included in the operational considerations for this analysis. table 5—rf and csor for varying injection rates. steam quality injection rate (bbl/day) oil recovery factor (%) cum. steam-oil ratio (bbl/bbl) cum. oil production (bbl) 0.8 400 46.159 2.002 538457.12 500 47.514 2.428 554441.62 600 52.015 2.566 606867.43 700 52.691 2.541 614627.5 conclusions this study utilized the cmg stars simulator to assess the impact of steam quality and injection rate on the effectiveness of steam-assisted gravity drainage (sagd) techniques. the methodology involved conducting multiple simulation scenarios with varying steam qualities and injection rates to analyze their influence on recovery factors and steam-oil ratios. the results clearly indicate that these parameters play a crucial role in determining the efficiency and success of sagd operations. 1. steam quality: the analysis revealed that higher steam quality leads to improved oil recovery while reducing the steam-oil ratio. the sensitivity analysis focused on steam qualities of 0.6, 0.7, and 0.8, with the highest recovery factor observed at a steam quality of 0.8. therefore, optimizing steam quality is essential for achieving better energy efficiency in sagd operations. 2. injection rate:the injection rate was identified as another critical factor in enhancing sagd process efficiency. higher injection rates result in improved recovery factors by expanding the steam coverage area. for instance, at an injection rate of 700 bbl/day under 950 psi-the maximum rate achieved-a significant increase in oil production was observed. optimizing the injection rate is, therefore, a key requirement for maximizing oil recovery in sagd processes. in conclusion, by strategically improving steam quality and injection rates, sagd operations in heavy oil fields can achieve optimal performance levels. this research underscores the importance of adjusting these parameters to enhance recovery factors and boost oil production. nomenclature bhp = bottom hole pressure, psi; csor = cumulative steam-oil ratio, bbl/bbl; eor = enhanced oil recovery, %; injection rate = volume of fluid injected into a well per day, bbl/day; owc = oil-water contact; rf = recovery factor, %; sagd = steam-assisted gravity drainage; sor = steam-oil ratio, bbl/bbl; steam quality = percentage of steam in a steam-water mixture, %; stf = surface fluid rate, stb/day; stw = surface water rate, stb/day; bo = formation volume factor; g = gravity, api; krow = relative permeability to oil; improved oil and gas recovery 12 krw = relative permeability to water; p = pressure, psi; sw = water saturation, %; t = temperature, °f; μ = viscosity, cp; ρ = density, lb/ft³. conflicting interests the author(s) declare that they have no conflicting interests. references butler, r. m. 2001. some recent developments in sagd. journal of canadian petroleum technology 40(1): 18-22. çağdaş, a. 2007. enhancing petroleum recovery from heavy-oil fields by microwave heating. ms thesis, middle east technical university, cankaya, turkey. chopra, s. and lines, l. 2008. introduction to this special section: heavy oil. the leading edge 27(9): 11041106. cmg stars manual. 2021. computer modelling group ltd. gates, i. d. and chakrabarty, n. 2006. optimization of steam-assisted gravity drainage (sagd) in ideal mc. murray reservoir. journal of canadian petroleum technology 45(1):54-62. li, h, xiong, b., zhang, h., et al. 2017. technical review on the development of single-well sagd in foreign heavy oil reservoirs. natural gas and oil 35(1): 84-88. li, l. 2014. the applicability study for sagd in the thin super heavy oil reservoir. phd dissertation, china university of petroleum (east china), qingdao, shandong, china. li, r., chen, z, wu, k, et al. 2020. review the effective recovery of sagd production for extra and super heavy oil reservoirs. science sinica technologica 50(6):729-741. luo, w. 2012. coupling of hydrocarbon solvents and hot water for enhanced heavy oil recovery. ms thesis, university of regina, regina, saskatchewan, canada. nduagu, e., sow a., umeozor, e., et al. 2017. economic potentials and efficiencies of oil sands operations: processes and technologies. report no. 164, canadian energy research institute, calgary, alberta, canada. santos, r. g., loh, w., bannwart, a. c., et al. 2014. an overview of heavy oil properties and its recovery and transportation methods. brazilian journal of chemical engineering 31(3): 571-590. singfield, a. 2016. breakthrough solvent tech promises benefits for oil sands. https://www.vistaprojects.com/solvent-technology-promises-oil-sands-benefits/ (accessed on 20 march 2024). swadesi, b., suranto, j., widiyaningsih, i., et al. 2020. optimization study of integrated scenarios on cyclic steam stimulation (css) using cmg stars simulator. journal of petroleum and geothermal technology 1(8):3315. tian, h. z. and sun, y. 2013. operation parameters optimization of steam flooding with vertical and horizontal wells. lithology and reservoir 25(3):127-131. wei, z. 2016. oil recovery strategies for thin heavy oil reservoirs. ms thesis, university of calgary, calgary, alberta, canada. world energy council. 2007. survey of energy resources 2007: natural bitumen definitions. https://www.osti.gov/etdeweb/servlets/purl/21115911 (accessed on 20 march 2024). https://www.vistaprojects.com/solvent-technology-promises-oil-sands-benefits/ https://www.osti.gov/etdeweb/servlets/purl/21115911 improved oil and gas recovery 13 masud babayev is a junior reservoir engineer at socar oil and gas research and design institute. he holds a master’s degree in petroleum-gas engineering from khazar university. his primary research interests are in simulation and modeling within the petroleum engineering field. dr. grigorii penkov is an associate professor at the department of petroleum engineering at khazar university, baku, azerbaijan. his research interests are the application of geo-mechanics in the petroleum industry and enhanced oil recovery. sardar asadov is a ph.d. candidate at the university of tulsa, specializing in numerical modeling of unconventional fields, analytical tank modeling for enhanced oil recovery (eor) activities, closed-loop reservoir management, history matching and field optimization using machine learning proxies. he holds a b.sc. in petroleum engineering from azerbaijan state oil academy and an m.sc. in petroleum engineering from istanbul technical university. abstract introduction methodology results and discussions conclusions nomenclature conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1261 received june 12, 2023; revised september 20, 2023; accepted november 16, 2023. *corresponding author: weirong.li@xsyu.edu.cn 1 exploring influential factors for composite flooding with polymer viscosity reducers in heavy oils min zhang, weirong li*, shide yan, xi’an shiyou university, xi’an, china; zhengbo wang, zhaoxia liu, research institute of petroleum exploration and development, petrochina, beijing, china; keze lin, china university of petroleum (beijing), beijing, china; hongliang yi, petrochina liaohe oilfield company, panjin, china abstract extracting heavy oil presents significant challenges due to its high viscosity, poor fluidity, elevated asphalt content, and the complexities involved in its development. traditional extraction methods often fall short of meeting the developmental needs for such oil. currently, the use of polymer viscosity reducer composite flooding technology has shown promising results both domestically and internationally in heavy oil extraction. while the prospects for this technology are encouraging, there is limited research on the primary factors of the polymer viscosity reducer affecting oil recovery, underscoring the need for further investigation. a numerical model was formulated using the stars module of cmg to assess the development of heavy oil extraction via viscosity reducer flooding, polymer flooding, and polymer with viscosity reducer composite flooding. the study contrasted the impacts of these varied injection methodologies on heavy oil recovery. results indicated that the composite flooding for the polymer and viscosity reducer enhanced the recovery rate by 48.22%, outperforming water flooding or single chemical flooding. both single-factor analysis and orthogonal design were employed to assess variables such as injection slug, polymer mass concentration, the mass concentration of viscosity reducer, injection timing, and the rate of chemical composite flooding. in terms of enhancing oil recovery, the injection plug volume had the most pronounced impact on recovery, while the timing of injection had minimal impact on efficiency. this research furnishes crucial technical backing for the enhancement of heavy oil reservoirs through chemical composite flooding. it significantly advances the deployment and application of polymer viscosity reducer chemical composite flooding in similar reservoirs. moreover, the findings are poised to offer pivotal references and direction for employing chemical composite flooding techniques in heavy oils. introduction heavy oil, refers to crude oil with a viscosity greater than 50 mpa∙ s under reservoir conditions or greater than 100 mpa∙ s for degassed crude oil. heavy oil is characterized by high viscosity, low mobility, high content of asphalt and heavy hydrocarbons, high cost, low recovery rates, and complex geological conditions, making its development challenging. most heavy oil reservoirs are difficult to develop using natural energy or water flooding methods. currently, the main development methods for heavy oil include thermal recovery techniques and cold recovery techniques. thermal recovery techniques mainly involve steam flooding and steam-assisted gravity drainage, steam-assisted gravity drainage, in-situ combustion, and electric heating techniques (yuan and improved oil and gas recovery 2 wang 2018). these techniques primarily lower the viscosity of heavy oil to enhance recovery rates. they involve injecting high-temperature and high-pressure steam, and hot water, or using electric heating cables to deliver heat to the reservoir, thereby increasing the reservoir temperature and reducing the viscosity of heavy oil. cold recovery of heavy oil refers to methods of developing heavy oil reservoirs without relying on hightemperature and high-pressure heat media generated by boilers. this approach uses reservoir treatment techniques, wellbore viscosity reduction techniques, and lifting techniques to lower the viscosity of crude oil and improve its flow performance, thereby increasing recovery rates (xue et al. 2022). cold recovery techniques for heavy oil mainly include dilution technology, microbial oil displacement technology, chemical oil displacement technology, etc (chugh et al. 2000). chemical oil recovery techniques for heavy oil mainly use chemical agents composed of polymers, alkalis, and surfactants for oil displacement. among these, polymer flooding is the most widely applied technology to enhance recovery rates (liu et al. 2020). the mechanism behind its enhanced recovery lies primarily in increasing the sweep efficiency and reducing the water-oil mobility ratio (amirian et al. 2018). asghari and nakutnyy (2008) conducted polymer flooding experiments on heavy oils with various viscosities, investigating the impact of permeability, displacement speed, and polymer concentration on the effectiveness of polymer flooding. the results showed that after water flooding, to further enhance recovery rates through polymer flooding, the injected polymer concentration needed to exceed a certain value; otherwise, the effect was minimal, and the degree of recovery enhancement by polymers was inversely proportional to the injection rate. wang and dong (2009) investigated the influence of polymer viscosity on heavy oil recovery rates. in the case where the viscosity of the heavy oil was 430 mpa·s, and a polymer slug of 0.5 pv was injected, the effective viscosity of the polymer was 3.6 mpa·s, and the recovery rate increased from 41.9%, as seen in water flooding, to 44.1%. wassmuth et al. (2007) conducted polymer flooding experiments on heavy oils with different viscosities and found that, under reasonable experimental conditions, the recovery rate from polymer flooding was twice that of water flooding. shi et al. (2010) conducted a study using numerical simulations to investigate the influence of residual resistance factors on incremental oil recovery in polymer flooding. when the rrf increased from 1.5 to 3, the average incremental oil production in polymer flooding increased by 4%. when the rrf reached 6, the incremental recovery rate was 18%. sedaghat et al. (2013) conducted polymer flooding experiments and numerical studies on a five-spot system with fractured heavy oil reservoirs. through their research, it was discovered that due to the distribution of the polymer solution within the matrix, in the case of a 45° fracture pattern, the recovery rate of longer fractures would increase, while in a 0° fracture pattern, there would be no change in the recovery rate. saboorian-jooybari et al.(2016) established the polymer flooding criteria for heavy oil reservoirs through experiments: reservoir depth less than 5250 ft, porosity greater than 21%, oil viscosity less than 5400 mpa.s, and crude oil gravity greater than 11°api. lu et al. (2021) discussed the mechanism of enhanced oil recovery by polymer flooding for changqing, daqing and other oilfields, and found that there was no positive correlation between polymer viscosity and polymer effect. viscosity reduction flooding is primarily achieved by reducing interfacial tension and improving the properties of the oil-water interface, causing the deformation of heavy oil emulsions into water-in-oil emulsions. this process decreases the viscosity and flow resistance of heavy oil, thereby increasing the recovery rate. guo et al. (2010) aimed to reduce the viscosity of high-viscosity oil in the tarim basin's tahe oilfield in xinjiang. they employed an orthogonal method to synthesize a heavy oil-soluble co-polymer viscosity-reducing agent. at 50°c, the addition of this viscosity-reducing agent lowered the crude oil viscosity from 12881mpa.s to 585mpa.s, achieving a viscosity reduction rate of 95.5%. ghloum et al. (2015) found through experiments viscosity of oil samples decreases with a reduction in temperature. however, when the effect of different viscosity reducers on representative oil sample was studied, at 5000 psi and at reservoir temperature of 190 °f, it was noticed that reduction in viscosity of oil sample from 16,230 centipoises to less than 850 centipoises could be achieved. wu et al. (2018)studied the viscosity-reducing effect on henan oilfield using anionicimproved oil and gas recovery 3 nonionic surfactants as viscosity reducers. at a temperature of 30°c, the viscosity of henan oilfield was 5888 mpa·s. with an oil-to-water ratio of 3:7 and a viscosity reducer concentration of 0.5%, the viscosity decreased to 29 5mpa·s, achieving a viscosity reduction rate of approximately 95%. liu et al. (2020) synthesized a watersoluble viscosity-reducing agent using anionic surfactant xj and nonionic emulsifying agent op-10. they conducted core-flooding experiments and micro-visual experiments on heavy oil and compared the experimental results with numerical simulation results. at 50°c, the viscosity of the test oil decreased from 1330 mpa·s to 8.49 mpa·s, achieving a viscosity reduction rate of 99%. when applying this viscosity-reducing agent to the j8 block, the daily oil production increased from 7.2 t/d to 15.4 t/d. liu et al. (2023) investigated the impact of temperature on the viscosity-reducing agent moo3-zro2/hzsm-5. the viscosity of heavy oil increased as the temperature rose. at a temperature of 220°c, the viscosity reduction effect became stable. at 280 degrees celsius, with a viscosity-reducing agent dosage of 1wt%, the viscosity reduction rate of the heavy oil was 82.26% . zhao et al. (2015) conducted an optimization study on suitable polymer and viscosity reducer systems for the ertan reservoir in the shengli oilfield. the recovery of water flooding was only 41.1%. however, using a polymer system with a mass fraction of 0.3% combined with a nonionic viscosity reducer system of 0.2% could increase the recovery rate by 18.67% compared to water flooding. sun et al. (2019) conducted research on the characteristics of high viscosity and poor mobility in block 25 of shengli oilfield. they employed chemical agents such as viscosity-reducing agents and polymers to study the dosage of these agents. experimental results indicated that the combined drive of polymer and viscosity-reducing agents effectively enhanced the ultimate recovery rate. the optimal injection volume for viscosity-reducing agents was 0.1 pv, while for polymers, it was 0.2 pv. the timing of the combined drive injection should follow 1 pv of water flooding. qi et al. (2023) proposed a composite drive approach involving an interfacial active polymer (iap) and emulsifying viscosity reducer (evr) to address the issue of lateral flow in high permeability channels encountered with traditional ovr. experimental results showed that the polymer-viscosity reducer composite drive could reduce the viscosity of heavy oil from 1000 mpa·s to 325.7 mpa·s. in the high permeability zone, the composite drive achieved an oil recovery rate of 89.85%. through the literature review above, it has been verified that composite flooding significantly improves recovery rates compared to single polymer/viscosity-reducing agent flooding. the mechanisms for increasing recovery rates using polymers and viscosity-reducing agents have been clarified. however, there has been no systematic analysis of the impact of factors such as polymer or viscosity-reducing agent mass concentration, plug size, injection rate, and viscosity on recovery. therefore, the main purpose of this study is to, based on understanding the oil recovery mechanisms of polymers and viscosity-reducing agents, perform sensitivity analysis and orthogonal design on the injection plug volume, polymer mass concentration, viscosity-reducing agent mass concentration, timing of polymer-viscosity-reducing agent composite flooding, and injection speed of the composite flooding, to clarify their respective effects on recovery rates. the structure of this paper is as follows: the introduction is presented first, followed by the second section introducing reservoir model, fluid model, and chemical agent parameters, along with a detailed description of the simulation scheme. the third section begins by comparing different injection methods for polymerviscosity-reducing agent composite flooding. it then performs a single-factor analysis on factors, including injection concentration, injection timing, and injection speed, followed by a comparison of the sensitivity of different parameters using an orthogonal design. the final section summarizes the main points and conclusions of this paper. methodology and numerical model reservoir model. using cmg software's stars module, a three-dimensional heterogeneous model was established with a grid size of 21×21×7. the grid dimensions were set as 21×10 m in the i direction, 21×10 m improved oil and gas recovery 4 in the j direction, and 7×2.5 m in the z direction. due to the fact that the reservoir in this block exhibits a lognormal distribution with a coefficient of variation of 0.65 and an average permeability of 2000 md, the horizontal permeability are uniform. however, the vertical permeabilities vary. from top to bottom layer, the permeability is set to be 100 md, 520 md, 1510 md, 2040 md, 2730 md, 3300 md, 3800 md. the well pattern is arranged in a five-spot configuration, and no influence from bottom water or edge water was observed in the reservoir. figure 1—display of three-dimensional numerical reservoir model. to simulate the actual reservoir conditions as closely as possible, the reservoir model and fluid model are based on the geological description and field conditions from the ying 8 block in shengli oilfield. the specific parameters are shown in table 1. table 1—reservoir and fluid parameter settings. attribute name value unit grid size in the x direction 210 m grid size in the y direction 210 m grid size in the z direction 17.5 m underground heavy oil viscosity 136 mpa∙s surface crude oil density 0.961 g/cm3 average porosity 0.31 % average permeability 2000 md oil saturation 55 % net-to-gross ratio 0.69 / reservoir reference depth 1400 m reservoir reference pressure 13 mpa reservoir temperature 57.6 ℃ improved oil and gas recovery 5 relative permeability curves. relative permeability curves can effectively describe the fluid flow characteristics of reservoirs within rock formations. figure 2 shows the relative permeability curves for oilwater and gas-liquid phases. according to the oil-water phase permeability curve, the water saturation values at the irreducible water saturation points are greater than 0.5, indicating a pronounced hydrophilic property of the reservoir. (a)oil-water phase permeability curve (b)gas-liquid phase permeability curve figure 2—block relative permeability curves. polymer viscosity concentration. the polymer viscosity concentration curve depicts the viscosity variation of polymer solutions at different concentrations. in polymer flooding simulation, using viscosity concentration curve enables a more accurate depiction of the rheological properties of polymer solutions and viscosity changes with concentration. by inputting the polymer viscosity concentration curve data into the stars software, the viscosity of polymer solutions can be calculated for different concentrations. the viscosityconcentration relationship curve is shown in figure 3. figure 3—polymer viscosity-concentration curve. polymer adsorption. the adsorption phenomenon refers to the retention of polymer molecules from polymer aqueous solutions as they flow over rock surfaces. a small amount of adsorption has a minor impact on the entire oil recovery process, but excessive polymer retention can affect the control of the water-oil mobility ratio. improved oil and gas recovery 6 the polymer mass concentration and static adsorption used in the established numerical model are shown in figure 4. figure 4—relationship between polymer mass concentration and adsorption capacity. inaccessible pore volume. the inaccessible pore volume is the proportion of the total rock volume occupied by the portion of pore volume where polymer molecules cannot enter the pore throats. in this simulation, the value of the inaccessible pore volume is set to about 10% to the total pore volume of the rock. residual resistance factor for the adsorbing component. residual resistance factor the adsorbing component is an indicator used to describe the residual resistance factor of polymers in the oil displacement process. in this simulation, the rrft value is set to 2. chemical reaction between viscosity reducer and heavy oil. after adding the viscosity reducer to the formation, the reducer reacts with heavy oil (oil) to form light oil (litt_oil) and water (water), the reaction formula is as follows. a reducer +b heavy oil→ c light_oil+d water,...........................................................................................(1) where a, b, c, and d represent the number of moles of viscosity reducer, heavy oil, light oil, and water, respectively. after the completion of the reaction, the viscosity of heavy oil is 300 mpa∙s, the viscosity of light oil is 30 mpa∙s, and the viscosity reduction rate of the viscosity reducer is 90%. simulation workflow. in the process of enhancing oil recovery (eor), water flooding is first carried out to obtain the recovery rate of water flooding. subsequently, the chemical injection methods were compared to verify the feasibility of chemical composite flooding of polymer viscosity reducer by measuring enhanced oil recovery. then, the single-factor analysis method was used to design the experiment, and the sensitivity analysis and orthogonal design of the five parameters of the polymer viscosity reducer composite flood, including injection slug, polymer/viscosity reducer mass concentration, injection timing, and injection rate of composite flooding. improved oil and gas recovery 7 figure 5—simulation workflow. results and discussion comparison of chemical injection methods. in this study, six different oil displacement methods were adopted for comparative experiments. the specific experimental steps are as follows. 1.the first injection method involves water flooding 2.the second method is to inject 0.6 pv of viscosity reducer with a 60% water cut. 3.the third injection method involves injecting 0.6 pv of polymer at a 60% water cut. 4.the fourth method is to first inject 0.3 pv of viscosity reducer, followed by injecting 0.3 pv of polymer. 5.the fifth method is to first inject 0.3 pv of polymer, followed by injecting 0.3 pv of viscosity reducer. 6.the sixth method involves injecting a composite system of 0.6 pv of polymer and viscosity reducer. in the experimental protocol, the mass concentration of the polymer was 1000 mg/l, the mass concentration of the viscosity reducer was 2000 mg/l, and the viscosity reduction rate was 90%. from table 2, it can be concluded that using polymer, viscosity reducer, injecting viscosity reducer first followed by polymer, or injecting polymer first followed by viscosity reducer, all contribute to an increased recovery rate for heavy oil. the recovery rate for oil displacement using a viscosity reducer is only 0.03% higher than that using polymer. the recovery rate for injecting polymer first followed by viscosity reducer is 0.45% higher than that of injecting viscosity reducer first followed by polymer. the recovery rate for polymer viscosity reducer composite flooding is 56.05%, which is 36.17% higher than water flooding, and more than 15% higher than all four other chemical injection methods. table 2—effects of different injection methods of chemical agents on enhanced oil recovery. injection scheme water flooding viscosity reducer polymer viscosity reducer+ polymer polymer+ viscosity reducer chemical composite flooding recovery (%) 19.88 36.83 36.80 40.14 40.59 56.05 eor (%) / 16.95 16.92 20.26 20.71 36.17 improved oil and gas recovery 8 as shown in figure 6, water flooding results in the least cumulative oil production, while the cumulative oil production variation among the four injection methods--using polymer, viscosity reducer, injecting polymer first followed by viscosity reducer, and injecting viscosity reducer first followed by polymer--is minimal. the chemical composite flooding exhibits the highest cumulative oil production with the most significant increase. figure 6—effect of different injection methods of chemical agents on cumulative oil production. figure 7 displays the viscosity oil production curves for the six injection methods. water flooding shows a gradual decrease in daily oil production. injecting polymer viscosity reducer composite flooding into heavy oil results in a rapid increase in daily oil production. during the period from 1000 to 1500 days, the daily oil production remains relatively stable without significant changes. however, after 1500 days, the daily oil production started to decline significantly. figure 7—daily oil curve of different injection methods of chemical agents. as shown in figure 8, in order to better compare the oil saturation of different chemical injection methods and composite flooding, we analyzed the first, fourth, and seventh layers of the model. in the chemical composite flooding, the oil saturation of the first layer is only low around the injection well, the oil saturation of improved oil and gas recovery 9 the fourth layer has decreased significantly, and the oil saturation of the seventh layer is the lowest. by comparing the oil saturation distribution maps of injecting polymer first followed by viscosity reducer, injecting viscosity reducer first followed by polymer, and chemical composite flooding in the first layer, we find that the displacement range of chemical composite flooding is broader and it exhibits a more effective displacement of crude oil. this is primarily because polymer viscosity reducer composite flooding fully utilizes the synergistic effect of polymer and viscosity reducer. the polymer creates a dense front that enhances the displacement effect, while the viscosity reducer reduces the viscosity of the displacing agent, improving its fluidity. the combination of these two factors further enhances the effectiveness of the composite flooding and reduces the oil saturation. layer polymer+ viscosity reducer viscosity reducer+ polymer chemical composite flooding 1st layer 4th layer 7th layer figure 8—oil saturation distribution for different injection methods. figure 9 is a viscosity comparison chart for different injection methods on january 1, 2035. in the chemical composite flooding, within the first layer of the model, the viscosity reducer only affects the area around the improved oil and gas recovery 10 injection well. the closer to the injection well, the greater the degree of viscosity reduction. in the fourth layer, the viscosity reducer has a broader range of influence and a stronger ability to reduce viscosity, except for a slightly less effective reduction in viscosity around the perimeter. in the seventh layer, the viscosity of the heavy oil around the perimeter is also reduced, resulting in the best viscosity reduction effect. compared to the first layer, the approach of injecting polymer first followed by viscosity reducer only affects the area around the injection well, and its viscosity reduction effect is weaker. injecting viscosity reducer first followed by polymer has a broader influence, surpassing the effectiveness of injecting polymer first followed by polymer. this indicates that under the same formation conditions, the injection sequence may lead to different effects on the viscosity reduction in composite flooding. layer polymer+ viscosity reducer viscosity reducer + polymer chemical composite flooding 1st layer 4th layer 7th layer figure 9—viscosity distribution of different injection methods and composite displacement of chemical agents. optimization of composite drive parameters of polymer viscosity reducer. in oil field development, polymer viscosity reducer are chemical additives used for reservoir improvement, primarily employed to improved oil and gas recovery 11 regulate the viscosity of the two-phase fluid of oil and water to enhance crude oil recovery. optimizing the polymer viscosity reducer drive parameters can more effectively implement reservoir development practices, leading to increased recovery rates, reduced production costs, slowed reservoir depletion, and achieving a more sustainable oil field development. this article focuses on the optimization of the injection slug volume, polymer mass concentration, viscosity reducer mass concentration, injection time, and injection rate in the injection section of the composite drive. chemical composite flooding injection slug volume. properly planning the plunger volume for composite flooding can achieve efficient oilfield development and also balance the investment cost of chemical flooding. to better verify the impact of injected plunger volume on recovery rates, four sets of experiments were conducted for comparison. under a water cut of 60%, injecting polymer at a mass concentration of 2000 mg/l and viscosity reducer at a mass concentration of 2000 mg/l, with an injection rate of 0.1 pv/a, the study investigated the variation in recovery rates and cumulative oil production for injected plunger volumes of 0.2 pv, 0.4 pv, 0.6 pv, 0.8 pv. as shown in table 3, the recovery rate of water flooding is 19.88%, the recovery rate is 35.60% when the volume of the injection composite flooding plug is 0.2 pv, which is 15.72% higher than that of water flooding, and the recovery rate is 64.25% when the volume of the composite flooding plug of the polymer viscosity reducer is 0.8 pv, which is 44.37% higher than that of water flooding, and the injection section slug is in the range of 0.2 pv-0.8 pv, the larger the volume of the injection section plug, the higher the degree of recovery. table 3—plug volumes of different composite sections enhance oil recovery. plan water flooding 0.2pv 0.4pv 0.6pv 0.8pv recovery (%) 19.88 35.60 46.47 56.03 64.25 eor (%) / 15.72 26.59 36.15 44.37 figure 10—effect of plugs of different volume sections of composite flooding on cumulative oil production. figure 10 illustrates the correspondence between the cumulative oil production and the size of the slug for water flooding and four different injection slug size schemes. the results reveal that cumulative oil production demonstrates an increasing trend with the augmentation of the injection slug volume, indicating that higher improved oil and gas recovery 12 production levels lead to greater cumulative oil yields. from the graph, it can be observed that when the injection slug size ranges from 0.2 pv to 0.6 pv, there is a rapid increase in cumulative oil production. however, as the injection slug size ranges from 0.6 pv to 0.8 pv, the rate of increase in cumulative oil production becomes smaller. moreover, augmenting the slug volume will also escalate economic costs. mass concentration of viscosity reducer in chemical composite flooding. to evaluate the effect of different viscosity reducer concentrations on the viscosity of heavy oil and its effect on oil production, we set the following experimental conditions: the composite flooding of polymer and viscosity reducer was injected at an injection rate of 0.1pv/a, with a total injection amount of 0.6pv and a polymer mass concentration of 2000mg/l. by studying the effects of various viscosity reducer effects on enhancing oil recovery, the aim is to highlight the different viscosity-reducing effects of these agents in composite flooding. as shown in table 4, within the range of viscosity reducer mass concentrations between 1000-3000 mg/l, the higher the mass concentration of the viscosity reducer, the higher the recovery rate. the recovery rate of the viscosity reducer mass concentration of 2000 mg/l increased by 8.67% compared to that of 1500 mg/l, while the recovery rate of the viscosity reducer concentration of 3000 mg/l only increased by 5.49% compared to the mass concentration of 2000 mg/l. this indicates that in the process of using polymer viscosity reducer composite flooding for oil recovery, a higher mass concentration of polymer is not necessarily better. table 4—effects of different viscosity reducer mass concentrations on enhanced oil recovery. oil recovery plan water flooding 1000mg/l 1500mg/l 2000mg/l 3000mg/l 80% 85% 90% 95% recovery(%) 19.88 47.42 60.37 69.04 74.53 eor (%) / 32.04 34.40 49.16 54.65 figure 10 displays the cumulative oil production at different viscosity reducer mass concentrations. compared to water flooding, higher viscosity reducer mass concentrations result in greater cumulative oil production. figure 11 illustrates the daily oil production at different viscosity reducer mass concentrations. when no viscosity reducer is added, the daily oil production follows a linear downward trend. when the water cut reaches 60%, varying concentrations of viscosity reducer are added. among them, at a viscosity reducer mass concentration of 3000 mg/l, the daily oil production increases the fastest, reaching a peak of 56 m3/day. during the 1000-2800-day period after adding the viscosity reducer, daily oil production remains relatively stable without significant fluctuations. beyond this time frame, daily oil production experiences a significant decline. when the viscosity reducer mass concentrations are 2000 mg/l, 1500 mg/l, and 1000 mg/l, the daily oil production initially rises and then falls, with the most pronounced decrease observed at a viscosity reducer mass concentration of 1000 mg/l. after six years of viscosity reducer injection, the daily oil production notably decreases. figure 12 illustrates the viscosity comparison of the seventh layer in the model with and without the addition of a viscosity reducer when the viscosity reducer mass concentration is 3000 mg/l. on the left side is the viscosity plot for january 2020, where no viscosity reducer is injected, and both the injection and production wells contain heavy oil with a viscosity of 300 mpa∙s. on the right side is the viscosity plot for january 2035, where the viscosity of the heavy oil has reduced from 300 mpa∙s to 30 mpa∙s, indicating a significant reduction in viscosity and an ideal viscosity reduction effect. improved oil and gas recovery 13 figure 10—effect of different viscosity reduction rates on cumulative oil yield in composite flooding. figure 11—effect of different viscosity reducing rates on daily oil production of composite flooding. figure 12—viscosity distribution. the left figure is the viscosity graph before injection of polymer viscosity reducer composite flooding, and the right figure is the viscosity graph after 15 years of polymer viscosity reducer composite flooding injection. improved oil and gas recovery 14 mass concentration of polymer in chemical composite flooding. in the chemical composite flooding involving polymer and viscosity reducer, injecting different polymer mass concentrations leads to varying oil displacement effects of the composite flooding. optimal selection of the polymer mass concentration contributes to the superior oil displacement performance of the polymer viscosity reducer composite flooding. to investigate the influence of polymer mass concentration on recovery rates, the following experiments were conducted: injecting the polymer viscosity reducer composite flooding at a rate of 0.1pv/a for a total volume of 0.6 pv, with a viscosity reduction rate of 90% for the viscosity reducer, under conditions with a water cut of 60%, while varying the polymer mass concentration. as shown in table 5, there is a positive correlation between the mass concentration of the polymer and the recovery rate. as the mass concentration of the polymer increases, the recovery rate also increases. the recovery rate of water flooding is 19.88%, while the recovery rate of polymer flooding with a mass concentration of 500mg/l is 61.86%, which is 41.98% higher than that of water flooding. polymers can modify the interactions between oil and water, forming barriers. the addition of polymers increases the viscosity of the flooding fluid and reduces the permeability of water in the pores, enhancing the oil permeability. therefore, compared to water flooding, polymer flooding can significantly improve the recovery rate. figure 13 displays the cumulative oil production for water flooding, using only viscosity reducer, and chemical composite flooding with different concentrations of polymer. compared to water flooding, whether using only a viscosity reducer or employing chemical composite flooding with various polymer concentrations, all show a significant increase in cumulative oil production. the higher the concentration of polymer, the greater the cumulative oil production. table 5—effects of different polymer mass concentrations on enhanced oil recovery. oil recovery plan water flooding 500mg/l 1000mg/l 1500mg/l 2000mg/l recovery (%) 19.88 61.86 64.82 68.52 71.87 eor (%) / 41.98 44.94 48.64 51.99 figure 13—cumulative oil production at different polymer mass concentrations. improved oil and gas recovery 15 injection timing of chemical composite flooding. the volume of the injection section slug is 0.6 pv, the mass concentration of the viscosity reducer is 2000 mg/l (the viscosity reduction rate is 90%), the mass concentration of the polymer is 1000 mg/l, and the polymer viscosity reducer composite flooding is designed to be injected when water cut is 60%, 70%, 80% and 90% respectively, and the recovery and cumulative oil obtained by the four schemes are shown in table 6 and figure14. table 6—compound flooding at different injection times. oil recovery plan water flooding 60% 70% 80% 90% days of water injection (days) 330 480 730 1050 recovery (%) 19.88 55.14 55.08 55.07 55.06 eor (%) / 35.26 35.20 35.19 35.18 the earlier the injection polymer viscosity reducer, the higher the degree of recovery, the composite flooding recovery rate of the polymer viscosity reducer injected at 60% is 55.14%, which is 35.26% higher than that of the water flooding recovery rate of 19.88%, and the composite flooding recovery rate of polymer viscosity reducer injection at 90% moisture content is 55.06%, which is only 0.08% lower than that of 60% water content. the effect of injection timing on recovery is very small compared to the effect of polymer viscosity reducer injected plugs on oil recovery. therefore, when carrying out composite drives infused with polymer viscosity reducers, it is not necessary to pay too much attention to the specific timing of injection. as shown in figure 14, although the strategy of early injection of polymer viscosity reducer over a 10-year period can increase cumulative oil production, the final cumulative oil production is not affected by the timing of injection. figure 14—effect of different injection timing of compound flooding on cumulative oil production. injection rate of chemical composite flooding. the injection speed of chemical compound flooding will impact the production efficiency of the oilfield, and selecting the appropriate injection rate can assist in achieving better oil displacement efficiency. in this study, when the water cut reaches 60%, a composite flooding of polymer viscosity reducer is injected. the volume of the injected compound slug is 0.6 pv, the mass concentration of the viscosity reducer is 2000 mg/l, with a viscosity reduction rate of 90%, and the polymer's mass concentration is 1000 mg/l. the effects of different injection speeds on the efficiency of chemical compound flooding are compared. improved oil and gas recovery 16 from table 7, it can be observed that as the injection rate increases, the recovery rate of water flooding shows an increasing trend. for the polymer viscosity reducer composite flooding, within the range of injection rates from 0.05pv/a to 1.00pv/a, the recovery rate increases. however, when the injection rate exceeds 0.10pv/a, the recovery rate starts to decrease. within the injection rate range of 0.05pv/a to 0.15pv/a, the highest incremental recovery rate of the composite flooding compared to water flooding occurs at an injection rate of 0.075pv/a, with a value of 37.09%. conversely, the lowest incremental recovery rate for the composite flooding is observed at an injection rate of 0.05pv/a, at 30.78%. within the range of injection rates from 0.075pv/a to 0.150pv/a, the difference in recovery rates for composite flooding is 1.08%, while the difference in recovery rates for water flooding is 3.13%. this indicates that changing the injection rate has minimal impact on the recovery rate of polymer viscosity reducer composite flooding. table 7—composite flooding with different injection velocities enhances oil recovery. injection rate(pv/a) 0.05 0.075 0.1 0.125 0.15 recovery (%) 47.64 56.15 57.23 56.82 56.37 water flooding recovery(%) 16.86 19.06 21.24 21.38 22.19 eor(%) 30.78 37.09 35.99 35.44 34.18 figures 15 and 16 depict the impact of water flooding and chemical composite flooding at various injection rates on cumulative oil production. for water flooding, a higher injection rate leads to greater cumulative oil production. the difference in cumulative oil production between an injection rate of 0.100 pv/a and 0.125 pv/a for water flooding is not significant. in the case of composite flooding, when the injection rates are 0.050 pv/a, 0.075 pv/a, and 0.100 pv/a, higher injection rates result in higher cumulative oil production. at injection rates of 0.100 pv/a, 0.125 pv/a, and 0.150 pv/a, during the early stages of extraction, cumulative oil production increases with higher injection rates. however, in the middle to later stages of extraction, there is no significant variation in cumulative oil production for injection rates of 0.125 pv/a and 0.150 pv/a. figure 15—effects of different injection speeds of water flooding on cumulative oil production. improved oil and gas recovery 17 figure 16—effect of different injection speeds on cumulative oil yield of composite flooding. figure 17—comparison of cumulative oil production at different injection rates. orthogonal design. an orthogonal design experiment is a design method to study multi-factor and multi-level, mainly using orthogonal table tools for overall design, comprehensive comparison, and statistical analysis. according to the orthogonality, some representative points are selected from the comprehensive experiment for experiments, these points have the characteristics of "uniform dispersion, neatness and comparable", and reasonable arrangement of experiments with orthogonal tables can greatly reduce the number of experiments and improve the efficiency of the experimental site (gong et al. 2008). improved oil and gas recovery 18 table 8—orthogonal design experiment table. serial number line number injection plug （pv） viscosity reducer concentration (mg/l) polymer concentration (mg/l) injection timing （%） injection rate （pv/a） eor （%） 1 0.3 1000 500 50 0.075 13.06 2 0.3 1500 1000 60 0.100 21.70 3 0.3 2000 1500 70 0.125 28.22 4 0.3 3000 2000 80 0.150 35.07 5 0.4 1000 1000 70 0.150 20.18 6 0.4 1500 500 80 0.125 23.56 7 0.4 2000 2000 50 0.100 38.05 8 0.4 3000 1500 60 0.075 40.39 9 0.5 1000 1500 80 0.100 26.83 10 0.5 1500 500 70 0.075 26.52 11 0.5 2000 2000 60 0.150 43.94 12 0.5 3000 1000 50 0.125 47.96 13 0.6 1000 2000 60 0.125 33.23 14 0.6 1500 1500 50 0.150 38.25 15 0.6 2000 1000 80 0.075 43.18 16 0.6 3000 500 70 0.100 52.79 in this experiment, five factors and four levels were selected, including polymer mass concentration, mass concentration of viscosity reducer, volume of polymer viscosity reducer composite flood injection segment, timing of composite drive injection, and composite flood injection rate, and adopted orthogonal table design, a total of 16 sets of experiments were required, and the parameter design of each group of experiments was shown in table 8. to visualize the sensitivity of each factor to enhanced oil recovery, a range analysis was performed using statistical methods, and the results are shown in table 9. table 9—orthogonal design results. factor mean value1 mean value2 mean value3 mean value4 range relative difference importance ranking injection plug（pv） 24.51 30.54 36.32 41.87 17.36 8.68 1 polymer concentration（mg/l） 28.98 33.26 33.42 37.58 8.60 2.15 3 viscosity reducer concentration （mg/l） 23.33 27.51 38.41 44.06 20.74 6.91 2 injection timing（%） 34.82 34.33 32.16 31.93 2.89 1.93 5 injection rate（pv/a） 30.79 34.84 34.37 33.24 4.05 2.03 4 improved oil and gas recovery 19 (a) (b) (c) (d) (e) figure 18—oil recovery increment under different parameters: (a) injection slug; (b) polymer concentration; (c) the mass concentration of viscosity reducer; (d)injection timing; (e) injection rate. analysis of table 9 shows that the importance of each factor is as follows: chemical composite flooding injection slug volume, chemical composite displacement adhesive mass concentration, chemical composite flooding injection timing, chemical composite flooding polymer mass concentration, and chemical composite flooding injection rate. the mass concentration of chemical composite flooding polymer, chemical composite flooding injection timing, and chemical composite flooding did not have a great effect on oil recovery, and the improved oil and gas recovery 20 volume of chemical composite flooding injection plug was the factor that had the greatest impact on the recovery effect. to further analyze the trend of the impact of each factor on oil recovery, the change in oil recovery with each factor is plotted based on the results of table 9, as shown in figure 18. it can be concluded that the volume of the injection volume increases, and so does the recovery rate. increasing the volume of the injection slug can expand the range of chemical agents, improve the chance of contact between chemical flooding agents and crude oil, increase the displacement efficiency of crude oil in reservoirs, and improve oil recovery. it also can be observed that as the mass concentration of the polymer increases, the overall increase in recovery rate also shows an upward trend (figure 18(b)). the slower increase in recovery rate when the polymer mass concentration increases from 1000 mg/l to 1500 mg/l may be due to having already achieved a certain level of enhanced production effect at lower concentrations. when the concentration is low, the polymer can form an effective displacement system with the crude oil, reducing the viscosity of the oil, improving the interaction between oil and water, and thereby increasing the recovery rate. however, as the concentration gradually increases, the additional amount of polymer may not significantly improve the displacement effect, as a high displacement efficiency has already been achieved, and further increasing the concentration has a relatively minor impact on enhancing the recovery rate. in chemical composite flooding, there is a positive correlation between the mass concentration of the viscosity reducer and increased oil recovery. the higher the mass concentration of the viscosity reducer, the more effectively it can reduce the viscosity of crude oil, enhance its interaction with crude oil, and consequently improve the oil recovery rate. the later the chemical composite flooding injection is initiated, the less effective the eor will be. later injection times can lead to uneven distribution of crude oil and chemical adsorption and repulsion, insufficient energy balance, and the release of crude oil may be limited, thus affecting the effect of enhanced oil recovery. when the chemical composite flooding rate exceeds 1.0 pv/a, the rate of increased recovery begins to decline. if the chemical composite flooding rate is too high, it might lead to insufficient contact and mixing between the polymer or viscosity reducer and the crude oil, diminishing their mutual interaction, reducing displacement efficiency, and subsequently lowering the enhanced oil recovery effect. conclusions in this paper, the effect of oil recovery on chemical composite flooding of heavy oil polymer viscosity reducer was studied, and the following conclusions were drawn: 1. polymer-viscosity reducer composite flooding has a better oil recovery effect compared to the four other methods of single polymer injection, single viscosity reducer injection, polymer injection followed by viscosity reducer injection, and viscosity reducer injection followed by polymer injection. this is because the polymer expands the sweep volume, while the viscosity reducer reduces the viscosity of the oil in the swept area, resulting in a synergistic enhancement effect. 2. factors influencing the recovery rate: the recovery rate is positively correlated with the volume of the injection slug, the concentration of polymer, and the concentration of viscosity reducer. the timing of injection has a minimal impact on the recovery rate. 3. the impact of harvesting efficiency follows the sequence in the following order: injection slug volume>viscosity reducer concentration>polymer concentration > injection rate> injection timing. improved oil and gas recovery 21 acknowledgments we would like to thank the project ‘ccus method screening and potential evaluation software development and test’ for their financial support and valuable discussion. we would like to thank the following people for their constructive discussions 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and wang, q. 2018. new progress and prospect of oilfields development technologies in china. petroleum exploration and development 45(4): 698-711. zhao, h., li, m., qu, q., et al. 2015. microscopic displacement mechanism of ordinary heavy oil by viscosity reducer and polymer flooding. journal of petrochemical universities 28(1):59-64. min zhang, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focused her research in areas involving reservoir simulation, chemical flooding, and enhanced oil recovery. weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. his research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dr. li holds a bachelor’s degree in petroleum engineering from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. shide yan, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation and enhance oil recovery. zhengbo wang, is a senior reservoir engineering in research institute of petroleum exploration and development, petrochina. he specializes in enhanced oil recovery. dr. wang holds a a phd degree in petroleum engineering from research institute of petroleum exploration and development, petrochina. zhaoxia liu, is a senior reservoir engineering in research institute of petroleum exploration and development, petrochina. she specializes in enhanced oil recovery. dr. liu holds a a phd degree in petroleum engineering from research institute of petroleum exploration and development, petrochina. keze lin, is a undergraduate student of china university of petroleum (beijing), beijing. hongliang yi, is a senior reservoir engineer in liaohe oilfield company of petrochina. he specializes in enhanced oil recovery. abstract introduction methodology and numerical model results and discussion conclusions acknowledgments conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1302 received august 1, 2024; revised august 14, 2024; accepted august 21, 2024. *corresponding author: hamzafalal84@gmail.com 1 an interaction between moringa oleifera biosurfactant and nanoparticles for foam stability, interfacial tension reduction and wettability alteration umar hassan, bayero university kano, kano, nigeria; mohammed falalu hamza*, bayero university kano, kano, nigeria and universiti teknologi mara, selangor, malaysia; hassan soleimani, universiti teknologi petronas, perak darul ridzuan, malaysia; bashir abubakar abdulkadir, universiti malaysia pahang alsultan abdullah, pahang, malaysia and gombe state university, gombe, nigeria; saifullahi shehu imam, bayero university kano, kano, nigeria; and sabiha hanim saleh，universiti teknologi mara, selangor, malaysia abstract foam has emerged as one of the most advanced techniques to address the gas mobility challenges encountered during gas flooding in oil reservoirs. due to environmental concerns, bio-surfactants derived from plants are increasingly recommended as alternatives to synthetic surfactants. this study focuses on synthesizing a moringa oleifera biosurfactant (ms) reinforced with silica nanoparticles (snps) to produce a nano-foam (ms/snps). adsorption isotherm studies, including the langmuir and freundlich models, were utilized to investigate the adsorption of ms onto snps. additionally, the physicochemical properties of the ms/snps foam, such as bubble size, foamability, foam stability, interfacial tension (ift), and contact angle (ca), were thoroughly examined. the results indicate that the ms synthesis was successful, with significant adsorption capacity onto snps. the maximum adsorption was achieved with 4 wt% ms and 0.4 wt% snps at 50°c and ph 9, fitting well with the freundlich isotherm model, showing an r2 value of 0.9725. according to the ross-miles foam test, ms exhibited greater foamability and stability, albeit with lower morphological quality compared to ms/snps. notably, ms/snps reduced the ift of the oil/brine system from 6.22 mn/m to a remarkably low 0.08 mn/m. moreover, ms/snps altered the rock/oil wettability by 24%, favoring more wettable conditions. introduction crude oil remains a predominant energy source and continues to play a crucial role in addressing global energy demands (hamza et al. 2018). projections indicate that global energy demand will increase by 30% by 2040, with oil consumption expected to rise from approximately 87 million barrels per day (mbpd) in 2010 to over 100 mbpd (ahmadi and shadizadeh 2013; zhang et al. 2020). petroleum reservoirs contain significant quantities of hydrocarbons entrapped within porous rock formations (aljuboori et al. 2019; hamza et al. 2020). given the depletion of conventional oil resources, coupled with rising energy demands, population growth, and rapid industrialization, there is an urgent need to enhance oil recovery from existing reserves (joshi et al. 2015). mailto:hamzafalal84@gmail.com improved oil and gas recovery 2 oil recovery is typically categorized into three stages: primary, secondary, and tertiary, the latter often referred to as enhanced oil recovery (eor). primary recovery relies on the natural drive mechanisms of the reservoir, while secondary recovery employs water injection to maintain reservoir pressure. however, these methods generally recover less than 30% of the original oil in place (ooip), leaving a substantial portion of hydrocarbons trapped due to factors such as wettability, capillary forces, and interfacial tension between the reservoir fluids and rock matrix (hamza et al. 2016). to maximize hydrocarbon extraction, eor techniques are employed once primary and secondary methods become ineffective. eor processes involve the introduction of external agents or energy to modify the physical and chemical interactions within the reservoir, thereby enhancing oil displacement (osama and ahmad 2020). extensive research has been conducted on various eor techniques, which are categorized based on the nature of the agents used or the mechanisms they invoke (alireza and delshad 2023). figure 1 illustrates a schematic of eor methods, highlighting the diverse chemical agents employed. chemical enhanced oil recovery (ceor) is particularly noteworthy due to its ability to alter wettability and reduce interfacial tension, thereby mobilizing trapped oil (hamza et al. 2018). ceor involves the injection of chemical solutions, such as alkalis, surfactants, nanoparticles (nps), and polymers, into the reservoir to improve oil recovery efficiency (salehi et al. 2014). these chemical agents interact with the oil/water/rock system to overcome the forces that trap oil, facilitating its movement toward production wells and ultimately enhancing recovery rates. eor methods gas eor co2 n2 h2 fuel gas chemical eor surfactant & foam polymer alkaline solutions nanoparticles thermal eor insitu combustion hot water steam injection electromagnetic heating other eor microbial acoustic, ultrasonic based techniques hybrid figure 1—classification of eor methods. surfactants play significant roles in most ceor systems, including surfactant flooding, polymer-surfactant flooding, and foam flooding (blaker et al. 2002). the primary advantage of surfactant-based systems lies in their ability to reduce interfacial tension (ift) and, in some cases, control gas mobility (hou et al. 2012; hamza et al. 2017). however, the effectiveness of surfactants is often compromised by harsh reservoir conditions, such as high temperature, pressure, salinity, and the specific characteristics of the crude oil. under these circumstances, surfactant flooding alone may not achieve optimal oil recovery (zhao et al. 2015). to address these limitations, ceor strategies involving hybrid materials-such as surfactant-polymer, polymer-nanomaterial, surfactant-nanomaterial, or polymer-surfactant-nanomaterial combinations-have been developed. the synergistic interaction between these hybrid components enhances the rheological properties of the system, improves thermal and salinity resistance, and enables the ceor hybrids to better withstand variations in crude oil properties (kamal et al. 2017). in recent years, there has been a growing interest in the improved oil and gas recovery 3 application of nanoparticles (nps) in conjunction with surfactants to mitigate the challenges associated with surfactant-based eor processes. this interest is driven by the potential benefits of surface-active complexes formed through electrostatic interactions between nps and surfactant molecules (yekeen et al. 2019). previous studies have demonstrated the successful generation and propagation of nanoparticle-stabilized foams in the presence of oil (nguyen et al. 2014). notably, nps have been explored as a means of reducing ift in porous media. for example, hydrophilic nps dispersed in brine have been shown to reduce ift from 14.7 to 9.3 mn/m. dispersing zno in brine led to an ift reduction from 13.38 to 11.60 mn/m, while fe2o3 dispersed in propanol reduced ift from 38.50 to 2.75 mn/m. similarly, al2o3 dispersed in propanol lowered ift from 38.50 to 2.25 mn/m. furthermore, increasing the concentration of hydrophilic nps from 0.01 to 0.05 wt.% resulted in a further ift reduction from 9.3 to 5.2 mn/m (hassan et al. 2021; yarima et al. 2022; hamza et al. 2022). atta et al. (2020) reviewed the advantages of nps as foam stabilizers, highlighting their ability to enhance foam stability under reservoir conditions. this improvement is attributed to the irreversible adsorption and accumulation of nps at the plateau boundaries and gas-liquid interfaces, which limits fluid-fluid contact, hinders gas diffusion, and reduces liquid drainage (hamza et al. 2017). natural surfactants offer advantages such as high biodegradability, low toxicity, multifunctionality, environmental compatibility, and broad availability, making them suitable for a variety of eor applications (ummusalma and hamza, 2022). these surfactants are typically derived from plant-based materials, including the stem bark, seeds, roots, and leaves. moringa oleifera (mo) is a plant native to india, commonly found in tropical and subtropical regions worldwide (kalibbala et al. 2009) (figure 2a). known as the "horseradish tree" or "drumstick tree," mo is highly resilient, capable of withstanding both moderate frost and severe drought, and is thus cultivated globally. due to its high nutritional content, every part of the tree is valuable for both nutritional and commercial applications (asante et al. 2014; lakshmipriya et al. 2016; oyeyinka et al. 2018). the leaves are rich in minerals, vitamins, and phytochemicals, and have been used to treat malnutrition and enhance breast milk production in nursing mothers. mo also exhibits antimicrobial, antidiabetic, anticancer, anti-inflammatory, and antioxidant properties. the seeds (figure 2b), widely utilized in industrial applications and water treatment as a natural coagulant, contain oils and essential fatty acids that can be extracted using solvents such as n-hexane, chloroform, diethyl ether, acetone, and ethanol (ali et al. 2017; emilianny et al. 2021). the oil, as illustrated in figure 2c, is rich in various beneficial components, including fatty acids. (a) plant (b) seeds (c) component distributions figure 2—moringa oleifera. methodology sample collection and pre-treatment. mature seeds of moringa oleifera were sourced from rano local government, kano state, nigeria. the plant species was authenticated at the herbarium research laboratory, bayero university kano, nigeria. following authentication, the seeds were dehulled, thoroughly cleaned, and improved oil and gas recovery 4 air-dried for three days. the dried seeds were then mechanically ground to a uniform particle size of 2 mm using a manual grinder. the ground sample was further dried in an oven at 30 °c for 30 minutes to remove any residual moisture. determination of moisture content. to determine the moisture content, the sample was weighed before and after oven drying. the initial and final masses were recorded, and the moisture content was calculated as a percentage based on the difference between the initial and final masses, as expressed by eq. 1. moisture content (%) = m1−m2 m2 × 100,.............................................................................................................(1) where, m1 and m2 are initial and final masses in g, respectively. determination of acid value. a precisely weighed 10.2 g sample was dissolved in 0.1 n alcoholic potassium hydroxide (koh) within a titration vessel. the solution was then titrated potentiometrically. the titration data, consisting of the potentiometric readings and corresponding volumes of titrant, were plotted to generate a titration curve. the end points were identified at distinct inflection points on the curve, and the acid value (in mg koh/g) were calculated using eq. 2. acid value = (a-b) ×m× 56.1 w ,..........................................................................................................................(2) where a is the sample titration volume of alcoholic koh solution used, ml ; b represents the volume corresponding to a for blank titration, ml; m is concentration of alcoholic koh solution, mol/l; w is a sample mass, g. determination of saponification value. a precisely weighed seed sample of 2g was placed into a flask containing 25ml of a solution composed of equal volumes of ethanol and potassium hydroxide (koh). the flask was connected to a reflux condenser via a soxhlet extractor and placed in a water bath, maintaining a temperature of 60 to 70oc for 30 minutes with continuous stirring. after the reaction, a few drops of phenolphthalein indicator were added to the extract, which was then titrated against 0.5n hydrochloric acid (hcl). a control experiment was conducted by repeating the entire procedure without the seed sample, serving as a blank. the saponification value was calculated using eq. 3. saponification value = (b−s)×n×56.1 m ,.................................................................................................................(3) where, b is the volume of titre blank, ml; s is the volume of titre value with sample, ml; n represents normality of titrating solution (koh used herein), eq/l; m is the mass of sample, g. extraction and synthesis. a sample of 30 g of prepared moringa oleifera seeds was placed into a soxhlet extractor, followed by the addition of 300 ml of ethanol. the extraction was conducted at 60-65°c, just below the boiling point of ethanol, and was repeated for approximately 9 reflux cycles over 3 hours. the resulting mixture of solvent and extracted oil was allowed to settle in a desiccator for 3 days until the solvent was fully evaporated. the purified oil extract was treated with diethyl ether and then left to air dry, eliminating any residual solvent odor. the oil yield was calculated as the ratio of the mass of extracted oil to the initial mass of the seed sample, expressed as a percentage. for the synthesis of moringa oleifera surfactant (ms), 20ml of extracted moringa oil was heated to 80-90°c for 30 minutes to simmer the oil. subsequently, 10g of naoh was added, and the mixture was maintained at 80°c for approximately 3 hours until a dark solid product formed. to confirm the completion of the reaction, a small portion of the solid was dissolved in distilled water, yielding a clear, uniform solution, as depicted in figure 3. improved oil and gas recovery 5 ftir analysis. the solid product was analyzed using fourier transform infrared spectroscopy (ftir) with a perkinelmer spectrum spectrometer to study its chemical properties by comparing its spectral absorptions with those of the extracted oil. a small amount of the solid sample was placed in the ftir spectrometer, where the absorption range was measured between 200 and 4000 cm-1. the transmittance was recorded against the wave number, allowing for the identification and characterization of functional groups within the sample. figure 3—synthesis of surfactant. formulation optimization. optimization of ms adsorption onto snps. to determine the optimal concentration of moringa oleifera surfactant (ms) adsorbed onto silica nanoparticles (snps), ms was prepared at various concentrations ranging from 1 to 5 wt%, with each solution containing a fixed snps concentration of 0.2 wt% (figure 4). the snps were dispersed in 0.3 wt% brine. the mixtures were agitated on an orbital shaker at 300 rpm for 60 minutes at a controlled temperature of 37 oc. after agitation, the mixtures were filtered through whatman filter paper. the filtrates were then analyzed using a uv spectrophotometer to determine the concentration of ms remaining in solution. the adsorption of ms onto snps at equilibrium was calculated using eq. 4, adsorption (%) = ci−cf ×v w × 100 ,....................................................................................................................(4) where ci is initial concentration of surfactant, wt% or mg/l; cf is final concentration of surfactant, wt% or mg/l; v is volume of ms/snps mixture used, ml; w is weight of snps, g. figure 4—optimization of ms concentration. optimization of snps dosage. to determine the optimum dosage of silica nps (snps) for maximum adsorption, various concentrations of snps ranging from 0.1 to 0.5 wt% (figure 5) were prepared. each concentration contained a fixed amount of moringa oleifera surfactant (ms) at the previously determined optimum concentration, which was 4wt% after observing adsorption behaviour with initially a fixed low improved oil and gas recovery 6 concentration of 1wt% of ms. the mixtures were agitated for 60 minutes at 300 rpm and 37°c. following agitation, the mixtures were filtered, and the filtrates were analyzed using a uv spectrophotometer to assess the concentration of ms remaining in solution. figure 5—optimization of snps dosage. optimization of contact time. for optimizing contact time, the fixed concentrations of ms (4 wt%) and snps (0.4 wt%) were used. the mixtures were agitated for varying periods of 30, 60, 90, 120, and 150 minutes (figure 6). after the specified agitation times, the mixtures were separated by filtration, and the filtrates were analyzed using a uv-visible spectrophotometer to determine the adsorption efficiency at each time interval. figure 6—contact time optimization of ms/snps. effect of temperature and ph on optimized formulation. after establishing the optimized conditions for concentration, dosage, and contact time, the effect of temperature on the formulation was evaluated. the mixture was heated to various temperatures of 20, 30, 40, 50, and 60 oc while maintaining constant shaking at 300 rpm. the samples were analyzed to determine the impact of temperature on the adsorption efficiency. to determine the optimum ph, the initial ph of the mixture (9.41) was adjusted to different values (2, 5, 7, 9, and 11) using 0.5n hcl and 0.5n naoh. a ph meter was used to achieve accurate ph adjustments. the resulting mixtures at these different ph levels were then analyzed using a uv spectrophotometer to assess the impact of ph on the adsorption process. foam studies. the ross-miles method, as illustrated in figure 7, was employed to evaluate the foamability and stability of moringa oleifera surfactant (ms) and the ms/silica nanoparticles (snps) formulation under optimized conditions (ummusalma and hamza 2023). for each solution, precisely 5 ml was transferred into a standardized burette (75×1.5 cm). the solution was then allowed to flow through the tap into a receiver vessel (measuring cylinder) positioned 9.5 cm below the tap. the turbulence generated during this process resulted in foam bubble formation. the maximum foam height was measured immediately after foam generation, and the half-life of the foam (t1/2) was recorded to assess the rate of foam degradation. foam height measurements were improved oil and gas recovery 7 taken above the water gradient, and it was crucial to maintain a constant distance between the burette and the measuring cylinder throughout the experiment. foamability and stability were determined based on average foam heights and stabilities, with each experiment being conducted in duplicate for accuracy. in addition, the ms/snps solution was prepared in brine (0.3%) and subjected to foamability and stability studies using the ross-miles method. figure 7—illustration of ross mile method. foam morphology analysis. the foam morphology is made up of the bubble size and distribution. using a high-resolution kern transmitted light microscope (obf-1), the foam microstructure was examined. in order to examine the bubble coalescence, changes in the size and dispersion of the bubbles were tracked at three different time intervals: 0, 5, and 10 minutes. the foam microscopic morphology was measured and captured on camera. interfacial tension (ift) measurement. the interfacial tension (ift) was measured using a spinning drop apparatus (svt20) at a temperature of 80°c and a rotational speed of 4000 rpm. the formulation of pure ms, ms/snps at optimum condition and brine baseline were prepared as shown in figure 8a. the ift between crude oil and brine systems was recorded to establish a baseline ift (freer et al. 2003).. the procedure involved the following steps: 1. the ift tube was filled with brine and placed in the chamber of the spinning drop apparatus. 2. the tube was initially spun at approximately 500 rpm, and a drop of crude oil was introduced into the brine using a syringe. 3. the rotation maintained the oil drop at the center of the tube. the rotational speed was then gradually increased to 4000 rpm to ensure the drop stabilized and elongated into a spherical or cylindrical shape (figure 8b). 4. during this process, the drop image was continuously captured by a high-resolution camera attached to the apparatus. the ift values were automatically computed using the young-laplace equation, as shown in eq. 5, σ = δdω2ɑ3 2α ,....................................................................................................................................................(5) improved oil and gas recovery 8 where d stands for drop diameter, m; ω is the angular frequency, rad/s; ɑ is the cap radius, m; σ is the ift mn/m; and α is shape parameter. this procedure was conducted for all formulations of moringa oleifera surfactant (ms) and ms/silica nanoparticles (snps). (a) formulations for ift & contact angle measurement (b) oil drop in continuous phase during ift measurement figure 8—ift measurement. contact angle measurement. the contact angle measurement was performed to assess the wetting behavior of a liquid droplet on a solid surface. this measurement provides insights into the extent to which the liquid spreads or repels on the surface. the contact angle, defined as the angle formed between the tangent lines at the liquid-solid and liquid-vapor (or liquid-air) interfaces, was determined using a drop shape analyzer. the procedure included: 1. a slice of reservoir sandstone (figure 9a) was immersed in brine and each formulation separately for 48 hours to ensure full saturation of the rock (figure 9b). 2. the contact angle for the oil/brine system as a control was first measured by placing the saturated sandstone on the drop shape analyzer. an oil drop was then placed on the rock surface. 3. the contact angle was recorded by measuring the tangent lines at the liquid-solid interface from both sides (figure 9c). 4. this procedure was repeated for each formulation to compare the wetting behavior. (a)slice of reservoir rocks (b)saturation of rock slice in ms, ms/snps and brine solution (c)oil drop on rock surface figure 9—contact angle measurement. improved oil and gas recovery 9 results and discussion physico-chemical analysis. the physicochemical properties of moringa oleifera oil (mo) are summarized in table 1. the results reveal that the seeds yield a higher oil content (21%), attributed to the low moisture content and the chemical composition of the oil, which remains liquid at room temperature (brontson et al. 2020). the saponification value, which indicates the number of milligrams of potassium hydroxide (koh) required to saponify one gram of oil, suggests the suitability of mo for surfactant synthesis. this value is indicative of a lower average acid chain length (jekayinfa and bamgboye 2007), which is consistent with the relatively low acid number observed (toscano et al. 2012). consequently, the synthesis process yielded approximately 25.23 grams of surfactant. table 1—physicochemical analysis results of moringa oleifera oil (mo). physico-chemical parameters values state at room temp. liquid color of oil dark brown yield of oil (%) 21 moisture content (%) 10.05 sap. (mgkoh/g) 221.04 acid no. (mgkoh/g) 0.16 mass of ms (g) 25.23 the infrared spectroscopy data, presented in table 2, indicates significant chemical transformations during the conversion of mo to the surfactant (ms). specifically, the absorption peaks at 2923 and 2852 cm-1 observed for both mo and ms correspond to the symmetric and asymmetric stretching vibrations of ch2 and ch3 groups in the fatty acid chains. the peak at around 1800 cm-1 in mo is associated with c=o stretching, indicative of ester bonds present in triglycerides (cleide et al. 2010). in contrast, the peak observed around 1600 cm-1 in ms is related to the stretching of c=c bonds, which signifies the formation of new chemical bonds during the surfactant synthesis. these peak assignments are consistent with the findings reported by paixão et al. (2018). table 2—ftir identification of functional groups in mo and ms. functional groups mo ftir (cm-1) ms ftir (cm-1) c–h & ch2 st. 2923 & 2852 2923 & 2852 -c=o st. 1800 -c=c st. 1600 -c-h bend 1500 1500 -c-o bend 1240 1100 long chain 700 700 adsorption studies. in this study, a uv spectrophotometer was employed for calibration to establish a reference curve for moringa oleifera surfactant (ms) concentrations ranging from 1-5 wt%. the calibration plot of absorbance versus concentration, shown in figure 10a, yielded an r-squared value of 0.9949, indicating a high degree of correlation and validating the use of this data for subsequent adsorption studies. effects of ms concentration. the experimental data from adsorption studies, depicted in figure 10b, illustrate the adsorption patterns relative to ms concentrations. it is evident that an increase in ms improved oil and gas recovery 10 concentration leads to a corresponding increase in adsorption capacity. this observation highlights the significant role of surfactant concentration in influencing the adsorption efficiency. the interactions between nps (nps) and surfactants, crucial for the adsorption process, are mediated by electrostatic attraction, hydrogen bonding, hydrophobic interactions, and other forces (peng et al. 2017; zhong et al. 2019). identifying the point of maximum adsorption is critical for optimizing performance. the maximum adsorption capacity of ms was determined to be 60.58% at a concentration of 4 wt%, indicating effective facilitation of adsorption onto nps and a substantial surface coverage of the snps (yot et al. 2014). effect of snps dosage. figure 10c illustrates the effect of snps dosage on adsorption capacity. the results reveal a significant impact of snps dosage on adsorption efficiency, with a maximum adsorption of 96% achieved at a dosage of 0.4 wt%. this enhanced adsorption is attributed to the ms molecular structure, its surface activity, and its hydrophobic/hydrophilic balance (abooali et al. 2020). effect of contact time. the determination of equilibrium time is crucial for understanding the adsorption dynamics of ms on snps. as illustrated in figure 10d, the adsorption of ms increases with time, reaching a maximum of 91.8% at 90 minutes. beyond this point, further increases in contact time do not significantly impact adsorption. this equilibrium time is influenced by various factors including the nature of the adsorbate and adsorbent, temperature, pressure, and agitation conditions (gaya 2021). knowing the optimal contact time is essential for designing applications requiring specific adsorption levels. effect of temperature. temperature plays a significant role in both the kinetics and thermodynamics of the adsorption process. increased temperature generally accelerates adsorption rates and can reduce the necessary contact time, although excessively high temperatures may lead to desorption of the adsorbate from the adsorbent. conversely, lower temperatures can slow down the adsorption process or prolong the required contact time (zheng et al. 2004). figure 10e shows that the highest adsorption capacity, 81.7%, was achieved at 50°c. this indicates that moderate temperatures can enhance adsorption efficiency by optimizing the interaction between the surfactant and nps under consistent operational conditions, including dosage, contact time, and concentration. temperature affects the adsorption process by altering the kinetic and thermodynamic properties of surfactant-nanoparticle interactions. at moderate temperatures, reduced thermal energy can facilitate greater adherence of ms molecules to the snps surface (yi et al. 2023). effect of ph. the impact of ph on adsorption was also investigated. the adsorption capacity of ms onto snps was observed to be effective at the normal basic ph of 9.41, with a peak adsorption capacity of 82.99% at ph9 (figure 10f). ph affects the surface charge of nps, which in turn influences the binding affinity of surfactant molecules (haq et al. 2020). adjusting ph can minimize electrostatic repulsion between surfactant molecules and nps, enhancing adsorption through stronger attractive forces (rattanaudom et al. 2021). pattamas et al. (2021) reported that surfactant solubility is often ph-dependent, and at certain ph levels, surfactants can reach their critical micelle concentration (cmc), forming micelles that are more favorable for adsorption onto nps. optimal ph values can stabilize the colloidal suspension of nps, preventing agglomeration or precipitation (manyangadze et al. 2020). tailoring the ph can fine-tune adsorption behavior for specific applications. in this study, the objective is to achieve strong adsorption between surfactants and nps to generate robust nps-reinforced foams. improved oil and gas recovery 11 a) calibration curve of ms concentration b) effects of ms concentration c) effects of snp dosage d) effects of ms contact time e) effects of temperature f) effect of ph figure 10—adsorption analysis result adsorption isotherm models. adsorption isotherms are essential for designing adsorption processes as they provide insights into the relationship between the solute concentration in solution, held constant at specific ph improved oil and gas recovery 12 and temperature, and the equilibrium amount of adsorbate (ms) adsorbed onto the adsorbent (snps). the equilibrium data were analyzed for their fit with the freundlich and langmuir isotherm models. the langmuir isotherm model, as described by foo and hamid (2010), assumes the formation of a monolayer of adsorbate on the adsorbent surface. this model presupposes that all adsorption sites are energetically equivalent, and there is no interaction between adsorbed molecules, even on adjacent sites. the linearized form of the langmuir isotherm equation is expressed as: ce qe = 1 qob + ce qo ,..................................................................................................................................................(6) where ce is the equilibrium concentration, mg/l; qe is the amount adsorbed per unit weight of the adsorbent, mg/g; qo and b are the langmuir constants associated with the determined maximum adsorption capacity, mg/g; and adsorption affinity coefficient, 1/mg. this model helps in understanding the adsorption capacity and efficiency of the adsorbent by providing information about the saturation point of adsorption and the interaction between the adsorbate and adsorbent. the graph plotted between ce/qe vs. ce, as illustrated in figure 11a, can be used to determine the constants qo and b. in contrast, the freundlich isotherm model describes adsorption on a heterogeneous surface with a nonuniform distribution of adsorption sites and heat of sorption. this model is applicable to multilayer adsorption processes. the freundlich isotherm is expressed in its logarithmic form as follows, log(�e) = log (�) + 1 � log(�e) ,..................................................................................................................... (7) where ce is the equilibrium concentration of the adsorbate in solution, mg/l; k is the freundlich constant indicative of the adsorption capacity, mg/g; n is the freundlich exponent related to the adsorption intensity and adsorption efficiency; and qe is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium, mg/g. the freundlich model provides insight into the adsorption capacity and intensity, particularly in systems where the adsorption sites are not homogeneous and adsorption occurs in multiple layers. as seen in figure 11b, the empirical constants k and ln were derived using the linear adjustments between the log qe and log ce values. in general, the adsorption isotherms data reveal that the ms/snps experiment fitted better with freundlich isotherm having r2 of 0.9725 than the langmuir with r2 of 0.9052. figure 11—(a) langmuir isotherm and (b) freundlich isotherm model for ms-snps. improved oil and gas recovery 13 formability and stability analysis. the foamability results are depicted in figure 12a. it is observed that the initial foam heights for both ms and ms/snps are similar, indicating that the presence of snps at a concentration of 0.4% did not significantly affect the foamability of the ms. this result suggests that the low concentration of snps used in this study may have been insufficient to impact foam formation significantly, which aligns with the findings of ray et al. (2006). but this finding contrasts with several studies reporting that snps can influence the foamability of various surfactants (arifur et al. 2023; zenaida et al. 2021; hassan et al. 2022). one possible explanation for this discrepancy could be the specific nature of the ms surfactant molecules used. although increasing the concentration of snps might influence foamability, this study focused on the optimum adsorption dosage to avoid potential formation damage. as time progresses, there is a noticeable decrease in foam heights for all samples. this decline is consistent with previous observations that brine affects initial foam heights (abbas et al. 2024; alireza and delshad 2023; hamza et al. 2022). the foam half-life (t1/2), defined as the time required for the foam to decompose to half of its initial volume, is shown in figure 12b. foam half-life is a key indicator of foam stability. while the exact number of degraded bubbles cannot be directly counted, foam height over time provides an indirect measure. foam heights were normalized using the ratio of heights at time t to initial heights t0. the foam half-lives for ms, ms/snps, and ms/snps+brine were found to be 5, 3.2, and 3.2 minutes, respectively. a longer foam half-life generally indicates better quality and stability of the foam, which is crucial in enhanced oil recovery (eor) foam experiments (hamza et al. 2017). figure 12—(a) foamability profile and (b) foam stability. microscopic analysis of foam bubbles. from the microscopic dimension analysis, the representative foams were examined by measuring bubble sizes and counting bubble numbers, with average foam bubble sizes presented in table 3. the data indicate that the bubble size in ms foams increased linearly with time. this trend suggests that as time progresses, bubbles grow larger until they rupture and collapse due to coalescence. in contrast, the addition of snps led to a decrease in bubble size. this alteration in the rheological properties of the liquid phase in the foam makes it more resistant to drainage and coarsening, thereby stabilizing the foam and preventing destabilization. the presence of brine also affected bubble sizes, demonstrating a linear increase with time. this observation supports the impact of brine on foamability, as previously noted. notably, a decrease in bubble size was observed with respect to ms at 0 and 5 minutes, followed by an increase. improved oil and gas recovery 14 the process of bubble coalescence can be categorized into three stages: particle collision, liquid film draining during collision, and rupture leading to larger particles. typically, large air packets entrained in high-velocity free surface flows break into smaller bubbles and move to areas of lower shear stress, where further bubble coalescence can occur (ummusalma and hamza 2022). table 3—foam bubble size and distribution. time (min) ms bubble size (cm) bubble distr. (cm) msnp bubble size (cm) bubble distr. (cm) msnp+brine bubble size(cm) bubble distr. (cm) 0.00 4.66 8.20-8.89 3.84 8.60-0.80 4.17 1.48-8.49 5.00 4.68 2.59-08.08 3.95 0.85-6.20 5.23 1.48-9.05 10.00 5.33 1.04-13.89 5.42 1.19-12.49 5.37 1.67-10.87 ift measurements. as shown in table 4, the average ift value for the oil/brine system was measured at 6.22 mn/m. this value represents the baseline interfacial force between the oil and brine, serving as a reference point for evaluating the effects of various treatments. the introduction of ms and ms/snps led to significant reductions in ift. specifically, the ift values dropped to an ultralow level of 0.001 mn/m for ms and 0.01 mn/m for ms/snps. these reductions highlight the effectiveness of the surfactant (ms) and nanoparticles (snps) in reducing interfacial tension. the dramatic decrease in ift is attributed to the surface-active properties of the surfactant and the nps. the surfactant molecules lower the ift by adsorbing at the oil-brine interface, while the snps enhance this effect through their own surface-active properties (li et al. 2013; hamza et al. 2018). achieving a low ift is crucial for successful enhanced oil recovery (eor) operations as it facilitates the release of oil from the reservoir. interestingly, snps alone were able to maintain the ift of ms at a nearly identical ultralow level. this result underscores the potential of combining nps with surfactants to sustain effective ift reduction. several studies have explored the synergistic effects of combining nps with surfactants to achieve significant reductions in ift (hamza et al. 2022; xiao et al. 2023). the ability of snps to maintain such low ift levels emphasizes their role in enhancing the performance of surfactants in eor applications. table 4—average value of ift. time (s) brine (mn/m) ms (mn/m) msnp (mn/m) 20 6.24 1.37×10-3 1.34×10-3 40 6.24 8.33×10-4 4.00×10-7 60 6.35 9.79×10-4 1.31×10-3 80 6.24 1.07×10-3 1.43×10-3 100 6.03 8.44×10-4 2.30×10-6 average 6.22 1×10-3 1×10-2 contact angle measurements. the illustration of some contact angle profiles for various fluids are presented in figure 13. from these profiles, the average contact angle for each fluid was calculated and presented in table 5. the baseline contact angle of the oil/brine system was found to be approximately 20.58±4.6°, serving as a control for evaluating the effects of ms and ms/snps mixtures. this control fluid exhibited the highest average contact angle, indicating a relatively low wettability of the surface. this lower wettability is likely due to minimal interactions between the reference fluid and the reservoir rock, resulting in reduced spreading (hassan et al. 2022). improved oil and gas recovery 15 in contrast, the introduction of ms and ms/snps led to significant reductions in the contact angle. specifically, the contact angle decreased from 20.58±4.60° in the baseline to 16.34±2.66° for ms and further to 15.67 ± 4.06 ° for ms/snps. this reduction demonstrates the effectiveness of both ms and ms/snps in improving wettability, which is indicative of their ability to reduce interfacial tension significantly. the observed differences in contact angle values reflect variations in wetting behavior and surface interactions with the reservoir rock (hassan et al. 2021). notably, the ms/snps mixture showed that snps acted synergistically with the ms surfactant, resulting in an approximate 24% reduction in ift. this synergy corroborates the substantial adsorption capacity of the ms/snps system discussed earlier. figure 13—contact angle profile. table 5—average values of contact angle. fluid average ca (o) % ca reduction brine 20.58 ± 4.60 ms 16.34 ± 2.66 20 ms/snps 15.67 ± 4.06 24 conclusions this study successfully extracted essential oils from a natural source and used them to synthesize a biosurfactant with high efficiency. significant adsorption of ms onto snps was observed, attributed to van der waals forces and electrostatic interactions between surface charges. the optimal conditions for nanofluid adsorption were determined to be 4 wt% ms and 0.4 wt% snps, at a temperature of 50°c and ph 9. these conditions align well with the freundlich isotherm model, showing an r² value of 0.9725. the foamability and stability studies demonstrated favorable results, including substantial interfacial tension (ift) reduction and improved wettability. this novel hybrid material shows promise for enhanced oil recovery (eor) applications, offering potential environmental benefits over traditional synthetic surfactants. additionally, it may present economic advantages for the oil and gas industry, particularly in light of the high costs associated with treating produced water using conventional synthetic surfactants. further research is recommended to explore the detailed chemistry of interactions between nps and surfactants to gain a deeper understanding of this phenomenon and optimize its applications. improved oil and gas recovery 16 acknowledgement the authors acknowledged bayero university kano, nigeria, universiti teknologi mara, malaysia and universiti teknologi petronas, malaysia. nomenclature a = volume of koh solution; b = blank ; b = adsorption affinity coefficient, 1/mg; ce = equilibrium concentration, mg/l; ci = initial concentration, wt% or mg/l; cf = final concentration, wt% or mg/l; ca = contact angle, o; ceor = chemical enhanced oil recovery; cmc = critical micellar concentration; d = drop diameter, m; eor = enhanced oil recovery; ftir = fourier transform infrared spectroscopy; ift = interfacial tension; k = freundlich constant; koh = potassium hydroxide; m = mass, g; m = molarity, mol/l; m1 = initial mass, g; m2 = final mass, g; mbpd = millions barrel per day; ms = moringa oleifera surfactant; mo = moringa oleifera oil; n = normality, eq/l; n = freundlich exponent; nps = nanoparticles; ooip = original oil in-place; qe = amount adsorbed per unit weight of the adsorbent, mg/g; qo = langmuir constants ; snps = silica nanoparticles; s = sample; t1/2 = half-life; uv = ultra violet; v = volume, ml; w = weight, g; h = foam height, cm; σ = ift, mn/m; ω = angular frequency, rad/s; ɑ = cap radius, m; α = shape parameter, m; improved oil and gas recovery 17 competing interests the author(s) declare that they have no conflicting interests. references abbas, k.m., mahboobeh, m., jagar, a., et al. 2024. performance evaluation of the green surfactant-treated nanofluid in enhanced oil recovery: dill-hop extracts and sio2/bentonite nanocomposites. energy & fuels 38(3):1799-1812. abooali, d., soleimani, r., and gholamreza-ravi, s. 2020. characterization of physico-chemical properties of biodiesel components using smart data mining approaches. fuel 266(1): 117075. ahmadi, m. a. and shadizadeh, s.r. 2013. induced effect of adding nano silica on adsorption of a natural surfactant onto sandstone rock: experimental and theoretical study. journal of petroleum science and engineering 112(1): 239247. ali, a., yusof, y.a., chin, n.l., et al. 2017. processing of moringa leaves 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b.a., soltero-m., j.f.a., et al. 2021. aqueous foams and emulsions stabilized by mixtures of silica nanoparticles and surfactants. chemical engineering journal advances 7(1):100116. zhang, j., gao, h., and xue, q. 2020. potential applications of microbial enhanced oil recovery to heavy oil. crit. rev. biotechnol. 40(1):459-474. zhao, g., dai, c., zhang, y., et al. 2015. enhanced foam stability by adding comb polymer gel for in-depth profile control in high temperature reservoirs. journal of physicochemical and eng. aspects 482(1):115-124. zheng, h., huang, f.k., and jiming, h. 2004. effect of contact time adsorption of rhodamine b, methyl orange and methylene blue colors on langsat shell with batch methods. j. phys.: conf. ser. 1788(1):012008. zhong, x., li, c., pu, h., et al. 2019. increased nonionic surfactant efficiency in oil recovery by integrating with hydrophilic silica nanoparticle. energy fuels 33(1):8522-8529. umar hassan is an assistant quality assurance/control officer at dangote petroleum refinery and petrochemical (dprp), nigeria. he holds bsc. (hons.) in industrial chemistry from bayero university kano, nigeria, in 2017, and currently a registered postgraduate (msc) student of physical chemistry (awaiting viva) in the department of pure & industrial chemistry, bayero university kano, nigeria. his research revolves around exploring the potential of nanotechnology for enhanced oil recovery. dr. mohammed falalu hamza is a senior lecturer in the school of chemistry & environment, universiti teknologi mara (uitm), malaysia. prior to joining uitm in 2024, dr. falalu has worked for about 11 years at the department of pure & industrial chemistry, bayero university kano (buk), nigeria. dr. falalu’s research focuses in nano chemistry with applications in enhanced oil recovery (eor), surfactant formulation, foam generation, nanoparticles modification, transport phenomena and formation damage. he holds b.sc. (hons.) in industrial chemistry from buk, nigeria, in 2009, msc in chemistry from university of kwazulu natal, south africa, in 2014, phd in applied sciences from universiti teknologi petronas (utp), malaysia, in 2019, and postdoctoral research at institute of hydrocarbon recovery, utp, malaysia, in 2023. dr. hassan soleimani is an associate professor of physics (wave propagation), universiti teknologi petronas where he has been working as a faculty member for 16 years. his research interests are in nanotechnology, electromagnetism, materials science, optics and geophysics. dr. hassan holds bsc. (hons.) in physics from university of isfahan, iran in 1992, msc. in physics from bahonar kerman university, kerman, iran in 1997, and phd in physics from university putra malaysia (upm), malaysia in 2010. dr. soleimani has served as a visiting scientist at university of cambridge, uk (2012), wright state university, usa (2013), university of patras, greece (2014), and griffith university, australia (2015). dr. bashir abubakar abdulkadir is a postdoctoral fellow with the centre for research in advanced fluid & processes, universiti malaysia pahang. he holds b.sc. (hons.) in chemistry from gombe state university (gsu), nigeria in 2010, msc. and phd in chemistry from universiti teknologi petronas, malaysia in 2015 and 2022, respectively. he has been a lecturer at gsu, nigeria and actively undertake research in polymer electrolytes as energy sources, catalysts and catalysis for hydrogen storage and production. dr. saifullahi imam shehu is a lecturer and researcher in the department of pure and industrial chemistry, bayero university kano (buk), nigeria. he holds phd in surface chemistry and catalysis from universiti improved oil and gas recovery 20 sains malaysia, in 2020, msc in physical chemistry from srm university, india in 2015, and bsc. (hons) in chemistry from buk, nigeria in 2010. his research interests are in environmental remediation, photocatalysis, fenton reactions, conversion of wastes to wealth and adsorption. dr. sabiha hanim saleh is an associate professor chemistry & environment in the school of chemistry & environment, universiti teknologi mara (uitm), malaysia. her research interests are in industrial waste utilization and green chemistry. dr. saleh holds phd in environmental health & waste management from universiti sains malaysia (usm) in 2010, msc. in environment from universiti putra malaysia (upm) in 1999, bsc. (hons.) in chemistry from universiti kebangsaan malaysia (ukm) in 1996, and diploma in science, institut teknologi mara (itm) in 1992. abstract introduction methodology results and discussion conclusions acknowledgement nomenclature competing interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1280 received march 7, 2023; revised april 7, 2024; accepted april 21, 2024. *corresponding author: skippin1994@yahoo.com 1 parametric evaluation on the interfacial tension response of agro-surfactant chukwuebuka francis dike*, nkemakolam chinedu izuwa, anthony kerunwa, nzenwa dan enyioko, enyang lilian ndoma-egba, chukwuebuka gabriel mbah, ogonnaya michael ogbuatu, federal university of technology, owerri, nigeria abstract the introduction of surface active agent such as surfactants reduces interfacial tension (ift) between the oilwater systems to yield higher oil recovery. this reduction continues with surfactant concentration until the critical micelle concentration is attained. the ift reduction capacity of surfactant in brine-oil system is impacted by the surfactant concentration, salt concentration, temperature variation and polymer concentration. in this study, parametric evaluation was conducted to determine the impact salinity, temperature and polymer on the ift value of costus afer extracts (cae), vernonia amygdalina extract (vae), carica papaya extract (cpe) and sodium lauryl sulfate (sls). from the result of ift at varying salinity, cae, vae and cpe is not suitable for high saline environment. from the result of ift at varying temperature, cae and cpe have dominant nonionic properties, while vae showed dominant anionic properties. from the result of ift at varying polymer, polymer introduction reduces the ift value of the surfactants. introduction chemical enhanced oil recovery (ceor) is the most widely used enhanced oil recovery (eor) approach (sedaghat et al. 2013), and deals with the introduction of surfactant, alkaline, polymer or their hybrid in improving oil recovery from reservoir rock (izuwa et al. 2021a). ceor improves oil recovery using mechanisms such as wettability alteration, interfacial (ift) reduction, mobility control, polymeric viscoelastic and permeability reduction (afolabi 2015). of the chemicals utilized in ceor are surfactant which reduces the ift between brine and water (kerunwa 2020). surfactant comprises of hydrophobic and hydrophilic group which influences its behavior in a brine-oil system. based on the hydrophilic head, surfactants can be categorized into zwitterionic (+ve and –ve), cationic (+ve), anionic (-ve_ and non-ionic (neutral) (schramm 2000). the anionic and nonionic surfactants are the most widely accepted for ceor (coung et al. 2017). the anionic surfactant are classified into sulfate, sulfonate, phosphate and carboxylate, while non-ionic surfactants are ether, ester, phenol, hydroxyl and amine (nikunji and tejas 2017). anionic surfactants are the most preferred for ceor due to their high effectiveness in lowering ift, low adsorption on sandstone and high temperature stability (jeirani et al. 2014). the combination of anionic and non-ionic surfactant enhances their tolerance in formation water with high salt concentration (sheng 2011). ift responses of surfactant in a brine and oil system can be impacted upon by parameters such surfactant concentration, alkaline concentration, salt concentration, temperature variation and polymer concentration. the introduction of surfactants concentration into brine-oil system reduces their ift until a point which further surfactant concentration increase yields no reduction in ift (ali et al 2020). this surfactant concentration is referred to as critical micelle concentration (cmc), and can be used to identify the best surfactant at low concentration (onykonwu and akaranta 2016). after the cmc ift values stabilizes or in some cases increase depending on the type and nature of the surfactant utilized. for crude oil with high total acid number (tan), the concentration of alkali in the solution mailto:skippin1994@yahoo.com 2 determine the percentage of in-situ surfactant which might or might not reduce ift. the ability of an alkali material to reduce ift is tied to its ph value (krumrine et al. 1982). when combined with surfactant, alkali further reduces the ift between oil-water systems. the salinity level of water-oil system particularly at low salt concentration could potentially reduce ift (obuebite et al. 2020). for solutions containing surfactantcontaining solution, ift value drops with increase in salt concentration until optimal salinity stage before further increase in salinity starts to increase ift (bera and mandal 2015). the introduction of polymers tends to increase viscosity of solutions and influence ift value. polymer have tendency to reduce ift at low concentration with surfactants (izuwa et al 2021b). the introduction of heat to surfactant based solutions, yield further reduction in their ift values (jiramet et al. 2017). in the study the ift response of the selected surfactants were characterized using fourier transform infrared spectroscopy (ftir) before been evaluated at varying salinities, varying temperature and varying polymer concentrations. costus afer extract (cae), vernonia amygdalina extract (vae), carica papaya extract (cpe) and sodium lauryl sulfate (sls) were used as surfactant while araucaria columnaris extracts (ace), terminalia mantaly extracts (tme) and xanthan gum (xg) were utilized as polymers. materials and methods materials. the material used for the study includes; 3 locally sourced agro-surfactant; carica papaya extracts (cpe) and vernonia amygdaline extracts (vae), conventional surfactant: sodium lauryl sulphate (sls), biopolymer: xanthan gum (xg), terminalia mantaly (tme) and araucaria columnaris (ace). industrial salt (nacl), agilent 19091s-433ui gas chromatograph (gc) system, attensio sigma 702/702et tensiometer, beaker, test-tube, syringe, weigh balance and crude oil. the crude oil was gotten from a field in the nigerdelta. the crude oil has api gravity of 34.97o, specific gravity of 0.84 and dynamic viscosity of 3.752cp (at room temperature). preparation of materials. the carica papaya extract and vernonia amygdaline extract was recovered from the tree, washed thrice with deionized water to remove unwanted materials and dried for 24hrs at room temperature. the dried leaves were crushed into smaller particles. the pulverized leaves were soaked in water (%wt concentration of the required ceor fluid) for 4hrs, before utilization for the lab evaluation. the costus afer stems were washed with deionized water three times to effectively remove unwanted material. the top, bottom and outer body of the stem were effectively removed to ensure that only the inner component of the costus afer stem. the inner component of the costus afer stem were sliced into smaller sizes before mechanical press was conducted to recover extracts. the extract were purified by filtration using api filter paper. gas-chromatography. the crude oil sample was evaluated using agilent 19091s-433ui gas chromatograph (gc) system fitted to a fused silica capillary column (30m x 0.5mm id) and connected to the agilent mass selective detector (msd). 1µ was introduced into the gc system using the automatic liquid sampler (als). the oven temperature was sustained for 0min at 50oc, 50-200oc at 15oc/min, 200-250oc at 10oc/min, 250-280oc for 1min. the mass spectrometer made use of 70ev electron energy, ion source temperature of 250oc and interface temperature of 280oc ftir evaluation. fourier transform infrared (ftir) evaluation was used for this study. m530 modelled bulk scientific infrared was used for the ftir experimental analysis. 0.5g of the local samples were mixed with 0.5g of potassium bromide (kbr) nanomaterial, after which 1ml of nujol (a solvent for preparation of sample by the spectrophotometer) was introduced into the samples using syringe to form a paste before introducing it to the apparatus and a wavelength of 600-4000cm-1 is used to derive spectra heights. the spectroscopy yields chart in absorbance spectra form, which indicates the molecular structure and chemical bonds present in the sample. the analytical spectra derived for each substance were then compared with the catalogue of the instrument to determine the functional group present. ift test. the ift analysis was used in the determination of the critical surfactant concentration of the locally sourced surfactants. attension sigma 702/702et tensiometer was utilized for the study. the procedures 3 utilized was obtained from operation manual of the tensiometer. the ift between the oil-brine systems was first determined before the introduction of surfactant with concentration depicted in table 1. the impact of salt concentration on surfactant’s ift was studied with brine formulation depicted in table 2. the impact of temperature variation on surfactant’s ift was studied with temperature ranges depicted in table 3. the impact of varying polymer concentration on surfactant’s ift was studied with formulation depicted in table 4. table 1—surfactant formulation for ift test. s/n surfactant surf. conc. (%wt) salt conc. (%wt) 1 cae 1%wt 5000ppm 2 vae 1%wt 5000ppm 2 cpe 1%wt 5000ppm 3 sls 1%wt 5000ppm table 2—brine formulation for ift test (nacl). s/n surfactant surf. conc. (%wt) brine formulation 1 cae 1%wt 10,000pm, 15,000ppm, 20,000ppm, 25,000ppm and 30,000ppm 2 vae 1%wt 10,000pm, 15,000ppm, 20,000ppm, 25,000ppm and 30,000ppm 3 cpe 1%wt 10,000pm, 15,000ppm, 20,000ppm, 25,000ppm and 30,000ppm 4 sls 1%wt 10,000pm, 15,000ppm, 20,000ppm, 25,000ppm and 30,000ppm table 3—temperature variation for ift test. s/n surfactant surf. conc. (%wt) salt conc. (%wt) temperature variation 1 cae 1%wt 5000ppm 27, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100 2 vae 1%wt 5000ppm 27, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100 3 cpe 1%wt 5000ppm 27, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100 4 sls 1%wt 5000ppm 27, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95 and 100 table 4—polymer variation for ift test. s/n polymer polymer concentration (%wt) 1 ace 0.25%wt, 0.5%wt and 1%wt 2 tme 0.25%wt, 0.5%wt and 1%wt 3 xg 0.25%wt, 0.5%wt and 1%wt 4 results and discussion gas-chromatography. table 5 shows the various component present in the crude oil. as shown in table 5, the crude oil comprised majorly of naphthalene, iso-alkane, n-alkane, alcohol, alkyl-alkanes, anhydrites, ester, carboxylic acid and aldehydes. the aldehyde recorded 24% of the crude, carboxylic acid recorded 15%, alkylalkane recorded 26%, iso-alkane recorded 13.37% while anhydride recorded close to 7.5% percent composition. the crude oil contained 51.819% paraffin, 32.293% naphthalene, 32.293% carboxylic acid and 0.9839% other compounds. eser (2013) grouped crude oil into paraffinic, paraffinic-napthaenic, naphthenic, aromaticnaphthenic, aromatic-asphaltic and aromatic-intermediates based on the relative abundance of paraffin, aromatics and naphthene compounds. the relative abundance of alkane and alkane related compounds in the crude oil, shows that the crude oil is a paraffinic crude oil and its in-line with its high api gravity result. table 5—compositional analysis of all components of crude oil. pk# rt area% library/id 1 5.212 0.08 decahydro-8a-ethyl-1,1,4a,6-tetram ethylnaphthalene bicyclo[3.1.1]heptane-2-carboxalde hyde, 6,6-dimethylcyclohexane, 1-(cyclohexylmethyl)-2-ethyl-, trans2 5.630 0.20 undecane octadecane decane, 2-methyl3 5.630 0.31 dodecane carbonic acid, prop-1-en-2-yl tridecyl ester carbonic acid, prop-1-en-2-yl tetradecyl ester 4 5.733 0.17 4-methyl-trans-3-thiabicyclo[4.4.0] decane naphthalene, 1,4,5-trimethylnaphthalene, 1,4,6-trimethyl5 5.909 0.31 decahydro-8a-ethyl-1,1,4a,6-tetramethylnaphthalene 3,7-dimethyl-6-nonen-1-ol 3-cyclohexene-1-carboxaldehyde, 1,3,4-trimethyl 6 5.991 0.21 4-methy-trans-3-thiabicyclo[4.4.0]decane naphthalene, 2,3,6-trimethylnaphthalene, 1,6,7-trimethyl7 6.153 0.59 p-menth-8(10)-en-9-ol, cisoctatriacontyl pentafluoropropionate e-2-tetradecen-1-ol 8 6.431 1.54 tridecane 2-piperidinone, n-[4-bromo-n-butyl]pentadecane 9 6.820 2.17 tridecane methoxyacetic acid, 2-tridecyl ester dodecane, 4,9-dipropyl10 6.911 0.82 cyclopentane, 1-pentyl-2-propyl3-methyl-4-(methoxycarbonyl)hexa-2, 4-dienoic acid 5 1,2-cyclohexanediol, cyclic sulfite, trans11 7.254 19.97 tridecane, 7-hexyldodecane, 2-methyl-8-propyldecane, 2-methyl12 7.922 0.26 pentadecane pentadecane pentadecane 13 7.996 0.37 dodecane, 2,6,10-trimethylmethoxyacetic acid, 4-tetradecyl ester methoxyacetic acid, 2-tridecyl ester 14 8.618 1.73 nonadecane hexadecane, 1-chlorohexadecane, 1-chloro15 9.282 4.84 octadecane, 1-chlorocarbonic acid, hexadecyl prop-1-en-2-yl ester tritetracontane 16 9.822 13.37 1-octadecene 1,2-benzisothiazole, 3-(hexahydro1h-azepin-1-yl)-, 1,1-dioxide z-8-methyl-9-tetradecen-1-ol acetate 17 9.917 6.70 nonadecane, 2-methylbatilol 1-octadecanesulphonyl chloride 18 23.117 2.7 2-dodecen-1-yl(-)succinic anhydrid squalene 17-pentatriacontene 19 24.77 14.90 propionic acid, 3-iodo-, heptadecyl ester 1-docosene 8-hexadecenal, 14-methyl-, (z)20 25.005 4.71 2-dodecen-1-yl(-)succinic anhydrid 1-hexacosene aspidospermidin-17-ol, 1-acetyl-19, 21-epoxy-15, 16-dimethoxy21 35.46 24.06 cyclopropaneoctanal, 2-octylerucic acid octadecane, 1-(ethenyloxy)ftir characterization. figures 1 to 4 provide a comprehensive evaluation through fourier transform infrared spectroscopy (ftir) of both agro-surfactants and synthetic surfactants. this analysis unveiled the hydrophobic and hydrophilic compositions of these chemicals, revealing a spectrum of functional groups.arranged in ascending order of wavelength, the identified functional groups include c-br, c-cl, r-o-r, h2c=ch3, h2c=ch, rnh3, rcooh, r-c≡n, ch2, r-s-c≡n, rchoh, r2choh, r2nh, r3n, and r3choh. remarkably, agro-surfactants such as cpe, vae, and cae demonstrated a striking similarity in their hydrophilic components (ether, amine, nitriles, carboxylic, and hydroxyl) as well as their hydrophobic tails 6 (methylene and ethene) when compared to the conventional surfactant sls. upon scrutinizing the ftir spectra of sls and cpe, it was noted that the ester functional group was absent, whereas vae and cae exhibited its presence. this observation underscores a notable resemblance in composition between synthetic and agro-surfactants. ahmed et al. (2019) categorically classified anionic surfactants into carboxylate, sulfate, sulfonate, and phosphate groups, while non-ionic surfactants predominantly comprise ether and hydroxyl groups. the presence of ester, hydroxyl, carboxylic, ether, and amine groups in the agro-surfactants suggests their potential to exhibit both non-ionic and anionic surfactant behavior. this versatility makes them suitable for applications in sandstone reservoirs and high salt concentration environments, aligning closely with the findings of tadros (2014). figure 1—ftir spectra for cae. figure 2—ftir spectra for cpe. 7 figure 3—ftir spectra for vae. figure 4—ftir spectra for sls. 8 interfacial tension. in figure 5, we delve into the interfacial tension (ift) responses of cae, vae, cpe, and sls. the data showcased reveals initial ift values of 12.43 mn/m, 9.98 mn/m, 11.35 mn/m, and 6.93 mn/m respectively for these surfactants. upon their introduction into the brine-oil system, a significant reduction in ift was observed. specifically, cae, vae, cpe, and sls contributed to reductions of 53.96%, 63.04%, 57.96%, and 74.33% respectively, when compared to the initial ift of the brine-oil system. these findings align closely with the research conducted by kerunwa (2020), which emphasizes the effectiveness of surfactants in diminishing the ift between brine-oil systems. moving forward, in figure 6, we further explore the impact of salinity on the ift responses of cae, vae, cpe, and sls. figure 5—interfacial tension (ift) of the surfactants. as illustrated in figure 6, the interfacial tension (ift) dynamics of various surfactants, including cae, vae, cpe, and sls, exhibit intriguing responses to changes in salinity levels. for cae, as salinity escalates from 5000 ppm to 30000 ppm, we observe a noteworthy rise in ift, increasing from 12.43 mn/m to 16.65 mn/m. however, there's a slight deviation in this trend as the salinity peaks at 20000 ppm, resulting in a temporary decrease in ift before resuming its upward trajectory. on the other hand, vae displays a consistent uptick in ift with increasing salinity, from 9.98 mn/m to 11.04 mn/m as salinity climbs from 5000 ppm to 30000 ppm. similarly, cpe records a progressive increase in ift from 11.35 mn/m to 12.92 mn/m over the same salinity range. interestingly, sls exhibits a nuanced response, with an initial increase in ift from 6.93 mn/m to 7.2 mn/m as salinity escalates from 5000 ppm to 10000 ppm, followed by a subsequent reduction in ift down to 6.16 mn/m as salinity further increases to 30000 ppm. these observations resonate with findings from bera and mandal (2014), suggesting that the relationship between salinity and surfactant ift values can vary, with both increases and decreases in ift being possible outcomes of salinity variations. 9 figure 6—impact of salinity on the ift of the surfactants. in figure 7, we delve into the interplay between temperature fluctuations and interfacial tension (ift) responses across various surfactants, namely cae, vae, cpe, and sls. the data reveals intriguing trends as temperatures climb from 27°c to the boiling point at 100°c. for cae, we observe a gradual decline in ift values from 12.43 mn/m at 27°c to 7.98 mn/m at 100°c. similarly, vae experiences a reduction from 9.89 mn/m to 7.75 mn/m over the same temperature range. cpe showcases a decline from 11.26 mn/m to 7.84 mn/m, while sls demonstrates a more pronounced drop from 6.82 mn/m to 4.89 mn/m. notably, non-ionic surfactants exhibit greater sensitivity to temperature changes compared to anionic surfactants. this aligns with findings by izuwa et al. (2021b), suggesting that the composition of surfactants influences their response to temperature variations. the response of cae and cpe to temperature variation change could be attributed to it having more non-ionic surfactant properties. vae and sls recorded similar ift reduction pattern and comprised of more anionic surfactant features. the reduction in ift value of the surfactant with increase in temperature is in-line with jiramet et al. (2017) study, which showed that increase in temperatures yields a drop in ift for define surfactant concentration. figure 7—impact of temperature on the surfactant ift behavior. 10 figures 8-10 depicts the impact of cae, tme, ace and xg polymer on the ift responses of vae, cpe and sls. as depicted in figure 8, the results from the cae tests indicate a noticeable decrease in ift from 12.43 to 8.78 mn/m and 8.71 mn/m with the introduction of 0.25% wt and 0.5% wt of tme respectively. however, with a further increase in tme concentration to 1% wt, there was a subsequent rise in ift from 8.71 to 10.33 mn/m. moving on to the vae trials, a decline in ift was observed from 9.98 to 9.47 mn/m and 9.06 mn/m with the addition of 0.25% wt and 0.5% wt of tme respectively. yet, when tme concentration was increased to 1% wt, there was an increase in ift from 9.06 to 9.7 mn/m. similarly, in the case of cpe experiments, there was a decrease in ift from 11.35 to 9.4 mn/m and 8.58 mn/m with 0.25% wt and 0.5% wt of tme respectively. however, with a further increase in tme concentration to 1% wt, there was a rise in ift from 8.58 to 8.83 mn/m. lastly, sls tests demonstrated a decline in ift from 6.93 to 5.78 mn/m and 5.67 mn/m with the inclusion of 0.25% wt and 0.5% wt of tme respectively. yet again, with an increase in tme concentration to 1% wt, there was a rise in ift from 5.67 to 5.73 mn/m. figure 8—impact of tme polymer on the surfactant ift behavior. as shown in figure 9, cae recorded ift drop from 12.43mn/m to 10.47mn/m and 8.78mn/m when 0.25%wt and 0.5%wt tme was introduced. further increase in ace concentration to 1%wt yielded ift rise from 8.78mn/m to 8.79mn/m. vae recorded ift drop from 9.98mn/m to 9.74mn/m when 0.25%wt ace was introduced. the ift however increased to 10.15mn/m at 0.5%wt ace before dropping to 9.68mn/m at 1%wt ace respectively. cpe recorded ift drop from 11.35mn/m to 10.12mn/m, 10mn/m and 9.91mn/m when 0.25%wt, 0.5%wt and 1%wt ace respectively. sls recorded ift reduction from 6.93mn/m to 6.02mn/m when 0.25%wt ace was introduced. further introduction of ace up to 0.5%wt and 1%wt concentrations, yielded a rise from 6.02mn/m to 6.09mn/m, and a drop from 6.09mn/m to 5.96mn/m respectively. 11 figure 9—impact of ace polymer on the surfactant ift behavior. in figure 10, cae recorded ift drop from 12.43 to 10.94 mn/m when 0.25% wt xg was introduced. further xg introduction from 0.5% wt and 1% wt increased ift from 10.94 to 11.28 mn/m, and reduced ift from 11.28 to 10.9 mn/m. vae recorded ift dropping from 13.34 to 10.19 mn/m and 9.66 mn/m at 0.25% wt and 0.5% wt xg concentration, respectively. further xg increase to 1% wt concentration yielded ift increase from 9.66 to 9.77 mn/m. cpe recorded ift increasing from 10.7 to 10.84mn/m and 10.98 mn/m for 0.25% wt and 0.5% wt xg concentration, respectively. further xg concentration introduction from 0.5% to 1% wt reduced ift from 10.98 to 10.72 mn/m. sls recorded an ift rising from 6.24 to 6.95 mn/m when 0.25%wt xg was introduced. further ace concentration yielded ift reduction from 6.95 to 6.92 mn/m and 6.83 at 0.5%wt and 1%wt polymer concentration, respectively. the reduction in ift of surfactant with polymer introduction was in-line with the observation of izuwa et al (2021b) study which indicated that polymer chemical tend to lower ift at low concentration with surfactants. this is also in agreement with abhijit et al (2011) study which confirmed the interaction of surface active agents and polymers, and also noted that further polymer concentration increase results in an increase in ift value. figure 10—impact of xg polymer on the surfactant ift behavior. 12 conclusions from the experimental analysis, the following conclusions can be made. 1. the presence of more alkane and alkane-related compounds characterized the crude oil as a paraffinic crude. 2. the surfactants reduced ift between brine-oil systems. sls recorded the least ift value of the surfactants utilized. 3. the local surfactants are not suitable for high saline environment. 4. cpe and cae have more non-ionic surfactant properties and are suitable for high temperature environment while vae have more anionic surfactant properties. 5. polymer at certain concentration reduces the ift values of the surfactant solution. conflicting interests the author(s) declare that they have no conflicting interests. reference abhijit, s., keka, o., ashis, s., et al. 2011. surfactant and surfactant-polymer flooding for enhanced oil recovery. advances in petroleum exploration and development 2(1): 13-18. afolabi, f. 2015. cost-effective chemical enhanced oil recovery. int. jour. of petrol. and petrochem 1(2): 111 ahmed, f.b., khaled, a.e., syed, m.m., et al. 2019. the effect of surfactant concentration, salinity, temperature, and ph on surfactant adsorption for chemical enhanced oil recovery: a review. jour. of petrol. explor. and prod. tech. 10:125-137. ali, e., amin, a., rafael, m.s., et al. 2020 mechanistic 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https://www.e-education.psu.edu/fsc432/content/elemental-analysis-and-ternary-classification-crude-oils. https://www.e-education.psu.edu/fsc432/content/elemental-analysis-and-ternary-classification-crude-oils. 13 obuebite, a. a., onyekonwu, m., and akaranta, o. 2020. an experimental approach to low cost, highperformance surfactant flooding. world journal of innovative research 8(1): 44-50. krumrine, p.h., falcone, j.s., and campbell, t.c. 1982. surfactant flooding 1: the effect of alkaline additives on ift, surfactant adsorption and recovery efficiency. spe j 22(4):503-513. sedaghat, m.h., ahadi, a., kordnejad, m., et al. 2013. aspect of alkaline flooding: oil recovery improvement and displacement mechanisms. middle east journal of scientific research 18: 258-263. sheng, j. 2011. modern chemical enhanced oil recovery, theory and practice, 1st edition. burlington:gulf professional publishing. tadros, t.f. 2014. an introduction to surfactants. berlin, boston:de gruyter. onyekonwu, m. and akaranta o. 2016. alkaline surfactant flooding in niger delta: experimental approach. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria. 2-5 august. spe-184271-ms. chukwuebuka francis dike is a master student in the department of petroleum engineering, federal university of technology owerri with research interest in enhanced oil recovery and reservoir engineering. nkemakolam chinedu izuwa is an associate professor in the department of petroleum engineering, federal university of technology owerri with research interest in reservoir engineering, enhanced oil recovery and gas engineering. izuwa holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, a master’s degree in petroleum engineering from university of port harcourt, and a phd degree in natural gas engineering from federal university of technology owerri. anthony kerunwa is a senior lecturer in the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum economics. kerunwa holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, a master’s degree in petroleum engineering from federal university of technology owerri, and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. nzenwa dan enyioko is a research technologist in the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids and enhanced oil recovery. enyioko holds a bachelor’s degree in geology from federal university of technology owerri. lilian ndoma-egba is a master’s candidate in the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids. chukwuebuka gabriel mbah is b.eng graduate of petroleum engineering with research interest in enhanced oil recovery. ogonnaya michael ogbuatu is a master’s candidate int the department of chemistry with research interest in petroleum chemistry. abstract introduction materials and methods results and discussion conclusions conflicting interests reference copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1328 received october 28, 2024; revised november 20, 2024; accepted december 30, 2024. *corresponding author: v.javanbakht@alumni.iut.ac.ir 1 separation of aromatic compounds from normal paraffinic petroleum mixture using geopolymer adsorbent based on metakaolin vahid javanbakht*, esfahan oil refining company, isfahan, iran; masoud fatemi, and maryam mehrabi, acecr institute of higher education (isfahan branch), isfahan, iran abstract metakaolin-based geopolymers are environmentally sustainable materials that can be synthesized from waste products. in this study, a metakaolin-based geopolymer adsorbent was synthesized, characterized, and evaluated for the removal of aromatic compounds from normal paraffin (c10-c13). the results indicated that modification of the geopolymer adsorbent with activated carbon enhanced its aromatic compound removal efficiency. however, when the activated carbon/metakaolin ratio exceeded 1:12, the removal efficiency declined. additionally, modification with hydrogen peroxide as a foaming agent resulted in a higher aromatic removal capacity compared to the unmodified geopolymer adsorbent. it was observed that increasing the temperature from 70 to 120 °c enhanced the aromatic removal efficiency by up to 21%. furthermore, increasing the adsorbent dosage from 0.001 to 0.1 g/l in petroleum samples led to an increase in aromatic compound removal. however, beyond this point, further increases in the adsorbent dosage resulted in a decrease in adsorption capacity. introduction aromatic hydrocarbons, characterized by the presence of one or more benzene rings, are key raw materials in the petrochemical industry. despite their high degree of unsaturation, aromatic hydrocarbons exhibit stability and resistance to addition reactions, making them significant environmental pollutants. the u.s. environmental protection agency classifies these compounds as carcinogenic. additionally, aromatic compounds have an inherently low cetane value, which poses a particular challenge in cold engine startup. high concentrations of polycyclic aromatic hydrocarbons (pahs) contribute to poor ignition performance in diesel engines, while also exacerbating environmental pollution. therefore, reducing the content of pahs in diesel and enhancing its cetane number is of considerable importance for both engine efficiency and environmental sustainability (liu et al. 2022). the separation of aromatics from surplus diesel fuel presents a promising approach to advancing the high-end development of the petroleum industry (li et al. 2023). the separation of aromatic and aliphatic hydrocarbons, a topic of study since the 1960s, remains a crucial process in the chemical industry (schwarz and malsch 2005; hadj-kali et al. 2017). however, the separation of aromatic hydrocarbons from linear and cyclic aliphatic hydrocarbons is challenging due to the proximity of their boiling points. furthermore, the similar physical and chemical properties of these compounds make their separation difficult in certain cases. the concentration of aromatic hydrocarbons in the feedstock plays a key role in determining the most suitable separation technology (ayuso et al. 2020). conventional methods for separating aromatic and aliphatic hydrocarbon mixtures, such as mailto:v.javanbakht@alumni.iut.ac.ir improved oil and gas recovery 2 extractive distillation, azeotropic distillation, and liquid–liquid extraction, are well-established (liu et al. 2018). however, these techniques are often challenging, expensive, and energy-intensive, particularly when separating aromatics from aliphatic mixtures due to their close boiling points and the tendency to form azeotropes (yao et al. 2019; feng et al. 2015). various methods have been developed for the removal of aromatic compounds from oily mixtures, including advanced oxidation processes (aops), adsorption, and biological processes (yang et al. 2015). among these, adsorption is widely regarded as an efficient and straightforward method for separation, and it has become a common technique in scientific research. activated carbon, in its normal or modified form, is frequently employed to remove aromatic organic compounds such as phenol (lyon-marion et al. 2018). in recent decades, polymerbased adsorbents have emerged as viable alternatives to activated carbon. geopolymers, which are inorganic polymeric aluminosilicate materials with an amorphous three-dimensional structure, are derived from industrial by-products such as fly ash, slag, and other waste materials. due to their excellent chemical and mechanical stability, minimal shrinkage upon formation, high-temperature resistance, and eco-friendly properties, geopolymers have gained significant attention for various applications (zhang et al. 2014). in separation processes, geopolymers have been utilized as membrane supports, catalyst supports, and adsorbents (monjezi and javanbakht 2023; eshghabadi and javanbakht 2024). for example, faghihian and mousazadeh (2007) investigated the separation of aromatic compounds from normal paraffin (c10-c14) using x13 molecular sieves. for the removal of cyclic aromatic compounds from water, kefi et al. (2011) employed titanium nanotubes, achieving removal efficiencies ranging from 90% to 100%. yao et al. (2015) utilized a co/mo (co3)2-layered double hydroxide (ldh) adsorbent, which demonstrated up to 94% removal of aromatic substances. costa et al. (2017) employed a mesoporous si-mcm-41 molecular sieve for the removal of polycyclic aromatic hydrocarbons, achieving adsorption efficiencies up to 93%. cyclodextrin-coated silica nanoparticles were used by topuz and uyar (2017) for the removal of aromatic compounds. kumar and mohan (2018) applied a mixture of 20% glycerin and 80% methanol for the extraction of aromatic compounds from kerosene. in the present study, geopolymer foams were synthesized using metakaolin in an alkaline activation medium with silicate precursors and hydrogen peroxide as a foaming agent. the resulting geopolymer foam was then employed as an adsorbent to remove aromatic compounds from normal paraffin (c10-c13) under various conditions. materials and methods materials. the analytical grade of the initial materials was used without further purification. sodium metasilicate (na2sio3), potassium hydroxide (koh), hydrogen peroxide (h2o2), sodium hydroxide (naoh), nitric acid (hno3), and were obtained from merck company, and metakaolin obtained from khorasan company. a diesel cut of aromatic (naphthalene and alkyl benzene) normal paraffin (c10-c13) compounds with 4000 mg/l aromatic concentration was obtained from eorc, iran. characterization. bet analysis for measuring surface area using bet device, belsorp mini ii model, bel japan co. scanning electron microscope (sem), mira iii model made in tescan for morphological analysis of the samples. a dr-5000 model, hach uv-vis spectrometer was used for measurement of sample concentration according to uop method 495-00. xrd analysis, pw1730 model, philips, was used for studying crystal structure by x-ray diffraction spectrometer ka cu ray 1/542 å wavelength and nickel filter. fabrication of the adsorbent. according to figure 1, 15 gr sodium hydroxide was dissolved in 30 ml of distilled water then 60 gr sodium silicate was added to the obtained alkaline solution. after homogenization, 60 gr metakaolin was added to the solution. after mixing, 8 ml hydrogen peroxide (30% v/v solution) was added to the resulted slurry gradually and mixed at 60°c for 2 h. considering the alkalinity of the combination, nitric acid 10 m was used for neutralization. the neutralized substances were filtered and dried in a furnace at 70 °c. to remove impure organic compounds, calcination was done at 500 °c for 24 h (by increasing temperature to improved oil and gas recovery 3 2°c/min). for fabricating adsorbent modified with activated carbon (ac-ads), 1:12, 1:6, and 1:3 ratio activated carbon were added to the initial suspension containing alkali sodium hydroxide, sodium silicate, and metakaolin. other stages were like stages of fabrication of base adsorbent (named ads). figure 1—the schematic representation of the adsorbent preparation. aromatic removal experiments. for aromatic removal experiments, a 1 g/l dose of the adsorbents in a sample of petroleum compounds with initial aromatic concentration of 4000 mg/l was prepared. then, mixtures containing the petroleum compounds and the adsorbents were shaken at temperatures of 70, 100, and 120 °c and 200 rpm, and sampling was performed at 12 h and their concentration was measured with the uv spectrophotometer. the amount of aromatic removal by the adsorbent was determined using the initial concentration c0 (mg/l), and the final concentration cf (mg/l) using the following equation, aromatic removal (%) = c0−cf c0 × 100% ............................................................................................................(1) results and discussion characterization results. sem images of produced adsorbents are shown in figure 2. based on sem images, the morphology of the ads particles is semi-spherical with relatively uniform size distribution but with agglomerating caused by small size of the particles. on the other hand, with modification of the adsorbent with activated carbon, structural changes are observed which is created a non-uniform porous but agglomerated structure in the ac-ads. improved oil and gas recovery 4 figure 2—sem images of the prepared adsorbents of ads (a) and ac-ads (b). figure 3 shows the xrd spectrum of produced adsorbents of ads (a) and ac-ads (b). the xrd pattern illustrates the amorphous characteristics of the prepared geopolymers with some crystalline structures. as observed, no significant changes occurred in the crystalline structure of the initial foam upon modification with activated carbon. figure 3—xrd analysis results for ads (a) and ac-ads (b). the nitrogen adsorption-desorption curve is shown in figure 4. the bet results show a typical iv isothermal curve and an h1 hysteresis loop according to the iupac classification. the hysteresis loop at high relative pressures reveals the mesoporous structure. according to the bet test data, the specific surface area (m2.g-1) are obtained about 10.14 and 39.33 for ads and ac-ads, respectively which represents the surface area increased with the increase of active components in the adsorbent structure. total volume of the pores (cm3.g-1) of 0.18 and 0.22, and average pore diameter of 72.10 and 22.24, were obtained for ads and ac-ads, respectively. (a) (b) improved oil and gas recovery 5 (a)ads (b)acads figure 4—bet analysis of fabricated adsorbents. the results of aromatic compounds removal by fabricated adsorbents. figure 5 shows the effect of temperature on removal of aromatic compounds by ads and ac-ads samples, for the petroleum compounds with initial aromatic concentration of 4000 mg/l. as observed, increasing the temperature results in a higher removal percentage of aromatic compounds by the adsorbents. according to the obtained results, the ac-ads shows a higher ability to aromatic removal in all of temperatures which can be resulted that the modification of the ads with activated carbon can improve the removal of aromatic compounds. figure 5—the effect of temperature on the removal of aromatic compounds by the ads and acads adsorbents for aromatic concentration of 4000 mg/l and 1 g adsorbent at contact time of 12 h. figure 6 shows the effect of hydrogen peroxide as a foaming agent for the adsorbent preparation on removal of aromatic compounds by ac-ads samples for the petroleum compounds with initial aromatic concentration of 4000 mg/l. the geo-polymerization process causes the formation of porous structures due to the bursting of oxygen bubbles formed by the hydrogen peroxide reaction in the geopolymer substrate (monjezi and javanbakht 2023). as it can be observed, the adsorbent modified with foaming agent, illustrates higher capability to aromatic removal which can because to pore creation in the adsorbent structure by hydrogen peroxide that increases the (a) (b) (a) (b) 0 5 10 15 20 25 70 100 120 a ro m at ic r em o v al ( % ) temperature (°c) ads ac-ads improved oil and gas recovery 6 active sites responsible for aromatic adsorption and finally increases the aromatic removal on the other hand, as it can be observed, increasing the temperature increases the aromatic removal with the adsorbent which is consistence with the previous results. for propose the mechanisms for aromatic compounds adsorption onto the prepared adsorbent, it can be mentioned that aromatic hydrocarbons have high viscosity and strong adsorption capacity (dang et al. 2019). as observed from the sem images, the prepared geopolymer consisted of non-flat and uneven surface which helps the mass transfer and uptake of the aromatic molecules onto the adsorbent. furthermore, electrostatic interaction and n–π interaction because of the presence of metal ions on the surface of the geopolymer such as al3+, may be the reason for uptake between the geopolymer surface and aromatic molecules. figure 6—the effect of hydrogen peroxide as a foaming agent for the adsorbent preparation on removal of aromatic compounds by ac-ads, initial aromatic concentration of 4000 mg/l, 1 g adsorbent at contact time of 12 h and for different temperatures. as shown in figure 7, by increasing the amount of adsorbent from 0.1 to 1 g, the aromatic removal increased which is due to the availability of more active sites for the adsorption process. furthermore, with more increase in the adsorbent dosage, the capacity of the adsorption decreases which may be due to increase in diffusion path length resulting from overlapping or aggregation of active sites for adsorption. figure 7—the effect of the adsorbent amount on the removal of aromatic compounds by ac-ads, initial aromatic concentration of 4000 mg/l. 0 5 10 15 20 25 70 100 120 a ro m at ic r em o v al ( % ) temperature (°c) without h2o2 with h2o2 0 2 4 6 8 10 12 14 0.1 0.5 1 5 a ro m at ic r em o v al ( % ) adsorbent amount (g) improved oil and gas recovery 7 on the other hand, modification of the geopolymer adsorbent with activated carbon more than 1:12 of ratio activated carbon/metakaolin, reduce the aromatic removal capability (figure 8). figure 8—the effect of the activated active content in the ac-ads on the removal of aromatic compounds, initial aromatic concentration of 4000 mg/l. conclusions a metakaolin-based geopolymer adsorbent was synthesized for the removal of aromatic compounds from normal paraffin. the results indicated that the modification of the adsorbent with activated carbon enhanced the removal of aromatic compounds. however, when the activated carbon/metakaolin ratio exceeded 1:12, the aromatic removal efficiency decreased. in contrast, modification of the geopolymer adsorbent with hydrogen peroxide as a foaming agent significantly improved its aromatic removal capability compared to the unmodified adsorbent. additionally, increasing the temperature from 70 to 120 °c resulted in an increase in the removal efficiency of aromatic compounds, with up to a 21% improvement. furthermore, as the adsorbent dosage was increased from 0.001 to 0.1 g/l in petroleum samples, the removal of aromatic compounds enhanced; however, further increases in the adsorbent dosage led to a decrease in the adsorption capacity. acknowledgment financial support for this work by the acecr institute of higher education (isfahan branch) is gratefully appreciated. conflicting interests the author(s) declare that they have no conflicting interests. references ayuso, m., navarro, p., palma, a. m., et al. 2020. separation of benzene from methyl cycloalkanes by extractive distillation with cyano-based ionic liquids: experimental and cpa eos modelling. separation and purification technology 234(1):116128. costa, j., jesus, r., silva, c., et al. 2017. efficient adsorption of a mixture of polycyclic aromatic hydrocarbons (pahs) by si-mcm-41 mesoporous molecular sieve. powder technology 308(1):434-441. 0 5 10 15 20 25 0 1:12 1:06 1:03 a ro m at ic r em o v al ( % ) activated carbon: adsorbent ratio improved oil and gas recovery 8 dang, y., yao, y., liu, y., et al. 2019. diffusion properties of aromatic hydrocarbons in mesoporous alumina: a molecular dynamics study. chemical engineering science 204(1):110-117. eshghabadi, f. and javanbakht, v. 2024. preparation of porous metakaolin-based geopolymer foam as an efficient adsorbent for dye removal from 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extraction of aromatics from diesel fuel using dual n-containing heterocyclic deep eutectic solvents. chemical engineering journal 476(1):146618. liu, h., wang, n., zhao, c., et al. 2018. membrane materials in the pervaporation separation of aromatic/aliphatic hydrocarbon mixtures a review. chinese journal of chemical engineering 26(1):1-16. liu, q., li, g., gui, c., et al. 2022. solvents evaluation for extraction of polycyclic aromatics from fcc diesel: experimental and computational thermodynamics. chemical engineering science 264(1):118205. lyon-marion, b. a., mittelman, a. m., rayner, j., et al. 2018. impact of chlorination on silver elution from ceramic water filters. water res. 142(1):471-479. monjezi, m. and javanbakht, v. 2023. a novel foam of geopolymer based on zsm-5 zeolite fabricated using templating emulsion/chemical foaming method and its application in batch and continuous dye removal systems. environ. prog. sustainable energy 42(1):14074, 1-14. schwarz, h. and malsch, g. 2005. polyelectrolyte membranes for aromatic–aliphatic hydrocarbon separation by pervaporation. journal of membrane science 247(1):143-152. topuz, f. and uyar, t. 2017. cyclodextrin-functionalized mesostructured silica nanoparticles for removal of polycyclic aromatic hydrocarbons. journal of colloid and interface science. torabian, a., kazemian, h., seifi, l., et al. 2010. removal of petroleum aromatic hydrocarbons by surfactant-modified natural zeolite: the effect of surfactant. clean 38(1):77-83. yang, z., liu, j., yao, x., et al. 2015. efficient removal of btex from aqueous solution by β-cyclodextrin modified poly (butyl methacrylate) resin. separation and purification 158(1):417-421. yao, c., hou, y., ren, s., et al. 2019. selective extraction of aromatics from aliphatics using dicationic ionic liquidsolvent composite extractants. journal of molecular liquids 291(1):111267. yao, j., liu, n., shi, l., et al. 2015. sulfated zirconia as a novel and recyclable catalyst for removal of olefins from aromatics. catalysis communications 66(1):126-129. zhang, z., provis, j. l., reid, a., et al. 2014. geopolymer foam concrete: an emerging material for sustainable construction. construction and building materials 56(1):113-127. vahid javanbakht is an associate professor of chemical engineering at acecr institute of higher education, where he has worked as faculty for the last 14 years and as researcher in esfahan oil refining company. his research interests are in industrial wastewater treatment and petroleum refining. he holds b. tech. m. tech., and ph.d. from isfahan university of technology, all in chemical engineering. masoud fatemi is a researcher of chemical engineering at acecr institute of higher education. he has worked as researcher for the last 10 years in iran chemical industries investment company. he holds b. tech. and m. tech. from acecr institute of higher education, both in chemical engineering. maryam mehrabi is a researcher of chemical engineering at acecr institute of higher education. she holds b. tech. and m. tech. from acecr institute of higher education, both in chemical engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1249 received january 12, 2023; revised february 24, 2023; accepted april 11, 2023. * corresponding author: weirong.li@xsyu.com.cn 1 numerical simulation of alkali-surfactant-alternated-gas(asag) injection: effects of key parameters qianqian shi, weirong li*, shihao qian,xin wei,tianyang zhang, and xu pan, xi’an shiyou university, xi’an, china abstract alkali-surfactant-alternated-gas (asag) alternating injection is a method used to enhance oil recovery. in the water injection stage of the wag process, chemicals (alkaline-surfactant) are added to the plug. this paper presents a numerical simulation study at the reservoir scale to analyze the influencing factors of asag process on improving recovery efficiency. the research results indicate that asag process can achieve an ultimate recovery efficiency of 67%, which is approximately 22% higher compared to water flooding. among the various influencing factors, injection rate, plug volume, and chemical concentration have a significant impact on the recovery efficiency. introduction gas flooding is considered the most effective method to enhance the recovery factor in light to medium oil reservoirs. water alternating gas (wag) is one of the gas flooding techniques that improves the recovery factor by altering the fluid distribution in the reservoir through alternating injections of water and gas. wag technology has been widely researched and applied over the past few decades, achieving successful outcomes in various types of reservoirs and geological environments. however, significant amounts of residual oil still remain in the reservoir after co2-wag. alkali-surfactant-alternated-gas (asag) injection is a method used to enhance the recovery factor. chemical agents (alkali-surfactant) are added to the water injection segment of the wag process. surfactants in this method primarily reduce interfacial tension, while alkalis assist in reducing interfacial tension with surfactants and can also minimize surfactant adsorption. gas injection complements reservoir energy, lowers crude oil viscosity, and allows for miscibility with the crude oil. the concept of asag injection was proposed by lawson et al. in 1980. from 2012 to 2014, laboratory studies conducted by guo et al. discovered that the alkali/surfactant/foam (asf) process exhibited lower sensitivity to salinity and enhanced recovery of the majority of residual oil after water flooding when as solution was introduced. additionally, under high salinity (230,000 ppm) and temperature (83°c) conditions, successful recovery of residual oil from carbonate rock samples was achieved through asag injection. in 2013, lou et al. found in their laboratory studies on asag injection that the process even yielded sufficient recovery of heavy oil. mailto:mfsnosy@yahoo.com 2 numerous scholars have conducted research on asag injection under different conditions, as shown in table 1. these studies have confirmed the enhanced oil recovery (eor) potential of asag injection and demonstrated that it can improve reservoir recovery more effectively compared to wag and sag injection methods. table 1—summary of someasag flooding studies author oilfield chemical slug gas ift(mn/m) srivastava et al.(2009) light to medium crude oil as、asp coinjected with gas co2 ultra-low cottin et al.(2012) medium-light crude oil as、s coinjected with gas n2、methane 0.003 guo et al.(2012) reservoir crude oil as coinjected with gas n2 0.008 luo et al.(2013) heavy crude oil aspag co2、flue gas 0.06 majidaie et al. (2015) crude oil viscosity of 1.6 cp aspag co2 0.003 the field test data by y. zhu et al. in 2013 also demonstrated the effectiveness of this technique in extremely low permeability (0.3md~3.5md) tight reservoirs. the study conducted by s. majidaie et al. in 2015 focused on the research of asag oil displacement using a specially developed as formulation, which can reduce the oil-water interfacial tension to an ultra-low value, helping to minimize water blockage effects. the research by s. jong et al. in 2016 also confirmed that the use of salinity gradient during asag oil displacement process can enhance foam stability, control mobility, and improve oil recovery. the study by r. phukan et al. in 2019 indicated that the performance of asag oil displacement is influenced by certain parameters, which need to be adjusted to improve oil recovery, including injection schemes, plunger size, plunger ratio, gas injection rate, total injected fluid volume, salinity gradient, etc. the aforementioned studies demonstrate that under low permeability reservoir conditions, asag oil displacement can achieve higher oil recovery compared to wag (water alternating gas) method, but it is affected by various factors. however, the quantitative evaluation of the influence of different parameters on residual oil recovery in asag oil displacement has not been conducted. although some scholars have attempted to study the factors affecting the improvement of oil recovery in asag, the discussions have been limited to certain aspects and are currently only at the laboratory core displacement experiment stage, lacking discussion at the reservoir scale. this study aims to explore and adjust various factors influencing the potential of improving oil recovery in asag oil displacement at the reservoir scale. numerical simulations will be conducted for water flooding, wag, and asag oil displacement methods to compare the recovery results under the same reservoir conditions. firstly, a geological model will be established using cmg·stars commercial software to simulate the oil displacement processes of the three methods. in addition, detailed single-factor analyses will be performed to investigate the impacts of geological parameters, fluid parameters, and process parameters on oil recovery. the purpose is to gain a better understanding of the effectiveness of asag oil displacement and maximize petroleum recovery by adjusting parameter variations. the following sections of this paper will establish the geological model and then conduct single-factor analyses on nine important parameters to identify scientifically reasonable and economically viable parameter values as references for the application of asag in actual reservoirs. 3 reservoir model and fluid characterization based on the geological data of a certain reservoir, establish a geological model with characteristic features. the model grid is 13×13×7, with 13×13 grids on the horizontal plane and seven layers vertically, each with a thickness of 3m. the model size is 260×260×21m, as shown in figure 1. the permeability varies in each layer of the model, with an average permeability of 30 millidarcies (md). the well pattern consists of a quarter of a five-spot well pattern. there is one injection well and one production well, with an injection-to-production ratio of 1:1. the injection rate is 0.1 pore volume per year (pv/a). table 2 shows the reservoir rock and fluid properties. figure 1—geological model map. table 2—reservoir rock properties and fluid properties reservoir rock properties fluid properties porosity，% 22 viscosity of water，mpa·s 1 depth，m 1200 viscosity of crude oil，mpa·s 1.25 temperature，℃ 85 density of the crude oil，g/m3 817 permeability，md 30 initial water saturation，% 20 coefficient of permeability variation 0.65 initial oil saturation，% 80 results and discussions base case.this article primarily conducts numerical simulations of three oil displacement processes: water flooding, wag (water-alternating-gas), and asag (alkali-surfactant-alternating-gas), as shown in figure 2. the wag process includes an initial water flooding stage, followed by alternating gas injection, and 4 subsequent water flooding. after reaching a 90% water cut in the reservoir during the initial water flooding, gas injection begins using the wag oil displacement method. a total of 24 cycles of alternating injections are performed at an injection rate of 0.1 pv/a, with each cycle injecting water and co2, totaling 0.6 pv. subsequent water flooding is then conducted until displacement is complete. asag is based on the wag process,after the initial water flooding stage, alkali and surfactant are added to the water to form an as (alkali-surfactant) chemical slug, which replaces the water. the oil displacement is then carried out by alternating injections of the as slug and gas, while maintaining the same number of cycles, injection rate, and total volume, throughout the entire simulation. water gas chemical slug(as) water flooding wag asag figure 2—diagram of different injection modes. the recovery factors of water flooding, wag, and asag were compared (figure 3). as shown in the figure, under the same reservoir conditions, asag has the highest recovery factor. after a certain period of water flooding, the increase in recovery rate slows down. to enhance the reservoir recovery factor, gas injection is introduced for wag. from the recovery rate curve, it can be observed that wag improves the recovery factor by approximately 10%. building upon wag, alkali-surfactant is added, resulting in asag. the addition of chemical agents enables the recovery factor to reach over 67%. figure 3—comparison of oil recovery factor with and water flooding andwag andasag. 5 figure 4 compares the daily oil production for three different processes. from the graph, it can be observed that after a certain period of water flooding, the oil production declines rapidly. the introduction of chemicals results in higher daily oil production compared to water flooding and wag injection, especially during the early stages of injection when the remaining oil saturation is high. asag demonstrates superior production enhancement effects. figure 4—comparison of oil rate with and water flooding andwag andasag. the gas-oil ratio of two production processes, wag and asag, is illustrated in figure 5 from the perspective of petroleum engineers or reservoir specialists. figure 5—comparison of gas oil ratio with andwag andasag. based on the graph, it can be observed that the gas-oil ratio (gor) increases more significantly in the wag process compared to the asag process, and the gor in wag is much higher than in asag. this indicates that gas breakthrough is more likely to occur during the wag oil displacement process, while the addition of alkali-surfactant can effectively delay gas breakthrough, reduce the gor, enhance the thorough contact and mixing of gas and crude oil, lower the interfacial tension, and thereby increase the recovery factor. 6 effect of reservoir rhythm. based on the reservoir permeability, it can be determined that the reservoir is a stratified reservoir. a stratified reservoir refers to a formation where particle sizes change from fine to coarse from bottom to top. in such formations, there is significant variation in vertical permeability, with lower permeability in the lower section and higher permeability in the upper section. in this model, the maximum permeability of the first layer is 52 md, decreasing progressively downwards, with the minimum permeability of the seventh layer being 8 md. to investigate the impact of reservoir stratification and varying permeability on recovery efficiency, this study examines the oil production and gas injection rates for each layer, quantitatively analyzing the primary producing layer positions under different vertical permeabilities. the cumulative oil production for each layer using asag and wag alternating injections is shown in figure 6. figure 6—comparison of oil production in each layer. from figure 6, it can be observed that both wag and asag oil reservoirs are concentrated in the upper section with slightly higher permeability. in terms of oil production per layer, asag yields higher oil production than wag, and the higher the permeability, the greater the difference in oil production. the oil production of the seventh layer is only 30% of the first layer. therefore, compared to the wag process, asag can improve the recovery factor across various permeability gradients, but it shows better results in higher permeability layers. this is because in the stratified reservoir, gas is influenced by lower density, and most of the co2 gas enters the high-permeability layers. the gas sweep range of asag is significantly larger than that of wag. by injecting chemical solution plugs and alternating gas into the formation, the asag process reduces the mobility of the water phase in high-permeability layers and controls the gas mobility, allowing more gas to enter the high-permeability layers. compared to wag, asag only contributes 2% of the incremental oil production from low-permeability layers. 7 figure 7—correlation of cumulative oil production in antirhythmic reservoirs. figure 7 represents a comparison curve of cumulative oil production under different injection methods with the same reservoir conditions. from the graph, it can be observed that after a certain period of water flooding, the oil production rate slows down. however, by changing the oil displacement method, such as employing wag or asag, the recovery factor can be significantly improved. in this particular reservoir, wag can enhance the recovery factor by approximately 9%, and when asag, it can further increase the recovery factor by over 11% compared to wag alone. effect of injection time. in this study, five injection timing schemes were set, namely, alternate injection of asag when the water cut of the reservoir reached 60%, 70%, 80%, 90% and 95% after water flooding. figure 8 compared the final recovery rate after asag under different water cuts of the reservoir. figure 8—comparison of recovery curves at different injection times. according to figure 8, it can be observed that when alternating injections of as and co2 are started at different timings, the ultimate recovery slightly varies, primarily in terms of the time to reach the maximum recovery factor. however, the impact on the ultimate recovery factor after displacement is not significant. from the changes in the curve, it can be seen that the earlier the chemical agent is introduced, 8 the earlier the maximum recovery factor is reached. however, the recovery trend for the five injection timings is the same. at a water saturation of 95%, the maximum recovery factor is achieved with asag injection, reaching 65.5%. nevertheless, the differences in the final recovery factor among the various methods are not very distinct. figure 9—comparison of water cut curves afterasag when the water cut is 60% and 95%. figure 9 shows the water saturation curve of the reservoir after asag injection at different timing points when the water saturation reaches 60% and 95% respectively. during the water flooding stage, the water saturation increases sharply. with the injection of chemicals at different timing points, the water saturation is reduced to varying degrees. the injection of asag for oil displacement starts at different water saturation levels, leading to significant variations in water saturation. when the water saturation is at 60%, the chemical injection begins, resulting in a rapid decrease in water saturation, which is maintained at a low level for a certain period of time. however, when the chemical injection is stopped, the water saturation quickly rises to above 0.9. when the water saturation exceeds 0.9, the peak of water saturation reduction increases during chemical injection, as shown in table 3. nevertheless, it can still maintain a low water saturation level for a certain period of time until the asag injection for oil displacement is completed. the earlier the chemical injection, the earlier the decline in water saturation and the more pronounced the improvement in water saturation. table 3—comparison of water cut content at different injection times injection times（water cut），% 60 70 80 90 95 minimum water cut，% 19.20 22.10 24.50 26.80 34.50 from table 3, it can be observed that there are variations in the peak values of water cut changes after chemical injection. the earlier the injection takes place, the lower the peak value. therefore, the earlier the chemical injection is performed, the better the effect. effect of injection rate. this study presents four different injection rate schemes, namely 0.1pv/a, 0.125pv/a, 0.15pv/a, and 0.2pv/a. the ultimate recovery factor of the asag method was compared for these four injection rates, and the results are shown in figure 10. 9 figure 10—comparison of asag recovery at different injection rates. according to figure 10, it can be observed that as the injection rate increases, the overall recovery factor of asag exhibits an initial increase followed by a decrease. when the injection rate increases from 0.1 pv/a to 0.125 pv/a, the recovery factor increases by approximately 2%. however, when the injection rate exceeds 0.125 pv/a, the recovery factor of asag gradually decreases. therefore, faster injection is not necessarily better. at a higher injection rate, the injection time for the chemical agent decreases, resulting in a shorter contact time with the crude oil, which hinders the full effectiveness of the chemical agent. table 4 and figure 11 compare the variations in water content using the highest and lowest recovery factors as examples. table 4—comparison of the lowest water cut when injection rate is 0.1pv/a and 0.125pv/a injection rate，pv/a 0.1 0.125 minimum water cut，% 23.5 30.1 figure 11—different injection rates water cut curve. 10 table 4 shows the minimum water cut values at injection rates of 0.1 pv/a and 0.125 pv/a. it can be observed that under different injection rates, the peak water cut varies, and overall, higher injection rates result in lower peak water cut. from figure. 11, it can be inferred that during the initial water flooding stage, with the same injection rate, the water cut curves completely overlap, indicating a sharp increase. during the chemical injection stage, as the injection rate decreases, the water cut decreases to varying degrees and can be maintained at a lower level for a longer period. when the injection rate is less than 0.125 pv/a, under the same injection volume, a higher injection rate leads to greater injection intensity, shorter total injection time, more significant water cut reduction, but a faster rise. considering the above results, the optimal injection rate for this reservoir condition is determined to be 0.125 pv/a. effect of cycle index. in the process of alternate injection, a higher viscosity as slug is injected into relatively high-permeability layers to improve the macroscopic sweep efficiency. the alternating injection cycles have a certain influence on the oil displacement effect of as and co2. when the alternating cycles are larger, the size of the slug is smaller, which may damage the chemical agent slug. when the alternating injection cycles are smaller, the size of the slug is larger, resulting in a longer displacement time and poorer flow control effectiveness. in this study, five simulation scenarios with different numbers of cycles were conducted while keeping the total injected volume of as constant. the scenarios included 6, 12, 18, 24, and 30 cycles. the ultimate recovery of asag was compared, and the results are shown in figure 12. figure 12—comparison of recovery efficiency with different cycles according to figure 12, it can be seen that with a constant total injection volume of as, the greater the number of cycles, the higher the recovery efficiency of asag. however, there is a maximum value, and the recovery efficiency of asag starts to decrease when the number of cycles reaches 30. therefore, it is evident that the number of alternate cycles is not the more, the better; instead, there exists an optimum value. in this study, the optimal value is 24 cycles. 11 figure 13—comparison curve of water content when the number of cycles is 6 and 24. the water cut curve from figure 13 indicates that an increase in cycle frequency leads to a more stable maintenance of lower water cut levels. consequently, at the 24th cycle, the recovery rate exceeds that of the 6th cycle. additionally, the oil saturation plot reveals that employing a reasonable alternating cycle frequency allows for a higher extraction of crude oil. （a）perform 6 cycles （b）perform 24 cycles （c）perform 30 cycles figure 14—oil saturation profile afterasag for 6, 24 and 30 cycles. according to figure 14, during the asag process, when the cycling is performed 6 times, the fourth, fifth, sixth, and seventh layers of the reservoir exhibit high oil saturation. as the number of cycles increases to 24, the oil saturation in these layers notably decreases. however, when the number of cycles reaches 30, the oil saturation in the fourth, fifth, sixth, and seventh layers increases significantly. this is because with a smaller number of alternate injection cycles, the plugging effect is larger, resulting in a longer displacement time and poorer fluid control. on the other hand, with a larger number of alternate cycles, the plugging effect decreases, leading to noticeable viscosity losses. therefore, considering the displacement effect, the best performance is achieved with 24 alternate injection cycles. to achieve the optimum recovery and make full use of the injected fluid, it is necessary to inject chemical and gas plugs at the right time during the asag process. in fact, a higher number of cycles result in higher residual oil recovery. this may be attributed to the increased number of cycles, which improves the contact between the chemical solution and co2. 12 effect of asag ratio. in petroleum extraction, the alternating injection of chemical agents and gas aims to enhance the oil recovery factor by altering the pressure and temperature in the reservoir, as well as inducing chemical reactions. the alternating cycle ratio refers to the time ratio between the injection of chemical agents and gas. modifying the alternating cycle ratio can have different impacts on the oil recovery factor, as outlined below: enhanced recovery factor: when chemical agents are injected into the reservoir, they react with the components in the crude oil, thereby altering its physical properties and making it more mobile. gas, on the other hand, increases the reservoir pressure, promoting the movement of crude oil towards the wellbore. by immediately injecting gas after chemical agent injection, the chemical reactions can be accelerated, facilitating the flow of crude oil and thus enhancing the recovery factor. cost savings: by adjusting the alternating cycle ratio, it is possible to reduce the usage of chemical agents and gas without compromising the recovery factor, leading to cost savings. it is important to note that different reservoirs and geological conditions require different alternating cycle ratios to achieve the optimal recovery factor and economic benefits. therefore, experimental and simulation analyses are necessary to determine the best alternating cycle ratio. the alternating cycle ratio refers to the proportion between the alkali-surfactant (as) slug and the gas (co2) in each cycle. in this study, four sets of alternating cycle ratio schemes were employed, namely 1:2,1:1,2:1, and 3:1, while keeping other parameters constant. the injection volume of as in each cycle was kept constant. a comparison was made with the water flooding and asag methods regarding the ultimate recovery factor, as shown in figure 15. figure 15—comparison of recovery efficiency at different alternating cycle ratios. from figure 15, it can be seen that different alternating injection ratios have a certain influence on the recovery factor during the injection process. the lowest recovery factor is observed when the ratio of as slug to gas is 1:2 during asag injection, and the increase in recovery rate is relatively slow. as the as slug increases, the recovery factor gradually increases, and the rate of production enhancement also accelerates. however, after a certain value of as slug increase, the recovery factor starts to decrease. the specific values of the recovery factor are shown in table 5. table 5—recovery of different alternating cycle ratios alternate cycling ratio 1:2 1:1 2:1 3:1 recovery factor，% 64.3 65.1 66.2 65.8 13 from table 5, it can be observed that maintaining a constant total volume of as injection, the difference in the ratio between as and co2 in the alternating cycles results in significant variations in the production cycle of the entire development process. an appropriate ratio for alternating cycles can increase the liquid absorption capacity of low-permeability layers and improve the oil displacement effect in these layers. in this model, the highest recovery efficiency of asag is achieved when the alternating ratio is 2:1, reaching 66.2%. effect of slug volume. this study established six different injection volume schemes for the as segment plug, namely 0.2pv, 0.4pv, 0.6pv, 0.8pv, and 1.0pv, in order to compare their ultimate water flooding and asag recovery factors. figure 16 illustrates the variations in reservoir water saturation under the minimum and maximum segment plug volumes. figure 16—comparison of water content curves when the volume of slug is 0.2pv and 1.0pv. from figure 16, it can be observed that under a constant injection rate, a larger volume of as slug results in a longer injection time for the chemical agent, prolonging the production cycle and extending the period of low water content. figure.17 compares the recovery efficiency of asag under different volumes of as slug. when the as slug volume injected is 0.2pv, the minimum recovery efficiency is 53.2%. on the other hand, when the as slug volume injected is 1.0pv, the maximum recovery efficiency is 66.8%. 14 figure 17—comparison of recovery efficiency at different slug volumes. from figure 17, it can be observed that the volume of the chemical plug is positively correlated with the recovery factor. when the volume of the plug increases from 0.2pv to 1.0pv, the recovery factor increases by 13.5%. however, after the volume of the plug reaches 0.8pv, the increment in the recovery factor starts to decrease significantly, reaching a maximum increase of only 5.8% and eventually less than 1%. this indicates that a larger volume of the chemical plug is not necessarily better. different reservoir conditions have an optimal volume for the chemical plug, and in this particular reservoir condition, the optimal volume for the as plug is 0.8pv. effect of surfactants concentration. in alkali-surfactant (as) flooding, surfactants play a crucial role. surfactants can form micellar structures between crude oil and water, allowing the mixing of initially immiscible liquids. this increases the contact area between the oil and water, enhancing dispersion and interfacial activity between the two phases. additionally, surfactants can reduce the viscosity of crude oil, making it more easily flowable. moreover, surfactants can form a thin film within the rock pores, rendering the rock surface hydrophilic and reducing the adhesion forces. this, in turn, decreases the retention of oil in the rock pores and improves the oil recovery. to analyze the effect of surfactant concentration on the oil recovery efficiency in asag flooding, this study employed three different surfactant concentration schemes: 1000 mg/l, 2000 mg/l, and 3000 mg/l. these concentrations were compared against the ultimate recovery efficiency achieved with water flooding and asag injection. figure 18 illustrates the variation in water saturation for the three surfactant concentrations. 15 figure 18—comparison of water cut changes under different surfactant concentrations. the change in the curve from the graph indicates that the addition of alkali-surfactant has significantly reduced the water content. furthermore, different concentrations of surfactant result in varying changes in water content. as the concentration increases, the decrease in water content becomes even lower. particularly, there is a more pronounced decrease in water content when the concentration increases from 1000 mg/l to 2000 mg/l. this is also reflected in the recovery factor, as shown in figure 19 for the recovery factor variation curve and summarized in table 6 for the recovery factor. figure 19—comparison of recovery curve of different surfactant concentrations table 6—recovery of asag at different surfactant concentrations surfactant concentrations，mg/l 1000 2000 3000 recovery factor，% 63.1 65.9 68.6 16 according to figure 19 and table 6, it can be observed that higher concentrations of surfactants result in higher recovery rates, but the rate of increase diminishes. increasing the surfactant concentration from 1000 mg/l to 3000 mg/l led to a 5.5% increase in recovery rate. this is because the surfactant concentration affects the interfacial tension between oil and water in the reservoir. the rate of increase in recovery rate decreases as the surfactant concentration increases, as the interfacial tension reaches an extremely low level (on the order of 10-3), making further reduction difficult. when the surfactant concentration increased from 1000 mg/l to 2000 mg/l, the recovery rate increased by 2.8%; however, increasing the surfactant concentration from 2000 mg/l to 3000 mg/l only resulted in a 1.7% increase in recovery rate. this indicates that higher surfactant concentrations are not necessarily better, as they come with higher costs and can cause secondary contamination to the formation. therefore, it is crucial to select the optimal surfactant concentration. in this reservoir's conditions, a surfactant concentration of 2000 mg/l is the most suitable choice. effect of alkali concentration. in the asag injection process, alkali plays a role in neutralizing acidic substances on the rock surface, thereby reducing the adhesion between the rock and the oil. in a combined flooding process, alkali serves two purposes: firstly, it neutralizes the acidic substances on the rock surface, reducing the adhesion between the rock and the oil, allowing the originally trapped oil in the rock pores to be released. secondly, alkali enhances the effectiveness of surfactants, accelerating the flow of oil and thereby increasing oil recovery efficiency. the synergistic effect between surfactants and alkali not only reduces the expensive usage of surfactants but also minimizes the adsorption loss of surfactants and polymers in the reservoir. additionally, the introduction of alkali partially substitutes for surfactants, significantly lowering the cost of the combined flooding system. in summary, the substitution of alkali for surfactants can significantly improve the economic benefits and development efficiency of the combined flooding system. in this study, four sets of alkali concentration schemes were employed, with alkali concentrations of 40,000 mg/l, 80,000 mg/l, 120,000 mg/l, and 160,000 mg/l, while keeping other parameters constant. these concentrations were compared for their ultimate oil recovery in both water flooding and asag injection processes. figure 20 shows the variation in water content at different alkali concentrations. figure 20—comparison of water cut curves under different alkali concentrations. 17 the water cut curve reveals that the water cut decreases as the concentration of alkali increases. the most significant change in water cut occurs when the alkali concentration increases from 80,000 mg/l to 120,000 mg/l. as the alkali concentration continues to increase, the degree of change becomes less pronounced. according to the recovery rate curve in figure 21, it can be observed that the recovery rate continues to increase with the increase in alkali concentration. this is because alkali has two effects: on one hand, it can reduce the interfacial tension between oil and water caused by surfactants; on the other hand, it can adsorb onto the rock surface as sacrificial agent, replacing surfactants and polymers, thereby enhancing the performance of surfactants. however, as the alkali concentration continues to increase, the growth rate of the recovery rate gradually slows down. this is because it becomes increasingly difficult to further improve the recovery rate when the interfacial tension reaches an ultralow level (on the order of 10-3). figure 21—comparison of recovery curves at different alkali concentrations. figure 22 shows the growth of the recovery rate for asag compared to water flooding at different alkali concentrations. at an alkali concentration of 160,000 mg/l, asag achieves the maximum increase in recovery rate of 17.2%; at an alkali concentration of 40,000 mg/l, the minimum increase in recovery rate is 10%. however, it can be seen from the graph that after increasing the alkali concentration to 120,000 mg/l, further increasing the alkali concentration results in a slower increase in the recovery rate. therefore, a higher alkali concentration is not necessarily better, but there is an optimal value that maximizes the increase in recovery rate. 18 figure 22—the increase in recovery efficiency at different alkali concentrations. it should be noted that the use of alkali needs to be adjusted based on specific conditions, as high alkali concentration may have adverse effects on groundwater environments. therefore, when using alkali-surfactant compound flooding in petroleum extraction, it is necessary to strictly control the dosage and concentration of alkali to ensure the safety and environmental protection of the oil extraction process. conclusions this article presents a geological characterization model based on actual parameters of a low-permeability oilfield. it mainly analyzes the influencing parameters and their degrees of impact on the asag displacement process. the following conclusions are drawn: 1. in the asag process, surfactants can reduce interfacial tension and viscosity of crude oil. surfactants can also form a thin film in the rock pores, making the rock surface hydrophilic and reducing rock surface adhesion. this leads to a decrease in the retention of crude oil in the rock pores and an increase in the recovery factor. alkaline substances neutralize the acidic materials on the rock surface, reducing the adhesion between rock and oil, and enhancing the effectiveness of surfactants. this accelerates oil flow and increases oil recovery efficiency. the synergistic effect between surfactants and alkalis can reduce the expensive surfactant dosage and minimize surfactant adsorption losses. 2. in asag process, the water saturation curve rapidly declines after the addition of chemicals and can maintain a low water saturation level for a prolonged period. after asag is completed, the water saturation rate increases again. the daily oil production curve exhibits a peak shape, and the overall trend decreases with time. the cumulative oil production curve shows a sudden increase in production after water flooding and entering the asag stage. after displacement for a certain period, the oil production gradually decreases, and the cumulative oil production curve becomes flat. 3. among the process parameters studied in this paper, the injection timing has almost no impact on the ultimate recovery factor but can change the time to reach the peak recovery factor. injection rate, injection cycle ratio, and plunger volume all have some degree of influence on the recovery factor. 4. chemical agent parameters are closely related to the improvement of recovery factor in asag. a larger chemical plunger leads to a higher recovery factor, but there is an optimal value that maximizes the recovery factor enhancement. the concentration of the chemical agent directly affects the degree of recovery, but a higher concentration is not necessarily better. there is an optimum value that maximizes the recovery factor while considering economic and environmental factors. 19 conflicts of interest the author(s) declare that they have no conflicting interests. references cottin, c., morel, d., levitt, d.,et al. 2012. alkali surfactant gas injection: attractive laboratory results under the harsh salinity and temperature conditions of middle east carbonates. paper presented at the abu dhabi international petroleum exhibition & conference society of petroleum engineers, abu dhabi, uae, november 11-13. spe-161727-ms. cottin, c., morel, d., levitt, d., et al. 2013. alkali surfactant gas injection-attractive laboratory results in carbonates under harsh salinity and high temperature. paper presented ior 2013-17th european symposium on improved oil recovery, april 11-13. gogoi, s.b. 2013. carbon-dioxide for eor in upper assam basin, in: m.z. hou, h. xie,p. were (eds.), clean energy systems in the subsurface: production, storage and conversion, springer, p. 13. guo, h., zitha, p.l.j., faber, r., et al. 2012. a novel alkaline/surfactant/foam en-hanced oil recovery process, spe j 17(2):1186–1195. lawson, j.b. and reisberg, j. 1980. alternate slug of gas and diute surfactant for mobility control during chemical flooding. paper presented at the spe/doe symposium on enhanced oil recovery society of petroleum engineers, tulsa, oklahoma, april 1-4. spe-8839-ms. luo, p., zhang,y., huang, s. 2013. a promising chemical-augmented (wag) process for enhanced heavy oil recovery. fuel 104:333–341. srivastava. m, zhang. j, nguyen, q. p., et al. 2009. a systematic study of alkaline-surfactant-gas injection as an eor technique. paper presented at the spe annual technical conference and exhibition, new orleans, louisiana, october 9-12. spe-124752-ms. majidaie, s., onur, m., and tan, i. m. 2015. an experimental and numerical study of chemically enhanced water alternating gas injection. petrol. sci. 12(2):470-482. zhu,y., hou, q., weng, r., et al. 2013. recent progress and effects analysis of foam flooding field tests in china. paper presented at the spe enhanced oil recovery conference, kuala lumpur, malaysia, july 12-15. spe-165211-ms. jong, s., nguyen, n.m., eberle,c.m., et al. 2016. low tension gas flooding as a novel eor method: an experimental and theoretical investigation. paper presented at the spe improved oil recovery conference. tulsa,oklahoma, usa, april 11-13. spe-179559-ms. srivastava, m., zhang, j., nguyen, q.p., et al. 2009. a systematic study of alkaline-surfactant-gas injection as an eor technique. paper presented at the spe annual technical conference and exhibition, october 4-7. spe-124752-ms. phukan, r., gogoi, s.b., tiwari, p. 2019. alkaline-surfactant-alternated-gas/co2 flooding: effects of key parameters. j. pet. sci. eng. 173:547–557. phukan, r., borgohain, s., gogoi, p., et al. 2019. optimization of immiscible alkaline-surfactant-alternated-gas/co flooding in an upper assam oilfield. paper presented at the spe western regional meeting, san jose,california, usa, april 23-26. spe-195262-ms. wang, l. 2022. production technology of low permeability oil field. journal of chemical engineering and equipment 9(1):23-35. 20 qianqian shi, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focused her research in areas involving reservoir simulation, chemical flooding, and enhanced oil recovery. weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. his research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. li holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. shihao qian, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. he holds a bs degree in petroleum engineering from xi’an shiyou university. xin wei, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused her research in areas involving reservoir simulation, chemical flooding, and enhanced oil recovery. tianyang zhang, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation, well testing, and production analysis. xu pan, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused her research in areas involving reservoir simulation, chemical flooding, and enhanced oil recovery. abstract introduction reservoir model and fluid characterization results and discussions conclusions conflicts of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi:10.14800/iogr.1255 received july 28, 2023; revised october 24, 2023; accepted december 20, 2023. * corresponding author: ilhem.s.y@gmail.com 1 aspen-hysys simulation of an adiabatic multi-packed bed reactor with inter-stage quenching for methanol synthesis sidi-yacoub ilhem*, feddag ahmed, abdelhamid ibn badis university, mostaganem, algeria; and khelifa ikram, gl3z gas liquefaction complex, sonatrach arzew, algeria abstract the aim of this study was to design a simple and user-friendly model for simulating the adiabatic multiphase fixed-bed reactor utilized in methanol synthesis at the methanol and synthetic resins complex in arzew, algeria. the process was based on the ici (imperial chemical industries) method, employing a copper oxide-based catalyst (cuo, zno, or al2o3). methanol is synthesized from syngas, which is a mixture of co, co2, and h2, and acts as the primary feedstock for methanol production in this reactor setup. the developed model provides the capability to predict methanol yield, control high temperatures resulting from exothermic reactions within each catalyst bed, and determine the necessary amount of quenching gas injection to reduce the temperature. through simulations, we achieved a crude methanol ratio of 3.41, closely matching the estimated ratio of 3.4 in the actual reactor. this outcome serves as strong evidence for the effectiveness of the designed model in simulating complex chemical reactors. building on these promising results, the study proceeded to the recycling simulation stage, where the mass of crude methanol was increased to 4.1%. this step indicates the model’s capacity to handle and optimize the recycling process, which is crucial for enhancing the overall efficiency and sustainability of methanol production in the complex. by accurately predicting process parameters and performance, the developed model proves to be a valuable tool for advancing methanol synthesis technologies and promoting more efficient industrial practices. introduction fixed-bed, multi-stage adiabatic reactors are commonly used in the chemical and petrochemical industries due to their cost-effectiveness in terms of operation and maintenance (cui and kær 2020). these reactors consist of a vertical cylindrical vessel that contains multiple layers of catalyst arranged in series. the catalyst beds are vertically stacked, resembling a large cylindrical column (bendjaouahdou and bendjaouahdou 2014). each bed consists of compact and fixed catalyst particles, as shown in figure 1. these reactors are primarily employed for heterogeneous and exothermic chemical reactions, and they are equipped with a cooling system to maintain a consistent temperature and prevent catalyst damage. various cooling techniques can be employed, including the quenching method. this method involves injecting a cold gas between the catalyst beds to mix with the hot gas generated from the exothermic reactions, thus lowering the temperature of the mixture before it enters the subsequent catalyst bed. mailto:ilhem.s.y@gmail.com effective temperature control is crucial for this approach. the temperature resulting from the chemical reactions in each catalyst bed needs to be determined in order to calculate the amount of cold gas required to control the temperature of the gas mixture. figure 1—multi-bed reactor with quenching systems. numerical simulations have become a rapid and efficient method for predicting and controlling fixedbed reactors and their associated cooling systems. the main goal of this study was to develop a userfriendly and practical model to simulate a multi-stage adiabatic reactor used in methanol synthesis within the arzew industrial area. the model was designed to facilitate temperature control and predict methanol production rates in each catalytic bed. for this purpose, we opted for the renowned aspen-hysys v11 software, known for its excellence in designing, controlling, and optimizing industrial processes. this software provides a wide range of unit operations and accurately determines solid catalyst properties and kinetics of heterogeneous chemical reactions(adeniyi et al. 2018). furthermore, the software allows for easy transition from batch to continuous mode by incorporating gas recycling functionality. this flexibility provides enhanced process control and efficiency. we started by presenting the methanol synthesis reactor in the cp1z complex of the arzew refinery, located in the industrial area of the el mahgoune plateau, 2 kilometers from the city of arzew and about 40 kilometers from the city of oran. the methanol synthesis follows the ici (imperial chemical industries) process and was conducted in an adiabatic catalytic reactor. the reactor was designed as a vertical cylindrical vessel and consists of four catalyst beds arranged in series. each catalytic stage comprises a tightly packed and stationary arrangement of catalyst particles. during the reaction, temperatures range from approximately 210°c to 270°c, and the pressure is maintained at 52 bar (ortiz et al. 2013). the exothermic nature of the reaction generates heat, which needs to be effectively managed to maintain optimal operating conditions. to control the temperature and remove excess heat, cold synthesis gas, also known as quench gas, is injected between the catalyst layers (lee 1989). the quench gas serves the purpose of cooling the reaction mixture. this injection of cold gas helps regulate and maintain the desired temperature levels within the reactor. figure 2—methanol synthesis reactor at the level of the cp1z complex of arzew. modeling approach fluid package. in this study, the peng-robinson equation of state was employed to calculate the thermodynamic properties of the reaction mixture. the peng-robinson equation is known for its accurate estimation of vapor pressure and fluid density. one of its advantages is that it requires minimal experimental data and allows for a concise simulation period (slattery 1972 ). the peng-robinson equation is defined by the coefficients ‘a’ and ‘b’, which are determined by the following relationships: 2 22      rt ap v b v bv b ,……………………………………………………………………………... (1) 2 2 0.0778 c c r tb p ,……………………...…………………………………………………………….…(2) 2 2 ( ) 0.45724 ( ) c c r ta t t p ,.……………...……………………………………………………………(3) 0.5 0.51 (1 )    rm t ,.……………………..……………………………………………………………(4) 20.37464 1.54226 0.26992   m ,.…..……………………………………………………………(5) �� = � �� ,…………………………………………………………….…………………………………..(6) the peng-robinson equation provides an effective framework for accurately modeling the thermodynamic behavior of the reaction mixture in the methanol synthesis process. kinetic theory of methanol synthesis. methanol is synthesized from a mixture of co, co2, and h2 gases, typically using a commercial cu/zno/al2o3 catalyst (blumberg et al. 2017; fuad et al. 2012). this catalyst enables the production of methanol under relatively ‘mild’ conditions (210-270 °c and 50-100 bar), as depicted in the equations presented in table 1. table 1—reaction formulas for methanol synthesis (graaf et al. 1990; moulijn et al. 2013 ) reaction reaction enthalpy (1)co + h2o ↔ co2 + h2 (2)co2 + 3h2 ↔ch3oh + h2o (3) co + 2h2 ↔ ch3oh -41 (kj/mol) -49.67 (kj/mol) -90.64 (kj/mol) in the literature, various kinetic models have been employed to describe the kinetics of methanol synthesis (skrzypek et al. 1995). bussche and froment (1996) and løvik (2001 ) conducted comprehensive evaluations of multiple processes investigated, each with its unique constraints. the behavior of kinetic laws is influenced by factors such as the catalyst type, the composition of the feed gas, and the reaction conditions (temperature and pressure). while some models assume that the synthesis gas comprises co and h2, others allow for the presence of co2 in the feed. in the past, producers believed that methanol synthesis relied solely on the hydrogenation of carbon monoxide (co). consequently, they removed all carbon dioxide (co2) from the feed gas through absorption (fossen et al. 2022). however, experiments conducted by waugh (2012) demonstrated that the presence of carbon dioxide in the gas mixture actually accelerates the methanol production process compared to feed gas containing only h2 and co (abate et al. 2015). in our study, we employed the kinetic theory developed by bussche and forment (1996) along with the equilibrium constants derived from the equations proposed by graaf et al (1990). this widely applicable theory has been experimentally validated, and adjustments have been made to its parameters by bussche and forment (1996) to enhance its suitability across various cases. the results of numerous experiments conducted by different researchers (nestler et al. 2018) indicate that methanol synthesis predominantly occurs through the hydrogenation of carbon dioxide rather than carbon monoxide. it is crucial to consider the water-gas shift (wgs) reaction when describing the methanol synthesis process (bussche and froment 1996). therefore, before converting carbon monoxide into methanol, it must undergo the water-gas shift reaction to produce carbon dioxide(goeppert et al. 2014; shi et al. 2020). co +h2o →���↔co2 + 3h2 →��� ch3oh + h2o,......................................................................................(7) our study focuses on two key reactions: the water-gas shift (wgs) transformation reaction and the hydrogenation of carbon dioxide, which yield methanol (bozzano and manenti 2016). reaction 1: co + h2o↔co2 + h2 2 2 2 2 2 2 2 2 2 1 1 1            eq h o co e co h co c h o a h b h o h p p k p k p p r k p k p k p p ,……………………………………………………………….(8) reaction 2: co2 + 3h2 ↔ ch3oh + h2o 2 3 2 2 2 2 2 2 2 2 1 2 3 11 1                       h o ch oh d co h eq h co c h o a h b h o h p p k p p p pk r k p k p k p p ,……………..…………………………………….(9) the values and initial reactions associated with the adsorption equilibrium constants as presented in eq. 8 and 9, are illustrated in figure 1 and detailed in table 2. as shown in table 2, the kinetics of reactions 1 and 2 are expressed in terms of pressure and reaction rate. 22 ( ) 2 ( ) ( ) 2 ( ) 3 3 3 1 3 2 2 2 2 3 4 5 8 2 2 9 2 2 2 . . . 2 2 . .2 .2 ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 .2 . .2 . . . . . . . . . ( ) h a g g g g h h k k s h s co s o s co co o s s co s s co s h s hco s s hco s s hco s o s hco s h s h co s s o s h s oh s s oh s h s k k k s k kh o s h o s k                                  2 1 1 2 2 2 2 5 5 ( ) ( ) t g t a a t h oo s k k c k k c k k c with k            figure 3—initial reactions associated with the adsorption equilibrium table 2—kinetic constants of reactions 1 and 2. k = a e (b/ rt) units a b 2h k bar−1/2 0.499 17197 2h ok bar−1 6.62e−11 124119 2 28 9( / )h o hk k k k mol/kg s bar2 3453.38 25 2 3 4( )a hk k k k k  1.07 36696 1k  mol/kg s bar 1.22e−1 -9476 table 3—equilibrium constants from the graaf’s equation (graaf et al. 1986)  10 1 3066log 10,592eqk t   bar-2  10 2 2073log 2,029eqk t    dimensionless the langmuir-hinshelwood-hougen-watson (lhhw) type integral equation, obtained from the kinetics and parameters developed by bussche and forment (1996), is employed by aspen-hysys to describe the methanol production kinetics (tripodi et al. 2017 ). this model accurately depicts the characteristics of both methanol production reactions. the lhhw kinetic model comprises a kinetic factor, a driving force expression, and an adsorption term (al-malah 2022).       driving_force kinetic_factor adsorption_term r ,………………………………………………………………(10) to incorporate the kinetic equation into the aspen hysys model, the units must be modified and changed from kilograms of catalyst to moles per volume of the gas phase.   3 gas 1mol mol s kgcat sm                    c hysysr r r ,…………………………………………………(11) the two reactions' rate expressions have been modified to: 2 2 2 2 2 2 2 10 8 1 1 1 0,5 11 94765 550803,5.10 exp 3,28.10 exp 17197 1241191 3453,4 0,499exp 6,62.10 exp                             co h o co h h o h h h o p p p p rt rtr p p p p rt rt ,………………..…(12) 2 2 2 3 2 2 2 2 2 11 2 2 3 1 0,5 11 36696 219993,08.exp 1,204.10 exp 17197 1241191 3453,4 0,499exp 6,62.10 exp                              co h h o ch oh h h o h h h o p p p p p rt rtr p p p p rt rt ,……………….(13) modeling of the fixed-bed adiabatic reactor. several studies have been conducted on the modeling of heterogeneous fixed-bed catalytic reactors, including deasch and frument (1971), frument (1972), and varma (1981). froment (1972) proposed the most commonly used categorization of fixed-bed reactor models, which can be classified into two main categories: pseudo-homogeneous models and heterogeneous models. heterogeneous models take into account fast reactions and significant thermal effects, requiring differentiation between fluid conditions at the surface and inside the catalyst particles. on the other hand, pseudo-homogeneous models assume that the entire catalyst surface is exposed to fluid conditions, treating the reactor as a single-phase system. froment's (1972) classification divides these models into six categories, consisting of three types of pseudo-homogeneous models and three types of heterogeneous models (elnashaie 1994). figure 4—forment's classification of fixed bed reactor models. according to the forment classification of fixed-bed reactor models shown in figure 4, the onedimensional plug flow reactor (pfr) model is the simplest of the pseudo-homogeneous models. we utilized the pfr reactor available in the aspen-hysys program library, which represents a tubular reactor assuming perfect radial mixing and zero axial dispersion (towler and sinnott 2022). choosing the pfr-hysys model enables us to incorporate the type of heterogeneous catalyst reaction using the lhhw (langmuir-hinshelwood-hougen-watson) formula. additionally, pfr-hysys offers an optional energy stream for heat storage or dissipation. in the absence of flow, hysys assumes that the reactor operates as an adiabatic system (hysys 2004), which corresponds to a fixed-bed adiabatic reactor for methanol synthesis. the pfr-hysys model represents a tubular reactor divided into subvolumes based on the total length and calculated throughout the entire pfr. the default number of subvolumes is 20, but it can be reduced to a minimum (hysys, 2004). therefore, we reduced the number of sections to one in order to simulate a methanol reactor with a single cylindrical vessel. for simulating the catalyst beds in the methanol reactor, we modeled each catalytic bed using a pfrhysys reactor with a diameter equal to that of the original methanol production reactor and a height equal to the height of each catalytic layer, as illustrated in figure 5. figure 5—representation of catalyst layers using four pfr reactors. aspen hysys offers the benefit of solving each installation component separately instead of attempting to solve them all at once (liu and karimi 2018). this capability enables solving the first bed by utilizing a small pfr-hysys model, followed by the second, third, and fourth beds in consecutive order. pressure drop. the pressure drops across fixed beds are calculated directly by the aspen hysys software using the ergun equation (grabow and mavrikakis 2011; sinadinovic-fiser et al. 2001).   3 150 11 1.75                c p p dp g g dz g d d ,……………………………………………………..(14) by incorporating the ergun equation and considering these parameters, the aspen hysys software accurately calculates the pressure drops in fixed beds. tables 4 through 6 provide technical information on the reactor utilized in the simulation. the molar fractions of the gaseous mixture at the inlet of the arzew reactor are presented in table 7. table 4—operating conditions of the reactor. parameters value reactor inlet flow rate (kmol/h) 14220 first catalytic bed flow rate (kmol/h) 9960 quench gas flow rate (kmol/h) 4260 inlet pressure (atm) 52 inlet temperature (°c) 230 quench gas temperature (°c) 70 table 5—characteristics of the reactor. parameters value number of catalytic beds 4 height of each catalytic beds (m) 0.75 reactor diameter (m) 3.9 void fraction 0.38 table 6—catalyst characteristics. parameters value solid density (kg/m3-solide) 1770 particle diameter (mm) 5.4 table 7—molar composition of the synthesis gas. feed composition molar fraction co 7.5 % co2 6 % h2 73.7 % h2o 0.13 % n2 3.26 % ch4 9.36 % ch3oh 0 process simulation the synthesis gas, at a pressure of 52 bars and a temperature of 70°c, is divided into two streams. the first stream is preheated to 230°c in a tubular heat exchanger by exchanging heat with the effluent from the reactor, and this stream is used as the feed for the reactor. the second stream, at a temperature of 70°c, acts as a quench gas to cool the reactants. the gaseous reaction mixture flows through the four catalytic stages from top to bottom, as illustrated in figure 6. figure 6—flowsheet of the methanol process designed in aspen hysys. due to the highly exothermic nature of both chemical reactions, it is crucial to cool the reaction mixture by introducing cold synthesis gas between the catalyst layers. this cooling operation is achieved by mixing the gas exiting each bed with a flow of quench gas in a mixer to maintain the temperature within the range of 230°c to 270°c. the gas leaving the reactor is then cooled to 130°c in a tubular heat exchanger, further cooled to 50°c using air-cooled heat exchangers, and finally cooled to 35°c using another heat exchanger that utilizes cooling water. the cooled gas is separated in the first flash separator to recover the crude methanol and any unreacted gas. to enhance the purity of the final product, a second flash separator is added at the liquid outlet of the first flash separator. temperature control. the primary aim of this endeavor is to effectively monitor and regulate temperature fluctuations occurring within the catalyst. as a result, we present the meticulous findings acquired during this simulation, which are comprehensively summarized in table 8. table 8—temperature and gas mixture flow rate for each of the four beds. catalytic bed catalytic bed inlet catalytic bed outlet quench flow (k mole/h) temperature (k°) flow (k mole/h) temperature (k°) flow (k mole/h) temperature (k°) 1 8532 217 8532 263 ,3 1706 70 2 9919 231,3 9919 255.6 1991 70 3 11740 225 .5 11740 249.9 1991 70 4 13330 224.7 13330 245.9 table 8 presents temperature readings at the inlet and outlet of each catalytic layer, along with the required flow rate of cold gas to be injected between consecutive catalyst beds. for example, in the first catalytic bed, the gas mixture temperature increased from 217 °c to 263 °c. before proceeding to the next stage, we injected 1706 mol/h of refrigerant gas at 70 °c to cool the mixture down to 231 °c. we followed the same procedure for layers 3 and 4. figure 7—evaluation of methanol synthesis temperature along the catalytic reactor. based on the results summarized in table 8 and figure 7, we concluded that simulating the reactor in this manner provides a clear understanding of the temperature variation of the gas mixture passing through the four catalyst layers, which is useful for controlling and studying temperature changes. figure 8—evaluation of the synthesis temperature of methanol in the four catalytic layers. additionally, it allows us to determine the amount of refrigerant gas needed to be injected at the inlet of each stage in order to lower the temperature. the temperature profiles for the four beds exhibit an increasing trend due to the exothermic nature of the two reaction. according to figures 7 and 8, we observed that the temperature gradient along the first bed is higher compared to the other three beds. this can be attributed to high concentration of reactants (co and co2) and low content of methanol in the initial feed flow rate. component conversion. the component molar fraction ratios for the four catalytic layers are shown in table 9 for the gas mixture. 11 table 9—molar fraction of the reaction mixture in each catalytic bed. mole fraction (%) composition first catalyst bed second catalyst bed third catalyst bed fourth catalyst bed inlet outlet inlet outlet inlet outlet inlet outlet co 7.5 6.66 6.78 6.15 6.36 5.72 5.96 5.4 co2 6 7.31 7.43 7.44 7.53 7.54 7.60 7.6 h2 73.7 70.07 70.42 69.8 70.20 69.55 69.93 69.35 h2o 0.13 1.12 0.9 1.08 0.91 1.06 0.93 1.06 methanol 0 2 1.6 2.56 2 .13 3.04 2,6 3.41 a noticeable shift in the molar percentages of all compounds is clearly observed between the inlet and outlet of each layer within the reactor. for instance, at the outlet of the initial catalytic bed, the concentration of methanol is measured at 2%. subsequent to the introduction of a precise quantity of refrigerant gas, the molar fraction decreases to 1.6%. subsequently, the methanol concentration increases to 2.5% at the outlet of the second bed and further rises to 3.04% at the outlet of the third bed. finally, the methanol concentration reaches 3.41% figure 9—reactions rate along the catalytic beds. as observed in figure 9, the rate of the methanol synthesis reaction initially decreased before stabilizing, while the water-gas shift reaction (wgs) increased, resulting in the production of co2. both reactions occur 12 simultaneously until reaching equilibrium after 50% of the bed length. since co2 is consumed by the methanol synthesis reaction, and also produced by the water-gas shift reaction, co and h2o combine to form co2, which then reacts with h2 to produce methanol. this is evident from the gradual decrease in the concentrations of co and co2, accompanied by an increase in the concentration of methanol, as the reaction progresses through each layer, as shown in figure 10. the slight increase in the mole fractions of the reactants (co and co2) at the inlet of each bed can be explained by the introduction of fresh syngas (quench gas). figure 10—components production rate along the catalytic beds. results comparison. we employed identical parameters to those of the arzew complex in our work, including the molar fraction of reactants at the reactor inlet, flow rate, and operating conditions. the simulation results were then compared with the actual design values. as shown in table 10, the values obtained using the aspen-hysys software closely resemble the data from the actual reactor, with minor deviations. these differences can be attributed to several factors, including the continuous variation in the flow rate of the cold quench gas, which leads to changes in the component ratios of the gas mixture at the layer level. 13 table 10—comparison of simulation results with real data. composition (molar fraction %) reactor inlet stream reactor outlet stream simulation result real data ch4 9.36 9,78 11.20 co 7.50 5.40 6.80 co2 6.00 7.60 5.74 n2 3.26 3.50 3.90 h2 73.70 69.35 65. 90 h2o 0.13 1.06 1.40 methanol 0 3.41 3.40 recycling of unconverted gas. upon analyzing the results of previous simulations, it becomes evident that the production of methanol is limited to approximately 3% due to thermodynamic constraints. this indicates a low conversion rate for the process, with a signify cant amount of reactants still present in the gas stream exiting the reactor. research studies have indicated that the average hydrogen conversion rate does not exceed 50% (timsina et al. 2022). figure 11—cycle of methanol process designed in aspen hysys. consequently, it is necessary to recover the unconverted syngas for reintegration into the synthesis loop. to enhance performance and efficiency, a flashing process is employed on the methanol reactor stream to separate crude methanol from the unreacted syngas. approximately 96.5% of the unreacted syngas is then recycled back into the methanol reactor (arthur 2010). the remaining portion of the syngas is purged to minimize the accumulation of inert gases such as ch4 and n2 within the reaction loop. the accumulation of these gases can have detrimental effects on the reaction 14 process within the reactor. however, it is important to limit the purging to avoid excessive removal of co and co2 from the inlet stream, as higher purge flow rates result in reduced methanol yields (abrol and hilton 2012). the pressure of the unreacted gas dropped to 43 bars after the flashing operation. consequently, the mixture is compressed to 52 bars after being combined with the syngas. the recycling loop represents a distinct mathematical process incorporated in aspen hysys (safari 2022). the calculation of this process follows a sequential modular approach, with iterative conversion of the recycling loops. thus, it is necessary to recover the unconverted syngas for reintegration into the synthesis loop. table 11 presents the methanol production rates obtained from these simulations, both before and after recycling. it is noteworthy that the methanol production rate exhibited a significant increase of 4.1%. table 11—production rates of methanol before and after recycling. methanol production flow rate before recycling after recycling 454,358 k mole/h 547,902 kmole/h 3.41%. 4.1% conclusions in this research, we investigated the effectiveness of multi-bed reactor simulation through the utilization of plug-flow reactors as a substitute for catalytic layers. taking the example of an arzew reactor for methanol synthesis, our study yielded highly consistent results with the actual design data of the arzew reactor. we obtained a comprehensive understanding of temperature variations within the reactor at each layer's inlet and outlet, enabling precise control of quench gas flow rates. additionally, we accurately determined the conversion rate of reactants and the percentage of methanol production throughout the reactor. furthermore, using aspen-hysys v11 simulation software, we successfully demonstrated the efficiency of using this method to study and control multistage reactors in continuous and discontinuous systems. therefore, we propose this simple and straightforward approach 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badis university (umab), algeria. khelifa ikram, is a ph.d in process engineering, djillali liabes university, sidi bel abbès, algeria. he is a process engineer at study and development department-gl3z gas liquefaction complex, algeria. abstract introduction modeling approach process simulation conclusions conflict of interest nomenclature references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1359 received january 19, 2025; revised february 10, 2025; accepted march 14, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 performance evaluation of mucuna solanie and periwinkle shell inhibitors as anticoating agents for corrosion inhibition obiukwu david nduji, chinwuba kevin igwilo, nnaemeka uwaezuoke, chukwuebuka francis dike*, federal university of technology owerri, owerri, nigeria abstract in the oil and gas industry, pipelines composed predominantly of refined metals are inherently susceptible to degradation when exposed to corrosive environments such as atmospheric oxygen, saline solutions, or microbial activity. conventional mitigation strategies—including material selection optimization, protective coatings, cathodic protection, and chemical inhibition—often rely on costly and environmentally detrimental synthetic inhibitors. this has necessitated the exploration of sustainable, cost-effective alternatives derived from natural sources. this study evaluates the corrosion inhibition efficacy of three bio-based coating materials formulated from locally sourced periwinkle shells (littorina littorea), mucuna solannie (ms) plant extract, and a hybrid composite (mps) integrating both materials. a weight loss methodology was employed to assess corrosion rates under simulated acidic (hcl), saline (3.5 wt.% nacl), and microbial (sulfate-reducing bacteria) conditions, reflecting common oilfield operational environments. results demonstrated that the mps hybrid inhibitor exhibited superior corrosion inhibition efficiency, achieving the lowest corrosion rates of 1.838×10⁻⁶ mm/year (acidic), 2.016×10⁻⁶ mm/year (saline), and 6.226×10⁻⁶ mm/year (microbial), outperforming standalone ps and ms inhibitors. these findings highlight the potential of composite bio-inhibitors as eco-friendly, highperformance alternatives for pipeline integrity management in petroleum production and transportation systems. introduction corrosion poses significant economic and safety challenges in the oil and gas industry due to the inherently corrosive impurities in crude oil and natural gas. this degradation manifests across three critical operational domains: production, transport/storage, and refining. key corrosive agents in oilfield environments include carbon dioxide (co₂), hydrogen sulfide (h₂s), and free water, which exacerbate metal dissolution in pipelines and wellbore infrastructure (paul et al. 2014). the prevalence of sweet (co₂-rich) and sour (h₂s-laden) crudes, coupled with operational extremes in temperature, pressure, and aqueous media—ranging from seawater to produced water—further accelerates corrosion kinetics (schweitzer 2013). carbon and low-alloy steels, the primary materials for onshore/offshore structures such as pipelines and desalination plants, exhibit inherent susceptibility to generalized or localized corrosion (malik et al. 1999). despite their enhanced strength and moderate corrosion resistance, these alloys thermodynamically favor oxidation to their native oxide states. corrosion rates are modulated by environmental variables, including dissolved salts, acidic species, microbial activity, flow velocity, and temperature gradients (schweitzer 2007). to mitigate these challenges, industry-standard strategies such as optimized material selection (callister and wiley 2007), protective coatings (schweitzer 2013), cathodic protection, and corrosion inhibitors are widely employed. among these, coatings have emerged as a versatile solution, functioning via three primary mechanisms: mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 (1) electrochemical inhibition, (2) barrier formation to isolate substrates from corrosive agents, and (3) sacrificial protection (popoola et al. 2014). advanced coatings now integrate passive-active dual functionality, combining barrier properties with active passivation to form protective interfacial layers (e.g., cr₂o₃ or al₂o₃). material classes span metallic (e.g., zn or al alloys for cathodic protection; buchheit et al., 2002), ceramic (e.g., tio₂ or sio₂ for microbial corrosion resistance; krishnamurthy et al., 2013), polymeric (e.g., epoxy or polyurethane for impermeability; lee et al. 2009), and hybrid systems that synergize adhesion, self-healing, and thermal stability (dolan and carson 2007). despite their efficacy, conventional coatings such as fusion-bonded epoxy (fbe), coal tar enamel (cte), and three-layer polyolefins entail high costs and environmental liabilities, particularly in resource-constrained regions like nigeria (thompson and saithala 2015). this study investigates sustainable, locally sourced alternatives: mucuna solannie (ms), a tropical legume (subfamily papilionaceae) with high proteinaceous content, and periwinkle shell (ps, littorina littorea), a calcareous agricultural waste. prior applications of ms include rheology modification in drilling fluids (duru et al., 2020) and cementitious extenders (igwilo et al. 2020a), while ps has been repurposed as a partial cement substitute (agbede and manasseh 2009). their hybrid composite (mps) is hypothesized to synergize organic-inorganic interactions, leveraging ms’s polymeric matrix for adhesion and ps’s caco₃-rich structure for ph buffering and barrier enhancement. by evaluating these materials under simulated oilfield conditions—acidic (hcl), saline (3.5 wt.% nacl), and microbial (sulfate-reducing bacteria) environments—this work advances the development of low-cost, eco-friendly inhibitors tailored to tropical resource economies. materials and methods materials. the materials employed in this study were mucuna solanie (abbreviated as ms), periwinkle shell (abbreviated as ps), thinner, water, and a neutral binder (alkyl resin). additionally, zinc oxide (zno), an anti-skin agent, and a mixed dryer were used. the apparatus included api 5l x52 carbon steel pipes, a painting brush, an analytical weighing balance (mettler toledo me204e with 0.1 mg precision), a hamilton mixer, and a beaker. sourcing of materials. mucuna solanie was procured from a market in enugu. periwinkle shell was sourced from a market in imo state. the thinner, zno, anti-skin agent, mixed dryer, and the neutral binder (alkyl resin) were all obtained from an industrial store. material processing. in the material processing stage, mucuna solanie and periwinkle shells underwent similar yet distinct processing procedures. for mucuna solanie, the collected samples were thoroughly washed with deionized water to remove surface impurities. subsequently, the washed samples were placed in a memmert un 55 laboratory oven with a temperature accuracy of ±1°c and dried at 50°c for 4 hours. after drying, the mucuna solanie was pulverized using a hamilton hbl500 industrial blender. the pulverized samples were sieved through a 250-mesh sieve to obtain powder with a uniform particle size. finally, the sieved powder was stored in an airtight container to prevent moisture absorption and contamination. the processing of periwinkle shells was similar. first, the shells were soaked in deionized water and gently scrubbed to remove adhering organic matter. then, they were also dried in the oven at 50°c for 4 hours. after that, the dried shells were crushed using the industrial blender, and the crushed particles were sieved through a 250-mesh sieve. the resulting powder was stored in an airtight container for subsequent experiments. methods. sample characterization. sample characterization is a crucial step to precisely identify the elements present and understand the inherent features of the samples. in this study, characterizing mucuna solannie and periwinkle shell was of utmost importance. this process aimed to determine their elemental compositions and potential characteristics, ensuring their suitability for the research within the context of petroleum engineering corrosion inhibition. as per previous research, igwillo et al. (2020b) have conducted similar characterizations on mucuna solannie and periwinkle shell, providing a valuable reference for our study. this prior work not only improved oil and gas recovery 3 validates the relevance of our chosen materials but also offers insights into the expected outcomes of our own characterization efforts. inhibitor formulation. for the formulation of corrosion-inhibiting coatings, three distinct types of inhibitors were designed. these include a mucuna solannie-based (ms-based) inhibitor, a periwinkle shell-based (ps-based) inhibitor, and a mucuna solannie-periwinkle shell hybrid (ms-ps hybrid) system. the specific formulations of these inhibitors are presented in table 1. this approach allows for a comprehensive evaluation of the individual and combined effects of mucuna solannie and periwinkle shell in corrosion inhibition, which is highly relevant to the challenges faced in petroleum engineering, such as protecting pipelines and equipment from corrosion in harsh oil and gas environments. table 1—inhibitor formulation for ms. s/n materials ms-based ps-based ms-ps hybrid 1 neutral binder 40g 40g 40g 2 periwinkle shell 0g 40g 40g 3 mucuna solanie 40g 0g 40g 4 thinner 15g 15g 15g 5 zno 4g 5g 4g 6 anti-skin 1g 1g 1g 7 mixed dryer 3g 3g 3g corrosion test. corrosion evaluation was carried out using the weight-loss method. the weight-loss approach was selected because of its capability to capture various types of corrosion by delving into the minute details of corrosion events. this method provides a comprehensive understanding of the corrosion process, which is crucial for accurately assessing the effectiveness of corrosion inhibitors in a petroleum engineering context. in this study, a total of 18 pipe specimens were employed for corrosion rate (cr) evaluation. prior to any testing, the diameter and length of each pipe were precisely measured. subsequently, these pipes were divided into two main groups: 9 pipes served as control specimens (cr control pipes), and the other 9 were used as coated specimens (cr coating pipes). the grouped pipes were further subdivided according to different environmental conditions relevant to the corrosion inhibition study. the specific details of these environmental conditions are presented in table 2. this systematic approach allows for a detailed comparison of corrosion rates under various scenarios, enabling a more in-depth analysis of the performance of the inhibitors in different oil and gas-related environments. table 2—environmental conditions for the corrosion inhibition study. s/n assumption ms ps ms-ps 1 acid (control) ms-control-acid ps-control-acid ms-ps-control-acid 2 acid (coating) ms-coating-acid ps-coating-acid ms-ps-coating-acid 3 salt (control) ms-control-salt ps-control-salt ms-ps-control-salt 4 salt (coating) ms-coating-salt ps-coating-salt ms-ps-coating-salt 5 microbial (control) ms-control-microbial ps-control-microbial ms-ps-control-microbial 6 microbial (control) ms-coating-microbial ps-coating-microbial ms-ps-coating-microbial improved oil and gas recovery 4 results sample characterization. sample characterization was conducted to identify the elemental features of the specimens. this step was crucial for determining whether the materials possess essential elements capable of reducing or mitigating corrosion. according to igwillo et al. (2020b), periwinkle shell was found to contain 79.48% calcium, along with 8.83% silicon, 2.13% silver, 2.13% yttrium, 1.55% niobium, 1.11% iron, 1.04% potassium, 0.95% chlorine, 0.86% sulfur, 0.58% aluminum, 0.42% oxygen, 0.33% carbon, 0.21% phosphorus, 0.13% sodium, 0.13% magnesium, and 0.13% titanium. mucuna solannie, on the other hand, had 39.18% potassium, 14.71% carbon, 7.89% phosphorus, 6.37% zinc, 5.11% iron, 5.05% sulfur, 4.55% calcium, 3.54% yttrium, 3.06% titanium, 2.7% chlorine, 2.08% oxygen, 1.95% silicon, 1.77% aluminum, 1.17% magnesium, and 0.86% sodium. as the results indicate, periwinkle shell is predominantly composed of calcium, while mucuna solannie mainly consists of potassium and carbon. corrosion inhibition study. acid environment. figures 1 to 3 illustrate the corrosion rates of pipes coated with mucuna solannie (ms), periwinkle shell (ps), and the mucuna solannie-periwinkle shell hybrid (mps) in an acid environment. as shown in figure 1, the ms-coated pipe in the acid environment did not show any signs of corrosion for the first 12 weeks. on the 15th week, it recorded a corrosion rate of 3.27×10⁻⁶ mm/year. after another 3 weeks, the corrosion rate decreased by 16.5% to 2.73×10⁻⁶ mm/year. on the 21st week, the corrosion rate increased by 71.4% to 4.68×10⁻⁶ mm/year. comparing the final corrosion rate of the coated pipe with that of the uncoated pipe, the application of the ms coating reduced the corrosion rate by 77.9%. in figure 2, the ps-coated pipe in the acid environment did not corrode for the first 6 weeks. at the 9th week of observation, it recorded a corrosion rate of 4.23×10⁻⁶ mm/year. this corrosion rate decreased by 2.51% and 1.99% at the 12th and 15th weeks of observation, respectively. at the 18th week of observation, the corrosion rate increased by 66.5%, and then dropped by 13.9% at the 21st week of observation. comparing the final corrosion rate of the coated pipe with the uncoated pipe, the introduction of the ps coating reduced the corrosion rate by 82.8%. as depicted in figure 3, the mps-coated pipe in the acid environment did not corrode for 18 weeks. at the 21st week, it recorded a corrosion rate of 1.83×10⁻⁶. comparing the final corrosion rate of the coated pipe with the uncoated pipe, the application of the mps coating reduced the corrosion rate by 91.3%. figure 1—corrosion rate of mucunie solannie inhibitor in acid environment. when comparing the corrosion rates of the pipes before and after inhibition, it is evident that the ms, ps, and mps coatings all reduced the corrosion rates of the pipes. this can be attributed to their functional groups, which 0.00e+00 5.00e-06 1.00e-05 1.50e-05 2.00e-05 2.50e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating improved oil and gas recovery 5 facilitate the formation of complexes with metal surfaces and ions, thereby occupying a large surface area and protecting the metals from corrosive agents (rajendran et al. 2005). the inhibitive power of these polymers is also associated with heteroatoms (oxygen and nitrogen) and cyclic rings, which are major adsorption sites (arthur et al. 2013). comparing figures 1 through 3, the mps-coated pipe exhibited the best corrosion inhibition performance, reducing the corrosion rate by 91.3%. as shown in figures 1 to 3, the control pipe showed a continuous increase in corrosion rate. this is due to the ability of the acid to dissociate the metals and the decrease in hydrogen ions as the sole cathodic reaction, which is consistent with the findings of aria et al. (2019). figure 2—corrosion rate of periwinkle shell inhibitor in acid environment. figure 3—corrosion rate of mucuna solannie-periwinkle shell inhibitor in acid environment. salt environment. figures 4 to 6 show the corrosion rates of pipes coated with ms, ps, and mps in a salt environment. in figure 4, the ms-coated pipe in the salt environment did not corrode for the first 3 weeks. after 6 weeks, it recorded a corrosion rate of 3.448×10⁻⁵ mm/year. this corrosion rate increased by 88.8% to 6.51×10⁻⁵ mm/year at the 9th week. it then decreased by 8.9% to 5.928×10⁻⁵ mm/year at the 12th week and increased by 45.9% to 8.649×10⁻⁵ mm/year at the 15th week. further investigation in the 18th and 21st weeks showed increases in the corrosion rate of 5.4% and 5.5%, respectively. comparing the final corrosion rate of the coated pipe with the uncoated pipe, the introduction of the ms coating increased the corrosion rate by 421%. 0.00e+00 5.00e-06 1.00e-05 1.50e-05 2.00e-05 2.50e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating 0.00e+00 1.00e-05 2.00e-05 3.00e-05 4.00e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating improved oil and gas recovery 6 the ps-coated pipe in the salt environment did not corrode for 6 weeks. during the 9th week of observation, it recorded a corrosion rate of 4.6×10⁻⁶ mm/year. this corrosion rate decreased by 25% to 3.45×10⁻⁶ at the 12th week of observation. during the 15th week of observation, the corrosion rate increased by 52.8% to 5.27×10⁻⁶ mm/year. further investigation in the 18th and 21st weeks showed decreases in the corrosion rate of 17.1% and 9.38%, respectively. as shown in figure 5, comparing the final corrosion rate of the coated pipe with the uncoated pipe, the introduction of the ps coating reduced the corrosion rate by 396%. figure 4—corrosion rate of mucuna solannie inhibitor in salt environment. the mps-coated pipe in the salt environment did not corrode for the first 15 weeks. at the 18th week, it recorded a corrosion rate of 2.32×10⁻⁶. from the 18th week to the 21st week, the corrosion rate decreased by 13.3%. as shown in figure 6, the corrosion rate of the corrosion-inhibited pipe remained zero for 15 weeks before increasing to 4.37×10⁻⁶ mm/year and then dropping to 3.96×10⁻⁶ mm/year. as observed from figures 4 to 6, the corrosion rate of the uncoated pipe increased over time compared to the coated pipes. figure 5—corrosion rate of periwinkle shell inhibitor in salt environment. microbial environment. figures 7 to 9 present the corrosion rates of pipes coated with ms, ps, and mps in a microbial environment. in figure 7, the ms-inhibited pipe showed an increase in corrosion rate to 2.805×10⁻⁴ and 3.3334×10⁻⁴ mm/year after 3 and 6 weeks, respectively. however, the corrosion rate continuously declined 0.00e+00 4.00e-05 8.00e-05 1.20e-04 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating 0.0e+00 5.0e-06 1.0e-05 1.5e-05 2.0e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating improved oil and gas recovery 7 until it reached 2.822×10⁻⁴ mm/year after the 21st week. comparing the corrosion rates of the coated and uncoated pipes, the corrosion rate of the coated pipe was higher, indicating that mucuna solannie is not a suitable inhibitor in a microbial environment. figure 6—corrosion rate of mucuna solannie-periwinkle shell inhibitor in salt environment. in figure 8, the ps-coated pipe and the uncoated pipe had similar corrosion rates after 6 weeks of investigation. after that, the corrosion rate of the ps-coated pipe was higher for an additional 9 weeks. this trend reversed, and the corrosion rate of the ps-coated pipe became lower than that of the uncoated pipe, indicating the long-term suitability of this local corrosion inhibitor. as shown in figure 9, the corrosion rate of the mps-coated pipe remained lower than that of the uncoated pipe, always indicating the suitability of the inhibitor in a microbial environment. microorganisms promote corrosion by synthesizing oxidizing agents, which can be metabolic or end-products of their interaction with the metal (iverson 1974). as observed in figure 7, the higher corrosion rate of the coated pipe compared to the uncoated pipe can be attributed to the increased synthesis of oxidizing agents and the reduction of the pipe/environment barrier for liquid contaminants, which is consistent with iverson’s (1974) study. in figure 8, the similar corrosion rates of the coated and uncoated pipes can be attributed to the oxidation process, which reduces the weight of the iron. in figure 9, the lower corrosion rate of the coated pipe compared to the uncoated pipe is due to the coating blend's ability to inhibit the corrosion process, create an effective barrier between the substrate material and the environment, and act as a sacrificial material, which is in line with the findings of popoola et al. (2014). figure 7—corrosion rate of mucuna solannie inhibitor in microbial environment. -1.00e-05 0.00e+00 1.00e-05 2.00e-05 3.00e-05 3 6 9 12 15 18 21c o rr o si o n r at e, m m /y ea r week cr. control cr. coating 0.0e+00 1.0e-04 2.0e-04 3.0e-04 4.0e-04 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating improved oil and gas recovery 8 figure 8—corrosion rate of periwinkle shell inhibitor in microbial environment. figure 9—corrosion rate of mucuna solannie-periwinkle shell inhibitor in microbial environment. conclusions this study investigated the corrosion inhibition performance of locally sourced mucuna solanie (ms), periwinkle shell (ps), and their hybrid composite (mps) as eco-friendly coating materials for carbon steel pipelines in acidic, saline, and microbial environments. the key findings are summarized as follows: 1. the mps hybrid coating demonstrated significantly enhanced corrosion inhibition compared to standalone ms and ps formulations across all tested environments. in acidic conditions, mps achieved a 91.3% reduction in corrosion rate, outperforming ps (82.8%) and ms (77.9%). similarly, in saline environments, mps maintained zero corrosion for 15 weeks, with a final corrosion rate of 3.96×10⁻⁶ mm/year, while ps reduced corrosion by 396% compared to uncoated pipes. under microbial exposure, mps exhibited sustained protection, maintaining lower corrosion rates than uncoated pipes throughout the 21-week study. this superior performance is attributed to the synergistic interaction between ps (calcium-rich, barrier-forming) and ms (potassium/carbon-rich, adsorption-active), which collectively enhance passivation and barrier integrity. 0.0e+00 1.0e-05 2.0e-05 3.0e-05 4.0e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating -1.0e-05 0.0e+00 1.0e-05 2.0e-05 3.0e-05 4.0e-05 3 6 9 12 15 18 21 c o rr o si o n r at e, m m /y ea r week cr. control cr. coating improved oil and gas recovery 9 2. the microbial environment posed the greatest challenge to inhibition performance, with ms-coated pipes exhibiting higher corrosion rates (up to 3.333×10⁻⁴ mm/year) than uncoated controls due to microbial synthesis of oxidizing agents. in contrast, mps resisted microbial degradation, likely due to its composite structure limiting biofilm adhesion and metabolite penetration. saline conditions also revealed materialspecific vulnerabilities: ms coatings increased corrosion rates by 421%, whereas ps and mps maintained protective efficacy, highlighting the importance of environment-specific inhibitor design. 3. the inhibition mechanism of ps and mps aligns with their elemental composition. ps’s high calcium content (79.48%) likely facilitated the formation of protective carbonate layers, while ms’s heteroatoms (oxygen, nitrogen) and cyclic organic compounds enabled chemisorption onto steel surfaces, blocking active corrosion sites. the hybrid mps combined these traits, creating a dual passive-active barrier that impeded corrosive ion diffusion and neutralized acidic/microbial agents. 4. the mps hybrid presents a cost-effective, sustainable alternative to conventional inhibitors (e.g., fbe, cte), particularly for resource-limited regions. its efficacy in harsh environments (e.g., offshore saline, sour gas pipelines) underscores its potential for field applications. however, the poor performance of ms in microbial settings necessitates caution in environments prone to microbiologically influenced corrosion (mic). future work the following future work was recommended: 1. long-term stability studies under fluctuating temperature/pressure conditions. 2. electrochemical analysis (eis, polarization) to quantify adsorption efficiency and mechanistic pathways. 3. field trials in operational oil/gas pipelines to validate scalability. conflicting interests the author(s) declare that they have no conflicting interests. reference agbede, o.i. and manasseh, j. 2009. suitability 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igwilo is a professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling engineering, completion engineering, drilling and completion fluids technology, reservoir simulation and corrosion. igwilo holds a bachelor’s degree and master’s degree in petroleum engineering from university of port harcourt, phd degree in petroleum engineering from federal university of technology owerri, nigeria. obiukwu david nduji is master’s student at the department of petroleum engineering, federal university of technology owerri with research interest in drilling engineering and corrosion. obiukwu holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, nigeria. nnaemeka uwaezuoke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling and well engineering. uwaezuoke holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, master’s degree in petroleum engineering from university of stavanger, norway, and a phd degree in petroleum engineering from federal university of technology owerri, nigeria. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids, enhanced oil recovery, reservoir engineering and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri, nigeria. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1282 received march 10, 2024; revised june 5, 2024; accepted july 4, 2024. *corresponding author: achinta.bera@spt.pdpu.ac.in 1 a case study on reservoir management and performance prediction of an indian oilfield for enhanced oil recovery tiene bema komba, rakesh kumar vij, and achinta bera*, pandit deendayal energy university, gandhinagar, india abstract kalol has nine pay zones and is a multi-layered field in gujarat, india. oil and gas are found in pay zones ii, iii, and iv, while oil is found in pay zones v, vi + vii, viii, ix + x, xi, and xii. water injection was being done through 104 wells at 2119 m3/d in pay zones k-iii, v, vi+vii, ix+x, and xii. horizontal, multi-lateral, and high-angle wells, microbial enhanced oil recovery technologies, pdb technology, hydrofracturing, stimulations of tight sandstone layer, and increasing the quantity and quality of water injection for effective pressure maintenance and improving the recovery factor are some of the technologies that have been tried to maintain the oil production rate from this brownfield. this research has examined novel ways for developing the field to maintain and improve production levels in order to maximize the recovery from the field with minimal capital and operating expenditure. introduction currently, global energy demand is increasing and the us iea report predicts that 2050 will require 47% more energy than it does today with oil remaining the largest source just ahead of surging renewables as shown in figure 1 (international energy agency 2021). additional demand needs to be catered to by enhanced production either from new or the existing matured fields. the discovery rate for the giant fields peaked in the late 1960s and early 1970s and declined remarkably in the last two decades (ivanhoe 1997; blaskovich 2000). about thirty giant fields comprise half of the world's oil reserves and most of them are classified as the mature field (babadagli 2007). the average oil recovery factor in the world is estimated to be only between 20% and 40% (muggeridge et al. 2014). enhancement of recovery over this “easy oil” depends on the availability of proper economic viability, technologies, and effective reservoir management strategies. most oil and gas reservoirs demand proper management as this can increase the productivity of the reservoir, thereby increasing in recovery factor (hickman 1995; raza 1990; satter 1994). to efficiently produce from petroleum reservoirs, sound reservoir management practices need to be implemented. pressure maintenance and enhanced oil recovery (eor) techniques can yield higher recovery than a reservoir with only primary recovery (ayoub 2015; ahmed 2010; vishnyakov et al. 2019). globally oil is distributed in a random way more resources in the middle east and developing countries like the usa, russia, canada, and china (rempel 2006; international energy agency 2004). in india, in spite of the large area and large population hydrocarbon resources are scarce and during the last 60 years aggressive exploration and exploitation only 15% of the demand for crude oil is being met by indigenous production. 80% of the demand is being met by importing from various countries. the hydrocarbon sector is mostly in the state sector wise mostly however after the liberalization of the economy private players and mncs (multinational mailto:achinta.bera@spt.pdpu.ac.in 2 companies) are playing significant roles. therefore, national oil companies (noc) like ongc (oil and natural gas corporation) and oil (oil india limited) are managing old and mature fields producing for 50 years and aggressively pursuing ior and eor methods to enhance recovery from these fields. india continues to produce more than 80% of its production from mature fields and pressured by the government on enhancing the production is greater day by day (gyani and mitra 2021). figure 1—global oil demand to grow through 2050 despite surging renewables (source: us energy information administration 2021). ganguli et al. (2016) examined the feasibility of co2-eor following by co2 storage in ankleshwar oil field which is a mature field at cambay basin. based on the characteristics of the present field encouraging results on the basis of good response from the conceptual model, the field has the potential to produce additional 10.4% of original oil in place and sequestrate about 15.04×106 metric ton of co2. oliveira et al. (2019) reported on the use of optimal reservoir management (orm) to reduce water production and/or excess water during oil recovery in an offshore mature field from brazil's campos basin. results often reveal a near 4% increase in oil production with a corresponding decrease in total water production and overall water injection. eson (1997) related the use of different artificial lift technologies to optimize the whittier oil field in los angeles. the progressing cavity pump (pcp) was chosen as an alternative lift system for this established oil field because, when compared to other possible lift system choices, it provided the best operational and financial advantages for this mature field. lawrence et al. (2002) emphasized using nitrogen tertiary recovery to manage mature fields. the residual reserves were doubled and the field life was increased by more than 10 years as a result of studies for modelling and simulation of the jay field in southeast united states. these improvements have enabled the tertiary nitrogen wag project to recover an additional 10% of the ooip compared to waterflood alone. qiannan et al. (2019) carried out experiments on surface-active polymer flooding for enhanced oil recovery by detection analysis and modern physical simulation technique based on reservoirs and fluids in daquing placanticline mature oil field ne china. the experiments show that surface-active polymer is a novel chemical agent with both viscosity-increasing ability and surface activity suitable for high water-cut mature oilfields. the surface-active polymer differs obviously from ordinary polymer and polymer-surfactant binary system in molecular aggregation, performance of viscosity and flow capacity which has larger molecular coils, higher viscosity and viscosity-increasing property, and poorer transmission and flow capacity. moreover, surface-active polymer can improve interface chemical properties, reduce oil-water interfacial tension, and make the reservoir rock turn water-wet. lall et al. (2021) investigateed the feasibility using condensate for eor in a mature field in trinidad tobago (tt). the overall methodology to accomplish the objectives required involves; selection of appropriate well, developing a pilot test using compositional reservoir model (cmg-gem) 3 and finally conducting an economic analysis of the strategy. the results of this study demonstrated that the injection of produced condensate can result in a 33% increase in permeability. tuning of the simulator to factor the increase in permeability from 300 to 420 md due to condensate treatment demonstrated an increase in the permeability will result in an increase in the rate of production of almost 46% (24 to 35 bopd) translating in an overall gain of 30,531 bbls of oil associated with a significant financial gain of approximately $4.7 mm tt over the 16-year period for one well. this study offers compelling evidence that the use of produced condensate in eor is an economically and environmentally friendly strategy for eor in trinidad. reservoir management in a mature field is therefore a challenge for professionals working in this area in e&p (exploration and production) industries. most of the mature fields are in the state of gujarat western onshore and in assam in north east area of india. in addition, western offshore fields like mumbai high, neelam, heera, and a few others are also mature fields. kalol field, the biggest onshore field in india is situated in the cambay basin about 16 km nnw of ahmedabad city. the field was discovered in 1961 and is on production for the last 60 years. spreading in an area of 400 sq. km, kalol is a multi-layered sandstone reservoir field with geological complexities in view tectonically active area. hydrocarbon is present in tertiary sequence mainly in oligo-miocene sands. in view of the challenges faced in the management of this mature field, kalol has been chosen for my research work in this report. kalol field has large well inventories, installations, and surface facilities. in the field, over 800 wells have been drilled so far. and the majority of sands are operating under depletion drive whereas in others, partial/active water drives are operative. in general, the sands are highly heterogeneous except for a few and very tight in nature with poor transmissibility (vij et al. 2010; das et al. 2006; jena 2008). the productivity is very low and the wells come into production only after hydrofracturing in most cases. the reservoir is characterized by poor facies dominated by siltstones. from a vintage point of view, the field is classified as mature whereas still young as has produced only 10% of initial oil in place (ioip) (vij et al. 2010; das et al. 2006; hanotia et al. 2015). induction of various technologies are been attempted to maintain the oil production rate from this brown (mature) field. the objective of this research is to identify the problems encountered during the production of mature fields and to discuss the innovative approaches conceptualize and implemented in the field for maintaining and enhancing the production level and improving the reservoir. this maximizes the recovery from the field with minimal capital and operating expenditure. description of kalol field kalol field is the largest onshore field in india located about 16 km nnw of ahmedabad city. spread over an area of 300 sq. km, the field was discovered in june 1961, when the first well drilled on the structure was produced from the pay zone k-ix+x. it is a multi-layered oil field, with half of its reserves trapped between horizons ix and x. it has 11 pay zones from k-ii to k-xii corresponding to the middle eocene age at depth of 1250-1600 m msl. the upper layers like k-ii, k-iii, and k-iv are oil and gas producers while k-v to k-xii are oil producers. k-ix+x is the main oil producer in the area with k-vii being the next best layer. majority of sands are operating under depletion drive whereas, in others, partial/active water drive is operative. in general, the sands are highly heterogeneous except a few and very tight in nature with poor transmissibility. the productivity is very low and the wells come on production only after hydrofracturing in most cases. the reservoir is characterized by poor facies dominated by siltstones. kalol field is one of the first few fields explored and developed by ongc. it is a major producing field of ahmedabad asset. the first well was drilled in 1961 and regular production started in 1966. it has an ioip of 140.54 mmt with an ultimate component of 21.54 mmt and after 43 years of production, a cumulative of 13.4 mmt has been produced which is 9.34% of iiop. technological schemes of development for pay zones ix+x and xii were prepared in 1964, and for ii, iii, & iv in 1971. the final development plan (fdp) of the kalol field was prepared by the indo-soviet team in 1982. fdp recommended drilling 140 wells, covering all pay zones. various measures for production enhancement such as water injection, work-over jobs, and artificial lift etc. were also recommended in the plan. as of followup action, a total of 127 out of planned 140 wells were drilled by 1990 and resulted in oil production of 1700 4 tpd which was double of pre-fdp. to date, 628 wells have been drilled with 359 flowing and 86 are water injectors. as on 01.01.10, the field is being produced oil with a rate of 1217 tpd and gas at 285000 m3/d. reservoir geology. the kalol field is located in the ahmedabad asset-mehsana tectonic block of the north cambay basin which is approximately 300 sq. km within india. figure 2 shows the location of kalol field in cambay basin. the field is multi-layered and highly heterogeneous with various faulted reservoirs. this field contains 11 producing sand sequences that have full field coverage. it has tight silts with very low permeability and sand has an inter-bedded coal layer. kalol structure is a longitudinal of length about 30 km and a width of 6-10km. the kalol structure is characterized by a set of two faults at 60˚ intersections namely kalol and sabarmati trends, the parallelism of the synclinal axis to the fault trend, and the acute angle intersection of the culmination to the field. figure 2—location map depicting kalol field in cambay basin (jena 2008). stratigraphy and lithology. in the kalol interval, there are prominent markers such as coal at the top of kalol, shale above sand ii, coal at the base of sand iv, and coal at the top of sands ix and xii. most of the sands are on depletion drives except for the partial aquifer support in sands ii, iv, and xii. the field has a wide variety of lateral and vertical permeability from to sand, from 1 md to around 100 md. the kalol field comprises a series of rollover structures developed on the hanging wall of nnw-sse trending, left-stepping listric normal faults. a system of ne-sw trending transfer faults delimits the individual anticlines or dissects them. hydrocarbon accumulation in the middle eocene deltaic clastic reservoirs (kalol formation) is found both in the hanging wall and footwall sides with differential fluid contacts. thickness distribution kalol formation (plate 1) shows an overall thinning along the trend of these rollover structures, thus signifying their synsedimentary nature. nearly uniform thickness of the overlying tarapur shale was observed over the oligocene. thus the trapping mechanism in the kalol field appears to have evolved during middle eocene-oligocene. the syndepositional roll-over features in the reservoir kalol sands are capped by tarapur shale, providing a regional top seal. 5 synthesis of the available source rock and geochemical data of olpad, cambay shale and intervening shale layers in the middle eocene-early oligocene sequence was done for the broach and ahmedabad blocks. representative source rock log for ahmedabad block was prepared from data of well kalol-263. in the ahmedabad block, the upper part of olpad formation contains oil-prone organic matter-rich source rock layers. the cambay shale has fair to excellent organic matter richness for the most part. the organic matter richness improves toward the upper part of cambay shale and is also, generally in the excellent range in the kalol and tarapur formation. the onset of oil generation was at 1475 m. trap generation in the kalol field structure is almost concomitant with the deposition of the reservoir sequence, including the intervening organic-rich shale. these structures were finally draped over by the tarapur shale (top seal) in the early oligocene. the stratigraphy (figure 3) as illustrated below shows the break out of intervals in the kalol formation. oils in this field show a great degree of genetic variation. such variations are observed between the oils of different fields, as also between various pools within a single field. this suggests a different source for different oils. good to excellent source rock characteristics are found not only in the cambay shale but also in the kalol and tarapur formations. thus the investing, organic-rich, shale layers of these formations may have sourced the oil in the adjacent reservoir sands. these evidences support the possibility of early generation and entrapment in the ahmedabad block. although oil accumulations above the oil generation window are found in most of the structures, biomarker studies on these oils suggest that they have attained only early to moderate maturity levels. the kalol reservoir is composed of alternating laminae of fine sand or silt and argillite on a scale ranging from greater than 1 mm sand/silt laminae to occasionally to less than 10 cm. most typically the laminae are seen to be of the order of 1 to 5 mm in thickness. shale/mudstone laminae tend to be more continuous, and although some bioturbation is present in the form of occasional sand-filled thallassinoides type horizontal ichnofossils and rare vertical skolithos burrows, the widespread preservation of unmodified bedding indicated that burrowing was probably quite sparse. also, vertical burrows are seen to be quite rare. figure 3—generalized stratigraphy of the kalol field (vij 2022). 6 structural pattern. the kalol field is an nw-se trending anticline and dissected several nw-se trending longitudinal and ne-sw trending cross faults as shown in figure 4. at wavel member pays these faults played a major role in hydrocarbon entrapment. these have less significance in the fluid distribution in sertha member pays. this anticline is bounded by wamaj-wadsar low at west and nardipur low towards east. many culminations and lows are observed within the anticline. the area is gently dipping at < 2˚. figure 4—current fault pattern at the top of k-ix sand. reservoir parameters. the sands in the kalol field are found at a depth of about 1000 m having thick oil of gravity 17º api. the sands represent a significant variety in reservoir characteristics (i.e., mineralogy, porosity, and permeability). kalol sands are argillaceous, silty, and sandy shale occasionally sideritic sandstone (sharma 2009). in kalol sands, due to active aquifer support, oil contribution from self-flowing wells is almost double compared to the production from wells on the artificial lift (das et. al. 2006). tables 1 and 2 show the lithology, petrophysical properties, drive mechanisms of various pay zones. the field is developed through various schemes and reviews over the past 60 years (table 3). the reservoirs are essentially tight and heterogeneous with moderate to poor permeability. the primary drive mechanism is depletion (table 2). the reservoir pressure has depleted from super-hydrostatic to sub-hydrostatic at present. water injection is essentially instrumental in pressure maintenance for such reservoirs. pay zone k-xii. this pay zone is on production since 1966 and is developed mainly in the north-western part of the field. the area is dissected by a number of nnw-sse trending strikes slips faults and has an anticline structure, having an axis nw-sse. gas oil contact (goc) has been established in the eastern and northern part of the sand. its channel axis runs nnw-sse and the facies and thickness deteriorate western and eastern flanks of the block. the sand has varying from 2 m to 8 m. the porosity ranges from 12-20% whereas the permeability is between 50-200 md. it has in place reserves of 12.98 mmt of oil in the pd category with an ultimate component of 5.50 mmt as on 1/4/2009. the cumulative production as on 1/4/2009 is 3.70 mmt of oil leading to a recovery of 28.9%. 7 water injection in this pay zone was initiated very early in 1972 and is now in the mature stage. good response to injection is observed in the majority of the area. asp (alkali-surfactant-polymer) eor is going in kalol xii. table 1—lithology, porosity and permeability of kalol sands. pay zone lithology porosity (%) permeability (md) coverage k-ii sandstone to siltstone, silty shale 20-27 5-10 central part of the field k-iii upper part is sand silt facies while lower part is sandy 13-30 8-150 throughout the field k-iv sandstone to siltstone with coal streaks 15-25 30-60 throughout the field k-v sandstone 20-25 30-50 east and south-east part of field k-vi+vii siltstone, occasionally carbonaceous 12-25 5-40 throughout the field k-viii siltstone, occasionally carbonaceous 12-20 5-30 southern part of field k-ix+x siltstone/ sandstone 15-20 throughout the field k-xi highly shaly sand 15-24 5-8 north-west part of field k-xii sandstone 12-20 50-200 north-west part of field pay zone k-xi. this pay zone is developed in nw block of the field. its thickness varies from 2 to 4 m and has channel axis that runs nnw-sse. pay zone xi has a porosity that varies from 15% to 24% and permeability ranging 5-8 md. the sand is highly shaly, heterogeneous and very tight in nature. it has in place reserves of 6.86 mmt of oil in pd category with an ultimate component of 1.22 mmt as on 1/4/2017. the cumulative production as 1/4/2017 is 0.28 mmt of oil leading to a recovery of 4.08%. pay zone k-ix + x. pay zone k-ix + x is extensively developed throughout the field. although k-ix and x are two different dynamic units, they have been good developed together in the field. in general, the sands are highly heterogeneous with good development of sand in the form of various independent pools. it has two prominent trends such as nnw-sse and ne-sw cross faults. the lithology of pay zone k-ix varies in different parts of the field. there is mainly the presence of siltstone and sandstone in the central and northeastern part. k-ix is widely spread throughout the field and it is developed towards the central region. kix + x together contain the major reserve of kalol field. the maximum pay thickness of k-ix is 8 m and that of k-x is 12 m. the porosity of the pay zone ranges from 15-20%. the pay zone k-ix+x has in-place reserves of 57.14 mmt of oil and 164.2 mmm3 of free gas pd category with an ultimate component of 7.34 mmt and 79.3 mmm3 respectively as on 1/4/2017. the cumulative production of oil and gas as on 1/4/2017 is 4.69 mmt of oil and 10.1 mmm3 of gas leading recovery of 8.2% and 6.15% respectively. pay zone k-viii. this pay zone is developed in patches in main block, southern block, and western block. the sand is highly shaly, heterogeneous, and tight in nature. the structure is dissected by a number of nw-se trending longitudinal and ne-sw cross faults. the sand thickness varies from 2 m to 6 m and has porosity varying from 12-20%. it consists of siltstone which is occasionally carbonaceous. k-iii is heterogeneous and requires hydraulic fracturing on regular basis. its permeability ranges from 5-30 md. it has in place reserves of 7.45 mmt of oil as in the pd category with an ultimate component of 0.34 mmt as on 1/4/2017. the cumulative production as on 1.1.2017 is 0.05 mmt of oil leading to a recovery of 0.67%. 8 pay zone k-vi + vii. pay zone k-vii is one of the main producing sand of kalol field. it is developed throughout the field along with localized development of k-vi in the southern and main blocks. the structure is dissected by number of nw-se trending longitudinal and ne-sw cross faults. the sand thickness varies from 2 m to 8 m and has porosity varying from 12-25%. it consists of siltstone which is occasionally carbonaceous. in general, the sand is highly heterogeneous and very tight in nature with poor transmissibility. the productivity of the wells is very low. the permeability ranges between 5-40 md and the well produces oil only after hydro-fracturing. the reservoir is producing under depletion drive and is under pressure maintenance in the southern and main blocks. pay zone k-vi + vii has in place reserves of 32.55 mmt of oil in pd category with an ultimate component 6.16 mmt as on 1/4/2017. the cumulative production as on 1/4/2017 is 2.46 mmt of oil leading to a recovery of 7.6%. pay zone k-v. the development of pay zone k-v is confined to southern and eastern part of the field. the sand is developed as two sub layers k-va and vb. sand k-va is the main producing sand developed locally in the eastern flank of the field whereas k-vb is developed in southern part and is very tight with poor productivity. pay zone k-v has in place reserves of 8.03 mmt of oil with an ultimate component of 2.05 mmt as on 1/4/2017. the cumulative production as on 1/4/2017 is 1.5 mmt of oil leading to a recovery of 18.00%. sand k-va. pay zone kv-va is the main producing sand developed in a low, with rising flanks toward east, west, and south part of the field. it has been discovered in 1997 through testing of k-va in exploratory well kl#484. the area is dissected by a number of nne-sse trending normal faults. gas cap is observed at 1350 m msl towards south and east and owc is observed at 1350 m msl which gives partial support. sand appears to be deposited as distributary mouth bars in deltaic regime and its thickness varies from 4 m to 8m. the porosity and permeability range from 20-25% and 3050 md respectively. the sand development is very good with high productivity. the sand is operating under depletion and is under pressure maintenance by water injection which was implemented in 2002. pay zone k-iv. pay zone iv is developed throughout the field forming separate blocks. major part of the main block is gas bearing whereas western block is oil bearing with a small gas cap. it is further subdivided into two litho units namely k-iva, k-ivb from the top to bottom. sub layer k-iva is prominently gas bearing, however small quantity of oil is present. sub layer k-ivb is mainly oil bearing. owc and gwc have been observed. the lithology varies from sandstones to siltstone however coal streaks are very common. there is vertical variation in facies and the pay thickness varies from 2 m to 15 m. it is producing under mixed drive with active aquifer support and gas cap with some blocks on depletion. pay zoneiv has in place reserves of 15.32 mmt of oil and 3435.95 mmm3 of gas in pd category with an ultimate component of 1.27 mmt and 2973.40 mmm3 as on 1/4/2017 respectively. the cumulative production as on 1/4/2017 is 1.06 mmt of oil and 1610.06 mmm3 of free gas leading to recovery of 6.9% and 46.9% respectively. pay zone k-iii. it is mainly developed in ene-wsw trending lobes northern, central and southern part of the field comprising both oil and gas. three prominent structures high are present in southern, central and north part of the area. the area is dissected by several longitudinal and transverse faults. pay zone k-iii is gas bearing in the north-central and south-west areas whereas in south east and north-west part is mainly oil bearing with small gas cap. the sand is mainly operating under strong aquifer support in northern part whereas in south it is under partial aquifer support and partly on depletion. k-iii covers almost the entire field and its upper part consists of sand-silt facies while lower part is more sandy. the degradation of the facies separates the channels and the thickness varies from 2.5 m to 6 m. the porosity and permeability of the pay zone range 13-30% and 8150 md respectively. it has in-place reserves of 7.63 mmt of oil and 2755.69 mmm3 of free gas with an ultimate component of 1.6 mmt and 2354.2 mmm3 as on 1/4/2017 respectively. the cumulative production as 1/4/2017 is 1.42 mmt of oil and 2350.71 mmm3 of gas leading to a recovery of 20.6% and 85.3% respectively. pay zone k-ii. the development of pay zone-ii is confined is developed in e-w trend in the central part of the field. major part of the main block is gas bearing whereas western block is oil bearing with a small gas cap. the area is dissected by number of nne-ssw trending faults and the lithology varies from sandstone to siltstone, silty shale. shale is out in the northern and southern margin of the block. kalol main fault separates gas bearing eastern block from oil bearing western block. gas water contact (gwc) is observed at 1300 m msl toward the eastern margin of sand whereas oil water contact (owc) is observed toward the western margin. the pay thickness varies from 2.5 m to 9 m while the porosity and the permeability range from 20-27% and 59 10 md respectively. it has in place reserves of 3.92 mmt of oil and 1797.39 mmm3 of free gas in pd category with an ultimate component of 0.50 mmt and 1160 mmm3 as on 1/4/2017 respectively. the cumulative production as on 1/4/2017 is 0.25 mmt of oil and 1148.27 mmm3 of gas leading to a recovery of 6.9 % and 64% respectively. issues related to kalol field. table 3 shows the development history of kalol field. the following issues are the challenges faced during the development of kalol field.  multilateral sandstone reservoir having isolated 11 pay zone.  variation in the lithology of the field from sandstone, siltstone and shale.  presence of coal streak.  tight sand required hf at a regular interval of time.  wide range of porosity and permeability of the reservoir.  the field is very heterogenous having a large number of sealing and communicating fault  lateral facies changes.  the crude oil property varies from layer to layer.  in some layer paraffin and resin content are significant high. table 2—drive mechanisms of various pay zones (das et al. 2006). pay zone producing fluid drive mechanism pressure maintenance ͌area sq.km k-ii oil and gas combination drive none 49 k-iii oil and gas northern partstrong aquifer southern partweak aquifer and depletion drive water injection 84 k-iv oil and gas combination drive with active aquifer support and some blocks on depletion none 173 k-v oil depletion drive with weak water aquifer water injection 46 k-vi+vii oil depletion drive water injection 142 k-viii oil depletion drive none 40 k-ix +x oil depletion drive water injection 199 k-xi oil depletion drive none 32 k-xii oil depletion drive water injection 30 10 table 3—field development history (vij et al. 2010). year plan implemented 1961 first well drilled 1964 trial production started 1971 technological scheme for k-ii, iii iv, xii 1982 final development plan (fdp) 1996 integrated development plan for kalol 2000 iorkalol 2003, 2007, 2009, 2011 performance review of sands k-iv & vi + vii , va, k-vii nw, k-vii 2011-2012 integrated study to review and update geological model of k-ix + x 2012-2013 released & dev. location for k-ix + x in 11th adb 2013-2014 released 4 locations for k-va sand 2013-2014 released 6 locations for k-x sand 2014-2016 geo cellular model under preparation by g & g team at integddn 2016-2017 released 5 locations for k-x sand 2016-2017 released 9 locations for kxi sand 20172018 released 3 locations in k-va sand, 6 locations in k-x sand , 2 locations in k-vii sand, 3 locations in k-ix & kvb, 1 location in kviii sand 2017-2018 performance review of sand k-xii & kxi ( 5 locations released for k-xii sand, 11 locations released for k-xi sand enhanced recovery screening of the field screening of kv-b using eorgui. the below data is provided:  api = 36 (degrees)  oil viscosity = 8.44 (cp)  oil saturation = 0.57  formation type = sandstone  reservoir thickness = < 20 (ft)  fluid composition = high % c1-c7  reservoir depth = 4675 (ft)  reservoir temperature = 176 (deg f)  reservoir permeability = 40 (md) the ranking percentage is on the side bar of the window, whereas the highest percentage is surfactant polymer/alkaline surfactant polymer method (100%), immiscible (83%) and combustion (60%). figure 5 shows the preferred chemical eor for kalol vb. 11 (a) input (b) output figure 5—eorgui result on kalol-vb. cmg simulation of kalol-va. reservoir model is used to predict flow of fluids through porous media, performance prediction of producing fields, making business decision as well as techniques to improve the reservoir performance by hydraulic fracturing, water injection and eor processes. five spot patterns, 4 injectors and one producer were used. the simulation data is provided in table 4. the model was run for 10 years for surfactant polymer flooding. figure 6 shows the 3d model of representing oil per unit area. the flooding was done at 50˚c. the graphs obtained as a result were compared to the water flooding and steam flooding using cmg. 12 table 4—cmg simulation data. geometry 5 spots reference depth 4600 ft reference pressure 2062 psi owc 4658.7 ft porosity 24% permeability kx, ky, kz 50, 50, 25 md gross thickness 19.68 ft net pay 13.12 figure 6—3d model of representing oil per unit area. figure 7 shows results for the surfactant-polymer (sp) flooding simulation which was run for 10 years. cumulative oil, rate, and water cut trends are shown in the graph. from the graph, it can be seen that the cumulative oil tends to increase whereas the oil rate starts to decline and become linear from 2025 onwards. water cut is increased in the initial years of simulation and then it follows a linear trend. figure 8 shows cumulative oil, water cut and oil rate trends for 10 years in case of implementation of steam injection at 150˚c. oil rate starts to decline and become linear from 2024, while water cut and cumulative oil gradually increase but less compared to surfactant polymer flooding. figure 9 shows how water injection will affect the reservoir parameters. in the case of water injection, oil rate declines early and cumulative oil tends to increase till 2024 rapidly. water cut is very high and indicates that excess water production can be encountered. comparison. from the results obtained for the three recovery methods; surfactant polymer (sp) flooding, steam injection and water injection, it can be clearly seen that water cut is delayed in case of sp flooding. cumulative oil which tends to increase is highest in case of surfactant polymer flooding and oil rate also is maintained higher in this method compared to other recovery methods. so if surfactant polymer flooding is implemented then additional 15% recovery can be made however it is less than the asp flooding which is additional 18% or more. 13 figure 7—prediction of surfactant polymer flooding. figure 8—steam injection simulation. figure 9—water injection simulation. 14 performance prediction of the field reservoir performance analysis of oil and gas fields is a continuous process to reassess the present state of the reservoirs. the review helps in taking decision for enhancement of oil and gas production to exploit the reservoir optimally and maximize ultimate oil recovery. the production performances analyzed based on oil, water and gas production data and corresponding pressure drop from the initial reservoir pressure with reservoir facies, by the way of cross plots of different variables. the greatest complexity is due to multiple factors, such as  completion in varying type of reservoirs such as pay sands , coal or multiple combination with wide permeability contrast  continuous or discontinuous reservoir type  types of completion such as casing perforation or slotted casing  nature of damage due to drilling/workover  the degree of accuracy of the production indices/measurement, and  adequate/inadequate pressure data. the present study is based on production, water cut and gor data available from inception to 1/4/2017. the production performance graphs have been collected through annual activity report, ahmedabad asset, ongc, 2017. using ofm, graphs for cumulative oil production, oil production rate, liquid production rate, water cut and gas oil ratios are generated. in this part of our research we will firstly analyse and interpret the production performance of each of 11 layers of kalol field and we will finally perform the production performance of the whole field. figure 10—performance plot of k-ii pay zone. k-ii pay zone. this pay zone is on production since 1980 and the production peaked in 1997 to around 55 m3/day but could not sustain and average production remained around 49 m3/day as shown in figure 10. no commercial water injection has been developed in the field. water breakthrough started in 1985 and result to water cut of 45%. in the late 1990 the gor increased and reached its peak in 1995 to approximately 1100 v/v and became stable at average of 150 v/v from 1999. the water cut reached its peak in 2012 with the value of 15 80%. as on 1/4/2017 there are 8 oil flowing wells and no injection wells. it has in place reserves of 3.92 mmt of oil and 1797.39 mmm3 of free gas in pd category with an ultimate component of 0.50 mmt and 1160 mmm3 as on 1/4/2017 respectively. the cumulative production as on 1/4/2017 is 0.25 mmt of oil and 1148.27 mmm3 of gas leading to a recovery of 6.9 % and 64% respectively. k-iii pay zone. the pay zone k-iii is on production since 1964 and the production peaked in 2002 to around 300 m3/day and sustain to an average rate of 100 m3/day. in 1986 the pay zone experienced water breakthrough leading to an increased water cut to around 80%. commercial water injection has started in 1990 in the field. water cut drastically increased from 1990 and became stable later on during the field production. in 1980, the gor started increasing and reached its peak in 1984 to approximately 2400 v/v and drastically decreased to an average minimum value of 50 v/v from 2002. as on 1/4/2017 the pay zone was under 12 oil flowing wells and 9 water injection wells. the performance plot of k-iii pay zone is shown in figure 11. it has in-place reserves of 7.63 mmt of oil and 2755.69 mmm3 of free gas with an ultimate component of 1.6 mmt and 2354.2 mmm3 as on 1/4/2017 respectively. the cumulative production as 1/4/2017 is 1.42 mmt of oil and 2350.71 mmm3 of gas leading to a recovery of 20.6% and 85.3% respectively. figure 11—performance plot of k-iii pay zone. 16 figure 12—performance plot of k-iv pay zone. k-iv pay zone. this pay zone is on production since 1972 and the production peaked in 1990 to around 300 m3/day but could not sustain and average production remained around 40-45 m3/day. the production started with high water cut of 42% which has been increased and stabilized at higher value of 80%. the field is producing with high water production. the commercial water injection has been developed in the field from 1991 and stopped in 1999. from 1980 the gor increased and reached its peak in 1996 to approximately 2900 v/v and drastically decreased to an average value of 200 v/v from 1999. as on 1/4/2017 there are 12 oil flowing wells and no injection wells. figure 12 shows the performance of k-iv pay zone.pay zoneiv has in place reserves of 15.32 mmt of oil and 3435.95 mmm3 of gas in pd category with an ultimate component of 1.27 mmt and 2973.40 mmm3 as on 1/4/2017 respectively. the cumulative production as on 1/4/2017 is 1.06 mmt of oil and 1610.06 mmm3 of free gas leading to recovery of 6.9% and 46.9% respectively. the performance plot of k-iv pay zone is shown in figure 12. k-v pay zone. the pay zone k-v is on production since 1980 and the production peaked in 2003 to around 600 m3/day and sustain to an average rate of 102 m3/day from 2013. in 2001 the commercial water injection has started in the field. water cut sharply increased from 2005 to an average of 50-60%. in 1997, the gor started increasing and reached its peak in 1998 to approximately 1900 v/v and drastically decreased to an average minimum value of 100 v/v from 2000. as on 1/4/2017 the pay zone was under 17 oil flowing wells and 4 water injection wells. pay zone k-v has in place reserves of 8.03 mmt of oil with an ultimate component of 2.05 mmt as on 1/4/2017. the cumulative production as on 1/4/2017 is 1.5 mmt of oil leading to a recovery of 18.00%. figure 13 shows the performance plot of k-v pay zone. k-vi+vii pay zone. pay zone k-vi+vii started producing from is on production since 1969 and the production started increasing considerably from 1987 and peaked in 1998 to around 460 m3/day to an average rate of 187 m3/day. commercial water injection started in the field from 1991. the initial gor was about 39 v/v which peaked in 1974 at around 1900 v/v and drastically decreased to an average of 100 v/v. the combined pay zone has low water cut at approximately 40%. as on 1/4/2017 there are 80 oil flowing wells and 25 injection wells. pay zone k-vi + vii has in place reserves of 32.55 mmt of oil in pd category with an ultimate 17 component 6.16 mmt as on 1/4/2017. the cumulative production as on 1/4/2017 is 2.46 mmt of oil leading to a recovery of 7.6%. the performance plot of k-vi+vii pay zone is shown in figure 14. k-viii pay zone. in pay zone viii, the production started from 1970 with the rate around 30 m3/d and peaked 1989 at around 145 m3/d. the production could not sustain at this rate, and average production remained stable at 10 m3/d. in 1986 the pay zone experienced the water breakthrough leading to water cut of 10 %. the water cut reached its peak in 2014 at 85% and the average water cut in this layer is estimated to be 70%. at the initial stage of the production through the pay, the gas oil ratio (gor) was very low up to negligible. gor suddenly increased and peaked to 4800 v/v in 1980, then decreased to minimal value. the average gor is estimated to be 200 v/v. no commercial water injection has been developed in the pay. as on 1/4/2017 the pay zone was under 3 oil flowing wells and no water injection wells. it has in place reserves of 7.45 mmt of oil as in pd category with an ultimate component of 0.34 mmt as on 1/4/2017. the cumulative production as on 1/1/2017 is 0.05 mmt of oil leading to a recovery of 0.67%. the performance plot of k-viii pay zone is shown in figure 15. figure 13—performance plot of k-v pay zone. 18 figure 14—performance plot of k-vi+ vii pay zone. figure 15—performance plot of k-viii pay zone. k-ix+x pay zone. the combined pay zone ix+x started producing from is on production since 1961 and the production started increasing considerably from 1969 and stated at an average rate 280 m3/day for a long period of time (1969-1983). the production rate then increased very highly and peaked in 1990 to around 1300 19 m3/day. the average production rate through the layer is estimated to be 314 m3/day. the commercial water injection started in the field from 1991. the layer has been produced for long period time with considerable amount of oil without water cut. the water breakthrough significantly started in 1980 and the average water cut is stated around 37-45%. the initial gor was about 250 v/v which peaked in 1967 at around 1450 v/v and drastically decreased to an average of 85 v/v. as on 1/04/2017 there are 76 oil flowing wells and 21 injection wells. the pay zone k-ix+x has in place reserves of 57.14 mmt of oil and 164.2 mmm3 of free gas pd category with an ultimate component of 7.34 mmt and 79.3 mmm3 respectively as on 1/4/2017. the cumulative production of oil and gas as on 1/4/2017 is 4.69 mmt of oil and 10.1 mmm3 of gas leading a recovery of 8.2% and 6.15% respectively. the performance plot of k-ix+x pay zone is shown in figure 16. figure 16—performance plot of kix+x pay zone. k-xi pay zone. in 1969 the production started in pay zone xi with the rate around 20 m3/d and peaked 1989 at around 80 m3/d. the production could not sustain at this rate, and average production remained stable at 13 m3/d. at initial age of production there was considerable water cut from the layer at around 30%. this water cut remained constant for long period of time and significantly increased from 1990. the water cut from the production of the pay is then stated to be very high at around 80-90%. at the initial stage of the production through the pay, the gas oil ratio (gor) was low as 100 v/v. gor considerably increased in 1991 and peaked to 2000 v/v, then decreased to minimal value. the average gor is estimated to be 100 v/v. no commercial water injection has been developed in the pay. as on 1/4/2017 the pay zone was under 5 oil flowing wells and no water injection wells. it has in place reserves of 6.86 mmt of oil in pd category with an ultimate component of 1.22 mmt as on 1/4/2017. the cumulative production as 1/4/2017 is 0.28 mmt of oil leading to a recovery of 4.08%. the performance plot of k-xi pay zone is shown in figure 17. 20 figure 17—performance plot of kxi pay zone. figure 18—performance plot of kxii pay zone. 21 k-xii pay zone. in k-xii, the production started from 1967 with the rate around 100 m3/d and increased significantly to peak in 1977 at around 800 m3/d. the production could not sustain at this rate, so it stated decreasing from 1989 and average production remained stable at 73 m3/d. the initial stage of the pay production is remarked by negligible water cut. in 1971, the commercial water injection started. in 1979 the pay zone experienced the water breakthrough leading to water cut of 30 %. the water cut reached its peak in 2011 at 85% and the average water cut in this layer is estimated to be 80%. at the initial stage of the production through the pay, the gas oil ratio (gor) was very low up to negligible. gor suddenly increased and peaked to 1800 v/v in 1998, then decreased to minimal value. the average gor is estimated to be 49 v/v. as on 1/4/2017 the pay zone was under 13 oil flowing wells and 1 water injection wells. it has in place reserves of 12.98 mmt of oil in pd category with ultimate component of 5.50 mmt as on 1/4/2009. the cumulative production as on 1/4/2017 is 3.70 mmt of oil leading to a recovery of 28.9%. water injection in this pay zone was initiated very early in 1972 and is now in mature stage. good response of injection is observed in majority of the area. the performance plot of k-xii pay zone is shown in figure 18. whole kalol field. here, the current status and performance of kalol field is provided by combining all the layer together and depicted in table 5. the field has been producing since 1961, with exploration and exploitation resulting in lateral and vertical field growth. in 1989, production reached the peak to around 2100 m3/day, but it could not be sustained, and average production stayed around 877 m3/day. additional accretion and exploitation could keep the rate at this level for longer time. despite the fact that water injection was started at an early stage in 1972 for a few reservoirs due to depletion, commercial water injection, on the other hand, could begin in 1990, resulting in low pressure areas in most reservoirs. the average field water cut is roughly 40%, with gor ranging from 100 to 250 v/v. however, the average gor is around 150 v/v. it has in place reserves of 151.9 mmt of oil in pd category with an ultimate component of 25.15 mmt as on 1/4/2017. the cumulative production as 1/4/2017 is 15.7 mmt. in the last 56 years, cumulative production has been 10.3% of in-place oil, indicating a lower exploitation index. various initiatives over the last two years have increased production from 825 to 975 m3/d. this could be accomplished by adopting proper reservoir management practices improving the number of flowing wells, frequent zone transfers in light of the reservoir's multilayered nature, effective water injection in a few layers, prioritization of potential development in field wells, aggressive hydrofracturing campaigns, artificial lift optimization, and ultimately proper layer-wise reservoir management. the performance of the kalol field is shown in figure 19. table 5—reserves status of kalol field as on 1/4/2017. oiip (pd) 151 mmt ultimate reserves (pd) 25.15 mmt cumulative production 15.7 mmt reserves (pd) 9.5 mmt recovery 10.3 % wells drilled 702 oil+ gas wells 502 water injectors 104 oil production rate 877 m3/d water injection rate 2119 m3/d pay zones 9 oil + free gas pay 3 oil pays 6 22 figure 19—performance graph of kalol field. figure 20 shows the production of different layers of kalol field from the inception to 2017. between the years 1964-1987, the sand k-xii was dominant in the term of production, followed by k-ix + x. the production was higher in k-ix+x from 1987 to 1995 then from 1995 to 2000, the total field production was equally shared through the pays k-vi+kvii, kix+x and kiii. from 2000-20017 the exploitation throughout the field is dominated by the layers k-iii, k-va, kvi+viii. since the inception of the field up to 2017, the pay zones k-xii and k-ix +x have produced the maximum amount of crude. figure 20—exploitation of different sands in different time periods. 23 techno-economic feasibility analysis as on 1/4/2019, a total of 752 wells have been drilled in the kalol field, of which 464 wells are currently oil producers, 118 wells are water injectors, 8 wells are effluent disposal, 28 wells are gas wells, 1 well is polymer injector, 83 wells are abandoned, 10 wells are yet to be abandoned, 10 wells are observation wells, 25 wells are future utility wells. table 6 shows economics analysis of the kalol field. table 6—economics analysis of the kalol field. revenues crude oil, mm$ 4407.32 natural gas, mm$ 99.74 other income, mm$ 235.17 change in stock, mm$ 7.31 total revenue, mm$ 4749.54 expenses stationaries levies, mm$ 1453.46 operating expenses, mm$ 1468.41 recouped cost, mm$ 423.40 provisions and write offs, mm$ 22.03 others, mm$ 3285 total expenses, mm$ 3400.15 profit/loss 1349.39 drilling project costs. 162 wells are planned to be drilled in various fields of kalol from 2019 to 2026. the incremental oil gain from the drilling of these development wells is estimated to be 0.949 mmt and incremental gas gain is 122.18 mmscm. ongc is oil major and strives to continually hike the production of hydrocarbon to meet the ever-growing national demand. in ahmedabad asset, about 905 mmt (3p) reserve as 1/4/2019 is available for exploitation in fields. development drilling is one of the main activities to the available reserve. table 7 shows the drilling projects and costs. table 7—drilling projects and costs. year 20192020 20202021 20212022 20222023 20232024 20242025 20252026 total no of wells to be drilled 27 27 25 23 20 20 20 162 average cost of drilling, $/m 35744 37174 38660 40593 42623 44754 46992 average depth, m 1600 1600 1600 1600 1600 1600 1600 drilling cost, mm$/well 57.2 59.5 61.9 64.9 68.2 71.6 15.2 drilling cost for the year, mm$ 1544.4 1606.5 1547.5 1490.4 1364.0 1432.0 1504.0 10488.8 24 chemical injection projects and costs. table 8 depicts the available chemicals and their costs per barrel of incremental oil from the surveyed asp projects. in the chemical injection project, the pre-slug was designed to have 0.097 of slug and 1450 ppm of polymer. the main flush is composed of 0.308 of slug where 1350 ppm of polymer, 1.25% of alkaline agents and 0.27% of surfactants. the post slug composed of 0.242 and 800 ppm of polymer. the individual chemical slug cost in us$/bbl incremental oil of pre-slug, main flush and post-slug was 0.42, 7.43, 0.53 respectively. the average chemical cost in us$/bbl incremental oil is 6.32 and the total drilling cost from 2019 to 2026 is estimated to be 10488.8 mm$. table 8—chemicals and costs. item chemical pre-slug main flush post-slug slug size, pv(1l) 0.097 0.308 0.242 polymer, ppm 1450 1350 800 alkiline agents, % 1.25 surfactants, % 0.27 alkiline cost , us $/lb 0.15 hpam cost , us $/lb 1.5 surfactant cost, us $/lb 3 individual chemical slug cost, us $/bbl inc. oil 0.42 7.43 0.58 total chemical cost, us $/bbl inc. oil 8.44 average chemical cost, us $/bbl inc. oil 6.32 conclusions the kalol field, india's largest onshore field, is located in the central part of the prolific cambay basin and has been operated by ongc, a national oil firm, for the past 60 years. continual exploration and exploitation activities resulted in field expansion both laterally and vertically, resulting in continuous growth of the initial oil in place, ultimate, and recovery factor improvement. although the field is old in terms of vintage, it is still young, having produced only 10.3% of in place oil. in light of the current operating strategies, the field is experiencing a mid-life crisis; however, recent efforts to focus attention on individual wells, induction of technologies, and water injection surveillance and monitoring have paid off handsomely in terms of increasing, sustaining, and maintaining production levels. the objective of our research was to maximize the recovery from the field with minimal capital and operating expenditure. the following conclusions are reached based on reservoir simulation and comparison of several ior approaches in the pay k-va:  since 2005, kalol v-a has been producing with secondary recovery via water injection, and continuing usage of water injection will result in a recovery of 39% until 2030.  if water injection is substituted by gas injection, the recovery rate will climb to 41% by 2030, resulting in a higher production rate.  asp flooding is proposed to boost the oil recovery from based on preliminary eor screening and analogy to a similar reservoir k-xii sand in the same field. we took the work a step further by doing a study on sp simulation and comparing the two ways.  it has been determined that while sp flooding can avoid the detrimental effects of alkali, it is not cost competitive with asp flooding and has a lower recovery rate. 25  in other hand, kalol layers are very tight and heterogeneous so the injectivity of is very less. thereby injection of asp was very difficult due to low injectivity and failed during the pilot test. so the most effective method for the recovery of the field becomes the immiscible gas injection. the data for the simulation was collected from reference articles and assumed whenever necessary. fields offer a tremendous potential for increasing the recovery factor from individual layers, and obtaining 20% recovery on a field scale does not appear to be a herculean task. the fundamental requirement for the field to sustain production is pressure maintenance through effective water injection and the introduction of eor technologies. a better knowledge of the geological and reservoir heterogeneity can help pave the road for future brown field utilization. conflict of interests the author(s) declare that they have no conflicting interests. references blaskovich, f. t. 2000. historical problems with old field rejuvenation. paper presented at the spe asia pacific conference on integrated modelling for asset management. paper presented at the spe asia pacific conference on integrated modelling for asset management, yokohama, japan, 25-27 april. spe-59471-ms. babadagli, t. 2007. development of mature oil fields—a review. journal of petroleum science and engineering 57(3): 221-246. das, s., singh, h., and tiwari, d. 2006. reservoir classification and geological remodeling of kalol sands of sobhasan complex, north cambay basin, india. proc., the 6th international conference and exposition on petroleum geophysics. kolkata, india, 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china. petroleum exploration and development 46(6): 1206-1217. tiene bema komba is working as a field engineer trainee in baker hughes, côte d'ivoire, west africa. he holds b.tech. and m.tech. in petroleum engineering from jawaharlal nehru technological university, kakinada, india and pandit deendayal energy university, gandhinagar, gujarat, india, respectively. his research interest includes reservoir engineering, enhanced oil recovery, and subsea production system. he did his internship in ongc india. rakesh kumar vij is a professor of practice of petroleum engineering at pandit deendayal energy university, gandhinagar. he also served as director-school of petroleum technology and dean-placement at the same university. he holds b.sc., m.sc., and m.phil. from university of delhi and ph.d. from dibrugarh university, india. he has 39 years’ experience in ongc india. his research interest includes reservoir management, enhanced oil recovery, co2 sequestration, and green hydrogen. achinta bera has been working as an assistant professor of petroleum engineering at pandit deendayal energy university, gandhinagar, gujarat, india since 2019. he holds b.sc. and m.sc. from university of calcutta and ph.d. from indian institute of technology (ism) dhanbad, india. his research interest includes reservoir characterization and modeling, enhanced oil recovery, unconventional energy resources, drilling fluids & cementing, co2 sequestration, and underground hydrogen storage. he has been listed as world’s top 2% scientists by stanford university ranking system. https://www.spglobal.com/commodityinsights/en/market-insights/latest-news/oil/100621-global-energy-demand-to-grow-47-by-2050-with-oil-still-top-source-us-eia https://www.spglobal.com/commodityinsights/en/market-insights/latest-news/oil/100621-global-energy-demand-to-grow-47-by-2050-with-oil-still-top-source-us-eia abstract introduction description of kalol field enhanced recovery screening of the field performance prediction of the field techno-economic feasibility analysis conclusions conflict of interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1320 received september 26, 2024; revised october 3, 2024; accepted october 10, 2024. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 performance study of afzeila africanamarantha arundinacea nanoparticles assisted for fluid loss control in waterbased drilling fluid anthony kerunwa, lilian enyang ndoma-egba, angela nwachukwu, nnaemeka uwaezuoke, nzenwa dan enyioko, ugochukwu ilozurike duru and chukwuebuka francis dike*,federal university of technology owerri, owerri, nigeria abstract drilling fluids (df) play a vital role in oil and gas well drilling operations, particularly given the increasing economic, technical, and environmental challenges associated with different wells and fields. however, during drilling, df often experiences filtrate (fluid) loss, which reduces the continuous phase volume and leads to an increase in mud cake thickness. to address this issue, various additives have been employed to enhance the properties of the mud filter cake and mitigate fluid loss. conventional fluid loss additives, such as carboxymethyl cellulose (cmc), have been widely used for this purpose; however, these chemicals are neither cost-effective nor environmentally sustainable, particularly in developing regions. consequently, ongoing research seeks suitable local alternatives to replace these materials. in this study, the efficacy of polymer-assisted nanoparticles for fluid loss control was evaluated. biopolymers including afzelia africana (aa) and maranta arundinacea root (mar) were tested, along with corncobs (cc) and silica oxide nanoparticles (sio2) as nanoparticle additives. cmc served as the conventional material for comparison. analytical methods including fourier transform infrared spectroscopy (ftir), rheological analysis, and filtration tests were conducted. ftir results revealed that cmc, aa, mar, cc, and sio2 exhibited similar functional groups, such as alcohol, aromatic carboxylic acid, and isothiocyanate. rheological testing demonstrated that the incorporation of sio2 and cc into aa-based and mar-based water-based drilling fluids (wbdf) enhanced their rheological properties. fluid loss tests further indicated that the inclusion of sio2 and cc improved the fluid loss control performance of the wbdfs, with cc having the most pronounced effect on both rheological and fluid loss performance. the study provides promising insights into sustainable and cost-effective approaches to improving drilling fluid performance using locally available resources, which could enhance drilling efficiency and reduce environmental impact. introduction the exploitation of crude oil and natural gas has experienced significant growth due to increasing global demand. as a result, rapid technological advancements, such as horizontal and directional drilling, have been implemented to enhance oil production efficiency (tour et al. 2019). drilling fluids (dfs) are crucial in the drilling of oil and gas wells, particularly given the complex economic, technical, and environmental challenges associated with various fields (foxenberg et al. 2008). dfs are often referred to as the "lifeblood" of wellbore mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 drilling activities in the petroleum industry (udoh and okon 2012). dfs consist of a dispersed phase and a continuous phase, which form the basis for their classification. they are typically categorized as water-based drilling fluids (wb-df), oil-based drilling fluids (ob-df), or pneumatic-based drilling fluids (pb-df), with wb-df being the most environmentally preferred option (kerunwa 2020). dfs perform several critical functions, including: 1) cooling and lubricating the drill string, 2) removing and transporting cuttings from the borehole, 3) managing subsurface formation pressures, 4) reducing friction between the drill string and the borehole, and 5) forming a thin, low-permeability filter cake to minimize fluid loss (skalle 2012; sayindla et al. 2017; kerunwa and gbaranbiri 2018). among these, the prevention of continuous phase loss is a key function, which is achieved by forming a low-permeability filter cake along the borehole wall (feng et al. 2009). thus, dfs are formulated to minimize unwanted filtrate loss and promote borehole stability (azar and samuel 2007). the formulation process aims to enhance borehole stability, form a thin filter cake, and reduce fluid loss (agwu and akpabio 2018). this process, referred to as fluid-loss control, involves the addition of specific chemicals to improve the filter cake properties and lower the filtration rate (bourgoyne et al. 1986). traditionally, fluid-loss control has been achieved using conventional additives such as polyanionic cellulose (pac) and carboxymethyl cellulose (cmc) (caenn and chillinger 1996). however, these commercial polymers are neither cost-effective nor environmentally sustainable for developing countries, leading to increased interest in local alternatives for fluid-loss control. previous studies have explored various biopolymers and local materials for their fluid loss control potential. for example, olatunde et al. (2012) investigated the use of gum arabic in water-based mud (wbm), while okon et al. (2014) evaluated rice husk for similar purposes. other studies have examined corn cob cellulose (nmegbu and bari-agara 2014), pleurotus tuber-regium (chinwuba et al. 2016), and combinations of local materials, such as rice husk, detarium microcarpum, and brachystegia eurycoma (okon et al. 2020). these studies demonstrated varying degrees of success, highlighting the potential of local materials in fluid loss control. furthermore, recent research has focused on the use of nanoparticles as promising fluid loss control additives (uwaezuoke 2022). studies by ismail et al. (2016) and dejtaradon et al. (2019) have shown that nanosilica and zno nanoparticles exhibit significant fluid loss control capabilities. cheraghian (2019) and gbadamosi et al. (2019) also reported improved fluid loss performance using silica nanoparticles. despite these advancements, the rheological limitations of nanoparticles and locally sourced materials prevent them from fully replacing conventional additives like cmc and pac-r. in this study, silica oxide nanoparticles (sio2-nps) were blended with two biopolymers, afzelia africana and maranta arundinacea, to enhance their fluid loss control properties in water-based drilling fluids (wbdf). materials and methods materials. the materials utilized in this study for fluid loss control analysis included both locally sourced additives and conventional materials. the locally sourced biopolymers used were afzelia africana (aa) and maranta arundinacea root (mar), which served as fluid loss control additives. in addition, nanoparticles were incorporated, specifically silica oxide (sio2) and corncobs (cc), to enhance fluid loss control performance. as a conventional fluid loss control additive, carboxymethyl cellulose (cmc) was used for comparison. among them, the aa, mar, and cc were sourced from a local market in the south-eastern part of nigeria, west africa. while cmc and sio2 were sourced from an industrial store and the locally sourced fluid loss control additives. other essential materials included bentonite, used as a viscosifier to maintain fluid consistency, and barite, employed as a weighting agent for density control. sodium hydroxide was used for ph control, and calcium carbonate was added to further stabilize the drilling fluid. the continuous phase of the drilling fluid consisted of water. improved oil and gas recovery 3 a variety of equipment was used to analyze the properties of the formulated drilling fluids. this included a hamilton beach mixer for blending, a ph meter to monitor the ph levels, and a buck 530 irspectrophotometer to identify functional groups. a low pressure-low temperature api filter press (lplt) was utilized for filtration testing, while a rotary viscometer was used to measure the rheological properties. additionally, a mud balance was employed for density measurements, along with a stopwatch and weighing balance for accurate time and weight measurements throughout the experimentation process. these materials and equipment collectively contributed to the comprehensive evaluation of the fluid loss control properties of the drilling fluids in this study. preparation of the locally sourced bio-polymer. to prepare the locally sourced biopolymers used in this study, the following procedures were followed for each material. afzelia africana (aa) preparation. afzelia africana pods were first subjected to a controlled heat treatment in an oven set to 60°c for 30 minutes. this process facilitated the extraction of the seeds from the pods. once the seeds were released, they were pulverized using an industrial-grade blender to produce fine nanoparticles. the pulverized material was then passed through a 0.062 mm mesh sieve to ensure uniform particle size. the sieved particles were stored in a sealed container to preserve their integrity for use in the formulation. corncobs (cc) preparation. corncobs were dehydrated in an oven at 60°c for 48 hours to remove any residual moisture. after the dehydration process, the dried corncobs were ground into finer particles using an industrial blender. to ensure particle uniformity, the ground corncobs were sifted through a mesh sieve. the resulting fine particles were stored in an airtight container to maintain quality for later use in the drilling fluid formulation. maranta arundinacea root (mar) preparation. the maranta arundinacea (mar) roots were first sliced into smaller pieces and blended with water to create a slurry. this slurry was allowed to stabilize for two hours before the water content was reduced. this process was repeated twice until a clear, transparent top layer of water was achieved. the transparent water was carefully removed by filtration, leaving behind a thick, dry substance. the remaining thick material was then dried in a laboratory oven for 48 hours at 45°c. once fully dried, the mar root was pulverized into fine powder using an industrial blender and sieved to achieve a consistent particle size. the powdered mar was stored in an airtight container to ensure its quality was preserved. these locally sourced biopolymers, along with conventional additives such as carboxymethyl cellulose (cmc) and silica oxide (sio2) nanoparticles, were used in this study to evaluate fluid loss control performance in water-based drilling fluids. figure 1 illustrates the powdered form of aa, mar, sio2, cmc, and cc, respectively. methods. ftir analysis. the ftir analysis was conducted using a buck 530 ir-spectrophotometer to examine the molecular structure and functional groups of selected materials: aa, mar, cc, sio2, and cmc. ftir produces an absorbance spectrum plot, which highlights the unique molecular arrangements and chemical bonds within these materials. the spectrum contains peaks that correspond to specific functional groups (e.g., alkanes, carboxylic acids, chlorides, and ketones) present in the material. each functional group absorbs infrared radiation at distinct wavelengths, allowing for their identification. these spectral data are then crossreferenced against a reference library to determine the precise range of values associated with the detected functional groups. improved oil and gas recovery 4 (a)aa (b)mar (c)sio2 (d)cmc (e)cc figure 1—additives powder. mud formulation. for the fluid loss experimental analysis, a total of seven mud samples were formulated. this included three independent mud samples: aa, cmc, and mar, as well as four hybrid samples: aa-cc, aa-sio2, mar-cc, and mar-sio2. the detailed composition of these formulations is presented in table 1. table 1—mud formulation utilized for the study. s/n mud type cmc aa mar cc sio2 1 cmc 1g nil nil nil nil 2 aa nil 1g nil nil nil 3 mar nil nil 1g nil nil 4 aa-cc nil 1g nil 0.2g, 0.4g, 0.6g, 0.8g and 1g nil 5 aa-sio2 nil 1g nil nil 0.2g, 0.4g, 0.6g,0.8g and 1g 6 mar-cc nil nil 1g 0.2g, 0.4g, 0.6g, 0.8g and 1g nil 7 mar-sio2 nil nil 1g nil 0.2g, 0.4g, 0.6g,0.8g and 1g improved oil and gas recovery 5 mixing procedure of mud sample formulation. the following procedure was followed for the preparation of the mud samples: 1. the required amount of each additive was precisely weighed using a standard weighing balance. 2. 350 ml of distilled water was measured using a scientific cylinder and added to the mud preparation process. 3. the water was then subjected to agitation using a hamilton beach mixer. 4. after initiating agitation, 15 g of bentonite was added to the water and mixed thoroughly for five minutes. 5. 0.5 g of sodium hydroxide (naoh) and 0.25 g of calcium carbonate (caco3) were subsequently introduced into the slurry and mixed for an additional two minutes. 6. 1 g of cmc was added to the solution and stirred for three minutes. 7. 10 g of barite was added to the solution and stirred for 15 minutes to achieve an even mixture. this procedure was repeated for the independent samples (aa, mar) as well as for the hybrid samples (aacc, aa-sio2, mar-cc, mar-sio2). the hamilton beach mixer was operated at medium speed, and the total mixing time required for each mud slurry was 30 minutes. table 2 provides the detailed composition of the water-based drilling fluid (wb-df) for both independent and hybrid samples, using 1 g of each respective additive. this process ensured a consistent and thorough mixing of the mud components to prepare the samples for subsequent fluid loss performance evaluations. table 2—composition of wb-df at 1g for both independent and hybrid sample. additives function cmcdf aa-df mardf aacc-df aasio2-df marccdf marsio2-df water (ml) base fluid 350 350 350 350 350 350 350 barite (g) weighting 10 10 10 10 10 10 10 bentonite (g) viscosifier 15 15 15 15 15 15 15 calcium carbonate (g) bridging agent 0.25 0.25 0.25 0.25 0.25 0.25 0.25 sodium hydroxide (g) ph control 0.5 0.5 0.5 0.5 0.5 0.5 0.5 cmc (g) fluid loss control 1 nil nil nil nil nil nil aa (g) nil 1 nil 1 1 nil nil mar (g) nil nil 1 nil nil 1 1 cc nil nil nil 1 nil 1 nil sio2 nil nil nil nil 1 nil 1 mud rheology. the rheological properties of the formulated mud samples were evaluated using a rotary viscometer. the prepared mud was poured into the viscometer cup, filling it up to the designated graduation mark, and the cup was securely mounted on the viscometer stand. the stand was then raised vertically to ensure that the rotating sleeve made proper contact with the mud. measurements were taken at rotor speeds of 300 rpm and 600 rpm to obtain the dial readings for each mud sample. based on these readings, key rheological parameters such as plastic viscosity (pv), yield point (yp), and apparent viscosity (av) were calculated using the following empirical formulas: plastic viscosity �� = θ600 − θ300,..............................................................................................................(1) yield point lb/100ft2 = θ300 − pv,............................................................................................................(2) improved oil and gas recovery 6 apparent viscosmeter cp = θ600 2 ,..............................................................................................................(3) these calculations helped to assess the flow behavior and viscosity properties of the formulated muds, which are critical for effective drilling operations. mud fluid loss. the mud filtration study was conducted under low pressure-low temperature (lplt) conditions using a standard api filter press. the filter press setup included six independent filter cells, each mounted on the system. prior to testing, the cells were thoroughly cleaned and dried to eliminate any debris, and the rubber gaskets were inspected for proper sealing compliance. figure 2 shows the api filter press and the rotary viscometer. the assembly of the filter press cells was completed in the following sequence: the base cap, followed by a rubber gasket, a screen, filter paper, another rubber gasket, and finally the cell body. 130 ml of the formulated drilling mud (prepared as per the compositions in tables 1 and 2) was introduced into each cell. the cell assembly was then tightened securely to ensure a proper seal. a 50 ml measuring cylinder was placed beneath the cell to collect the filtrate. the cells were pressurized to 100 psi using inert gas to simulate typical reservoir conditions. after 30 minutes, the volume of filtrate was measured and recorded. additionally, the thickness of the filter cake formed on the filter paper was measured using a vernier caliper and documented in x/32-inches units. this procedure allowed for the evaluation of fluid loss characteristics and the effectiveness of the formulated muds in minimizing filtrate loss and creating a stable filter cake. (a) api filter press (b) ofite rotary viscometer figure 2—equipment used to measure mud filtration. result ftir characterization. figures 2 to 6 shows the ftir spectra of aa, mar, cmc, cc and sio2, respectively. aa showed the presence of functional group such as alkyl halides, aromatics, carboxylic, aliphatic amines, isothiocyanate, alkyne, alkane and alcohol (figure 2). mar showed the presence of functional group such as alkyl halides, aromatics, amine, isothiocyanate, alkyne, alkane, alkene and alcohol (figure 3). cmc showed the presence of functional group such as alkenes, aliphatic amines, alkyl halideds, phenol, aromatics, isothiocyanate, carbon dioxide, carboxylic acid, aldehydes, alkanes, alcohol (figure 4). cc showed the presence improved oil and gas recovery 7 of functional group such as alkyl halides, aromatic amine, amines, aromatic, isothiocyanate, carboxylic acid, aldehyde, amine salt and alcohol (figure 5). sio2 showed the presence of functional group such as alkynes, aromatics, alkenes, amines, isothiocyanate, carboxylic acid, alkanes and alcohol (figure 6). figure 2—ftir spectra of afzelia africana (aa). figure 3—ftir spectra of marantha arundinacea (mar). improved oil and gas recovery 8 figure 4—ftir spectra of carboxyl methyl cellulose (cmc). figure 5—ftir spectra of corn cubs (cc). figure 6—ftir spectra of sio2-nps. improved oil and gas recovery 9 a comparative analysis of the spectra (figures 2 to 6) reveals several common functional groups among the materials. alcohols, aromatics, carboxylic acids, and isothiocyanates detected in cmc were also present in the locally sourced materials aa, mar, cc, and sio2. however, phenol, which was found in cmc, was absent in the spectra of aa, mar, cc, and sio2. additionally, alkenes were present in cmc, sio2, and mar, but absent in aa and cc. overall, the ftir analysis indicates that the locally sourced materials share a number of similar functional groups with the conventional material (cmc), suggesting their potential as alternative fluid loss control additives. rheology. table 3 provides a detailed overview of the rheological properties of the formulated water-based drilling fluids (wbdfs). the analysis includes the assessment of plastic viscosity, yield point, apparent viscosity, and gel strength. plastic viscosity. the base pv values for cmc, afzelia africana (aa), and maranta arundinacea (mar) were 11 cp, 5 cp, and 4 cp, respectively. the introduction of corncobs (cc) into aa-wbdf led to a 20% increase in pv at 0.2 g concentration, with further increases in cc concentration resulting in an 80% rise in pv. similarly, adding sio2 to aa-wbdf caused a 20% increase in pv at 0.2 g concentration, with up to a 60% increase as concentration rose. for mar-wbdf, the introduction of cc initially did not increase pv at 0.2 g concentration but resulted in up to a 75% increase at higher concentrations. the addition of sio2 to marwbdf showed a 25% increase in pv at 0.2 g concentration, with further increases up to 50% at higher concentrations. yield point. the yp for cmc, aa, and mar was recorded at 10 lb/100ft², 4 lb/100ft², and 4 lb/100ft², respectively. introducing cc into aa-wbdf caused a 100% increase in yp at 0.2 g concentration, though yp values decreased as the concentration increased, eventually dropping by 25%. adding sio2 to aa-wbdf increased yp by 25% and 75% at 0.2 g and 0.4 g concentrations, respectively, but further increases in concentration resulted in yp drops of 25%, 50%, and finally 0%. for mar-wbdf, the introduction of cc caused a 50% yp increase at 0.2 g concentration, with a peak increase of 100% at 0.8 g before dropping back to 50% at 1 g concentration. the addition of sio2 to mar-wbdf resulted in 25% and 50% increases in yp at 0.2 g and 0.4 g concentrations, respectively, with further increases leading to up to 50% yp enhancement at 1 g concentration. apparent viscosity. the av values for cmc, aa, and mar were 16 cp, 7 cp, and 6 cp, respectively. the introduction of cc into aa-wbdf improved av by 42.9% at 0.2 g concentration and increased further to 64.3% at higher concentrations. similarly, adding sio2 to aa-wbdf resulted in av improvements of 42.9% to 64.3%, depending on the concentration. in mar-wbdf, cc enhanced av by 16.7% at 0.2 g concentration and up to 66.7% at 1 g concentration. sio2 also improved av in mar-wbdf by 25% at 0.2 g concentration and up to 50% at higher concentrations. gel strength. gel strength analysis showed that at 0.8 g concentration, cc enhanced the gel strength of aawbdf from an initial 10 and 15 lb/100 ft² to 22 and 24 lb/100 ft². sio2, at 1 g concentration, further increased gel strength to 24 and 26 lb/100 ft² for aa-wbdf. for mar-wbdf, cc at 1 g concentration improved gel strength from 8 and 11 lb/100 ft² to 20 and 21 lb/100 ft². sio2, at the same concentration, enhanced gel strength from 8 and 11 lb/100 ft² to 19 and 21 lb/100 ft². overall, the results show that the addition of cc and sio2 to both aa and mar-based wbdfs significantly improved their rheological properties. however, the aa blends exhibited rheological performance closer to that of the cmc-based wbdf, indicating its potential as an alternative to conventional fluid loss control additives. improved oil and gas recovery 10 table 3—rheological properties of the formulated water-based drilling fluids (wbdf). s/n materials formulation θ600 θ300 pv yp av 10 secs 10 mins 1 cmc 32 21 11 10 16 20 30 2 aa 14 9 5 4 7 10 15 3 mar 12 8 4 4 6 8 11 4 aa-cc 1g:0.2g 20 14 6 8 10 20 21 5 1g:0.4g 21 14 7 7 10.5 18 23 6 1g:0.6g 20 14 6 8 10 20 21 7 1g:0.8g 23 15 8 7 11.5 22 24 8 1g:1g 23 14 9 5 11.5 20 23 9 aa-sio2 1g:0.2g 20 14 6 8 10 21 23 10 1g:0.4g 20 14 6 8 10 21 25 11 1g:0.6g 21 14 7 7 10.5 21 23 12 1g:0.8g 20 13 7 6 10 22 24 13 1g:1g 23 15 8 7 11.5 24 26 14 mar-cc 1g:0.2g 14 10 4 6 7 11 14 15 1g:0.4g 15 11 4 7 7.5 13 17 16 1g:0.6g 17 12 5 7 8.5 18 18 17 1g:0.8g 18 13 5 8 9 19 20 18 1g:1g 20 13 7 6 10 20 21 19 mar-sio2 1g:0.2g 15 10 5 5 7.5 12 15 20 1g:0.4g 16 11 5 6 8 14 16 21 1g:0.6g 17 11 6 5 8.5 17 18 22 1g:0.8g 18 12 6 6 9 19 20 23 1g:1g 18 12 6 6 9 19 21 fluid loss. the fluid loss performance of the formulated water-based drilling fluids (wbdfs) was evaluated and is presented in figures 7 and 8. figure 7 shows the fluid loss volume for cmc-wbdf, aa-wbdf, and mar-wbdf after 30 minutes. the results indicate that cmc-wbdf recorded a fluid loss volume of 15 ml, demonstrating superior fluid loss control. in comparison, mar-wbdf and aa-wbdf exhibited higher fluid loss volumes of 24 ml and 35 ml, respectively. cmc-wbdf's better fluid loss performance is attributed to its high cellulose content, which improves its ability to form an effective filter cake (agwu et al. 2019). figure 8 compares the fluid loss performance of hybrid formulations, including mar-sio2, mar-cc, aasio2, and aa-cc blends. the introduction of sio2 to mar-wbdf resulted in incremental reductions in fluid loss by 4.17%, 12.5%, 16.67%, 25%, and 29.17% at 0.2 g, 0.4 g, 0.6 g, 0.8 g, and 1 g concentrations, respectively. similarly, the addition of cc to mar-wbdf decreased fluid loss by 4.17%, 12.5%, 16.67%, 29.17%, and 33.33% at the same concentrations. in contrast, the addition of sio2 to aa-wbdf caused an increase in fluid loss volume by 5.71%, 11.43%, 17.14%, 14.29%, and 14.29% at 0.2 g, 0.4 g, 0.6 g, 0.8 g, and 1 g concentrations, respectively. the addition of improved oil and gas recovery 11 cc to aa-wbdf similarly increased fluid loss, but to a lesser extent, with a consistent increase of 5.71% at concentrations up to 0.8 g, and 11.43% at 1 g concentration. it is clear that mar-wbdf blends (mar-sio2 and mar-cc) demonstrated superior fluid loss control compared to aa-wbdf blends (aa-sio2 and aa-cc) (figure 8). at a 1g:1g formulation, mar-cc achieved the best performance, recording the lowest fluid loss volume of 16 ml, followed by mar-sio2 at 17 ml, while aa-cc and aa-sio2 recorded significantly higher fluid loss volumes of 39 and 40 ml, respectively. the exceptional performance of mar-cc is attributed to its increased cellulose content, which aids in effectively plugging pore spaces within the rock, reducing fluid loss. comparing figures 7 and 8, the introduction of cc and sio2 into mar-wbdf significantly enhanced fluid loss control, making it comparable to cmc-wbdf. figure 7—fluid loss of aa-wbdf, mar-wbdf and cmc-wbdf. figure 8—fluid loss volume of mar-sio2, mar-cc, aa-sio2 and aa-cc wbdfs. improved oil and gas recovery 12 table 4—mud filter cake. s/n materials formulation mud cake 1 cmc 1g 2 2 mar 1g 2.5 3 aa 1g 3 4 aa-cc 1g:0.2g 4 1g:0.4g 3.5 1g:0.6g 3 1g:0.8g 3 1g:1g 3 5 aa-sio2 1g:0.2g 4 1g:0.4g 4 1g:0.6g 3.5 1g:0.8g 3.5 1g:1g 3.5 6 mar-cc 1g:0.2g 2.5 1g:0.4g 2.5 1g:0.6g 2.5 1g:0.8g 2 1g:1g 2 7 mar-sio2 1g:0.2g 2.5 1g:0.4g 2.5 1g:0.6g 2.5 1g:0.8g 2 1g:1g 2 mud cake thickness. table 4 provides the mud cake thickness for the various wbdf formulations. cmc recorded a mud thickness of 2/32 inches, mar recorded 2.5/32 inches, and aa recorded 3/32 inches. the introduction of cc into aa-wbdf resulted in varying thicknesses, ranging from 4/32 inches at 0.2 g to 3/32 inches at higher concentrations. adding sio2 to aa-wbdf similarly produced mud thicknesses between 4/32 inches and 3.5/32 inches. for mar-wbdf, the introduction of cc resulted in a consistent mud thickness of 2.5/32 inches at lower concentrations, which reduced to 2/32 inches at higher concentrations. similarly, the addition of sio2 to marwbdf maintained a mud thickness of 2.5/32 inches, which decreased to 2/32 inches at higher concentrations. overall, as shown in table 4, the mud cake thickness of the aa and mar formulations decreased with the introduction of cc and sio2. when compared with cmc-wbdf, the mar blends demonstrated comparable mud thickness values. the reduction in mud cake thickness observed in these formulations can be attributed to their ability to form effective filter cakes, which help reduce the volume of fluid lost to the reservoir rock. the standard api fluid loss value for wbdf is typically around 15 ml (dankwa et al. 2018). the results indicate that the mar-cc formulation meets this standard, making it a viable alternative for fluid loss control in drilling fluids. improved oil and gas recovery 13 conclusions from the experimental study conducted, the following conclusion can be drawn: 1. afzelia africana (aa), maranta arundinacea root (mar), and corncobs (cc) exhibited similar functional groups, including alcohols, aromatics, carboxylic acids, and isothiocyanates, as those present in silica oxide (sio2) and carboxymethyl cellulose (cmc). 2. the addition of sio2 and cc to both aa-wbdf and mar-wbdf resulted in notable improvements in their rheological properties. 3. based on the rheological analysis, cc-aa wbdf and sio2-aa wbdf displayed rheological characteristics that were comparable to those of cmc-based wbdf. however, cc-aa wbdf demonstrated superior rheological performance. 4. the incorporation of sio2 and cc into aa-wbdf and mar-wbdf significantly enhanced their fluid loss control capabilities. 5. from the fluid loss control study, cc-mar wbdf and sio2-mar wbdf exhibited fluid loss control properties similar to cmc-based wbdf, with cc-mar wbdf displaying superior overall performance. 6. at a 1g:1g formulation, cc-mar and sio2-mar recorded fluid loss volumes of 16 and 17 ml, respectively. 7. cc had the most pronounced impact on both rheology and fluid loss control performance in wbdf formulations. overall, these findings suggest that cc and sio2 are promising additives for improving the performance of water-based drilling fluids, with cc showing particularly strong potential as a fluid loss control agent and rheology enhancer. conflicting interests the author(s) declare that they have no conflicting interests. references agwu, o.e. and akpabio, j.u. 2018. using agro-waste materials as possible filter loss control agents 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technology-recent advances, new perspectives and applications, ed. m. zoveidavianpoo, chap. 1, 1-15. london: intechopen. anthony kerunwa is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum economics. kerunwa holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri, owerri, nigeria, and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. lilian ndoma-egba is a master’s candidate at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids. ndoma-egba holds a bachelor’s degree in oil and gas engineering from all nations university, ghana. angela nwachukwu is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in reservoir, production, drilling engineering and flow assurance. nwachukwu holds a bachelor’s, master’s and phd degree in petroleum engineering from federal university of technology owerri, nigeria. nnaemeka uwaezuoke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling and well engineering. uwaezuoke holds a bachelor’s improved oil and gas recovery 15 degree in petroleum engineering from federal university of technology owerri, nigeria, master’s degree in petroleum engineering from university of stavanger, norway, and a phd degree in petroleum engineering from federal university of technology owerri, nigeria. nzenwa dan enyioko is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids and enhanced oil recovery. enyioko holds a bachelor’s degree and master’s in geology from federal university of technology owerri, nigeria. ugochukwu ilozurike duru is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in multiphase flow in pipe, flow assurance, well engineering, fluid hydraulics, petroleum economics, and production enhancement. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids, enhanced oil recovery, reservoir engineering and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri, nigeria. abstract introduction materials and methods result conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1288 received june 24, 2024; revised august 7, 2024; accepted september 25, 2024. *corresponding author: deryaevannaguly@gmail.com 1 analysis of the commercial evaluation of oil deposits using the material balance method annaguly deryaev*, scientific research institute of natural gas of the state concern “turkmengas”, ashgabat, turkmenistan abstract the study of the commercial evaluation of oil deposits using the material balance method is currently extremely important for the energy industry, as it helps to optimize oil production processes, increase resource efficiency, and make informed decisions on field development in the context of a changing energy paradigm and aspirations for sustainable development. the purpose of this study is to investigate the method of commercial evaluation of oil deposits using the material balance. in this study, methods of analyzing geological data, mathematical modelling of deposits, calculating the material balance, and forecasting of oil production were used. as a result of the study of the commercial evaluation of oil deposits by the material balance method, it was found that this method helps to more accurately assess the initial oil reserves in the fields and effectively optimize their production processes, which is key to effective management of oil resources and ensuring the sustainable development of the oil industry. the results of the study showed that the method of commercial evaluation of oil deposits using the material balance provides an accurate assessment of the initial oil reserves in the fields and effectively considers changes in the volumes and properties of oil fluids during production, which is key to optimizing the processes of oil production and management of oil resources. the results of the analysis of changes in the field helped to determine the efficiency of oil production, identify the dynamics of changes in reserves, and forecast further production, which significantly affects management decision-making and planning for the development of oil projects, emphasizing the importance of the material balance method for the sustainable use of oil resources and efficient operation of fields. introduction oil continues to be one of the most important energy resources in the world, as it provides vital economic sectors such as energy production, transportation, and industry. in this regard, the importance of issues related to the evaluation of oil reserves, its efficient production, and sustainable use is growing. one of the most important methods of analyzing and measuring oil reserves in the fields is the commercial evaluation of oil deposits using the material balance method. the use of this method not only helps to accurately determine the initial oil reserves in the fields, but also to assess the effectiveness of its production processes, analyse the dynamics of changes in the field, and predict the volume of further production. these aspects play a key role in the management of oil resources and planning the development of the oil industry in the face of constant changes and challenges facing the energy industry. the study of the commercial evaluation of oil deposits using the material balance method is important in the context of energy strategy and sustainable development. the need for such a study is conditioned by a number of mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 factors. oil is the main source of energy for many industries, transport, and household use, therefore, effective management of oil resources and optimization of their production are critically important for ensuring energy security and economic development. given the changing climatic conditions and the desire to reduce the carbon footprint, efficient oil production and use require modern methods and technologies to minimise the negative impact on the environment. thus, conducting a commercial evaluation of oil deposits using the material balance method is of strategic importance for the energy industry, the economy, and the environment, aimed at optimizing production processes, improving resource efficiency, and reducing negative environmental impacts. the study of the commercial evaluation of oil deposits using the material balance method is an urgent topic reflected in the works of various researchers. tlepov and churikova (2023) focused on the evaluation of the effectiveness of methods for analyzing oil production in the fields. issenov (2021) explored the impact of modern technologies on improving the accuracy of estimating oil reserves in fields. lopes et al. (2021) aimed at forecasting the dynamics of changes in oil reserves. imanbayev et al. (2022) analysed the efficiency and stability of the fields in the conditions of variable factors. laherrère et al. (2022) conducted a comparative analysis of various methods of evaluating oil reserves. cheng et al. (2022) investigated the issues of resource management in oil production. tariq et al.(2021) analyzed the application for optimizing the processes of oil and gas production in various fields. pang et al. (2021) investigated the influence of environmental factors on the assessment of oil reserves and developed methods for accounting for these factors. askari et al. (2021) conducted an analysis of the efficiency of using various types of wells. guo et al. (2022) explored the possibilities of application for optimizing oil production under various climatic and geological conditions. these papers generally show a wide range of interests and the relevance of the topic of commercial evaluation of oil deposits using the material balance method in the modern scientific environment. however, the problem requiring additional study is the gaps in understanding the influence of various factors, such as geological features of deposits and changes in the physicochemical properties of oil on the results of the evaluation using the material balance method. further research in this area should be aimed at a deeper analysis of the relationships between various parameters and the development of improved methods for estimating oil reserves using the material balance. the purpose of this study is to analyse the method of commercial evaluation of oil deposits using a material balance to improve the processes of extraction of oil resources and increase their efficiency in use. materials and methods various methods were used to analyse the geological data, including geophysical and geochemical methods to investigate geological structures and field characteristics. these methods included collecting information on the distribution and properties of rocks, analyzing gravitational and magnetic fields, studying the composition of fluids and other techniques, which helped to more fully and accurately assess the geological situation and potential of the deposit. the application of such methods has made it possible to determine more precisely the geological features of the fields and their potential for oil production. a comprehensive evaluation of the efficiency of the use of oil resources was carried out, which included an analysis of the results of calculations, modelling, and forecasting. this evaluation was aimed at determining the technical and economic efficiency of field development and the use of oil resources in the oil and gas industry. the analysis considered various aspects, including production volumes, development costs, technical capabilities, and economic indicators of projects. this provided informed decisions and helped to optimize the processes of extraction and use of oil resources to increase their efficiency and sustainability in the long term. to carry out mathematical modelling of deposits, special models were created that reflected the geological structure and the main processes of oil production. these mathematical models allow analyzing various aspects of the behaviour of deposits in different time periods and predicting their dynamics in the future. the main purpose of using such models was to optimize development strategies based on the predicted characteristics and properties of deposits, which contributed to more efficient management of oil and gas production processes. improved oil and gas recovery 3 forecasting of oil production on an industrial scale was carried out using the obtained data, models, and calculations. this included an assessment of future production considering various parameters such as reserves, technological capabilities, and economic factors. this approach helped to determine the technological and economic parameters of the projects, and to plan long-term strategies for field development. the forecasting results were used to make informed decisions on optimizing oil production and developing effective project management strategies in the oil industry. to determine the volume and composition of oil reserves and production processes, calculations of the material balance were carried out. this process included an analysis of the initial hydrocarbon reserves in the reservoir, production volumes over time, and engineering parameters necessary to optimize production processes. calculations of the material balance helped to more accurately evaluate the available oil and gas reserves, and predict and optimize the processes of their extraction from deposits. this is an important component of the planning and management of production operations in the oil industry. an example of the successful application of the material balance method is illustrated by the evaluation of oil and gas reserves at four fields: kumertau, dolinsk, cheleken, and goturdepe. this evaluation was carried out by the state commission on mineral reserves under the cabinet of ministers of turkmenistan. using the material balance method, it was possible to analyse and consider the entire life cycle of these deposits, starting from initial reserves to production and operation processes. this approach facilitated a more accurate evaluation of the resource potential of each deposit and helped to make informed decisions on their development and management. results an example of a successful application of the material balance method is the evaluation of oil and gas reserves at four fields (kumertau, dolinsk, cheleken, and goturdepe) by the state commission on mineral reserves under the cabinet of ministers of turkmenistan (scr). however, it should not be assumed that the material balance method will always be applied successfully [11]. currently, the volumetric method of calculating oil and gas reserves is the most universal and should not be replaced by the material balance method. nevertheless, given the expansion of pilot production and the increased possibilities of hydrodynamic and physicochemical studies of oil and gas deposits, the material balance method should be given more attention at the current stage of its development. in the course of prospecting and exploration, it is necessary to collect and evaluate a number of key parameters for the successful assessment and further development of oil and gas deposits. it is important to determine the average initial reservoir pressure, which is achieved through measurements at several initial wells located at different elevations. it is also necessary to measure the average current reservoir pressure on deposits, regularly measuring the current pressures in technically sound wells during the operation of the field. to fully understand the characteristics of the deposit, it is also important to determine the saturation pressure of oil and gas at several points of the deposit, considering its hypsometric diversity (al-rubaye et al. 2021). the physicochemical properties of reservoir oils and gases also require special attention, including component composition, density, compressibility coefficients, gas solubility, and other parameters. this requires conducting research on deep samples of oil and gas from several wells, which will cover the entire thickness of the deposit. it is necessary to consider the production of oil, gas, and water from all wells within the reservoir, and to analyse the average initial and operational gas factors (roozshenas et al. 2021). the analysis of the physicochemical properties of reservoir oil, including salts, gases, density and compressibility coefficients, requires a careful approach, and it is recommended to study deep samples of reservoir water. it is also necessary to investigate the compressibility of various lithological reservoir rocks, which is important for determining the effective volume of the deposit. considering that most of these parameters are related to the volumetric method and are important for the development of oil and gas deposits, a more thorough approach to their research is required, which meets the basic requirements of the instructions on mineral reserves. improved oil and gas recovery 4 the definition of the material balance equation is based on one of the following two principles: preserving the mass and preserving the volume of pores that originally contained oil and gas. the first principle assumes that the amount of hydrocarbons or their weight remains unchanged in volume units during the extraction and production processes. the second principle indicates the preservation of the volume of pores that were originally filled with oil and gas in the deposits. both of these principles serve as the basis for the development of material balance equations, which are used to analyse and predict the processes of production and operation of oil and gas fields. in a reservoir with the initial presence of oil and gas, their amount, together with the extracted ones, should remain unchanged, which reflects the principle of conservation of mass (xue et al. 2021). the preservation of the volume of pores initially filled with hydrocarbons is also always considered in the development of the reservoir, even with the possible occupation of part of the pore space with water. this method does not consider the influence of pore water, since it is assumed to be closely related to the rock, which does not affect the movement of oil, gas, and water. thus, the material balance method is dynamic, reflecting the state of the reservoir depending on the dynamics of production and pressure changes. the equation of material balance can have different forms depending on the goals and conditions set by the authors at different times. basically, the oil deposits of southwest turkmenistan are developed under a mixed displacement regime (dissolved gas and high-pressure modes). for such deposits, the initial balance reserves of oil are calculated using the material balance method using the equation, 𝑄𝑜 = 𝑄𝑜.𝑝.[𝑏1+(𝑟𝑝−𝑟𝑜)]𝑣−(𝑊−𝑤) 𝑏1−𝑏0 ,.............................................................................................................................(1) when conducting appropriate laboratory and field studies, the parameters included in this equation can be relatively easily obtained as of any date of deposit development. the only exception is the volume of water embedded in the deposit, which is practically impossible to determine directly. there are many methods for determining the volume of water embedded in the reservoir (al-shargabi et al. 2022). the volume of water embedded in the reservoir is most accurately and simply obtained based on the watered volume from the beginning of development to the calculation date; considering the initial and current oil content contours. for numerous reasons (multi-time flooding of reservoirs in facilities, lack of sufficient geophysical measurements in flooded areas), it is often not possible to determine the current contours of oil content. when determining the oil reserves of the deposits of south-west turkmenistan (cheleken, goturdepe), a method obtained using mathematical statistics from the material balance equation and the equation for determining the volume of water embedded in the deposit is used. the volume of water embedded in the deposit is determined from the eq. 2, 𝑊 = 𝑄𝑜.𝑝.𝑏0 + 𝑊 − 𝑋(𝑃0 − 𝑃),.......................................................................................................................(2) where x is determined based on the analysis of the development of productive formations in the initial stage of operation, by distinguishing the moment of drainage of deposits only in elastic and dissolved gas modes, when it can be assumed that the volume of water introduced is zero. a number of geological and energy features and conditions for entering deposits into development (insignificant oil-saturated volumes, the presence of bottom and intermediate waters, large fragmentation, unequal degree of activity of contouring waters, simultaneous commissioning of most wells within a short time) do not allow confidently distinguishing the time of manifestation of drainage regimes throughout the entire volume of operational facilities. in this regard, eq. 2 can be used in a different way. substituting eq. 3 into eq. 1, 𝑄𝑜 = 𝑄𝑜.𝑝.[(𝑏1−𝑏0)+(𝑟𝑝−𝑟𝑜)𝑣] 𝑏1−𝑏0 + 𝑋 𝑃0−𝑃 𝑏1−𝑏0 ,................................................................................................................(3) or 𝑄𝑜 = 𝑄𝑜.𝑝. [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ] + 𝑋 𝑃𝑜−𝑃 𝑏1−𝑏0 ....................................................................................................................(4) improved oil and gas recovery 5 in eq. 4, the values of the initial balance reserves of oil (qo) and the specific elastic capacity are constant, and the variables are – 𝑄𝑜.𝑝. [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ] and 𝑃𝑜−𝑃 𝑏1−𝑏0 . then, separating the variables, 𝑄𝑜.𝑝. [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ] = 𝑄𝑜 − 𝑋 𝑃𝑜−𝑃 𝑏1−𝑏0 ,...................................................................................................................(5) or denoting, 𝑦 = 𝑄𝑜.𝑝. [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ],....................................................................................................................................(6) 𝑍 = 𝑃𝑜−𝑃 𝑏1−𝑏0 ,..........................................................................................................................................................(7) obtain, 𝑦 = 𝑄0 − 𝑋𝑍 ....................................................................................................................................................(8) since the field data and the data of deep samples carry certain errors, when determining the value of balance reserves, it is most rational to use the methods of mathematical statistics, making calculations for several dates. in this case, using the least squares method, x is defined from the expression, 𝑋 = − 𝑛 ∑ 𝑌𝑍−∑ 𝑌 ∑ 𝑍 𝑛 ∑ 𝑍2−(∑ 𝑍)2 ,.............................................................................................................................................(9) where n represents the sample size (the number of dates for which calculations are performed to determine reserves). substituting the values of y and z in eq. 9, 𝑋 = −𝑛 ∑ 𝑄𝑜.𝑝.[1+ (𝑟𝑝−𝑟0)𝑣 𝑏1−𝑏0 ] 𝑃0−𝑃 𝑏1−𝑏0 +∑ 𝑄𝑜.𝑝.[1+ (𝑟𝑝−𝑟0)𝑣 𝑏1−𝑏0 ] ∑ 𝑃0−𝑃 𝑏1−𝑏0 𝑛 ∑( 𝑃0−𝑃 𝑏1−𝑏0 ) 2 −(∑ 𝑃0−𝑃 𝑏1−𝑏0 ) 2 ......................................................................................(10) substituting the value of x found in this way into eq. 8, we obtain qo, 𝑄0 = ∑ 𝑌 𝑛 + 𝑋 ∑ 𝑍 𝑛 ,.............................................................................................................................................(11) or 𝑄0 = ∑ 𝑄𝑜.𝑝.[1+ (𝑟𝑝−𝑟0)𝑣 𝑏1−𝑏0 ] 𝑛 + 𝑋 ∑ 𝑃0−𝑃 𝑏1−𝑏0 𝑛 ....................................................................................................................(12) substituting formula 5 into formula 9, an equation is derived that determines the initial balance reserves of oil without determining the specific elastic capacity, 𝑄0 = ∑ 𝑄𝑜.𝑝.[1+ (𝑟𝑝−𝑟0)𝑣 𝑏1−𝑏0 ] ∑( 𝑃0−𝑃 𝑏1−𝑏0 ) 2 ∑ 𝑄𝑜.𝑝.[1+ (𝑟𝑝−𝑟0)𝑣 𝑏1−𝑏0 ]( 𝑃0−𝑃 𝑏1−𝑏0 ) ∑ 𝑃0−𝑃 𝑏1−𝑏0 𝑛 ∑( 𝑃0−𝑃 𝑏1−𝑏0 ) 2 −(∑ 𝑃0−𝑃 𝑏1−𝑏0 ) 2 ..........................................................................(13) in the presence of a gas cap, eqs. 1 and 2 will take the following form, 𝑄𝑜 = 𝑄𝑜.𝑝.[𝑏+(𝑟𝑝−𝑟𝑜)]𝑣−(𝑊−𝑤)𝑄𝑔.(𝑣−𝑣𝑜) 𝑏1−𝑏0 ,..............................................................................................................(14) 𝑊 = 𝑄𝑜.𝑝.𝑏0 + 𝑤 − 𝑄г(𝑣 − 𝑣0) − 𝑋(𝑃0 − 𝑃),..............................................................................................(15) where, qg. is gas reserves of the gas cap; υ0 is volume coefficient of the gas at the initial reservoir pressure. therefore, the proposed method for determining the initial balance reserves of oil can be applied to a complex reservoir with free gas. the undeniable advantage of this technique is that the extracted water, which in many improved oil and gas recovery 6 cases includes hydrodynamically “foreign” water, does not affect the amount of balance reserves. table 1 provides an example of calculating the initial balance reserves of oil using this method. the inventory is calculated for 5 dates. when choosing dates, it is necessary to consider the specifics of the development of deposits; the proposed technique gives the most correct results during the development of the object with the predominant development of the dissolved gas regime. thus, this technique helps to determine the initial balance reserves of oil without first determining the volume of water embedded in the deposit and the specific elastic capacity of the deposit (formation and reservoir fluid). it boils down to establishing a pattern between two complex variables: 𝑄𝑜.𝑝. = [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ], characterising the released volume in the process of oil production; 𝑃0−𝑃 𝑏1−𝑏0 , characterising the degree of drop in reservoir pressure due to oil extraction and degassing. the main task in calculating stocks using this method is to select the dates for which calculations are made. to do this, it is necessary to analyse the drainage regime based on the data from the exploitation of oil deposits and field studies. the analysis showed that the nature of the drainage regime transition is mainly preserved (table 1). in the initial stage, a predominantly elastic drainage regime develops. during this period, the reservoir pressure is higher than the saturation pressure. due to the fact that in some wells or zones the reservoir pressure falls below the saturation pressure, although the weighted average reservoir pressure is higher than the saturation pressure, the gas factor increases, and the dissolved gas regime participates in oil recovery. during this period, the deposit is usually not fully drilled, the calculation of reserves for this period leads to underestimated results, since instead of the initial balance reserves of oil, the drained part is determined. the beginning of the second period is the moment when the reservoir pressure drops to saturation pressure. this period is characterised by an increase in the magnitude of the gas factor. after a certain time has elapsed, depending on the reservoir filtration properties, the rate of drilling and development of the deposit, the value of the gas factor stabilises, and then begins to fall. usually during this period, the facility is fully drilled, and all balance reserves are under development. the end of this period is the beginning of the intensive introduction of water, characterised by an increase in the water content in the production of wells. this is the beginning of the third period – the period of displacement of carbonated oil by water. the second period meets all the requirements of the proposed methodology, therefore, reserves are calculated according to the development data of this period. thus, the dates for calculating reserves should cover the period of deposit development from the moment of comparing the current reservoir pressure with the critical saturation pressure to the moment when the share of the dissolved gas regime in oil displacement decreases. in this case, the interval between the counting dates is taken, based on the duration of the period under consideration, from 0.5 to 1 year. as already noted, the proposed method represents the equation of material balance in the form of a straight line and is based on finding the unknown (qo) of this equation. in this case, the variables are the indicators 𝑄𝑜.𝑝. = [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ] (conventionally denoted as indicator a), and 𝑃0−𝑃 𝑏1−𝑏0 (conditionally–indicator b). the graph of the relationship between these indicators has a broken character, moreover, with a decrease in indicator b, indicator a grows (figure 1). improved oil and gas recovery 7 table 1—example of calculating the initial balance reserves of oil. date accumulated oil production qa.p., thousand tonnes oil production due to elastic mode qo.e., thousand tonnes qo.p.=q a.p.qo.e., thousand tonnes accumulated gas production qa.g., thousand m3 oil production due to the elastic mode qg.e., thousand m3 1 124.3 108.8 15.5 104,877 85,324 2 150.9 42.1 136,325 3 181.9 73.1 173,261 4 210.5 101.7 197,803 5 233 124.2 214,655 the volume coefficient of the gas υ gas content in reservoir oil, m3/m3 b1=b+(r0-r) υ b1-b0 𝑄𝑜.𝑝. = [1 + (𝑟𝑝 − 𝑟𝑜)𝑣 𝑏1 − 𝑏0 ] 𝑃0 − 𝑃 𝑏1 − 𝑏0 1.4927 172.9 1.6412 0.0592 1,070.4 1,081 1.4007 134.6 1.7626 0.1806 1,122.3 719.8 1.3589 117.2 1.8693 0.2873 1,415.8 556.9 1.3338 106.8 1.953 0.371 1,522.6 479.8 1.317 99.8 2.0333 0.4513 1,557.6 421 date qo.p.=qa.p.-qo.e., thousand m3 qo.p., thousand m3 average gas factor, g p, m3/m3 current reservoir pressure p, atm volume coefficient of gas, υ 1 19,553 18.8 1,037.8 286 0.004 2 51,001 51.2 996.6 220 0.0048 3 87,937 88.9 989.7 190 0.0055 4 112,479 133.6 909.7 172 0.006 5 129,331 151 856.7 160 0.0065 date volume coefficient of the gas, υ balance oil reserves according to the calculation of q ó.p., thousand m3/thousand tonnes initial balance reserves of oil 𝑄0 = 𝑄0 + 𝑄𝑜.𝑒., thousand tonnes 1 1.4927 1,878.2 1,654 2 1.4007 1,545.2 3 1.3589 4 1.3338 5 1.317 improved oil and gas recovery 8 figure 1—diagram of changes 𝑄𝑜.𝑝. = [1 + (𝑟𝑝−𝑟𝑜)𝑣 𝑏1−𝑏0 ] = 𝑓 ( 𝑃0−𝑃 𝑏1−𝑏0 ). in the initial period of deposit development, the growth rate of indicator a is the lowest. the calculation of reserves for this period gives drained oil reserves, not true balance reserves. during the transition to the second period – the period of operation of the deposit under the dissolved gas regime – the growth rate of indicator a increases. this indicates the drainage of all balance oil reserves. in the third period, the indicator under study grows much steeper, due to the intensive introduction of marginal or underlying water into the oil part. thus, the correctness of the choice of dates for which reserves are calculated and which are substantiated by the analysis of the development of the deposit can be verified by building a relationship between indicators a and b. figure 2—dynamics of reservoir pressure. improved oil and gas recovery 9 figure 3—dynamics of reservoir pressure. an equally important role in calculating oil reserves by the material balance method is played by the correct determination of the average reservoir pressure of the counting object and saturation pressure (fuentes-cruz and vásquez-cruz 2022). the traditional way to determine the average reservoir pressures is to build isobar maps. in cases where there is no possibility (insufficient number of measurements on one date) or there is no need (does not lead to clarification of the average reservoir pressure), a correlation dependence of its drop in the process of oil recovery is found to predict reservoir pressure. it has been revealed that the drop in reservoir pressure is described by the parabola equation, power or exponential equations, and rarely by the equation of a straight line (figures 2 and 3). usually, the correlation dependence of the reservoir pressure drop is found over time (sami and ibrahim 2021). such dependencies do not consider the “peaks” and drops in oil production, but smooth them out and, therefore, when calculating for these dates, especially when calculating reserves using the material balance method, they can lead to significant errors. therefore, at present, the correlation dependence of the drop in reservoir pressure of deposits in south-west turkmenistan is determined not by time, but depending on the accumulated production of oil (qa.p.). to do this, a graph of the reservoir pressure drop over time is plotted (figures 2 and 3), and the accumulated production of oil is considered in the calculations. then, based on the characteristics of the dependence, the regression equation is selected. as a rule, this is a second-order equation, 𝑃 = 𝑎 + 𝑎1 𝑄𝑎.𝑝. + 𝑎2𝑄2 𝑎.𝑝. ...........................................................................................................................(16) in cases where the dependence obeys the equation of a straight line, the coefficient a2=0. the unknowns a, a1, and a2 are determined from expressions derived using the least squares method, 𝑎2 = [∑ 𝑄𝑎.𝑝. 2 (𝑄𝑎.𝑝. 2 ) 2 𝑛 ][∑ 𝑄𝑎.𝑝. 2 𝑃− 𝑄𝑎.𝑝. 2 ∑ 𝑃 𝑛 ]−[∑ 𝑄𝑎.𝑝.𝑃− ∑ 𝑄𝑎.𝑝. ∑ 𝑃 𝑛 ][∑ 𝑄𝑎.𝑝. 3 𝑃− ∑ 𝑄𝑎.𝑝. 9 ∑ 𝑄𝑎.𝑝. 𝑛 ] [∑ 𝑄𝑎.𝑝. 2 − (𝑄𝑎.𝑝. 2 ) 2 𝑛 ][∑ 𝑄𝑎.𝑝. 4 − (𝑄𝑎.𝑝. 2 ) 2 𝑛 ]−[∑ 𝑄𝑎.𝑝. 3 − 𝑄𝑎.𝑝. 2 ∑ 𝑄𝑎.𝑝. 𝑛 ] 2 ,....................................................(17) 𝑎1 = [∑ 𝑄𝑎.𝑝. 4 (𝑄𝑎.𝑝. 2 ) 2 𝑛 ][∑ 𝑄𝑎.𝑝. 2 𝑃− ∑ 𝑄𝑎.𝑝. ∑ 𝑃 𝑛 ]−[∑ 𝑄𝑎.𝑝. 2 𝑃− 𝑄𝑎.𝑝. 2 ∑ 𝑃 𝑛 ][∑ 𝑄𝑎.𝑝. 3 𝑃− ∑ 𝑄𝑎.𝑝. 2 ∑ 𝑄𝑎.𝑝. 𝑛 ] [∑ 𝑄𝑎.𝑝. 2 − (𝑄𝑎.𝑝.) 2 𝑛 ][∑ 𝑄𝑎.𝑝. 4 − (𝑄𝑎.𝑝. 2 ) 2 𝑛 ]−[∑ 𝑄𝑎.𝑝. 3 − 𝑄𝑎.𝑝. 2 ∑ 𝑄𝑎.𝑝. 𝑛 ] 2 ,....................................................(18) improved oil and gas recovery 10 𝑎 = ∑ 𝑃 𝑛 − 𝑎1 ∑ 𝑄𝑎.𝑝. 𝑛 − 𝑎2 ∑ 𝑄𝑎.𝑝. 2 𝑛 ,........................................................................................................................(19) where, n indicates the number of reservoir pressure measurements for wells. the drop in reservoir pressure also obeys the equations, 𝑃 = 𝑎 𝑄𝑎.𝑝. −𝑎 ,....................................................................................................................................................(20) 𝑃 = 𝑎𝑙−𝑎1𝑄𝑎.𝑝...................................................................................................................................................(21) logarithmising these equations, respectively, obtain 𝑙𝑔 𝑃 = 𝑙𝑔 𝑎 − 𝑎1 𝑙𝑔 𝑄𝑎.𝑝.,..............................................................................................................................(22) substituting 𝑙𝑔 𝑃 = 𝑃′, and 𝑙𝑔 𝑎 = 𝑎′,.............................................................................................................................(23) into: 𝑙𝑔 𝑄𝑎.𝑝. = 𝑄𝑎.𝑝. ′ ,and 𝑎1𝑙𝑔𝑙 = 𝑎1....................................................................................................................(24) 𝑝′ = 𝑎′ − 𝑎1𝑄𝑎.𝑝. ′ ...........................................................................................................................................(25) 𝑝′ = 𝑎′ − 𝑎1𝑄𝑎.𝑝............................................................................................................................................(26) calculations by determining the unknowns a1, a1 and а1 1 of these equations can be performed using dependencies eqs. 18 and 19, setting 𝑄𝑎.𝑝. 2 = 0 (he condition for obtaining а2=0) и а2=0. when describing the drop in reservoir pressure by the parabola equation, at different signs between a1 and a2, it is necessary to determine the limits of its applicability. to do this, eq. 16 is differentiated and equated to zero as 𝑃′ = 𝑎1 + 𝑎2𝑄𝑎.𝑝. = 0...................................................................................................................................(27) hence, the cumulative oil production up to which the found correlation equation is valid will be 𝑄𝑎.𝑝. = − 𝑎1 2𝑎2 ..................................................................................................................................................(28) processing data from reservoir pressure measurements to establish one or another dependence and comparing these dependencies is a time-consuming calculation work. processing of this data on modern computing tools significantly speeds up this process and further increases the reliability of choosing one or another dependence. the saturation pressure is usually determined by averaging data from deep field sampling studies. this method does not consider the nature of the change in saturation pressure, both in area and in power. as is known, for an oil and gas deposit, the maximum saturation pressure equal to the initial reservoir pressure of the gas cap is observed on the surface of the gas-oil contact. moving away from the gas-oil contact, both in area and in power (in depth), the saturation pressure decreases (wang et al. 2023). the results of actual measurements are taken as initial data, as well as data determined according to the methodology. according to this method, the dependence of saturation pressure on: 1. distance (vertically) between the goc plane and the average level of the oil saturated layer (o). 2. distance (horizontally) between the initial position of the goc and the well (ℓ). the equation of this dependence is found in the form, 𝑃𝑠𝑎𝑡. = 𝑃𝑠𝑎𝑡.𝑚𝑎𝑥 + 𝐶1𝐻 + 𝐶2ℓ,....................................................................................................................(29) where, рsat.max is the maximum saturation pressure; c1, c2 are coefficients. therefore, the equation determined the value of saturation pressures for wells in which there are no actual measurements. as practice has shown, the difference between saturation pressures, defined as arithmetic mean and weighted average values, for highly productive facilities reaches 10 atm. (mpa), which significantly affects improved oil and gas recovery 11 the determination of accumulated oil and gas recovery, initial values of the volume coefficient, and the gas content of oil. there is another way to determine the saturation pressure, which is based on the results of laboratory studies to determine the dependence of the volume coefficient (b) and the gas content (r) of oil on the pressure drop of oil taken from the first wells of each horizon. based on the results of these studies, a graph is constructed (figure 4). it can be seen from these graphs that there is an area where b and r are practically constant, despite the drop in reservoir pressure. after reaching the critical pressure, the values of the gas content and the volume coefficient begin to fall, obeying the equation of the straight line. as the practice of studying deep samples has shown, this equation is valid up to 50 atm (5 mpa), sometimes up to 30 atm (3 mpa). figure 4—change in the volume coefficient and gas content of oil from pressure. this critical pressure is the saturation pressure. not all operational facilities can identify the transition zone and determine psat, which is due to many geological reasons, as a result of which the selected deep sample does not characterise the initial equilibrium state of the gas and oil system. but despite this, these graphs reflect the dependence of b and r on pressure and are used to determine them at various stages of development. when calculating oil reserves using the material balance method, correlation equations of these dependencies are usually used, 𝑏 = 𝑎 + 𝑎1𝑃,...................................................................................................................................................(30) 𝑟 = 𝑎1 + 𝑎1𝑃...................................................................................................................................................(31) substituting reservoir pressure values in eqs. 30 and 31, it is easy to determine b and r for this period at various stages. the determination of the initial volume coefficient (b0) and gas content (ro) is carried out in the same way, only instead of reservoir pressure in eqs. 30 and 31, the value of the critical saturation pressure (psat.) is set. the objects of operation at the nebit-dag and cheleken fields, which were put into operation in the period before the war and during the second world war, did not take deep samples at the time. for such objects, the dependences of the drop b and r on pressure are calculated. in west turkmenistan, such calculations were carried out for the first time when calculating the reserves of the cheleken deposit, the results of which were approved by the state reserves committee of the union of soviet socialist republics (deryaev 2023). below is an example of determining the dependencies of the volume coefficient and the gas content of oil on pressure for one of the calculation facilities of the cheleken field. calculations are made based on data on the fractional composition of the gas. r b 10 0.0 6 20 30 40 improved oil and gas recovery 12 the study determines the volume of oil in reservoir conditions, if it occupies 1 m3 on the surface, at a saturation pressure psat is 26 mpa, oil density is 0.82 t/m3, reservoir temperature is 75℃. based on these data, according to the standing’s nomogram (figure 5), the gas content of oil is determined to be 157.5 m3/m3. based on the volume content of the gas, the gas content, and the mass and volume of the gas in the liquid phase, the mass of the gas components and their volume in the liquid phase are determined, assuming that the weight of the gas in the formation is dissolved in oil (table 2). table 2—mass of gas components and their volume in the liquid phase. components mass of individual gas components per 1 m3 of oil, kg volume of components in the liquid phase per 1 m3 of oil, l methane 0.8943*157.5*0.714=100.9 0.8943*157.5*2.26=319.3 ethane 0.0445*157.5*1.35=9.5 0.0445*157.5*3.36=25.6 propane 0.0258*157.5*1.97=8 0.0258*157.5*3.66=15 butane 0.015*157.5*2.85=6.8 0.015*157.5*4.2=10 pentane 0.0072*157.5*3.22=3.7 0.0072*157.5*4.85=5.5 hexane+higher 0.0036*157.5*3.81=22 0.0036*157.5*5.49=3.1 carbon dioxide 0.0029*157.5*1.25=0.6 0.0029*157.5*0=0 nitrogen 0.0067*157.5*1.964=2.1 0.0067*157.5*1.19=1.2 oil 820.6 1,000 total 954.2 1,377.7 thus, the volume of 1 cubic metre of oil with dissolved gas in reservoir conditions is 1.3777 m3, and its mass is 954.2 kg. however, due to the fact that the reservoir temperature for ethane and methane is above their critical temperature, these gases are in a dissolved state in reservoir oil, and not in liquid. the density of the ethane + higher mixture was determined, and then, using the value, the density of the reservoir oil was determined. the mass of the components from propane and above is equal to (table 2), 954.2-(100.9+9.5)=843.8 kg............................................................................................................................(32) and the volume of these components is, 1,377.7-(319.3+23.6)=1,034.8 ........................................................................................................................(33) the density of the mixture from propane and above will be, 843.8 1,034.8 = 0.815 ................................................................................................................................................(34) percentage of ethane in the mixture of hydrocarbons ethane + higher is, 9.5∗100 954.2−100.9 = 1.11%........................................................................................................................................(35) figure 6 shows the density of the mixture ethane + higher is 0.792 t/m3. to calculate the density of oil, the percentage of methane in the hydrocarbon mixture consisting of methane and higher hydrocarbons is determined, 100.9∗100 954.2 = 10.6% ...........................................................................................................................................(36) improved oil and gas recovery 13 figure 7 shows the density of reservoir oil as 0.68 tonnes/m³. this value requires correction to account for the compressibility of the liquid and its thermal expansion. the compressibility correction is 0.027. therefore, considering this correction, the density of oil in the reservoir will be equal to 0.680+0.027=0.707 t/m3.................................................................................................................................(37) the correction to the density of formation oil due to temperature change is determined, which is 0.05. consequently, the density of oil will be 0.707-0.05=0.657 t/m3.....................................................................................................................................(38) the gas content of the standing’s nomogram will be 80 m3/m3 (figure 5). figure 5—standing’s nomogram (source: guo et al. 2022). figure 6—determination of correction for reservoir oil compressibility. considering that the mass of 1 cubic metre of oil in reservoir conditions is 962.7 kg, its volume will be equal to 1,452 litres, assuming a density of 0.657. hence, the volume coefficient of oil, calculated from the data of the fractional composition of gas, is equal to 1,452/1,000=1.452. since the change in the volume coefficient and gas content of oil from pressure obeys the equation of a straight line, it is sufficient to determine their values for 0.06 0.04 0.02 0 3.5 c o rr ec ti o n f o r o il d es ti n y , t/ m 3 7 improved oil and gas recovery 14 another arbitrarily selected point of reservoir pressure, for example 14 mpa. the mass and volume of gas components in the liquid phase are determined (table 3). table 3—mass and volume of gas components in the liquid phase. components mass of individual gas components per 1 m3 of oil, kg volume of components in the liquid phase per 1 m3 of oil, l methane 62.2 197.1 ethane 5.9 14.6 propane 5 9.2 butane 4.2 6.1 pentane 2.2 3.4 hexane+higher 1.3 2 carbon dioxide 0.4 nitrogen 1.2 0.8 oil 820.6 1,000 total 903 1,233.2 the mass and volume of the components from propane and above, respectively, are 834.9 kg and 1021.5l, therefore, the density will be 0.817. based on the density of the mixture and the percentage of ethane (0.7%), the density of the ethane + higher mixture was found to be 0.795. figure 7 denotes the density of oil by the calculated value of the density of the mixture (0.795) in the methane content (6.9%). it is 0.726 t/m3. the correction for compressibility is 0.011, and for expansion is 0.046. ultimately, the density of oil will be 0.691 t/m3. then the volume coefficient will be 1.307. based on these two points, the dependencies between the volume coefficient and the gas content of oil and pressure are determined using mathematical statistics in the following form, 𝑏 = 1.1378 + 0.0121р𝑟𝑒𝑠.,............................................................................................................................(39) 𝑟 = 6.46 р𝑟𝑒𝑠. − 10.4[𝑚3/𝑚3]......................................................................................................................(40) the volume coefficient of the gas is also determined based on the fractional composition of the gas. to do this, first of all, pseudocritical pressures (pr) and temperature (tr) are determined (table 4). improved oil and gas recovery 15 table 4—determination of pseudocritical pressures and temperatures. components content of the mixture, ci, % critical absolute pressure, pi, mpa critical temperature, ti, °k methane 92.99 4.58 190.5 ethane 2.29 4.82 305.28 propane 1.21 4.2 369.78 butane 0.42 3.64 4.07 pentane 0.94 3.747 425 hexane+higher 0.71 3.29 460.78 carbon dioxide 0.18 7.29 304.1 nitrogen 1.26 3.349 126 figure 7—graph for determining the compressibility factor. the pseudocritical pressure and temperature were determined by the equations (table 4): 𝑃𝑟 = ∑ 𝑃𝑖𝐶𝑖 100% = 4.64 𝑀𝑃𝑎,..........................................................................................................................(41) 𝑇𝑟 = ∑ 𝑇𝑖𝐶𝑖 100% = 200∘𝐾.................................................................................................................................(42) further, the given pseudocritical pressures and temperatures were determined, 𝑃𝑅 = 𝑃𝑟𝑒𝑠.+1 𝑃𝑟 ,.................................................................................................................................................(43) improved oil and gas recovery 16 𝑇𝑅 = 𝑇𝑟𝑒𝑠. 𝑇𝑟 = 70∘𝐶+273 200∘ = 1.715.....................................................................................................................(44) the reduced pseudocritical pressure is determined at various reservoir pressures (table 5). table 5—presented pseudocritical pressure at different reservoir pressures. reservoir pressure, pres., mpa 35 30 25 20 15 10 reduced pseudocritical pressure, pr 7.6 6.5 5.4 4.3 3.2 2.2 compressibility factor, z 1.01 0.95 0.91 0.87 0.88 0.89 volume coefficient of gas, υ 0.00346 0.0038 0.00436 0.00521 0.00702 0.01073 the compressibility factor (z) is determined based on (figure 5), the accuracy of which is 1%. the volume coefficient of the gas was determined using the formula, 𝑣 = 0.000352𝑍 𝑇𝑟𝑒𝑠. 𝑃𝑟𝑒𝑠. ........................................................................................................................................(45) as the results of subsequent studies have shown, the presence of nitrogen in the gas up to 19% increases the error to ±2%, and the content of co2 and h2 more than 2% requires appropriate corrections when introduced (figure 7). the gases of the deposits under study contain 1-1.5% nitrogen, co2 0.15-0.3%, and the amendments become impractical (figure 8). figure 8—change in the volume coefficient of gas from pressure. the gas factor plays an important role in calculating reserves. during the development of oil deposits with a gas cap, as the reservoir pressure drops in the extraction zone (in the oil part), the gas cap expands, which leads to gas contamination of well products, and sometimes gas cap gas breakthrough (development of so-called “gas cones”). 35 pressure, mpa 10 5 15 20 25 30 0 0 0.01 0.0075 0.005 0.0025 g as v o lu m e co ef fi ci en t improved oil and gas recovery 17 the gas breakthrough from the gas cap, in addition to the deterioration of the oil recovery process, makes it difficult to determine the value of the true gas factor, which is the most important technological parameter of the deposit operation (wen et al. 2023). naturally, failure to account for a gas breakthrough can lead to significant errors both in substantiating geological and technical measures for rational development and in assessing oil and gas reserves. for example, failure to account for a gas breakthrough can lead to an increase in the balance reserves of oil, and therefore dissolved gas, when calculated using the material balance method by several (sometimes dozens) times. when evaluating the reserves of oil deposits in western turkmenistan, a methodology was used to assess the true gas factors and its changes (dynamics) in the process of oil recovery based on actual development materials based on establishing the relationship between gas content, gas factor, and current reservoir pressure. under the condition of uniform reduction of reservoir pressure in all areas of the deposit, the value of the gas factor is determined by the gas content and the ratio of the current reservoir pressure and saturation pressure (wang et al. 2022). due to the decrease in reservoir pressure during development below the saturation pressure, as is known, a more intensive release of dissolved gas from oil occurs in the reservoir. however, the gas factor exceeds the gas content of oil, and the degree of its excess is determined mainly by the ratio of reservoir pressure and saturation pressure. based on the actual data of the development of operational facilities of the goturdepe field: graphs of the relationship between the ratio of the gas factor to the gas content – 𝑟𝑝 𝑟 and reservoir pressure to saturation pressure–p res./psat. processing of the actual data on the second group of deposits provides the following dependence, 𝑟𝑝 𝑟 = 1 + 90.47−6.1225𝑃𝑟𝑒𝑠./𝑃𝑠𝑎𝑡.........................................................................................................................(46) with a significant drop in reservoir pressure (pres./psat.≤0.6), the proposed correlation relationship gives overestimated results. this is explained by the fact that at this time, the formation of secondary gas caps is observed in the studied objects and, naturally, an increase in the gas factor. to exclude this phenomenon, the gas factors were calculated from the expression, 𝑟𝑝 = 𝑄0𝑟0−𝑄𝑟𝑒𝑠𝑖𝑑.2 𝑄𝑜.𝑝. ,.............................................................................................................................................(47) where, qo is initial balance reserves of oil; q resid. is residual oil balance reserves; qm is accumulated oil production; r 0 is initial gas content; r is current gas content. as can be seen from figure 9, the curves characterising these dependencies are divided into two groups. the first is characterised by a sharp incommensurable excess of the gas factor over the gas content with a slight decrease in reservoir pressure below the saturation pressure. this group includes deposits, obviously, a sharp increase in the gas factor is determined by the flow of gas from the gas cap into production wells. another group of curves, which includes deposits that do not have a gas cap, is characterised by a comparative slope to the left. the excess of the gas factor over the gas content here is determined precisely by the degree of reduction of reservoir pressure below the saturation pressure, that is, the degree of degassing of reservoir oil (mullins et al. 2023). a similar graph was constructed using calculated gas factors (figure 10). improved oil and gas recovery 18 figure 9—relationship between the ratio of the gas factor to the gas content. figure 10—dependence of reservoir pressure on saturation pressure. when processing this data, the following dependence was obtained, 𝑟𝑝 𝑟 = 5.028 − 4.28 𝑃 𝑃𝑠𝑎𝑡. + 0.48 ( 𝑃 𝑃𝑠𝑎𝑡. ) 2 .......................................................................................................... (48) this dependence gives correct results even at pres./psat.=0.4 and below. thus, when developing oil and gas deposits, the following method is proposed for determining the volume of associated gas that broke out of the gas cap during oil recovery (soomro et al. 2022): 1. with known values of reservoir pressure and gas content, the above dependencies determine the possible value of the true gas factor, the average for the entire period of development, and through it the accumulated production of dissolved gas. 2. the volume of associated gas released from the gas cap is defined as the difference between the measured and calculated values of gas production. the determination of recoverable oil reserves (oil recovery coefficient) can also be performed using the material balance method. for this purpose, the so-called displacement indices are determined, which show the improved oil and gas recovery 19 share of participation of each regime in the oil production process. displacement index of the water pressure regime: 𝐼𝑤.𝑟. = 𝑊−𝑤 𝑄𝑜.𝑝. [𝑏1+(𝑟р−𝑟0)𝑣] (iw.r.:water regime displacement index). displacement index of the dissolved gas regime: 𝐼𝑑.𝑔. = 𝑄0(𝑏1−𝑏0)𝑊−𝑤 𝑄𝑜.𝑝. [𝑏1+(𝑟р−𝑟0)𝑣] (id.g.:dissolved gas mode displacement index). the displacement index of the gas cap regime: 𝐼𝑔.𝑐. = 𝑄𝑔.(𝑣−𝑣0)𝑊−𝑤 𝑄𝑜.𝑝. [𝑏1+(𝑟р−𝑟0)𝑣] (ig.c.:displacement index of the gas cap regime). the sum of the displacement indices of all regimes involved in the development of the deposit should be 1. displacement indices characterise not only the drainage regime, but also the proportion of oil, and the volume of deposits that are influenced by one or another regime. if a deposit is developed under a mixed regime, then each area (part of the oil) will be characterised by its own oil recovery coefficient, more or less (based on other geological and field conditions) different from the oil recovery of other areas. in this case, the oil recovery coefficient for the deposit, in general, will be determined based on the displacement indices and based on the oil recovery coefficients, from the conditions of development of the deposit in a pure water-pressure (gas or dissolved gas) mode, 𝜂 = 𝐼𝑤.𝑟.𝜂𝑤. + 𝐼𝑑.𝑔.𝜂𝑑.𝑔. + 𝐼𝑔.𝑐.𝜂𝑔.𝑐.,.................................................................................................................(49) where: n – oil recovery coefficient of the facility; nw. – oil recovery coefficient when the facility is developed only in water-pressure mode; nd.g. – oil recovery coefficient when the facility is developed only in the dissolved gas mode; ng.c. – oil recovery coefficient when the facility is developed only in the gas cap mode. the oil recovery coefficients of many deposits in south-western turkmenistan, including the nk3 horizon of the okarem field, were substantiated using this method. when approving the oil and gas reserves of the okarem field, due to insufficient information, the oil recovery coefficient of the nk3 oil and gas horizon was adopted based on general considerations of the equally probable influence of various reservoir energies, without considering the conditions and nature of their manifestation. the characteristic of the development of the nk3 horizon shows that the deposit in question is drained under a mixed regime. this means that the dissolved gas regime, the water pressure regime and the gas cap regime are simultaneously manifested in different ratios in the formation. elastic forces act only in the initial period of development and in this case have little effect on the results of the oil recovery process (guo et al. 2023). extrapolation of the displacement indices of the gas cap, dissolved gas and water pressure modes shows that they asymptotically approach 0.2, 0.1, and 0.7, respectively (figure 11). from the studies, the oil recovery coefficients of the water-pressure regime – 0.463, the dissolved gas regime – 0.2 (to determine the oil recovery coefficient in the dissolved gas regime, a graph was constructed using data from the laboratory of underground hydrodynamics of the all-union petroleum research institute), and the gas cap – 0.25 (figure 12). under such conditions, the expected oil recovery coefficient of the nk3 horizon of the okarem field will be 0.394. considering the accuracy of the initial data and the accepted calculation methods, the value of the oil recovery coefficient is rounded to 0.4. improved oil and gas recovery 20 figure 11—dynamics of displacement indices of the nk3 horizon of the okarem field. figure 12—graph of the dependence of the oil recovery coefficient in the dissolved gas regime on the viscosity and volume coefficient (b) of oil and on the solubility coefficient (γ). in cases where the displacement index of the water pressure regime is 0.85 or higher, the gas released from the oil only favourably affects the process of oil movement to the bottom of production wells, without reducing the oil recovery coefficient. therefore, for such cases, as an oil recovery coefficient of an object, in general, its value for a clean water pressure regime is taken (a number of counting objects of the goturdepe field). summarising the above, it can be concluded that the material balance method, in the presence of reliable initial data, gives good results both in assessing the initial balance reserves of oil and in determining the oil recovery coefficient (recoverable reserves). in addition, this method can be successfully applied in the analysis of the development of an operational facility to determine the proportion of each type of energy involved in oil production. discussion the analysis of the commercial evaluation of oil deposits by the material balance method is a key tool for determining the volume of oil reserves and forecasting their operational efficiency. this method is based on a thorough analysis of data on oil production, production volumes, physicochemical properties of oil reservoirs, and the parameters of wells and production systems. improved oil and gas recovery 21 according to jing et al. (2021), numerical modelling of the purification of marine heavy oil by hydrocyclones is an important tool for predicting and optimising the purification process of oil products. hydrocyclones are devices used to separate liquid mixtures into components of different densities by centrifugal forces. in the context of offshore oil production, where heavy oils with a high content of viscous and dense fractions are often found, hydrocyclones can be an effective means for pre-refining oil before further processing. numerical modelling allows analysing the operation of hydrocyclones considering various parameters, such as the diameter of the hydrocyclone, flow velocity, concentration of heavy fractions in oil. these data are consistent with the theses given in the previous section. the simulation allows optimising the operation parameters to achieve maximum cleaning efficiency with minimal energy and resource consumption. this approach helps to reduce the loss of valuable oil, improve product quality, and reduce the negative impact on the environment by using resources more efficiently when refining oil on offshore platforms or during onshore processing. oil remains a strategic resource providing the main sectors of the economy, and it is important to consider its effective use. the commercial evaluation of oil deposits using the material balance method plays a key role in this process, allowing not only to determine reserves and production efficiency, but also to predict the further development of the industry and manage resources in a changing energy environment and challenges facing the oil sector. referring to the definition of al-obaidi (2021), the analysis of hydrodynamic methods for increasing oil recovery is an important area of research in the oil industry, since these methods play a crucial role in increasing the production of hydrocarbons from deposits. hydrodynamic methods are aimed at changing the physical and chemical parameters of the reservoir and well equipment to increase the permeability of the reservoir, reduce the viscosity of oil, improve its lifting and expand the drainage zone. one of the most common methods is the introduction of water, steam, or chemicals into the reservoir. this may include technologies such as drainage wells, the introduction of polymers, surfactants, or foam generators. hydrodynamic models allow analysing the impact of such methods on fluid dynamic processes in the reservoir and predict their effectiveness. by analysing various implementation scenarios, it is possible to determine the optimal strategies for specific fields, which allows maximising oil production and reducing production costs. before analysing the commercial evaluation of oil deposits, the material balance method collects and further analyses data on current oil production from a specific field. these data include parameters such as well flow rates (the volume of oil production over a certain period of time), reservoir pressures, temperatures, oil composition (for example, density, viscosity, impurity content), and other characteristics. further, these data are used to build a material balance, which is the main tool for evaluating oil reserves at the field. the material balance considers the flow of oil into the system (reserves in the reservoir, resource base, possible replenishment) and the outflow of oil from the system (production). in fact, this is an analysis of material flows in the system, which allows estimating the volume of oil produced, its changes over time, and predicting the dynamics of production. huang et al. (2024) determined that the assessment of the productivity of shale gas wells is an important stage in the development and operation of shale deposits. there are several assessment methods that can determine the potential of wells and predict their performance. one of the main methods is the analysis of data from geophysical and geological studies, which allows assessing the properties of rocks, the structure of the formation, and the probability of the presence of gas and oil wells. with the help of seismic data and drilling of test wells, it is possible to identify potential areas for drilling production wells and predict their performance. another method for evaluating the productivity of shale gas wells is numerical modelling. this approach considers complex physicochemical processes occurring in the formation and well, such as rock fracturing, gas and liquid flows, the influence of hydraulic fracturing technologies, and other parameters. numerical models help to predict well performance under various operating conditions and plan optimal strategies for shale gas production. this approach helps to improve the efficiency of field development, minimise risks, and optimise production costs. these results confirm the above study, since modern methods of evaluating the productivity of shale gas wells not only increase the accuracy of forecasts, but also provide a deeper understanding of the physical and chemical processes in the formation, which is key to the successful operation of shale deposits. one of the main advantages of the material balance method is its relative simplicity and the ability to obtain an initial estimate of oil reserves improved oil and gas recovery 22 based on available data. this method also enables production forecasts to be made and optimal field development strategies to be determined, which is an important aspect of oil company planning. saha (2022) has found that the use of remote sensing and geographic information systems (gis) is becoming increasingly common in hydrocarbon exploration due to its ability to provide a broad and objective overview of territories, and analyse various aspects of the geological structure and composition of the earth’s surface. remote sensing, based on the analysis of the spectral characteristics of reflected and emitted radiation, allows detecting signs of the presence of hydrocarbons, such as changes in soil characteristics or the presence of characteristic geological formations. it is possible to agree with this opinion that the combined use of remote sensing and gis helps to comprehensively analyse and visualise spatial data, including information about the geological structure, topography, relief, geochemical indicators, and other factors affecting the distribution of hydrocarbons. this allows not only detecting potential deposits, but also assessing their potential, determining the optimal locations for drilling and development, and predicting the characteristics of hydrocarbon reserves. this approach significantly improves the efficiency of exploration and helps to reduce the cost of searching and developing new hydrocarbon deposits. however, it must be borne in mind that the material balance method has its limitations. it does not always consider changes in the physicochemical properties of reservoir fluids during production, such as changes in the composition of oil or its properties under the influence of production. this may lead to insufficient accuracy of forecasts and estimates of reserves. in addition, when working with complex fields where various types of oil deposits and complex geological structures are present, the material balance method may be less effective due to a simplified approach to modelling production processes. as noted by dordzie and dejam (2021), the effectiveness of various oil production methods has a significant impact on the commercial evaluation of deposits. various extraction methods, such as the use of artificial uplifts, hydraulic fracturing technologies, thermal extraction methods, drainage and gas lift systems, have their own characteristics and effectiveness in various conditions of the geological and technological environment. the effectiveness of the chosen extraction method directly affects production volumes, production costs, the degree of economic feasibility of field development, and the environment. for example, hydraulic fracturing (or fractionation) technology has become widespread in the production of shale hydrocarbons in recent decades. it allows extracting oil from reservoirs with low permeability, which was previously difficult or impossible. however, this method requires significant investments in technological equipment, preparation and treatment of the formation, and may also raise concerns due to environmental problems associated with it, such as water pollution and seismic activity. thus, the effectiveness of oil extraction methods must be evaluated considering all aspects to ensure a balance between economic efficiency and environmental sustainability. the combination of the material balance method with other methods of analysis and modelling provides a more complete and reliable picture of oil reserves, production efficiency, and optimal field development strategies. the combined approach considers various factors affecting the oil production process and minimises risks when making decisions in the oil industry. in general, the analysis of the commercial evaluation of oil deposits by the material balance method is an important tool for the initial assessment of oil reserves and planning their development. however, to obtain more accurate and reliable data, it is often necessary to combine it with other assessment and modelling methods, such as numerical reservoir modelling and hydrodynamic analysis. hou et al. (2021) determined that the estimated final production of shale oil and gas depends on several key geological factors that determine the opportunities and limitations in the extraction of hydrocarbons from shale formations. one of the main factors is the rock permeability. shale horizons are often characterised by low permeability due to the microscopic pore size and impermeability to liquid and gas. this creates difficulties when passing hydrocarbons through the porous structure of rocks, which reduces final recovery. another important factor is the presence and structure of cracks in shale formations. fracturing of the rock can significantly increase permeability and facilitate the extraction of hydrocarbons. geological features of the formation, such as the thickness of shale formations, their geomechanical properties, composition, the presence of a gas shell, also have an impact. all these factors determine the conditions of production and its efficiency, and also require a comprehensive analysis and improved oil and gas recovery 23 assessment when developing strategies for the extraction of shale hydrocarbons. in addition, factors such as the geographical location of the deposit and its environment must be considered. for example, the availability of infrastructure, the possibility of conducting geological research and production, and potential environmental risks and social aspects are important in the development and implementation of shale hydrocarbon production projects. all these factors together determine the ultimate success of the project and its impact on the economy and the environment. thus, the analysis and consideration of all these factors are necessary for the development of effective and sustainable strategies for the extraction of shale hydrocarbons. conclusions the analysis of the commercial evaluation of oil deposits by the material balance method is an important tool in the oil and gas industry for determining oil reserves, forecasting production, and developing optimal strategies for exploration and production at fields. the use of this method provides a comprehensive understanding of the condition of the deposit, its geological structure, and operational capabilities. in the presence of reliable initial data, the material balance method demonstrates high efficiency both in evaluating initial oil reserves and in determining the oil recovery coefficient (recoverable reserves), and it can also be successfully applied to analyse the development of an operational facility to determine the proportion of each type of energy involved in oil production. this method provides an opportunity to estimate the remaining oil reserves in the field using data on current production, reservoir properties, and physical parameters of wells. this is important for planning long-term operation and making strategic decisions. in addition, the analysis of the material balance method allows forecasting oil and gas production based on data on technological processes and production dynamics. this helps to optimise the mining process and manage resources more efficiently. the results of the analysis also help to determine the optimal strategies for field development, including the choice of production methods, investment planning, and optimisation of production processes. however, the material balance method has its limitations. for example, it is necessary to consider changes in the physicochemical properties of reservoir fluids during the extraction process, which affects the accuracy of forecasts. in addition, this method may be less effective when working with complex fields where various types of oil deposits and complicated geological structures are present. in such cases, additional analysis and modelling methods are required to more accurately evaluate and predict hydrocarbon production. nevertheless, with the correct interpretation of the data and consideration of all factors, the analysis by the material balance method remains an important tool for the assessment and development of oil fields. one of the constraints of this study is the limited availability of data on the physicochemical properties of reservoir fluids in various fields, which may affect the accuracy of forecasts and estimates when using the material balance method for analysing oil deposits. for a more complete understanding of the commercial evaluation of oil deposits using the material balance method, additional study of the effect of changes in the physicochemical properties of reservoir fluids on the accuracy of forecasts and methods of adaptation to work with complex deposits is necessary. nomenclature qo = initial oil reserves; qo.p. = oil production accumulated over time; b1 = volume coefficient of oil in a two-phase system, determined from the expression b1=b+(ro-r)o; bo = initial volume coefficient of oil; b = current volume coefficient of oil; rp = average gas factor; ro = initial solubility of gas in oil; r = current solubility of gas in oil; υ = volume coefficient (current) of reservoir gas; improved oil and gas recovery 24 w = volume of water embedded in the reservoir; w = volume of extracted water; x = specific elastic capacity of the deposits; p = pressure; qg. = gas reserves of the gas cap; υ0 = volume coefficient of the gas at the initial reservoir pressure. references tlepov, a.s. and churikova, l.a. 2023. analysing methods of oil production stimulation at the uzen field. bulletin of western kazakhstan innovation-technological university scientific journal 28(4): 173-178. issenov, s.m. 2021. problem issues and ways to increase the efficiency of seismic survey. oil and gas 121(1): 52-68. lopes, m., von hohendorff filho, j.c., and schiozer, d.j. 2021. the effect of dynamic data adjustments in production system simulation models on oil production forecasting applied to reservoir simulation models. journal of petroleum science and technology 11(1):17-28. imanbayev b.a., sagyndikov 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131(1):105810. guo, d., xie, h.p., chen, l., et al. 2023. in-situ pressure-preserved coring for deep exploration: insight into the rotation behavior of the valve cover of a pressure controller. petroleum science 20(4):2386-2398. jing, j., zhang, s., qin, m.,et al. 2021. numerical simulation study of offshore heavy oil desanding by hydrocyclones. separation and purification technology 258(1):118051. al-obaidi, s.h. 2021. analysis of hydrodynamic methods for enhancing oil recovery. journal of petroleum engineering & technology 6(3):2026. huang, y., li, x., liu, x., et al. 2024. review of the productivity evaluation methods for shale gas wells. journal of petroleum exploration and production technology 14(1):25-39. saha, s.k. 2022. remote sensing and geographic information system applications in hydrocarbon exploration: a review. journal of the indian society of remote sensing 50(1):1457-1475. dordzie, g. and dejam, m. 2021. enhanced oil recovery from fractured carbonate reservoirs using nanoparticles with low salinity water and surfactant: a review on experimental and simulation studies. advances in colloid and interface science 293(1):102449. hou, l., yu, z., luo, x., et al. 2021. key geological factors controlling the estimated ultimate recovery of shale oil and gas: a case study of the eagle ford shale, gulf coast basin, usa. petroleum exploration and development 48(3):762-774. annaguly deryaev is a principal researcher at the department of well drilling, scientific research institute of natural gas of the state concern “turkmengas”. his research interests are the oil and gas industry, optimisation of oil production processes, and sustainable development of the oil industry. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1313 received september 14, 2024; revised september 22, 2024; accepted october 8, 2024. *corresponding author: christian.okalla@futo.edu.ng 1 effect of hydrate on the deliverability of underground gas storage (ugs) reservoir charlie iyke c. anyadiegwu, christian emelu okalla*, anthony kerunwa, nmesoma precious ebosie, daniel chinedu nwachukwu, federal university of technology owerri, owerri, nigeria abstract the study investigates the impact of hydrates on the deliverability of underground gas storage (ugs) reservoirs, specifically focusing on depleted wells. utilizing matlab (2024) for numerical problem coding and microsoft office excel (2013) for data collation and plotting, the research simulates the effects of hydrate formation within a gas well. data was sourced from open literature and includes parameters such as gas gravity, tubing dimensions, pressures, temperatures, and constants for the inflow performance relationship (ipr) model. key metrics, such as gas gravity, tubing inside diameter, and reservoir pressure, were used to model the gas storage well's behavior. the study varied the hydrate film thickness from 0.0 to 1.0 inch to assess its influence on gas deliverability. the governing equations for ipr and tubing performance relationship (tpr) were employed, integrating the hydrate film's impact by modifying the inner diameter of the tubing. the ipr equation was rearranged to compute the flowing bottom-hole pressure as a function of flow rate. the tpr equation was adjusted to account for hydrate thickness, leading to a new model that predicts gas deliverability under varying hydrate conditions. the solution procedure involved computing average temperature and pressure, critical temperature and pressure, pseudoreduced temperature and pressure, and average compressibility factor. these computations facilitated the generation of gas flow rates and the plotting of ipr and tpr curves for different hydrate thicknesses. results indicated that as hydrate film thickness increases, the tpr curve shifts from horizontal to vertical, signifying reduced gas flow rates and increased bottom-hole pressures. a hydrate thickness of 0.0 inches resulted in a flow rate of 1470 mscf/day, while a thickness of 1.0 inch reduced the flow rate to 20 mscf/day. this reduction in flow rate and increase in bottom-hole pressure illustrate the adverse effects of hydrate deposition on gas well deliverability. in conclusion, the presence of hydrates significantly decreases the deliverability of gas storage wells. to mitigate these effects, the study recommends the use of hydrate inhibitors and insulation of pipelines to prevent heat loss, thereby avoiding hydrate formation. introduction natural gas plays a pivotal role in meeting global energy demands, and underground gas storage (ugs) reservoirs are essential for ensuring a stable and reliable supply of natural gas to consumers. depleted wells, characterized by lower reservoir pressures, are commonly repurposed for ugs operations due to their existing infrastructure (chu et al. 2023). however, the presence of hydrates in such reservoirs poses a significant challenge to the deliverability and overall efficiency of these storage facilities (muhammed et al. 2023) hydrates are solid compounds formed by the combination of water and natural gas molecules under specific temperature and pressure conditions (wang and economides 2009). in ugs reservoirs in depleted wells, the potential for hydrate formation is heightened due to the reduced reservoir pressures and temperatures commonly associated with these mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 conditions. the formation of hydrates can have several adverse effects on reservoir performance, with a direct impact on deliverability. as natural gas is injected into depleted wells during periods of excess supply and withdrawn during periods of high demand, the thermodynamic and kinetic factors influencing hydrate stability become critical. hydrate formation can lead to reduced permeability within the reservoir rock and near the wellbore, creating flow restrictions that impede the movement of natural gas (dillon 2002). this restriction in flow can result in a decline in well deliverability, making it essential to understand and address the hydrate-related challenges specific to ugs operations in depleted wells. to assess and manage the impact of hydrates on ugs reservoir deliverability, it is crucial to delve into the underlying mechanisms of hydrate formation, considering both thermodynamic and kinetic aspects. thermodynamically, hydrates are stable under specific pressure and temperature conditions, and these conditions are often encountered in depleted wells. kinetic considerations involve understanding the rate at which hydrates form and dissolve, which is essential for predicting and mitigating hydrate-related issues during injection and withdrawal cycles. figure 1 highlights the purpose of uss. figure 1—purpose of underground storage system (uss) (al-shafi et al. 2023). previous studies have highlighted the operational challenges associated with hydrates in ugs reservoirs, emphasizing the need for effective mitigation strategies. chemical inhibitors, thermal methods, and depressurization techniques are among the potential strategies to prevent and manage hydrate-related challenges in depleted wells. these strategies need to be tailored to the unique conditions of depleted wells to ensure their effectiveness and efficiency (vrålstad et al. 2018). in addition to mitigation strategies, continuous monitoring and advanced reservoir management techniques are vital for detecting and addressing hydrate-related issues in realtime. advanced monitoring technologies, such as downhole sensors and surveillance systems, offer valuable insights into reservoir conditions, enabling timely intervention to prevent or manage hydrate formation. improved oil and gas recovery 3 storing gases underground is an effective way to manage excess renewable energy, allowing for reserves that can be used when demand outstrips supply. when geological conditions are unsuitable for underground storage, large-scale above ground containment becomes necessary. however, comparing these options reveals regional differences in renewable electricity-based energy systems (elberry et al. 2021a). with technological advancements, hydrogen storage has become a viable method for seasonal storage, making it crucial to fully exploit the integration of variable renewable energy sources (vres) into the grid (elberry et al. 2021b). figure 2 shows underground natural gas storage. figure 2—underground natural gas storage (energy information administration 2015). several volumetric metrics are used to define the core characteristics of an underground storage facility and the gas it holds. it's essential to differentiate between facility attributes, like capacity, and gas attributes, like actual inventory levels. these metrics include: 1. total gas storage capacity: this is the maximum volume of gas that an underground storage facility can hold, considering its design, physical characteristics of the reservoir, installed equipment, and site-specific operating procedures. 2. total gas in storage: this refers to the volume of gas stored in the facility at a given time. 3. base gas (or cushion gas): this is the volume of gas kept as a permanent inventory in a storage reservoir to maintain adequate pressure and deliverability rates during the withdrawal season. 4. working gas capacity: this is the total gas storage capacity minus the base gas. 5. working gas: this is the volume of gas in the reservoir above the base gas level and is available for use in the market. 6. deliverability: often expressed in millions of cubic feet per day, this measure indicates the amount of gas that can be withdrawn from a storage facility daily. it can also be expressed in dekatherms per day (a therm is 100,000 btu, approximately equal to 100 cubic feet of natural gas; a dekatherm is about one thousand cubic feet). deliverability varies with the gas amount in the reservoir, reservoir pressure, compression capability, surface facilities' configuration, and other factors. generally, the deliverability rate is highest when the reservoir is full and decreases as working gas is withdrawn. 7. injection capacity (or rate): this is the daily amount of gas that can be injected into a storage facility, usually expressed in mmcf/day or dekatherms/day. injection capacity depends on factors similar to those affecting improved oil and gas recovery 4 deliverability. however, the injection rate inversely varies with the total gas amount in storage. it is lowest when the reservoir is full and increases as working gas is withdrawn. none of these measures for any given storage facility are fixed or absolute. table 1 summarizes and compares the mechanisms, strengths, limitations, and applications of various hydrate prediction models. table 1—hydrate prediction model. model mechanism strength limitation applicability thermodynamic model these models predict the pressure and temperature conditions at which hydrates will form in a gas mixture (bhatnagar and gao 2022). they rely on thermodynamic equilibrium principles and utilize equations of state to describe the behavior of gas and water components within the system. thermodynamic equilibrium models are computationally efficient and provide a basic framework for hydrate formation prediction. these models assume a system at equilibrium, which may not always be the case in real-world ugs scenarios with dynamic pressure and temperature conditions. additionally, they may not account for the complex interactions between the reservoir rock and the gas-water mixture. while these models offer a starting point for hydrate prediction in depleted wells, their limitations necessitate using them in conjunction with other methods for a more accurate assessment. kinetic models these models consider the kinetics of hydrate formation, accounting for the rate at which gas molecules are incorporated into the hydrate structure (aghajanloo et al. 2024). they involve complex mathematical equations that describe mass transfer, heat transfer, and the surface chemistry involved in hydrate formation. kinetic models provide a more realistic picture of hydrate formation by incorporating reaction rates and nonequilibrium conditions. this can be particularly valuable in depleted well ugs where pressure and temperature fluctuations might occur. kinetic models are computationally expensive and require a deeper understanding of the specific reservoir characteristics and gas composition. additionally, validating these models with real-field data can be challenging. kinetic models offer a more accurate prediction of hydrate formation risk in depleted wells compared to equilibrium models. however, their complexity and data requirements necessitate careful evaluation before implementation. pore-scale network models these models represent the pore space within the reservoir rock as a network of interconnected channels (makwashi and ahmed 2021). they simulate the flow of gas, water, and heat through this network, allowing for a detailed analysis of hydrate formation within the reservoir rock itself. pore-scale network models offer valuable insights into the spatial distribution of hydrates within the reservoir and their impact on flow behavior. this can be crucial for optimizing wellbore placement and production strategies in depleted wells. these models are computationally very demanding and require detailed information about the pore structure of the reservoir rock, which can be challenging to obtain. additionally, their complexity makes them less suitable for real-time decision making. pore-scale network models can be valuable tools for understanding hydrate formation processes in depleted wells. however, their computational intensity and data demands limit their widespread use in practical applications. improved oil and gas recovery 5 methodology software suite. matlab (version 2024) software suite was employed in this study for coding of the numerical problem. matlab was used to simulate the effect of hydrate in a gas well. microsoft office excel (2013) software suite was used in this study for the collation and plotting of simulation results. data collection. the data used for this study was collected from open sources (guo et al. 2007) and are as defined in table 2. table 2—input data for a gas storage well. input parameter value units gas gravity, 𝛾𝑔 0.71 − tubing inside diameter, 𝑑𝑖 2.259 inch tubing relative roughness, 𝜖 𝑑𝑖⁄ 0.0006 − measured depth at tubing shoe, l 10,000 feet inclination angle, 𝜃 0 degree wellhead pressure, 𝑝ℎ𝑓 800 psia wellhead temperature, 𝑇ℎ𝑓 150 ℉ bottom-hole temperature, 𝑇𝑤𝑓 200 ℉ reservoir pressure, 𝑝𝑟 2000 psia c-constant in back-pressure ipr model, c 0.01 𝑀𝑠𝑐𝑓 𝑑 − 𝑝𝑠𝑖2𝑛⁄ n-exponent in back-pressure ipr model, n 0.8 − governing equations. the governing equations for this study are the inflow performance relationship (ipr) and tubing performance relationship (tpr) for a gas well as given in eq. 1 and 2, respectively (guo et al. 2017), as follows, 𝑞𝑠𝑐 = 𝑐(𝑝𝑟 2 − 𝑝𝑤𝑓 2) 𝑛 ,......................................................................................................................................(1) 𝑝𝑤𝑓 2 = 𝑒𝑠𝑝ℎ𝑓 2 + 6.67∗10−4(𝑒𝑠−1)𝑓𝑀𝑍𝑎𝑣 2𝑇𝑎𝑣 2𝑞𝑠𝑐 2 𝑑𝑖 5 cos 𝜃 ,................................................................................................(2) where qsc is the gas flow rate, c is the c-constant in ipr model, pr is the reservoir pressure, pwf is the flowing bottom-hole pressure, n is the n-exponent in the ipr model, s is the skin factor, fm is the friction factor, zav is the average gas compressibility factor, tav is the average temperature, di is the internal tubing diameter, and θ is the pipe angle of inclination. model development. the effect of hydrate on the deliverability of a storage gas reservoir can be investigated by considering a well as shown in figure 3. the flow involves simultaneous flow of gas, water, and hydrates. as shown, some of the hydrates are deposited on the pipes inner walls resulting in a decrease in the flow area. hence, in this study we used the thickness of the hydrate film for this investigation. that is; the thickness of the hydrate film was increased from 0.0 inch through 1.0 inch and its effect on the deliverability examined. first, we computed the inflow performance relationship (ipr) flowing bottom-hole pressure for the gas storage well as a function of flow rate. this was achieved by rearranging eq. 1 into eq. 3. 𝑝𝑤𝑓 = √𝑝𝑟 2 − ( 𝑞𝑠𝑐 𝑐 ) 1 𝑛 2 ,.......................................................................................................................................(3) improved oil and gas recovery 6 where rh is the inner radius of the hydrate film, ri is the inner radius of the pipe, and dh is the thickness of the hydrate film. figure 3—multiphase gas-water-hydrate flow in a vertical well. second, the thickness of the hydrate film is modeled into the tpr model. this is achieved by the removing the hydrate thickness from the inner pipe diameter. we also assumed that the hydrate thickness in the pipe is constant. as shown in figure 3, rh = ri − δh.......................................................................................................................................................(4) in terms of diameter, eq. 4 can be rewritten as: dh = di − 2δh ...................................................................................................................................................(5) equation defines the area for multiphase flow of the gas-water-hydrate multiphase flow. notice that dh = di for δh = 0.0. we modified eq. 2 by introducing the effect of the film thickness, δh on the tpr equation with the aid of eq. 5. that is pwf = √esphf 2 + 6.67∗10−4(es−1)fmzav 2tav 2qsc 2 (di−2δh)5 cos θ 2 .................................................................................................(6) eq. 6 is used in computing the tpr for the hydrate film thickness 0.0 inch through 1.0 inch. the average temperature and compressibility factor method was employed in this study. we also employed the bottom-hole pressure as the solution node. solution procedure. in this section, we will describe the solution procedure employed in computing the ipr and tpr. average temperature and pressure. the first step was the computation of the average temperature and average pressure with the aid of eqs. 7 and 8, respectively. improved oil and gas recovery 7 tav = ( thf+twf 2 ) + 460,....................................................................................................................................(7) pav = ( phf+pr 2 ) .......................................................................................................................................(8) critical temperature and pressure. the second step is the computation of the critical temperature and critical pressure of the gas as functions of the gas gravity as defined in eqs. 9 and 10, respectively. tpc = 168 + 325γg − 12.5γg 2 ,.......................................................................................................................(9) ppc = 667 + 15γg − 37.5γg 2 ........................................................................................................................(10) pseudo-reduced temperature and pressure. the third step is the computation of the pseudo-reduced temperature and pressure with the aid of eqs. 11 and 12, respectively. tpr = tav tpc ,.........................................................................................................................................................(11) ppr = pav ppc ..........................................................................................................................................................(12) average compressibility factor. the fourth step is the computation of the average z-factor with the aid of the (brill and beggs 1974) z-factor correlation. zav = a + ( 1−a eb ) + cppr d,..............................................................................................................................(13) where a = 1.39(tpr − 0.92) 0.5 − 0.36tpr − 0.10,...................................................................................................(14) c = 0.132 − 0.32 log(tpr),.............................................................................................................................(15) e = 9(tpr − 1),...............................................................................................................................................(16) f = 0.3106 − 0.49tpr + 0.1824tpr 2 ,...........................................................................................................(17) d = 10f,..........................................................................................................................................................(18) b = (0.62 − 0.23tpr)ppr + ( 0.066 tpr − 0.037) ppr 2 + 0.32ppr 6 10e ........................................................................(19) skin factor and skin factor exponent. the fifth step is the computation of the skin factor and the skin factor exponent as defined in eqs. 20 and 21, respectively. s = 0.0375γgl cos( θ 57.3 ) zavtav ,...................................................................................................................................(20) es = exp(s).....................................................................................................................................................(21) friction factor. the sixth step is the computation of the friction factor with the aid of the nikuradse friction factor correlation (guo et al. 2007) for fully turbulent flow in rough pipes as defined in eq. 22, fm = ( 1 1.74−2 log( 2ε di ) ) 2 ,....................................................................................................................................(22) absolute open flow. the seventh step is the computation of the absolute open flow or maximum flow rate with the aid of eq. 1 @ pwf = 0, qsc = cpr 2n......................................................................................................................................................(23) improved oil and gas recovery 8 gas flow rate generation. the eight step is the generation of gas flow rate in the range from zero to absolute open flow in steps of aof divided by 14 as defined in eq. 24. qsc = 0 ∶ aof 14⁄ ∶ aof................................................................................................................................(24) inflow performance relationship. the ninth step is the computation of the inflow performance relationship for generated gas flow rates as defined in eq. 25. ipr(i) = √pr 2 − ( qsc(i) c ) 1 n 2 ...............................................................................................................................(25) tubing performance relationship. the tenth step is the computation of the tubing performance relationship for the generated gas flow rates and the different hydrate film thickness as defined in eq. 26. tpr(i) = √esphf 2 + 6.67∗10−4(es−1)fmzav 2tav 2qsc 2(i) (di−2δh)5 cos θ 2 ......................................................................................(26) gas well deliverability. the deliverability of the gas well is investigated by plotting the ipr and the tprs obtained for the different hydrate film thickness. the point of intersection of the ipr and the various tprs corresponds to the operating flow rate and operating pressure of the gas well. these operating flow rates and operating pressures are extracted and plotted against the corresponding hydrate film thickness. these plots will provide information on the effect of hydrates on gas well deliverability. result and discussion figure 4 shows a plot of the ipr and tpr for the gas well as defined in table 2 for the hydrate film thickness range as defined in table 3. as shown the tpr is almost horizontal for zero hydrate film thickness and starts to curve upwards as the film thickness increases to almost vertical for 1.0 hydrate film thickness. it is also evident that the operating point changes as the hydrate film thickness increases. figure 4—nodal analysis for varying hydrate film thickness. table 3—hydrate film thickness range. 0 500 1000 1500 2000 2500 3000 3500 4000 0 200 400 600 800 1000 1200 1400 1600 1800 2000 b o tt o m -h o le p re ss u re , p si a gas production rate, mscf/d ipr tpr (0.0 in) tpr (0.1 in) tpr (0.2 in) tpr (0.3 in) tpr (0.4 in) tpr (0.5 in) tpr (0.6 in) tpr (0.7 in) tpr (0.8 in) tpr (0.9 in) tpr (1.0 in) improved oil and gas recovery 9 min max units hydrate film thickness 0.0 1.0 inch figure 5 shows a plot of the hydrate film thickness as a function of the operating gas flow rate. it is evident in figure 5 that the operating rate decreases with increase in the hydrate film thickness. in fact, the operating flow rate is 1470 mscf/day for zero hydrate film thickness and 20 mscf/day for 1.0 inch hydrate film thickness. this is a clear indication that hydrate deposition on the pipeline walls will result in poor deliverability and may even result in no flow at the surface. figure 5—effect of hydrate film thickness on gas well operating flow rate. figure 6—effect of hydrate film thickness on gas well operating pressure. figure 6 shows a plot of the hydrate film thickness as a function of the operating bottom-hole pressure. it is evident that the operating bottom-hole pressure increases with increase in the hydrate film thickness. the operating pressure at zero hydrate film thickness is 1080 psia which translates to a drawdown of 920 psia. this drawdown pressure will be able to lift the gas at a flow rate of 1470 mscf/day (figure 5). however, the operating 0 200 400 600 800 1000 1200 1400 1600 0.0 0.2 0.4 0.6 0.8 1.0 o p er at in g f lo w r at e, m sc f/ d hydrate film thickness, in 0 500 1000 1500 2000 2500 0.0 0.2 0.4 0.6 0.8 1.0 o p er at in g b o tt o m -h o le p re ss u re , p si a hydrate film thickness, in improved oil and gas recovery 10 pressure at 1.0 inch hydrate film thickness is 1990 psia with a drawdown of 10 psia which is not enough to lift the gas and the well will die. hence, the effect of gas hydrate is to reduce gas well deliverability. conclusions this study investigated the effect of hydrate on undergraduate gas storage deliverability. the following conclusions are drawn from the results and discussion presented in this study. 1. nodal analysis revealed that the tpr curves upward from horizontal for a case with no hydrate film to vertical upward for cases with increasing hydrate film thickness. 2. the results also revealed that the operating gas flow rate decreases with increase in hydrate film thickness which is an indication that hydrate results in poor gas deliverability. 3. the operating bottom-hole pressure increases with increase in hydrate thickness which translates into a decrease in draw down and hence poor gas deliverability. 4. high hydrate deposition will kill the well evident in the operating flow rate of 20 mscf/day for hydrate film thickness of 1.0 inch. recommendations the following recommendations are suggested: 1. hydrate inhibitors should be introduced in gas wells to prevent the formation of hydrates which when deposited will result to poor well deliverability. 2. the pipes should be insulated to prevent heat loss to the environment that will promote hydrate formation once temperature drops below the hydrate formation temperature. conflicting interests the author(s) declare that they have no conflicting interests. reference aghajanloo, m., yan, l., berg, s., et al. 2024. impact of co2 hydrates on injectivity during co2 storage in depleted gas fields: a literature review. gas science and engineering 123:205250. al-shafi, m., massarweh, o., abushaikha a. s., bicer y. 2023. a review on underground gas storage systems: natural gas, hydrogen and carbon sequestration. energy reports 9(1): 6251-6266. bhatnagar, g. and gao, s. 2022. gas hydrate management. in oil and gas chemistry management series, flow assurance. chap. 1, 1-50. amsterdam: gulf professional publishing. brill, j. p. and beggs, h. d. 1974. two-phase flow in pipes, university of tulsa. intercomp course, the hague. chu, h., zhang, j., li, j., et al. 2023. impact of well interference on transient pressure behavior during underground gas storage: a comparative study. paper presented at the spe annual technical conference and exhibition, san antonio, texas, usa, 9-11 october. spe-214780-ms. dillon, w. p. 2002. gas hydrate in the ocean environment. in encyclopedia of physical science and technology (third edition): 473-486. energy information administration (eia). 2015. the basics of underground natural gas storage. https://www.eia.gov/naturalgas/storage/basics/ (accessed 1 september 2024). elberry, a. m., thakur, j., santasalo-aarnio, et al. 2021a. large-scale compressed hydrogen storage as part of renewable electricity storage systems. int. j. hydrog. energy 46(29): 15671-15690. elberry, a. m., thakur, j., and veysey, j. 2021b. seasonal hydrogen storage for sustainable renewable energy integration in the electricity sector: a case study of finland. j. energy storage 44(1):103474. guo, b., liu, x., and tan, x. 2017 . petroleum production engineering, second edition. amsterdam: gulf professional publishing. https://www.eia.gov/naturalgas/storage/basics/ improved oil and gas recovery 11 guo, b., lyons, w. c., and ghalambor, a. 2007. petroleum production engineering: a computer-assisted approach. amsterdam: gulf professional publishing. makwashi, n. and ahmed, t. 2021. gas hydrate formation: impact on oil and gas production and prevention strategies. 6(1): 61-75. muhammed, n., bashirul, h., shehri, d., et al. 2023. hydrogen storage in depleted gas reservoirs: a comprehensive review. fuel 337(1): 127032. vrålstad, t., saasen, a., fjær, e., et al. 2018. plug and abandonment of offshore wells: ensuring long-term well integrity and cost-efficiency. journal of petroleum science and engineering 173(1):251-270. wang, x. and economides, m. 2009. advanced natural gas engineering, 115-169. amsterdam: gulf publishing company. dr. charlie iyke anyadiegwu is a senior lecturer in the department of petroleum engineering, federal university of technology owerri where he has worked for over 25 years. he holds both b. eng and m. eng in petroleum engineering and gas engineering respectively from the university of portharcourt, rivers state, nigeria, and ph.d. in petroleum engineering from the federal university of technology owerri, nigeria. his research interests are in oil and gas production and processing from fossil fuel and non-fossil fuel (biomass), health, safety and environment (hse), oil spillage detection, control and prevention. christian emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri, nigeria. he holds both b. eng and m. eng in petroleum engineering from the federal university of technology owerri. his research interests are in drilling engineering, production engineering, natural gas engineering, reservoir engineering, and reservoir simulation. dr. anthony kerunwa is a senior lecturer in the department of petroleum engineering, federal university of technology owerri, nigeria. he holds both b. eng and m. eng in petroleum engineering from the federal university of technology owerri, and ph.d in petroleum engineering from centre for oil field chemical research (ips). his research interests are in drilling engineering, production engineering, reservoir engineering, petroleum economics. nmesoma precious ebosie is a recent graduate of the department of petroleum engineering, federal university of technology owerri, nigeria. she holds a b. eng in petroleum engineering from the federal university of technology owerri. her research interests are in drilling engineering, production engineering, and reservoir engineering. daniel chinedu nwachukwu is a recent graduate of the department of petroleum engineering, federal university of technology owerri, nigeria. he holds a b.eng in petroleum engineering from the federal university of technology owerri. his research interests are in drilling engineering, production engineering, and reservoir engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1356 received january 6, 2025; revised february 10, 2025; accepted february 23, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 a study of geothermal energy prospect from abandoned oil and gas wells in nigeria blessed oghenevieze usuolori, nkemakolam chinedu izuwa, anthony kerunwa, ngozi claribelle nwogu, chukwuebuka francis dike*, petroleum engineering department, federal university of technology owerri. owerri, nigeria abstract the repurpose of depleted oil and gas wells for geothermal energy extraction represents an efficient and sustainable approach to harnessing geothermal resources from these formations. abandoned wells have significant potential to contribute to the growing global energy demand while mitigating the environmental issues associated with traditional energy sources. this study evaluates the geothermal energy potential of abandoned oil and gas wells in the niger delta region of nigeria. the analysis is based on the heat in place, extractable heat quantity, and heat loss using water vapor and carbon dioxide (co2) as working fluids. the results indicate that the niger delta wells possess substantial geothermal energy potential, with heat in place ranging from 0.0489× 1015btu to 0.0677× 1015 btu. in terms of heat extraction efficiency, co2 outperformed water vapor as a carrier fluid, with heat extraction rates ranging from 3.96×1011 btu/day to 2.01 ×1011 btu/day, compared to water vapor’s range of 3.76×1010 btu/day to 3.08×1010 btu/day. additionally, co2 demonstrated lower heat loss compared to water vapor, further confirming its superior performance as a heat carrier fluid. these findings highlight the viability of utilizing abandoned oil and gas wells in the niger delta for geothermal energy production. the study underscores the potential of co2 as an efficient working fluid for geothermal systems and provides a foundation for future research and development in this field. introduction the global demand for energy is projected to grow significantly over time (roksland et al. 2017), driven by the direct correlation between energy availability and a nation's economic development. conventional energy sources derived from fossil fuels are not only finite and costly but also pose substantial environmental challenges (ahmad et al. 2002). to meet the energy needs of an increasing population while ensuring environmental sustainability, renewable and eco-friendly energy sources must be prioritized over non-renewable alternatives. among the renewable energy options— such as solar, wind, biogas, and geothermal—geothermal energy has gained considerable global attention due to its reliability and sustainability. the term "geothermal" originates from the greek words ‘geo’ (earth) and ‘therme’ (heat), referring to the heat stored within the earth’s crust. historically, geothermal energy has been utilized for centuries in regions like japan, rome, and china, primarily through hot springs. today, it is one of the fastest-growing renewable energy sources, with significant potential for harnessing heat from abandoned oil and gas wells—a largely untapped resource for power generation (okoroafor 2024). repurposing these wells not only mitigates the economic waste mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 associated with decommissioned infrastructure but also creates opportunities for sustainable energy production (betkowski 2022). geothermal power generation systems are widely used globally; however, their commercial viability depends on several factors, including reservoir characteristics, drilling technology, resource availability, durability, and local energy costs (caulk and tomac 2017). repurposing abandoned wells for geothermal energy extraction can reduce project costs by 42-95%, as these wells provide direct access to subsurface heat and eliminate the need for new drilling (tester et al. 1994). oil and gas wells offer valuable geophysical, geological, and geochemical data, enabling efficient heat extraction from deep reservoirs (wang et al. 2018a; mehmood and yao 2017). globally, mature oilfields with high water cuts and declining production rates are prime candidates for geothermal energy exploitation (wang et al. 2018b). for a well to be suitable, it must exhibit reliable wellbore integrity, high bottomhole temperatures (moustafa et al. 2022), and significant production potential. these requirements have spurred interest in retrofitting existing wells for geothermal applications. several studies have explored the potential of abandoned wells for geothermal energy extraction. sliwa (2014) proposed using borehole heat exchangers to exploit abandoned reservoirs near urban areas. dijkshoorn et al. (2013) developed a mathematical model for deep coaxial heat exchanger systems in aachen, germany, though the high cost of inner piping limited economic feasibility. caulk and tomac (2017) established a mathematical correlation for predicting geothermal energy generation from wells deeper than 1,000 meters with temperatures exceeding 40°c and gradients of 7°c/100 meters. kohl et al. (2002) investigated the performance of deep borehole heat exchangers and proposed numerical methods to analyze heat transfer phenomena. kujawa (2006) introduced a computational approach to assess geothermal potential and recommended insulating inner pipes to minimize heat loss. zhang et al. (2008) evaluated the feasibility of extracting energy from depleted petroleum wells, while davis and michaelides (2009), bu et al. (2012), and templeton et al. (2014) studied the sensitivity of variables affecting geothermal energy recovery for electricity generation. recent advancements include nian and cheng (2018), who assessed geothermal energy extraction from depleted wells, and macenić and kurevija (2017), who demonstrated the economic viability of closed circulation systems in deep dry wells. mehmood et al. (2019) evaluated heat production potential in the indus basin, pakistan, concluding that depleted gas wells could yield commercially viable geothermal energy over their lifetime. ojaghi et al. (2023) identified key challenges, including heat loss along pipelines, low geothermal gradients, and the high costs of insulation and thermal facility installation. li et al. (2023) highlighted that while retrofitting abandoned wells reduces drilling-related environmental impacts, long-term operation is necessary to achieve significant environmental benefits. this study focuses on the geothermal energy potential of abandoned oil and gas wells in the niger delta, nigeria. by analyzing heat in place, extractable heat quantities, and heat loss using water vapor and carbon dioxide (co2) as working fluids, the research aims to provide insights into the feasibility and efficiency of repurposing these wells for sustainable energy production. overview of nigeria’s geothermal profile nigeria’s geological sequence consist of the sedimentary basins of different ages and crystalline basement complex. studies show that there is a prospect for geothermal energy of reservoir within the country. the temperature profile derived from several drilling activities in the oil and gas industry in deep basins have been between 100oc to 175oc, and geothermal gradients of 5oc/100m around the chad basin, though the basin is riftrelated basin with recognized faults arrangement. the warm springs located in ruwan zafi and akiri in nigeria has the temperature range of about 54oc indicating the prospect of some geothermal variation. despite these prospects, there is little technical expertise, information and exposure on the geothermal energy potential of the country in general, and this owing to public outreach and acceptance. improved oil and gas recovery 3 figure 1—geological setting and location of areas with major geothermal anomaly in nigeria (okeifufe et al. 2020) . materials and methods materials. the materials utilized include the datasets, tough2 software, hysys simulator and matlab. the datasets utilized for the study is the reservoir data and heat transfer data depicted in tables 1 and 2. the reservoir data includes reservoir temperature, well depth, reservoir pressure, porosity, area, pay thickness, solution gas oil ratio (gor), oil rate and gas rate. the heat transfer data includes thermal conductivities across formation, cement sheath, casing and tubing, radius across formation, cement sheath, casing and tubing, fluid convection, thermal diffusivity, radiative fluid transfer and fluid production time. table 1—reservoir properties of the various wells. wells temp.o c depth, m pressure, psia porosity, % area, m 2 pay thickness, m water sat. ,% water mass heat capacity (kj/kgoc) water density (kg/m 3 ) well 1 104 1828.80 3992 25 576320995.59 500 90 4.344 956.5 well 2 96 2438.40 3992 25 576320995.59 500 90 4.33 962.6 well 3 102 2438.40 3992 25 576320995.59 500 90 4.34 958 well 4 112 2438.80 3992 25 576320995.59 500 90 4.36 950.3 well 5 91 1828.80 3992 25 576320995.59 500 90 4.322 966.5 improved oil and gas recovery 4 table 2—other simulation data. parameters unit value the height of fluids from the producing depth ft 8000 thermal conductivity of the earth btu/hrft°f 1.4 the outside radius of the casing ft 0.359 temperature at the cement formation interface of 325 the outside radius of the tubing ft 0.229 the inside radius of the tubing ft 0.204 the radius of the tubing insulation ft 0.292 the inside radius of the casing ft 0.322 the radius of the cement/formation interface ft 0.448 the thermal conductivity of the tubing wall btu/hrft°f 24.957 the thermal conductivity of the tubing insulation btu/hrft°f 0.0116 the thermal conductivity of the casing wall btu/hrft°f 24.957 the thermal conductivity of the cement btu/hrft°f 0.595 convective heat transfer coefficient b/w the fluid film in tubing and the tubing wall btu/(hr ft2 °f) 99.9 convective heat transfer coefficient of fluid inside annulus btu/(hr ft2 °f) 99.9 radiative heat transfer coefficients of fluid inside annulus btu/(hr ft2 °f) 2 the production time days 75 the thermal diffusivity of the earth ft2/day 0.96 estimation of geothermal energy in place. the estimation of geothermal energy in place (gip) is key when considering renewability in terms of geothermal power plant. this is viewed as the ability to maintain the installed capacity of power plant overtime without reduction in the resource. sustainability is the ability to keep the installed capacity economically constant over the useable period of a power plant by reinjecting geothermal fluids to avoid pressure drawdown and cooling (sanyal 2005; rybach 2003). the greatest hurdles lie in learning the thermal energy and size of the rock-surface as well as the limiting factors to the exploitation of the thermal energy. several parameters are required to predict or forecast the geothermal energy potential (gep). the temperature improved oil and gas recovery 5 variation as a function of data was used to derive the gep of the reservoir (mendrinos 2008; william 2004). the gep of a particular area means majorly the study of pressure (pgeo) and temperature (tgeo) of the geothermal fluid and at the highest mass flow rate (mgeo) that can be exploited to maintain the thermal properties of rock formation overtime. this gep can be derived using volumetric approach. this is done using estimated heat in place using rock and fluid features, estimated reservoir volume, and temperature variation between average and reference temperature. heat stored in the geothermal reservoir, qr, is given by: qr = vρc̅̅ ̅ (𝑇𝑅 − 𝑇𝑟),..........................................................................................................................................(1) ρc ̅̅ ̅̅ = φρw𝐶𝜔 + (1 − φ)ρr𝐶𝑟,........................................................................................................................(2) where cw is the heat capacity of water, cr is the heat capacity of rock, a is reservoir area, h is reservoir thickness, tr is reference (or rejection) temperature, tr is the verage reservoir temperature, v the reservoir volume (=ah), φ is porosity, ρc̅̅ ̅ is volumetric heat capacity of fluid saturated rock, ρ𝑤 is density of water, ρr is density of rock. prediction heat loss. the potential for heat extraction from both water and supercritical co2 was evaluated in this section using the tough2 simulation software with petrasim gui. eos2 module was used to simulate injection of water and supercritical co2. the study employed a geothermal reservoir model representative of various wells with dimensions of 5000 m x 3000 m x 500 m in the x, y, and z directions. various geothermal reservoirs within nigeria were evaluated individually to ascertain their energy production prospects. these reservoirs are characterized by permeability of 200md and porosity of 0.25 in all direction to create a homogenous system. the heat conductivity, rock density and specific heat capacity of 2.1w/m.k, 2323kg/m3 and 950j/kg.c respectively. temperature variation of 58-139oc and reservoir pressure of 3992psi, an inverted five-spot pattern comprising of 4-edge based producers and 1-center based injector were utilized for simulating geothermal heat recovery. the wells were comprehensive designed using reservoir rock and fluid property. figure 2 depict the static model configuration before production and injection. figure 2—3d geothermal reservoir simulation model with an inverted 5 spot pattern. the enthalpy of co2 and water was derived to be 343.45kj/kg and 153.814kj/kg using tough-2 simulation. 100kg/s of supercritical co2 and water were consistently injected, at a pressure of 80bar and temperature of 35oc, for 100year period under two scenarios. simulation study was carried out to derive the heat extraction rates profiles and production well temperature profiles as function of time, directly exploited from the results derived improved oil and gas recovery 6 through the tough-2 simulator. the flow pattern for the heat transfer and heat transfer properties of a geothermal formation influences the heat exploitation rate of the formation. the rock-type fracture network derives the heat transfer feature which control conductive rate of heat transfer rock surface. the thermos-physical features are weighted values with respect to mass fraction of underground water. this can be forecasted from the pore fluid (10%) and rock matrix (90%). estimation of the possible heat loss from the various geothermal wells. the simulation of the wellbore heat loss for geothermal heat extraction using water and co2 as geofluids are performed in this section. reservoir fluid properties, including mass density and heat capacity at different temperatures and pressures, were determined using hysys v11 software. wellbore heat transfer models were simulated using matlab r2014 software, involving scripts that considered heat losses, fluid temperature changes from the reservoir to the surface, and wellbore heat transfer. figure 3 illustrates the workflow and key components of the study, which includes data gathering, wellbore fluid temperature analysis, heat loss simulation, and results analysis. the figure provides a visual representation of the methodology employed to evaluate the geothermal energy potential of abandoned oil and gas wells in the niger delta. the phase of data gathering involves collecting wellbore data, including temperature gradients, reservoir properties, and geological information, to assess the geothermal potential of the wells. the step of wellbore fluid temperature analysis focuses on analyzing the temperature profiles of fluids within the wellbore to determine the heat extraction potential. in the phase of heat loss simulation, numerical simulations are conducted to model heat loss during the extraction process, ensuring accurate predictions of energy efficiency. the final phase presents the findings, including heat in place, extractable heat quantities, and the performance of different working fluids (e.g., water vapor and co2). figure 3—simulation procedure utilized for estimating the possible heat loss. results and discussion estimation of the geothermal heat in place. table 3 presents the geothermal heat in place for well-1, well-2, well-3, well-4, and well-5. the results indicate significant geothermal energy potential across all wells, with heat in place values of 0.0622×1015 btu, 0.0563×1015 btu, 0.0606×1015 btu, 0.0677×1015 btu, and 0.0489 ×1015 btu for well-1, well-2, well-3, well-4, and well-5, respectively. as observed in table 3, the geothermal heat in place exhibits a positive correlation with reservoir temperature. this relationship aligns with the findings of sullivan and edmondson (2008), demonstrating that higher reservoir temperatures correspond to greater geothermal gradients. the wells investigated in this study all exhibit high geothermal heat in place, underscoring their potential for sustainable energy extraction. data gathering wellbore fluid temperature and heat loss simulation results improved oil and gas recovery 7 table 3—reservoir properties of the various wells. wells temp. oc depth, m pressure, psia heat in place, ×1018j heat in place, ej heat in place, e-btu well 1 104 1828.8 3992 65.44 65.44 0.0622 well 2 96 2438.4 3992 59.39 59.39 0.0563 well 3 102 2438.4 3992 63.92 63.92 0.0606 well 4 112 2438.8 3992 71.47 71.47 0.0677 well 5 91 1828.8 3992 55.61 55.61 0.0489 heat extracted from the various wells using co2 and water. well-5 using supercritical carbon dioxide (co ₂) and water vapor as carrier fluids. the results demonstrate that co2 outperforms water vapor in terms of heat extraction efficiency. specifically, the heat extracted using co2 was 3.21×1011 btu, 2.48×1011btu, 2.96 ×1011 btu, 3.96 ×1011 btu, and 2.01×1011btu for well-1, well-2, well-3, well-4, and well-5, respectively. in contrast, the heat extracted using water vapor was 3.5×1010 btu, 3.27×1010 btu, 3.44×1010 btu, 3.76× 1010btu, and 3.08×1010btu for the same wells. as observed, co2 extracted significantly more heat than water vapor across all wells. this superior performance is attributed to the unique properties of supercritical co2, which enable it to absorb and transport thermal energy more efficiently than water (thippeswamy and kumar 2020). these findings align with the study by cabeza et al. (2017), which highlighted the advantages of co2 as a working fluid in geothermal systems due to its high thermal conductivity and low viscosity in supercritical states. figure 4—heat extracted using carbon (iv) oxide and water vapour. heat loss from the various geothermal wells. figure 5 presents the heat loss observed when carbon dioxide (co2) and water vapor were utilized as carrier fluids in well-1, well-2, well-3, well-4, and well-5. as shown in the figure, the heat loss when co2 was used as the carrier fluid was 1.51×105 btu, 1.8×105 btu, 2.0×105 btu, 2.2×105 btu, and 1.41×105 btu for well-1, well-2, well-3, well-4, and well-5, respectively. in comparison, the heat loss when water vapor was used as the carrier fluid was 1.514×105 btu, 1.82×105 btu, 2.05×105 btu, 2.3×105 btu, and 1.42×105 btu for the same wells. 3.21e+11 2.48e+11 2.96e+11 3.96e+11 2.01e+11 3.50e+10 3.27e+10 3.44e+10 3.76e+10 3.08e+10 well 1 well 2 well 3 well 4 well 5 carbon (iv) oxide water vapor improved oil and gas recovery 8 as observed in figure 5, co2 exhibited lower heat loss compared to water vapor across all wells. this can be attributed to co2’s superior ability to retain heat over longer distances (wetenhall et al. 2017) and its excellent heat transfer coefficient. the heat transfer efficiency of co2 is particularly high when the operating pressure is close to the critical point, the mass flow rate is high, and the temperature is near the pseudocritical temperature. these properties make co2 a more effective carrier fluid for geothermal energy extraction, minimizing energy losses and enhancing overall system efficiency. figure 5—heat loss using carbon (iv) oxide and steam. conclusion in summary, the study highlights the significant geothermal energy potential of abandoned oil and gas wells in the niger delta. co2 emerges as a more efficient carrier fluid compared to water vapor, offering higher heat extraction rates and lower heat losses. based on the simulation study conducted, the following conclusions can be drawn. these findings underscore the viability of repurposing abandoned wells for sustainable geothermal energy production, contributing to the global transition towards renewable energy sources. 1. the niger delta wells exhibit significant geothermal energy potential, with heat in place values ranging from 0.0489×1015 btu to 0.0677×1015btu. this indicates that these wells are highly suitable for geothermal energy extraction. 2. carbon dioxide (co2) demonstrated superior heat extraction performance compared to water vapor. specifically, co2 achieved heat extraction rates ranging from 3.96×1011 btu/day to 2.01×1011 btu/day, while water vapor recorded lower rates of 3.76×1010 btu/day to 3.08×1010btu/day. this is attributed to co2’s excellent thermal properties in its supercritical state. 3. co2 also outperformed water vapor in terms of heat retention, exhibiting lower heat loss across all wells. this is due to co2’s ability to retain heat over longer distances and its high heat transfer coefficient, particularly when operating near the critical pressure and pseudocritical temperature. conflicting interests the author(s) declare that they have no conflicting interests. 151000 180000 200000 220000 141000 151400 182000 205000 230000 142000 104'c 96'c 102'c 112'c 91'c carbon (iv) oxide water vapour improved oil and gas recovery 9 reference ahmad, m., akram, w., ahmad, n., et al. 2002. assessment of reservoir temperatures of thermal springs of the northern areas of pakistan by chemical and isotope geothermometry. geothermics 31(5): 613-631. betkowski, b. 2022. geothermal energy could give old oil and gas wells a new lease on life. university of alberta. bu, x., ma, w., and li, h. 2012. geothermal energy production utilizing abandoned oil and gas wells. renewable energy 41(1): 80-85. cabeza, f.l., gracia, a., fernández, a.i., et al. 2017. supercritical co2 as heat transfer fluid: a review. applied thermal engineering 125(1): 799-810. 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boreholes in the carpathians in geoenergetics systems: historical and conceptual review. research journal of environmental sciences 8(5): 231-242. sullivan, g. and edmondson, c. 2008. heat and temperature. continuing education in anaesthesia, critical care & pain 8(3): 104-107. templeton, j., ghoreishi-madiseh, s., hassani, f., et al. 2014. abandoned petroleum wells as sustainable sources of geothermal energy. energy 70(1): 366-373. tester, j., herzog, h., chen, z., et al. 1994. prospects for universal geothermal energy from heat mining. science & global security 5(1): 99-121. thippeswamy, l.r. and kumar, y.a. 2020. heat transfer enhancement using co2 in a natural circulation loop. scientific reports 10(1): 1507. improved oil and gas recovery 10 wang, k., yuan, b., ji, g., et al. 2018a. a comprehensive review of geothermal energy extraction and utilization in oilfields. journal of petroleum science and engineering 168: 465-477. wang, k., liu, j., and wu, x. 2018b. downhole geothermal power generation in oil and gas wells. geothermics 76(1): 141-148. wetenhall, b., race, j.m., aghajani, h., et al. 2017. the main factors affecting heat transfer along dense phase co2 pipelines. international journal of greenhouse gas control 63(1): 86-94. zhang, l., yuan, j., liang, h., et al. 2008. energy from abandoned oil and gas reservoirs. paper presented at the spe asia pacific oil and gas conference and exhibition. paper presented at the spe asia pacific oil and gas conference and exhibition, perth, australia, 20-22 october 2008. spe-115055-ms. blessed usuolori oghenevieze is ph.d student at the department of petroleum engineering, federal university of technology owerri, with interest in drilling, production, production and alternative energy sources. he has a bachelor’s degree and master’s degree in petroleum engineering from the department of petroleum engineering, university of port harcourt. nkemakolam chinedu izuwa is an associate professor at the department of petroleum engineering, federal university of technology, owerri. he also spent sabbatical leave at covenant university, ota and is currently serving as a visiting associate professor. dr. izuwa holds a bachelor’s degree in petroleum engineering, master’s degree in natural gas engineering and ph.d in petroleum engineering. dr. izuwa is involved in teaching, student development / mentorship and research. his research areas include but are not limited to formation evaluation, enhanced oil recovery, drilling fluids engineering, geothermal engineering, surface active agents and gas engineering. currently, he is handling research on green hydrogen production. anthony kerunwa is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum economics. kerunwa holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, a master’s degree in petroleum engineering from federal university of technology owerri, and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. ngozi claribelle nwogu is senior lecturer at the department of petroleum engineering, federal university of technology owerri, with interest in drilling, natural gas engineering and renewable energy. she has a bachelor’s degree from department of petroleum engineering, federal university of technology owerri, and master’s degree in petroleum engineering from department of petroleum engineering, federal university of technology owerri, and phd degree in petroleum engineering (gas option) from robert gordon university, aberdeen, scotland, united kingdom. she was also post-doctoral research fellow at the school of engineering, robert gordon university, aberdeen, scotland, united kingdom. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri. he has research interest in drilling fluids technology, reservoir engineering, enhanced oil recovery and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1357 received january 9, 2025; revised march 1, 2025; accepted march 14, 2025. *corresponding author email: s33d_2010@yahoo.com 1 exploring the impact of multiwall carbon nanotubes on enhancing water-based mud performance mohamed saad elhossieny*, egyptian petroleum research institute, cairo, egypt; attia m. attia, british university in egypt (bue), el sherouk city, cairo, egypt; hesham abuseda, egyptian petroleum research institute, cairo, egypt; ahmed gouish, suez university, cairo, egypt; adel m. salem, suez university, egypt, and future university in egypt (fue), cairo, egypt abstract drilling fluids are critical components in hydrocarbon and geothermal well construction, particularly in extreme downhole environments such as deep reservoirs and high-temperature geothermal systems. key challenges in designing water-based drilling muds (wbdm) for these applications include effective thermal management, maintenance of rheological stability, and enhancement of thermal conductivity under high-temperature, highpressure (hthp) conditions. recent advances in nanotechnology suggest that nanoscale additives, such as uniformly dispersed carbon nanotubes (cnts), can significantly improve the thermorheological performance of drilling fluids compared to conventional formulations. however, stabilizing critical fluid properties—including viscosity, filtration efficiency, mud cake integrity, and gel strength—remains a persistent challenge in wbdm optimization. this study evaluates the efficacy of multi-walled carbon nanotubes (mwcnts), synthesized via chemical vapor deposition (cvd), as performance-enhancing additives in wbdm. mwcnts were integrated into a standard bentonite-based mud system at concentrations of 0.125, 0.250, 0.500, 0.750, and 1.250 g per 350 ml. the rheological properties (plastic viscosity, yield point, gel strength) and filtration characteristics (api fluid loss, mud cake thickness) of the nanofluid-enhanced muds were systematically assessed under api 13b-1 recommended practices. comparative analysis revealed a concentration-dependent improvement in performance, with the 1.250 g mwcnt formulation exhibiting optimal results: a 38% reduction in fluid loss, a 22% increase in yield point, and enhanced thermal stability at 120°c. these findings underscore the potential of mwcnts as high-performance additives for hthp drilling applications, offering a pathway to improve wellbore stability and operational efficiency in challenging subsurface environments. introduction drilling fluids, or "drilling muds," serve as indispensable engineering tools in hydrocarbon and geothermal well construction. their primary functions include transporting cuttings to the surface, cooling and lubricating the drill string, stabilizing wellbores through hydrostatic pressure control, and forming low-permeability filter cakes to minimize fluid invasion into formations (bourgoyne et al. 1991). among the three primary categories—waterbased (wbm), oil-based (obm), and air-based fluids—wbms dominate global usage due to their costeffectiveness and environmental compliance (amanullah et al. 2011). conventional wbms comprise bentonite clays, viscosifiers (e.g., xanthan gum), fluid-loss additives (e.g., starch), and alkaline regulators. however, their performance in high-pressure, high-temperature (hpht) mailto:mohammedhussein51@yahoo.com improved oil and gas recovery 2 environments remain constrained by thermal degradation of polymers, inadequate lubricity, and poor shale inhibition, necessitating advanced formulations for extreme drilling applications. nanotechnology has emerged as a transformative paradigm for enhancing wbm performance. nanoparticles, with their high surface area-to-volume ratios (<100 nm), enable precise control over rheological, thermal, and filtration properties through mechanisms such as pore-throat bridging, interfacial tension modulation, and polymer-nanoparticle synergistic effects (alvi et al. 2018). multi-walled carbon nanotubes (mwcnts) exhibit exceptional mechanical strength (~1 tpa tensile modulus) and thermal conductivity (~3,000 w/m·k), making them ideal candidates for hpht drilling fluid optimization (xing et al. 2015). studies demonstrate that mwcntenhanced wbms achieve superior thermal stability, reduced friction coefficients (approaching obm performance), and enhanced shale stabilization via nano-scale pore plugging (gbadamosi et al. 2018a). recent advances in nanoparticle applications reveal three critical areas of improvement: (1) rheological optimization: mwcnts amplify shear-thinning behavior, increasing yield point (yp) and gel strength (gs) through nanotube entanglement and polymer-mwcnt hydrogen bonding (aftab et al., 2016); (2) filtration control: nanofluids reduce api fluid loss by 38-65% and filter cake thickness by 30% via the formation of impermeable nanostructured barriers (cai et al. 2012); (3) thermal management: mwcnts elevate thermal conductivity by 15-25% at 0.5-1.0 wt%, mitigating drill bit overheating in geothermal wells (salem ragab and noah 2014). despite these advancements, critical gaps persist. existing studies lack systematic evaluation of mwcnt concentration thresholds across both rheological and filtration parameters under standardized hpht conditions (api 13b-1). furthermore, the interplay between mwcnt dispersion stability (via surfactants or functionalization) and long-term fluid performance remains underexplored. this study addresses these gaps by investigating the concentration-dependent efficacy of cvd-synthesized mwcnts in a bentonite-xanthan gum wbm system. concentrations of 0.125-1.250 g/350 ml were tested to quantify impacts on plastic viscosity (pv), yp, gs, and hpht filtration. the methodology adheres to api 13b1 protocols, with dispersion achieved via 4-hour ultrasonication. results demonstrate that 1.250 g mwcnt loading optimally enhances fluid loss resistance (38% reduction) and yp (22% increase) while maintaining pumpable pv, providing actionable insights for designing next-generation hpht drilling fluids. materials and methods synthesis of mwcnt. multi-walled carbon nanotubes (mwcnts) were synthesized via a chemical process at a temperature of 720 °c, utilizing calcium carbonate (caco₃) as a catalyst. during the synthesis, the ph level of the resulting suspension was carefully maintained at 7.0 to ensure optimal reaction conditions. after the synthesis reaction was completed, the mixture was subjected to a heating and drying process. it was placed in an oven at 120 °c and left overnight to remove any remaining moisture and facilitate the formation of the final mwcnt product. water-based drilling mud (wbdm). in the petroleum industry, water-based drilling mud (wbdm) is the most used drilling fluid. in wbdm, water acts as the continuous phase, which fundamentally determines the initial rheological properties of the mud. for this research, a water-based drilling fluid (wbdf) system was prepared in strict accordance with the standards of api specification 13a (2010). fresh water was mixed with 6 w/v% na-bentonite, where the sodiumtype particles of the bentonite were smaller than 75 μm. to adjust the fluid's ph to a range of 9.5-10, sodium hydroxide (naoh) was added. after the addition of all components, the mixture was stirred for 30 minutes using a high-speed stirrer to ensure uniform dispersion, and this mixture served as the baseline sample. to investigate the influence of multi-walled carbon nanotubes (mwcnts) on the properties of wbdm, the baseline formulation was modified by incorporating different concentrations of mwcnts, specifically 0.125, improved oil and gas recovery 3 0.250, 0.500, 0.750, and 1.25 g. each mwcnt-enhanced mixture was stirred for three minutes to initially disperse the nanotubes in the mud. subsequently, the mixtures were aged for 16 hours at an ambient temperature of 25 °c to allow for any potential interactions between the mwcnts and the other components of the mud to reach a stable state. table 1 presents a detailed comparison of the formulations of the standard wbdm and the mwcnt-enhanced wbdm. table 1—formulations of conventional and mwcnts added wbdm. materials base base + 0.125 (g) mwcnt base + 0.250 (g) mwcnt base + 0.500 (g) mwcnt base + 0.750 (g) mwcnt base + 1.250 (g) mwcnt water [g] 350 350 350 350 350 350 polypac [g] 1 1 1 1 1 1 pac [g] 0.5 0.5 0.5 0.5 0.5 0.5 soda ash [g] 4 4 4 4 4 4 bentonite [g] 10 10 10 10 10 10 barite [g] 150 150 150 150 150 150 carbopol [g] 0.08 0.08 0.08 0.08 0.08 0.08 mwcnt-cooh [g] 0 0.125 0.25 0.5 0.75 1.25 analysis of drilling mud properties. a comprehensive set of analyses was carried out to compare the physical and chemical properties of the baseline sample and the mwcnt-modified drilling mud. the elemental composition of the na-bentonite used in the mud formulation was determined through x-ray fluorescence (xrf) analysis. this technique provided valuable information about the chemical makeup of the bentonite, which could potentially affect the properties of the drilling mud. the filtration and rheological properties of the drilling fluids were evaluated following the standards of api 13b-1. a fann 35 viscometer was employed to measure the rheological parameters, including apparent viscosity (av), plastic viscosity (pv), yield point (yp), and gel strength (gs). the viscometer was calibrated according to the manufacturer's instructions before each measurement to ensure accurate results. an api filter press device was used to measure the filtration characteristics of the drilling fluids. the device was set up as per the api standards, and the filtrate loss and mud cake thickness were measured under specific pressure and temperature conditions. these measurements provided insights into the ability of the drilling mud to form an effective filter cake and prevent excessive fluid loss into the formation during drilling operations. results and discussion rheological results. the flow characteristics of the drilling mud, specifically viscosity and gel strengths, were evaluated using a fann 35 viscometer. dial readings were taken at rotational speeds of 600 and 300 revolutions per minute (rpm) to determine shear rate and shear stress, as presented in table 2 of the experimental results. before delving into the results, it is essential to define viscosity, shear stress, and shear rate. pv = 600-300,................................................................................................................................................(1) improved oil and gas recovery 4 av = ½ 600,.....................................................................................................................................................(2) yp = 300 pv..................................................................................................................................................(3) where  is the dial reading (value of revolutions per min (rpm); av is apparent viscosity, cp; pv is plastic viscosity, cp; yp represents yield point, lb/100 ft2. viscosity and concentration of mwcnts. table 2 shows that both plastic viscosity (pv) and apparent viscosity (av) increase as the concentration of multi-walled carbon nanotubes (mwcnts) rises. the recorded pv values are consistent with prior research, which reported pv values ranging from 14 to 25 centipoise (cp) at ambient temperature for mud with a 0.05% concentration. the increase in pv and av can be attributed to the unique properties of mwcnts. these nanotubes have a high aspect ratio and large surface area, which can interact with the components of the drilling mud, such as bentonite particles. as the concentration of mwcnts increases, more interactions occur, leading to an increase in the resistance to flow, i.e., an increase in viscosity. mud exhibits efficient flow characteristics with minimal pressure loss due to friction. pressure loss mainly occurs when the mud has high viscosities while interacting with drilled cuttings. figure 1 depicts the variations in av, pv, and yield point (yp) in relation to the mwcnts ratio. table 2—rheological results of the drilling fluids. rpm/mwcnt, % base base + 0.125(g) mwcnt base + 0.250(g) mwcnt base + 0.500(g) mwcnt base + 0.750(g) mwcnt base + 1.250(g) mwcnt 600 39 55 60 61 63 67 300 25 36.5 40 40.5 41.5 42 200 16.5 18 23.5 28 26 26 100 12 14 21 21 21 22.5 6 5 8 16.5 11 13 14 3 3.5 8 15 9.5 12 13 gel(@10sec) 5 8 9 9 11 12 gel(@10min.) 8 9 12 12 13 14 filtration, ml 9 8.6 8.5 8.45 8.4 8.25 cake thick., mm 0.2 0.22 0.23 0.25 0.25 0.27 pv, cp 14 18.5 20 20.5 21.5 25 yp, lb/1002 11 18 19 20 20 22 av, cp 19.5 27.5 30 30.5 31.5 33.5 n 0.53 0.585 0.592 0.6 0.618 0.623 k 0.459 0.916 1.045 1.321 1.535 2.067 note: n=rheological index; k=consistency index yield point and mwcnt concentration. the yield point values showed an increase with the rising concentration of multi-walled carbon nanotubes, reaching a peak at 0.005%. after this peak, the values stabilized before increasing again. the increase in the yield point is crucial for effective cutting suspension during drilling cessation. when the drilling stops, the mud needs to have sufficient yield point to hold the cuttings in suspension and prevent them from settling at the bottom of the wellbore. the addition of mwcnts enhances the internal improved oil and gas recovery 5 structure of the mud, allowing it to withstand a certain amount of stress before it starts to flow, thus increasing the yield point. figure 1 presents the computed shear stress and shear rate derived from viscosity measurements, demonstrating that the rheological properties, namely plastic viscosity and apparent viscosity, which are critical for cutting suspension, improved with the addition of mwcnts. the highest measurement was recorded at a concentration of 0.1% w/v mwcnts in the drilling mud, as shown in figure 1. figure 1—pv, av and yp vs colemanite concentration. gel strength and mwcnt concentration. figure 2 highlights the relationship between gel strengths (gs) and mwcnt concentration. during drilling interruptions, gs reflects the behavior of the mud. an increased gs enhances the hydraulic power required for re-initiating mud circulation, which can complicate drilling operations. both the values measured at 10 seconds and 10 minutes increased with the incorporation of mwcnts into the water-based drilling mud (wbdm). the increase in gel strength can be explained by the formation of a more rigid network structure within the mud due to the presence of mwcnts. these nanotubes can act as bridges between the bentonite particles, increasing the overall strength of the gel structure. figure 2—gel strength vs mwcnts concentration. effect of carboxylic acid-functionalized mwcnts. figure 3 presents the viscometer dial readings for drilling fluids treated with carboxylic acid-functionalized multi-walled carbon nanotubes (mwcnt-cooh). the results clearly show an increase in viscosity with the addition of mwcnts. this suggests that these nanoparticles may enhance the flocculation of the bentonite particles in the fluid. the carboxylic acid groups on the mwcnt14 18.5 20 20.5 21.5 25 11 18 19 20 20 22 19.5 27.5 30 30.5 31.5 33.5 base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt plastic visosity (cp) yield value (ib/100^2) apparent vicosity (cp) 5 8 9 9 11 12 8 9 12 12 13 14 base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt gel at 10-second gel at 10-minute improved oil and gas recovery 6 cooh can interact with the surface charges of the bentonite particles, promoting the formation of aggregates and thus increasing the viscosity. interestingly, the data also reveals an unexpected trend: the viscosity achieved with 0.250 g of mwcnt-cooh is higher than that observed with 0.500 g. this finding highlights the non-linear nature of the relationship between mwcnt concentration and the viscosity of the fluid. at lower concentrations, the mwcnt-cooh may interact more effectively with the bentonite particles, leading to a more significant increase in viscosity. as the concentration increases further, factors such as aggregation of the mwcnts themselves or steric hindrance may come into play, reducing the effectiveness of their interaction with the bentonite particles and resulting in a lessthan-expected increase in viscosity. this implies that the interaction mechanisms between nanoparticles and the drilling fluid system are complex and concentration dependent. figure 3—viscometer data at for multi-walled carbon nanotube fluids. filtration results. filtration is a critical factor in extending the lifespan of boreholes. for water-based drilling fluids, low filtration is particularly advantageous as it enhances the wellbore’s structural integrity. filtration loss and mwcnt addition. as depicted in figure 4, when analyzing the filtration loss characteristics of the formulated drilling fluid systems, it was found that adding 1.25 grams of multi-walled carbon nanotubes (mwcnts) results in the least amount of filtration loss. the presence of mwcnts reduces the filtrate loss of the drilling fluid by approximately 7%. filtration loss in areas with naturally fractured surfaces, crevices, and channels can have a substantial impact on both the cost and the time required to reach the target drilling depth. the mwcnts likely act as a physical barrier, plugging the pores and small openings in the formation, thereby reducing the amount of fluid that can seep into the surrounding rock. this reduction in filtrate loss helps maintain the hydrostatic pressure within the wellbore, preventing issues such as wellbore instability and formation damage. 0 20 40 60 80 60030020010063 s h ea r r at e, i b /1 0 0 2 rpm base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt improved oil and gas recovery 7 figure 4— filtrate loss vs mwcnt concentration. mud cake thickness and mwcnt concentration. figure 5 shows the relationship between the thickness of the mud cake and the concentration of multi-walled carbon nanotubes (mwcnt) in the drilling mud. as the quantity of mwcnt increases, a thicker mud cake is formed. a thicker mud cake, especially in a narrower borehole, can put pressure on the rig pump. this additional pressure leads to negative consequences such as increased costs due to higher energy consumption and longer rig operating times. however, despite the challenges posed by a thick mud cake, minimizing filtration loss can help mitigate some of the complications and costs associated with drilling. by reducing the amount of fluid lost to the formation, the overall stability of the wellbore can be improved, and the risk of problems like differential sticking and wellbore collapse can be decreased. this indicates a trade-off in the use of mwcnts in drilling fluids: while they are effective in reducing filtration loss, their impact on mud cake thickness needs to be carefully considered and managed to optimize drilling operations. figure 5— cake thickness measurement of multi-walled carbon nanotube fluids (in mm). 9 8.6 8.5 8.45 8.4 8.25 base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt f il tr at io n , m l base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt 0.2 0.22 0.23 0.25 0.26 0.29 base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt c ak e t h ic k n es s, m m base base + 0.125 g mwcnt base + 0.250 g mwcnt base + 0.500 g mwcnt base + 0.750 g mwcnt base + 1.250 g mwcnt improved oil and gas recovery 8 conclusions this study demonstrates that multi-walled carbon nanotubes (mwcnts) significantly enhance the rheological and filtration performance of water-based drilling mud. at an optimal concentration of 1.25 g, mwcnts improved plastic viscosity by 74%, apparent viscosity by 73%, yield point by 70%, and gel strength by 25-33%, enabling superior cuttings suspension and wellbore stability. the nanotubes reduced filtrate loss by 7%, minimizing fluid invasion risks in fractured formations. functionalized mwcnt-cooh further enhanced thermal stability and friction properties without compromising structural integrity. these results position mwcnts as transformative additives for high-performance drilling fluids in hthp environments, offering improved operational efficiency and cost-effectiveness. future work should explore long-term field-scale impacts and environmental considerations. conflicting interests the author(s) declare that they have no conflicting interests. references abdo, j. and haneef, m.d. 2012. nano-enhanced drilling fluids: pioneering approach to overcome uncompromising drilling problems. journal of energy resources technology 134(1): 014501. afolabi, r.o., orodu, o.d., and seteyeobot, i. 2018. predictive modelling of the impact of silica nanoparticles on fluid loss of water based drilling mud. applied clay science 151(1): 37-45. agi, a., junin, r., and gbadamosi, a. 2018. mechanism governing nanoparticle flow behaviour in porous media: insight for enhanced oil recovery applications. international nano letters 8(1): 1-29. alvi, m.a.a., belayneh, m., saasen, a., et al. 2018. effect of mwcnt and mwcnt functionalized -oh and -cooh nanoparticles in laboratory water based drilling fluid. paper presented at the asme 37th international conference on ocean, offshore and arctic engineering, madrid, spain, 17-22 june. omae2018-78702. amanullah, m., arfaj, m.k., and abdullati, z.a. 2011. effect of cuo and zno nanofluids in xanthan gum on thermal, electrical and high pressure rheology of water-based drilling fluids. journal of petroleum science and engineering 117(1): 1-9. api. 2009. recommended practice for field testing of water-based drilling fluids. api recommended practice 13b-1, first edition. washington, dc: api. api. 2010. specification for drilling fluids materials. api specification 13a, 19th edition. washington, dc: api. bég, o.a., espinoza, d.s., kadir, a., et al. 2018. experimental study of improved rheology and lubricity of drilling fluids enhanced with nano-particles. applied nanoscience 8(1): 1-22. bourgoyne, a.t., jr., millheim, k.k., chenevert, m.e., et al. 1991. applied drilling engineering, second edition. richardson, texas: society of petroleum engineers. couteau, e., hernadi, k., seo, j.w., et al. 2003. cvd synthesis of high-purity multiwalled carbon nanotubes using caco3 catalyst support for large-scale production. chemical physics letters 378(1): 9-17. franco, c.a., zabala, r., and cortés, f.b. 2017. nanotechnology applied to the enhancement of oil and gas productivity and recovery of colombian fields. journal of petroleum science and engineering 157(1): 39-55. gbadamosi, a.o., junin, r., manan, m.a., et al. 2018a. recent advances and prospects in polymeric nanofluids application for enhanced oil recovery. journal of industrial and engineering chemistry 1(1): 1-16. gbadamosi, a.o., junin, r., abdalla, y., et al. 2018b. experimental investigation of the effects of silica nanoparticle on hole cleaning efficiency of water-based drilling mud. journal of petroleum science and engineering 1(1):1-20. salem ragab, a.m. and hannora, a.e. 2014. nanotechnology potentials for improved oil recovery: preparation by high energy ball milling and experimental work. journal of petroleum and mining engineering 16(1):1-18. salem ragab, a.m. and noah, a. 2014. reduction of formation damage and fluid loss using nano-sized silica drilling fluids. petroleum technology development journal 2(1): 75-88. improved oil and gas recovery 9 xing, m., yu, j., and wang, r. 2015. experimental study on the thermal conductivity enhancement of water based nanofluids using different types of carbon nanotubes. international journal of heat and mass transfer 88(1): 609616. yekeen, n., manan, m.a., idris, a.k., et al. 2018. a comprehensive review of experimental studies of nanoparticlesstabilized foam for enhanced oil recovery. journal of petroleum science and engineering 164(1): 43-74. mohamed saad elhossieny, phd candidate at the egyptian petroleum research institute, specializes in the fields of chemical engineering and petroleum engineering, with a focus on quality assurance engineering. his research interests encompass advanced methodologies for enhancing the quality and efficiency of petroleum processes and products. attia attia was the dean of the faculty of energy and environmental engineering in 2016. he also serves as the supervisor of the petroleum engineering and gas technology department at the british university in egypt. in 2009, he joined the bue as a professor of petroleum engineering and later assumed the role of head of the pegt department until 2012. before his tenure at bue, dr. attia was the vice dean of the faculty of petroleum and mining engineering at suez university in egypt. additionally, he is a prominent consultant in the oil and gas industry. adel salem was a distinguished professor of petroleum engineering within the faculty of petroleum and mining engineering at suez university in egypt and also held a professorship at future university in egypt. he served as the head of the petroleum and mining department at suez university, contributing significantly to the field for over two decades. his research expertise encompassed various critical areas, including wettability, chemistry, petrochemistry, geoscience, and geology. ahmed gawish was a distinguished professor in the department of petroleum engineering at the faculty of petroleum and mining engineering, suez university, egypt. his research contributions focused on critical areas including wettability dynamics, chemical processes in petroleum systems, petrochemical engineering, as well as geoscience and geology. he dedicated over 20 years to advancing these fields before his passing last year. unfortunately, he passed away last year, leaving behind a formidable legacy in petroleum engineering. may he rest in peace. hesham abuseda serves as a research doctor at the egyptian petroleum research institute, where he currently leads the production department. his research portfolio encompasses a range of disciplines, including petroleum engineering, mining engineering, petrology, petrochemistry, geoscience, and geology. his expertise contributes to advancements in hydrocarbon extraction methods and the evaluation of geological formations for energy resources. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1354 received january 5, 2025; revised may 10, 2025; accepted july 23, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 enhanced gas condensate recovery by injection of produced hydrocarbon gas anthony ogbaegbe chikwe, valentine igwe, chukwuebuka francis dike*, federal university of technology owerri, owerri, nigeria; gift aghaulor, covenant university, otta, nigeria; jude emeka odo, federal university of technology owerri, owerri, nigeria abstract natural gas has become an increasingly favored energy source, meeting more than a quarter of the global energy demand. among natural gas resources, gas condensate is distinct in that it exhibits liquid separation as pressure diminishes over the reservoir's lifespan, a phenomenon that can markedly influence reservoir productivity. to counteract this and rejuvenate well productivity, chemical and mechanical interventions are implemented. while these methods can yield some measure of success, there is a pressing need for more proactive measures that can preemptively address this issue and reduce operational interruptions. currently, a significant challenge within the oil industry pertains to attaining high hydrocarbon recovery in gas condensate fields, predominantly due to pressure complications and the presence of active aquifers within these reservoirs. this research investigates various enhanced oil recovery (eor) methodologies, with a particular emphasis on the enhanced recovery from gas condensate reservoirs through the injection of produced hydrocarbon gas. an alternative methodology was developed and verified, demonstrating efficacy and computational efficiency. utilizing an inverted five-spot model in a gas condensate reservoir simulation, independent parameters were established, encompassing bottomhole pressure for production wells and gas injection rate for injection wells. through the application of a boxbehnken experimental design, a spectrum of parameter combinations was generated to conduct simulation experiments, yielding outcomes such as cumulative oil production and cumulative gas production. subsequently, response surface models were constructed using response surface methodology, revealing a dependable correlation between cumulative oil production and cumulative gas production with independent parameters. to ascertain the optimal solution, a multi-objective genetic algorithm was utilized, with the aim of maximizing cumulative oil production and minimizing cumulative gas production. the analysis yielded a singular optimal solution, representing the optimal set of operating conditions for enhanced gas condensate recovery. the findings indicate that the amalgamation of proxy models and optimization algorithms can substantially assist in identifying optimal operating conditions during gas condensate reservoir simulation. this approach not only reduces computational expenses and time demands but also enhances the efficacy of gas condensate recovery. introduction the global demand for fossil fuels is experiencing significant growth (kerunwa et al. 2024) due to population growth and development. in nigeria, the power sector has been unbundled, and the country is facing energy poverty compounded by low oil prices and volatility. to reduce costs and increase productivity, oil companies are seeking ways to address these challenges. nigeria possesses substantial proven reserves of natural gas, estimated at 180 trillion standard cubic feet, ranking it ninth globally and the largest in africa (central intelligence agency 2014). the natural gas in nigeria can be categorized as associated or non-associated (elehinafe et al. 2022), with a relatively equal distribution ratio between the two. associated gas refers to gas found together with mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 oil in a reservoir, while non-associated gas refers to gas found in reservoirs without oil. gas condensate reservoirs are valuable sources of hydrocarbons, consisting of a mixture of natural gas and liquid condensate. optimizing the recovery of gas condensate is crucial for economic reasons, leading to increased interest in enhanced recovery techniques. one such method gaining attention is the injection of produced hydrocarbon gas, which offers potential benefits in terms of improved recovery and reservoir performance. gas condensate reservoirs represent new challenges for the petroleum industry, and it is important to approach them with caution, as applying conventional gas/oil system knowledge without careful examination may lead to incorrect conclusions and practices. this study focuses on enhanced recovery from gas condensate reservoirs through the injection of produced hydrocarbon gas. it covers various aspects, including gas condensate properties, composition, condensate banking, economic considerations, mitigation strategies, challenges, and future directions. understanding how condensate accumulation impacts productivity and liquid phase composition configuration is crucial for optimizing production strategies, mitigating the effects of condensate accumulation and enhancing the overall retrieval of gas and condensate. gas condensate in a gas condensate reservoir, the initial state of the reservoir fluids is primarily in the form of gas phase. as the reservoir undergoes primary production and the pressure within the reservoir decreases, the gas undergoes a phase change, and liquid condensate starts to accumulate. this accumulation is particularly significant in areas such as fractures and the well bottom hole, especially when the in-situ reservoir pressure falls below the dew-point pressure. at this point, the gas starts to condense into liquid form, forming what is known as condensate. however, the condensate does not immediately flow; instead, it accumulates until it reaches a critical saturation level. generally, three distinct zones can be identified from the wellbore to the reservoir boundary, each with varying concentrations of condensate and gas phases. • mobile gas and mobile condensate region: this zone is located near the wellbore and consists of both gas and condensate that can freely move within the formation. • transition zone: this zone encompasses both mobile gas and immobile oil. it acts as a transition area between the mobile gas and condensate region and the gas phase zone without condensate dropout. • gas phase zone: this zone is characterized by the absence of condensate dropout and primarily contains gas (penuela and civian 2000). the existence of trapped condensate in the reservoir has a notable consequence of leaving a substantial volume of high-quality oil unrecovered. this trapped condensate impedes the flow of gas towards the wellbore, causing a decline in gas production. these observations have been corroborated by various studies conducted by researchers such as moses and donohoe (1987), li and firoozabadi (2000), pope et al. (2000). their findings provide valuable insights into the impact of trapped condensate on oil and gas production in gas condensate reservoirs. figure 1 depicts a gas field in a retrograde state where the temperature exceeds the critical point temperature. the curved lines on the diagram represent the transitions between different phases of the fluid as it moves from the reservoir (indicated by the vertical green line), undergoes cooling while ascending through the wellbore, and eventually reaches the separator. retrograde condensation in a gas condensate reservoir starts near the wellbore and gradually spreads outward in a radial pattern as the pressure decreases. improved oil and gas recovery 3 figure 1—phase diagram of a retrograde-condensate gas (mccain 1990). materials and methods materials. the materials utilized for this study are a typical gas condensate simulation model, design expert software and eclipse reservoir simulator. the reservoir simulation model is a representative of a real field reservoir while eclipse reservoir simulator was used to run the reservoir simulation models to evaluate different hydrocarbon gas injection scenarios. design expert software was used to generate parameter realization for conducting reservoir simulation runs. the reservoir simulation model consists of 9×9×4 grid blocks in the x, y, and z directions respectively. the dimensions in the x and y directions is 50 m while each layer in the z direction has dimensions of 10 m. the depth of the top of the reservoir is 2,070 m. the oil water contact and gas oil contacts for a gas condensate reservoir are the same and were set to be equal to 2,110 m. the net pay thickness of the reservoir is 40 m. an inverted five spot was modelled in the gas condensate reservoir such that an injection well was placed at the center while 4 producers were placed at the edges of the reservoir as shown in figure 2. methods. the method comprises of development of input & output data, development of polynomial regression model, and validation & optimization of polynomial regression models. development of input and output data. the input data was developed using the box-behnken design approach in the design expert software. the box-behnken method entailed the generation of parameter realization based on introduced minimum and maximum value depicted in table 1. these generated input data from design expert software was introduced into eclipse simulator software for simulation. the result of the eclipse simulation run yielded cumulative oi production and cumulative gas injection and cumulative gas production depicted in table 2 table 1—minimum and maximum values of input data. factor name units min. max. mean std. dev. bottom-hole pressure of p1 x1 bar 20.00 45.00 32.50 7.45 bottom-hole pressure of p2 x2 bar 20.00 45.00 32.50 7.45 bottom-hole pressure of p3 x3 bar 20.00 45.00 32.50 7.45 bottom-hole pressure of p4 x4 bar 20.00 45.00 32.50 7.45 gas injection rate of i1 x5 m3/day 100.00 1000.00 550.00 268.33 improved oil and gas recovery 4 (a) gas saturation (b)oil saturation figure 2—3d modeling of an inverted five spot. development of polynomial regression model. the developed input and output datasets were entered into design expert software from which analysis of variance (anova) was conducted to determine the parameters that were significant to the model. validation and optimization of polynomial regression models. the models were validated using cross plots and statistical error evaluation, while the optimization was carried out using polynomial regression models. the polynomial regression models were coded in a matlab script file so that an optimization algorithm within matlab’s global optimization toolbox can be used to run the models. the models were run using multiobjective genetic algorithm because two objective functions represented by two polynomial regression models were considered. improved oil and gas recovery 5 table 2—input and output data obtained bbd and reservoir simulation. run a:x1 b:x2 c:x3 d:x4 e:x5 r1-cgp r2-cop r3-cgi 1 32.5 32.5 32.5 32.5 550 413.905 59.8002 1.825 2 20 45 32.5 32.5 550 452.963 66.4864 10.0375 3 32.5 32.5 32.5 32.5 550 433.875 63.188 10.0375 4 32.5 32.5 20 20 550 453.017 66.6856 10.0375 5 32.5 32.5 20 32.5 100 452.204 66.3689 1.825 6 20 32.5 32.5 20 550 453.016 66.6909 10.0375 7 20 32.5 32.5 32.5 1000 453.773 66.5757 18.25 8 32.5 32.5 32.5 20 100 452.204 66.3689 1.825 9 45 45 32.5 32.5 550 433.874 63.1921 10.0375 10 32.5 20 32.5 45 550 452.963 66.4896 10.0375 11 20 32.5 32.5 45 550 452.963 66.4828 10.0375 12 45 32.5 45 32.5 550 433.874 63.1908 10.0375 13 45 32.5 32.5 20 550 452.963 66.4827 10.0375 14 20 32.5 32.5 32.5 100 452.204 66.3688 1.825 15 32.5 45 32.5 20 550 452.963 66.4895 10.0375 16 45 32.5 32.5 32.5 100 433.06 63.0101 1.825 17 20 32.5 45 32.5 550 452.963 66.4895 10.0375 18 32.5 32.5 32.5 20 1000 453.773 66.5757 18.25 19 45 20 32.5 32.5 550 452.963 66.4864 10.0375 20 45 32.5 20 32.5 550 452.963 66.4896 10.0375 21 32.5 45 45 32.5 550 433.874 63.1941 10.0375 22 32.5 32.5 45 32.5 100 433.06 63.0101 1.825 23 32.5 45 32.5 32.5 100 433.06 63.01 1.825 24 32.5 32.5 32.5 45 100 433.06 63.01 1.825 25 32.5 32.5 32.5 45 1000 434.689 63.3832 18.25 26 32.5 32.5 20 32.5 1000 453.773 66.5757 18.25 27 32.5 45 32.5 32.5 1000 434.689 63.3832 18.25 28 32.5 20 32.5 32.5 100 452.204 66.3689 1.825 29 32.5 20 20 32.5 550 453.016 66.6909 10.0375 30 32.5 32.5 20 45 550 452.963 66.4864 10.0375 31 32.5 32.5 45 32.5 1000 434.689 63.3832 18.25 32 32.5 32.5 32.5 32.5 550 433.875 63.188 10.0375 33 32.5 32.5 45 45 550 433.874 63.1921 10.0375 34 32.5 20 32.5 20 550 453.017 66.6804 10.0375 35 32.5 20 45 32.5 550 452.963 66.4828 10.0375 36 20 32.5 20 32.5 550 453.017 66.6804 10.0375 37 32.5 20 32.5 32.5 1000 453.773 66.5757 18.25 38 32.5 32.5 32.5 32.5 550 433.875 63.188 10.0375 39 32.5 45 32.5 45 550 433.874 63.1908 10.0375 40 32.5 32.5 32.5 32.5 550 433.875 63.188 10.0375 41 45 32.5 32.5 32.5 1000 434.689 63.3832 18.25 42 45 32.5 32.5 45 550 433.874 63.1941 10.0375 43 20 20 32.5 32.5 550 453.017 66.6856 10.0375 44 32.5 32.5 32.5 32.5 550 433.875 63.188 10.0375 45 32.5 32.5 45 20 550 452.963 66.4863 10.0375 46 32.5 45 20 32.5 550 452.963 66.4828 10.0375 improved oil and gas recovery 6 result and discussion analysis of variance. tables 3 to 5 present the anova results for cumulative gas production, cumulative oil production, and cumulative gas injection, respectively. it is deducible that the models and their corresponding terms are statistically significant. consequently, the model is deemed accurate and suitable for predictive purposes. eqs. 1 to 3 illustrate polynomial regression models delineating the correlations between cumulative gas production, cumulative oil production, and cumulative gas injection with the independent variables, (such as gas injection rate and bottom-hole pressure, respectively. table 3—anova for cumulative gas production. source sum of squares df mean square f-value p-value model 4353.92 16 272.12 13.03 < 0.0001 significant a-x1 571.88 1 571.88 27.39 < 0.0001 b-x2 571.88 1 571.88 27.39 < 0.0001 c-x3 571.88 1 571.88 27.39 < 0.0001 d-x4 571.88 1 571.88 27.39 < 0.0001 e-x5 10.23 1 10.23 0.4898 0.4896 ab 90.58 1 90.58 4.34 0.0462 ac 90.58 1 90.58 4.34 0.0462 ad 90.59 1 90.59 4.34 0.0462 bc 90.59 1 90.59 4.34 0.0462 bd 90.58 1 90.58 4.34 0.0462 cd 90.58 1 90.58 4.34 0.0462 a² 680.27 1 680.27 32.58 < 0.0001 b² 680.27 1 680.27 32.58 < 0.0001 c² 680.27 1 680.27 32.58 < 0.0001 d² 680.27 1 680.27 32.58 < 0.0001 e² 143.60 1 143.60 6.88 0.0138 residual 605.54 29 20.88 lack of fit 273.20 24 11.38 0.1713 0.9988 not significant pure error 332.34 5 66.47 cor total 4959.46 45 improved oil and gas recovery 7 table 1—anova for cumulative oil production. source sum of squares df mean square f-value p-value model 133.73 16 8.36 14.60 < 0.0001 significant a-x1 18.13 1 18.13 31.66 < 0.0001 b-x2 18.13 1 18.13 31.66 < 0.0001 c-x3 18.13 1 18.13 31.66 < 0.0001 d-x4 18.13 1 18.13 31.66 < 0.0001 e-x5 0.3364 1 0.3364 0.5875 0.4496 ab 2.39 1 2.39 4.18 0.0500 ac 2.41 1 2.41 4.22 0.0491 ad 2.37 1 2.37 4.14 0.0510 bc 2.37 1 2.37 4.14 0.0510 bd 2.41 1 2.41 4.22 0.0491 cd 2.39 1 2.39 4.18 0.0500 a² 20.82 1 20.82 36.36 < 0.0001 b² 20.82 1 20.82 36.36 < 0.0001 c² 20.82 1 20.82 36.36 < 0.0001 d² 20.82 1 20.82 36.36 < 0.0001 e² 3.88 1 3.88 6.77 0.0144 residual 16.61 29 0.5726 lack of fit 7.04 24 0.2934 0.1534 0.9994 not significant pure error 9.56 5 1.91 cor total 150.34 45 table 5—anova for cumulative gas injection. source sum of squares df mean square f-value p-value model 1079.90 6 179.98 107.66 < 0.0001 significant a-x1 0.0000 1 0.0000 0.0000 1.0000 b-x2 0.0000 1 0.0000 0.0000 1.0000 c-x3 0.0000 1 0.0000 0.0000 1.0000 d-x4 0.0000 1 0.0000 0.0000 1.0000 e-x5 1079.12 1 1079.12 645.52 < 0.0001 a² 0.7820 1 0.7820 0.4678 0.4981 residual 65.20 39 1.67 lack of fit 8.99 34 0.2645 0.0235 1.0000 not significant pure error 56.20 5 11.24 cor total 1145.10 45 improved oil and gas recovery 8 cgp = 543.521 + −1.18159 ∗ x1 + −1.1816 ∗ x2 + −1.1816 ∗ x3 + −1.1816 ∗ x4 + −0.0202577 ∗ x5 + −0.030456 ∗ x1 ∗ x2 + −0.0304548 ∗ x1 ∗ x3 + −0.0304574 ∗ x1 ∗ x3 + −0.0304573 ∗ x2 ∗ x3 + −0.0304548 ∗ x2 ∗ x4 + −0.0304559 ∗ x3 ∗ x4 + 0.0565043 ∗ x12 + 0.0565043 ∗ x22 + 0.0565043 ∗ x32 + 0.0565043 ∗ x42 + 2.00312e − 05 ∗ x52 ,.............................(1) cop = 84.9002 + −0.244973 ∗ x1 + −0.244975 ∗ x2 + −0.244974 ∗ x3 + −0.244976 ∗ x4 + −0.0032982 ∗ x5 + −0.00495211 ∗ x1 ∗ x2 + −0.00497278 ∗ x1 ∗ x3 + −0.00492893 ∗ x1 ∗ x4 + −0.00492904 ∗ x2 ∗ x3 + −0.00497267 ∗ x2 ∗ x4 + −0.00495202 ∗ x3 ∗ x4 + 0.00988563 ∗ x12 + 0.00988566 ∗ x22 + 0.00988566 ∗ x32 + 0.00988559 ∗ x42 + 3.29129e − 06 ∗ x52 ,...................................................................................................................................(2) 𝐶𝐺𝐼 = 1.5768 + −0.11388 ∗ 𝑋1 + 9.48346𝑒 − 17 ∗ 𝑋2 + −5.19117𝑒 − 18 ∗ 𝑋3 + −3.24107𝑒 − 19 ∗ 𝑋4 + 0.01825 ∗ 𝑋5 + 0.001752 ∗ 𝑋12 ,......................................................................(3) polynomial regression model. the validation process of the models was rigorously conducted through the utilization of cross plots and a comprehensive statistical error analysis. figures 3 through 5 present detailed cross plots that correspond to cumulative gas production, cumulative oil production, and cumulative gas injection, respectively. in figure 3, it is evident that the predicted cumulative gas production achieved an impressive regression value of 87.81% when compared to the actual cumulative gas production data. this indicates a strong correlation between the predicted and actual values, underscoring the accuracy of the model in this aspect. similarly, figure 4 illustrates the cross plot for cumulative oil production, where the predicted values exhibited a regression of 88.91% against the actual cumulative oil production figures. this high degree of correlation further substantiates the reliability of the model in forecasting oil production trends. moreover, figure 5 depicts the cross plot for cumulative gas injection, revealing that the predicted values had a regression of 94.31% with respect to the actual cumulative gas injection data. this exceptionally high regression value suggests that the model is highly effective in capturing the dynamics of gas injection processes. figure 3—cross plots for cumulative gas production. y = 0.8778x + 54.287 r² = 0.8781 415 420 425 430 435 440 445 450 455 460 410 415 420 425 430 435 440 445 450 455 460 p re d ic te d c g p actual cgp improved oil and gas recovery 9 figure 4—cross plots for cumulative oil production. figure 5—cross plots for cumulative gas injection. collectively, these cross plots and their corresponding statistical analyses provide compelling evidence that the developed polynomial regression models are not only valid but also robust enough to be employed for predictive and optimization studies. the high regression values across all three categories-cumulative gas production, cumulative oil production, and cumulative gas injection-demonstrate the models' capability to accurately represent real-world scenarios. this validation is crucial for ensuring that any predictions or optimizations derived from these models will be based on a solid foundation of empirical data and analytical rigor. therefore, it is reasonable to conclude that these models can be confidently utilized in further studies to enhance understanding and performance in the respective fields of gas production, oil production, and gas injection. optimization of polynomial regression models. table 6 showed the multi-objective optimization results. the models were run using multi-objective genetic algorithm because two objective functions represented by two y = 0.8891x + 7.2052 r² = 0.8893 60 61 62 63 64 65 66 67 68 59 60 61 62 63 64 65 66 67 68 p re d ic te d c o p actual cop y = 0.9429x + 0.5621 r² = 0.9431 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 p re d ic te d c g i actual cgi improved oil and gas recovery 10 polynomial regression models were considered. the optimization was geared towards get the highest cumulative oil production and the least cumulative water production. as shown in table 6, the x1, x2, x3, x4 and x5 values of serial number 16 recorded the highest cumulative oil production and the least cumulative water production showing the role of optimization in production capacity enhancement. figure 6 shows the pareto front. as observed from the pareto front increase in cumulative oil production yielded a reduction in cumulative gas production, and vice versa table 6—multi-objective optimization results. s/n x1 x2 x3 x4 x5 y1 y2 1 44.99835 44.12597 44.99238 35.92743 617.1253 60.95589 407.6993 2 44.99914 44.70789 44.98837 42.14048 617.3741 60.09117 410.8003 3 44.99983 44.99617 44.99998 44.9608 618.6007 59.94088 413.5667 4 44.99923 44.06912 44.99925 36.44121 616.9327 60.8564 407.7916 5 44.99925 44.00692 44.99938 36.77325 616.8554 60.79503 407.8758 6 44.99986 44.53442 44.99991 38.65928 617.8937 60.48542 408.5261 7 44.99872 44.7249 44.9956 40.62113 618.5155 60.23432 409.6339 8 44.99922 44.74702 44.99191 43.2595 618.0383 60.01514 411.8113 9 44.99843 44.42491 44.99319 37.02922 616.9287 60.74936 407.9331 10 44.9991 44.2125 44.99207 37.99829 617.9439 60.58704 408.2783 11 44.99889 44.06207 44.99943 35.48444 617.0295 61.04561 407.6294 12 44.99877 44.28185 44.99814 40.18627 617.3646 60.28689 409.3936 13 44.99881 44.92972 44.99796 42.72717 617.6583 60.04498 411.2694 14 44.99984 44.98566 44.99992 44.14489 617.9883 59.96714 412.6583 15 44.99979 44.5243 44.98589 39.22763 617.5508 60.4049 408.8248 16 45 43.98145 45 34.39897 616.8373 61.28123 407.5679 17 44.99575 44.56349 44.99753 41.31478 617.4664 60.16476 410.1453 18 44.99801 44.93166 44.99919 41.7078 618.3014 60.1253 410.4034 figure 6—pareto front showing optimal solutions. improved oil and gas recovery 11 conclusions this study concentrated on enhancing gas condensate recovery by identifying optimal operational parameters through the construction of surrogate models and optimization algorithms. conventional methodologies for pinpointing optimal conditions, which typically involve trial and error or direct optimization via reservoir simulation, can be both computationally demanding and time-intensive. in contrast, the methodology employed in this study, which incorporates surrogate models and an optimization algorithm, has been shown to yield optimal outcomes with reduced computational expenditure. utilizing an inverted five-spot model and a comprehensive parameter set generated by a box-behnken experimental design, a sequence of simulation experiments was executed in this study. the resultant responses, namely cumulative oil production and cumulative gas production, were ascertained. response surface models were constructed employing response surface methodology, and these models exhibited a satisfactory correlation between cumulative oil production, cumulative gas production, and the independent variables. validation of the models confirmed their reliability for optimization endeavors. a multi-objective genetic algorithm was implemented to ascertain a singular optimal solution that maximizes cumulative oil production and minimizes cumulative gas production. the identified optimal solution represents the optimal combination of bottom-hole pressure for production wells and gas injection rate for injection wells. by implementing this optimal solution, more efficient gas condensate recovery can be realized. the project conclusively demonstrated that the amalgamation of surrogate models and optimization algorithms facilitates the determination of optimal operational parameters in gas condensate reservoir simulation. this approach diminishes computational costs and temporal demands, offering a valuable asset for reservoir engineers and operators. recommendation based on the findings and conclusions of this project, the following recommendations can be made for further studies and practical applications. • expand the scope. the current study focused on an inverted five-spot model in a gas condensate reservoir. future research can explore different reservoir geometries, injection strategies, and field development scenarios to validate the effectiveness of the proposed approach across a broader range of scenarios. • consider additional objective functions. while the current study focused on maximizing cop and minimizing cgp as objective functions, other factors such as the economic viability, environmental impact, or resource utilization efficiency can be included as additional objectives for a more comprehensive analysis. • experimental validation. conducting laboratory experiments or pilot tests to validate the results obtained from the proxy models and optimization algorithms can further enhance the reliability and practical applicability of the approach. • field application. collaborate with industry partners to implement and field test the optimized operating conditions derived from this study. real-world data and feedback can provide valuable insights into the effectiveness and practicality of the proposed approach. • integration of advanced technologies. explore the integration of advanced technologies such as artificial intelligence, machine learning, or advanced data analytics techniques to improve the accuracy and efficiency of proxy models and optimization algorithms. conflicting interests the author(s) declare that they have no conflicting interests. improved oil and gas recovery 12 references central intelligence agency. 2014. the world factbook 2014.https://www.cia.gov/library/publications/the-worldfactbook/ (accessed 1 january 2025). elehinafe, f.b., nwizu, c.i., odunlami, o.b., et al. 2022. natural gas flaring in nigeria its effects and potential alternativesa review. journal of ecological engineering 23(8): 141-151. kerunwa, a., izuwa, n.c., dike, c.f., et al. 2024. review on the utilization of local asp in the niger-delta for enhanced oil recovery. petroleum and coal 66(1): 256-273. li, d. and firoozabadi, a. 2000. asphaltene deposition in porous media: effects of ph and pressure. journal of petroleum science and engineering 27(1): 95-105. mccain, w.d. 1990. the properties of petroleum fluids. tulsa, usa: pennwell books. moses, m.o., and donohoe, r.j. 1987. enhanced oil recovery. upper saddle river, new jersey: prentice hall. peñuela, g. and civan, f. 2000. predicting microbial plugging in porous media using a population balance model. journal of petroleum science and engineering 26(1): 209-219. pope, g.a., sepehrnoori, k., and delshad, m. 2000. a compositional streamline simulator for three-phase threecomponent flow in petroleum reservoirs. spe reservoir evaluation & engineering 3(4): 344-355. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri. he has research interest in drilling fluids technology, reservoir engineering, enhanced oil recovery and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri. https://www.cia.gov/library/publications/the-world-factbook/ https://www.cia.gov/library/publications/the-world-factbook/ copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1336 received december 10, 2024; revised december 22, 2024; accepted december 29, 2024. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 performance evaluation of palm kernel shell as pitting corrosion inhibitor nnaemeka uwaezuoke, oko emmanuel onya, nnaji okechukwu christopher, chukwuebuka francis dike*, ibuchukwu stanley onwukwe, federal university of technology owerri, imo state, nigeria abstract pitting corrosion is a critical issue in the petroleum industry, leading to substantial economic losses and environmental hazards, such as equipment failures, product contamination, and catastrophic system breakdowns. the conventional reliance on synthetic corrosion inhibitors, while effective, raises concerns regarding their environmental impact and potential health risks. moreover, the use of imported inhibitors introduces additional cost and logistical challenges. recent trends have focused on developing sustainable and environmentally benign alternatives derived from locally available materials. this study evaluates the feasibility of palm kernel shell ash (pksa), an abundant agricultural byproduct, as an eco-friendly corrosion inhibitor for petroleum production equipment. experimental results demonstrate that pksa significantly mitigates corrosion rates, offering a cost-effective and environmentally sustainable alternative to traditional inhibitors. x-ray fluorescence (xrf) analysis reveals that pksa comprises approximately 27 mol% mgo, 14 mol% sio2, 29 mol% cao, 7.72mol% k2o, and 4.9mol% al2o3, compounds known for their corrosion-inhibiting properties. the inhibition mechanism is attributed to the formation of a protective film on the metal surface, composed of calcium and magnesium compounds, which prevents the penetration of aggressive corrosive agents. corrosion rate reduction is observed through weight loss measurements, with a gradual decline beginning at around 200oc, highlighting the potential of pksa as a viable corrosion control solution for petroleum systems. introduction corrosion presents a significant global challenge in various engineering systems and structural components. within the petroleum industry, the presence of corrosive substances in crude oil raises concerns about the damage inflicted on pipelines and machinery during production and transportation (oyewole et al. 2021). pitting corrosion is characterized by the formation of small, deep pits on metal surfaces, which can compromise the structural integrity of equipment. mild steel, commonly used in the petroleum industry, is particularly vulnerable to this form of corrosion when exposed to chloride ions in saline environments. the consequences of corrosion are often numerous, and the effects on the safe, reliable and efficient operation of equipment or structures are often more serious than the simple loss of a mass of the metal. consequently, the need to control corrosion of petroleum production equipment continues to be a major concern to the engineer (alawode and ogunleye 2011), as failure of various kinds may occur, and expensive replacements required even though the amount of metal destroyed may be small. assessing the extent of internal corrosion at the bottom of equipment such as storage tanks can be challenging (jiang et al. 2017). failing to accurately monitor internal corrosion can have catastrophic consequences. as a result, there has been a need for effective corrosion inhibitors in acidizing industries that can be combined with mineral acids mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 during regular treatment of industrial equipment. a corrosion inhibitor is a substance that slows down the process of corrosion. it is typically added in small amounts to pickling acids in flow systems, such as pipes, either continuously or intermittently. the purpose of using inhibitors is to prevent or reduce the rate of corrosion on metallic materials. these inhibitors work by impeding the partial reactions that cause corrosion through the formation of a dense film layer. this layer acts as a barrier between the corroding surface and the surrounding environment (oguzie et al. 2013). one approach that has attracted significant interest is the use of natural compounds as corrosion inhibitors. unlike traditional synthetic inhibitors, natural extracts offer the advantage of being environmentally friendly and sustainable. amongst all-natural sources, plants have emerged as particularly promising candidates due to their diverse range of bioactive constituents (safian et al. 2023). the use of biomaterials in general and agrowaste in particular is a subject of great interest nowadays not only from the technological and scientific points of view, but also socially, and economically, in terms of employment, cost and environmental issues. biowastes are produced from a large variety of sources and agro-wastes are a class of these wastes. agro-wastes are gotten from animal and plant sources. these wastes contribute to the problem of environmental pollution and the growing cost of handling the problems of environmental pollution is a world problem being tackled by various organizations around the world. nwaobakata and agunwamba (2014) suggested that a wise alternative is to utilize these wastes and extract useful substances from them and therefore reduce the cost of disposing the wastes and the environmental damages imposed on our environment by these wastes. this has led to their synthesis to nanoparticles form uwaezuoke (2022) and utilization as utilization as alternatives for conventional materials in drilling (uwaezuoke et al. 2022), production and enhanced oil recovery. most of these inhibitors are organic compounds that contain nitrogen, sulfur or oxygen atoms within their structures. they work by absorbing onto the metal surface and creating a protective barrier against corrosive attacks (umoren et al. 2016). several plants have been utilized by corrosion inhibitors by several authors. kumar and mohana (2014) utilized pterolobium hexpetalum and celosia argentea for corrosion inhibition using weight loss and electrochemical impedance spectroscopy. from the result of their study there was an increase in inhibition efficiency with increase in concentration and decrease in inhibition efficiency with increase in temperature. chevalier et al. (2014) conducted a corrosion inhibition study in hcl using anibaros aeodora at constant temperature. from the result of their experimental study the increase in concentration yielded an increase in inhibition efficiency. chigondo and chigondo (2016) carried out a corrosion inhibition study in salt water environment using neem as material and weight loss as evaluation method. from the result of their experimental study, hussain et al. (2016) carried a corrosion inhibition study in hcl environment using elaeis guineensis as material, and weight loss, potentiodynamic polarization & electrochemical impedance spectroscopy as method. the result of their experimental increase in temperature yielded reduction in inhibition efficiency while increase concentration yielded increase in inhibition efficiency. murthy and vijayaragavan (2017) carried out corrosion inhibition by weight loss test in h2so4 and hcl environment using hibiscus sabdariffa. from the result of their experimental study, increase in concentration yielded increase inhibition efficiency. chinwego (2017) carried out corrosion inhibition study in nacl using a blend of palm and jatropha leaf. from the result of the experimental study, the palm-jatropha lead blend yielded inhibition efficiency of 60.9%. this study focuses on the use of locally sourced materials available in regions with significant petroleum production activities. the evaluation of carbon steel corrosion in the produced water of crude oil is of great interest to the petrochemical industry due to costly economic and human losses (deyab and abd el-rehim 2014). carbon steel is the most economical and common material used in the oil and gas industry (deyab et al. 2016). large amounts of palm kernel shells are produced during the extraction of palm oil from palm fruits and these shells must be used for a variety of purposes. research is currently being conducted on a variety of topics, such as the use of palm kernel shells as an additive in drilling fluids, livestock feed, construction aggregates, reinforcement for metals and polymeric composites, wastewater detoxifier, abrasive in automotive components, and bioenergy (borah and das 2022; saad et al. 2021). improved oil and gas recovery 3 by utilizing these materials, the research promotes sustainable practices and reduces the reliance on imported chemical inhibitors. the study is conducted using mild steel samples, a standard material in the petroleum industry, and simulates saline environments to replicate actual operational conditions. the findings of this study are expected to contribute to the development of cost-effective and environmentally friendly corrosion inhibitors. this research has the potential to influence corrosion management strategies in the petroleum industry and reduce the environmental impact of corrosion. methodology the methodology for this study involves the preparation and testing of mild steel samples in a controlled laboratory environment. the experimental setup includes the following parts. collection of samples. palm kernel shells (figure 1) were obtained from eziobodo in owerri, imo state nigeria. figure 1—palm kernel shell. preparation of mild steel and palm kernel shell ash. the palm kernel shell was cleaned and dried, they were packed in graphite crucible and crushed to obtained palm kernel shell ash figure 2. figure 2—palm kernel shell particulate. production of nanoparticles. the sol gel method was applied in producing the palm kernel shell ash nanoparticles. 50g of sodium hydroxide mixed in one dm3 of water was added to 100 g of palm kernel ash, put in an erlenmeyer flask and stirred for about 2 hours before the solution was filtered to remove the residue which is carbon figure 3. the filtrate was then allowed to cool at room temperature, then hydrochloric acid of weight 0.5 mols was added and stirred for hydrolysis condensation reaction to occur until ph of 7 was attained with a ph meter and ageing was done at 65℃ for 8 hours in an oven to obtain the gel. improved oil and gas recovery 4 figure 3—the palm kernel shell ash filtrate. characterization of nanoparticles. the size of the nanoparticles as well as their form and structure were observed with scanning electron microscope, x-ray fluorescence spectrometer was utilized for the composition analysis of the produced nanoparticles, x-ray diffractometer, xpertpro panalytical, lr 39487c was used to obtain the x-ray diffraction patterns of palm kernel ash nanoparticles. sample weight of 10 mg was heated from 10 to 861℃ with a heating rate of 10℃/min in nitrogen atmosphere. thermal gravimetric analysis (tg) was assessed using perkin-elmer pyris 6 tga analyzer. morphology and particle dimension of produced nano-silica were observed with an sem (zeiss ultra plus) and edx at secondary electron image (sei) and high vacuum (hv) mode with 20 kv accelerating voltage. the analysis was performed using an rh (rhodium) anode or source, with an x-ray energy of 30.0 kev and a silicon drift detector (sdd) type filter. the concentrations were calibrated or quantified using a specific method which was the gaussian fitting approach. results the experimental results demonstrate that all three inhibitors significantly reduce the corrosion rate of mild steel in a saline environment. coconut shell ash and neem leaves extract exhibit mixed-type inhibition behavior, affecting both anodic and cathodic reactions. periwinkle shell powder primarily influences the cathodic reaction by reducing hydrogen evolution. x-ray fluorescence (xrf) analysis. as an analytical technique, xrf identifies the presence and proportion of elements in a material so that the chemical composition can be established. remarkably, table 1 shows calcium oxide, magnesia silica, alumina and potassium oxide as the major components of the sample. the high silica, magnesia and alumina contents imply potential inhibition property which reveals why ash generated from pks has been studied as a potential corrosion inhibitor for petroleum equipment. table 2 presents oxygen, calcium, magnesium and silicon as the major elemental constituents of pks as well as aluminum and phosphorus. calcium oxide (cao) also known as quicklime and which form 29.34 mol% of the sample, can react with water to form calcium hydroxide which can help neutralize acidic corrosive substances like hydrogen sulfide and carbon dioxide to form neutral substances, reducing their corrosive effects and protecting the metal surfaces from corrosion. silica (sio2) which forms 14 mol% of the sample and is also known as silicon dioxide can help inhibit corrosion by forming a protective layer on metal surfaces, reducing the reactivity of the metal and preventing the formation of corrosive compounds. silica has a high affinity for water and can help reduce moisture levels, making it more difficult for corrosive substances to form. improved oil and gas recovery 5 table 1—percentage chemical composition (by weight) of pks from xrf analyses. layer component type concn error units mole% error 1 sio2 calc 13.091 2.162 wt.% 14.014 2.315 1 v2o5 calc 0.016 0.077 wt.% 0.006 0.027 1 cr2o3 calc 0.025 0.052 wt.% 0.010 0.022 1 mno calc 0.206 0.050 wt.% 0.186 0.045 1 fe2o3 calc 8.380 0.170 wt.% 3.375 0.069 1 co3o4 calc 0.068 0.060 wt.% 0.018 0.016 1 nio calc 0.013 0.041 wt.% 0.011 0.035 1 cuo calc 0.323 0.042 wt.% 0.261 0.034 1 nb2o3 calc 0.071 0.046 wt.% 0.020 0.013 1 moo3 calc 0.034 0.054 wt.% 0.015 0.024 1 wo3 calc 0.044 0.167 wt.% 0.012 0.046 1 p2o5 calc 7.987 0.969 wt.% 3.619 0.439 1 so3 calc 3.680 0.546 wt.% 2.956 0.438 1 cao calc 25.587 0.654 wt.% 29.348 0.750 1 mgo calc 17.211 29.342 wt.% 27.466 46.825 1 k2o calc 11.304 0.440 wt.% 7.719 0.301 1 bao calc 0.000 0.000 wt.% 0.000 0.000 1 al2o3 calc 7.696 5.624 wt.% 4.855 3.548 1 ta2o5 calc 0.078 0.156 wt.% 0.011 0.023 1 tio2 calc 0.694 0.118 wt.% 0.559 0.095 1 zno calc 0.267 0.039 wt.% 0.211 0.031 1 ag2o calc 0.048 0.266 wt.% 0.013 0.074 1 cl calc 2.847 0.243 wt.% 5.166 0.441 1 zro2 calc 0.062 0.046 wt.% 0.032 0.024 1 sno2 calc 0.268 1.920 wt.% 0.114 0.819 improved oil and gas recovery 6 table 2—elements information. element line code cond code ratio method intensity (c/s) error (c/s) intensity method conc conc method calibration coefficient o ka 0 none 0.000 0.0000 gaussian 36.474 none 0.000 mg ka 1 none 1.754 2.9903 gaussian 10.380 fp 0.000 al ka 1 none 6.699 4.8948 gaussian 4.073 fp 0.000 si ka 1 none 56.493 9.3315 gaussian 6.119 fp 0.000 p ka 1 none 102.801 12.4708 gaussian 3.486 fp 0.000 s ka 1 none 78.302 11.6121 gaussian 1.474 fp 0.000 cl ka 1 none 191.786 16.3779 gaussian 2.847 fp 0.000 k ka 1 none 847.580 33.0175 gaussian 9.384 fp 0.000 ca ka 1 none 1850.114 47.3105 gaussian 18.287 fp 0.000 ti ka 1 none 65.336 11.1164 gaussian 0.416 fp 0.000 v ka 1 none 1.896 9.1934 gaussian 0.009 fp 0.000 cr ka 1 none 4.700 9.9539 gaussian 0.017 fp 0.000 mn ka 1 none 54.823 13.3120 gaussian 0.159 fp 0.000 fe ka 1 none 2408.342 48.9013 gaussian 5.861 fp 0.000 co ka 1 none 24.437 21.3226 gaussian 0.050 fp 0.000 ni ka 1 none 4.961 15.5713 gaussian 0.010 fp 0.000 cu ka 1 none 142.870 18.7667 gaussian 0.258 fp 0.000 zn ka 1 none 131.957 19.4233 gaussian 0.214 fp 0.000 zr ka 1 none 23.897 17.8785 gaussian 0.046 fp 0.000 nb ka 1 none 26.194 17.0293 gaussian 0.057 fp 0.000 mo ka 1 none 10.310 16.0164 gaussian 0.023 fp 0.000 ag ka 1 none 1.943 10.8470 gaussian 0.044 fp 0.000 sn la 1 none 5.743 41.1054 gaussian 0.211 fp 0.000 ta la 1 none 9.752 19.4500 gaussian 0.064 fp 0.000 improved oil and gas recovery 7 alumina (al2o3) also known as aluminum oxide, forms 4.9 mol% of our sample, and can also form a thin, impermeable layer on metal surfaces, preventing corrosive substances from penetrating. potassium oxide (k2o) which forms 7.7 mol% also has the same effect and can also be used to enhance protective coatings and paints by enhancing their barrier properties. alumina’s hardness and chemical inertness make it an effective barrier against corrosion. alumina can also inhibit pitting corrosion by reducing the formation of pits and crevices, which can lead to localized corrosion. magnesia (mgo), also known as magnesium oxide which forms 27.466 mol% of the sample is known for its protective properties and can form a barrier against corrosive substances. it is often used in coatings and paints to protect metal surfaces from corrosion. magnesia and calcium oxide have antimicrobial properties which can inhibit the growth of microorganisms that contribute to microbial corrosion. the presence of these elements in the sample shows that palm kernel shell ash can serve in coatings and paints, additives in drilling and production fluids, corrosion inhibition in pipeline transportation, protection lines and wraps, high temperature and pressure environments and corrosive environments with acidic substances to reduce equipment damage, extend lifespan and minimize downtime furthermore, its availability and affordability together with other properties like relatively high porosity, surface area and strength-to-weight ratio makes the agricultural waste a potential solid biocatalyst (nwosu-obieogua et al. 2022). xrd crystallinity analysis. the compositional analysis of pks provides a background understanding of its chemical configuration. figure 4 presents a comparison between xrd crystallinity analysis of raw pks and activated carbon from pks. xrd patterns of raw pks demonstrated the coexistence of carbon and oxygen atoms at peaks of 2θ = 22◦, 28◦ and 52◦ respectively figure 4. in te ns ity ,c ps inhibita refikite silicon oxide chaoite epsomite marialite 2θ, ° figure 4—xrd crystallinity analysis. figure 5 shows the percentage composition of the minerals in the sample. for instance, results showed that the sample is 53% refikite, with figure of merit of 5%. similarly, it is 2.9% epsomite with figure of merit of 3%. in figure 6, the peaks represent refikite, epsomite and marialiate between 2θ = 15◦ and 20◦ respectively due to the impurities during the preparation of the sample from the pks. the broad xrd array of extracted silica nanoparticles at theta = 15◦, which is distinctive of amorphous solid, confirms the formation of amorphous silica; similar results were obtained by other researchers (sapawe et al. 2018). other peaks at 2θ = 11o, 32◦, 42◦ and 55◦ represent the nature of the pks nanoparticles and is consistent with other studies (imoisili et al. 2020; ikubanni et al. 2020; jabarullah et al. 2021). improved oil and gas recovery 8 figure 5—percentage composition of the minerals in the pks sample tested. figure 6—phase data view. table 3 shows the evaluation report of the samples for more a detailed information. for instance, it revealed the presence of epsomite and refikite as the peak values of figure 6, while the qualitative analysis output (table 4) showed refikite, silicon oxide, chaoite, epsomite, and marialite. the values in parenthesis show figures of merit. improved oil and gas recovery 9 table 3—peak list. no. 1 2 2θ, ° 17.76(9) 18.63(2) d, å 4.99(3) 4.758(6) height, cps 424(53) 545(61) fwhm, ° 2.9(3) 0.32(19) int. i., cps° 1472(157) 259(47) int. w., ° 3.5(8) 0.47(14) asymmetry 5(3) 5(12) decay(ηh/mh) 0.4(3) 1(2) size, å 29(3) 266(162) phase name epsomite: 201 refikite: 131, silicon oxide chemical formula mgso4 ·7 h2o c20h32o2, sio2 norm. i. 100 17.56 profile type split pseudo-voigt split pseudo-voigt table 4—qualitative analysis results. phase name formula figure of merit refikite c20h32o2 0.892 silicon oxide sio2 1.238 chaoite c 2.850 epsomite mgso4 ·7h2o 2.750 marialite (na3.35 ca0.38 k0.24 ) ( si8) 2.752 tga measures the weight loss of a material as a function of temperature, which can provide information about thermal stability, decomposition, and phase transformations. the results of thermal gravimetric analysis (tga) are shown in figure 7. the curve shows a gradual weight loss starting around 200°c, with a more significant weight loss occurring between 400°c and 600°c, suggesting potential decomposition or phase changes of some of these calcium silicate or calcium aluminosilicate compounds present in the sample within this temperature range. two-step weight losses were observed. the loss in weight up to 310◦c (step 1) is ascribed to dehydration caused by the loss of physically adsorbed h2o. however, chemically bound water from the sol-gel production method was ascribed to the loss in weight from 330 to 500◦c (step 2) (mueller et al. 2003). above 550◦c, no further weight loss was observed indicating thermal stability of extracted nano silica. improved oil and gas recovery 10 figure 7—thermo-gravimetric analysis of palm kernel shell. the thermal behaviour of pks shows that the agricultural waste decomposes under heat in two stages due to its constituents. the first stage occurs at an onset of 10 ℃ up until 205 ℃ with weight loss attributed to vaporization of moisture content. the second stage is initiated at 250 ℃ and lasts up to 635 ℃ with one distinct derivative thermo-gravimetric (dtg) peaks which occurs at t=400 ◦c and marks the onset of the decomposition of hemicellulose and degradation of cellulose (acevedo-paez et al. 2019). table 5 shows the elemental composition in terms of atomic and weight concentrations. it is possible to say that carbon is the dominant element. with the carbon, it is also possible to infer that nanomaterials such as carbon nanotubes (cnts) and graphenes etc could be found, which could enhance its performance as corrosion control material. improved oil and gas recovery 11 table 5—atomic concentrations of elements in analyzed sample. element number element symbol element name atomic conc. weight conc. 6 c carbon 81.31 74.21 7 n nitrogen 15.01 15.98 26 fe iron 0.53 2.26 20 ca calcium 0.63 1.93 14 si silicon 0.48 1.02 13 al aluminium 0.49 1.00 19 k potassium 0.30 0.88 15 p phosphorus 0.37 0.86 16 s sulfur 0.24 0.60 12 mg magnesium 0.27 0.49 11 na sodium 0.25 0.44 17 cl chlorine 0.12 0.34 22 ti titanium 0.00 0.00 scanning electron microscopy (sem). figure 9 shows the eds of the microstructure of the pksa np. as observed from figure 9, the dominant element is carbon. sem imaging has been used to study the morphology of the pksa sample. the morphology of the palm kernel shell ash nanoparticles (pksa np) by scanning electron microscope/energy dispersive spectrometry (sem/eds) is shown in figure 10. it shows the sem micrograph of silica nanoparticles produced from palm kernel shell ash at ×200,000 magnification. the particles were observed to be spherical in shape with reduced silica-silica agglomeration. the organic molecules in the waste contain c and o which may provide electron pairs for the waste to adsorb onto the metallic surface. this would lead to a partial blockage of the metal and as a result, limit corrosion in the aggressive solution (thakur and kumar 2021). it is feasible to suggest that this waste belongs to the class of inhibitory compounds because it contains both c and o atoms. figure 9—eds of the microstructure of the pksa np. improved oil and gas recovery 12 figure 10—sem image of samples. conclusions this research demonstrates the potential of locally sourced materials in inhibiting pitting corrosion on petroleum production equipment. the results demonstrate that pksa is a effective corrosion inhibitor containing about 27 mol% magnesia, 14 mol% silica, 29 mol% cao 7.72 mol% k2o and 4.9 mol% alumina which are all compounds with high capacity for corrosion inhibition. the inhibition mechanism is attributed to the formation of a protective layer on the metal surface, comprising calcium and magnesium compounds present in pksa. conflicting interests the author(s) declare that they have no conflicting interests. references alawode, a.j. and ogunleye, i.o. 2011. maintenance, security and environmental implications of pipeline damage and ruptures in the niger delta region. pacific journal of science and technology 12(1):565-573. acevedo-paez, j., duran, j.m., posso, f., et al. 2019. hydrogen production from palm kernel shell: kinetic modeling and simulation. int. j. hydrogen energy 44(1):123-130. borah, b. and das, b.m. 2022. a review on applications of bio-products employed in drilling fluids to minimize environmental footprint. environ. challenges 6(1):100411. chevalier, m., robert, f., amusant, n., et al. 2014. enhanced corrosion resistance 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sustainable inhibitors for corrosion mitigation in aggressive corrosive media: a comprehensive study. j. bio-tribo-corrosion 7(1):67-68. umoren, s.a., eduok, u.m., solomon, m.m., et al. 2016. corrosion inhibition by leaves and stem extracts of sida acuta for mild steel in 1m h2so4 solution investigated by chemical and spectroscopic techniques. arabian journal of chemistry 9(1):209-224. uwaezuoke, n. 2022. polymeric nanoparticles in drilling fluid technology. in drilling engineering and technologyrecent advances, new perspectives and applications, ed. m. zoveidavianpoo, chap. 1, 1-15. london: intechopen. uwaezuoke, n., okoro, v., igwilo, k.c., et al. 2022. characterization of amuda-isuochi nigerian clay deposit for potential industrial applications. international journal of engineering research in africa 62(1):1-18. nnaemeka uwaezuoke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling and well engineering. uwaezuoke holds a bachelor’s degree in petroleum engineering from federal university of technology owerri; master’s degree in petroleum improved oil and gas recovery 14 engineering from university of stavanger, norway; and a phd degree in petroleum engineering from federal university of technology owerri,nigeria. oko emmanuel onya is a graduate of petroleum engineering from the department of petroleum engineering, federal university of technology owerri, nigeria, with research interest in drilling engineering and corrosion control. nnaji okechukwu christopher is a graduate of petroleum engineering from the department of petroleum engineering, federal university of technology owerri with research interest in reservoir engineering and corrosion control. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids, enhanced oil recovery, reservoir engineering and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering. ibuchukwu stanley onwukwe is a professor at the department of petroleum engineering, federal university of technology owerri with research interest in reservoir engineering, enhanced oil recovery, natural gas engineering, petroleum production and petroleum economics. onwukwe holds a bachelor’s, master’s and a phd degree in petroleum engineering from federal university of technology owerri, nigeria. abstract introduction methodology results conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1262 received june 2, 2023; revised september 14, 2023; accepted november 14, 2023. *corresponding author: weirong.li@xsyu.edu.cn 1 an innovative method for hydraulic fracturing parameters optimization to enhance production in tight oil reservoirs shide yan,weirong li*, min zhang, xi’an shiyou university, xi’an, china; zhengbo wang, zhaoxia liu, research institute of petroleum exploration and development, petrochina, beijing, china; keze lin, china university of petroleum (beijing), beijing, china; hongliang yi, petrochina liaohe oilfield company, panjin, china abstract the hydraulic fracturing technology for horizontal wells is one of the key techniques for the effective development of tight oil and gas reservoirs. optimizing fracturing parameters can significantly enhance fracturing effectiveness, reduce development risks, and improve oil and gas production as well as economic efficiency. rapid and accurate optimization of hydraulic fracturing construction parameters for tight oil horizontal wells has always been a challenge in reservoir development and management. this study introduces a novel workflow for optimizing fracturing parameters by combining reservoir numerical simulation and machine learning techniques. the paper first establishes a single-well numerical model using commercial simulator, and calibrates the reservoir model through matching historical production data. eight main parameters are selected, and an initial feature dataset is generated using monte carlo method, while production dataset is obtained from reservoir numerical simulation. subsequently, various machine learning algorithms are employed to construct fracture productivity models under different combinations of reservoir and hydraulic fracture parameters. the selected machine learning model with best performance is then integrated with an economic evaluation model to establish an optimization model for hydraulic fracturing parameters optimization for tight oil horizontal wells. the research indicates that the production prediction model established based on the cnn-lstm method exhibits a high level of accuracy. the optimization model for hydraulic fracturing parameters in tight oil horizontal wells can rapidly optimize fracturing parameters. the proposed methodology in the paper has the potential to enhance horizontal well production and improve economic benefits in tight oil horizontal wells, and can also be applied to similar field development and engineering parameter optimization scenarios. introduction currently, crude oil and natural gas play crucial roles in the global energy landscape, providing abundant energy and resources for people's production and daily lives. simultaneously, the extraction of conventional oil and gas resources is encountering increasingly formidable challenges worldwide, prompting unconventional oil and gas resources to emerge as a significant avenue for the development of the oil and gas industry (zou et al. 2015). unconventional oil and gas resources primarily encompass tight oil, oil sands, shale gas, and natural gas hydrates. their extraction poses significant challenges and comes with high costs; however, they are characterized by substantial development potential and abundant resources (rezaee 2022). regarding tight oil, it is commonly co-produced alongside shale gas. led by the united states, effective development of tight oil has also been achieved in canada and argentina, with production in 2020 reaching 25 million tons and 5.2 improved oil and gas recovery 2 million tons, respectively, while the total production of tight oil and shale oil in the united states reached 350 million tons (kelsey et al. 2016). substantial remaining oil in tight reservoirs remains untapped, prompting the utilization of fracturing techniques after depletion-based extraction to boost output and extend production cycles (todd and evans 2016). given the high drilling costs and potential environmental issues associated with hydraulic fracturing, researches aimed at enhancing recovery in tight oil reservoirs have become exceptionally significant. the hydraulic fracturing technology for horizontal wells is an advanced technique used to enhance oil and gas recovery rates. its fundamental principle involves injecting fracturing fluid into a horizontal well under high pressure, creating fractures within rock fissures. this process enhances reservoir permeability and effective porosity, consequently increasing the recovery rate of oil and gas (wu et al. 2012). as a result, optimizing fracturing parameters is crucial for successful hydraulic fracturing. the methods for optimizing fracturing parameters encompass traditional empirical formulas, physical simulations, statistical approaches, and machine learning techniques. these methods aim to enhance the productivity and economic efficiency of horizontal wells by optimizing parameters, such as fracturing fluid concentration, viscosity, and injection pressure.the following outlines the evolution of models and optimization of fracturing parameters: cleary (1980) utilized experimental data and mathematical models to establish a set of design formulas for predicting fracture pressure and length during hydraulic fracturing. these formulas aimed to optimize hydraulic fracturing design, enhancing efficiency and recovery. yang et al. (1996) introduced a method employing multivariate optimization techniques for hydraulic fracturing design. by constructing a comprehensive hydraulic fracturing model, this approach incorporated various factors, such as hydraulic fracturing parameters and reservoir properties, and conducted comprehensive parameter optimization to achieve optimal fracturing outcomes. elrafie and wattenbarger (1997) employed computational fluid dynamics simulations to model the hydraulic fracturing process. sensitivity analyses were performed on fracturing parameters and well spacing. by contrasting production from horizontal and vertical wells, recommendations for optimal horizontal well and fracturing designs for the reservoir were proposed. dahaghi (2010) employed numerical simulation methods to analyze gas recovery and carbon dioxide sequestration processes. different parameters' impacts on reservoir pressure, pore pressure, and saturation were explored. it was found that utilizing logarithmically spaced locally refined grids accurately simulated the volume fractured region of horizontal wells during hydraulic fracturing simulations. cipolla et al. (2010) introduced an analysis method for reservoir properties and productivity characteristics, along with a fluid dynamics model. this enabled the holistic modeling of complex fracture networks in tight reservoirs, validated through microseismic monitoring results. zhou et al. (2014) employed data mining techniques to assess production performance in the marcellus shale gas region. they applied classification and regression algorithms from machine learning to process and model the data, subsequently validating their models. the study demonstrated that data-driven methods effectively predicted shale gas well production performance, offering valuable insights for optimizing production control. schuetter et al. (2018) utilized data analysis methods to construct predictive models for unconventional shale oil and gas reservoir production. they employed multivariate linear regression and k-nearest neighbors algorithms, evaluating and optimizing their models. the results indicated that both methods were effective for predicting reservoir production in shale oil and gas formations, exhibiting high predictive accuracy across different datasets. luo et al. (2019) utilized three machine learning methods (neural networks, decision trees, and support vector machines) to perform extensive data analysis on bakken shale oil horizontal wells. leveraging historical production data and multiple influencing factors such as geological attributes, fracturing parameters, and production strategies, they established predictive models. the outcomes demonstrated that machine learning models accurately forecasted well production performance and offered recommendations for production optimization. duplyakov et al. (2020) employed machine learning techniques for optimizing hydraulic fracturing design using field data. they improved oil and gas recovery 3 developed a digital database and employed various machine learning algorithms to analyze and model field data, predicting optimal fracturing design parameters and production enhancement. the effectiveness of the model was validated through field experiments, demonstrating the potential of utilizing machine learning methods for optimizing hydraulic fracturing design. dong et al. (2022) addressed issues with traditional trial-and-error-based hydraulic fracturing parameter optimization methods by introducing a hybrid optimization approach that combines machine learning and evolutionary algorithms. this method utilized machine learning algorithms to construct a hydraulic fracturing model based on experimental data. subsequently, evolutionary algorithms were employed to optimize critical parameters within the model, ultimately yielding the optimal combination of fracturing parameters. however, optimizing fracturing parameters in tight oil reservoirs presents several challenges and difficulties, such as the lack of precise physical models and limited data. with the rapid advancement of data science in recent years, big data analytics methods have found extensive application in the field of oil and gas exploration and development (zhan et al. 2019; li et al. 2022). simultaneously, machine learning-driven optimization of hydraulic fracturing parameters in horizontal wells necessitates substantial well group data, but this also gives rise to issues such as large data volumes and high costs. to address these challenges, this research aims to introduce a novel process for optimizing fracturing parameters. specifically, it involves the utilization of reservoir numerical simulation and machine learning techniques to optimize hydraulic fracturing parameters in horizontal wells. by combining numerical simulation with machine learning, it becomes possible to achieve an optimized prediction of fracture morphology, production capacity, and fracturing parameters in horizontal well hydraulic fracturing. such a comprehensive approach harnesses the strengths of both methods, establishing predictive models from extensive experimental data to further enhance the efficiency and precision of hydraulic fracturing. the following is a detailed explanation of the structure of the article. section 2 presents the machine learning methods employed for parameter optimization, encompassing modeling and prediction of sequential data, along with the requisites for data and model establishment, including dataset generation. the optimal machine learning model is identified in section 3, followed by a single-factor sensitivity analysis of fracturing parameters. the practical optimization of fracturing parameters outlined in section 4. section 5 encompasses discussion and future prospects of this study. the conclusion is presented in section 6. methodology and workflow the establishment of a machine learning production prediction model requires robust data support, which can be achieved through the integration of datasets from reservoir numerical simulation, fracturing simulation, and historical production fitting. however, in cases where high-quality real data is scarce or unavailable, synthetic data obtained from numerical or analytical simulations can be utilized (kulga et al. 2017). this subsection introduces geological description of study area, tuning reservoir parameters through historical production matching, and employing reservoir numerical simulation to generate production datasets. and then, it introduces three machine learning algorithms used to forecast production in this study. improved oil and gas recovery 4 figure 1—structural flowchart for fracturing parameter optimization. figure 1 illustrates the workflow for the design of fracturing parameter optimization. it begins with the establishment of a geological model for the study area, followed by historical fitting through hydraulic fracturing. subsequently, a machine learning-required dataset is generated based on the range and distribution of geological parameters and fracturing parameters. three machine learning models are established and compared. finally, the best production prediction machine learning model is selected and further integrated with an economic model to establish the fracturing parameter optimization model, which is then subjected to optimization case studies. figure 2—simplified geological map of the chang 7 formation in the ordos basin. (a) depicts the tectonic framework of the ordos basin (data source: hou et al. 2023). improved oil and gas recovery 5 research area. the yanchang formation, consisting of seven segments, is an important reservoir in the pankou area of ordos basin. it is distributed in the yan’an region of shaanxi province and shizuishan region of ningxia, at the border between shaanxi and inner mongolia. it is considered as one of the key areas for oil and gas exploration and development in this region. as shown in figure 2, the study area is located in the secondary structural unit of the yishan slope, in the southwestern part of the ordos basin. this region is an important reservoir for tight oil and shale gas production, with abundant potential oil and gas resources. in the research field, the chang 7 section of the yanchang formation is a crucial reservoir unit known for its abundant tight oil resources and high-quality characteristics. however, an analysis of the core physical properties data in the study area reveals that the overall physical properties of this reservoir are poor (wang et al. 2015). the porosity distribution of the sandstone ranges from 3.07% to 18.75%, with an average value of 10.77%. the permeability distribution ranges from 0.03 to 3.23 md, with an average value of 0.18 md. this reservoir is characterized by low porosity and extremely low permeability, and the presence of microfractures makes it the primary pathway for oil and gas migration (xiao et al. 2017). as a result, fractures and microfractures are the main locations for oil and gas accumulation in this reservoir. additionally, the reservoir in the study area exhibits strong heterogeneity, with significant variations in the effectiveness of hydraulic fracturing. dataset generation. before establishing a machine learning production forecasting model, the primary task is to build a single well geological model, as it forms the basis for optimizing fracturing parameter design. in the numerical model, it is necessary to input the geological information and reservoir properties of the target well group, as well as the fracturing construction parameters, and set appropriate boundary conditions and numerical methods. by solving the model equations, it is possible to predict the fracturing effect and productivity of the target well group, which is of crucial significance for optimizing fracturing parameters. establishment of numerical model. based on the geological model of the seven sections of the guping well group leader, a geological model of multi-stage fractured horizontal well (mfhw) was established using the commercial simulator (petrel). the reservoir petrophysical parameters, hydraulic fracturing parameters, and boundary conditions were determined. multiple data sources, including seismic data, well logging data, and core data were imported into the simulator for interpretation and analysis, resulting in an accurate threedimensional reservoir model which provides a reliable basis for optimizing fracturing parameters and predicting production rates. table 1 presents the reservoir and hydraulic fracturing parameters for the mfhw. by considering these reservoir and hydraulic fracturing parameters, an accurate geological model for the horizontal well was constructed to optimize fracturing design and predict production. figures 3 illustrate the schematic diagram of the reservoir model established. this model was constructed based on a comprehensive evaluation of various geological parameters and hydraulic fracturing parameters, aiding in the optimization of fracturing design and production rate prediction. figure 3—conceptual illustration of a single well geological model for petrel horizontal wells. improved oil and gas recovery 6 table 1—geological parameters and hydraulic fracture parameters for horizontal wells. parameter value x length (m) 2000 y length (m) 500 z length (m) 18 reservoir temperature (℃) 80 reservoir length (m) 1200 formation pressure (mpa) 20 reservoir thickness (m) 20 porosity (%) 11.17 permeability (md) 0.14 oil saturation (%) 51.53 after establishing the numerical model, the hydraulic fracture network simulation of a typical well group was conducted using the fracturing simulation software petrel-kinetix. during the fracturing operation, the fluid intensity and proppant intensity are two parameters that need to be balanced. higher fluid intensity may require higher pumping pressure to extend the fractures, while higher proppant intensity can provide better fracture support but may also increase the demand for fluid pumping. therefore, when selecting the parameters, it is necessary to balance the fluid intensity and proppant intensity according to specific requirements in order to achieve the optimal fracturing effect. the specific selected parameters are shown in table 2. table 2—liquid strength and sand strength. parameter value fracture length (m) 283.1 fracture height (m) 11.91 fracture permeability (md) 102.3 sand proportion (%) 18.2 single well injected fluid volume (m3) 30477 single-stage fluid volume (m3) 1270 single well sand volume (m3) 3398.5 single-stage sand volume (m3) 141.6 single-stage displacement (m3/min) 9 fracture spacing (m) 58.2 the natural fracture characteristics of reservoirs primarily encompass two key aspects: the storage capacity and the fluid flow properties. taking the natural fractures in the long 7 formation of the ordos basin as an example, specific data is given in table 3. improved oil and gas recovery 7 table 3—natural fracture characteristics of long 7 formation. well number well #18-#30 fracture direction (°) formation strike: n60°w, formation dip: 30 degrees fracture length (μm) 1200 fracture width (μm) 50 fracture description asphalt filled porosity (%) 0.014 figure 4 illustrates the hydraulic fracturing effect of a typical well. the blue lines represent the positions of natural fractures, while the hydraulic fracturing network is depicted by varying shades of color indicating the width of the fractures, with darker shades representing wider fractures. by comparing these fractures, it is possible to assess the effectiveness of hydraulic fracturing and determine whether it has successfully expanded the fracture network, thereby increasing the permeability and productivity of the reservoir. additionally, the overlap between the natural fractures and the hydraulic fracturing network can be analyzed to gain further insights into the coverage and effectiveness of hydraulic fracturing. figure 4—hydraulic fracturing network. production history match. production history match refers to the process of comparing historical production data with numerically simulated production data in order to validate and adjust the accuracy of the numerical simulation model (zhang and awotunde 2016). figure 5 illustrates the basic workflow of history matching. the parameters are only output when the difference between the fitted values and the actual values is smaller than a specific threshold value. improved oil and gas recovery 8 figure 5—workflow of production history match. table 4 presents the initial values and history matching results of the basic fluid and reservoir parameters for the established numerical model of this study. table 4—initial and final values of parameters. parameter initial value final value permeability (md) 0.14 0.05 porosity (%) 11.17 11 oil saturation (%) 51.53 55 fracture permeability(md) 112.6 102.3 natural fracture permeability(md) 0.65 0.42 generation of production dataset. according to the actual conditions of the yanchang formation reservoir in the pankou area of ordos basin, the range of various geological factors of the reservoir were determined through analysis and statistical analysis of field data, including core analysis and well logging, combined with comparison and validation using numerical models. the range for each reservoir parameter in the study area are presented in table 5. figure 6 illustrates the distribution of reservoir parameters in typical well groups within the study area. improved oil and gas recovery 9 table 5—range and boundary of geological parameters. parameter minimum maximum length of reservoir section (m) 400 1600 porosity (%) 9 12 permeability (md) 0.01 0.25 oil saturation (%) 45 70 (a) reservoir length (b) porosity (c) permeability (d) oil saturation figure 6—distribution of reservoir parameters. by collecting fracturing data from typical production wells in the target area and comparing them with fracturing data from similar wells with similar geological structures, well types, well depths, lithologies, etc., the range of fracturing parameters can be preliminarily determined. additionally, referencing existing fracturing improved oil and gas recovery 10 experiments and empirical data also helps to establish the range of these parameters. the range for each fracturing parameter are presented in table 6. figure 7 presents the distribution of fracturing parameters of typical well groups in the study area. it is aware that adjustments and optimizations of the parameters should be made based on the specific conditions onsite to ensure the effectiveness. figure 7—distribution of fracturing parameters. table 6—ranges and boundary of fracturing parameters. parameter minimum maximum fracturing spacing (m) 30 100 single-stage fluid volume (m3) 500 1500 single-stage sand volume (m3) 50 250 single-stage displacement (m3/min) 5 15 improved oil and gas recovery 11 numerical simulations are run to generate production dataset based on the combination of reservoir and fracturing parameters in the above ranges. table 7 presents the distribution characteristics of the production dataset, while figure 8 shows the distribution of cumulative oil production. a total of 2698 sets of dynamic production data were obtained, including reservoir parameters, such as reservoir thickness, porosity, permeability, and oil saturation, as well as hydraulic fracturing parameters, such as fracture spacing, singlestage fluid volume, single-stage sand volume, and single-stage displacement. the dataset also includes monthly oil production over ten years. table 7—characteristics of production dataset generated by numerical simulation. interval length (m) porosity (%) perm. (md) saturation (%) fracture spacing (m) fluid volume (m3) sand volume (m3) displacement (m3/min) cum.oil production (t) sum 2698 2698 2698 2698 2698 2698 2698 2698 2698 average 1244 10.99 0.15 55.0 64 1025 161 10 28033 stand. dev. 704 1.16 0.08 6.6 26 739 86 3 4524 minimum 400 9.00 0.01 45.0 30 500 30 5 3156 25% 750 9.75 0.10 52.0 40 750 50 7 8024 50% 1000 10.82 0.15 57.5 60 1000 125 10 15816 75% 1250 11.35 0.20 63.0 80 1250 200 13 23578 maximum 1600 12.00 0.25 70.0 100 1500 250 15 35916 figure 8—distribution of cumulative oil production in the production dataset. machine learning algorithms for production forecasting. machine learning refers to the process of automatically adjusting the parameters of algorithm models by learning patterns and rules from a large amount of data, with the aim of improving the accuracy of prediction and classification. the basic principle of neural networks involves training the model to map input data to output data, establishing a relationship between the two. machine learning methods can be broadly categorized into supervised learning and unsupervised learning . supervised learning involves training the model using known input and output data samples to predict the improved oil and gas recovery 12 output for new unknown data. on the other hand, unsupervised learning aims to discover the structure and patterns within the data itself through analysis and learning without any given output samples.the following briefly introduces these three machine learning methods used for production forecasting in this study. cnn method. convolutional neural network (cnn) is a deep learning technique used for analyzing data with grid-like structures, such as images, speech, and text. compared to traditional neural networks, cnn can automatically learn features from input data while reducing the number of parameters, thus improving the efficiency and accuracy of the model (albawi et al. 2017). figure 9 depicts the structure of a one-dimensional convolution. in cnn, the convolutional layers extract features from input images, while the pooling layers are used to reduce the size and number of parameters in the feature maps, preventing overfitting. the fully connected layers combine the output features from the convolutional and pooling layers to perform classification or regression tasks. figure 9—cnn one-dimensional convolutional structure diagram. lstm method. long short-term memory (lstm), a type of recurrent neural network (rnn) model, is designed for handling sequence data. as shown in figure 10, lstm utilizes three gates to control the flow of information: the forget gate, input gate, and output gate. these gates allow lstm to selectively retain or forget information and produce predictions at the current time step. as a result, lstm has been widely applied in sequence data processing tasks such as natural language processing, speech recognition, and stock prediction. figure 10—lstm neural network unit structure diagram. cnn-lstm method. cnn-lstm is a complex neural network architecture that combines the characteristics of cnn and lstm, making it suitable for modeling and predicting sequential data. as shown in figure 11, it improved oil and gas recovery 13 first processes the sequential data through convolutional layers to extract spatial features. then, the output of the convolutional layers is fed into the lstm layer, which learns the temporal dependencies in the sequence through its memory cells and gate units. lastly, the output of the lstm layer is passed to the output layer for prediction. figure 11— cnn-lstm neural network unit structure diagram. analysis of model training results this section evaluates the predictive accuracy of different machine learning models through correlation analysis, selects the optimal one, followed by conducting a univariate sensitivity analysis of hydraulic fracturing parameters. finally, it introduces the case study of fracturing parameters optimization through instance-specific investigations. correlation analysis. correlation analysis involves the application of statistical methods to assess the degree of association between two or more variables. in data analysis and modeling, the utilization of pearson correlation coefficient analysis is employed to investigate the interrelationships among variables, determining their connections, and deciding whether to incorporate these variables within the model. this yields valuable guidance for feature selection and model refinement. the pearson correlation coefficient is a statistical measure used to gauge the extent of linear association between two variables. typically denoted by the symbol r, the correlation coefficient's values range from -1 to 1. a r value of 0 signifies the absence of a linear relationship between the two variables. a r value of -1 indicates a perfect negative correlation, while a r value of 1 signifies a perfect positive correlation between the variables. improved oil and gas recovery 14 figure 12—pearson correlation coefficient heatmap. figure 12 displays the pearson correlation coefficient heatmap between input parameters and cumulative oil production. the intensity of colors reflects the degree of correlation between them, accompanied by corresponding correlation coefficient values. reservoir parameters exhibit notable correlations with cumulative oil production, particularly the highest correlation observed between reservoir thickness and cumulative oil production at 0.67. subsequently, oil saturation, permeability, and porosity follow with correlations of 0.27, 0.25, and 0.18, respectively. the correlation between hydraulic fracturing parameters and cumulative oil production is relatively weak, with a coefficient of -0.18. conversely, there is stronger correlation among hydraulic fracturing parameters, notably the highest correlation being between single-stage fluid volume and fracturing spacing , as well as single-stage sand volume, at 0.54. the magnitudes of the correlation coefficients between various features do not induce multicollinearity issues, thus ensuring the model's stability and accuracy. machine learning optimization model. we utilized the particle swarm optimization (pso) algorithm, which is an intelligent optimization technique based on collective cooperation and global exploration, drawing inspiration from the migration and clustering behaviors observed in avian foraging processes. pso algorithm involves adapting particle values by driving changes through the objective function. this is accomplished by dynamically comparing the optimal positions independently found by individual particles with the optimal position discovered by the entire population. we applied the pso algorithm to optimize the hyperparameters of the cnn model, and the training outcomes are illustrated in figure 13. the model exhibited a root mean improved oil and gas recovery 15 square error (rmse) of 1364.99 and a coefficient of determination (r2) of 0.961 on the training dataset. on the testing dataset, the model achieved an rmse of 1588.35 and an r2 of 0.955. figure 13—the performance of the cnn model. particle swarm optimization (pso) was used to optimize the parameters of lstm model, and the accuracy of the model was not improved. the training outcomes post pso optimization are illustrated in figure 14. following optimization, the model exhibited a root mean square error (rmse) of 1320.53 and a coefficient of determination (r2) of 0.943 on the training dataset. on the testing dataset, the model achieved an rmse of 1740.03 and an r2 of 0.937. figure 14—the performance of the lstm model. through iterative optimization with the pso algorithm, a superior combination of parameters for the cnnlstm model was obtained, enhancing its fitting capacity and predictive accuracy. the training outcomes are depicted in figure 15. ultimately, the optimized model achieved an rmse of 1286.01 and an r2 of 0.981 on the training set, and an rmse of 1393.91 and an r2 of 0.963 on the testing set. the iterative optimization with the pso algorithm significantly improved the performance of the cnn-lstm model, enhancing its precision and predictive ability on both the training and testing datasets. the optimized model is now better equipped to accurately predict the target variable and provide more reliable results. improved oil and gas recovery 16 figure 15—the performance of the cnn-lstm model. after optimizing the three models, distinct production prediction models have been obtained. the next step is to assess these models and select the optimal one. model performance evaluation employs metrics, such as rmse and r2. on the testing dataset, a comparison is made among the three machine learning models that have undergone pso parameter optimization, based on rmse and r2. figure 16 illustrates the comparison of rmse and r2 on the testing dataset for the three machine learning models following pso parameter optimization. the results demonstrate that the cnn-lstm-pso model exhibits the smallest rmse (1393.91) and the highest r2 (0.963) on the testing dataset. consequently, the cnn-lstm-pso model is chosen as the optimal production prediction model. it is important to emphasize that this conclusion is specifically applicable to the current dataset and task. if applied to different datasets or tasks, a re-evaluation of model performance is necessary to determine the optimal model choice. figure 16—rmse and r2 comparison on the testing dataset for different machine learning models after optimization. sensitivity analysis. sensitivity analysis is a crucial method for evaluating how a model responds to variations in input parameters. it plays a significant role in optimizing model performance and enhancing decision quality. improved oil and gas recovery 17 in the context of univariate sensitivity analysis, the values of each parameter are altered individually to observe the corresponding changes in net present value (npv). this aids in making more accurate decisions by understanding how the model's output reacts to parameter adjustments. economic evaluation. this model comprehensively considers reservoir parameters, hydraulic fracturing parameters, and economic benefits with the aim of maximizing the economic returns of oil wells. it serves as a vital decision-making reference for oilfield development. the model’s inputs encompass the reservoir parameters of the target well, such as reservoir thickness, porosity, permeability, and oil saturation. by incorporating optimized hydraulic fracturing parameters, it predicts the production of the target well. these production predictions are then applied in the economic evaluation model to calculate the npv under the given hydraulic fracturing parameter sets. the model construction process is illustrated in figure 17. figure 17—structure of the economic evaluation model. univariate sensitivity analysis. during the process of univariate sensitivity analysis, the initial values of reservoir and hydraulic fracturing parameters are established. reservoir parameters keep the same for all the cases, including reservoir length of 1200 m, porosity of 11%, permeability of 0.05 md, and oil saturation of 55%. maintaining other hydraulic fracturing parameters constant, while the fracturing spacing individually various and is set to be 40 m, 55 m, 70 m, 85 m, and 100 m, to conduct the sensitivity analysis and explore the impact of fracturing spacing on npv. figure 18 illustrates the results. it can be observed from figure 18 that npv increases with fracturing spacing increasing, but there might be an optimal fracturing spacing where npv starts to decrease after the certain threshold. in the context of conventional wells, reducing the fracturing improved oil and gas recovery 18 spacing could lead to a higher number of fracturing stages, resulting in a significant increase in fluid and proppant volume per well. this, in turn, would escalate fracturing costs. the rise in costs could potentially offset the benefits gained from increased production, leading to a decline in npv. therefore, the optimal fracturing spacing may vary across different oilfields and scenarios, necessitating a balanced consideration of costs and benefits. figure 18—sensitivity analysis of fracturing spacing on npv. based on the results presented in figure 19, variations in npv under different single-stage fluid volumes (500m3, 750m3, 1000m3, 1250m3, and 1500m3) are evident. from figure 19, it can be observed that the npv reaches its peak when the single-stage fluid volume reaches 1000 m3. single-stage fluid volume is a critical parameter in hydraulic fracturing, affecting injection rates, fracture propagation, and proppant permeation. increasing the single-stage fluid volume often leads to higher oil well production. however, it also escalates costs and environmental impact, thereby potentially reducing npv. hence, the optimal single-stage fluid volume varies based on distinct well and geological conditions. figure 19—sensitivity analysis of single-stage fluid volume on npv. improved oil and gas recovery 19 by examining different single-stage sand volumes (50 m3, 100 m3, 150 m3, 200 m3, and 250 m3), we have observed variations in npv. it is evident from figure 20 that the impact of single-stage sand volume on npv is relatively limited. however, a significant reduction in npv becomes apparent when the single-stage sand volume is increased to 150 m3. this implies that raising the single-stage sand volume beyond 150 m3 may have an adverse effect on npv. figure 20—sensitivity analysis of single-stage sand volume on npv. when considering single-stage displacement of 5 m3/min, 7.5 m3/min, 10 m3/min, 12.5 m3/min, and 15 m3/min, the variations in npv were observed. the changing outcomes are presented in figure 21. the study reveals that within a certain range, increasing the single-stage displacement can notably enhance the npv. elevating the single-stage displacement leads to a corresponding increase in oil well production, with a relatively minor impact on fracturing costs. consequently, a positive correlation exists between the single-stage displacement and oil well production. augmenting the single-stage displacement proves beneficial in improving oil well yields, thereby augmenting the npv. figure 21—sensitivity analysis of single-stage displacement on npv. improved oil and gas recovery 20 fracturing parameters optimization example finally, the fracturing parameters for horizontal wells were optimized using the pso algorithm, with the objective of maximizing npv. following a predefined objective function, the algorithm iteratively searched for the optimal solution. figure 22 illustrates the construction process of the npv fracturing parameters optimization model for mfhws. figure 22—structure of npv fracturing parameters optimization model. by analyzing on-site data, the initial values for geological and fracturing parameters for the experimental well are provided as follows: reservoir length of 1200 m, porosity of 11%, permeability of 0.05 md, oil saturation of 55%, fracturing spacing of 58.2 m. the pso algorithm is then utilized for optimizing the fracturing parameters, with the primary objective being to maximize the npv. through multiple iterations, the optimal combination of fracturing parameters is determined to achieve the maximization of economic benefits for horizontal wells. table 8 presents the initial values, ranges, and the final values after optimization using the pso algorithm for the fracturing parameters. table 8—fracturing parameters optimization results with npv as the objective. fracturing parameters initial value range of values optimum value fracture spacing (m) 58.2 [30,100] 83.05 single-stage fluid volume (m3) 1000.0 [500,1500] 1125.00 single-stage sand volume (m3) 141.6 [50,250] 91.00 single-stage displacement (m3/min) 9.0 [5,15] 11.82 improved oil and gas recovery 21 figure 23 illustrates the iterative process of optimizing fracturing parameters using the pso algorithm. the horizontal axis represents the iteration number, while the vertical axis represents the npv. the results indicate that as the number of iterations increases, the range of npv values gradually converges. through continuous iterations, the npv value stabilized at $5.84 million, successfully achieving the economic benefit target. by optimizing the fracturing parameters, it is possible to maximize well production and economic benefits, reduce unnecessary operations and resource wastage, lower costs, and attain the highest economic returns. figure 23—iterative process of npv for fracturing parameters optimization using pso algorithm. discussion and prospects fracturing parameter optimization holds significant importance in oil and gas exploration as it can maximize well productivity and economic returns. with the continuous advancement of technology, the utilization of machine learning for production forecasting and fracturing parameter optimization is expected to gain broader applicability. however, through the analysis and discussion of the empirical results, it is evident that there are several areas where the model can be enhanced. firstly, to better accommodate diverse geological conditions and reservoir characteristics, further research is warranted to explore the response patterns of different types of reservoirs. additionally, improving the quantity and quality of available data and adopting more sophisticated algorithms and models can enhance the precision of predictions and the efficiency of optimization. moreover, delving into multi-objective optimization algorithms that consider multiple targets and constraints can lead to more comprehensive optimization strategies. these measures collectively contribute to the advancement of reservoir optimization and oilfield development, addressing the identified limitations in the current model. in the future, machine learning and deep learning technologies will continue to evolve, and real-time online analysis will become a crucial trend in fracturing parameter optimization. real-time online analysis will enable timely monitoring and collection of operational data, production data, geological data, etc., which can be directly input into optimization models for analysis and decision-making. this approach allows for immediate feedback on the current reservoir status and performance, assisting engineers in real-time adjustments and optimization of fracturing parameters to adapt to ever-changing oilfield conditions. furthermore, the future of fracturing parameter optimization will involve a greater consideration of multidisciplinary factors. knowledge from various disciplines such as geology, geophysics, and rock mechanics will be integrated into optimization models to build more comprehensive and holistic optimization strategies. this interdisciplinary approach will lead to the creation of solutions that take into account a broader range of influences and factors. improved oil and gas recovery 22 in summary, fracturing parameter optimization will leverage advanced technology and data analysis to establish intelligent and efficient models, providing effective support and decision-making for oilfields. the advancements in machine learning, deep learning, and real-time online analysis will enhance the intelligence and automation of optimization models, enabling them to adapt to the actual reservoir conditions and drive the efficient development of oilfields. conclusions this paper integrated numerical simulation and machine learning techniques in the field of oil and gas reservoir development to establish a comprehensive workflow for optimizing hydraulic fracturing parameters. this study obtained a best machine learning-based production prediction model based on the synthetic production dataset generated from numerical simulation. the particle swarm optimization (pso) algorithm was applied to optimize fracturing parameters by maximizing well productivity and economic returns, minimizing unnecessary operations and resource waste, thus reducing costs and achieving maximum economic benefits. the main conclusions are follows. 1. the cnn-lstm model was identified as the optimal production prediction model. 2. from univariate sensitivity analysis, it is clear that increasing the single-stage fluid volume and the singlestage displacement can notably enhance the npv; there is an optimal fracturing spacing corresponding to the highest npv; while increasing the single-stage sand volume beyond a certain threshold may have an adverse effect on npv. conflicting interests the author(s) declare that they have no conflicting interests. references albawi, s., mohammed, t. a., alzawi, s. 2017. understanding of a convolutional neural network. paper presented at the 2017 international conference on engineering and technology (icet), 21-23 august. 17615756. 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colorado, 22-24 july. urtec-2019-47-ms. zhang, x. and awotunde, a. a. 2016. improvement of levenberg-marquardt algorithm during history fitting for reservoir simulation. petroleum exploration and development 43(5): 876–85. zhou, q., dilmore, r., kleiter, a., et al. 2014. evaluating gas production performances in marcellus using data mining technologies. paper presented at the unconventional resources technology conference, denver, colorado, 25-27 august. urtec-1920211-ms. zou, c., zhai, g., zhang, g., et al. 2015. formation, distribution, potential and prediction of global conventional and unconventional hydrocarbon resources. petroleum exploration and development 42(1): 14-28. shide yan, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation and enhance oil recovery. weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. his research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. li holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. improved oil and gas recovery 24 min zhang, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focused her research in areas involving reservoir simulation, chemical flooding, and enhanced oil recovery. zhengbo wang, is a senior reservoir engineering in research institute of petroleum exploration and development, petrochina. he specializes in enhanced oil recovery. dr. wang holds a a phd degree in petroleum engineering from research institute of petroleum exploration and development, petrochina. zhaoxia liu, is a senior reservoir engineering in research institute of petroleum exploration and development, petrochina. she specializes in enhanced oil recovery. dr. liu holds a a phd degree in petroleum engineering from research institute of petroleum exploration and development, petrochina. keze lin, is a undergraduate student of china university of petroleum (beijing), beijing. hongliang yi, is a senior reservoir engineering in liaohe oilfield company of petrochina. he specializes in enhanced oil recovery. abstract introduction methodology and workflow (a)reservoir length (b)porosity (c)permeability (d)oil saturation analysis of model training results fracturing parameters optimization example discussion and prospects conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1308 received august 26, 2024; revised september 2, 2024; accepted september 22, 2024. *corresponding author: umer.engr@hotmail.com 1 experimental investigation of agricultural wastes effect on drilling mud properties mian umer shafiq*, ucsi university, cheras, malaysia and ucsi-cheras low carbon innovative hub research consortium, kuala lumpur, malaysia; deena n. vivegananthan, hextar kimia sdn bhd, malaysia; momna khan, nfc institute of engineering and technology multan, pakistan; hisham ben mahmud, utp malaysia, perak, malaysia; lei wang, chengdu university of technology, chengdu, china; maryam jamil, shenzhen university, shenzhen, china abstract the future of the oil and gas industry increasingly depends on the development of environmentally sustainable drilling fluids through the utilization of waste materials that have a minimal impact on ecosystems. conventional drilling muds typically contain chemical additives, water, oil, and drill cuttings, which pose significant environmental risks. to reduce reliance on toxic chemicals in drilling fluids, this study explores the potential of using natural additives such as palm oil fuel ash (pofa), wood ash (wa), and rice husk (rh). water-based drilling muds were formulated with these additives at varying concentrations (0.6, 0.8, and 1 wt%) and particle sizes (75, 150, and 212 μm). the performance of these modified muds was compared against a standard mud without additives. the optimal formulation, identified through experimental analysis, was 0.8 wt% of 212 μm rh. rice husk was found to significantly enhance the filtration properties and rheology of the drilling mud, demonstrating its efficacy as an additive. the evaluation of locally sourced agricultural waste as additives not only reduced costs and improved mud performance but also substantially mitigated the environmental impact. introduction the viscosity of drilling fluids is significantly influenced by temperature. at lower temperatures, both gel strength and apparent viscosity tend to increase, particularly when the fluid remains static. as noted by zhao et al. (2017), an increase in rheological parameters can be problematic, as it leads to elevated pressures and higher equivalent circulating density (ecd). high-viscosity drilling fluids exhibit greater resistance to flow (neshat and shadizadeh 2016). therefore, to mitigate fluid loss and minimize near-wellbore damage, it is essential to design drilling mud with appropriate properties. as reservoir depth increases, so do temperature and pressure, resulting in changes in mud properties such as yield point (yp) and plastic viscosity (pv). maintaining the stability of these parameters is particularly challenging, as they are critical for effective hole cleaning and ecd control. the permeability of the formation may decrease due to damage caused by the invasion of drilling fluid filtrate (chen and mohanty 2014), while the formation of a filter cake from solid particles can further reduce the absolute permeability around the wellbore. in recent years, environmental regulations and safety concerns have become major priorities in the oil and gas industry. to address these issues, the additives applied in this research are designed to be environmentally friendly, ensuring minimal harm to the ecosystem. additives are introduced to drilling fluids to alter their rheological and surface properties (olatunde et al. 2012), providing benefits such as minimizing fluid loss and mailto:annagderyaev@outlook.com improved oil and gas recovery 2 reducing reservoir damage during drilling. currently, the industry is investigating additives that offer a combination of environmental compatibility, thermal stability, and multifunctionality (galindo et al. 2015). the performance of various additives in the market varies, with common types including weighting agents, viscosifiers, lost circulation materials, lubricating agents, shale stabilizers, and rheological control agents (ghazali et al. 2015). the growing expansion of agro-waste has led to an increase in raw residues from agro-industrial processes, crops, and livestock. agro-waste production is estimated at approximately 998 million tons annually, making effective waste management crucial. the 3rs principle — reduce, reuse, recycle — has been introduced to promote environmental sustainability. the primary objective of this hierarchy (figure 1) is to minimize waste while maximizing the benefits of waste utilization. consequently, replacing synthetic polymers with locally available materials such as wood ash, fuel ash, and rice husk is an important step toward sustainable development. figure 1—hierarchy concept of 3rsreducing, reusing, and recycling. due to the increasing demand for hydrocarbon production, it is essential to adopt innovative methods for oil and gas resources extraction. drilling operations account for approximately 8% of operating expenditures (opex). typically, two types of drilling fluids are employed: water-based mud (wbm) and oil-based mud (obm). extensive research has been conducted on wbm, focusing on enhancing its properties by incorporating various additives such as weighting agents, viscosifiers, and stabilizers. initially, drilling mud was formulated with clay; however, to manage high-pressure formations, a higher density mud was required, which led to the addition of heavy minerals. in 1922, barite was introduced as a weighting material in drilling mud by the national pigments and chemical company (apaleke et al. 2012). since then, various other additives, including surfactants, salts, colloidal solutions, alkalis, organic polymers, and weighting agents, have been utilized. the selection of these additives is typically determined by the characteristics of the formation and the associated project costs. current formulations of water-based drilling fluid. to leverage the advantages of oil-based muds, such as reduced environmental impact and lower fluid disposal costs, high-performance water-based drilling fluids (hpwbfs) were developed. these fluids are designed to enhance borehole cleaning and wellbore stability, typically consisting of a mixture of potassium chloride (kcl) and polymers such as xanthan gum, partially hydrolyzed polyacrylamide (phpam), and polyamide derivatives for dehydration. an environmentally friendly improved oil and gas recovery 3 aluminum-based high-performance water-based drilling mud (hpwbm) was developed by ramirez et al. (2007) and successfully applied in an exploratory well in the argentinian magellan strait, replacing oil-based mud with minimal environmental impact. in contrast, ramy et al. (2016) formulated a new hpwbf using a combination of salt and polymers with varying mud weights, but this formulation proved less environmentally friendly. the oil and gas industry is often viewed as environmentally risky due to the use of hazardous chemicals. as a result, significant research has been conducted to develop more environmentally sustainable drilling fluids (kumar et al. 2013). the emphasis on natural additives and eco-friendly materials has grown, aiming to reduce both overall drilling costs and environmental pollution. table 1 highlights the advantages and disadvantages of high-performance water-based muds. a key focus in current drilling fluid development is environmental sustainability. udoh and okon (2011) created a water-based drilling mud that posed fewer environmental risks when combined with eco-friendly additives and demonstrated efficacy in drilling through shale beds. however, the silicates in the fluid posed potential risks to the rock, leading thaemlitz et al. (1999) to propose the use of micro-sized spherical polymer beads to enhance lubrication. to address challenges in high-pressure high-temperature (hpht) formations, thaemlitz et al. (1999) developed a chromium-free, environmentally friendly fluid. hpht reservoirs, which contain significant quantities of hydrocarbons, are defined by wellbore pressures exceeding 0.8 psi/ft and temperatures around 300 ° f (yunita et al. 2016). designing muds capable of withstanding these extreme conditions remains a significant challenge. organic polymers are commonly added to drilling fluids to minimize filtrate loss during operations (amani and al-jubouri 2012), but their high cost necessitates alternative solutions in many regions (okon et al. 2014). table 1—water-based mud pros and cons (friedheim et al. 2012). disadvantages advantages the salt can be dissolved which increased mud weight cost-effective and cheap hydrocarbon flow can be impeded by wbdf environmentally friendly in some sense wbdf supports the dispersal and disintegration of clays easy accessibility and availability wbdf is incompetent to penetrate shale or water-sensitive shale fast penetration rate the ability of wbdf to corrode iron components to mitigate harmful environmental impacts, hector et al. (2002) explored the use of potassium silicate in drilling mud, which was later repurposed as a fertilizer. similarly, warren et al. (2003) formulated a drilling fluid containing amphoteric cellulose ether (ace), a water-soluble, eco-friendly polymer that is low-cost and has minimal solid content. in another approach, davidson et al. (2004) developed a drilling fluid based on a carbohydrate derivative complexed with iron, which effectively removed hydrogen sulfide. ramirez et al. (2005) created a biodegradable drilling fluid designed to maintain borehole stability and enable drilling through healing shale. however, the presence of asphalt in the formulation limited its environmental friendliness. dosunmu et al. (2010) introduced an oil-based drilling fluid (obdf) utilizing groundnut oil and palm oil, which demonstrated not only environmental benefits but also potential to enhance crop growth. meng et al. (2012) investigated the use of carbon ash as an additive in drilling fluids, studying its effects on fluid flow, rheology, and filtration loss. the results indicated that carbon ash enhanced the properties of waterbased mud, particularly by improving yield point. subsequently, mahto and jain (2013) employed fly ash, an industrial byproduct, in water-based mud (wbm), observing an increase in yield point without significantly altering physical properties. improved oil and gas recovery 4 negm et al. (2015) emphasized the importance of replacing harmful substances in drilling mud with naturally less toxic additives. this aligns with the petroleum industry's ongoing efforts to develop low-cost, environmentally safe additives that also improve performance and efficiency. field operations such as stimulation, completion, drilling, and production often encounter challenges that can be addressed by modern, environmentally friendly drilling fluids (ndubi and ben mahmud 2019). nanotechnology has also become a focus in the petroleum industry, particularly for mitigating the environmental concerns associated with oil-based and water-based drilling fluids. nano-silica, one of the more promising nanoparticle additives, has shown potential, but achieving optimal results requires precise concentration when added to synthetic-based mud. table 2—existing studies of agro-waste utilization in drilling mud author additive s fluid size of particle concentr ation apparent viscosity , cp plastic viscosit y, lbs initial gel strength , lb/100ft2 yield point, lbs/100 ft2 10-min gel strength, lb/100ft2 cake thickness, mm filtrate loss, ml (niemuth 2013) fly ash wbm 1-100nm 1-3 wt.% 28.75 17.5 5 22.5 9 0.3 6 (okon et al. 2014) rice husk wbm 125μm 5,10,15,2 0g 18 8 2.15 9.56 4.78 3.2 16.5 (meng et al. 2014) carbon ash wbm 0.2, 0.4, 0.6, 0.8 wt. % 13.5 5 8.3 2 21 (alflah et al. 2015) gum arabic wbm 0.15 0.425mm 0.76 9.4, 13.44, 17.15, 21.44wt. % 12.5 10 2 23 (ghazali et al. 2015) corn starch wbm 250μm. 2,4,6,8,1 0g 5 37 40 2.5 31 (hossain and wajheeu ddin 2016) grass wbm 300, 90, 35μm 0.25, 0.50, 0.75, or 1.0 g 11 8.5 3 4 15 12.2 (onuh 2017) corn cobs & coconut shells wbm 2,4,6,8,1 0g 16 (seteyeo bot et al. 2017) rice husk obm 125μm 75g 119.5 93 24 53 63 1.21 17 improved oil and gas recovery 5 this study attended to experimentally investigate the performance of different agricultural wastes on the water-based drilling mud. all the recent wastes mentioned in table 2 were tested on different parameters of mud. therefore, the main aim of this project is to widen the application of present agricultural by-products and waste i.e., pofa in drilling mud to determine its performance in improving mud rheology and filtration properties. materials the rice husk and pofa were collected from the local village located near miri, sarawak, and lambir palm oil mill respectively. while the wood ash (carbon ash) was provided by a plywood company in miri, sarawak. all these wastes’ material was collected free of cost as they are readily available in malaysia and are often dumped in landfills. table 3 shows the materials used in this research and their purpose. table 3—materials and purposes. materials purposes distilled water to prepare water-based drilling fluid bentonite to be added in water-based mud rice husk rheological additive de-ionized water ph meter calibration wood ash ago-waste additive pofa agro-waste additive experimental methods rice husk preparation. rice husk was initially dried to remove all the moisture content by placing it using the crucible inside the oven at 45°c for about 4 hours. the dried husk was grounded into a smaller size using a mortar pestle, sieved to obtain fine particles (75, 150, and 212 μm), and later plastic container was used to seal it with aluminum foil. schematic diagram of rice husk preparation is shown in figure 2 while figure 3 shows the prepared rice husk. figure 2—rice husk preparation schematic diagram. improved oil and gas recovery 6 figure 3—rice husk. preparation of pofa. to achieve the required particle size, a combustion process was performed on pofa by putting it in a crucible and placing it into a clean furnace for 4 hours at 500°c. finally, it was then sieved to obtain the desired particle sizes (75, 150, and 212 μm) and placed in a plastic container, which was sealed with aluminum foil. the whole procedure is presented in figure 4, while figure 5 represents prepared pofa. figure 4—pofa preparation schematic diagram figure 5—palm oil fuel ash (pofa). wood ash preparation. wood ash is obtained by burning the wood. plywood was purchased and combusted in the furnace using a crucible for 4 hours at 800°c. finally, it was then sieved to obtain the desired particle sizes (75, 150, and 212μm) and placed in a plastic container, which was sealed with aluminum foil. the whole procedure is presented in figure 4 while figure 6 represents prepared wood ash. improved oil and gas recovery 7 figure 6—wood ash. preparation of mud samples. preparation of base fluid. a fresh wbm of 350 ml of distilled water with 15 grams of bentonite was prepared in a beaker of 500 ml. fann multi-mixer was used to ensure even mixing of the bentonite by continuously stirring it for 15 minutes. preparation of mud samples with additives. the total weight of mud played a decisive role in the concentration of additives to be added to the mud. 0.6 wt%, 0.8 wt%, and 1 wt% (3.5g/350ml) concentrations of additives were applied respected to the drilling muds. once bentonite solution was prepared, additives were added and stirred for almost 10 mins to ensure uniform mixing. table 4 shows the formulation of wbm with different additives. table 4—drilling mud prepared with various additives. additive size, (microns) concentration, (wt%) bentonite, (grams) distilled water, (ml) rice husk, (grams) palm oil fuel ash, (grams) wood ash, (grams) 15 350 212 1 15 350 3.5 212 1 15 350 3.5 212 1 15 350 3.5 150 0.8 15 350 2.8 150 0.8 15 350 2.8 150 0.8 15 350 2.8 75 0.6 15 350 2.1 75 0.6 15 350 2.1 75 0.6 15 350 2.1 results and analysis drilling muds without additives. density measurement. density measurement is very important to control the formation pressure, especially high-pressure drilling zones. different particles and additives are used to form a drilling mud. figure 7 showed the results of the density measurement. with the increase in the size of rice husk and the number of husk particles, it was observed that the density of mud increased. however, due to the high density of mud, the penetration rate of drilling mud decreases (krishnan et al. 2016) due to the holddown effect. usually, the mud weight is kept low during the early stages of drilling and increased while drilling deeper into the formation to optimize the penetration rate and mitigate well control (bamaga et al. 2013). the density of mud increased gradually when rice husk has been added therefore, it can be used as a weighting agent. improved oil and gas recovery 8 the density of standard mud is lowest (8.8 ppg) without the addition of any weighing agent because of the less solid content present in the bentonite. thus, the high quantity of solid particles in rice husk leads to an increase in mud density. figure 7—drilling fluid density when various concentrations and particle sizes of rice husk added. hpht filtration properties. filter properties of drilling mud were determined after incorporating rice husk. 17ml fluid loss was observed and a 3mm thick mud cake was formed when drilling fluid without any additives was tested at hpht conditions. table 5 represent the effects of rice husk with different particle sizes on filtration loss properties of the drilling mud. the loss of filtrate volume was improved when rice husk was added (figure 8). reduction of 44%, 52%, and 62% in mud filtrate volume was observed when 212μm rice husk was added into drilling fluid at 0.6wt%, 0.8wt%, and 1wt% concentrations respectively, as shown in figure 9(a). figure 9(b) shows the filtrate loss when 150 μm-sized rice husk was added to the drilling fluid. further decrease in filtration loss was observed to a maximum of 52% when rice husk (150 μm in size) concentration increased to 1wt%. it was also noticed that the thickness of mud cake was increased by increasing rice husk content, as presented in table 5. this shows that the presence of more rice husk decreases the pore spaces in the mud cake (ba et al. 2013). it was also noticed that the thickness of mud cake formed by drilling fluid incorporating rice husk is thinner compared to the base fluid mud cake (table 5). this is because of the high compressibility of rice husk under high-pressure conditions (korotkova et al. 2016). the fluid loss is reduced up to 45% when drilling fluid was added with 75μm rice husk as shown in figure 9(c). therefore, rice husk can be used as a filtration loss control agent. moreover, when the particle size was increased, the fluid loss decreased, which indicates that bigger particles enhance the linkage of solids. table 5—filtration properties of drilling fluid comprised of various size of rice husk. filtration test 212 μm 150 μm 75 μm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm base fluid 9.5 3 9.5 3 9.5 3 0.60% 5 2.2 6.7 2.4 8.5 2.6 0.80% 4.5 2.2 6.5 2.45 8.5 2.6 1.00% 4 2.3 5 2.5 8 2.7 improved oil and gas recovery 9 (a)212 μm (b) 150 μm (c) 75 μm figure 8—filtrate volume after 30 min of bentonite dispersion when added various sizes of rh to base fluid. (a)212 μm (b) 150 μm (c) 75 μm figure 9—filtrate loss difference when added various sizes of rh to base fluid. drilling muds with wood ash particles. density measurement. the effect of wood ash on drilling fluid density is shown in figure 10. it was observed that the density of drilling fluid was decreased with the addition of wood ash. it could be due to the clay particles enhanced dispersity with the addition of wood ash. moreover, by adding the wood ash, the bentonite particle aggregation decreased. however, density decreases by decreasing the wood ash particle size. it could be because the absorbed wood ash improved the dispersity of the clay particles (meng et al. 2012). hpht filtration properties. table 6 showed the drilling fluid properties after adding wood ash of different sizes. it was observed that increasing the concentration of wood ash increases the filtration loss of bentonite dispersion as shown in figure 11. this is due to the electrostatic adsorption of drilling mud, which is responsible for the reduction in agglomeration between bentonite particles (meng et al. 2014). improved oil and gas recovery 10 figure 10—drilling fluids density when added various particle sizes and concentrations if wood ash. there was also a significant effect of particle size on mud cake thickness and filtration loss. large additives reduce the fluid loss and increase the mud cake thickness, which resulted in a strong and impermeable mud cake. the results of filtrate loss are presented in figure 12. the least filtrate loss was observed when the drilling fluid consists of 75 μm of wood ash at 0.6 wt%. table 6—filtration properties of drilling fluid comprised of various size of wood ash. filtration test 212 μm 150 μm 75 μm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm base fluid 9.5 3 9.5 3 9.5 3 0.60% 5 3.33 5.5 3.17 5.5 3.1 0.80% 5.5 3.35 6.55 3.24 6.5 3.15 1.00% 6.5 3.38 8.5 3.29 8 3.2 (a)212 μm (b) 150 μm (c) 75 μm figure 11—filtrate volume after 30 min of bentonite dispersion when added various sizes of wood to base fluid. improved oil and gas recovery 11 (a)212 μm (b) 150 μm (c) 75 μm figure 12—filtrate loss difference when added various sizes of wood to base fluid. drilling muds with pofa particles. density measurement. the density of mud after adding pofa is shown in figure 13. the value of density range between 9.46 ppg and 9.55 ppg after adding pofa. the density value increased by adding the pofa because solid content increased in the bentonite solution. the highest value of density was obtained using 1 wt% of 212 μm pofa. figure 13—drilling fluids density when added different particle sizes and concentrations of pofa. hpht filtration properties. figure 14 shows that the filtrate loss was decreased when the amount of pofa increased compared to the base mud. by adding pofa, the filtrate loss of drilling fluid was decreased as well. the potential of pofa to be used as a filtrate control agent is shown in figure 15, where a maximum 52% reduction in filtrate loss was observed. the highest filtrate loss of 11.8 ml was obtained when using 0.6 wt% of 212 μm (figure 15 a). but all the drilling muds that incorporated with pofa showed less filtrate loss compared to standard mud loss (17 ml). with the reduction in the size of pofa particles, filtration loss also decreases, because the smaller particles of pofa offered a high surface area, which enables effective plugging and sealing of the pores. however, it was observed that the thickness of mud cake increases with increasing the particle size and concentration of pofa, as seen in table 7. however, thicker mud cakes posed problems during drilling and cementing. therefore, the size and concentration of additives should be optimized to avoid drilling problems with less fluid loss. improved oil and gas recovery 12 table 7—filtration properties of drilling fluid comprised of various size of pofa filtration test 212 μm 150 μm 75 μm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm filtrate volume @7.5 min, ml mud cake thickness, mm base fluid 9.5 3 9.5 3 9.5 3 0.60% 6.8 3.16 5.5 3.1 5.1 3.08 0.80% 6.5 3.18 5.3 3.16 4.8 3.13 1.00% 6 3.22 5 3.2 4.5 3.15 the permeable formation can be damaged significantly due to filtrate invasion, which causes water blocking, clay swelling, or particle plugging (fleureau 1992). the thickness and permeability of filter cake depend on the particle size distribution as large particles tend to form less permeable filter cake (wu et al. 2015). figure 16 shows the same results that drilling fluid with rice husk demonstrated better fluid loss control. the low permeability results were obtained because of the development of bridging and cross-linking between bentonite and additive particles. rice husk particles contain lignin, which helps in the flocculation and binding strength of particles, creating a low permeable seal of filter cake when high pressure is applied (seteyeobot et al. 2017). that is why the rice husk is responsible for the compressibility at high-pressure conditions without decreasing the borehole diameter. (a)212 μm (b) 150 μm (c) 75 μm figure 14—filtrate volume after 30 min of bentonite dispersion when added various sizes of pofa to base fluid. improved oil and gas recovery 13 (a)212 μm (b) 150 μm (c) 75 μm figure 15—filtrate loss difference of bentonite dispersion when added various sizes of pofa to base fluid. viscosity analysis. figure 16 shows the viscosities of drilling fluids with different additives. the low plastic viscosity is desired to avoid internal resistance while the high apparent viscosity is desired as it shows the flowability of the fluid. the highest value of apparent viscosity was achieved by 212 μm rice husk at 0.8 wt%. therefore, it is favorable as an alternative option for viscosifiers. the value of mud yp should be low but when it is high enough, it could hold solid particles and allows effective hole cleaning (power and zamora 2003). drilling fluid having 0.8 wt% of 212 μm rice husk was selected because it showed the highest yp as shown in figure 17. the relationship between the bridging particles and filtration loss was discussed by song et al. (2016). the decline in filtrate loss was observed with the increase in the concentration of bridging particles shown in figure 18. the ph tests were conducted to find the concentration of hydrogen ions in the drilling mud (vryzas and kelessidis 2017). the ph value of the drilling fluid changed with the addition of rice husk as presented in table 8. the increase in ph value was observed when rice husk was added to the drilling fluid, which means that the mud becomes more alkaline. grass particles were used by hossain and wajheeuddin (2016) as an additive to control corrosion. it was noticed that the ph value was increased, which ultimately can mitigate the corrosion process. therefore, rice husk can be considered as an alternative ph control environmentally friendly agent. (a) plastic viscosity (b) apparent viscosity figure 16—drilling fluids viscosity when added with designated additives. improved oil and gas recovery 14 figure 17—drilling fluids yield points when added with designated additives. (a) filtration volume (b) filtration loss figure 18—filtrate volume of drilling fluids comprised of designated additives. table 8—ph values of drilling fluids consisting of agricultural additives. test material ph unit base fluid 0.8 wt% of 212 μm rice husk 0.6 wt% of 75 μm wood ash 0.6 wt% of 212 μm pofa drilling fluid alkaline ppg 9.42 9.54 9.51 10.14 filtrate fluid 9.52 9.93 9.90 9.93 effect on drilling properties. the experimental evaluation of palm oil fuel ash (pofa), rice husk (rh), and wood ash in water-based mud formulations highlights their effectiveness in enhancing key properties of drilling fluids. the optimal formulation, consisting of 0.8% rice husk with a particle size of 212 µm, led to a notable 29% improvement in viscosity compared to standard mud. this increase in viscosity results in higher equivalent circulating density (ecd), which, while beneficial for well control, may decrease the rate of penetration (rop) and increase the risk of differential sticking. rice husk emerged as the most effective agent for controlling fluid loss, reducing it by 52%, compared to reductions of 30% with wood ash and 35% with pofa. these results demonstrate the potential of agro-wastes improved oil and gas recovery 15 in controlling mud rheology and reducing fluid loss during drilling operations. in addition, viscosity enhancements of approximately 15% were observed for wood ash and pofa under optimal conditions. the overall benefits of incorporating agro-waste materials into water-based drilling mud include improved control over filtrate loss, reduced mud cake thickness, and increased mud density. the increased density can help in managing formation pressures, making these additives particularly valuable for deep-well drilling operations where pressure control is critical. this suggests that agro-wastes may offer a sustainable, costeffective alternative to conventional drilling fluid additives while also contributing to environmental protection. conclusions the effects of palm oil fuel ash (pofa), rice husk, and wood ash on the properties of water-based mud have been experimentally evaluated and compared with standard mud formulations. the optimal composition was found to be 0.8% rice husk (rh) with a particle size of 212 µm, resulting in a 29% improvement in viscosity compared to the standard mud. this substantial increase in viscosity leads to a rise in equivalent circulating density (ecd) and a decrease in penetration rate, with the added risk of differential sticking. rice husk proved to be the most effective filtration control agent in the water-based drilling fluid, reducing fluid loss by 52%. comparatively, fluid loss was reduced by 30% with wood ash and 35% with pofa. these findings indicate that agro-wastes exhibit significant potential in managing mud rheology and controlling fluid loss volume. additionally, the viscosity improvements achieved with wood ash and pofa under optimal conditions were approximately 15%. overall, the use of agro-wastes as additives in drilling mud effectively controls filtrate loss and reduces mud cake thickness. furthermore, the increase in mud density achieved through the addition of these materials suggests that these additives could aid in managing formation pressure at greater depths. acknowledgment we thank the support by the “ministry of science and technology of the people’s republic of china, 2023yfe0120700” and ucsi university (reig-fetbe-2023/021). we also acknowledge lambir palm oil mills, sarawak malaysia for providing us the agro-waste free of cost to be used in this research. conflicting interest the author(s) declare that they have no conflicting interests. references alflah, s., balola, a. a., and ibrahim, a. a. 2015. effects of gum arabic addition on the behaviour of water base drilling fluids. journal of engineering and computer science 16(3): 1-8. amani, m. and al-jubouri, m. j. 2012. an experimental investigation of the effect of ultra-high pressures and 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seteyeobot, i., uma, j. a., enaworu, e., et al. 2017. experimental study of the possible use of locally derived plantain peelings and rice husk as additives for oil based mud at high temperature high pressure conditions. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 29-31 july. spe189075-ms. song, k., wu, q., li, m., et al. 2016. water-based bentonite drilling fluids modified by novel biopolymer for minimizing fluid loss and formation damage. colloids and surfaces a: physicochemical and engineering aspects 507(1): 58-66. thaemlitz, c.j., patel, a.d., coffin, g., et al. 1999. new environmentally safe high-temperature water-based drillingfluid system. spe drilling & completion 14(3):185-189. spe-37606-pa. vryzas, z. and kelessidis, v. c. 2017. nano-based drilling fluids: a review. energies, 10(4): 1-12. warren, b., van der, h.p., stewart, w. 2003. application of amphoteric cellulose ethers in drilling fluids. paper presented at the international symposium on oilfield chemistry, houston, texas, 5-7 february. spe-80210-ms. wu, g., qu, p., sun, e., et al. 2015. physical, chemical, and rheological properties of rice husks treated by composting process. bioresources 10(1): 227-239. yunita, p., irawan, s., and kania, d. 2016. optimization of water-based drilling fluid using non-ionic and anionic surfactant additives. procedia engineering 148(1): 1184-1190. zhao, x., qiu, z., huang, w., et al. 2017. mechanism and method for controlling low-temperature rheology of waterbased drilling fluids in deepwater drilling. journal of petroleum science and engineering 154(2): 405-416. mian umer shafiq currently working as an assistant professor with a professional engineer title at the department of chemical and petroleum engineering at ucsi university, malaysia. he has both industrial and academic experience for more than 12 years. he completed his phd degree in petroleum engineering from curtin university, malaysia. he completed his masters and bachelor ’s degree in petroleum engineering from utp, malaysia and uet, lahore, respectively. his research interests focus on production optimization, stimulation, acidizing, underground gas storage, reservoir simulation, geopolymers and drilling mud design. deena n. vivegananthan is working as a technical sales engineer at hextar kimia sdn bhd, malaysia. she completed her bsc degree in petroleum engineering in 2018 from curtin university, malaysia. momna khan, is a lecturer in petroleum and gas engineering at nfc iet multan, where she has worked as faculty for the last 2.5 years. she holds b.sc. from nfc iet multan, m.sc. from university of engineering and technology, lahore, and phd (in progress) from university of engineering and technology lahore, all in petroleum and gas engineering. hisham ben mahmud is an associate professor with a professional engineer title at the department of petroleum engineering, faculty of engineering, universiti teknologi petronas. he has industrial and academic experience for more than 15 years with well-known international organizations and universities in australia, libya and malaysia. he obtained his phd majoring in flow assurance from curtin university, australia, graduate diploma of oil & gas from university of western australia, australia, master of science in engineering studies, from sydney university, australia, and bachelor of engineering in chemical engineering from tripoli university. he is a chartered engineer of institute of engineers australia (ea), a graduate member of board of engineer malaysia (bem), a member of society of petroleum engineers (spe), and a fellowship of advance higher education (fhea). improved oil and gas recovery 18 lei wang is a professor of petroleum engineering at chengdu university of technology. his research interests are in reservoir simulation, hydrocarbon phase behavior, cryogenic fracturing, chemical and gas eor, and underground gas storage. he holds a b.s. (hons.) in environmental engineering and an m.s. degree in petroleum engineering, both from china university of petroleum (east china), and a phd degree in petroleum engineering with a minor in chemical engineering from colorado school of mines, usa. maryam jamil, is a ph.d. scholar at shenzhen university, china. his research interest are in photonic time crystal and application. abstract introduction materials experimental methods results and analysis conclusions acknowledgment conflicting interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1344 received december 6, 2024; revised january 5, 2025; accepted february 1, 2025. *corresponding author: eaniyom@gmail.com 1 prediction of leak on gas pipeline using a hybrid machine learning model aniyom ebenezer* and anthony chikwe, federal university of technology, owerri, nigeria abstract leak detection is an important problem during transportation of natural gas through pipelines for downstream operations. the investigation into solving this problem has led to the adoption of data science and machine learning approaches providing an optimal solution to this problem. in this study, a machine learning hybrid model was developed to detect natural gas leakages in pipelines. the hybrid model referred to as voting regressor assembles two machine learning models, the random forest regressor and the xgboost regressor for improving performance during leak detection. the input parameters to the hybrid model are temperature, pressure, and flow rate. results from this study showed an improvement in the performance of the hybrid model (voting regressor) in comparison to others in leak detection. this is depicted by an accuracy score of 93% and an error of 0.44%, and a recommended approach for leak detection. introduction pipeline networks are built with the goal of moving various chemical and petrochemical products over long distances in liquid and/or gas phase conditions. pipelines are extremely secure when compared to other modes of transportation, but they may have to operate under different circumstances, necessitating appropriate operation inspection. the need to transport fluid from the site of production to the place of use has resulted in a rapid increase in the number of pipelines being built (chris and saguna 2007). due to the toxic and hazardous nature of the products flowing through the pipeline, these products could cause accidents and environmental hazards if leaks occur. these leaks are sometimes caused by complexities of environmentally or human induced factors and disturbances generated along the pipeline flow network (obibuike et al. 2020). with the increasing awareness and empathy for the environment, most of the leakage from gas pipelines have shown cost effective and the demand for reliable detection systems is very high (boaz et al. 2014). this implies that the financial costs usually incurred by the company is often significantly high; including the cleaning cost of the environment and the payment for the pollution as being stated by the environmental guidelines and standards for the petroleum industry in nigeria (egaspin), which was issued to the department for petroleum resources (dpr) at the ministry of petroleum products in 1991 (olawuyi and tubodenyefa 2019). to avoid any further pipelines incidents and saving the environment, the promising solution is implementing better pipeline monitoring and leak detection equipment and practices. if proper maintenance is carried out, pipelines can last void of leaks (boaz et al. 2014). early detection of leaks and probably identification of the location using various best techniques allows for shutdown and cleanup works to avoid further pollution and spillage. there is a need to have a reliable leak detection system in oil and gas industries since this has become a priority when transporting petroleum products through a pipeline. because uncontrolled release of gas into the mailto:v.javanbakht@alumni.iut.ac.ir improved oil and gas recovery 2 atmosphere has both environmental and economic impact on both the industry staff and to the host community. although there has been a huge technological improvement over the decades, there still exists leaks and failures in practices adopted by most industries (skalle and aamodt 2020). thus, the early detection of leakages in the gas pipeline offers several advantages amidst the economic advantages; safety of the gas transportation, environment gas quality protection, and avoiding pipeline breakages which could be used for subsequent transportation (nicola et al. 2018). leak detection methods over the years, there have been different leak detection methods adopted over the years to monitor the integrity of a pipeline (bose and olson 1993). leak detection systems have been broadly classified into three major categories which are, biological methods, hardware-based methods, software-based methods. biological methods of leak detection. this is a traditional method for detecting leaks, it requires the presence of experienced personnel that walk along a pipeline, where they seek unusual occurrences close to the pipeline. it involves smelling of substances that may have been released as a result of the leak which occurred there. other times, it involves listening to noises which are generated because of the escaping substance from the pipeline. with this, the outcome from such an occurrence largely depends on the wealth of the experience which these personnel have. most times, this method also involves the use of trained dogs with a highly sensitive smell of substance which are released from the leak. hardware based methods for leak detection. several hardware devices can be used or are being used to assist the detection and localization of a leak. this method can be subdivided into four different types with respect to the principles of which these devices are designed as follows. visual devices. just as the name implies, it involves the detection of leaks through the identification of temperature changes within the surrounding environment of the pipeline. the method involves the use of vehicles, helicopters or portable systems which cover hundreds of miles per day. in recent times, there were several other devices which have been developed. this comprises the use of ir cameras to capture the effect of leak drops which are independent of the physical properties of the substances inside the pipeline. research was conducted on the use of temperature sensors such as multi-sensor electrical cable and optical time domain reflectometry (turner 1991). acoustic devices. according to vocabulary.com, acoustic devices are those devices which are used for amplifying or transmitting sounds. when leaks occur, it generates noise as the fluid escapes from the pipeline. the gas escape with a wave speed that is affected by the physical properties of the fluid in the pipeline. the acoustic detectors are designed such that they detect the wave as well as the leak. sampling devices. vapor monitoring devices can also be used for the purpose of leak detection, as it helps to detect the vapor level of the hydrocarbon in the pipeline surroundings. all these are possible with the help of a gas sampling device. pressure wave detectors. the wave produced during leak is usually propagated from the upstream to the downstream at the leak site. when these waves travel with a speed of sound, pressure transducers can be used to measure the pressure gradient with respect to time as stated by turner (turner 1991). software based methods for leak detection. the software-based methods, as stated by turner (1991) and other researchers in the 90s, depend on some parameters of the gas or the pipeline. these parameters include pressure, temperature, flowrate of the gas through the pipeline and other data which are provided by scada (supervisory control and data acquisition) system. bose and olson (1993) classified the software-based technique into four categories as follows. improved oil and gas recovery 3 flow or pressure change. this technique largely depends on the assumption that a high rate of change in flow or pressure at the upstream or downstream (inlet or outlet) sections of the pipeline signals the occurrence of a leak as stated by mears. mass or volume balance. this method allows for the detection of leaks with low rate of change in pressure or flow. it works with the principle of changes with respect to either mass or the volume dynamic model based system. dynamic models are mathematical models developed to account for the fluid flow within the pipeline. this involves measurement of several quantities and other physical equations that can help to achieve this fitness. some equations include the equation of the conservation of mass, the equation of the conservation of momentum, the equation of conservation of energy, the equation of state, etc. there are several software packages which could be used to achieve this as well. pressure point analysis (ppa). this technique is largely based on the assumption that if there is a pressure drop in the pipeline, there is a probability of leaks occurring. thus, it works with statistical correlations for the analysis of these measurements. intelligent models for leak detection. intelligent models are models which have computational intelligence, and which can learn specific tasks from either data or experiments. there exist several intelligent models which could be used for the different applications (akinsete and oshingbesan 2019). researchers have been on the scheme to improve the accuracy of the prediction of leak in a gas pipeline. thus, the engagement of intelligent & artificial models which work with by training the computer to understand patterns in a dataset and make accurate predictions for response needed. five intelligent models have been explored to ascertain the possibilities in the prediction of leak accurately. the models they used were gradient boosting, decision trees, random forest, support vector machine, and artificial neural networks were used for the data stream. in their research, the results obtained showed that support vector machine and artificial neural networks are better regressors than others. although, the random forest regressor and the decision trees can detect about 0.1% of the nominal flow in about 2hours. at the end of their experiment, they observed that the intelligent models performed comparatively well when other trade-offs are being considered (akinsete and oshingbesan 2019). santos et al. (2014) affirmed that the use of neural networks could be used to accurately predict leaks and their magnitudes. still on the application of machine learning models, alkhudhair et al. (2022) used machine learning models to predict anomaly that exist in the pipeline. in their research, they implemented five different machine learning models to predict occurrences which could be referred to as anomalies. the result of their experiment indicated that the use of support vector machine algorithm as well outperformed other models with an accuracy of 97.4% in detecting leakages in a pipeline. some of the models applied for leak detection in a gas pipeline are reviewed below. k-nearest neighbor (knn). the knn algorithm is a classification and regression problem model, which could be used to tackle both classification and regression tasks. it is an algorithm of the supervised learning machine type, which could also be used as outlier detection. it is a non-parametric learning algorithm; in that it does not assume anything about the underlying data. knn works by memorizing positions in the dataset with the corresponding values for which it can make predictions after model training (aniyom et al. 2022), thus it is very ease to implement and can be used for leak detection problems (dakheel et al. 2019). as one of the algorithms applied in the research, they implemented this algorithm for the intrusion detection in gas pipeline as needed in the gas distribution industry. in their research, they discovered the algorithm performed better than other models with an accurate score of 97%. although, may not perform optimally upon deployment due to the complex nature of gas distribution pipelines (dakheel et al. 2019). random forest. random forest is a machine learning algorithm which is most times regarded to as an ensemble learning method which can be used for classification and regression problem and for other task operations (akinsete and oshingbesan 2019). it is made up of n-collections of decision trees and it is largely improved oil and gas recovery 4 based on the bootstrap aggregation concept, which helps reduce the variances experienced in the datasets. it computes the average number of leaf nodes for improved performance accuracy (ekeopara et al. 2022). support vector machine.the support vector machine (svm) is primarily defined by the separating hyperplanes. it can be used for predictions across classification and regression problems. it aids in the distinguishing between instances of different categories where the separating line (hyperplane line) finds the optimal separating plane between points in the different classes. it allows for hard and soft margins which reduces errors and other biases (aniyom et al. 2022). when applying svm for regression problems, it adopts the loss function for the penalization of the loss function which most times lead to sparse representation of the rule. methodology this research applies to the machine learning algorithms for the prediction of leak pressure and location at several intervals of a natural gas pipeline. there exist several intelligent models which can be used for predictive analysis with machine learning. but machine learning as a field of study is largely classified into broad groups. supervised machine learning model. supervised learning machine model is an approach of creating an intelligent model by training the model on input data which have labels or targets inclusive. thus, it is that form of machine learning model which works on structured dataset (data in rows and columns) with well-defined features. here the computer is fed with a structured dataset and allowed to learn through the data, then predictions are made with respect to the trained data. this approach is only valid for datasets with the labels (dakheel et al. 2019). the supervised ml is further classified into two methods: regression and classification methods. these are used for solving problems associated with any of the categories (aniyom et al. 2022). unsupervised machine learning model. this approach is used to uncover the hidden patterns that are resident in a data. the dataset used in this approach does not have the target variable or the label. it can either be structured or unstructured. the widely used approach for solving unsupervised kind of problems is the clustering algorithms (ekeopara et al. 2022). model development in this study, gas pipeline x data was obtained for the analysis and the regression prediction of leak on gas pipeline. figure 1 shows the workflow for the methodology, it also shows the steps that were followed to the actualization of the predictions respectively. the procedure for model development involves the following. data description ingestion. the data used for the training of this model is a gas pipeline x dataset from the niger delta region in nigeria. the data was obtained from scada measurements of pressure, temperature and flowrate for inlet and outlet conditions of the gas pipe. in the ingestion of the data, both microsoft excel and python were used to understand the dataset and for the performance of other analysis necessary for the prediction of leak. the field data was used to validate and measure the performance of the models. the data represents 542 leak case pipeline which has been recorded with the following features of the pipe being recorded. data wrangling. this entails the modification of data for the machine learning models to appreciate it and to perform better. this was done visually with the use of microsoft excel, here the assessment of the dataset was done by scanning eyes through the dataset and the use of python to programmatically access it as well. here, improved oil and gas recovery 5 the errors related to the datasets were corrected with all visualizations. this section also involves the computation and analysis of data with python and its dependent libraries. figure 1—model development workflow. feature engineering. standard scaler. the features in the input variables were engineered for better performance of the models. the engineering done was the with the standardscaler algorithm. the standardscaler is used to resize the distribution of values so that the entire dataset will have a common means of observed values of 0 and standard deviation of 1. it was imported from the sklearn library for python. data split. data splitting is the process of dividing the dataset into two categories, the train and test dataset. the train dataset is used for the training of the model while the test dataset is used to test and predict the target variable. in this project, the split ratio used is 80:20 for train and test dataset respectively. hyper parameter tuning. searching for optimal parameters for the models helps improve the performance of the models during predictions and validations of the model with test dataset. the two ml algorithms proposed to be embedded inside the voting regressor were subjected to hyper tuning to obtain the best parameters for the prediction. the algorithm used for hyper parameter tuning is the gridsearchcv. gridsearchcv is the process of performing hyper parameters tuning to determine the optimal values for a given model. it has been observed that the performance of a model is largely dependent on the values of the hyper parameters. the gridsearchcv is a scikit-learn (sklearn) model_selection package, which was accessed using the ‘import’ keyword in python. the two models for which this algorithm was used upon are the random forest regressor and the xgboost regressor. random forest hyper parameters. the random forest regressor was subjected to tuning to reduce the loss function and six parameters of the algorithm were tuned for the best performing values using the gridsearchcv and results are displayed in table 1. improved oil and gas recovery 6 table 1—random forest hyper parameter and best value. s/n hyper parameter best value 1 bootstrap true 2 max_depth 1000 3 max_features auto 4 min_samples_leaf 1 5 min_samples_split 2 6 n_estimators 1800 xgboost hyper parameters. xgboost algorithm was also tuned to obtain the best performing values of its parameters. this algorithm was tuned using the gridsearchcv tuning algorithm, and the manual tuning also was applied for optimal performance. the increase in performance shows the place of tuning in machine learning projects. after several hours of tuning, the model attained its optimal performance at the following parameters and values displayed in table 2. table 2—xgboost hyperparameter and best value. s/n hyper parameter best value 1 n_estimators 1800 2 max_depth 4 3 eta 0.5 4 subsample 0.4 5 colsample_bytree 0.9 the tuning of the hyper parameters was done on the two single models only as they were embedded into the voting regressor and as such there was no need for the tuning of the voting regressor since these single models are expected to perform extremely well inside the voting regressor. after the tuning of the hyper parameters to be used for the building of the model, the actual process of the building of the single models was done with each of these models being trained independent of the other before the embedding itself was done. thus, there was room for the measurement of the single models and the validation of these single models to ascertain the performance of the voting regressor as it was being built. leak detection models performance metrics. after the models were successfully trained and predictions made, it was important to evaluate the performance of the models to estimate the loss function of the model. during model training the aim is to reduce the loss function to the minimum point. the metrics used for this study are as follows. i. mean absolute error (mae) ii. mean square error (mse) iii. root mean square error (rmse) iv. coefficient of determination score (r2 score) improved oil and gas recovery 7 mean absolute error. it is a measure of errors between paired observations expressing same phenomenon. it is the amount of error that exists in a measurement, which shows the difference between true value and predicted values. eq. (1) shows the mathematical equation for mae. ��� = �=1 � |��−��|� � ,...........................................................................................................................................(1) where, mae is mean absolute error; yi = predicted value; xi = true value; n = total no. of data points. mean square error. it measures the average of the squares of the errors, i.e. it measures the average of the squares of the errors. it accounts for the number of errors in mathematical and statistical models, it basic mathematical principle is shown in eq. (2). mse = 1 n i=1 n yi − ŷi 2 � ...............................................................................................................................(2) where,mse is mean square error;n = total no. of data points; yi is rue or observed values;ŷi is predicted values. root mean square error (rmse). this is the square root of the mean of the square of all of the error. it is considered an excellent general purpose error metric for numerical predictions. it is a frequently used measure of the differences between values predicted by the model and values observed. it is given by eq. (3). ���� = �=1 � ��−ŷ� 2 � � .....................................................................................................................................(3) where, rmse represents root mean square error; n is total no. of data points; yi is true or observed values; ŷi is predicted values. coefficient of determination score. this is known as the r-squared score. it is the proportion of the variation in the dependent variable that is predicted from the independent variable. the best possible score is 1.0 and it can be negative (since some models can be arbitrarily worse). it can be represented by eq. (4). �2 = 1 − ��� ��� ,...................................................................................................................................................(4) where r2 is coefficient of determination; rss is sum of squares residuals; tss is total sum of squares. results and discussion also, a visualization to show the relationship between the leak and output pressures versus the pipeline length, to understand the flow nature and the point where the leak occurred. figure 2—pressures versus pipeline length (miles). improved oil and gas recovery 8 model validation. validation of the model was done using the test data, after the predictions of the leak were executed. figures 3 through 5 show the regression plots for the single models that were used for the assemble voting regressor. the regression plots show how the models were fitted towards the regression line which depicts the accuracy level of the models in predicting the leak as against the actual field data. figure 3—regression for random forest. figure 4—regression for xgboost. figure 5—regression for voting regressor. improved oil and gas recovery 9 deviation from the regression line experienced in the regression plots from the models developed above are the because of irregularities and unconformities experienced in the dataset. it shows that 100% cannot be attained. the models all performed well by predicting over 90% of the leak experienced in the gas pipeline, with minimized errors of less than 2.0 in infinity range. figure 6 shows the statistical errors metrics which include mean square error (mse), mean absolute error (mae), and root mean square error (rmse). from the plot it is observed that the voting regressor algorithm had a minimal error, since the loss function was optimally reduced. with this minimal error experienced with the voting regressor, it is reliable upon deployment as it will perform better compared to the since models with almost complete reduction in the loss function. figure 6—error percentage plots. the accuracy of the models was measured using the sklearn metric functions to evaluate the performance of the models with respect to the actual field data. the r-squared metric was used for the evaluation of the performance of these models. table 3—models’ accuracy using statistical metrics. random forest xgboost voting regressor mae 0.3836 0.5447 0.4478 mse 1.1777 1.1275 1.0674 rmse 1.0852 1.0618 1.0331 r2 score 0.92 0.92 0.93 accuracy on train 0.99 0.999 0.999 accuracy on test 0.92 0.92 0.93 the r-squared metric is a statistical measure that represents the proportion of the variance for a target variable which is explained by the input parameters. table 3. shows the accuracy scores of the single models improved oil and gas recovery 10 and that of the voting regressor. from the table it was observed that the voting regressor had the best performance of above 1% increase in the accuracy and the r2 score. this implies that the voting regressor can predict leak in gas pipelines with higher accuracy than the single models. conclusion data analytics has gained more relevance in the oil and gas industry recently as the industry seeks to analytically use data for optimal productivity and reduction of cost/time management purposes. as data is growing in this industry, the ability of the industry to use this data alongside intelligent models to solve problems is very important and as well useful in the detection of leaks in oil and gas pipelines. in reservoir engineering and other disciplines in the oil and gas industry, history matching is often done, and futuristic predictions are made towards the prediction of either the optimal production rate or the oil in place in a particular reserve. the same is applied in the use of intelligent models to make predictions towards future occurrences in a gas pipeline, with respect to existing dataset recorded. machine learning models are data driven models, and as such they make use of the basic gas pipeline operational parameters to make predictions of leaks and the locations for which the leak occurs. the problem of detecting leaks is a two-way solution, the first is a classification solution where the model is expected to predict if a leak will occur or not (a yes-or-no-targetsolution). the other solution is the regression solution, where the model is expected to either predict the leak location or the leak pressure or both as the case maybe. the solution provided by this project is anchored on the latter to predict both the leak pressure and the leak location. the results obtained from the models are impressive. the machine learning models perform when compared relatively with the transient models (in use in most gas industries). because of the limitations in other models the data driven models are now seen to be more effective when it comes to leak detection. from the results obtained above the voting regressor performed better and will absolutely perform best upon deployment. from the results, it is evident that machine learning models can be used for the predictions and of leaks in a gas pipeline with bigger data volumes. the result indicates that the machine learning models could be used alongside the transient models and leak alarms for effective detection of leaks across gas pipeline networks. although these models have not been deployed in real time predictions, as such more research can be done in this regard and deployment executed in a pilot gas pipeline plant. conflicting interests the author(s) declare that they have no conflicting interests. reference akinsete, o. and oshingbesan, a. 2019. leak detection in natural gas pipelines using intelligent models. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 5-7 august, spe198738-ms. alkhudhair, a. a., aljubran, f., and alzannan, r. m. 2022. an anomaly detection model for oil and gas pipelines using machine learning. computation 10(138): 1-15. aniyom, e., chikwe, a., and odo, j. 2022. hybridization of optimized supervised machine learning algorithms for effective lithology. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 1-3 august. spe-212019-ms. boaz, l., kaijage, s., and sinde, r. 2014. an overview of pipeline leak detection and location systems. paper presented at the 2nd pan african international conference on science, computing and telecommunications, arusha, tanzania, 14-18 july. bose, j. r. and olson, m. k. 1993. taps’s leak detection seeks greater precision. oil and gas journal 12(2):123-135. chris, t. and saguna, a. 2007. pipeline detection techniques. annals computer science series 5(1):1-17. improved oil and gas recovery 11 dakheel, a. h., dakheel, a. h., and abbas, h. h. 2019. intrusion detection system in gas-pipeline industry using machine learning. periodicals of engineering and natural sciences 7(3): 1030-1040. ekeopara, p., odo, j., and obah, b., et al. 2022. hybridized probabilistic machine learning ranking system for lithological identification in geothermal resources. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 1-3 august. spe-212015-ms. nicola, c. i., nicola, m., and hurezeanu, i. 2018. pipeline leakage detection by means of acoustic emission technique. journal of mechanical engineering and automation 8(2): 59-67. obibuike, u. j., kerunwa, a., and udechukwu, m., et al. 2020. mathematical approach to determination of the pressure at the point of leak in natural gas pipeline. international journal of oil, gas and coal engineering 6(1):1-15. olawuyi, p. d. and tubodenyefa, d. z. 2019. review of the environmental guidelines and standards for the petroleum industry in nigeria. in institute for oil, gas, energy, environment and sustainable development (ogees institute), afe babalolauniversity, ado ekiti, nigeria. santos, r. b., sousa, e. o., and de silva, f. v., et al. 2014. detection and on-line prediction of leak magnitude in a gas pipeline using an acoustic method and neural network data processing. brazilian journal of chemical engineering 31(1): 145-153. skalle, p. and aamodt, a. 2020. downhole failures revealed through ontology engineering. journal of petroleum science and engineering 191(3): 107-128. turner, n. c. 1991. hardware and software techniques for pipeline integrity and leak detection monitoring. paper presented at the spe offshore europe, aberdeen, united kingdom, 3-6 september. spe-23044-ms. aniyom ebenezer is a petroleum engineer and data science researcher specializing in energy systems and data-driven engineering solutions. he holds a b.eng. in petroleum engineering from the federal university of technology, owerri. currently as a graduate trainee engineer at hydroserve oil services, he has also worked as a data science intern at qwasar and a researcher at elitar consult. his research interests include machine learning applications in the oil and gas industry, digital transformation, and process optimization. anthony ogbaegbe chikwe is a senior lecturer in the department of petroleum engineering, federal university of technology, owerri. he holds both bsc and msc degree in petrochemical engineering from the university of oil and gas, moscow. he also holds post graduate certificate in advanced studies in academic practice from newcastle university upon tyne, uk and ph.d degree in petroleum engineering from the federal university of technology, owerri. his research interests are in production, reservoir, natural gas and drilling engineering. he is also a fellow of the higher education academy, uk. abstract introduction leak detection methods methodology model development results and discussion conclusion conflicting interests reference copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1274 received january 9, 2024; revised february 10, 2024; accepted february 21, 2024. *corresponding author: lichen1125@foxmail.com 1 key technology of efficient exploitation of coalbed methane in qinshui basin of cnooc chen li , lichun sun, cnooc research institute co., ltd, beijing, china; hansen sun, china united coalbed methane co., ltd, beijing, china; ruyong feng, haiqiao wang, jiahao cao, songnan liu, jian wang, cnooc research institute co., ltd, beijing, china abstract three key technologies have been developed for the development of coalbed methane in qinshui basin. the first technology is the gas content analysis technology coupled with isothermal adsorption theory and production dynamics. by fitting bottom-hole flow pressure and critical desorption pressure of coal reservoir, combined with the isothermal adsorption curve of coal reservoir, the gas content of the reservoir can be accurately predicted. this technique provides important geological parameters for evaluating coal reservoirs. the second technology is production system optimization technology based on reservoir seepage mechanism and numerical simulation analysis. velocity sensitive response, stress sensitive effect and gas-water two-phase flow are considered in the process of production system optimization. by understanding the main contradictions in different production and discharge stages of coalbed methane wells and taking the final cumulative gas production and peak gas production as optimization objectives, the quantitative optimization method of coalbed methane drainage and production system is formed. one optimization system for each coalbed methane well and one optimization system for each day has been realized. this technology is used throughout the entire production cycle of a coalbed methane well. the third technology is the efficient development technology of horizontal well in coal seam with fractured coal structure.through numerical simulation study, it is clear that no. 15 coal seam in panhe block is suitable for integrated horizontal well development. in the early stage of horizontal well drilling, problems such as wall instability, drilling depth of some wells is not up to the design, and the length of horizontal section of real drilling is not up to the design. aiming at this problem, the stability model of borehole wall of panhe river is established by using the four-dimensional geostress modeling technique. the model reveals that the collapse pressure of horizontal wells is higher than that of vertical wells, and complex accidents such as collapse block are more likely to occur. in view of this feature, suspension agent, drainage aid and inhibitor are selected to improve the return of pulverized coal pressure, promote the fracturing fluid backflow, reduce the viscosity of mineral collision, and select a new type of active water fracturing fluid system. the successful application of the three key technologies provides a strong support for the efficient development of coalbed methane in qinshui basin, and also provides a technical reference for the efficient development of other coalbed methane basins. introduction coalbed methane refers to the methane that exists in coal seams. coalbed methane mainly exists in two ways: free and adsorption. the methane in coal seam is mainly adsorbed, and the free gas is little. the adsorbed gas is adsorbed in the coal matrix in a dynamic equilibrium manner. in the process of exploitation, with the decrease improved oil and gas recovery 2 of formation pressure, the adsorbed gas gradually resolves from the adsorbed state to free gas. the free gas enters the natural fracture system and participates in the flow through diffusion. eventually methane flows through natural fractures into hydraulic fractures and eventually into the wellbore. after nearly 10 years of development, qinshui basin has become the largest investment area of offshore unconventional oil and gas exploration and development. from 2013 to 2020, cnooc’s onshore unconventional natural gas development has entered a stage of rapid development, with its output rising from 435 million cubic meters to 2.18 billion cubic meters. starting from 2021, cnooc’s onshore unconventional development has accelerated and entered a leapfrog development stage. with the cumulative output reaching 3.59 billion cubic meters in 2021 and the maximum daily gas production reaching 14.07 million cubic meters. cnooc has made remarkable achievements in the development of coalbed methane in qinshui basin. panhe block has become the first national demonstration project for coalbed methane development. shizhuang block has begun to take shape in scale and efficient development. shouyang block has implemented an integrated exploration and development plan and has begun to achieve results. at present, cnooc has 8 blocks in qinshui basin, with a total area of 7309 square kilometers, and proved geological reserves of coalbed methane of 1198.25 hundred million square meters, which is the main battlefield for the development of coalbed methane of cnooc. at present, panhe gas field is in the stable production stage of the old gas field, and the effect of increasing and stabilizing production is obvious, and the development technology is constantly innovative. the panhe block mainly develops no. 3 coal and no.15 coal. no. 3 coal was developed earlier, and the development mode was vertical well development. no.3 coal is currently in the decline stage, the main task is to reduce its decline rate. the technologies used mainly include negative pressure extraction and optimize production system (li et al. 2019; wang et al. 2011). no.15 coal will be officially put into production in 2019. the method used for no.15 coal is large-scale horizontal well development (liu et al. 2020), assisted by optimize production system and increase the number of horizontal wells per unit area (xu et al. 2019; qin and wang 2019). in the drilling process of no.15 coal, embedding temporary plugging drilling fluid technology is adopted, which effectively avoids the collapse of the wall of a well and has a good reservoir protection effect in the drilling process (wang et al. 2018). although no. 15 coal has been put into operation for less than three years, its output has surpassed the vertical well and become the main force contributing to the output of panhe block. the main coal seam developed in shizhuang south block is no. 3 and no. 15 coal. in recent years, the main workload of shizhuang south block is the treatment of low production and low efficiency wells and the optimization of well pattern. by studying the fracture distribution characteristics of shizhuang south block, the calculation model between stress, strain and fracture parameters is established. at present, the geological characteristics and natural fracture distribution characteristics of shizhuang south block have been basically clarified (zhang et al. 2022; liu 2017; guo 2018). the evaluation model of key characteristic parameters of shizhuang south block is established. based on logging data, the evaluation model can explain the industrial composition of coal reservoir, coal structure, gas content, critical desorption pressure, langmuir parameter, permeability, etc. the model realizes the transformation of productivity discrimination from relying on experience to data-driven, and realizes the application of big data in coalbed methane development (yang 2021; li and ling 2019; miao et al. 2016; wu et al. 2014; huang et al. 2013; meng et al. 2008). calculation of gas content of coalbed methane coalbed methane isothermal adsorption equation. it is very important to evaluate the gas content of coalbed methane in exploration stage and development stage. the coal reservoirs are organic reservoirs, and the coalbed methane reserves are calculated using gas content rather than free gas saturation in the pores. currently, the gas content comes from laboratory isothermal adsorption tests of coal core. coalbed methane is a kind of gas with relatively poor economic benefit, and the development mode is mainly low-cost development. in the improved oil and gas recovery 3 process of development, there are few gas content tests. it is necessary to find an effective method to evaluate the distribution of gas content in the reservoir. in the original state of coalbed methane, for unsaturated coalbed methane reservoir, the initial formation pressure is greater than the critical desorption pressure. in the process of production, the pressure in the formation is gradually reduced through the early drainage process. when the reservoir pressure drops to the critical desorption pressure, coalbed methane begins to desorption, and enters the natural fracture system to participate in the flow, and is finally extracted. therefore, the production system of drainage and depressurization gas recovery is the characteristic of coalbed methane development (figures 1 and 2). figure 1—adsorption, diffusion and darcy flow in coalbed methane. figure 2—change of gas content in coalbed methane development. improved oil and gas recovery 4 figure 3—t2 spectrum characteristics of no. 3 coal in szn block. the adsorption curve of high rank coal in southern qinshui basin belongs to type i, and the adsorption and desorption process of coalbed methane can be described by langmuir isothermal adsorption equation. according to the t2 spectrum characteristics of coal samples, the pores in the coal seam are mainly adsorption pores, followed by seepage pores, and few fracture holes (figure 3). according to the isothermal adsorption test data, the fitting relationship between the isothermal adsorption test data of coalbed methane in qinshui basin and the langmuir isothermal adsorption curve is very good (figure 4 and table 1). figure 4—gas content fitting map of szn block. table 1—data from seven samples from two wells. the samples the correlation coefficient correlation coefficient squared decision coefficient sample 1 0.9999 0.9999 0.9998 sample 2 0.9999 0.9999 0.9998 sample 3 0.9999 0.9997 0.9997 sample 4 0.9995 0.9991 0.9991 sample 5 0.9997 0.9995 0.9995 sample 6 0.9947 0.9894 0.9889 sample 7 0.9996 0.9992 0.9992 improved oil and gas recovery 5 based on the isothermal adsorption theory, the langmuir equation is used to establish the calculation method of air content. langmuir equation can be expressed as: � = ��� �+�� ...........................................................................................................................................................(1) in the formula, v is the gas content of coalbed methane, m3/t, p is the reservoir pressure, mpa, vl is langmuir volume, m3/t; pl is langmuir pressure, mpa. the gas content of coal seam corresponding to the original reservoir pressure pi is the maximum adsorption amount of coal seam, that is, the saturated gas content vi . for unsaturated coalbed methane reservoir, the measured gas content vc is less than the saturated gas content. when the coal reservoir pressure is reduced to the pressure pc corresponding to the measured gas content, coalbed methane begins to desorption from coal to free state, so the measured gas content of coal seam corresponds to the critical desorption pressure. the gas content calculation formula 1 shows that when p is the critical desorption pressure, the corresponding gas content is the original gas content of the coal seam. therefore, the initial gas content of coal seam can be calculated according to the critical desorption pressure. �� = ���� ��+�� ,........................................................................................................................................................(2) where pc is the critical desorption pressure, mpa; vi is saturated gas content, m3/t. calculation of gas content in coal reservoir. according to eq. 2, the key to calculating the gas content is to calculate the formation pressure when gas desorbed, that is, the critical desorption pressure of coalbed methane reservoir. according to the principle of seepage in the formation, the pressure reduction in the formation will be "funnel-shaped" distribution along the wellbore. before the pressure wave reaches the boundary, one end of the funnel is the bottom-hole pressure and the other end is the original formation pressure. the lowest pressure in the formation is at the bottom of the well. according to langmuir isothermal equation, the first desorption place is the bottom of the well. therefore, the bottom-hole pressure when gas desorbed is the critical analytical pressure of coal reservoir. as long as the bottom-hole pressure is measured, the critical desorption pressure can be obtained, and then the gas content value of the well can be obtained according to the langmuir isothermal equation. at present, there are two main errors in measuring bottom-hole pressure when gas desorbed. first, due to the effect of well storage, when the coal reservoir begins to desorption, coalbed methane gradually flows into the wellbore and rises to the oil jacket ring control, which is detected by the pressure gauge, so there is a lag phenomenon in time. the second is the accuracy of the pressure gauge. when the pressure change range in the wellbore is small, the pressure gauge cannot detect, and when the pressure gauge begins to have degrees, the bottom hole flow pressure is already below the critical desorption pressure. therefore, it is necessary to correct the data when calculating the critical desorption pressure. through the analysis of the causes of error, it can be found that the main factors affecting the test error include: gauge specifications, well structure and coal seam depth. under the same conditions, the correction can be made using linear regression (figure 5). improved oil and gas recovery 6 figure 5—linear regression corrects for critical desorption pressure according to langmuir isothermal and linear regression equation, the gas content can be expressed as, vc = apgvl+bvl apg+pl+b ,..................................................................................................................................................(3) where a and b is the linear regression coefficient. field application. block profile. ph block is located in the southeastern slope zone of qinshui basin, and the main coal seam is no.3 coal of shanxi formation. ph block is located in the delta front, the coal forming environment is favorable, and it is in the development area of thick coal belt. the block area is 17 square kilometers.the structure of the demonstration area is simple, with north-south folds and ph syncline in the middle. the top surface of the area is low in the middle, and the two wings are high. calculation of block critical desorption pressure. based on the test data of the parameter well, the correlation between the critical desorption pressure of coal in block no. 3 and the bottom pressure of the gas well is analyzed, and the linear regression diagram of the two is established (figure 6). through correlation analysis, the relationship between the critical desorption pressure of no. 3 coal in ph block and the bottomhole pressure of the gas desorbed can be obtained as follows, pc = 1.3263pg + 0.7131.................................................................................................................................(4) figure 6—relationship between critical desorption pressure and bottomhole pressure in ph block. improved oil and gas recovery 7 gas content calculation of block single well. there are relatively many gas content test data in ph block. based on the laboratory gas content test data, isothermal adsorption curves of different regions can be obtained. combining the isothermal adsorption curves of each block and formula 4, the gas content of the current production wells in ph block can be calculated, and then the gas content of the whole region can be evaluated (figure 7). figure 7—isothermal adsorption curve turtle diagram. block plane gas content calculation. combined with the isothermal adsorption curve of each block and formula 4, the gas content of each production well in the ph block can be calculated, and then the gas content of the whole ph block can be obtained (figure 8). figure 8—calculation results of gas content in ph block. improved oil and gas recovery 8 by comparing the calculated results with the measured results, the error of the calculated results by this method can be controlled within 8%. through the comparison of 6 wells, the average error of gas content calculation of this method is 2.63%, and the calculation accuracy is high. the method provided in this paper has high accuracy in calculation (table 2). the error in table 2 are defined as, error = �������� ��� �������−���������� ��� ������� �������� ��� ������� × 100%..................................................................................(5) table 2—comparison of measured gas content with calculated gas content. well name measured gas content (m3/t) calculated gas content (m3/t) error well 1 30.9 29.6 4.2% well 2 27.6 28.1 1.8% well 3 27.8 27.6 0.7% well 4 15.91 15.75 1.0% well 5 10.73 10.63 0.9% well 6 9.45 10.13 7.2% optimization of coalbed methane production system the effective permeability of reservoir decreases due to gas-water two-phase flow. in the production process of coalbed methane, the phase of single-phase water flow in the early stage is transformed into the phase of gas-water two-phase flow. in addition to the change of flow pattern, the effective permeability of the reservoir will be reduced. a large number of studies have shown that the permeability at the isotonic point in coal reservoir is 0.2 times of the absolute permeability. reasonable control of the arrival time of the two-phase flow can not only reduce the reservoir pressure to the maximum extent and promote the desorption of adsorbed gas, but also increase the drainage and production efficiency and increase the economic benefit of the development of coalbed methane wells. when the reservoir pressure is lower than the critical desorption pressure, the reservoir begins to produce gas and the coal seam enters the phase of gas-water two-phase flow. according to the phase permeability curve of the reservoir, when the two-phase flow stage enters, the sum of the two-phase permeability is less than the single-phase flow permeability, and the permeability of the reservoir is actually reduced. therefore, extending the single-phase flow of the reservoir as far as possible is conducive to the production of reservoir fluids, but when the single-phase flow stage is too long, most of the energy in the formation is used to produce water, which is not conducive to the production of gas in the reservoir. therefore, there is an optimal pressure control time, which can not only satisfy the production of water in the reservoir, but also facilitate the production of gas in the reservoir. on the basis of the same geological model, different pressure control times are set to simulate the reservoir pressure drop during production. the final pressure drop funnel shows that when the pressure control time of well a is 4 months, the final pressure drop funnel is the lowest, and the reservoir desorption effect is the best (figure 9). improved oil and gas recovery 9 figure 9—production of 10/20/38 months pressure drop funnel. the optimal pressure control time is inversely proportional to reservoir permeability and gas content, and positively proportional to reservoir porosity. the optimal pressure control time can be determined by drawing method and numerical simulation method. with the decrease of reservoir permeability, the optimal pressure control time increases (figure 10). this is mainly due to the decrease of permeability, the deterioration of reservoir flow capacity, the decrease of pressure drop rate, and the increase of the time to reach the optimal pressure control state. with the decrease of coal gas concentration, the optimal pressure control time increases (figure 11). with the increase of reservoir porosity, the optimal pressure control time increases (figure 12), mainly because the porosity increases, the water in the reservoir increases, and the time required for drainage to the optimal pressure control state increases. the relationship diagram of pressure control time under different reservoir conditions is established, which is convenient to directly find the optimal pressure control time according to different reservoir conditions in the application process. in the actual application process, the method of combining numerical simulation and chart is mainly used to predict the optimal pressure control time. figure 10—optimal pressure control time under different permeability. improved oil and gas recovery 10 figure 11—optimal pressure control time under different coal gas concentration. figure 12—optimal pressure control time under different porosity. effect of pulverized coal migration on seepage capacity of reservoir. in the process of coalbed methane development, the fluid velocity in the reservoir is too high to cause the coal powder to migrate. when the fluid velocity in the reservoir exceeds the velocity that can carry the pulverized coal, the pulverized coal that has been deposited in the reservoir will re-participate in the flow. when the fluid velocity in the reservoir exceeds the velocity that can denude the reservoir, the coal powder attached to the coal seam will fall off and participate in the flow. more pulverized coal enters the fracture system, blocking the flow channel and causing permeability damage. at the same time, if the flow velocity is too high, the fluid will carry the coal powder out of the reservoir and increase the permeability of the reservoir. therefore, in the process of drainage, there is an optimal flow rate, which can bring out part of the coal powder without stripping the coal powder in the reservoir. the current numerical simulation software for oil and gas development cannot simulate pulverized coal migration in coal seams. the main research method is core displacement test, in which the permeability changes of the core are measured by different flow rates, so as to obtain the best flow rate of the core. the core is usually used to represent the pulverized coal migration of the whole block. after obtaining the permeability of coal seam under different seepage velocities, combined with numerical simulation, the gas production curves under different drainage velocities can be obtained. by targeting peak gas production or cumulative gas production during the production cycle, the extraction rate can be optimized. effect of matrix shrinkage on optimization of drainage and production system. the coalbed methane reservoir itself has the characteristics of brittleness and adsorbed gas. compared with other gas reservoirs, the permeability in coal seam is more sensitive to pressure changes during development. on the one hand, due to the greater brittleness of the coal seam matrix and the existence of cracks, in the production process, due to the reduction of reservoir pressure, the overlying strata will compress the coal seam and reduce the permeability improved oil and gas recovery 11 (figure 13). on the other hand, as production proceeds, the adsorbed gas is desorbed from the substrate. this phenomenon will cause the pressure balance around the matrix to be broken, the pressure on the matrix will increase, the matrix will be compressed, the cracks between the matrices will increase, and the permeability of the entire matrix system will increase (figure 14). figure 13—the compression of overburden causes the matrix permeability to decrease. figure 14—adsorption gas desorption results in increased matrix permeability. at present, there are many models describing the contraction and expansion of coalbed methane reservoirs, but there are four mainstream models, all of which describe the relationship between pressure and porosity permeability in coalbed methane reservoirs. through this model, an analytical solution model of coalbed methane reservoirs can be established considering the contraction/expansion of coalbed methane reservoirs. at present, there are many equations describing stress sensitivity and matrix shrinkage, but the four mentioned in the introduction are more widely used. seidle and huitt models: ϕ ϕi = 1 + 1 + 2 ϕi cm 10−6 vl pi pl+pi + p pl+p ,.................................................................................................(6) palmer and mansoori models： � �� = 1 + ��� �� � − �� + �� �� � � �� �� ��+� − �� ��+�� ,.............................................................................................(7) shi and durucan models: � = ���−3�� �−�� ...............................................................................................................................................(8) when the local layer pressure is higher than the desorption pressure pd (pi > p > pd): σ − σi =− ν 1−ν p − pi ,.....................................................................................................................................(9) when the layer pressure is lower than or equal to the desorption pressure(pd ≥ p > 0): σ − σi =− ν 1−ν p − pi + e 3 1−ν εl p p+pε − pi pε+pi ,.........................................................................................(10) improved oil and gas recovery 12 constant exponential permeability model: i =− 1 k ∂k ∂p ,........................................................................................................................................................(11) the symbol in this formula indicates that the change of permeability is inversely proportional to the change of pressure. the equation 6 is integrated and the initial conditions are taken into account.when permeability is the original permeability of the reservoir and pressure is the original pressure of the reservoir, we get: k ki = e−i pi−p ...................................................................................................................................................(12) high efficient development technology of horizontal well in coal seam with fractured coal structure development status of horizontal wells in major coalbed methane blocks. at present, cnooc has deployed a certain number of horizontal wells in the four main blocks of panhe, shizhuang south, shizhuang north and shouyang in qinshui basin. among them, 22 horizontal wells will be implemented in panhe block in 2019 and 60 horizontal wells in 2020. no. 3 coal is developed by vertical well, and no. 15 coal is developed by horizontal well. from the current gas production effect, the average daily gas output per well of horizontal wells is 8818 cubic meter , and the cumulative production will be 200 million square meters in 2021. although horizontal wells began to be used on a large scale in 2019, their output has surpassed vertical wells and become the main contributor to the output of panhe block (figure 15). horizontal wells are characterized by fast production speed, high output per well and high cumulative production. from the current gas production effect, the gentle and updip development effect is the best, and the convex, concave, fluctuating and downdip development effect is poor. downdip horizontal wells are prone to accumulation of formation water at the toe end, resulting in pressure plugging, and the effective length of horizontal wells is reduced. there is a negative correlation between the number of sidetracking and the output of horizontal wells: the sidetracking of horizontal wells in panhe block is often caused by drilling through the roof, resulting in communication between the roof limestone and the coal seam, and external water entering the coal seam, affecting the drainage and pressure reduction of the coal seam, and reducing the output of horizontal wells (table 3). figure 15—superimposed map of daily gas production in panhe block. improved oil and gas recovery 13 table 3—horizontal well trajectory and gas production in panhe block. panhe block well number average gas production/m3▪d-1 updip 33 8684 downdip 1 4929 gently 6 9234 convex type 5 7325 concave type 1 5443 wave pattern 14 4572 at present, there are 15 horizontal wells in no.3 coal in shizhuang south block, including 6 staged fracturing wells and 9 screen completion wells. the average gas production of staged fractured horizontal wells is 3392 cubic meter per day, and the average gas production of screen completion wells is 1988 cubic meter per day. there are 9 newly put into operation horizontal wells in shizhuang north block, some of which have high bottom-hole flow pressure, high output and high production potential. however, production results were uneven, with high production rates reaching 4416 cubic meter per day. the development effect of horizontal wells in shouyang block is very different, and the production difference between wells is mainly affected by geological and engineering factors. efficient development of horizontal wells in panhe block. according to the geological parameters of no.15 coal seam in panhe block, the numerical simulation of different well types is carried out. the research shows that the horizontal well development in panhe block has a good effect. the numerical simulation results show that under the current geological conditions of panhe block, the peak gas production of horizontal wells will be 5.6 times that of vertical wells, the average gas production will be 3.8 times that of vertical wells, and the 20year production degree will be 1.3 times that of vertical wells. horizontal wells are suitable for development in panhe block (table 4). the numerical simulation shows that when the length of horizontal section is more than 1000 meters, the recovery degree and cumulative gas production do not increase significantly (figure 16). when the well spacing exceeds 300 meters, the increase of peak gas production of a single well slows down (figure 17). when the well spacing is small, the controlled reserves are small, resulting in the reduction of cumulative gas production per well. the comprehensive comparison shows that the recommended reasonable well spacing between 250 meters and 300 meters. improved oil and gas recovery 14 table 4—comparison of development indicators of horizontal straight wells. development index vertical wells horizontal wells ratio peak gas production (m3/d) 1854 10384 5.6 average gas production (m3/d) 865 3253 3.8 20 years of cumulative gas production (104m4) 632 2374 3.8 20 years of recovery (%) 57.8 72.4 1.3 figure 16—horizontal wells of different lengths produce gas repeatedly in panhe block. figure 17—horizontal wells with different well spacing produce gas repeatedly in panhe block. in the early process of horizontal well drilling in panhe block, wellbore instability often occurred in horizontal well drilling, and the drilling depth of some wells did not meet the requirements of the design depth, and the length of the horizontal section in real drilling did not meet the requirements of the design horizontal section length. wall instability accidents lead to problems such as drilling pipe sticking, drilling leakage, feed abandonment, coal seam sidetracking, advance drilling and completion difficulties, etc., thus losing a lot of construction time and increasing the comprehensive cost of drilling and completion. the four-dimensional improved oil and gas recovery 15 geomechanical model of shaft wall stability in panhe shows that the collapse pressure of coal seam in panhe is high and it is easy to collapse. the collapse pressure of horizontal wells is higher than that of vertical wells, and complex accidents such as collapse are more likely. wellbore instability and collapse are the main factors that lead to complex drilling and completion conditions. the average formation pressure of panhe block is 0.8 g/cc, which is slightly lower than the normal formation pressure. except that the collapse pressure of coal seam exceeds the formation pressure, the collapse pressure of other sand and mudstone intervals is less than 0.5 g/cc. the fracture pressure of coal seam is slightly higher, the fracture pressure of no. 3 coal seam is 2.1 g/cc, and the fracture pressure of no.15 coal seam is above 2.15 g/cc. the average fracture pressure of other sand-mudstone intervals is 2.04 g/cc. the three-pressure profile of the horizontal section of the coal seam is calculated. the average collapse pressure of the horizontal section of the coal seam is about 1.14 g/cc, and the average rupture pressure is between 2.1-2.4 g/cc. based on 3d geomechanical model and 3d numerical model of oil and gas reservoir, a four-dimensional dynamic geostress analysis method was established with dynamic pore pressure field as the boundary condition (zhu et al. 2018). in the later production process of the block, with the production of each well in the block, the direction of the ground stress will be deflected to a certain extent. by improving the plugging performance of drilling fluid system and adjusting drilling fluid density, the complexity of horizontal wells was reduced by 65% and the sidetracking frequency by 53%. in the process of fracturing with ordinary active water and 2% kcl fracturing liquid system, due to the “loose, brittle and soft” coal seam, a large amount of pulverized coal and coal cuttings are formed under the erosion of high-speed fluid, resulting in fracture damage. a new type of active water fracturing fluid system was optimized by optimizing suspension agent, drainage aid and inhibitor to promote the return of pulverized coal after pressure and fracturing fluid, and reduce the collision of viscous minerals. the system has good compatibility, little damage to the permeability of coal and rock, and good reservoir protection effect, which can meet the field demand (figure 18). the field fracturing test of the new fracturing fluid system has been applied to five wells, and the effectiveness of the new fracturing fluid system has been verified. figure 18—active water fracturing fluid optimization system. improved oil and gas recovery 16 conclusions in this study, we conducted geological research, production analysis, numerical simulation, and summarize the conclusions as follows. 1. through the fitting of bottom-hole flow pressure and critical desorption pressure, combined with the production dynamic parameters of coalbed methane wells, the gas content of a single well can be accurately calculated. this method can provide accurate and valuable geological parameters for the evaluation of coalbed methane reserves and the optimization of the development of sweet spots. 2. the drainage and production system affects the production of coalbed methane wells, and a suitable drainage and production system can improve the flow environment of the reservoir. the main factors affecting the drainage and production system include the transformation of unidirectional two-phase flow affecting the absolute permeability, the precipitation and denudation of coal powder, and the matrix shrinkage effect of coal reservoir. 3. the collapse pressure of panhe coal seam is high, and the collapse block is easy to happen. the collapse pressure of horizontal wells is higher than that of vertical wells, and complex accidents such as block collapse are more likely to occur. at present, the fracturing fluid system forms a large amount of pulverized coal and coal dust under the erosion of high-speed fluid, which causes fracture damage. the optimized fracturing fluid system can promote the fracturing fluid flowback and reduce the viscosity collision. acknowledgement we appreciated the fund “research and application of main controlling factors of coalbed methane productivity in gujiao block” for support. conflicting interests the author(s) declare that they have no conflicting interests. references guo, y. 2018. study on fracture characteristics of no.15 coal seam in shizhuang south area, qinshui basin. china university of petroleum (east china), qingdao, china. huang, y., zhou, d., and yao, g. 2013. prediction of coalbed methane resources by random simulation and genetic neural network method. geological science and technology information 153(6): 73-79. li, f. and ling, g. 2019. coal seam gas content prediction based on bp neural network model. proceedings of the 25th annual conference of beijing force society. li, n., feng, r., liu, y., et al. 2019. stimulation effect of negative pressure extraction for cbm wells, panhe block, qinshui basin. natural gas exploration and development 42(2): 118-122. liu, y., hou, y., and hu, q. 2020. efficient cbm development technology of no. 15 coal seam in qinnan panhe block. china coalbed methane 17(1): 9-14. liu, z. 2017. study on fracture characteristics of no.3 coal seam in shizhuang south area, qinshui basin. ms thesis, china university of petroleum (east china), qingdao, china. meng, z., tian, y., and lei, y. 2008. bp neural network model and application for coal seam gas content prediction. journal of china university of mining and technology 163(4): 456-461. miao, y., yang, j., and lu, w. 2016. prediction of gas production parameters of coalbed methane single well based on grey support vector machine. computer application 36(2): 108-111. qin, s. and wang, r. 2019. study on gas drilling technology and supporting technology for l-type horizontal well in panhe block. coal science and technology 47(9): 132-137. improved oil and gas recovery 17 wang, g., wu, j., xiong, d., et al. 2011. fine stable controlling technologies of water drainage and gas production in the panhe cbm gas field-southern qinshui basin. natural gas industry 31(5): 31-34. wang, h., zhang, p., yu, j., et al. 2018. application of mosaic temporary plugging drilling fluid for cbm development in no.15 coal seam of panhe block. coal technology 37(3): 93-95. wu, j., chang, y., liu, b., et al. 2014. bp neural network is used to predict gas content distribution in coal seam. journal of chongqing university of science and technology (natural science edition) 80(1): 96-98. xu, w., liu, s., and meng, l. 2019. analysis on the production performance and its influencing factors of no.15 coal seam in the panhe block. china mining magazine 28(12):155-160 yang, b. 2021. research on cbm reservoir productivity classification and intelligent evaluation in shizhuangnan area, qinshui basin. yangtze university, jingzhou, china. zhang, w., guo, b., kong, p., et al. 2022. fracture morphology inversion and effect evaluation of cbm refracturing in southern shizhuang block. unconventional oil and gas 46(1): 119-128. zhu, h., tang, x., liu, q., et al. 2018. 4d multi-physical stress modelling during shale gas production: a case study of sichuan basin shale gas reservoir, china. journal of petroleum science and engineering 167(2018): 929-943. chen li is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. he worked as postdoc in peking university from 2016 to 2018. he holds a phd degree from research institute of petroleum exploration and development, and has a master degree from china university of geosciences, beijing, and bachelor degree from southwest petroleum university. lichun sun is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. hansen sun is currently working in the china united coalbed methane co., ltd, mainly engaged in research work in the development of conventional and unconventional oil and gas fields. ruyong feng is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. haiqiao wang is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. jiahao cao is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. songnan liu is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. jian wang is currently working in the cnooc research institute ltd., mainly engaged in research work in the development of conventional and unconventional oil and gas fields. abstract introduction calculation of gas content of coalbed methane optimization of coalbed methane production system high efficient development technology of horizonta conclusions acknowledgement conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. doi: 10.14800/iogr.1242 received may 13, 2023; revised june 20, 2023; accepted july 25, 2023. *corresponding author: amoniogolo@yahoo.com 1 effect of gas injection rates on the performance of a thin oil rim: a simulation study naomi amoni ogolo, university of port harcourt, rivers state, nigeria; victor molokwu, harriotwatt university, edinburg, united kingdom; mike onyekonwu, university of port harcourt, rivers state, nigeria abstract oil recovery from thin oil rims under a strong aquifer and large cap is challenging. low oil recovery efficiency, water coning, gas cusping and the upward and downward shifts of the oil water contact (owc) and gas oil contact (goc) respectively are major issues. however, studies have shown that injecting natural gas at the owc can significantly improve oil recovery efficiency and reduce water production. but the effect of varying gas injection rates on the performance of such reservoirs needs to be studied, and that is the focus of the simulation conducted in this work. the model of a thin oil rim with a strong underlying aquifer and large gas cap in the niger delta was simulated under six different gas injection rates at the owc to study the performance of the reservoir. results show that as gas injection rate increased, the oil recovery efficiency and gas-oil-ratio (gor) increased almost linearly with the exception of gas injection rate of 2500 mscf/d which is not strong enough to push back water influx into the reservoir. the highest recovery efficiency was almost 62% at the highest gas injection rate of 15000 mscf/d which also gave the highest gor and an insignificant volume of produced water. every gas injection rate has its merits and demerits but the critical factors are oil recovery efficiency, volume of produced water and gor. hence, it is recommended that gas injection rates at the owc be carefully selected based on goals the operating company wants to achieve. introduction several techniques that can improve oil recovery efficiency from thin oil rim reservoirs have been suggested and studied. among the successful techniques are the use of horizontal wells (akpabio et al. 2013), up dip water injection at the gas oil contact (goc) and down dip gas injection at the oil water contact (owc) (razak et al. 2011; olabode 2020). other effective methods that have been reported include simultaneous oil and gas production, water injection at the goc (uwaga and lawal 2006; billiter et al. 1998 and 1999; and chan et al. 2011), and the down hole water sink technique (wojtanowicz 2006). in a particular thin oil rim reservoir study in the niger delta, five methods of oil production from a thin oil rim with a strong aquifer and large gas cap were studied by simulation. results showed that the technique of gas injection at the owc yielded the highest oil recovery efficiency, lowest volume of produced water and highest gas oil ratio (gor). other methods such as water production and disposal, and water production and re-injection as edge water obtained better oil recovery factors than the use of horizontal wells (ogolo et al. 2017). in a subsequent study, a combination of two good techniques was explored to find out if combining techniques can further increase oil recovery efficiency. it was observed that alternate water injection at the goc and gas injection at the owc resulted in the highest recovery efficiency against the single technique of gas injection at the owc. but the increase in oil recovery efficiency was not significant enough to justify the cost mailto:amoniogolo@yahoo.com 2 of deploying two techniques in one reservoir. it was therefore recommended that a single effective technique be optimized rather than combining two good methods (ogolo et al. 2018). optimizing the single technique of gas injection at the owc of a thin oil rim by investigating the effect of gas injection rates on oil recovery efficiency, water production and gor constitute the objectives in this research work. statement of theory and definitions production of oil from thin oil rims with a thickness range between 20 to 50 ft, especially in the presence of a strong underlying aquifer and a large gas cap can be very challenging. although water encroachment into oil reservoirs is desirable because of its good sweep efficiency, but in thin oil rims it is a dilemma necessitating striking a balance since water coning can constitute a problem. under a strong water drive from an underlying aquifer, water coning gives rise to early water breakthrough, and an enormous volume of produced water can render oil recovery uneconomical adding to the fact that disposing such large volumes of formation water is expensive. movement of the fluid contacts can cause oil smearing--pushing oil into the gas and water zones which reduces oil recovery factor. gas cusping results in large gor which poses another challenge like in the niger delta region of nigeria where there is no market for the large volumes of produced gas. the lateral extent of some thin oil rim reservoirs are vast, containing substantial amounts of hydrocarbon resources that efforts are made to exploit them despite the difficulties. a production technique that can enhance oil recovery efficiency, maintain the fluid contacts and minimize oil and gas production will be ideal for oil production in thin oil rims. previous studies have indicated that the strategy of injecting gas at the oil water contact in a thin oil rim is a good option with the disadvantage of large gor which can be recycled if gas disposal poses a problem. in this work, a sensitivity analysis on the effect of various gas injection rates at the owc of a thin oil rim is conducted by simulation. description of applications of equipment and processes this is a simulation study using eclipse software package and is a continuation of previous studies on effective oil production techniques from thin oil rims with strong aquifers and large gas caps (ogolo et al. 2017 and 2018). the thin oil rim reservoir from the niger delta that was modeled and used in previous studies is the same oil rim used in this work. the reservoir model is presented in figure 1 while the rock and fluid properties of the reservoir are presented in table 1. the reservoir has a large gas cap and a strong underlying aquifer and the study was projected for more than 30 years. this simulation involves injecting natural gas into the thin oil rim at the owc and studying how the change of gas injection rate affects oil recovery efficiency, water production and gor. the reservoir has several oil producing wells and gas injection wells, and six gas injection rate scenarios were explored. the injection rates are 2500, 5000, 7500, 10000, 12500 and 15000 mscf/d and total gas injected from the wells are 7500, 15000, 22500, 30000, 37500 and 45000 mscf/d, respectively. figure 1—a view of the thin oil rim model. 3 table 1—reservoir rock and fluid properties. rock and fluid property property value average reservoir properties depth, ft 10421 porosity(�) 0.23 permeability (�), md 1292 reservoir thickness, ft 45 net to gross 0.81 initial reservoir pressure (��), psia 4540 initial water saturation (���) 0.15 formation water compressibility (��), psi-1 2.986×10-6 rock compressibility (��), psi-1 1.1767×10-6 initial fluid properties viscosity ( ��� ), cp 0.42110 formation volume factor ( ���), rb/stb 1.512 saturation pressure ( ��), psia 4540 instantaneous gor, scf/stb 963.5 average aquifer properties porosity (��) 0.24 permeability ( ��), md 1292 thickness, ft 70 inner radius ( ��), ft 5604 results and discussion results of the simulation study are presented and discussed. figure 2 presents gas production from gas wells and subsequent injection into the thin oil rim at the six selected injection rates of 2500, 5000, 7500, 10000, 12500 and 15000 mscf/d. figure 3 is the oil production corresponding to each gas injection rate. the oil production at gas injection rates of 5000 mscf/d and above were all in close ranges and followed the same pattern--very high at the start of production and then gradually declined over the years. but the oil production at gas injection rate of 2500 mscf/d did not follow that pattern--oil production was significantly low at the start of production for about six years after which there was a spike which significantly exceeded other cases and fluctuated for about 10 years. after about 20 years of production, the oil production rate fell below other cases and followed the same path as others. 4 figure 2—simulated gas production and injection rates into the thin oil rim. figure 3—field oil production rate. the water production presented in figures 4 and 5 show that the gas injection rate of 2500 mscf/d gave the highest water production rate. this is because the gas injection rate was not strong enough to minimize water encroachment into the reservoir. hence to control water influx into a reservoir by injecting gas at the owc, a simulation study should first be conducted to determine the rate of gas injection that can significantly push back invading water. the rates of water influx for gas injection rate of 5000 mscf/d and above are minimal and within the range of 500 to 950 stb/d (figure 5). but the rate of water influx for the gas injection rate of 2500 mscf/d is very enormous, about 160000 stb/d as shown in figure 4. figure 6 is a semi log plot of the results showing all the cases on one graph. 5 figure 4—field water production rate for 2500 mscf/d gas injection rate. figure 5—field water production rate for higher gas injection rates. figure 6—a semi log plot of water production rate for the six cases. figures 7 to 9 show the cumulative volume of produced water for more than 35 years of production from the thin oil rim which reiterate observations made in figures 4 to 6. it is observed in figures 7 and 8 that the cumulative volume of produced water from a gas injection rate of 2500 mscf/d is outrageous compared to that of gas injection rates of 5000 mscf/d and above. note that the highest gas injection rates did not give the lowest 6 volume of produced water after 35 years of production as observed from figure 8. this means that the relationship between gas injection rate and volume of produced water may not be linear. however, this was not the trend from the beginning of production in 1970 which appeared to be linear, the trend changed inversely at the tenth years of production in 1980. the reason for this change in trend requires further research work. figure 9 is a semi log plot of the results showing all the cases on one graph. figure 7—cumulative volume of produced water especially for 2500 mscf/d gas injection rate. figure 8—cumulative volume of produced water at different gas injection rates. figure 9—cumulative volume of produced water on a semi log plot. 7 figures 10 and 11 are results of the gor as gas injection rates vary, and as expected the gor increased as gas injection rate increased from 5000 to 15000 mscf/d. however, at gas injection rate of 2500 mscf/d, the gor is insignificant compared to higher gas injection rates because of the large volume of encroaching water in the reservoir. it is observed from figure 12 that the relationship between gas injection rate and gor is approximately linear as expected. but this was not the pattern from the beginning in 1970 as observed from figure 10, the pattern which was inverse changed in the twelfth and half year (1982) after production started. this is also an area for further research which might have a relationship with results of cumulative volume of produced water presented in figure 8. figure 10—field gas-oil-ratio. figure 11—gas-oil-ratio with gas injection rates. figure 12—gas-oil-ratio with gas injection rates: blue line is gas-oil-ratio, dash is the trend curve. 8 results of oil recovery efficiency are presented in figures 13 to 15. the highest oil recovery efficiency which is one of the most important factors to consider during production is about 62% and was attained at the highest gas injection rate of 15000 mscf/d. it is observed that oil recovery efficiency increased as gas injection rate increased, noting the exceptional and interesting case of the lowest gas injection rate of 2500 mscf/d. the oil recovery efficiency of this case was almost 58% despite the fact that the gas injection rate was low. this is because water encroachment from the underlying aquifer improved sweep efficiency which supported oil production. figure 13—field oil recovery efficiency. figure 14 is plotted for the sake of clarity and it shows that the oil recovery efficiency at 2500 mscf/d gas injection is good, even better than cases of gas injection rates at 5000 and 7500 mscf/d but the main disadvantage is the large volume of produced water as presented in figures 4 to 9 which will involve high cost of disposal. starting from gas injection rate of 5000 mscf/d where the rate of water production is significantly reduced, (excluding the case of gas injection rate of 2500 mscf/d) it is observed that oil recovery efficiency has almost a linear relationship with gas injection rate as presented in figures 14 and 15. figure 14—recovery efficiency of different gas injection rate. 9 figure 15—an almost linear trend of recovery efficiency with gas injection rate. this study shows that each gas injection rate has its merits and demerits and the objectives of the operating company should determine the gas injection rate that will be selected. if the goal is to maximize oil recovery efficiency with minimal water production, then the highest gas injection rate can be selected with the disadvantage of a very high volume of produced gas (high gor) which can be recycled (ogolo et al 2017) if managing the gas poses a challenge. if the target is to minimize the volume of produced gas (low gor) with fairly good oil recovery efficiency, then a low gas injection rate could be selected, but a very large volume of produced water should be expected. this stresses the importance of conducting a gas injection rate sensitivity analysis by simulation when the technique of gas injection at the owc in a thin oil rim is proposed. conclusions the conclusions drawn from this work are as follows: 1. in gas injection technique at the owc for optimizing oil recovery from a thin oil rim with a strong aquifer and large gas cap, gas injection rate is a sensitive factor that can determine oil recovery efficiency, volume of produced water and gor. 2. it is important to conduct a simulation sensitivity analysis on gas injection rate at the owc of a thin oil rim reservoir if gas injection technique is considered to be deployed. this is in order to carefully select the injection rate that will aid the operating company achieve its objectives. 3. the rate of gas injection at the owc should be strong enough to push back water influx and significantly improve oil recovery efficiency if part of the objective is to drastically reduce water production from the reservoir. 4. gas injection rate at the owc in a thin oil rim tends to exhibit a linear relation with oil recovery efficiency. recommendation before embarking on gas injection at the owc as a technique to optimally improve oil recovery efficiency and minimize water production from thin oil rims with a strong aquifer and large gas cap, a simulation sensitivity analysis on the gas injection rate should be conducted. the gas injection rate should be strong enough to push back invading water in order to prevent the fluid contacts from shifting if this constitutes part of the company’s goal. 10 acknowledgement we thank laser engineering and resources consultants limited for providing us with data from a thin oil rim reservoir with a large gas cap and strong aquifer from the niger delta region of nigeria which was used in the simulation work. conflict of interest the authors do not have any conflict of interest to disclose. references akpabio, j. u., akpanikka, o. i., and isemin, i. a. 2013. horizontal well performance in thin oil rim reservoirs. international journal of engineering sciences and research technology 2(2): 219-225. billiter, t. c. and dandona a. k. 1998. breaking of a paradigm: simultaneous production of gas cap and oil column. paper presented at the spe annual technical conference and exhibition, new orleans, louisiana, usa, 4-7 september. spe-49083-ms. billiter, t. c. and dandona, a. k. 1999. simultaneous production of gas cap and oil column with water injection at the gas/oil contact. spe reservoir evaluation and engineering 2(5): 412-419. chan, k. s., kifi, a. m., and darman, n. 2011. breaking oil recovery limit in malaysian thin oil rim reservoirs: water injection optimization. paper presented at the international petroleum technology conference, bangkok, thailand, 1-8 november. iptc-14157-ms. ogolo, n. a., molokwu, v. c., and onyekonwu, m. o. 2017. proposed technique for improved oil recovery from thin oil rim reservoirs with strong aquifers and large gas caps. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 1-9 july. spe-189126-ms. ogolo, n. a., molokwu, v. c., and onyekonwu, m. o. 2018. techniques for effective oil production from thin oil rim reservoirs. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 1-14 august. spe-193382-ms. olabode, o. 2020. effect of water and gas injection schemes on synthetic oil rim models. journal of petroleum exploration and production technology 10:1343-1358. razak, e. a., chan, k. s., and darman, n. 2011. breaking oil recovery limit in malaysian thin oil rim reservoirs: enhanced oil recovery by gas and water injection. paper presented at the spe asia pacific enhanced oil recovery conference, kuala lumpur, malaysia, 1-5 july. spe-143736-ms. uwaga, a. o. and lawal, k. a. 2006. concurrent gas cap and oil-rim production: the swing gas option. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, abuja, nigeria, 1-13 july. spe-105985-ms. wojtanowicz, a. k. 2006. down-hole water sink technology for water coning control in wells. geology 23(1):575586. naomi amoni ogolo is a petroleum engineer with area of specialization in reservoir engineering. she holds a post graduate diploma in petroleum technology and gas engineering, a master of engineering in petroleum and gas engineering and a ph.d in petroleum engineering, all from the university of port harcourt. she is a member of several professional organizations including society of petroleum engineers (spe). as at the time this study was conducted, she was a research fellow in institute of petroleum studies, university of port harcourt. dr. ogolo’s areas of interest include improved oil and gas recovery from petroleum reservoirs, flow assurance, natural gas hydrates, and environmental recovery and preservation from oil and gas industrial activities. victor molokwu has a b. eng. in petroleum engineering from the university of benin in nigeria and a master of science degree in petroleum engineering and project development from the institute of petroleum studies, university of port harcourt in nigeria. he is a ph.d candidate in the institute of geoengineering, heriot watt university, edinburgh, united kingdom. victor has several years of experience in reservoir development studies. his research interests include physics-based deep learning, numerical methods, reservoir simulation, well test analysis and production data analysis. he has published articles in these related research areas. 11 mike onyekonwu is a professor in petroleum and gas engineering of university of port harcourt and a seasoned professional in reservoir engineering. he has served in various capacities in university of port harcourt, as well as in various national and international bodies. he is the managing consultant of laser engineering and resources consultant limited. prof. onyekonwu obtained a first class degree in petroleum engineering from university of ibadan in nigeria. he has a master’s degree and ph.d in petroleum engineering from stanford university, california, usa. he is a member of several professional organizations including society of petroleum engineers (spe). he has published more than one hundred articles and four books. he is interested in proffering solution to problems that plague the oil and gas industry and takes delight in mentoring young ones. abstract introduction statement of theory and definitions description of applications of equipment and proce results and discussion conclusions recommendation acknowledgement conflict of interest references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1353 received january 05, 2025; revised march 18, 2025; accepted may 27, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 an investigation into the optimization of electrically submersible pumps through the application of machine learning anthony kerunwa, chimuanya winifred ibewuike, lilian enyang ndoma-egba, ndubuisi okereke, chukwuebuka francis dike*, federal university of technology owerri, owerri, nigeria abstract an electrical submersible pump, commonly abbreviated as esp, is a type of dynamic displacement pump that is specifically designed and employed to extract crude oil from the wellbore when the natural pressure differential is insufficient to facilitate this process effectively. the esp operates on the principle of generating momentum to lift fluids, transferring them from the inlet to the outlet of the system. in its pursuit to enhance oil production, the esp system encounters a variety of constraints that can be broadly categorized into pressure-related, pumpspecific, fluid-related, and motor-related issues. to ensure the system's optimal performance and design, it is crucial to conduct a comprehensive analysis of these constraints. in this study, the random forest (rf) algorithm was employed as a powerful analytical tool to investigate the aforementioned constraints and to assess their influence on the rate of oil production. to develop the model, a dataset comprising 36 instances from an oilfield located in the niger-delta region was utilized. following the development of the model, a thorough statistical evaluation and validation process was conducted to ensure the reliability and accuracy of the findings. the results of the study were quite promising, with the random forest algorithm demonstrating a regression score of 99.66%, indicating an exceptionally high level of accuracy in predicting the oil production rate. additionally, the mean absolute error (mae) was recorded at 0.00866, the mean squared error (mse) at 0.0001019, and the root mean squared error (rmse) at 0.0101. these statistical metrics collectively suggest that the random forest algorithm provided predictions that were very close to the actual values of the oil production rate. upon validation, the random forest algorithm was found to yield values that were in close proximity to the real oil production rates, further underscoring its effectiveness as a predictive tool in the context of oilfield operations. this study not only highlights the potential of machine learning algorithms in addressing complex engineering challenges but also provides valuable insights that could inform the design and operation of esp systems to maximize their efficiency and productivity. introduction fossil fuels contribute about 85% of the energy demand globally with 87mmstb/day and 37mmmstb/year (sheng 2011; kerunwa et al. 2024a), and this has created the need for continuous production despite several associated hurdles. conventional oil well undergoes natural supplemental, secondary and tertiary recovery phases in their production life (avwioroko et al. 2014). at the natural supplemental phase, the reservoir relies on her natural energy for crude oil recovery. (akpoturi and ofesi 2017), but when these energy drops, secondary recovery approach consisting of water or natural gas flooding is injected to maintain pressure and recover oil (austad et al. mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 2010). when the secondary recovery approach becomes ineffective due to capillary and viscous forces, enhanced oil recovery (eor) techniques comprising of injection of chemicals and methods excluding natural gas and oil are deployed (kerunwa et al. 2024b; dike et al. 2024). the reservoir presents various challenges that necessitate the application of multiple engineering techniques to facilitate the flow of oil from the wellbore. however, the fluids encounter an additional obstacle at the wellbore. in some instances, crude oil ascends to the surface with ease, a phenomenon that is contingent upon the intersection of the inflow performance relationship (ipr) and the vertical lift performance (vlp) (okologume and ofesi 2016). conversely, crude oil that has entered the wellbore may struggle to reach the surface due to constraints such as the presence of water, a limited amount of entrapped natural gas, and a minimal differential pressure, which can be attributed to increased bottomhole pressure and decreased reservoir pressure (elshan 2013). consequently, to enable the extraction of crude oil trapped in the wellbore to the surface, a technique known as artificial lift is required (bellarby 2009). close to 50% of oilfield globally utilizes artificial lift to enhance crude production (guo et al. 2007). the artificial lift system can be categorized into pump and gas lift system. the pump system makes use of positive or dynamic displacement mechanism in creating pressure differential needed to lift the crude from the wellbore to the surface (bellarby 2009). the progressive cavity pump (pcp) and sucker rod pump (srp) fall under positive displacement pumps while electrical submersible pump (esp) and hydraulic pump (hp) are described as dynamic pumps. the gas-lift system utilizes the differential head by reducing the density of crude oil, which in turn reduces drawdown and well’s inflow rate. among the pumps, esp have recorded widespread acceptance due to its performance and durability. esp functions by lifting fluid from inlet to outlet under a momentum it creates. its mode of operation can be defined as dynamic and centrifugal displacement (ikekeazu and anerobic 2020). the pump generates hydraulic power as result of the action of electric motors and injects energy needed to produce fluid for oil recovery. the fluid flows into the system through the impeller to the diffuser. the impeller provides the wellbore heads pressure through high-speed rotation, while the exerted kinetic energy by the impeller in turn is transformed to kinetic energy by the diffuser (zhu and zhang 2018). in achieving its goal of improved oil production, esp systems face several constraints which could be pressure-based, pump-based, fluid-based and motor-based. this is needed for this constraint to be effectively managed and/or overcome for optimal production. studies on oil production by artificial lift using esp design have been carried out by several authors. gomaa et al. (2020) carried out electrical submersible pump (esp) design on a vertical well. from the result of their experimental design, a pump with 106 stages, with required horsepower of 571hp and temperature of 255 of recorded 64% efficiency and recorded 13479.2rb/day. kerunwa et al. (2022) carried out a study of esp on field production network optimization in an oilfield in the niger-delta. from the result of their study, a 1.16% and 2.66% oil rate increase was achieved without optimization, while with optimization, 2.66% oil rate was achieved. several studies have been carried out on oil production by esp design, but these studies have not considered the impact of these esp design parameters in oil rate production. in this study random forest machine learning (rf-ml) was utilized to optimize the parameters that the highest design parameters required to attain the best oil rate. methodology the materials employed in this study encompass the scikit-learn package, a python program, and a well dataset. the scikit-learn package is a globally recognized machine-learning program that possesses predictive and statistical functionalities. the dataset utilized in this study comprises 36 entries, featuring independent variables such as operating frequency, water-cut, gas separation, intake pressure, discharge pressure, generated pump head, pump power, and pump efficiency, with motor efficiency and motor speed serving as dependent variables (table 1). improved oil and gas recovery 3 table 1—data utilized for the study. oil flow rate variable data pressure data pump data oil rate (stb/d) ope. freq. (hz) water cut (%) gas sep. eff. (%) intake pressure (psi) discharge pressure (psi) pump head gen. (ft) pump power (hp) pump eff. (%) motor eff. (%) motor speed (rpm) 1533.3 50 45 50 2547.79 2721.92 499.378 16.74 54.3392 63.5558 2941.56 1509.8 50 45 55 2549.79 2726.15 505.44 16.6948 54.3108 63.4929 2941.6 1487.7 50 45 60 2551.69 2730.14 511.116 16.6535 54.2775 63.432 2941.64 1465.9 50 45 65 2553.55 2732.02 516.612 16.6117 54.238 63.3706 2941.68 0 50 50 50 0 0 0 0 0 0 0 0 50 50 55 0 0 0 0 0 0 0 0 50 50 60 0 0 0 0 0 0 0 0 50 50 65 0 0 0 0 0 0 0 0 50 55 50 0 0 0 0 0 0 0 0 50 55 55 0 0 0 0 0 0 0 0 50 55 60 0 0 0 0 0 0 0 0 50 55 65 0 0 0 0 0 0 0 2100 60 45 50 2499.21 2752.89 726.532 30.2447 60.4534 71.7619 3497.54 2086.8 60 45 55 2500.36 2757.98 737.212 30.6753 61.2217 72.2969 3499.55 2073.7 60 45 60 2501.5 2763.05 747.871 31.1049 61.988 72.8306 3501.55 2060.7 60 45 65 2502.65 2768.07 758.395 31.5287 62.7437 73.357 3503.51 1319.4 60 50 50 2553.37 2852.04 840.438 28.0311 54.0685 70.9984 3514.55 1290.4 60 50 55 2556.09 2856.24 844.204 27.8095 53.5598 70.8398 3515.08 1263.4 60 50 60 2558.62 2860.14 847.692 27.6022 53.0847 70.6916 3515.57 1236.7 60 50 65 2561.13 2864 851.112 27.3957 52.6128 70.5443 3516.06 0 60 55 50 0 0 0 0 0 0 0 0 60 55 55 0 0 0 0 0 0 0 0 60 55 60 0 0 0 0 0 0 0 0 60 55 65 0 0 0 0 0 0 0 2444.7 70 45 50 2469.03 2792.11 924.87 48.5702 56.2451 77.3177 4063.68 2429.5 70 45 55 2470.36 2797.55 935.764 48.6507 56.5599 77.333 4063.5 2414 70 45 60 2471.72 2802.97 946.555 48.7254 56.8629 77.3471 4063.33 2398.5 70 45 65 2473.08 2808.32 957.117 48.7947 57.1502 77.36 4063.18 1960.8 70 50 50 2493 2882.37 1094.44 49.6665 60.1615 77.5133 4061.23 1946.5 70 50 55 2494.37 2887.23 1103.44 49.7044 60.3437 77.5198 4061.15 1930.7 70 50 60 2495.9 2892.49 1113.2 49.7388 60.5361 77.5256 4061.07 1916.3 70 50 65 2497.27 2897.25 1121.93 49.7691 60.7009 77.5307 4061.01 1105.7 70 55 50 2560.46 2993.12 1195.07 41.6485 48.9004 75.1619 4079.5 1074.9 70 55 55 2563.67 2997.28 1197.27 41.1825 48.2276 75.0305 4080.56 1047.5 70 55 60 2566.52 3000.98 1199.21 40.7685 47.6298 74.9139 4081.51 1021.3 70 55 65 2569.24 3004.51 1201.06 40.3723 47.0583 74.8026 4082.5 improved oil and gas recovery 4 data process. the dataset was inspected to confirm the unavailability of irregularities and errors such as missing values and duplicates. using datafram.isna () key within the python program it was observed that the entire data were present in the entry. the entries check confirmed that there were no missing values or duplicate values in the data. data visualization. data visualization was carried out to see the relation between the various variables present within the dataset. in attaining this, the multivariate visualization technique using pearson correlation heatmap was utilized. the choice of correlation heatmap is tied to its ability to provide comprehensive overview of relationship between the variables within the dataset. feature engineering. feature engineering was also conducted to identify and select those variables from the dataset that significantly contributes to the target variable oil rate. using standard scale options, data normalization was carried out before the logarithmic transformation of target variables was carried out. this transformation is critical for variance stabilization and distribution normalized aimed at achieving linear correlation and appropriate model. the transformed target variables a-times yields better model performance, based on regression metrics. this procedure is vital especially when original data exhibits extreme values, heteroscedasticity (non-constant variance) or skewness. model selection. in this study, random forest (rf) algorithm from scikit-learning package of python software was utilized. scikit-learning package of python software comprises several algorithms such as linear regression (lr) algorithm, neural network and support vector (sv) algorithm. the choice of rf machine learning (rf-ml) is tied to its bagging technique setup which aids it to utilize the ensemble learning method for regressor in machine learning, and its potential to capture non-linear correlation and interaction features in very complex manner. there is variation in the chosen requirement for grouping the number of branches and nodes. the number of trees present in rf is one of the most vital hyper-parameters of rf which is used to determine the performance of the model. data splitting. in the data splitting stage, the dataset was split into the training set (80%) and the testing set (20%). this was carried out to ensure that ml model is sufficiently trained on a large data (training data) while retaining a separate portion for analysis to confirm how well the model will perform with the unseen data (testing data). model training. the rf algorithm utilized a diverse combination of decision trees with branches and nodes for grouping and regression. the root node (at the treetop) was divided to yield two branches which are defined by satisfactory observations. for the regression, partitions are selected to lower the variations of samples labels. while the training was going on, the hyper properties of the model were tuned using grid search optimization approach to derive the optimal input properties of the models. the optimization methodology was utilized to update the input features of the model. the expected primary outcome to be derived from the learning model is to derive the optimal oil rate. model validation. after the training using rf-model, the model was validated using indices to determine its performance in comparison with actual dataset. the metrics used for the regression task included mean square error (mse), mean absolute error (mae), regression (r2) and root mean square error (rmse) comparison with existing model. the model was compared with actual field data, and kerunwa et al. (2022) approach in eq. (1) through (5). h = pdischarge−psunction 0.433 ,......................................................................................................................................(1) improved oil and gas recovery 5 pdischarge = pwf − 0.433yld ............................................................................................................................(2) where h represents the pumping head, ft; pdischarge signifies the discharge pressure, psi; psunction denotes the suction pressure, psi; yl and d correspond to the specific gravity of the production fluid and the depth of the production interval in feet, respectively. dpump = d − pwf−psunction 0.433yl ................................................................................................................................(3) where dpump is the minimum pump depth, ft. the quantity of stages in esp is specified as, ns = z ls ..............................................................................................................................................................(4) where ns denotes the number of design stages; z represents the total dynamic head, measured in feet; and ls signifies the lift per stage. the equation for esp motor horsepower calculation is given as, phm = phsnsρf ..................................................................................................................................................(5) where phm represents the motor horsepower; phs denotes the horsepower per stage; ns signifies the number of stages; and ρf corresponds to the specific gravity of the fluid. results and discussion multivariate analysis. figure 1 illustrates the pearson correlation heatmap for all variables within the dataset. it illustrates a robust positive correlation between the oil production rate and several operational parameters, including operating frequency, pump power, pump efficiency, motor efficiency, and motor speed. this suggests that a reduction in these variables would have a substantial effect on the oil production rate from the well. conversely, the oil production rate exhibited a moderate positive correlation with discharge pressure and pump head generation, indicating that decreases in these factors do not significantly influence the oil production rate. furthermore, the oil production rate demonstrated a strong inverse correlation with water-cut and intake pressure, and a moderate inverse correlation with gas separator efficiency. the strong inverse correlation indicates that increases in water-cut and intake pressure result in a decrease in the oil production rate, whereas the moderate inverse correlation suggests that enhancements in gas separator efficiency led to a marginal reduction in the oil production rate. model performance. table 2 presents the goodness-of-fit metrics for the model generated by the machine learning algorithm. it is evident that the logistic regression model achieved a regression accuracy of 99.66% in proximity to the actual dataset, signifying its efficacy as a model. the mean squared error (mse) of 0.0001019 indicates a minimal average squared discrepancy between the predicted and actual values. furthermore, the root mean squared error (rmse) of 0.0101 suggests a minor deviation between the actual and predicted values. this is corroborated by the mean absolute error (mae) values. table 2—model evaluation result. model mae mse rmse r2 (%) random forest regression 0.00866 0.0001019 0.0101 99.66 improved oil and gas recovery 6 figure 1—correlation heat-map. upon a thorough examination of figure 2, it becomes quite apparent that the various data points are indeed distributed in a manner that closely aligns with the trend-line. this observation serves to strongly corroborate the reliability and accuracy of the developed model. consequently, this lends significant support to the notion that the model is well-suited for use in subsequent research endeavors. furthermore, when the model was applied to the actual oil rate dataset, the results were nothing short of impressive, as evidenced by the near-perfect fit that is clearly illustrated in figure 3. this remarkable alignment between the model's predictions and the actual data points further underscores the model's efficacy and potential utility in practical applications. figure 2—scatterplot with trend line. improved oil and gas recovery 7 figure 3—trend analysis. comparison of models. figure 4 illustrates a detailed comparison between the oil production rates that were forecasted by the current study, the actual production data collected from the field, and the predictions that were previously made by kerunwa et al. (2022). as can be clearly observed in the figure, the oil production rates that were projected by the methodology employed in this study are found to be in closer agreement and more accurately reflect the real-world production data when compared to the predictions generated by the approach outlined by kerunwa et al. (2022). this striking similarity between the predicted rates from this study and the actual field data serves to validate and reinforce the effectiveness and reliability of the proposed rf-ml algorithm in accurately forecasting oil production rates. this outcome not only underscores the superiority of the rf-ml algorithm but also highlights its potential as a robust tool for making precise and dependable predictions in the domain of oil production forecasting. figure 4—comparison with previous approach and actual field data. conclusion in the realm of machine learning (ml) research, the application of the random forest regression algorithm has yielded several significant conclusions. firstly, the random forest regressor demonstrated an impressive 99.6% regression accuracy, which clearly indicates that the model developed through this approach is highly suitable and effective for the intended purpose. this high level of accuracy suggests that the model can make precise predictions and generalizing well from the training data to new, unseen data. furthermore, when compared to existing models in the field, the random forest algorithm exhibited superior performance. this superior performance suggests that the random forest model not only meets but exceeds the standards set by previous 7 7.2 7.4 7.6 0 1 2 3 4 5 6 o il r at e kerunwa et al. (2022) this study actual field oil rate improved oil and gas recovery 8 models, thereby establishing itself as a robust and reliable tool for the task at hand. specifically, the random forest model has shown promise in the domain of oil prediction, where accurate and reliable predictions are crucial for various applications, including resource management, market analysis, and strategic planning. the success of the random forest regressor in achieving such high regression accuracy and outperforming existing models underscores its potential for widespread adoption in industries that relieve predictive analytics. the algorithm's ability to handle complex datasets and provide accurate forecasts makes it an invaluable asset for researchers and practitioners alike. as a result, the random forest regression algorithm emerges as a powerful tool in the arsenal of machine learning techniques, particularly for those seeking to enhance their predictive capabilities in the field of oil prediction. conflicting interests the author(s) declare that they have no conflicting interests. reference avwioroko, j.e., taiwo, o.a., mohammed, i.u., et al. 2014. a laboratory study of asp flooding on mixed wettability for heavy oil recovery using gum arabic as a polymer. paper presented at the spe nigeria annual international conference and exhibition, lagos, nigeria, 5-7 august 2014. spe-172401-ms. akpoturi, p. and ofesi, s.f. 2017. enhanced oil recovery using local alkaline. nigerian jour. of tech. 36(1):515-522. austad, t., alireza, r., and tina, p. 2010. chemical mechanism of low salinity water flooding in sandstone reservoirs. paper presented at the spe improved oil recovery symposium, 24-28 april. spe-129767-ms. bellarby, j. 2009. well completion design. amsterdam, netherlands: elsevier. dike, c., izuwa, n. c., kerunwa, a., et al. 2024. parametric evaluation on the interfacial tension response of agrosurfactant. improved oil and gas recovery 8(1):1-12. elshan, a. 2013. development of expert system for artificial lift selection. master thesis, cankaya ankara, turkey: middle east technical university. gomaa, s., abdelhady, a., ramzi, h., et al. 2020. electrical submersible pump design in vertical oil wells. pet petro chem eng j. 4(5): 000237. guo, b., lyon, w., and ali, g. 2007. petroleum production engineering “a computer-assisted approach”. amsterdam, netherlands: elsevier. ikekpeazu, g.e. and anerobi, j. i. 2020. oil recovery by artificial lift systems (als): a review. int. jour. of innovation. sci. and research. tech. 5(1):1-9. kerunwa, a., obibuike, j.u., okereke, n.u., et al. 2022. evaluation of electrical submersible pump on field production network optimization in niger delta oilfield. open journal of yangtze gas and oil 7(1): 26-47. kerunwa, a., izuwa, n.c., dike, c.f., et al. 2024a. review on the utilization of local asp in the niger-delta for enhanced oil recovery. petroleum and coal 66(1): 256-275 kerunwa, a., dike, c.f., izuwa, n.c., et al. 2024b. performance evaluation of agro-materials for surfactant-polymer flooding. petroleum and coal 66(1): 308-317. okologume, c.w. and ofesi, s.f. 2016. comparative evaluation of artificial lift methods on a niger-delta field. academic research international 7(1): 1-16 sheng, j. 2011. modern chemical enhanced oil recovery, theory and practice 1s t ed. burlington: gulf professional publishin. zhu, j. and zhang, h. 2018. a review of experiments and modeling of gas liquid flow in electrical submersible pumps. energies 11(1):180-195. anthony kerunwa is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum economics. dr. kerunwa holds a bachelor ’s degree in petroleum engineering from federal university of technology owerri, a master’s degree in petroleum engineering from federal university of technology owerri, improved oil and gas recovery 9 and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. chimuanya winifred ibewuike is a b.eng graduate of petroleum engineering with interest in artificial lift design. lilian enyang ndoma-egba is a research technologist at the department of petroleum engineering, federal university of technology owerri. she has research interest in drilling fluids technology and cementing design. ndoma-egba holds a bachelor’s degree in oil & gas engineering, and master’ degree in petroleum engineering. ndubuisi okereke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in flow assurance, production optimization, drilling, reservoir engineering and procurement. okereke holds a bachelor’s degree in civil engineering, from federal university of technology owerri, master’s degree and phd degree in subsea engineering from cranfield university. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri. he has research interest in drilling, drilling fluids technology, reservoir engineering, enhanced oil recovery and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1292 received july 6, 2024; revised august 17, 2024; accepted september 19, 2024. *corresponding author: fatemeh.saberi@ndus.edu 1 computational fluid dynamics study to access the effect of non-newtonian fluid flow variables on drilling mud in annular oil well fatemeh saberi* and sara vashaghian, university of north dakota, grand forks, united state; pourya asoude, shahid beheshti university, tehran, iran; ahmed e. radwan, jagiellonian university, kraków, poland abstract during the drilling operations, a non-newtonian fluid type comes out of the space between the drill bit and the well diameter. after the drilling operation, to strengthen the well and prepare an insulating membrane around the well, a metal shell with a diameter smaller than the diameter of the well is installed at a distance from the well and often outside the center. in the well, the fluid inside the mud wells is directed from the drilling to the outside. the main problem that has attracted the attention of researchers is the investigation and calculation of the physics of fluid flow inside these circular spaces. studying flow physics in laboratories is very expensive, which increases the cost of product design and the product's final price. the movement of drilling mud between the drill bit and the well can be simulated as a non-newtonian fluid flow inside eccentric tubes where the inner tube is rotating, using computational fluid dynamics. this study aims to numerically simulate the parameters affecting the physics of drilling mud fluid (non-newtonian fluid) in the space between two non-central cylinders. the flow is incompressible, and with increasing rotation speed, the greater penetration of the boundary layer into the shear stress ring penetrates more inside. it causes the non-newtonian viscosity values to decrease. it penetrates the mainstream and decreases the non-newtonian viscosity, more significant than the rotational velocity effect. introduction engineers in the oil and gas industry usually face non-newtonian fluid flow in drilling activities. in the context of non-newtonian fluid, the behavior of drilling fluids is significantly influenced by their rheological properties, which dictate how these fluids respond to applied stress. non-newtonian fluids, unlike newtonian fluids, exhibit a change in viscosity with varying shear rates, making their flow characteristics complex and highly dependent on the specific conditions encountered during drilling operations. the drilling fluid plays a crucial role in maintaining wellbore stability and optimizing reservoir recovery, a function that can be understood through its non-newtonian behavior. its effects can be both beneficial and detrimental, depending on the fluid's properties and the specific well conditions. drilling fluid helps to support the wellbore walls, preventing collapse and maintaining stability, while also inhibiting shale swelling and dispersion, which can lead to wellbore instability (goshtasbi et al. 2013; abbasi et al. 2024; barati et al. 2023; bina et al. 2020; bina et al. 2012; elyasi et al. 2023; hashemi et al. 2024; saberi et al. 2024a). additionally, the fluid helps to remove cuttings and debris from the wellbore, reducing the risk of wellbore instability caused by accumulated cuttings. however, drilling fluid can also cause formation damage, which can reduce reservoir permeability and affect recovery (makarian et al. 2023a; mailto:fatemeh.saberi@ndus.edu improved oil and gas recovery 2 larki et al. 2024). the fluid's invasion into the formation can lead to clay swelling and dispersion, emulsion formation, and precipitation of solids, all of which can reduce permeability. furthermore, fluid loss can occur, reducing the reservoir's hydrocarbon saturation and leading to decreased hydrocarbon recovery. there are some ways to recognize hydrocarbon saturation and evaluate the behaviour of fluids through porous media such rock physics, which fluids with some properties such as seismic velocities and density are investigated (makarian et al. 2023b). to optimize drilling fluid performance, it is essential to select a fluid formulation that aligns with the nonnewtonian flow characteristics required for the specific well conditions. this involves adjusting the fluid's rheological properties, such as yield point, plastic viscosity, and gel strength using additives and control measures. strategies like lost circulation materials (lcms) and fluid loss additives can effectively manage fluid invasion and minimize formation damage, ensuring sustained drilling fluid effectiveness throughout the drilling process. therefore, understanding these non-newtonian flow variables of drilling fluids is therefore critical for enhancing wellbore stability, mitigating risks, and maximizing reservoir recovery through optimized drilling performance. salubi et al. (2022) and liu et al. (2022) investigated the physical characteristics of non-newtonian fluid flow velocity in annular channels, and employed an aqueous solution of sodium carboxymethyl cellulose (cmc, a weakly elastic shear-thinning polymer) to model drilling mud in the interannual space. moreover, deshmukh and dewangan (2022) utilized three shear-thinning aqueous solutions of cmc, xanthan gum, and laponite/cmc mixture. in the last test he carried out, the concentric ring was 2.5 times larger than the previous two studies in spite of the same diameter ratio. the agreement between the cmc results indicated that the flow characteristics are similar to the newtonian fluid in the laminar flow regime. brethouwer (2023) for air and light and dai et al. (2023), and deshmukh and dewangan (2022) studied fluid flow physics in the concentric computational domain for newtonian and non-newtonian fluids experimentally. the rotation speed decreases rapidly from the rotating inner cylinder in most of the core region, and the rotation penetration decreases as the reynolds number increases. the rotation creates a uniform axial mean flow and increases the flow resistance. nino et al. (2022) shows that the non-newtonian fluid's rotation increases the crossflow components' turbulence intensity. as described by vipulanandan and mohammed (2020), at the beginning of the drilling process, the drilling mud (initial penetration 1) penetrates rapidly into the formation as soon as drilling starts. penetration and deposition of solid mud particles in the porous medium cause an internal mud cake to form within a few minutes. after that, most solid mud particles settle on the well wall, forming an external mud cake. this mud cake controls the penetration of the drilling fluid into the formation (mirhashemi et al. 2022; vipulanandan and mohammed 2020). there are laboratory and analytical methods to determine the radius of drilling mud invasion. in laboratory methods, the radius of penetration is determined by measuring the electrical resistance of the formation (gamal et al. 2021). dewan and chenevert conducted experiments based on water-based drilling mud to study mud cake growth (chenevert and dewan 2001). they designed an experiment to determine acceptable mud cake parameters and proposed a mathematical model to predict cake thickness and permeability using parameters such as cake mass, fluid density. some researchers strived to numerically simulate the sensitivity analysis with the same theory. they developed and expanded the properties of mud cake and rock, seepage flow, and mud cake (wu et al. 2004; sepehrnoori et al. 2005). li et al. (2022) developed a hydro mechanical model by the effect of time-dependent mud cake to evaluate the impact of water-based drilling fluid on properties of mud cake and wellbore stability. carollo et al. simulated the equations of motion with a numerical method (finite difference technique). using dipole coordinates. they obtained the velocity characteristics for newtonian fluid flow in eccentric annular geometries (carollo et al 2023; saberi et al. 2024b; saberi and hosseini-barzi, 2024; saberi et al. 2023; vashaghian et al. 2024; zanjirabadi et al. 2024). puranik et al. (2023) considered the heat transfer effect on peristaltic motion of newtonian fluid flow. by implementing a perturbation method, they achieved an approximate solution for velocity and temperature for such and evaluated the pressure at constant flow rate. ershadnia et al. (2020) developed a physical-based and data-driven solution for laminar flow of non-newtonian fluids in rotating annular media. they investigated the importance of coaxial rotation of inner cylinder on overall pressure loss while focusing on the dynamics of pressure loss ratio. using a finite difference numerical solution, improved oil and gas recovery 3 miao et al. (2023) studied the laminar flow of non-newtonian fluids in the ducts of a section. they investigated the volume flow rate in a pressure gradient. in this study, the frictional behavior of non-newtonian fluids in drilling operations was done using computational fluid dynamics (cfd) approach. numerical fluid flow analysis in an eccentric ring, with newtonian and non-newtonian fluids, helps understand the physics of the fully developed turbulent fluid flow. due to the complex geometry of an annular space, cfd simulation studies of newtonian and non-newtonian power-law fluid flow can greatly contribute to accurate analysis. this project investigated the effect of parameters affecting fluid flow physics, such as fluid flow rate and wall rotation speed. simulation method in this study, a fully developed turbulent flow simulation of newtonian and non-newtonian fluids in drilling operations have been carried out using fluent, a commercial computational fluid dynamics (cfd) code developed by ansys. these solvers are based on the finite volume method; the flow domain is discretized into a limited set of volumes or control cells. in cfd models, each governing equation is integrated numerically on a control volume, so the relevant quantity (mass, momentum, energy, etc.) is solved and obtained on each cell. fluent provides a measure of control by providing user-selectable discretization strategies and alternative solutions. care must be taken in choosing the discretization and solution methods considering the complex fluid flow in the annular channel. governing equation. the differential equations governing the flow of non-newtonian fluids are based on the navier-stokes equation and are defined as follows (eqs. 1 through 2), 𝜕𝜌 𝜕𝑡 + 𝜕 𝜕𝑥𝑖 (𝜌𝑢𝑖) = 0,............................................................................................................................................(1) 𝜕 𝜕𝑡 (𝜌𝑢𝑗) + 𝜕 𝜕𝑥𝑖 𝜕𝑢𝑖𝑢𝑗 = − 𝜕𝑃 𝜕𝑥𝑗 + 𝜕 𝜕𝑥𝑖 (𝜇 + 𝜇𝑡) ( 𝜕𝑢𝑖 𝜕𝑥𝑗 + 𝜕𝑢𝑗 𝜕𝑥𝑖 ) + 𝜌𝑔𝑖....................................................................... (2) the power law governs the viscosity is defined as follows (eq. 3), μk × 𝛾𝑛−1......................................................................................................................................................... (3) where n =0.75 which is the power law index (flow behavior index: n=1, newtonian; and n<1, non-newtonian flow); k is consistency index, equal to 0.044; γ is local shear rate. fluent software offers several turbulent models to solve problems; the robust and reasonable accuracy of the turbulence model explains its popularity in industrial flow and heat transfer simulations. is a semi-empirical model, and the extraction of model equations is based on phenomenological considerations and empiricism. this model includes the standard equations of turbulence kinetic energy transfer (k) and its dissipation rate (ε). the equation of kinetic energy of disturbance k and its dissipation rate ε is obtained from the following transfer equations (eqs. 4 and 5), 𝜕 𝜕𝑡 (𝜌𝑘) + 𝜕 𝜕𝑥𝑖 (𝜌𝑘𝑈𝑖) = 𝜕 𝜕𝑥𝑗 [(𝜇 + 𝜇𝑡 𝜎𝑘 ) 𝜕𝑘 𝜕𝑥𝑗 ] + 𝐺𝑘 + 𝐺𝑏 − 𝜌𝜖 − 𝑌𝑀 + 𝑆𝑘,..........................................................(4) 𝜕 𝜕𝑡 (𝜌𝜀) + 𝜕 𝜕𝑥𝑗 (𝜌𝜀𝑈𝑖) = 𝜕 𝜕𝑥𝑗 [(𝜇 + 𝜇𝑡 𝜎𝑘 ) 𝜕𝜀 𝜕𝑥𝑗 ] + 𝐶𝜀 𝜖 𝑘 (𝐺𝑘 + 𝐶3𝜖𝐺𝑏) − 𝐶2𝜖𝜌 𝜖2 𝑘 + 𝑆𝜀...............................................(5) these equations represent the kinetic energy production of fluid turbulence caused by average velocity gradients. c1e, c2e and c3e are constants. furthermore, 𝜎𝑘and 𝜎𝜀 are the turbulent prandtl number for k and ε, respectively. furthermore, sk and se are user-defined source terms. the turbulent viscosity 𝜇𝑡 is computed as follows (eq. 6), improved oil and gas recovery 4 𝜇𝑡 = 𝜌𝐶𝜇 𝑘2 𝜖 ,........................................................................................................................................................6) where 𝐶𝑘 is constant. the default values for the constants c1e, c2e, ck, sk and se. are 1.44, 1.92, 0.09, 1.0, and 1.3, respectively. these default values work well for various wall-bounded and free-shear flows. in the current research, the governing equations of three-dimensional turbulent flow are addressed by employing the finite volume discretization technique, in which control volume cells are employed for the velocity components by the simple method. the pressure correction relation, derived from the continuity equation, is figured out to gain a pressure correction field utilized in order to update the velocity and pressure fields. these guessed fields are gradually improved by iteration until convergence to be gained for the updated fields. the discrete conservation equations are addressed iteratively so that they gain convergence. for instance, when the changes in the solution variables (residuals) from one iteration to the next are within the convergence criteria, being set to keep the residual velocity and x-y-z at appropriate convergence was gained utilizing under-relaxation factors from 0.2 to 0.3 and 0.5 to 0.7 for pressure and momentum, respectively. model geometry and grid generation. gambit software was used to generate geometry and grid. different types of cells can be used for a three-dimensional computing domain, including hexagonal, tetrahedral, pyramidal, wedge, and hybrid cells. the grid independence and numerical results for three cases have been studied (figures 1 to 3) figure 1—eccentric annuli geometry. figure 2—eccentric annuli mesh distributions. improved oil and gas recovery 5 figure 3—line a, b, c in eccentric annuli geometry plane. for the boundary conditions, the mass flow rate (1.3, 2.6, and 5.2 kg/s) and the rotation speed of the inner wall (0, 300, and 600 rpm) were considered. the simulations were performed under steady-state conditions, and fluid was considered incompressible. isothermal conditions are assumed. the boundary condition of non-slip was considered on the inner and outer walls. results and discussion tangential velocity. the first simulation studies the tangential velocity effect of the inner surface. we changed the boundary condition of the inner surface to various speeds to examine the effect of the rotation of the inner surface(cylinder) on axial velocity, laminar viscosity, turbulent viscosity, and turbulent kinetic energy profiles at 0, 300 and 600 rpm in the positive z direction(counter clockwise). a, b, and c lines are assumed to plot different profiles in specific surfaces in essential regions to fully understand the behavior of be examined variables. axial velocity. figure 4 shows the axial velocity counters in 0, 300 and 600 rpm rotational velocity. with the increase in rotational velocity in q=2.6, the maximum of the counters is moved and the velocity profiles are not symmetric anymore. moreover, the profile is more and more homogenous. that means fluid moves more homogeneously in the z direction, and less axial velocity gradient is observed. it is essential to mention that in all of the counters, the mass flux is maintained at 2.6 kg/s. the effects caused by the boundary layer decrease in a, b and c, respectively, due to the increased distance between the two circular surfaces. therefore, when the rotational speed is zero, the axial velocity in section a is lower than b and c. nevertheless, with the increase of rotational speed due to the reduction of the effect of the boundary layer in this area, we see an increase in the maximum speed in this area and, vice versa, a decrease in the maximum speed in the other three lines, b and c. figure 5 shows the axial velocity profiles at a, b, and c lines. as shown in line a, the average axial velocity is increased at a higher tangential velocity. thus, more fluid is passed through the surface. however, at b and c surfaces, the axial velocity decreased significantly with the increase of tangential velocity. it is also evident that the maximum amount of fluid is passed over the wider region (line c). the results are acceptable as more homogenous profiles will be created with increased axial velocity. improved oil and gas recovery 6 figure 4—the contour of axial velocity in eccentric annuli (rotational velocity effect). figure 5—the axial velocity profile in lines a, b and c in eccentric annuli (rotational velocity effect). laminar viscosity. laminar viscosity contours and profiles are shown in figures 6 and 7, respectively. figure 6 shows that the laminar viscosity contours are smoothed with increased rotational velocity. in other words, as rotational velocity increases, a more shear rate is applied to the bulk fluid. thus the non-newtonian fluid will have lower viscosity and less rigid changes are observed in the laminar viscosity counters. the same has happened in the laminar viscosity profiles at the a, b, and c regions shown in figure 7. in all cases, the laminar viscosity is changed according to the change in axial velocity and, thus, shear rate profiles. the maximum of the plots, in which we observe maximum velocity, is shifted in all cases because of the shift in velocity profiles. for example, at line c, the rotational velocity affects the axial velocity profile and shifts it to be higher at bigger x values. this results in a significant decrease in laminar viscosity in these regions. so the maximum is shifted to more significant x values. improved oil and gas recovery 7 figure 6—the contour of laminar viscosity in eccentric annuli (rotational velocity effect). figure 7—the laminar viscosity profile in line a, b and c in eccentric annuli (rotational velocity effect). turbulent viscosity. turbulent velocity characterizes the chaotic and irregular fluid motion that defines turbulent flow, leading to significant fluctuations in velocity and pressure. unlike the smooth layers observed in laminar flow, turbulent flow exhibits non-uniform axial velocity profiles, indicating varying levels of resistance and energy transfer along the flow direction. the presence of dual velocity maxima offers regions of increased turbulence intensity and flow acceleration driven by pressure differentials. furthermore, while laminar viscosity refers to the fluid's internal resistance under laminar conditions, turbulent flow complicates this concept as effective viscosity, influenced by turbulence, becomes variable and is often described as turbulent or eddy viscosity. this interplay of axial velocity and viscosity highlights the intricate dynamics of turbulent flow, necessitating a detailed analysis to understand the overall flow characteristics thoroughly. moreover, in the specific context of computational fluid dynamics in drilling operations, turbulent velocity refers to the disorderly and tumultuous movement of fluid particles within the annular space between non-central cylinders. figures 8 and 9 manifest the turbulent counters and profiles, respectively. turbulent flow is generally difficult to explain. as we can see, there are two maximums in the contours and profiles. improved oil and gas recovery 8 figure 8—the contour of turbulent viscosity in eccentric annuli (rotational velocity effect). figure 9—the turbulent viscosity profile in line a, b and c, in eccentric annuli (rotational velocity effect). turbulent kinetic energy. figure 10 displays the contour of turbulent kinetic energy, highlighting how it is distributed in the annuli when the inner surface rotates at different speeds. notably, the depiction shows how the intensity of turbulent kinetic energy evolves as the rotational velocity of the inner surface escalates. specifically, as the rotational velocity increases, the distribution of turbulent kinetic energy becomes more pronounced, with higher energy levels observed near the rotating inner surface. the scale depicted in the figure, which corresponds to turbulent kinetic energy, indicates that at higher rotational speeds, the energy values increase significantly, indicative of intensified turbulence. these concepts are important for recognizing regions of high and low turbulence utilized for optimizing drilling operations by ensuring efficient fluid flow and minimizing wear on equipment. improved oil and gas recovery 9 figure 10—the contour of turbulent kinetic energy in eccentric annuli (rotational velocity effect). figure 11 reveals an array of essential information analysis by providing the turbulent kinetic energy profiles along three different lines, denoted as a, b, and c, traversing the eccentric annular region. these profiles provide a detailed view of how turbulent kinetic energy varies at specific radial positions. based on the figures, line a, positioned closest to the inner rotating surface, shows the highest difference turbulent kinetic energy with speed variations because of the direct influence of rotational velocity. the visualization indicates that the red line, corresponding to the lowest rotational speed, exhibits the least energy, while the green and blue lines, associated with higher speeds, demonstrate progressively heightened energy levels. the significant distance between these lines indicates a strong influence of rotational speed in proximity to the inner surface. moving on to line b, situated at a mid-radial location, a moderate distribution of turbulent kinetic energy is observed. the red line shows higher energy levels compared to other lines, but the differences are less pronounced than in line a, reflecting the diminishing influence of rotational velocity with increasing radial distance. the reduced distance between the lines shows a more uniform energy distribution. lastly, line c, positioned near the outer stationary surface, shows the lowest levels of turbulent kinetic energy. the red, green, and blue lines converge more closely, indicating minimal influence of rotational velocity at this position, with the minimal separation between the lines suggesting a nearly uniform energy distribution, irrespective of the rotational speed. figure 11—the turbulent kinetic energy profile in lines a, b and c, in eccentric annuli (rotational velocity effect). mass flux. the second simulation studies the mass flux effect of the bulk fluid. we changed the volume flux amount of the bulk fluid at the same tangential speed (300rpm) to examine the effect of total mass flux on axial velocity, laminar viscosity, turbulent viscosity, and turbulent kinetic energy profiles at 1.3, 2.6 and 5.2 kg/s mass flux of bulk fluid. a, b, and c lines are assumed to plot different profiles at specific surfaces in essential regions to fully understand the behavior of the examined variables. improved oil and gas recovery 10 axial velocity. figure 12 shows the axial velocity counters at 1.3, 2.6 and 5.2 kg/s total mass flux of bulk fluid with the inner surface rotating at 300 rpm. with the increase in total mass flux, there is a significant increase in axial velocity, as expected. the critical fact is that the maximum counters and profiles (figure 10) are placed in the same position, and no shift in contours is observed. however, the profiles are less homogenous and rigid changes are observed in the profiles. that means fluid is moving more at specific wider regions than narrow regions at a higher mass flux (q=5.2) compared to lower mass fluxes (q=1.3). figure 13 shows the axial velocity profiles at a, b and c lines. as shown in line a, the average axial velocity increases, and more rigid profiles are obtained at higher mass fluxes as mentioned. in line a, since the two walls are close, the effects of the boundary layer between the two walls have grown more. therefore, with the increase in the speed of the main flow, there is no significant increase in the maximum speed of this area. similarly, b compared to c. figure 12—the contour of axial velocity in eccentric annuli (mass flux effect). figure 13—the axial velocity profile in lines a, b, and c in eccentric annuli (mass flux effect). laminar viscosity. laminar viscosity contours and profiles are shown in figures 14 and 15, respectively. as figure 14 shows, the laminar viscosity contours are being smoothed with the increase of mass flux. in other words, as mass flux increases, a more shear rate is applied to the bulk fluid. thus, the non-newtonian fluid will have lower viscosity and less rigid changes are observed in the laminar viscosity counters. the same has happened in the laminar viscosity profiles at the a, b and c regions shown in figure 15. in all cases, the laminar viscosity changes according to the change in mass fluxes and thus, shear rate profiles. the maximum of the plots, in which we observe maximum velocity, is maintained in all cases because the tangential velocity is fixed at 300 rpm in all cases. improved oil and gas recovery 11 figure 14—the contour of laminar viscosity in eccentric annuli (mass flux effect). figure 15—the laminar viscosity profile in line a, b, and c in eccentric annuli (mass flux effect). turbulent viscosity. vorticity is a vector measure of the local rotation of fluid elements in a flow field, defined mathematically as the curl of the velocity field. it indicates the tendency of fluid particles to spin, providing crucial insights into the chaotic nature of turbulent flow where regions exhibit varying degrees of rotation. in turbulent flows, the interactions of vortices with high vorticity facilitate energy transfer, leading to kinetic energy dissipation into thermal energy and promoting turbulent mixing. this enhanced mixing improves momentum and mass transfer, which is essential in applications like chemical reactions and heat exchangers. additionally, vorticity is critical for understanding the development of flow structures, such as boundary layers and wakes, influencing how fluids interact with surfaces and affecting drag and lift forces. figures 16 and 17 show the turbulent counters and profiles, respectively. with the increase in the speed of the primary flow, the energy of the vorticity increases, and the viscosity of the turbulence also increases. improved oil and gas recovery 12 figure 16—the contour of turbulent viscosity in eccentric annuli (mass flux effect). figure 17—the turbulent viscosity profile in lines a, b, c in eccentric annuli (mass flux effect). turbulent kinetic energy. figure 18 shows the contour of turbulent kinetic energy in eccentric annuli, focusing on the effect of mass flux. the contours illustrate how turbulent kinetic energy is distributed within the annuli when the mass flux of the bulk fluid is varied. as the mass flux increases, the turbulent kinetic energy also increases, indicating more intense turbulence. specifically, at higher mass fluxes (e.g., 5.2 kg/s), the contours show higher energy levels compared to lower mass fluxes (e.g., 1.3 kg/s). this increase in turbulent kinetic energy with mass flux is critical for understanding fluid dynamics, as higher turbulence can enhance mixing and impact the efficiency of drilling operations. the scale of turbulent kinetic energy in the figure helps quantify these changes, showing a clear correlation between mass flux and turbulence intensity. figure 18—the contour of turbulent kinetic energy in eccentric annuli (mass flux effect). improved oil and gas recovery 13 figure 19 presents the turbulent kinetic energy profiles along lines a, b, and c within eccentric annuli, focusing on the effect of mass flux. the profiles demonstrate the variation of turbulent kinetic energy corresponding to different mass flux values (q) of 1.3, 2.6, and 5.2 kg/s. line c, positioned near the outer stationary surface shows the highest turbulent kinetic energy. the blue line, representing a mass flux of 5.2 kg/s, displays the most significant energy levels, followed by the green line (q=2.6 kg/s) and the red line (q=1.3 kg/s). the significant distance between these lines indicates a substantial impact of mass flux on turbulent kinetic energy in proximity to the outer surface. line b, positioned at a mid-radial location, along with line a, near the outer stationary surface, show the lower turbulent kinetic energy. here, the red, green, and blue lines converge more closely, indicating a diminished effect of mass flux. the smallest distance between the lines suggests a nearly uniform distribution of turbulent kinetic energy regardless of mass flux. figure 19—the turbulent kinetic energy profile in line a, b, c in eccentric annuli (mass flux effect). conclusions the objective of this study is to numerically simulate the parameters affecting the physics of drilling mud fluid (non-newtonian fluid) in the space between the drill bit and the wellbore wall using computational fluid dynamics. the key findings of this study are, 1. fluid moves more homogeneously in the z direction, and less axial velocity gradient is observed. 2. the axial velocity decreased significantly with the increase of tangential velocity. the results are acceptable as more homogenous profiles will be created with increased axial velocity. as rotational velocity increases, a more shear rate is applied. 3. with the increase in total mass flux, there is a significant increase in axial velocity, as expected 4. with the increase in the speed of the main flow, there is no significant increase in the maximum velocity 5. as mass flux increases, a more shear rate is applied to the bulk fluid. thus, the non-newtonian fluid has lower viscosity and less rigid changes are observed in the laminar viscosity. nomenclature ρ = density; u = velocity; t = time; μ = viscosity; μt = turbulence viscosity; g = gravity; n = power law index; improved oil and gas recovery 14 k = consistency index; γ = local shear rate; k = turbulence kinetic energy; ε = turbulence dissipation rate; gk = constant; gb = constant; ym = constant; c1e = constant; c2e = constant; ck = constant; c3e = constant; sk = user-defined source terms; se = user-defined source terms; σk = turbulent prandtl number for k; σε = turbulent prandtl number for ε; conflicting interests the author(s) declare that they have no conflicting interests. references abbasi, v., ahmadi, m., mohtarami, e., et al. 2024. experimental and numerical failure mechanism evaluation of anisotropic rocks using extended finite element method. theoretical and applied fracture mechanics 131(1):104411. barati, 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fluid loss method and characterized using vipulanandan models. journal of petroleum science and engineering 189(1):107029. wu, j., torres-verdin, c., sepehrnoori, k., et al. 2004. numerical simulation of mud-filtrate invasion in deviated wells. spe reserv. eval. & eng. 7(2)143-154. dai, x., he, l., and j. chen. 2023. a method for matching the refractive index and dynamic viscosity of transparent replicas of rock for flow visualization. journal of visualization 26(2): 275-287. zanjirabadi, h. r., saberi, f., rahimzadeh, b., et al. 2024. petrology investigation of apatite minerals in the esfordi mine, yazd, iran. international journal of geological and environmental engineering 18(4): 118-124. fatemeh saberi is a ph.d. student in the department of geology & geological engineering at the university of north dakota, usa. her research interests include sedimentology, surface processes, unconventional resources, and the characteristics of carbonate reservoirs. improved oil and gas recovery 16 sara vashaghian is a ph.d. student in the department of geology & geological engineering at the university of north dakota, usa. her research focuses on geology, geothermal energy, and the oil & gas industry. she is affiliated with the university of north dakota. pourya asoudeh is a master’s student in the department of geology & geological engineering at shahid beheshti university, iran. his research interests include sedimentology, surface processes, unconventional resources, and the characteristics of carbonate reservoirs. ahmed e. radwan is a researcher at the institute of geological sciences, jagiellonian university, kraków, poland, where he specializes in petroleum geosciences, geophysics, environmental geotechnics, geochemistry, and reservoir engineering. he holds a position within the faculty of geography and geology at jagiellonian university. radwan’s expertise encompasses a broad range of geological and geophysical research, contributing to advancements in petroleum exploration and environmental geotechnics. he is actively engaged in research and publications, with a focus on geosciences and reservoir engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1351 received january 5, 2025; revised march 15, 2025; accepted may 20, 2025. *corresponding author: eng_ebrahim2010@hotmail.com 1 diagnosis and control of excessive water production in a yemeni oilfield ebrahim bin martaa*, suez university, suez, egypt; mohamed solimana, king saud university, riyadh, saudi arabia; mohamed khamisb, and ali wahbaa, suez university, suez, egypt abstract the phenomenon of excessive water production (ewp) poses a multifaceted challenge to the oil and gas industry, affecting both economic and environmental dimensions. the identification of this issue is contingent upon the utilization of various methodologies, encompassing well testing, well logging, reservoir modeling, and analytical methodologies. prominent among these is the water-oil ratio (wor) diagnostic plot technique, which stands out as the most straightforward and cost-efficient method for identifying the root causes of ewp issues. this research undertakes an examination of the diagnosis and management of ewp across nine wells within a yemeni oilfield. the outcomes substantiate the presence of water production issues within all the wells under scrutiny. upon comparing chan's standard diagnostic plot with various wor diagnostic plots, it becomes evident that the primary mechanism of ewp in all wells, except for two, is multilayer channeling via fractures or zones of elevated permeability. considering this, it is advised to employ mechanical solutions for wells exhibiting near-wellbore water channeling, whereas chemical solutions are deemed more appropriate for addressing water production issues in other wells. the utilization of gel treatment methodologies, particularly those involving preformed particle gels, is recommended as a chemical solution approach. furthermore, the study's outcomes indicate the necessity of a well selection process, ensuring the selection of suitable well candidates and the application of the appropriate water shutoff technique. introduction the production of water is one of the most significant technical, environmental, and economic challenges that oil production faces. water production decreases the useful lifespan of the oil reservoir and causes major issues such as fine migration, hydrostatic loading, and tube corrosion (nmegbu et al. 2020). the environmental effects of managing, processing, and discarding produced water can have a significant negative influence on the profitability of oil extraction processes. the biggest waste stream resulting from the oil industry is produced water (canbolat and biotech 2016). on a global basis, oil companies are anticipated to produce 210 million barrels of water per day (khatib and verbeek 2002). water production in the usa was roughly 21 billion bbls of water per year (clark and veil 2009), which is significantly more than the yearly productions of oil and gas, which are 1.9 billion bbl and 23.9 tcf, respectively (eai 2006). although it is more prevalent in outdated wells, problems with water production can also arise in newly drilled wells (joseph and ajienka 2010). in gas wells, higher gas injection is needed to lift the gas from the wellbore to the surface when there is an excessive amount of water production (ahmad et al. 2012). overproduction of water can be caused by a well issue (mechanical failure) or by other reservoir-related issues such as water coning, water breakthrough in high permeability zones, or water channeling from the water table to the well through faults or natural fractures (al hasani et al. 2008). in general, it is simpler to address water production issues related to well integrity, but when reservoirs are involved, managing water mailto:eng_ebrahim2010@hotmail.com improved oil and gas recovery 2 production becomes more challenging (alexis 2010). to prevent unnecessary water production from planned wells, it is important to comprehend the formation features and field-specific issues (mcintyre et al. 1999). identification of the water production mechanism (wpm) is necessary for effective management of the water that is produced. the diagnosis of the wpm must be made with great precision before treatment (chou et al. 1994; kabir 2001; mcintyre et al. 1999; prado et al. 2005; sidiq and amin 2008). accurate diagnosis in complex flow regimes, especially in fractured deposits where water production may occur earlier than expected, is sometimes difficult and expensive to achieve (sarkar et al. 2002). coning and channeling are the main issues that result in the world's excessive water production (ewp), while the other issues are not as prevalent (mahgoup and khair 2015; sarkar et al. 2002; seright et al. 1998). evidently, the two main components that contribute to the efficiency of the shut-off operation are comprehending the mechanism of ewp and locating the entrance of water in the wellbore. finding water production mechanisms (wpms) within a wellbore can be achieved through the utilization of either of two diagnostic techniques or strategies. a variety of analytical and empirical procedures that utilize production data make up the second category, while the first category mostly comprises survey and logging instruments (chan 1995; reynolds and kiker 2003). for many operators, it has been common practice to utilize production logging tool (plt) to identify the water inlet, choose the shutting-off strategy, and schedule the task. it's important to emphasize that due to the intricate nature of fluid entry mechanisms and the fluid dynamics involved in multi-phase flow within horizontal wellbores, advanced plt is still constrained by certain limitations (al hasani et al. 2008; hamdoon et al. 2024). the water production mechanism has been studied through the development of various methods and techniques. most of them involve specialized plots, such as time versus the linear water cut (hwan 1993), graphical representations of linear water oil ratio (wor) (higgins and leighton 1974), semi-log of wor (mungan 1975), x-plot technique (ershaghi and abdassah 1984), wilhite’s wor approach (willhite and waterflooding 1986), novotny's technique (novotny 1995), diagrams of the wor in log-log format (chan 1995), the egbe and dulu approach (egbe and appah 2005), and the technique of yortsos et al. (yortsos et al. 1999). the most widely utilized technique for identifying the water production mechanism is to utilize log-log plots of the wor and its derivative (d(wor)/dt) as a function of time (chan 1995). it has been demonstrated that this approach is the most successful in identifying the source of problems with water production (alexis 2010; hamdoon et al. 2024). according to abass and merghany (2011) and al hasani et al. (2008), employing wor plots in both vertical and horizontal wells is instrumental in diagnosing issues of excessive water production. furthermore, the derivative approach is considered a singular and cost-effective method for identifying such problems. oil corporations are attempting to decrease water production through the implementation of water shut-off activities to enhance profitability. water shut-off actions in the oil and gas sector can be carried out mechanically (utilizing a packer to insulate the wet zone and compress cement, and then selectively reperforating the higher part) or chemically (with polymers and other chemical compounds). several studies have effectively utilized diagnostic plots to pinpoint the mechanism and dynamics of excessive water production in oilfields. in this study, we focused specifically on wor diagnostic plots due to their proven efficacy as analytical and empirical tools for analyzing oil production data and identifying water production issues. since the field under study lacked plt data, we analyzed production data utilizing chan's diagnostic plots (the quickest, most dependable, and least expensive diagnostic technique available). by utilizing the wor diagnostic plot, we successfully diagnosed excessive water production in a yemeni oilfield. subsequently, based on the diagnostic results, we recommended the appropriate water shut-off method to provide a practical solution to the water production issues. controlling excessive water production. the primary issue with excessive water production during production in oilfields is the cost of separating, processing, and discarding extra water. these significant problems put a burden on the budgets of oil exploration and production corporations. thomas et al. (2000) and permana et al. improved oil and gas recovery 3 (2015) stated that reducing the amount of water produced will save operating expenses and, consequently, enhance company profitability. water shut-off is the best strategy for controlling and, in certain occurrences, avoiding excessive water production in oilfields (alexis 2010; sarkar et al. 2002). in order to ascertain nitrogen foam's capability to manage excessive water, liu et al. (2012) looked into how the nitrogen foam solution affected the shut-off process. through numerical modeling, they model the injection of foam into three vertical wells and one horizontal well. their findings show that water control can be much improved in a horizontal well, but the shut-off technique did not work in the vertical wells that were evaluated. on the other hand, sun and bai (2017) carried out a thorough study of water control strategies employed in horizontal wells in order to provide water control options for different types of completions. the techniques for shutting off the water were thoroughly reviewed by taha and amani (2019), who started by describing the problem of water production and then moved on to discuss several traditional mechanical and chemical options. many choices for controlling water production were thoroughly explained by kassab et al. (2021). the initial stage was water reduction techniques, which involved two recycling and reusing approaches as well as three distinct applications in three different wells. to determine the optimal solution, every problem requires a distinct approach. consequently, it is important to precisely ascertain the nature of the problem before attempting to treat water production issues (elphick and seright 1997). there are numerous sophisticated techniques for controlling and attacking wpms. the most popular classifications for these techniques are mechanical, chemical, and completion solutions (bailey et al. 2000). reynolds and kiker (2003) state that while every approach is effective for certain wpms, it is rarely effective for others. mechanical solutions include things like packers, plugs, and sleeves, whereas chemical solutions include things like cement, gels, resins, foams, emulsions, and polymers. multilateral wells, double completions, and sidetracks are a few instances of alternative completion techniques. in a recent study, chen et al. (2022) discussed the mechanisms and impacts of water shut-off using blind pipe in high water cut oil wells. their conclusion suggests that the findings from the research can offer technical guidance for implementing water shut-off strategies and improving oil recovery using blind pipes in the designated oil reservoirs. mechanical packers can seal large openings near the wellbore as well as in the well hardware. in some cases, however, by getting into the tiny cracks or matrix that mechanical packers are unable to reach, sealing materials can shut-off the excessive water. depending on the type of issue with water production, bin marta et al. (2024) reviewed the materials and procedures that can be taken into account to control and avoid the water production issue. in fact, there are a variety of control choices available (mechanical, chemical, and combination solutions), depending on what kind of issue arose at the well. in most cases, a combination of remedies is needed to solve various issues effectively. cost is a crucial consideration that will increase in combination with the complexity of the issue. the best choice for the candidate will assist in determining the appropriate approach. combination solutions are frequent when there are several difficulties and shut-off solutions (mechanical or chemical) depend on the complexity of the issue. in cases of flow behind casing, leaks in the casing, and near-wellbore issues, mechanical solutions are the best option. additionally, it might address water-out zones without creating issues with crossflow or the rise of oil water contact (owc). precise fluid placement is essential for chemical treatments. coiled tubing with inflated packers might be utilized to make sure that the majority of treatment fluids are put in the target zone without posing a hazard to oil zones (bailey et al. 2000). figure 1 illustrates the procedure of coiled tubing dual injection, which involves pumping protection fluid downward from the coiled tubing to the annulus of the casing and transporting treatment fluid through the coiled tubing. for the past thirty years, the development and usage of gels to decrease water production and create stream barriers has been the focus of technical efforts for water control. different types of gels were employed in different ways. numerous articles have documented the effective usage of preformed particle gels (ppgs), microgels, and submicron-sized particles to reduce water production from established oil fields. for instance, ppgs have been improved oil and gas recovery 4 effectively used in over 5,000 wells (bai et al. 2013). diagnosis of the reservoir issue, selection of a suitable candidate choice of gel, design of parameters, and placement of gel are all necessary for the successful application of gel therapies. the special benefits that particle gels offer over conventional in-situ gels make them very exciting options. figure 1—water shut-off with chemical treatment fluid (adapted from bailey et al. 2000). one of the important things that may affect the success of water shut-off operations is the proper well selection process. before choosing a good candidate for water shut-off treatments, a great deal of data must be reviewed based on the available previous studies (kabir et al. 1999). however, not all data and information are available and ready to be reviewed so that wells selection candidate were carried out using the available data as follows: production history. selected wells for water shut-off treatments have a significant amount of water production, i.e. produced water > 4,000 bwpd. wor and its derivative (d(wor)/dt) plotted against time in a diagnostic log-log manner as explained by chan (1995) can be very helpful to determine characteristic trends for different mechanisms whether the well has channeling or coning or combination. those mechanisms were selected as consideration to select water shut-off treatments candidate. completion history. historical water shut-off treatments which might have ever been completed at selected wells or offset wells were reviewed. since there were good results of water shut-off treatments. this effort was going to be carried out again. wellbore schematic and well log. both data were reviewed and selected the wells which have perforation interval > 5 ft. structural map and cross-sections. both data were reviewed to avoid selecting the well located at the lowest structure of the field and as reference to comparing selected wells to other wells’ location in the same structure. it is imperative to perform an in-depth evaluation of the intervention technique and to promote the expected outcomes based on production performance data. figure 2 depicts the steps of the most proficient method to assess water production issues successfully. this technique is all-inclusive. it might not, nevertheless, be applied to all reservoirs because each one might have unique characteristics. improved oil and gas recovery 5 figure 2—flow diagram for intervention process and investigation of high-water-production wells. no yes start evaluation production data performance evaluation water production ? continue monitoring no yes diagnostic plot plt mechanica l problem? yes sonic tool detect leakage? no yes treatment improve? still producing? no yes no improve? yes further diagnostic plots conning / channeling ? no yes treatment/shut-off no stop evaluation improved oil and gas recovery 6 methodology data pertaining to production were compiled from the field, and subsequent procedures were executed to identify the issues associated with excessive water production. the initial phase in ascertaining the presence of water production issues involved the creation of a flow rate diagram delineating both water and oil production. subsequently, the water production issues within the wells under examination were preliminarily investigated employing a recovery plot, decline-curve analysis, and production history plot. per the recovery plot depicted in figure 3, wells experiencing water production issues generally exhibit water production rates that have surpassed the economic wor threshold. figure 3—recovery plot sample (modified after bailey et al. 2000). water production commonly exhibits an immediate increase in tandem with oil production in wells experiencing water production issues (figure 4). figure 5 illustrates the analysis of decline curves, indicating that when production is characterized by a linear trend, the reservoir's discharge is normal, and deviations in the graph’s slope denote alterations in water production. 1 10 100 0 5 10 15 20 25 30 w a te r o il r a ti o ( w o r ) cumulative oil production (mmbbl) wor economic limit e x tr ap o la te d o il p ro d u ct io n e x p ec te d o il p ro d u ct io n improved oil and gas recovery 7 figure 4—a sample plot of production history (modified after bailey et al. 2000). figure 5—decline curve analysis sample (modified after bailey et al. 2000). after confirming the existence of the water production problem, the chan diagnostic plot was applied to investigate the water production mechanism. figure 6 illustrates how diagnostic plots are supposed to differentiate between the various mechanisms of water production. in a production well, log-log diagrams of the wor time derivatives versus time are thought to be able to differentiate between water coning, channeling resulting from layers with high permeability, and normal with a high water cut. for determining the cause of the issues with water production, the derivative method is thought to be the most suitable approach. as a result, this method is regarded as a one-of-a-kind approach and has been proposed as a 0.1 1 10 100 1000 10000 1 10 100 1000 10000 o il o r w a te r fl o w r a te ( b b l/ d a y ) time (days) oil water 0.1 1 10 100 1000 0 20 40 60 80 100 120 o il o r w a te r fl o w r a te ( b b l/ d a y ) cumulative oil production (mmbbl) oil water improved oil and gas recovery 8 straightforward, speedy, and cost-effective strategy for identifying mechanisms of excessive water production. the following is an illustration of the method for distinguishing and diagnosing water issues. first and foremost, we utilize the actual rate of water and oil production to determine the value of the wor and its derivative (d(wor)/dt) by applying eqs. (1) and (2): wor = qw qo ,........................................................................................................................................................(1) d(wor) dt = (wor2−wor1) (t2−t1) ......................................................................................................................................(2) thereafter, we plot the wor and its derivative (d(wor)/dt) versus time on a log-log scale. finally, based on the chan diagnostic plots as depicted in figure 6 and with the assistance of table 1, we can verify the mechanism and cause of the water production issue. figure 6—chan diagnostic plots (modified after chan 2010): a) bottom water coning; b) multilayer channeling; c) bottom water coning with late time channeling behavior; d) thief zone. improved oil and gas recovery 9 table 1—the mechanisms and causes of water production problem (adapted from changalvaie 2012). slope of the wor slope of the wor derivative (d(wor)/dt) the probable cause of the water problem positive slope positive slope multilayer channeling positive slope negative slope water coning (cusping) positive linear slope horizontal line shifting of the owc case study the study area is in a noteworthy hydrocarbon-rich area in the east-central part of the republic of yemen. this oilfield was discovered in the year 2000 following the drilling of the second exploration well. it is located approximately 550 kilometers east of yemen’s capital, sana’a. the field extracts oil from the lower cretaceous clastic deposits, commencing oil production in 2001. the study area, characterized by a flat topography, lacks distinct geological features and is situated at an elevation of around 950 meters above sea level. presently, the field experiences an average water cut of about 98%. cased-hole completions are predominant in this field, and early production involved a combination of outputs from multiple interval perforations. the available dataset in this field includes core plug data, petrophysical data, production data, pressure volume temperature (pvt) data, as well as geological and seismic structural data. core data consists of measurements of porosity and permeability, along with experimental assessments of oil and water relative permeability, water saturation, and capillary pressure. however, plt data was missing. hence, only production data is utilized for the analysis of this study. according to both petrophysical and seismic structural data, the reservoir rocks predominantly consist of clean, porous, and permeable sandstone zones interspersed with claystone interbeds. through well logging analysis, the clastic reservoir of this field is encountered at depths of approximately 4,817 ft. based on the well-logging data analysis, the reservoir has been subdivided into four distinct subunits, each exhibiting varying reservoir characteristics and hydrocarbon potential. notably, the first and third subunits emerge as the primary hydrocarbon-bearing units. more specifically, the first subunit stands out as the most favorable unit, boasting the highest hydrocarbon saturations (oil saturation up to 65%) and optimal reservoir attributes. across the first subunit, the average petrophysical parameters fall within the ranges of 4-21% for shale volume, 16-23% for total porosity, 11-19% for effective porosity, and 0-65% for hydrocarbon saturation. conversely, the second subunit demonstrates inferior reservoir characteristics, with shale volume exceeding 30% and effective porosity falling below 15%. on the other hand, according to pressure and pvt data analysis, the reservoir fluid type is dead oil, exhibiting a notably low gas-liquid ratio (glr). results and discussion determination of the water production issue. the presence of the water production problem is determined by using three different types of plots. the first is known as the recovery plot, which shows the cumulative oil production and the logarithm of the wor in graphical form, where the wells with excessive water production problems have water production exceeded the wor economic limit (the rate of wor at which the expense of managing delivered water is comparable to the cost of produced oil). in this case, water control procedures are required. the second graph is a logarithmic illustration of the flow rates of oil and water produced over time, referred to as the production history plot. it can be utilized to identify any "uncorrelated behaviors" during the field life cycle (ilk et al. 2007). in wells experiencing issues with water production, there is typically a concurrent decrease in oil production and an increase in water production (bailey et al. 2000). improved oil and gas recovery 10 figure 7—recovery plots for six selected wells a)w-1, b) w-2, c) w-4, d) w-9, e) w-11, f) w-28. improved oil and gas recovery 11 figure 8—production history plots for six selected wells: a)w-1, b) w-2, c) w-4, d) w-9, e) w-11, f) w28. improved oil and gas recovery 12 figure 9—decline curve analysis for six selected wells: a)w-1, b) w-2, c) w-4, d) w-9, e) w-11, f) w-28. plotting production rates versus time or the overall production of a field or well is the third form of plot known as decline-curve analysis (bailey et al. 2000). it is often applied to forecast future well performance and identify production issues (guo et al. 2007). any abrupt changes in the decline’s slope could be the result of an excess of improved oil and gas recovery 13 water being produced. the accumulation of damage or severe pressure depletion, for example, may be signs of other problems rather than a water production issue; therefore, it is important to take into account any divergence from the anticipated future output predictions (bailey et al. 2000). as seen in figure 7, recovery plots have been created for six wells that were chosen for the current investigation (w-1, w-2, w-4, w-9, w-11, and w-28 wells). water is produced approximately eight times more frequently than oil. the field's economic range is defined as the amount of water produced for every barrel of oil produced. that is, the proportion of water to oil is equivalent to one. most of the graphs show identical results for exceeding the water production wor economic limit, which indicates the existence of excessive water production problems. figure 8 illustrates production history plots for six selected wells under study. water production has increased, and oil production has simultaneously decreased, which means these wells have a problem with water production. on the other hand, figure 9 displays decline curve analysis diagrams for six wells in the research region that corresponds to the clastic sandstone reservoir. all the plots demonstrate that typical reservoir discharge occurs when production is represented by a straight-line diagram and that water production is indicated by a change in the graph's slope, which confirms the occurrence of excessive water production. diagnosing the water production problem. the approach of the wor diagnostic diagram was utilized on nine wells in the oilfield to identify the origins of issues related to water production. the wor and d(wor)/dt loglog diagrams were plotted versus time utilizing the real production data for nine wells that were chosen for the current investigation (w-1, w-2, w-4, w-9, w-10, w-11, w-14, w-15, and w-28 wells), as shown in figures 10 to 13. these graphs provide an image of the production activities of the past and present. it was discovered that these graphs were useful for figuring out the production trends and root causes of water production issues. the derivative of wor has been discovered: an approach for identifying whether multilayer channeling or water coning is the major cause of a well's excessive water production issue. the diagnostic plot’s appearance may change because of production alterations. the production well's drawdown pressure as well as the corresponding injection wells' injection rates and layer injection distributions could alter because of these alterations. an excellent illustration of the wor and d(wor)/dt deviations from the linear slope in the second period could be found in figure 10. (a) w-1 (b)w-4 figure 10—multilayer channeling with production changes. figure 11 provides a good illustration of a multilayer sandstone formation’s typical production procedure. observe that both the slope and the initial wor departure point are identified clearly. during this second period, improved oil and gas recovery 14 the d(wor)/dt diagram clearly shows a linear and positive slope, suggesting a water channeling scenario. the extent of this period ranged between 2,500 and 4,500 production days. in many cases, a near-wellbore issue might unexpectedly happen during a typical displacement and production process. figure 12 depicts such a dramatic problem occurring in two sandstone wells under the study (w-10 and w-15). wor was steady at first, but it was higher than 1. after applying a waterflood, the wor rose quickly and had a linear slope. as of late, the wor rise has been accelerating, and the slope has nearly reached infinity. this analysis was supported by the trend and progression of d(wor)/dt. the crest of d(wor)/dt was very high (about 500). the starting wor for certain reservoirs may be extremely high. figure 13 provides a nice illustration. it's for a normal well (w-14) in the study area that produces from a sandstone formation. the original wor was about 7 (80% water cut); this might result from a high initial water saturation. normal displacement behavior is shown by the linear slope of the overall wor trend. (b) w-2 (b)w-9 (c) w-1 (b)w-28 figure 11—multilayer channeling of various wells. improved oil and gas recovery 15 (d) w-10 (b)w-15 figure 12—near wellbore water channeling. figure 13—high wor with normal displacement of w-14. conclusions and recommendations a diagnosis of excessive water production was established for nine wells in the yemeni oilfield based on the production history data that was available. the analysis is carried out using a chan diagnostic plot, a production history plot, a recovery plot, and a decline curve analysis. from this investigation, the most significant conclusions and recommendations are as follows: 1. all wells under study exhibit the existence of excessive water production issues, as confirmed by recovery plots, production history plots, and decline curve diagrams. 2. the findings indicate that multilayer channeling through fractures and/or zones with high permeability, alongside near-wellbore water channeling, are the main factors contributing to excessive water production observed in the field under investigation. improved oil and gas recovery 16 3. it is recommended to implement the well selection process to ensure the selection of the well candidate and apply the proper water shut-off technique to get the best water control before doing any water shutoff activities. 4. based on the diagnosis results, it is recommended to apply the mechanical solution to the wells of nearwell channeling, while the chemical solution is the best option to solve the water production problem in the studied field. 5. the application of gel treatment technology must be implemented carefully to achieve the chemical water shut-off treatment. preformed particle gels (ppgs) are recommended due to their distinct benefits over conventional in-situ gels. 6. it is recommended that before doing any water shut-off activities, operators in the field advocate the implementation of the carbon/oxygen log to compare whether the perforation intervals have been watered out and whether fluid contacts have been shifted. 7. the diagnosis results indicated that the water cut in the investigation region was so high. as a result, it is advised to convert some of these wells to observation wells for use in the well interference test, which can be used to estimate the permeability direction and aid in the design of a good water flooding activity. nomenclature ewp = excessive water production wpms = water production mechanisms wpm = water production mechanism plt = production logging tool wor = water oil ratio d(wor)/dt = derivative of the water oil ratio owc = oil water contact wso = water shut-off ppgs = preformed particle gels bwpd = barrel water per day pvt = pressure volume temperature t = cumulative time. conflicting interests the author(s) declare that they have no conflicting interests. references abass, e., and merghany, s. 2011. integration of technical problems and diagnosis of high water cut-sudanese oil fields case. journal of science and 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https://www.eia.gov/petroleum/supply/weekly/(accessed 1 november 2024). willhite, g. p. 1986. waterflooding. spe textbook series. richardson, tx. xiaofang, l. and honggang, 2014. research and application of horizontal well plugging water technology. petrolchemical industry application 33(1): 46-49. sun, x. and bai, b. 2017. comprehensive review of water shutoff methods for horizontal wells. petroleum exploration and development journal 44(6):1022-1029. liu, y., liu, h., and pangaea, z. 2012. numerical simulation of nitrogen foam injection to control water cresting by bilateral horizontal well in bottom water reservoir. the open fuels and energy science journal 5(1): 53-60. yortsos, y. c., choi, y., yang, z., et al. 1999. analysis and interpretation of water/oil ratio in waterfloods. society of petroleum engineers journal 4(4): 413-424. ebrahim bin martaa is a ph.d. candidate in department of petroleum engineering, faculty of petroleum and mining engineering, suez university, suez, egypt. mohamed solimana worked as a professor in department of petroleum engineering, faculty of petroleum and mining engineering, suez university, suez, egypt. mohamed khamisb worked as a assistant professor in department of petroleum and natural gas engineering, college of engineering, king saud university, riyadh, saudi arabia. ali wahbaa worked as a assistant professor in department of petroleum engineering, faculty of petroleum and mining engineering, suez university, suez, egypt. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1337 received december 10, 2024; revised january 6, 2025; accepted march 1, 2025. *corresponding author: idudje.henry@fupre.edu.ng 1 application of electrokinetics-assisted flooding for enhanced oil recovery in niger delta henry e. idudje, federal university of petroleum resources effurun, owerri, nigeria; angela n. nwachukwu, ugochukwu i. duru, michael i. onyejekwe, and stanley i. onwukwe, federal university of technology owerri, owerri, nigeria abstract as global oil demand continues to increase, conventional reservoir extraction methods have proven inadequate to meet current production requirements. to address this challenge, this study explores economically viable enhanced oil recovery (eor) techniques, focusing on the application of direct current (dc) electrokinetics in a niger delta reservoir. experimental investigations demonstrated that electrokinetic enhanced oil recovery (ekeor) combined with alkylpolyglycoside (apg) surfactant at varying concentrations (1-3%) and different voltage levels achieved significant improvements. specifically, ek-eor with apg resulted in an incremental oil recovery improvement of 14-22%, enhanced sweep efficiency, reduced interfacial tension, and improved reservoir wettability compared to conventional surfactant eor methods. furthermore, ek-eor with mgo nanofluid achieved even higher recovery rates, yielding incremental recoveries of 19-26%, surpassing the performance of ek-eor with apg. mgo nanofluid flooding also exhibited superior mobility control and recovery efficiency compared to apg, as evidenced by the experimental results. to support these findings, a predictive model was developed to estimate recovery rates based on surfactant or nanofluid concentration and applied voltage. the ek-eor technology leverages multiple electrokinetic mechanisms, including joule heating, electrophoresis, electroosmosis, electromigration, and electrochemically enhanced reactions. however, further research is necessary to optimize the application of apg and other surfactants or nanofluids in ek-eor-assisted flooding. a deeper understanding of the underlying mechanisms and the potential of hybrid techniques could significantly enhance the efficiency and economic feasibility of this innovative approach in petroleum engineering. introduction electrokinetic-enhanced oil recovery (ek-eor) is an emerging technology that utilizes the application of a low direct current (dc) between a subsurface anode and cathode in the producing well to improve oil recovery. this technology offers several advantages, including fluid viscosity reduction, permeability enhancement, and decreased water cut, as highlighted by wittle et al. (2008). the electrical current facilitates hydrodynamic fluid movement from the injection well to the production well, improving recovery efficiency. however, a comprehensive systematic review of the literature is essential to critically evaluate laboratory results, establish the effectiveness of the ek-eor mechanism, and identify potential future research directions, as noted by ikpeka et al. (2022). mailto:idudje.henry@fupre.edu.ng improved oil and gas recovery 2 simulation insights indicate that ek-eor alone has limited effectiveness, with a reported success rate of approximately 45%. published laboratory experiments have further shown that interstitial clay significantly affects the electro-osmotic permeability of reservoir rocks, a key determinant of ek-eor performance. limitations such as salt deposition on the cathode and gas generation (oxygen and chlorine) at the anode also pose challenges to the widespread adoption of this technology (farhadi et al. 2022; abou et al. 2012). these findings underscore the need to explore hybrid approaches, such as ek-assisted surfactant flooding, which leverage the benefits of electrokinetics alongside other eor methods. given that hydrocarbons will continue to play a critical role in meeting global energy demand (kulmar 2010; tian and wang 2017), the development of environmentally sustainable extraction methods is of paramount importance. amidst growing concerns about the environmental impact of oil and gas production, researchers are increasingly focused on innovative and sustainable solutions to maximize recovery while minimizing ecological footprints (ghosh et al. 2012). this research aims to address these challenges by advancing the understanding and application of ek-assisted surfactant flooding as a sustainable and efficient eor technology. the enhancement of oil recovery from reservoirs has garnered significant global interest and remains a dynamic area of research. this focus is driven by the growing demand for energy, the decline in new oil discoveries, and the critical role that enhanced oil recovery (eor) and improved oil recovery (ior) technologies play in ensuring the future energy supply. these methods have become indispensable for addressing the challenges of declining production from mature reservoirs and meeting global energy demands (alvarado and manrique 2010; iglauer et al. 2004; zhang 2020). electrokinetic (ek) oil recovery is influenced by five primary mechanisms: joule heating, electromigration, electrophoresis (ep), electroosmosis, and electrochemically enhanced reactions. these mechanisms play a pivotal role in enhancing oil displacement and recovery within reservoirs. joule heating increases the reservoir temperature, reducing oil viscosity and improving mobility. electromigration facilitates the movement of ions and charged particles, while electrophoresis promotes the transport of charged oil droplets toward the production well. electroosmosis enhances fluid flow through capillary pathways by generating pressure gradients, and electrochemically enhanced reactions alter the chemical composition of the reservoir fluids, improving displacement efficiency. while the specific details of these mechanisms are extensively discussed in prior studies (wittle et al. 2008; haroun 2009; chilingar et al. 2014; rehman and meribout 2012), they were not elaborated upon in this study to maintain focus on experimental observations and results. experimental setup and flooding fluids for core flooding studies the flooding fluids used in the core flow studies consisted of alkyl polyglycoside (apg) solutions at concentrations of 1%, 2%, and 3%, as well as mgo nanofluid solutions at 1% and 2%, prepared in deionized water. niger delta sandstone cores, saturated with brine, were brought to oil saturation at irreducible water saturation (swirr) conditions using filtered crude oil of medium api gravity (alotaibi and nasr-el-din 2011). the sandstone core plugs used in the experiments had approximate permeabilities of 24.5% and 18%, and the flow studies were conducted using light oil density. following these experiments, the same core plugs were cleaned and reused for subsequent experiments with medium-density crude oil. tables 1 and 2 provide detailed oil and core petrophysical properties recorded at each stage of the flooding experiments. improved oil and gas recovery 3 table 1—petrophysical properties of core plug. cores length (cm) diameter (cm) dry weight (g) wet weight (g) bulk volume (ml) pore volume (ml) porosity (%) oiip (ml) core a 7.20 3.60 139. 8 157. 8 73.29 18.0 24.5 17.95 core b 7.10 3.40 180. 3 192.4 64.46 12.1 18.0 11.60 table 2—fluid properties of crude oil density (g/cm3) specific gravity api type viscosity (cp) pressure (psi) 0.868 0.867 31.50 light <10 15 the experiments were conducted in multiple sets and phases. in the first set of experiments on core a was injection of brine through the core at a constant pump pressure of 15 psi of rate of about 10 ml/min of water flooding (wf) alone until there is a water cut. in the second phase surfactant flooding (sf) alone was injected until ultimate recovery was achieved. in the third phase, potential for additional recovery was examined by applying the dc field onto the existing hydrodynamic field, this is done at different concentration of apg (1, 2, 3%) surfactant and at different voltage (2,4,6 and 8v), respectively. in the fourth phase the sf was conducted simultaneously with dc application from the beginning of each test after wf ultimate recovery was achieved. in the second set of experiments on core b, the same procedure as in the first set. but on different petrophysical core properties and same crude oil properties. the four distinct features of the experiments were the following, 1. core saturation: before the commencement of wf, core plugs a and b were brought to natural reservoirs condition by flooding with brine then followed by crude oil to get to connate water saturation (swc) condition. 2. wf: the core plugs were loaded into the stainless-steel core holder having rubber sleeves specially designed and connected electrically to the dc box with the cathode at the producing end and the anode at the injection end. all core flood experiments were conducted under pump pressure of 15psi. 3. brine solution was injected at the rate of 10 ml/min. the produced fluid was collected in an oil water separation and measuring device. at each step, water flow continued until no further oil recovery was possible. all the experiments were conducted at room temperature. 4. sf: sf alone was injected until ultimate recovery was achieved. the surfactant solution was injected at the rate of 10 ml/min. the produced fluid was collected in an oil water separation and measuring device. at each step, surfactant flow continued until no further oil recovery was possible before the collection. 5. application of dc: the electrode configuration used during dc application was the distributor at injection side as anode and the distributor at production end as cathode. in both sets of experiments involving dc (seq and smf), different voltages (2,4,6 and 8v) at different concentration of surfactant was applied. the schematic of experimental set up is shown in figures 1 and 2. improved oil and gas recovery 4 figure 1—a schematics setup of an electrokinetic core flooding equipment (fupre lab). figure 2—a schematics setup of an electrokinetic core flooding equipment (fupre lab). experimental data analysis ek-eor recovery analysis for core a at 15.0 psia. tables 3 and 4 present the recovery performance of ekeor under sequential and simultaneous flooding methods, respectively, across varying apg concentrations (1%, 2%, 3%) and applied voltages (2v, 4v, 6v, 8v) on core a. in table 3, sequential flooding (seq) shows a progressive increase in recovery as both apg concentration and voltage increase, with maximum recovery observed at 3% apg and 8v (5.0 ml). water flooding (wf) and surfactant flooding (sf) alone yield comparatively lower recovery, indicating the added benefit of applying voltage in sequential processes. table 4 highlights the superior performance of simultaneous flooding (smf), where recovery significantly outperforms sequential methods, reaching 13.0 ml at 3% apg and 8v. recovery increases steadily with both apg concentration and voltage, demonstrating the synergistic effect of combining flooding techniques with electrical pump valve + dc source data collection incoming air for bpr bpr effluent collector v core holder confining pressure + convection oven set to 600c bpr – back pressure regulator w a te r s u rf a ct c r u d e g a s bypass one-way check valve pressure gauge improved oil and gas recovery 5 energy. these results underscore the effectiveness of simultaneous flooding in maximizing oil recovery, particularly under high voltage and apg concentration conditions. table 3—ek-eor sequential recovery for core a at different apg concentration and voltage @ 15psi. core a apg concentration (%) avg. rec. water flooding (ml)(wf) avg. rec surf. flooding (ml)(sf) rec. seq. flooding @2v(ml) (seq) rec. seq. flooding @4v(ml) (seq) rec. seq. flooding @6v(ml) (seq) rec. seq. flooding @8v(ml) (seq) 1 3.05 4.30 2.8 3.0 3.0 3.8 2 3.15 5.03 3.1 3.3 3.2 4.0 3 3.25 5.90 3.6 4.0 4.4 5.0 table 4—ek-eor simultaneous recovery at different apg concentration and voltage @ 15psi. core a apg concentration (%) avg. rec. water flooding (ml)(wf) rec. sim. flooding @2v(ml) (smf) rec. sim. flooding @4v(ml) (smf) rec. sim. flooding @6v(ml) (smf) rec. sim. flooding @8v(ml) (smf) 1 3.05 8.0 9.0 10.0 10.3 2 3.15 9.0 10.2 11.3 11.9 3 3.25 11.5 11.7 12.5 13.0 ek-eor recovery analysis for core a at 30.0 psia. table 5 illustrates the ek-eor recovery performance for core a at 30.0 psia pump pressure under sequential (seq) and simultaneous flooding (smf) methods with varying apg concentrations (1%, 2%, 3%) and applied voltages. the data demonstrates that recovery efficiency improves consistently with increased apg concentration and voltage for both methods. sequential flooding yields a maximum recovery of 3.5 ml at 3% apg and 4v, showing moderate efficiency enhancements compared to water flooding (wf) and surfactant flooding (sf) alone. in contrast, simultaneous flooding exhibits significantly higher recovery potential, achieving 9.0 ml at 3% apg and 4v. the results indicate that simultaneous flooding consistently outperforms sequential methods, particularly at higher apg concentrations, highlighting its superiority in enhancing oil recovery under increased pressure conditions. the ek-eor recovery performance for core a under 15.0 psia and 30.0 psia pump pressures show notable differences in efficiency across sequential (seq) and simultaneous flooding (smf) methods. at 15.0 psia, the sequential flooding method achieves a maximum recovery of 3.2 ml at 3% apg concentration and 8v, while simultaneous flooding significantly outperforms with a maximum recovery of 7.3 ml under the same conditions. in contrast, at 30.0 psia, sequential flooding exhibits a slightly higher maximum recovery of 3.5 ml at 3% apg and 4v, but simultaneous flooding demonstrates a substantial improvement, achieving a maximum recovery of 9.0 ml under similar conditions. comparing the two pressure conditions, the overall recovery efficiency increases with higher pressure (30.0 psia) for both methods. the relative enhancement is more pronounced for simultaneous flooding, which benefits significantly from the combined effects of elevated pressure, voltage, and apg concentration. these results indicate that increasing pump pressure amplifies the effectiveness of ek-eor processes, particularly for simultaneous flooding, making it a more efficient strategy for oil recovery in higher-pressure scenarios. improved oil and gas recovery 6 table 5—ek-eor sequential and simultaneous recovery at different apg concentration and voltage@ 30psi. core a apg concentratio n (%) avg. rec. water flooding(ml) (wf) avg. rec surf. flooding(ml) (sf) rec. seq. flooding @2v(ml) (seq) rec. seq. flooding @4v(ml) (seq) rec. sim. flooding @2v(ml) (smf) rec. sim. flooding @4v(ml) (smf) 1 2.40 4.25 2.20 2.70 6.00 7.0 2 2.48 4.70 3.00 3.00 6.50 8.2 3 2.80 4.70 3.20 3.50 7.0 9.0 ek-eor recovery analysis for core b at 15.0 psia. tables 6 and 7 summarize the ek-eor recovery performance for core b under sequential and simultaneous flooding methods at a pump pressure of 15.0 psia. table 5 demonstrates that sequential flooding (seq) yields increasing recovery efficiencies with both higher apg concentrations and voltages. the maximum recovery (3.20 ml) is achieved at 3% apg and 8v. however, the recovery for water flooding (wf) and surfactant flooding (sf) alone remains comparatively low, indicating limited effectiveness without the application of voltage. table 6, on the other hand, reveals the enhanced recovery potential of simultaneous flooding (smf), with recovery volumes notably exceeding those of sequential methods. the highest recovery (7.30 ml) is observed at 3% apg and 8v. simultaneous flooding shows a consistent trend of improved recovery with increased apg concentrations and applied voltages, further highlighting its effectiveness as a more efficient eor method. these results underscore the potential of simultaneous flooding in maximizing oil recovery under controlled pressure and optimized conditions. table 6—ek-eor sequential recovery for core b at different apg concentrations and voltages @ 15psi. core b apg % conc. avg. rec waterfloodin g (ml)(wf) avg. rec surf. flooding (ml)(sf) rec. seq. flooding @2v(ml) (seq) rec. seq. flooding @4v(ml) (seq) rec. seq. flooding @6v(ml) (seq) rec. seq. flooding @8v(ml) (seq) 1 2.10 2.53 1.80 2.10 2.20 2.40 2 2.18 3.00 2.00 2.60 2.00 2.60 3 2.05 3.50 2.80 2.90 2.50 3.20 table 7—ek-eor simultaneous recovery for core b at different apg concentrations and voltages @ 15psi. core b apg % conc. avg. rec water flooding (ml)(wf) rec. sim. flooding @2v(ml) (smf) rec. sim. flooding @4v(ml) (smf) rec. sim. flooding @6v(ml) (smf) rec. sim. flooding @8v(ml) (smf) 1 2.10 4.50 4.80 4.70 4.80 2 2.18 6.80 6.20 6.40 5.80 3 2.05 7.20 6.80 6.80 7.30 ek-eor recovery with mgo nanofluid on core a at 15.0 psia. tables 8 and 9 summarize the ek-eor recovery performance for core a at 15.0 psia pump pressure using mgo nanofluid under sequential (seq) and simultaneous flooding (smf) methods with different nanofluid concentrations (1% and 2%) and applied voltages. table 8 demonstrates that sequential flooding achieves increasing recovery efficiencies as nanofluid concentration and voltage increase. the maximum recovery (7.0 ml) occurs at 2% nanofluid and 8v, indicating a moderate enhancement compared to water flooding (wf) and nanofluid flooding (nf) alone. table 9 highlights improved oil and gas recovery 7 the superior recovery performance of simultaneous flooding, achieving significantly higher recoveries, with a maximum of 15.3 ml at 2% nanofluid and 8v. this indicates that simultaneous flooding benefits substantially from the synergistic effects of nanofluid, voltage, and pressure, demonstrating a significant improvement over sequential method. the results confirm that the integration of nanofluid with ek-eor enhances oil recovery, particularly under simultaneous flooding conditions, making it a more effective approach for improving oil recovery efficiency. table 8—ek-eor sequential recovery for core a at different nanofluid concentration and voltage @ 15psi. core a nanofluid (mgo) concentratio n (%) avg. rec water flooding (ml) (wf) avg. rec nano. flooding (ml)(nf) rec. seq. flooding @2v(ml) (seq) rec. seq. flooding @4v(ml) (seq) rec. seq. flooding @6v(ml) (seq) rec. seq. flooding @8v(ml) (seq) 1 3.0 6.0 3.3 3.8 4.5 6.5 2 3.15 7.0 4.2 4.8 6.2 7 table 9—ek-eor simultaneous recovery for core a at different nanofluid concentration and voltage @ 15psi. core a nanofluid (mgo) concentration (%) avg. rec water flooding (ml) (wf) rec. sim. flooding @2v(ml) (smnf) rec. sim. flooding @4v(ml) (smnf) rec. sim. flooding @6v(ml) (smnf) rec. sim. flooding @8v((ml) (smnf) 1% 3.0 9 10.3 12.3 13.8 2% 3.2 9.5 11.5 13.5 15.3 ek-eor recovery with mgo nanofluid on core b at 15.0 psia. tables 10 and 11 summarize the ek-eor recovery results for core b using mgo nanofluid under sequential (seq) and simultaneous flooding (smf) methods at 15.0 psia pump pressure with varying nanofluid concentrations (1% and 2%) and applied voltages. table 10 shows that sequential flooding yields increasing recovery efficiencies as both nanofluid concentration and voltage rise, with the maximum recovery of 4.6 ml observed at 2% nanofluid and 8v. despite the improvement over water flooding (wf) and nanofluid flooding (nf) alone, the recovery remains moderate compared to simultaneous methods. table 11, in contrast, demonstrates the significantly higher recovery achieved through simultaneous flooding, with a maximum of 7.8 ml at 2% nanofluid and 8v. this highlights the enhanced synergistic effect of nanofluid and electric field in the simultaneous flooding process, further amplified under increased voltage and nanofluid concentration. these results confirm the superior efficiency of simultaneous flooding as a more effective ek-eor strategy for improving oil recovery, particularly in the presence of nanofluids. table 10—ek-eor sequential recovery for core b at different nanofluid concentration and voltage @ 15psi. core b nanofluid (mgo) concentratio n (%). avg. rec water flooding(ml) (wf) avg. rec nano. flooding (ml) (nf) rec. seq. flooding @2v(ml) (seq) rec. seq. flooding @4v(ml) (seq) rec. seq. flooding @6v(ml) (seq) rec. seq. flooding @8v(ml) (seq) 1 2.10 2.93 2.40 2.90 3.50 3.80 2 2.18 3.5 3.00 3.30 4.20 4.60 improved oil and gas recovery 8 table 11—ek-eor simultaneous recovery for core b at different nanofluid concentration and voltage @ 15psi. core b nanofluid (mgo) concentration (%). avg. rec water flooding (ml)(wf) rec. sim. flooding @2v(ml) (smnf) rec. sim. flooding @4v(ml) (smnf) rec. sim. flooding @6v(ml) (smnf) rec. sim. flooding @8v((ml) (smnf) 1 2.10 5.00 5.50 5.70 6.20 2 2.18 5.30 5.80 6.90 7.80 comparative analysis comparison of oil recovery via waterflooding and surfactant flooding with apg. table 12 and figure 3 summarize the average oil recoveries achieved through waterflooding and surfactant flooding for core a and core b at varying apg concentrations (1-3%). for waterflooding, core a shows a slight increase in recovery from 17.03% at 1% apg to 18.16% at 3% apg, while core b exhibits a non-linear trend, with recovery peaking at 18.79% at 2% apg before decreasing to 17.67% at 3%. conversely, for surfactant flooding, both cores show a significant increase in recovery as apg concentration rises. core a demonstrates the highest recovery of 32.96% at 3% apg, while core b achieves a recovery of 30.17% under the same conditions. the bar chart visually reinforces the substantial enhancement in recovery using surfactant flooding compared to waterflooding, particularly at higher apg concentrations. these results highlight the superior efficiency of surfactant flooding in improving oil recovery, especially at optimal apg concentrations, for both core a and core b. table 12—oil recovery of waterflooding and surfactant flooding. apg concentration, % core a core b avg. rec. water flooding, % avg. rec. surf. flooding, % avg. rec. water flooding, % avg. rec. surf flooding, % 1 17.03 24.02 18.1 21.81 2 17.59 28.1 18.79 25.86 3 18.16 32.96 17.67 30.17 improved oil and gas recovery 9 figure 3—average oil recovery of water and surfactant flooding. comparison of ek-eor oil recovery for core a. table 13 and figure 4 presents the oil recovery performance via sequential and simultaneous ek-eor surfactant flooding for core a at 15 psia under varying apg concentrations (1–3%) and voltages (2v, 4v, 6v, 8v). for sequential flooding, oil recovery increases with both higher apg concentration and applied voltage. the maximum recovery is achieved at 3% apg and 8v, with an average recovery of 27.93%. conversely, simultaneous flooding exhibits significantly higher recoveries across all conditions, with the maximum recovery of 72.63% recorded at 3% apg and 8v. simultaneous flooding consistently outperforms sequential flooding, demonstrating a marked enhancement in recovery efficiency due to the synergistic effects of surfactant flooding, electric field application, and higher apg concentrations. these results highlight the superior efficiency of simultaneous ek-eor flooding in optimizing oil recovery, particularly under higher voltage and apg concentration conditions. table 13—oil recovery via sequential and simultaneous ek-eor surfactant flooding for core a at 15 psia. apg concentration, % avg. rec. ek-eor surf. seq. flooding (%) avg. rec. ek-eor surf. sim. flooding (%) 2v 4v 6v 8v 2v 4v 6v 8v 1 15.64 16.75 16.75 21.23 44.69 50.28 55.87 57.54 2 17.32 18.44 17.88 22.35 50.28 56.98 63.13 66.48 3 20.11 22.35 24.58 27.93 64.25 65.36 69.83 72.63 17.03 17.59 18.16 24.02 28.1 32.96 18.1 18.79 17.67 21.81 25.86 30.17 0 10 20 30 40 50 1 2 3 a v g . r ec o v er y ( % ) concentration, % core a avg. recovery of water flooding core a avg. recovery of surfactant flooding core b avg. recovery of water flooding core b avg. recovery of surfactant flooding improved oil and gas recovery 10 figure 4—average oil recovery of sequential and simultaneous ek-eor surfactant flooding for core a comparison of ek-eor oil recovery for core b. table 14 and figure 5 illustrate the oil recovery performance of core b via sequential and simultaneous ek-eor surfactant flooding at 15 psia with varying apg concentrations (1%, 2%, 3%) and applied voltages (2v, 4v, 6v, 8v). sequential flooding shows a gradual increase in recovery with both apg concentration and voltage. the highest recovery of 27.60% is observed at 3% apg and 8v, indicating moderate improvement compared to lower concentrations and voltages. however, simultaneous flooding exhibits substantially higher recoveries, reaching a maximum of 65.93% under the same conditions. the bar chart in figure 5 visually emphasizes the superior performance of simultaneous flooding compared to sequential flooding across all conditions. the recovery trends highlight the synergistic effects of apg concentration, electric field, and simultaneous flooding, which collectively enhance oil recovery efficiency. these results demonstrate that simultaneous flooding is a more effective approach for ek-eor applications in core b. table 14—oil recovery via sequential and simultaneous ek-eor surfactant flooding for core b at 15 psia. apg concentration, % avg. recovery via sequential flooding (%) avg. recovery via simultaneous flooding (%) 2v 4v 6v 8v 2v 4v 6v 8v 1 15.52 18.10 18.97 20.69 38.79 41.38 43.52 46.38 2 17.24 22.41 23.06 23.84 48.62 50.45 53.17 57.82 3 24.13 25.15 26.60 27.60 60.07 62.62 64.00 65.93 0 20 40 60 80 100 2v 4v 6v 8v 2v 4v 6v 8v avg. recovery via sequential flooding(%) avg. recovery via simultaneous flooding (%) r ec o v er y ( % ) 1% apg conc. 2% apg conc. 3% apg conc. improved oil and gas recovery 11 figure 5—average oil recovery of sequential and simultaneous ek-eor surfactant flooding for core b comparison of oil recovery using nano-ek-eor with mgo nanofluid for core a. table 15 summarizes the oil recovery results from nano-ek-eor using mgo nanofluid under sequential and simultaneous flooding methods for core a at 15 psia, with nanofluid concentrations of 1% and 2% and voltages ranging from 2v to 8v. sequential flooding shows a consistent increase in recovery efficiency with higher voltage and nanofluid concentration. the maximum recovery of 39.11% is observed at 2% nanofluid and 8v, demonstrating moderate improvement compared to lower concentrations and voltages. simultaneous flooding, however, achieves significantly higher recoveries, with a peak value of 85.47% under the same conditions. figure 6 visually highlights the superior performance of simultaneous flooding across all conditions, particularly at higher voltages and nanofluid concentrations. the results underscore the enhanced synergistic effects of nanofluid and electric field in simultaneous flooding, making it a more effective strategy for improving oil recovery compared to sequential flooding. table 15—oil recovery via sequential and simultaneous ek-eor-nano flooding for core a at 15 psia. nano (mgo) flooding (%) avg. recovery via sequential flooding (%) avg. recovery via simultaneous flooding (%) 2v 4v 6v 8v 2v 4v 6v 8v 1% 18.44 21.23 25.14 36.31 50.28 57.54 68.72 77.09 2% 23.46 26.82 34.64 39.11 53.07 64.25 75.42 85.47 figure 7 shows the oil recovery performance of mgo for sequential and simultaneous flooding in cores b. as observed, the introduction of sequential electro-kinetics at varying voltage, improved oil recovery. this is attributed to mobility alteration effect of electro-kinetics on crude oil through crude oil viscosity reduction which enables better sweep efficiency by the nanoparticles. as observed too, the introduction of ek in simultaneous mode yielded better crude oil recovery, and this attributed to the enhanced impact of heated mgo concentration and reduced crude oil viscosity to enable more suitable sweeping of entrapped crude oil to the wellbore. 0 20 40 60 80 100 2v 4v 6v 8v 2v 4v 6v 8v avg. recovery via sequential flooding(%) avg. recovery via simultaneous flooding (%) r ec o v er y (% ) 1% apg conc. 2% apg conc. 3% apg conc. improved oil and gas recovery 12 figure 6—recovery via nano-ek-eor sequential and simultaneous flooding from core a figure 7—recovery via nano-ek-eor sequential and simultaneous flooding from core b. figure 8 shows the comparison of oil recovery between ek-eor nanoflooding and ek-eor surfactant flooding. as observed, ek-eor-nf recorded better recovery than ek-eor-sf in both sequential and simultaneous flooding. as observed too, the simultaneous flooding of ek recorded better oil recovery with both sf and nf than sequential flooding. 0 20 40 60 80 100 2v 4v 6v 8v 2v 4v 6v 8v nano ek-eor sequential flooding(%) nano ek-eor simultaneous flooding(%) r ec o v er y ( % ) 1% (mgo) 2% (mgo) 0 20 40 60 80 100 2v 4v 6v 8v 2v 4v 6v 8v nano ek-eor sequential flooding(%) nano ek-eor simultaneous flooding(%) r ec o v er y ( % ) 1% (mgo) 2% (mgo) improved oil and gas recovery 13 figure 8—comparison of oil recovery between ek-eor nano flooding and ek-eor surfactant flooding. oil recovery differences between surfactant and water flooding across apg concentrations. table 16 presents the differences in oil recovery between surfactant flooding (sf) and water flooding (wf) for core samples a and b across varying apg concentrations (1%, 2%, 3%). for core a, the recovery difference increases significantly with higher apg concentrations, starting from 6.99% at 1% apg, rising to 10.51% at 2%, and reaching a maximum of 14.8% at 3%. similarly, for core b, the recovery differences also increase with apg concentration, albeit at a slightly lower magnitude compared to core a, ranging from 3.7% at 1% apg to 7.07% at 2% and 12.5% at 3%. these results demonstrate that surfactant flooding substantially outperforms water flooding, with the enhancement more pronounced at higher apg concentrations. the differences between core a and core b suggest that the efficiency of surfactant flooding may depend on core-specific properties, such as porosity or permeability, alongside apg concentration. table 16—enhanced oil recovery across the concentrations core samples rec. difference bet. sf and wf @1% apg conc. (%) rec. difference bet. sf and wf @2% apg conc. (%) recovery difference bet. sf and wf @3% apg conc. (%) a 6.99 10.51 14.8 b 3.7 7.07 12.5 comparison of ek-eor nano and surfactant flooding recoveries at 8v. table 17 and figure 9 compare the oil recovery achieved through ek-eor nano flooding (nf) using mgo and ek-eor surfactant flooding (sf) with apg under sequential and simultaneous flooding methods at 8v potential and concentrations of 1% and 2%. sequential flooding demonstrates higher recoveries for nano flooding, with 36.31% and 39.11% at 1% and 2% concentrations, respectively, compared to 21.23% and 22.35% for surfactant flooding. similarly, simultaneous flooding achieves significantly better recoveries for nano flooding, reaching 77.09% and 85.47% for 1% and 2% concentrations, respectively, compared to 57.54% and 66.48% for surfactant flooding. the bar chart in figure 9 visually reinforces the superior performance of nano flooding over surfactant flooding across all conditions, particularly under simultaneous flooding. these results highlight the enhanced efficiency of mgo nano flooding in improving oil recovery, attributed to the synergistic effects of nanoparticles and the applied electric field, which outperform the conventional surfactant-based method. 36.31 39.11 77.09 85.47 21.23 22.35 57.54 66.48 0 20 40 60 80 100 recovery @ 1% conc. (8v) recovery @ 2 % conc. (8v) recovery @ 1% conc. (8v) recovery @ 2 % conc. (8v) sequential flooding simultaneous flooding r ec o v er y ( % ) ek-eor nf(mgo) ek-eor sf (apg) improved oil and gas recovery 14 table 17—recovery of ek-eor nano flooding (nf) and ek-eor surfactant flooding (sf) at 8v potential. means of recovery sequential flooding simultaneous flooding 1% of conc. (8v) 2% of conc. (8v) 1% of conc. (8v) 2 % of conc. (8v) ek-eor nf(mgo) 36.31% 39.11% 77.09% 85.47% ek-eor sf (apg) 21.23% 22.35% 57.54% 66.48% figure 9—comparison of oil recovery between ek-eor nano flooding and ek-eor surfactant flooding. modeling of experimental data all experimental data and results from core flood experiments pertaining to simultaneous and sequential flooding are presented tables 18 and 19. 36.31 39.11 77.09 85.47 21.23 22.35 57.54 66.48 0 20 40 60 80 100 recovery @ 1% conc. (8v) recovery @ 2 % conc. (8v) recovery @ 1% conc. (8v) recovery @ 2 % conc. (8v) sequential flooding simultaneous flooding r ec o v er y ( % ) ek-eor nf(mgo) ek-eor sf (apg) improved oil and gas recovery 15 table 18—experimental data for nano flooding. x1 x2 x3 x4 y nano fluid concentration (wt %) current density(volt) core porosity (%) simultaneous flooding oil recovery (ml) 0.01 2 0.245 1 9 0.02 2 0.245 1 9.5 0.01 4 0.245 1 10.3 0.02 4 0.245 1 11.5 0.01 6 0.245 1 12.3 0.02 6 0.245 1 13.5 0.01 8 0.245 1 13.8 0.02 8 0.245 1 15.3 0.01 2 0.18 1 5 0.02 2 0.18 1 5.3 0.01 4 0.18 1 5.5 0.02 4 0.18 1 5.8 0.01 6 0.18 1 5.7 0.02 6 0.18 1 6.9 0.01 8 0.18 1 6.2 0.02 8 0.18 1 7.8 0.01 2 0.245 2 3.3 0.02 2 0.245 2 4.2 0.01 4 0.245 2 3.8 0.02 4 0.245 2 4.8 0.01 6 0.245 2 4.5 0.02 6 0.245 2 6.2 0.01 8 0.245 2 6.5 0.02 8 0.245 2 7 0.01 2 0.18 2 2.4 0.02 2 0.18 2 3 0.01 4 0.18 2 2.9 0.02 4 0.18 2 3.3 0.01 6 0.18 2 3.5 0.02 6 0.18 2 4.2 0.01 8 0.18 2 3.8 0.02 8 0.18 2 4.6 improved oil and gas recovery 16 table 19—surfactant core flooding experimental data. x1 x2 x3 x4 y1 surfactant concentration (wt%) current density (volt) core porosity (%) simultaneous flooding oil recovery (%) 0.01 2 0.245 1 8.0 0.02 2 0.245 1 9.0 0.03 2 0.245 1 11.5 0.01 4 0.245 1 9.0 0.02 4 0.245 1 10.2 0.03 4 0.245 1 11.7 0.01 6 0.245 1 10.0 0.02 6 0.245 1 11.3 0.03 6 0.245 1 12.5 0.01 8 0.245 1 10.3 0.02 8 0.245 1 11.9 0.03 8 0.245 1 13.0 0.01 2 0.18 1 4.50 0.02 2 0.18 1 6.80 0.03 2 0.18 1 7.20 0.01 4 0.18 1 4.80 0.02 4 0.18 1 6.20 0.03 4 0.18 1 6.80 0.01 6 0.18 1 4.70 0.02 6 0.18 1 6.40 0.03 6 0.18 1 6.80 0.01 8 0.18 1 4.80 0.02 8 0.18 1 5.80 0.03 8 0.18 1 7.30 0.01 2 0.245 2 2.8 0.02 2 0,245 2 3.1 0.03 2 0.245 2 3.6 0.01 4 0,245 2 3.0 0.02 4 0.245 2 3.3 0.03 4 0,245 2 4.0 0.01 6 0.245 2 3.0 0.02 6 0,245 2 3.2 0.03 6 0.245 2 4.4 0.01 8 0,245 2 3.8 0.02 8 0.245 2 4.0 0.03 8 0,245 2 5.0 0.01 2 0.18 2 1.80 0.02 2 0.18 2 2.00 0.03 2 0.18 2 2.80 0.01 4 0.18 2 2.10 0.02 4 0.18 2 2.60 0.03 4 0.18 2 2.90 0.01 6 0.18 2 2.20 0.02 6 0.18 2 2.00 0.03 6 0.18 2 2.50 0.01 8 0.18 2 2.40 0.02 8 0.18 2 2.60 0.03 8 0.18 2 3.20 improved oil and gas recovery 17 the data in tables 20 and 21 were analyzed using design expert software. analysis of variance (anova) was conducted to determine parameters that are influential to the model. anova results for surfactant and nano fluid flooding scenarios are shown, respectively. table 20—analysis of variance results for the surfactant coreflood experimental data. source sum of squares df mean square f-value p-value model 518.10 7 74.01 312.80 < 0.0001 significant a-a 24.50 1 24.50 103.54 < 0.0001 b-b 5.15 1 5.15 21.77 < 0.0001 c-c 16.52 1 16.52 69.81 < 0.0001 d-d 12.65 1 12.65 53.48 < 0.0001 ad 5.61 1 5.61 23.71 < 0.0001 cd 30.23 1 30.23 127.76 < 0.0001 c² 7.25 1 7.25 30.66 < 0.0001 residual 9.46 40 0.2366 cor total 527.57 47 table 21—analysis of variance results for the nano fluid flooding experimental data. source sum of squares df mean square f-value p-value model 380.10 8 47.51 381.96 < 0.0001 significant a-a 6.89 1 6.89 55.42 < 0.0001 b-b 0.8957 1 0.8957 7.20 0.0133 c-c 117.75 1 117.75 946.61 < 0.0001 d-d 57.34 1 57.34 460.98 < 0.0001 ab 0.4203 1 0.4203 3.38 0.0790 bc 6.81 1 6.81 54.72 < 0.0001 bd 1.94 1 1.94 15.56 0.0006 cd 36.98 1 36.98 297.29 < 0.0001 residual 2.86 23 0.1244 cor total 382.96 31 according to the anova results shown in table 20 and 21, the model derived from the data in tables 18 and 19 and all the parameters to the model are significant. this is because the model or its parameters have p-values less than 0.05 depicted as < 0.0001. based on this assertion, the model for predicting oil recovery due to surfactant and nano fluid flooding can be outputted and presented as shown in eqs. (1) and (2), respectively. 𝑌𝑠𝑢𝑟𝑓𝑎𝑐𝑡𝑎𝑛𝑡 = −13.8633 + 213.125 ∗ 𝑋1 + 0.146927 ∗ 𝑋2 + 84.7148 ∗ 𝑋3 + 7.92527 ∗ 𝑋4 + 83. 75 ∗ 𝑋1 ∗ 𝑋4 + 54.6311 ∗ 𝑋3 ∗ 𝑋4 + 99.049 ∗ 𝑋3^2 ,....................................................(1) 𝑌𝑛𝑎𝑛𝑜 𝑓𝑙𝑢𝑖𝑑 = −17.5404 + 38.75 ∗ 𝑋1 + −0.679808 ∗ 𝑋2 + 124.808 ∗ 𝑋3 + 10.4452 ∗ 𝑋4 + 10. 25 ∗ 𝑋1 ∗ 𝑋2 + 6.34615 ∗ 𝑋2 ∗ 𝑋3 + 0.22 ∗ 𝑋2 ∗ 𝑋4 + 66.1538 ∗ 𝑋3 ∗ 𝑋4............................(2) improved oil and gas recovery 18 validation of model. a model can be validated using existing equations or using data used for its development or by conducting the experiment and inserting experimental data into the model to ascertain if results from experiment are in close agreement with results from the model. figures 10 and 11 illustrate cross-plots of actual versus predicted oil recovery for surfactant flooding and nano flooding, respectively. both graphs demonstrate strong correlations between observed and predicted values, as indicated by high coefficients of determination (r² = 0.982 for surfactant flooding and r² = 0.9926 for nano flooding). the data points align closely with the 1:1 trend line in both cases, suggesting that the predictive models are highly accurate in capturing the recovery mechanisms for each flooding method. the slightly higher r² for nano flooding implies that the model is even more precise in predicting oil recovery for nano flooding compared to surfactant flooding. these results validate the reliability of the models for predicting performance and highlight their potential application in optimizing enhanced oil recovery processes. figure 10—cross plot of actual vs predicted oil recovery due to surfactant flooding. figure 11—cross plot of actual vs predicted oil recovery due to nano flooding. r² = 0.982 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 p re d ic te d o il r ec o v er y ( % ) actual oil recovery (%) r² = 0.9926 0 2 4 6 8 10 12 14 16 0 2 4 6 8 10 12 14 16 18 p re d ic te d o il r ec o v er y ( % ) actual oil recovery (%) improved oil and gas recovery 19 conclusions this study demonstrates the efficacy of ek-eor coupled with apg surfactant flooding and mgo nanofluid flooding in niger delta sandstone core plugs. key findings reveal that concurrent nf-dc flow significantly outperforms sequential flow in recovery enhancement. both methods address critical challenges of water scarcity and surfactant cost in conventional waterflooding, offering environmentally constrained oilfields a viable alternative to reduce operational costs and fluid disposal burdens. apg surfactant flooding achieves: 1. incremental oil recovery of 14-22% ooip through interfacial tension reduction and wettability alteration toward water-wet conditions. 2. enhanced sweep efficiency due to improved mobility control. 3. operational advantages include lower chemical concentration requirements and reduced implementation costs. mgo nanofluid flooding demonstrates: 1. superior incremental recovery of 19-26% ooip, attributed to nanofluid retention mechanisms increasing contact time within pore matrices. 2. favorable mobility ratio adjustment and residual oil saturation reduction. 3. extended reservoir effects through nanoparticle adsorption/retention, though accompanied by higher material cost and environmental concerns regarding nanoparticle disposal. while mgo nanofluids exhibit higher recovery efficiency than apg surfactants, their economic viability is constrained by elevated nanoparticle costs and unquantified long-term reservoir impacts. apg systems offer costeffective implementation but require optimization of concentration thresholds to maximize recovery. both technologies show potential for field applications pending further research into mgo environmental mitigation strategies and apg formulation improvements for low-permeability formations. acknowledgments the authors are grateful to the management and staffs of the department of petroleum engineering, federal university of petroleum resources, delta state nigeria. for providing the laboratory facilities to conduct the laboratory experiment. conflicting interests the author(s) declare that they have no conflicting interests. references abou, s. n., shrestha, r., sarma, h. k. 2012. a new approach optimizing mature waterfloods with electrokineticicsassisted surfactant flooding in abu dhabi carbonate reservoirs. paper presented at the spe kuwait international petroleum conference and exhibition, kuwait city, kuwait, 10-12 december. spe-163379-ms. alotaibi, b. and nasr-el-din, h. 2011. electrokinetics of limestone particles and crude-oil droplets in saline solutions. spe reserv eval eng. 14(1): 604-611. alvarado, v. and manrique, e. 2010. enhanced oil recovery: field planning and developments in heavy oil recovery methods. energy and fuels 24(2): 1140-1151. chilingar, g. v., haroun, m., and shojaei, h. 2014. electrokinetics for petroleum environmental engineers. new york: john wiley and sons. improved oil and gas recovery 20 farhadi, h., mahmoodpour, s., ayatollahi, s., et al. 2022. novel experimental evidence on the impact of surface carboxylic acid site density on the role of individual ions in the electrical behavior of crude oil/water. journal of molecular liquids 362(1):119730. ghosh, b., al-shalabi, p. e. e., and haroun, m. 2012. the effect of dc electrical potential on enhancing sandstone reservoir permeability and oil recovery. petroleum science and technology 30(1):2148-2159. haroun, m., al hassan, s., ansari, a., et al. 2009. smart nano-eor process for abu dhabi carbonate reservoirs. paper presented at the abu dhabi international petroleum conference and exhibition, abu dhabi, uae, 11-12 november. spe-162386-ms. iglauer, s., wu, y., shuler, p. j., et al. 2004. alkyl polyglycoside surfactants for improved oil recovery. paper presented at the spe/doe symposium on improved oil recovery, tulsa, oklahoma, 17-19 april. spe-89472-ms. ikpeka, p. m., ugwu, j. o., pillai, g. g., et al. 2022. effectiveness of electrokinetic-enhanced oil recovery (ek-eor): a systematic review. journal of engineering and applied science 69(1):125-137. kulmar, g. 2010. electrical methods for enhanced oil recovery: a review. journal of petroleum science and technology 28(10): 1033-1046. rehman, m. m. and meribout, m. 2012. conventional versus electrical enhanced oil recovery: a review. journal of petroleum exploration and production technology 2(4): 157-167. tian, h. and wang, m. 2017. electrokinetic mechanism of wettability alternation at oil-water-rock interface. surface science reports 72(6): 369-391. wittle, j. k., hill, d. g. and chilingar, g. v. 2008. direct electric current oil recovery (eeor)-a new approach to enhancing oil production. paper presented at eh unconventional oil challenging conventional expectations, edmonton, canada, 10-12 mar. zhang, y. 2020. optimizing surfactant and polymer concentrations for enhanced emulsion stability in sp flooding. energy and fuels 34(4): 4513-4522. henry e. idudje, spe, is a lecturer of petroleum engineering at federal university of petroleum resources, effurun, nigeria, where he has worked as a researcher for the last 6 years. his research interests are in production engineering, reservoir engineering, and enhanced oil recovery. he holds b.eng. (hons.) from the university of port harcourt, rivers state nigeria, m. eng. from the university of benin, edo state nigeria and, phd from the federal university of technology owerri, imo state, nigeria, all in petroleum engineering. angela n. nwachukwu, spe, is a senior lecturer of petroleum engineering at federal university of technology owerri, imo state, nigeria, where he has worked as a faculty for the last 16 years. his research interests are production engineering, flow assurance, and reservoir engineering. he holds b.eng. (hons.) from the federal university of technology owerri, imo state, nigeria, m. eng. from the federal university of technology owerri, imo state, nigeria and phd from the federal university of technology owerri, imo state, nigeria, all in petroleum engineering. ugochukwu i. duru, spe, has worked as a faculty at petroleum engineering of federal university of technology owerri, imo state, nigeria for the last 18 years. his research interests include production engineering, multiphase flow assurance, and reservoir engineering. he holds b.eng. (hons.) from the federal university of technology owerri, imo state, nigeria, m. eng. from the federal university of technology owerri, imo state, nigeria, and phd from the federal university of technology owerri, imo state, nigeria, all in petroleum engineering. michael i. onyejekwe, spe, is a senior lecturer, petroleum engineering at federal university of technology owerri, imo state, nigeria, where he has worked as a faculty for the last 18 years. his research interests are production engineering, multiphase flow assurance and reservoir engineering. he holds b.eng. (hons.) from the federal university of technology owerri, imo state, nigeria, m. eng. from the university of ibadan, oyo state, nigeria, and phd from the federal university of technology owerri, imo state, nigeria, all in petroleum engineering. improved oil and gas recovery 21 stanley i. onwukwe, spe, is a professor of petroleum engineering at federal university of technology owerri, imo state, nigeria, where he has worked as a faculty for the last 22 years. his research interests are production engineering and reservoir engineering. he holds b. eng. (hons.) from the federal university of technology owerri, imo state, nigeria, m. eng. from the federal university of technology owerri, imo state, nigeria, and phd in the federal university of technology owerri, imo state, nigeria, all in petroleum engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1362 received february 9, 2025; revised february 20, 2025; accepted february 26, 2025. *corresponding author: umer.engr@hotmail.com 1 mineral analysis of dolomite formation during carbonate acidizing using chelating agents mian umer shafiq, nazarbayev university, astana, kazakhstan; hisham ben mahmud, utp malaysia; bandar seri iskander, ipoh, malaysia; lei wang, chengdu university of technology, china; maryam jamil, shenzhen university, shenzhen, china; sophia nawaz gishkori, university of gujrat, gujrat, pakistan abstract during carbonate acidizing, the reaction between hydrochloric acid (hcl) and carbonate minerals is particularly rapid, especially in high-temperature wellbore environments. due to the swift reaction kinetics and the rapid consumption of acid, deep penetration is often limited, resulting in the formation of small wormholes and localized dissolution, which minimizes skin damage. to address these challenges, chelating agents have been introduced as an alternative for reacting with dolomite formations. chelating agents, being slower-reacting acids, have demonstrated effectiveness in high-temperature environments. in this study, three chelating agents—hedta (hydroxyethylenediaminetetraacetic acid), glda (l-glutamic acid diacetic acid), and edta (ethylenediaminetetraacetic acid)—were employed to interact with guelph dolomite core samples under highpressure (1000 psi) and high-temperature (180°f) conditions. the reacted dolomite samples were subsequently analyzed for changes in various properties, including mineralogy, grain size distribution, porosity, and morphology. mineralogical and grain size distribution analyses revealed that glda and hedta were effective in dissolving calcite, while edta demonstrated a higher effectiveness in dissolving ankerite. additionally, mineral locking analysis indicated that glda and hedta successfully disrupted the bond between quartz and calcite, which may contribute to an increase in reservoir permeability. introduction in sandstone acidizing, the primary objective is to remove or dissolve fine particles and other damage that cause bridging or blockages within the pore spaces. in carbonate reservoirs, which are primarily acid-soluble, acidizing operations typically create conductive pathways referred to as "wormholes." these wormholes serve as highly permeable flow paths, significantly enhancing hydrocarbon flow (ghommem et al. 2015; wilson 2016). in these formations, carbonates are expected to dissolve completely at slow injection rates near the wellbore (fredd and fogler 1998). however, the use of hydrochloric acid (hcl) in carbonate acidizing presents several drawbacks, including excessive corrosion, insufficient etching duration, and the formation of oil sludge due to crude asphaltenes. the following sections will discuss some of the acids developed over recent decades for matrix acidizing, highlighting their benefits and limitations. experimental studies have demonstrated the influence of various factors on matrix acidizing, such as the injection rate of acid, rock properties, the acid's reaction rate with the rock, permeability, porosity, mineralogy, mailto:umer.engr@hotmail.com improved oil and gas recovery 2 pore structure, and mineral distribution (qiu et al. 2011; maheshwari and balakotaiah 2013). over the past few decades, matrix acidizing has been extensively applied to treat formations such as low-temperature reservoirs (<100°c), clean sandstones (<10% dolomite), and clean dolomites (morgenthaler 2013). however, reservoirs with these properties are increasingly rare. today, deeper, hotter, and more heterogeneous reservoirs with complex mineralogies require acidizing treatment. to enhance the effectiveness of acidizing in both sandstone and carbonate formations and mitigate the adverse effects of precipitation, the development of new technologies is essential. the behavior of foam and its impact on porous carbonate formations has been extensively studied (ettinger and radke 1992). they investigated the in-situ generation of foam during carbonate acidizing in a 1-ft long sample, which facilitated deeper penetration into the formation and the creation of deeper wormholes. as a result, this method uses less acid compared to conventional techniques. this foam-assisted acidizing technique enhances the wormhole formation process, while also allowing for the use of lower acid flow rates in areas prone to face dissolution. the in-situ foam generation is particularly effective in formations where low acid injection rates are required, or in heterogeneous formations where some zones accept acid more slowly. the foam system is especially well-suited for low-permeability formations, such as dolomites (hoefner, 1987), as it confines the acid to the primary flow path, ensuring efficient acid utilization within that channel. at a flow rate of 0.25 cm³/sec, conventional stimulation resulted in the dissolution of most of the core, leading to a significant increase in permeability. therefore, the foam system proves to be highly efficient in generating wormholes. additionally, low-carbon steel tubes may develop rust that could be damaged by hydrochloric (hcl) acid. the hcl acid can break down this rust, releasing iron ions (fe3+), which may precipitate and potentially harm the reservoir and production well. according to gdanski (1998) and nasr-el-din et al. (2002), mud acid decomposes quickly at the wellbore due to the rapid reaction, resulting in the formation of precipitates and limiting acid penetration into the formation. limited research has been conducted on carbonate acidizing due to its relatively straightforward nature, but in recent years, substantial progress has been made in understanding this process (shafiq and mahmud 2017; hassan and al-hashim 2017; shafiq et al. 2023). the matrix acidizing process in carbonate formations differs significantly from sandstone acidizing, primarily because the entire carbonate rock is reactive, whereas in sandstone, only a small portion is reactive. this leads to the formation of large flow channels (depending on pore size) in certain areas of the rock, while other areas remain unaffected. this dissolution pattern results from the heterogeneous nature of carbonate formations. since the pore sizes in carbonates are often macroscopic, these conductive channels can accommodate high-flow rates of fluid, thereby significantly increasing the permeability of the rock. in contrast, sandstone stimulation generally leads to a homogeneous permeability increase throughout the sample due to pore-scale dissolution across the entire rock (bernadiner 1992). nasr-el-din et al. (2007) developed an acidic chelate-based mixture aimed at mitigating secondary and tertiary reactions, providing long-lasting effects in sensitive sandstone formations. however, the application of these chelates is generally limited to high-temperature formations with high dolomite content and low clay content. the response of dolomite to acidizing differs from that of limestone formations due to the temperaturedependent reaction between dolomite and hydrochloric acid (hcl) (hoefner 1987). previous studies have indicated that dolomite formations experience more dissolution compared to limestone. carbonate rocks, which are sedimentary in nature, are primarily composed of carbonate minerals, including limestone (caco3) and dolomite (camg(co3)2). these minerals tend to react rapidly with hcl or other acids, creating wormholes even under low-temperature conditions. the process of wormhole formation is illustrated in figure 1. improved oil and gas recovery 3 figure 1—wormhole pattern in dolomite acidizing (al-harthy 2009). eq. 1 represented the mechanism of reaction between hcl and dolomite. 4hcl + camg(co3)2 → mgcl2 + cacl2 + 2co2 + 2h2o,..........................................................................(1) thus, the existence of wormholes in dolomite formation is the reason for productivity increment which is formed in the near wellbore region by formation dissolution and creation of new flow paths but not by removing the formation damage like in sandstone formation. according to hawkins (1990), the formula for skin factor is mentioned in eq. 2. s = k ks − 1 ln rs rw ,..........................................................................................................................................(2) where s is the skin in the simulated or damaged area; ks is permeability; and rs is the radius of the stimulated or damaged area around the wellbore. if the value of ks is very large compared to k, then k/ks can be neglected. the value of wellbore radius (rw) is constant for calculation; therefore, skin value is dependent on rs. therefore, a high rs value represents a similar effect to negative skin which shows a stimulated zone (buijse and van domelen 1998). conclusively, it can be said that narrow and long wormholes are better compared to wide and short ones to enhance reservoir production. the application of chelating agents on sandstone and carbonate formations has developed as an effective enhanced oil recovery (eor) technique (shafiq et al. 2022). the thorough recovery mechanisms that are leading to significant oil recovery due to the use of these chemicals are not fully understood. however environmental issues and less dissolving power of these agents is the point of concern (almubarak et al. 2017). methodology and materials to perform acidizing experiments, fluids, and core flooding apparatus were used that consist of the following parts and functions. fluids. during various stages of experimental work, three different types of fluids were utilized. these fluids used are different chelating agents like glda, hedta, and edta. properties and descriptions of chelating agents used in this project are mentioned in table 1. core sample. the guelph dolomite core samples utilized in this study were procured from kocurek industries inc, hard rock division, located in caldwell, texas, usa. these samples exhibit inherent heterogeneity, with porosity and permeability characteristics tailored to meet specific experimental requirements. petrophysical analysis indicates that the samples are well-sorted, clean formations demonstrating moderate porosity (17%) and very low permeability (10 md). it should be noted that due to the heterogeneous nature of the formation, these petrophysical properties may vary between individual core plugs. mineralogical composition analysis reveals that the guelph dolomite is predominantly composed of ankerite (93-95%) and feldspar (3-5%), with trace amounts of calcite and aluminosilicates present. the cementing material primarily consists of quartz (85-90%), accompanied by clays (6-8%), dolomite (1-2%), and minor improved oil and gas recovery 4 quantities of iron sulfide. for identification and reference purposes, the samples were systematically labeled using the nomenclature "dolomite" followed by alphabetical designations (e.g., dolomite a, dolomite b). this classification system facilitates accurate tracking and comparison of experimental results across different samples. table 1—chelating agent and their properties. chelating agent properties and description it is a colorless amino polycarboxylic acid and is water soluble. it is used to remove limescale and it can sequester metal ions such as calcium and iron. it is being applied during acidizing due to its stability and less corrosive nature at high temperatures. the the most popular, powerful, economical, and all-purpose chelating agent. disodium salt edta disodium salt density: 860 mg/ml1 (at 20 °c), formula: c10h16n2o8 it is a colorless amino polycarboxylic acid. a chelating agent with similar effectiveness to edta. very useful in the petroleum industry acidizing procedure to stabilize iron at a high ph value and is soluble at a low ph value. it has less corrosivity at high temperatures. formula: c10h18n2o7 the latest, strong, and green chelate. it is readily biodegradable and safe and can be used in cleaning applications, as an alternative to edta, phosphates, and phosphonates, it is good solubility over a broad ph spectrum. it is usually originating from a natural sustainable source. formula: c9h9no8na4 procedure. core flooding tests were done to acidify the core sample. figure 2 shows how, after being placed inside the core holder, the core sample was contained at 1000 pressure using a syringe pump. the inlet and exit wings were made sure to be closed before confinement, and the intake wing was connected to the hplc pump. using heating tape and a temperature controller, the core holder is heated to the appropriate temperature of 180° f. one cc/min of acid was administered after the core holder had been heated for around 24 hours. the pressure changes at the input and output are measured using pressure transducers. once the pressure drop was steady, the acid stopped flowing. the core sample was placed in the oven to dry for 24 hours after the confining pressure was removed and the fittings were unplugged. improved oil and gas recovery 5 figure 2—core flooding setup (shafiq et al. 2023). tescan integrated mineral analysis (tima). tima is an advanced automated mineralogy system based on scanning electron microscopy (sem), equipped with backscattered electron (bse) imaging, cathodoluminescence (cl), and four energy-dispersive x-ray spectroscopy (eds) detectors. this configuration enables rapid and high-resolution analysis of mineralogical and textural properties. tima provides comprehensive characterization capabilities, including mineral and elemental mapping, mineral associations, quantitative mineral abundance, porosity distribution, particle size analysis, and size-by-size liberation analysis. these features make it a powerful tool for reservoir rock characterization, process optimization, and geochemical studies. a notable application of this technique was demonstrated in the case study by ward et al. (2017), which utilized tima to analyze grain size, mineral chemistry, texture, and mineralogical changes in the sedimentary deposits of boodie cave. procedure. the tima analysis begins with the preparation of a polished thin section, which is then imaged using backscattered electron (bse) and energy-dispersive x-ray (edx) techniques to identify individual mineral grains. each mineral particle is scanned at a predefined resolution by multiple edx detectors. the acquired edx spectra are automatically compared against the tima mineral classification database, enabling precise mineral phase identification and high-resolution mineral mapping.for this study, the following analyses were performed using tima: (1) elemental mass analysis: quantification of elemental composition. (2) element behavior analysis: distribution and association of elements within the mineral matrix. (3) mineral locking analysis: identification of mineral intergrowths and associations. (4) mineral mass analysis: quantitative determination of mineral abundances. (5) mineral location (panorama): spatial distribution of minerals within the sample. (6) grain size analysis: measurement of individual grain dimensions. (7) particle size distribution: statistical analysis of particle sizes. (8) density distribution analysis: variation in mineral density across the sample. (9) porosity distribution analysis: quantification and spatial distribution of porosity. the analyses were conducted on sandstone and dolomite formations treated with two distinct acid systems. the first phase of the study focused on the interaction of pre-flush stage acids with the rock matrix, while the second phase evaluated the effects of chelating agents on mineral dissolution and texture alteration. a detailed discussion of each analysis and its results is presented in the following section. and pressure transducers improved oil and gas recovery 6 results and discussion this section presents a comprehensive analysis of the effects of three chelating agents on guelph dolomite core samples. to evaluate the interaction of these chelates with all mineral phases present in the rock matrix, the experiments were conducted on unreacted guelph dolomite core samples rather than preflushed samples. this approach ensures a clear understanding of the chelates' reactivity with the native mineralogy of the formation. elemental analysis. guelph dolomite is a carbonate rock primarily composed of ankerite, with heterogeneous permeability and porosity distributions. it also contains minor amounts of other carbonate minerals, such as calcite and dolomite. due to its mineralogical homogeneity, the initial elemental composition of all core samples was consistent, providing a reliable baseline for comparative analysis. post-acidizing elemental analysis (figure 3) revealed no significant changes in the elemental composition of the guelph dolomite samples. this observation can be attributed to the dominance of ankerite, which acts as an insoluble matrix mineral in this formation. in contrast, the same chelating agents demonstrated effective dissolution of ankerite in sandstone formations, highlighting the mineral-specific reactivity of these chelates. despite the lack of significant elemental changes, further analyses were conducted to elucidate the reaction mechanisms between the chelating agents and the dolomite formation. these additional investigations provide critical insights into the chemical interactions and potential applications of chelates in carbonate reservoirs. figure 3—guelph dolomite's elemental mass before and after its interaction with chelating chemicals. elemental deportment analysis. elemental deportment refers to the distribution and association of specific elements within distinct mineral phases. figure 4 illustrates the deportment of calcium in the guelph dolomite core sample, primarily hosted in dolomite and calcite minerals. the analysis revealed that glda (l-glutamic acid n,n-diacetic acid) demonstrated a higher capacity to dissolve calcium from both dolomite and calcite compared to the other chelating agents tested. this finding appears contradictory to the earlier elemental analysis, which indicated no significant changes in elemental composition. this discrepancy can be explained by the relative nature of elemental analysis. in cases where one element dissolves while another remains unaffected, the relative percentage of the undissolved element increases. conversely, if both elements dissolve in equal proportions, their relative mass percentages remain unchanged, masking the dissolution process in the overall elemental analysis. magnesium, another key element in the guelph dolomite, is primarily hosted in ankerite and dolomite minerals. as previously discussed, ankerite exhibited negligible dissolution in the presence of all tested chelating agents. however, glda was observed to dissolve a small fraction of dolomite, as evidenced by the improved oil and gas recovery 7 results presented in figures 4 and 5. this selective dissolution behavior underscores the mineral-specific reactivity of chelating agents and highlights the importance of deportment analysis in understanding chemical interactions at the mineralogical level. figure 4—calcium deportment in guelph dolomite before and after reaction with chelating agents. figure 5—magnesium deportment in guelph dolomite before and after reaction with chelating agents. mineral analysis. figure 6 presents the mineral mass changes in the guelph dolomite sample after treatment with the three chelating agents. the analysis revealed a notable increase in the relative weight percentage of dolomite, which can be attributed to the dissolution of other mineral phases within the sample. among the tested chelates, hedta (hydroxyethyl ethylenediamine triacetic acid) and glda (l-glutamic acid n,ndiacetic acid) demonstrated significant effectiveness in dissolving calcite. furthermore, both edta (ethylenediaminetetraacetic acid) and hedta were observed to cause partial dissolution of ankerite, albeit to a limited extent. this finding aligns with the earlier discussion on the mineralspecific reactivity of chelating agents. in contrast, the relative weight of quartz increased, indicating its resistance to dissolution during the acidizing process. this behavior is consistent with the inert nature of quartz under the experimental conditions. these results highlight the selective dissolution capabilities of chelating agents, with glda and hedta showing particular efficacy in targeting calcite, while edta and hedta exhibited minor reactivity toward ankerite. the persistence of quartz further underscores the importance of mineralogical composition in determining the outcomes of acidizing treatments. improved oil and gas recovery 8 figure 6—mineral mass in guelph dolomite when reacted with chelating agents. mineral locking analysis. mineral locking refers to the intergrowth or association of different mineral phases within a rock matrix. figure 7 illustrates the locking of calcite with ankerite and dolomite in the guelph dolomite core sample. the analysis revealed that glda (l-glutamic acid n,n-diacetic acid) and hedta (hydroxyethyl ethylenediamine triacetic acid) were highly effective in breaking down the mineral locking between calcite and ankerite/dolomite. in contrast, edta (ethylenediaminetetraacetic acid) showed negligible effectiveness in disrupting these mineral associations. this finding underscores the potential of glda and hedta as effective agents for dolomite acidizing treatments. figure 7—calcite mineral locking in guelph dolomite before and after reaction with chelating agents. dolomite, on the other hand, was primarily locked with ankerite but also existed as free mineral surfaces, as depicted in figure 8. since dolomite exhibited minimal solubility in the presence of all three chelating agents, its relative mineral mass increased due to the dissolution of other minerals, particularly calcite (as discussed in figure 9). the dissolution of calcite not only contributed to the increase in dolomite's relative mass but also enhanced the free surface area of dolomite, potentially improving permeability and fluid flow pathways within the rock matrix. ankerite, which was locked with calcite, dolomite, and quartz, showed no significant change in its mineral associations after treatment with the chelating agents (figure 9). this observation is consistent with the insolubility of ankerite under the experimental conditions, further highlighting the mineral-specific reactivity of the tested chelates. improved oil and gas recovery 9 figure 8—dolomite mineral locking in guelph dolomite when reacted with chelating agents. figure 9—ankerite mineral locking in guelph dolomite when reacted with chelating agents. grain size distribution analysis. figures 10 through 12 illustrate the grain size distribution of key minerals in the guelph dolomite core sample before and after acidizing. the size ranges selected for analysis were based on the predominant grain sizes of each mineral within the sample. ankerite exhibited the largest grain sizes, indicating the presence of coarse-grained ankerite within the core sample. as shown in figure 10, no significant change was observed in the number of ankerite grains after acidizing, confirming its resistance to dissolution by the tested chelating agents. this finding aligns with previous observations regarding the insolubility of ankerite under the experimental conditions. in contrast, figure 11 demonstrates a noticeable reduction in the number of calcite grains, particularly in the presence of glda (l-glutamic acid n,n-diacetic acid) and hedta (hydroxyethyl ethylenediamine triacetic acid). this reduction confirms the effective dissolution of calcite by these chelating agents, further supporting their potential for targeted mineral dissolution in carbonate formations. however, as depicted in figure 12, only a minimal change was observed in the quantity of dolomite grains, indicating limited reactivity of the chelates with dolomite. this result is consistent with the earlier findings that dolomite remains largely unaffected by the tested chelating agents. improved oil and gas recovery 10 figure 10—ankerite grain size distribution in guelph dolomite prior to and after chelating agent reaction. figure 11—calcite grain size distribution in guelph dolomite prior to and after chelating agent reaction. figure 12—dolomite grain size distribution in guelph dolomite prior to and after chelating agent reaction. panorama analysis. figures 13 through 18 provide a detailed visual representation of dissolution patterns and pore space formation in the guelph dolomite core samples following treatment with the chelating agents. in these images, the ankerite matrix is highlighted in orange, while calcite is represented in pink. the analysis reveals the formation of new pore spaces and the partial disintegration of the mineral matrix in all acidized improved oil and gas recovery 11 samples, demonstrating the effectiveness of the chelating agents in altering the rock's microstructure. the rectangular markers in figures 13 through 18 highlight specific areas where dissolution or changes in the rock matrix occurred after acidizing. these markers provide a clear visual comparison between the preand postacidizing conditions, enabling a detailed assessment of the chelating agents' effectiveness. edta-treated sample. figures 13 and 14 display the general overview and close-up images of the core samples treated with edta (ethylenediaminetetraacetic acid). figures 13(a) and 14(a) depict the core samples before acidizing, showing the intact mineral matrix with no visible dissolution. in contrast, figures 13(b) and 14(b) illustrate the same samples after treatment with edta (ethylenediaminetetraacetic acid). the rectangular markers in figures 13 and 14 indicate areas where dissolution has occurred, primarily affecting calcite and creating new pore spaces. while some dissolution is evident, the extent of matrix alteration is relatively limited compared to the other chelating agents. (a)before acidizing (b) after acidizing figure 13—calcite and ankerite dissolution after reaction with edta on dolomite a. (a)before acidizing (b) after acidizing figure 14—calcite and ankerite dissolution after reaction with edta on dolomite b. hedta-treated sample. figures 15 and 16 illustrate the panoramic and detailed views of the core sample after reaction with hedta (hydroxyethyl ethylenediamine triacetic acid). the images show more pronounced dissolution of calcite and the creation of additional pore spaces, highlighting hedta's effectiveness in enhancing rock permeability. figures 15(a) and 16(a) show the samples before acidizing, while figure 15(b) and 16(b) display the samples after treatment with hedta (hydroxyethyl ethylenediamine triacetic acid). the rectangular markers in figures 15 and 16 point to areas where significant dissolution of calcite has taken place, resulting in the formation of new pore spaces and enhanced connectivity within the rock matrix. improved oil and gas recovery 12 figure 15—calcite and ankerite dissolution after reaction with hedta on dolomite a. figure 16—calcite and ankerite dissolution after reaction with hedta on dolomite b. glda-treated sample. figures 17 and 18 present the overall panorama and close-up images of the core sample treated with glda (l-glutamic acid n,n-diacetic acid). the dissolution of calcite and the formation of new pore spaces are most evident in these images, underscoring glda's superior performance in matrix alteration and pore network development. figures 17(a) and 18(a) present the samples before acidizing, and figures 17(b) and 18(b) show the samples after treatment with glda (l-glutamic acid n,n-diacetic acid). the rectangular markers in figures 17(b) and 18(b) highlight extensive dissolution of calcite and the creation of a well-developed pore network, demonstrating glda's superior performance in matrix alteration and permeability enhancement. figure 17—calcite and ankerite dissolution after glda reaction. improved oil and gas recovery 13 figure 18—calcite and ankerite dissolution after glda reaction in summary, the panorama analysis confirms that all three chelating agents-edta, hedta, and gldawere effective in generating new pore spaces within the dolomite core samples. however, glda and hedta demonstrated significantly greater efficacy in dissolving calcite and enhancing pore connectivity compared to edta. these findings highlight the potential of glda and hedta as effective agents for acidizing treatments in carbonate reservoirs. porosity distribution analysis. table 2 presents the pore size distribution in the dolomite core sample, categorized into tiny (9.6-30 µm), medium (30-67 µm), and large (67-146 µm) pores, before and after treatment with the chelating agents. the results highlight the effectiveness of each chelate in enhancing porosity through the creation of new pore spaces, which is critical for improving reservoir permeability and hydrocarbon recovery. overall porosity enhancement. hedta generated the highest total number of new pore spaces, with 3,047 pores, demonstrating its superior ability to enhance porosity in dolomite formations. glda produced 2,112 new pore spaces, indicating its strong potential for reservoir stimulation, though slightly less effective than hedta. while edta resulted in only 543 new pore spaces, showing limited effectiveness in porosity enhancement. pore size-specific performance. hedta created 2,743 new tiny pores, while glda produced 1,947. this suggests hedta's greater effectiveness in generating smaller pores, which can enhance permeability in tight carbonate reservoirs. hedta also demonstrated strong performance in creating medium-sized pores, further contributing to its overall porosity enhancement. glda outperformed hedta in the formation of larger pore spaces, creating a significant number of large voids. in contrast, hedta contributed only two large pores, highlighting glda's unique capability to develop larger flow pathways, which are essential for improving fluid connectivity in the reservoir. table 2—initial and final pore size distribution of dolomite formation. pore size (µm) number of pore spaces reaction with hedta reaction with edta reaction with glda initial edta new pores initial hedta new pores initial glda new pores 9.6<30 46013 48756 2743 46560 47031 471 49095 51042 1947 30<67 417 718 301 458 527 69 502 656 154 67<146 16 18 2 16 19 3 25 36 11 total 46445 49492 3047 47034 47577 543 49622 51734 2112 improved oil and gas recovery 14 hedta emerged as the most effective chelating agent for overall porosity enhancement in the dolomite sample, with a total increase of 3,047 new pore spaces. however, glda demonstrated superior performance in creating larger pore spaces, which are critical for enhancing fluid flow in carbonate reservoirs. these findings underscore the importance of selecting the appropriate chelating agent based on the desired pore size distribution and reservoir characteristics to optimize stimulation treatments. particle size distribution. figure 19 presents the distribution of tiny, medium, and large particles in guelph dolomite samples before and after acidification with the tested chelating agents. the results demonstrate that all chelates effectively preserved a significant portion of solid particles while simultaneously dissolving targeted minerals, thereby enhancing pore space and overall porosity. this dual capability highlights the chelates' ability to balance mineral dissolution with particle integrity preservation, which is critical for maintaining reservoir stability during acidizing treatments. edta dissolved a total of 3,879 particles, including 235 particles (47-199 µm), 137 particles (199-520 µm), 73 particles (520-985 µm), and 11 particles (985-1590 µm), as shown in figure 19(c). the dissolved minerals primarily included ankerite and calcite, which are the dominant minerals in the dolomite matrix. hedta dissolved a similar total of 4,549 particles. glda demonstrated superior performance, dissolving 4,010 tiny particles. it outperformed both hedta and edta in dissolving medium and large-sized particles, making it the most effective chelate for creating clean pore networks in dolomite formations. glda emerged as the most effective chelating agent for acidifying dolomite formations, as it dissolved the highest number of particles across all size ranges. this capability not only enhances porosity but also improves permeability by creating well-connected pore networks. the results, summarized in table 3, underscore the importance of selecting the appropriate chelating agent based on the desired particle size distribution and mineral dissolution targets for optimal reservoir stimulation. table 3—number of particles in guelph dolomite sample before and after reaction with chelating agents. pore size (µm) number of particles reacted with edta reacted with hedta reacted with glda initial reacted dissolved initial reacted dissolved initial reacted dissolved 9.6< 47 47874 43995 -3879 56012 51911 -4101 44428 40418 -4010 47< 199 3778 3543 -235 4374 4085 -289 3343 3024 -319 199< 520 587 440 -147 458 354 -104 455 291 -164 520< 985 189 116 -73 125 81 -44 139 62 -77 985< 1590 57 46 -11 75 64 -11 96 80 -16 total 52485 48140 -4345 61044 56495 -4549 48461 43875 -4586 improved oil and gas recovery 15 (a) tiny particles (b) medium particles (c) large particles figure 19—number of particles in the sample of guelph dolomite before and after treatment with chelating agents. improved oil and gas recovery 16 particle density distribution analysis. figure 20 illustrates the density distribution of particles in the guelph dolomite sample, providing insights into the dissolution behavior of the chelating agents based on mineral density. the sample is predominantly composed of ankerite, which has a density of approximately 2.97 g/cm³, along with other minerals such as calcite (density: 2.71 g/cm³) and heavier mineral phases. (a) heavier minerals (b) calcite (c) ankerite figure 20—distribution of particle density in guelph dolomite before and after treatment with chelating chemicals. heavier minerals. figure 20(a) shows minimal dissolution of particles in the higher density range (3.0–6.7 g/cm ³ ), indicating that the chelating agents were less effective in dissolving heavier mineral phases. this suggests that the dissolution process is highly dependent on mineral density, with lighter minerals like calcite being more susceptible to chelate-induced dissolution. calcite. the chelating agents demonstrated high efficacy in dissolving calcite, as evidenced by the significant reduction in the number of particles within this density range (figure 20(b)). this finding aligns with earlier results, highlighting the selective dissolution of calcite by hedta, glda, and, to a lesser extent, edta. ankerite. as shown in figure 20(c), the majority of particles fall within the density range of 2.8–3.0 g/cm³, consistent with the presence of ankerite. the solubility of ankerite was relatively low, resulting in only a slight improved oil and gas recovery 17 change in the number of particles after acidizing. this confirms the limited reactivity of the chelating agents with ankerite, as previously discussed. the particle density distribution analysis confirms the mineral-specific reactivity of the chelating agents, with calcite showing the highest dissolution rates due to its lower density, while ankerite and heavier minerals remained largely unaffected. these findings underscore the importance of considering mineral density and composition when designing acidizing treatments for carbonate reservoirs. the results also validate the effectiveness of chelating agents like hedta and glda in selectively dissolving target minerals to enhance porosity and permeability. conclusion this study investigated the effects of three chelating agents — edta, hedta, and glda — on guelph dolomite core samples to evaluate their effectiveness in mineral dissolution and porosity enhancement. key findings from the analysis are summarized as follows: 1. the initial elemental composition of the dolomite samples remained largely unchanged after acidizing, likely due to the high concentration of ankerite, which acted as an insoluble matrix mineral. 2. calcite was effectively dissolved by hedta and glda, demonstrating their strong reactivity with this mineral. dolomite, which was locked with ankerite, showed significant mineral locking removal when treated with glda and hedta, highlighting their ability to disrupt mineral associations and enhance pore connectivity. 3. the analysis revealed that the number of ankerite grains remained largely unchanged, consistent with its low solubility. in contrast, the number of calcite grains decreased significantly, particularly in samples treated with glda and hedta, confirming their effectiveness in dissolving calcite. 4. hedta emerged as the most effective chelate for enhancing porosity, generating 3,046 additional pore spaces in the dolomite formation. this underscores its potential for improving reservoir permeability. 5. all chelating agents dissolved a significant number of solid particles, with glda demonstrating superior performance in dissolving medium and large-sized particles. this capability makes glda particularly effective in creating clean, well-connected pore networks. 6. the analysis confirmed that glda was more effective than hedta and edta in acidifying dolomite formations, particularly in dissolving lighter minerals like calcite while preserving the integrity of denser minerals such as ankerite. this study provides valuable insights into the mineral-specific reactivity and porosity-enhancing capabilities of chelating agents in dolomite formations. hedta and glda demonstrated superior performance in dissolving calcite, removing mineral locking, and enhancing pore connectivity, making them highly effective for carbonate reservoir stimulation. these findings highlight the importance of selecting the appropriate chelating agent based on reservoir mineralogy and desired outcomes to optimize acidizing treatments and improve hydrocarbon recovery. acknowledgment we acknowledge the australian research council for allowing the usage of the tescan integrated mineral analysis (tima) instrument at the john de laeter centre of curtin university with the support of the geological survey of western australia, the university of western australia, and murdoch university. we thank the support by the “ministry of science and technology of the people’s republic of china, 2023yfe0120700”. improved oil and gas recovery 18 conflicting interests the author(s) declare that they have no conflicting interests. references al-harthy, s. 2009. options for high-temperature well stimulation. oil field review 20(4):15-24. almubarak, t., ng, j. h., and nasr-el-din, h. 2017. oilfield scale removal by chelating agents: an aminopolycarboxylic 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elemental, mineral and microscopic investigation of sandstone matrix acidizing at hpht conditions. journal of petroleum research 7(3):448-458. shafiq, m. u., h. k. ben mahmud, l. wang, m. khan, n. qi, k. abid, s. n. gishkori. 2023. mineral analysis of sandstone formation using chelating agents during sandstone matrix acidizing. journal of petroleum research 8(3): 404-412. ward, i., merigot, k., and mcinnes, b. i. a. 2017. application of quantitative mineralogical analysis in archaeological micromorphology: a case study from barrow is., western australia. j archaeol method theory 25(1): 45-68. improved oil and gas recovery 19 wilson, a. 2016. sandstone-acidizing system eliminates need for preflush and post-flush stages. j pet technol 68(6): 59-60. spe-0616-0059-jpt. mian umer shafiq is currently an assistant professor and professional engineer at the school of mining and geosciences, nazarbayev university, kazakhstan. with over 12 years of combined industrial and academic experience, he specializes in petroleum engineering. dr. shafiq earned his phd in petroleum engineering from curtin university, malaysia, and holds a master’s and bachelor’s degree in petroleum engineering from universiti teknologi petronas (utp), malaysia, and the university of engineering and technology (uet), lahore, respectively. his research expertise spans production optimization, well stimulation, acidizing, underground gas storage, reservoir simulation, geopolymers, and drilling fluid design. hisham ben mahmud is an associate professor and professional engineer in the department of petroleum engineering at universiti teknologi petronas (utp), malaysia. with over 15 years of experience in academia and industry, he has worked with renowned international organizations and universities in australia, libya, and malaysia. dr. mahmud holds a phd in flow assurance from curtin university, australia, a graduate diploma in oil & gas from the university of western australia, a master of science in engineering studies from the university of sydney, and a bachelor of engineering in chemical engineering from tripoli university. he is a chartered engineer with the institute of engineers australia (ea), a graduate member of the board of engineers malaysia (bem), a member of the society of petroleum engineers (spe), and a fellow of advance higher education (fhea). lei wang is a professor of petroleum engineering at chengdu university of technology, china. his research focuses on reservoir simulation, hydrocarbon phase behavior, cryogenic fracturing, chemical and gas enhanced oil recovery (eor), and underground gas storage. dr. wang holds a bachelor of science (honors) in environmental engineering and a master of science in petroleum engineering from the china university of petroleum (east china), as well as a phd in petroleum engineering with a minor in chemical engineering from the colorado school of mines, usa. maryam jamil is a phd candidate in optical engineering at the college of physics and optoelectronics engineering, shenzhen university, china. her research explores spatial and temporal photonic crystals, with a focus on their applications in advanced optical devices and related fields. through her work, she aims to develop innovative theoretical models and experimental techniques to enhance the performance of photonic systems. sophia nawaz gishkori is a phd scholar in the department of chemical engineering at the university of gujrat, pakistan. her research focuses on wastewater treatment using nanotechnology. in addition to her academic pursuits, she has served as a visiting lecturer in the department of chemical engineering at nfc institute of engineering and technology (nfciet), multan, pakistan. abstract introduction methodology and materials results and discussion conclusion acknowledgment conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1334 received november 17, 2024; revised december 1, 2024; accepted december 25, 2024. *corresponding author email: mohammedhussein51@yahoo.com 1 investigation of locally sourced sand as proppants in hydraulic fracturing operations hussein mohammed, ifeanyichukwu michael onyejekwe, stanley ibuchukwu onwukwe, federal university of technology owerri, imo state, nigeria abstract hydraulic fracturing is a critical reservoir stimulation technique that enhances hydrocarbon recovery by generating fracture networks to facilitate fluid flow from the reservoir to the wellbore. while conventional proppants effectively support fracture conductivity, their high cost drives the need for alternative, cost-efficient options. this study evaluates the potential of natural sands as economical proppants for hydraulic fracturing. the sands were characterized using x-ray fluorescence (xrf) to assess their chemical composition and mechanical properties. to improve strength and minimize fines generation, locally sourced sands were coated with epoxy resin. an economic analysis was conducted to determine the feasibility of employing these sands in field operations. the findings demonstrate that quartz and topaz sands meet api iso standards and are viable alternatives for hydraulic fracturing applications, offering a balance of performance and cost-effectiveness. introduction in response to the challenges posed by traditional proppants, there is growing interest in exploring locally sourced sands as an alternative proppant material. by sourcing proppants locally, operators can reduce transportation costs and minimize the environmental impact associated with long distance transport. therefore, leveraging on indigenous sands as proppant in nigeria for hydraulic fracturing, suggests a potential viable solution to reduce dependence on imports, create local content economic opportunities, and mitigate operational costs. hydraulic fracturing, or fracking, has become a cornerstone technology for extracting oil and natural gas from unconventional reservoirs, such as shale formations (moghadasi et al., 2019; ifeanyichukwu et al., 2024). this process involves injecting a high-pressure fluid mixture—comprising water, sand, and chemical additives—into subsurface rock formations (taylor et al. 2009). the applied pressure induces fractures in the rock, facilitating the release of trapped hydrocarbons and enabling their flow to the surface for recovery. over recent decades, hydraulic fracturing has significantly increased global energy reserves and transformed the oil and gas industry (rojas et al. 2023). a critical component of this process is the use of proppants, granular materials introduced into the fractures to maintain their openness after hydraulic pressure is withdrawn (soane et al. 2011). proppants maintain the fractures open, creating permeable pathways that enable hydrocarbons to flow from the reservoir to the wellbore. without proppants, fractures would rapidly close under the surrounding rock pressure, significantly impeding hydrocarbon flow (bandara et al. 2022). common proppant materials include sand, ceramic particles, and resin-coated materials, with sand being the most widely used globally due to its abundance, cost-effectiveness, and favorable physical properties (wahab et al. 2022; tang et al. 2018). however, advancements in hydraulic fracturing technologies and the growing need for higher efficiency have spurred interest in alternative proppant materials and sourcing strategies (mohamad-sobri 2013). the high cost of conventional proppants often escalates mailto:mohammedhussein51@yahoo.com improved oil and gas recovery 2 oil production expenses, whereas locally sourced sands, derived from nearby geological formations, present an economical and practical alternative to imported sands (gaber and ibrahim 2020). furthermore, utilizing locally sourced sands can bolster regional economies and enhance supply chain resilience by reducing reliance on external suppliers (agrawal and gernand 2020; zwalatha et al. 2024). zwalatha et al. investigated the suitability of luwa sands for use as proppants in hydraulic fracturing operations. the sands were collected from the luwa river in toro, bauchi state, nigeria, and coated with epoxy resin to enhance their properties. experimental evaluations were conducted following api-recommended practices to assess the sand's potential as a proppant. characterization results demonstrated that luwa sand meets the requirements for use as a proppant and performs competitively against international standards. additionally, wahab et al. (2022) noted that sands composed predominantly of silica grains are the most suitable naturally occurring materials for proppants in hydraulic fracturing processes. gaber and ibrahim (2021) analyzed pure silica sands along the red sea coast of sinai and the eastern desert for their suitability as fracturing sands. their study focused on wadi dakhal white sand and sand dunes found along the bahariya oasis road (karama oil field). results showed that the silicon dioxide (sio2) content was 99% for wadi dakhal and 95% for karama field sands. the sands exhibited crush resistance in the range of 5500–6500 psi, turbidity at 2%, and rounded to sub-rounded grain shapes, aligning with iso 13503-2 standards. the grain size distribution ranged between 30/50 and 40/70 mesh (710 μm to 210 μm). similarly, elochukwu and kenneth (2020) investigated baram and tanjung sands for potential use as proppants. baram sand, with its larger grain size, was found to support high permeability under low closure stress, making it suitable for hydraulic fracturing at shallow depths. building on this foundation, the current research focuses on a comprehensive evaluation of the characterization, performance, and economic viability of quartz and topaz sands as proppants for hydraulic fracturing operations. materials and methods this study utilized quartz sand, topaz sand, resin-hardener, and various laboratory instruments, including a highprecision analytical balance, a hydraulic universal testing machine, and an edxrf system for elemental analysis. hydrochloric acid and ammonium bifluoride were used as reagents in sample preparation. measurements focused on assessing sand properties such as density, particle size, and composition, carried out under controlled laboratory conditions. collection of materials. the topaz and quartz sands are sand deposit in the agwatashi river situated in the obi local government area of nasarawa state in nigeria at latitude 8o22” n and longitude 8o46” e with a climate type of wet tropical savanna. a field trip of the agwatashi river was carried out and the obtained sands were characterized in the laboratory to evaluate the potential use as proppant in hydraulic fracturing operations. figure 1 is a sample of quartz and topaz sands. figure 1—sample of the sands. improved oil and gas recovery 3 sample preparation. the sand (quartz and topaz) was collected and classified for laboratory testing and characterization. the samples were washed, dried, and weighed. the sand sample was weighed prior to washing to remove impurities and contaminants. it was re-weighed to determine the loss of contaminants in percent and ensure it was bacterial free for characterization. characterization of the sands. the locally sourced sands were characterized to determine their suitability as a proppant. this followed the standard protocols known as api std 19c (2018). recommended practice (api rp 56) and standard organisation for standardization (iso 13503-2) recommendation. x-ray fluorescence (xrf). x-ray fluorescence (xrf) was used to investigate the elemental composition of the samples. x-ray fluorescence was conducted on the sands (quartz and topaz) under helium (he) atmosphere using palladium (pd) x-ray tube at a voltage of 60 kv and current 10µa with 10 mm beam spot size, and silicon (si) drift detector comprised of peltier electronic circuit cooling system. elemental detection limits from low partsper-million (ppm) to high weight percent (%wt.). the sands are put into the machine, and then the machine starts to rotate. as it rotated, the elemental structure of the sands was being displaced on the computer screen. sieve test. sieve analysis was conducted to assess the particle size distribution of granular materials and to ensure a consistent methodology for sieve evaluation. sieve analysis was conducted by allowing the sand to pass through a series of sieves of progressively smaller mesh size and weighing the amount of sand that is stopped by each sieve as a fraction of the whole mass (martins et al. 2021). the equipment and materials used for the sieve analysis procedure include the following: sieve sets, stsj-4a high frequency sieve shaker, weighing balance and brushes. sieve test of mesh size 20/40 was prepared. the essence of the 20/40 mesh sand is to obtain sand particles that fall within the diameter size range of (850 µm-425 µm). this was achieved using sieve stack in order of decreasing sieve openings of 16 (1.180 mm), 20 (0.850 mm), 25 (0.710 mm), 30 (0.600 mm), 35 (0.500 mm), 40 (0.425 mm), and 50 (0.300 mm). the sieve test was conducted to get sand within the range of 850 µm-425 µm (20/40 mesh) size. sphericity and roundness. sphericity and roundness test were conducted to evaluate the degree at which the sands approximate the shape of a perfect sphere. however, the roundness procedure was done to measure the sharpness of the sand’s edges and corners. sphericity and roundness tests are conducted to evaluate the proppant shapes. the most common used method of determining roundness and sphericity is the use of the krumbein/sloss chart as shown in figure 2. in this study, twenty (20) individual particles were randomly selected for evaluation of particle sphericity and roundness. the sphericity of each selected particle was determined by comparison to the krumbein/sloss chart. the corresponding number of sphericities for each particle selected was observed. the arithmetic average of the recorded sphericity numbers was calculated and reported as average particle sphericity to the nearest 0.1 unit. the roundness value for each of the selected particles was determined using the same procedure as for the sphericity measurement. in addition, the arithmetic average of the recorded roundness numbers was evaluated and recorded as the average particle roundness of sand to the nearest 0.1 unit. improved oil and gas recovery 4 figure 2—chart for estimation of sphericity and roundness (api> 0.6). acid solubility. the acid solubility test was conducted to examine the suitability of a proppant for use in applications where the proppant can encounter acids. the preferred method of testing acid solubility was the use of a solution of 12:3 hci: hf acid (12% by mass of hci and 3% by mass of hf) (api std 19c). the solubility of a proppant in 12:3 hci: hf showed that the number of soluble materials (carbonates, feldspars, iron oxides, clays) present in the proppant. the method of preparation of a solution of 12:3 hci: hf acid involved the addition 47.2g of pure nh4f2 to 500 ml of distilled water in a 1000 ml graduated cylinder. 361 ml of a 37% hcl was added to the mixture in the cylinder and diluted to 1000 ml with distilled water. the mixture was stirred to ensure complete mixing. the resulting mixture is the prepared 12:3 hcl: hf acid that was used for the test. the percentage of mass dissolved in the acid is calculated by eq. (1), 𝑆 = 𝑚𝑆 + 𝑚𝑓+𝑚𝑠𝑓 𝑚𝑠 𝑥 100...................................................................................................................................(1) where, 𝑆 represents the acid solubility (in %), ms denotes the mass of the sand sample (in grams), mf refers to the mass of the filter paper (in grams), and mfs is the mass of the dried filter paper along with the sand sample (in grams). turbidity. turbidity test was conducted to evaluate the number of suspended particles or other finely divided matter present in the sand. turbidity tests measure an optical property of a suspension that results from the scattering and absorption of light by the particulate matter suspended in the wetting fluid (ismaeel and tayeb 2024). turbidity meters of the incident light beam were normal to the detection path of the detector; this is the preferred method of measurement and expressed in nephelometric turbidity unit (ntu). the turbidity test was conducted by addition of 100 ml of demineralized water to 70 g of the sample in a 250 ml flask. quartz and topaz sand were allowed to stand in the water for 15 minutes and the flask was put into a shaker bottle. the degree of frequency of the shaker bottle was set to 7 rpm based on recommended literature, and the bottle was allowed to agitate for 20 seconds. the flask was later removed from the shaker bottle and stood for 5 to 10 minutes. 30 ml of the water and silt suspension was removed from the water volume with the use of a syringe. the suspendedparticle sample placed in the test and palintest calibrated turbidimeter was recorded. bulk density. bulk density test was conducted to evaluate the bulk density of the proposed sands as proppants. the bulk density indicates the mass of the proppants that fills a unit volume. it can be used to evaluate the mass of the proppant needed to fill a fracture. the equipment that was used to determine the bulk density was a improved oil and gas recovery 5 calibrated cylinder and a weighing balance. the procedure for the bulk density was determined, and the volume of the cylinder was done by weighing the dry, empty cylinder with a flat glass and the mass. the cylinder was filled with water and a plate moved into contact with the upper edge of the cylinder, cutting off the edge of water in the plane. the glass plate was held firmly, the excess water was removed, and the gross mass was obtained. the bulk density was calculated and expressed in grams per cubic centimeter, shown in eq. (2), 𝜌𝑏𝑢𝑙𝑘 = 𝑚𝑝 𝑣𝑐𝑦𝑙 ..................................................................................................................................................(2) where,𝑚𝑝 is the net mass, expressed in grams, of the sand, equal to 𝑚𝑓+𝑝 − 𝑚𝑓; 𝑣𝑐𝑦𝑙 , is the volume of the cylinder, expressed in cubic centimetres. crush resistance. crush resistance tests were investigated on the sands to evaluate the amount of proppant that was crushed at a given stress. tests are carried out on the sands samples that have been sieved so that all particles tested are within the specified size range specified by the api and iso recommendation. the amount of proppant crushed at each stress level was measured. the test results provide the indications that the stress level where the proppant crushing was excess and the maximum stress to which the proppant sample should be subjected. a 2500 kn hydraulic universal testing machine, a cell for proppant crush resistance test, test sieves, pan and lid, a weighing balance, a high frequency sieve shaker and a stopwatch was used for the test. loss on ignition (loi). the loss on ignition (loi) test was conducted to evaluate the number of combustible materials on the sand. the sands (topaz and quartz) were weighed, and their masses recorded. these samples were subjected to heating at 900oc in a furnace for 12 hours, the samples were allowed to cool, and their individual masses were recorded. the mass loss from each of the samples showed the amounts of ignitable materials on the sands. eq. (3) was used to evaluate the loi. ∆𝑚𝐿𝑂𝐼 = (𝑚𝑠+ 𝑚𝑓) 𝑚𝑠 𝑥 100..................................................................................................................................(3) where, ∆𝑚𝐿𝑂𝐼 represents the loss on ignition (%); 𝑚𝑠 is the mass of the sand before firing (g); 𝑚𝑓 is the mass of the sand after firing (g). hardness. mohs hardness scale was used to evaluate for the relative resistance of the quartz and topaz sands. this was done by scratching the sands against other substances of known hardness on the mohs hardness scale. in this case, there are twelve (10) minerals in the test kit with each number standing for a hardness value. the mineral that could not be scratched by quartz and topaz sands is said to have the same hardness value as the sands. on the mohs scale, talc has a hardness value of 1, gypsum 2, calcite 3, fluorite 4, apatite 5, orthoclase 6, quartz 7, topaz 8, corundum 9, and diamond 10 in an order of increasing hardness value. resin-coated sand (rcs). a resin-coated proppant was produced from the diglycidyl ether of bisphenol-a (dgeba) e-51 epoxy resin and an epoxy hardener using a simple method adopted from us4460717a and ep1757382a1 patents. the procedures used for the modification of the sand involved the following methods: the sand was washed and allowed to dry. the epoxy resin and hardener were measured and mixed in the ratio 3:1 respectively using a measuring cup. the mixture was stirred vigorously using wooden sticks, a dropper was used to drop the mixture on the sand. the slurry of the sand and epoxy resin was then mixed to ensure the epoxy encapsulates the whole of the sand. when the epoxy resin and sand mixture was about to set, the individual grain with the resin coating were transferred to a plane surface and allowed to cure for 48 hours at room temperature of 29oc. improved oil and gas recovery 6 results and discussion figures 3 and 4 showed the results of the x-ray fluorescence test (xrf) of the characterization of the quartz and topaz sands. the results showed that quartz sand contained 79.93% of silicon oxide (𝑠𝑖𝑜2). it also contained aluminium oxide (𝐴𝑙2𝑜3) of 2.021% and magnesium oxide (mgo) of 0.53%. similarly, topaz sand contained 72.81%, aluminium oxide of 1.453% and mgo of 0.86%. these elements are the major constituent in the sands. the results showed that the sand was majorly composed of silicon oxide (𝑠𝑖𝑜2). liang et al. (2016) reported that sand that have high silica content are best candidate as proppant in hydraulic fracturing operation and have economic advantages. the work of hu et al. (2014) and curimbaba and kerr de paiva cortes (2011) all reported that good proppant should contain up to 70% of silicon oxide to be suitable for use in hydraulic fracturing operations. the proposed proppant gave a higher value of the recommended proppant as suggested from the literature. it is also interesting to note that quartz and topaz sands used in this study meet the required standard based on the api and iso recommended standard. figure 3—xrf result for quartz sand. figure 4—xrf result for topaz sand. improved oil and gas recovery 7 sieve test result. table 1 showed the results of the sand sieving test for quartz sand. the sieve sizes range from 1.18-0.300 (mm). it can be observed that sieve size reduces as sample weight increases until reached at mesh size of 40 mm. the percentage retained increases at each mesh size sample, percentage passing of the sand at 100% reduces at each sand passing. table 1—sand sieve test for quartz sand. sieve number sieve size (mm) mass retained (𝑆𝑤 ) (g) retained on sieve (𝑆𝑤 × 100)/𝑇𝐷𝑆 passing (%) cumulative retained (%) 16 1.18 0.00 0.00 100 0.00 20 0.850 54.71 2.43 97.57 2.43 25 0.710 279.48 12.42 85.15 14.85 30 0.600 854.92 37.97 47.18 52.82 35 0.500 949.28 42.19 5.00 95.01 40 0.425 111.56 4.96 0.00 100 pan 0.00 0.00 0.00 0.00 note: total dry sand (𝑇𝐷𝑆) = 2250 g table 2 showed similar behavior for the topaz sand. sample weight increases as percentage retained increases. the results of the sieve test showed that the sand is evenly distributed. in addition, the different mesh size of the sand was used to determine the mass retained and the percentage retained of the sand to obtain the particle size distribution of the sand. the cumulative percentage of the sand was retained at 100%. table 2—sand sieve test for topaz sand. sieve number sieve size (mm) mass retained (𝑆𝑤 )(g) retained on sieve (𝑆𝑤 × 100)/𝑇𝐷𝑆 passing (%) cumulative retained (%) 16 1.18 0.00 0.00 100 0.00 20 0.86 56 2.47 97.53 2.47 25 0.71 281.91 12.47 85.06 14.94 30 0.60 862.34 38.12 46.94 53.06 35 0.551 951.83 42.09 4.85 95.15 40 0.43 110.00 4.87 0.00 100 pan 0.00 0.00 0.00 0.00 *note:total dry sand (𝑇𝐷𝑆) of topaz = 2262 g figures 5 and 6 depict the particle size distribution curves for quartz and topaz sands. both sands exhibit a steep portion of the curve between 0.6 mm and 0.85 mm, indicating that most particles fall within this size range. this uniformity aligns with the studies of heagy et al. (2014), which highlight the importance of well-sorted sands for effective proppant performance in hydraulic fracturing. the flatter regions at the extremes suggest minimal coarse and fine particles, which are desirable for maintaining consistent fracture conductivity as noted by guo and tan (2017). overall, the particle size distribution results suggest that both quartz and topaz sands have potential as proppants which is in consonance with the findings of zhang et al. (2020), who identified mediumimproved oil and gas recovery 8 sized proppants as optimal for fracture stability and hydrocarbon flow. further testing of other properties, such as crush resistance, is necessary to confirm their suitability, as emphasized by duchnowska et al. (2023). figure 5—percent passing (%) against sieve diameter (mm) for quartz sand. figure 6—percentage passing (%) against sieve size (mm) for topaz sand. sphericity and roundness test result. tables 3 and 4 present the results of the quartz and topaz sand selected at random for the sphericity and roundness test. the table of the results showed that the quartz sand had sphericity of 0.7 which was obtained by dividing the total sum by the number of samples. similarly, for the topaz sand, the sphericity was 0.7 also obtained by the average of the total sum of samples divided by the number of samples. the results agree with both iso 13503-2 and api rp 56, which specify a sphericity of ≥ 0.6. the sphericity results of 0.62 from kamel et al. (2019) are consistent with the current study. according to api/iso standards, the recommended best practice is for sand samples to have a sphericity and roundness of ≥ 0.6 to be suitable as proppants. table 5 presents the average comparison of quartz and topaz sands, indicating an average roundness of 0.7. 0 20 40 60 80 100 120 0.1 1 10 p er ce n t p as si n g ( % ) sieve diameter (mm) 0 20 40 60 80 100 120 0.1 1 10 p er ce n t p as si n g ( % ) sieve diameter (mm) improved oil and gas recovery 9 table 3—sphericity and roundness for quartz sand (20/40 mesh size). sample code number quartz sand sample code number quartz sand sphericity roundness sphericity roundness qs 1 0.9 0.5 qs11 0.8 0.7 qs 2 0.7 0.7 qs12 0.6 0.5 qs 3 0.8 05 qs13 0.5 0.7 qs 4 0.9 0.6 qs14 0.7 0.8 qs 5 0.7 0.9 qs15 0.9 0.9 qs 6 0.9 0.7 qs16 0.5 0.9 qs 7 0.9 0.7 qs17 0.7 0.5 qs 8 0.5 0.9 qs18 0.6 0.6 qs 9 0.6 0.8 qs19 0.6 0.7 qs 10 0.7 0.6 qs20 0.5 0.8 table 4—sphericity and roundness for topaz sand (20/40 mesh size). sample code number topaz sand sample code number topaz sand sphericity roundness sphericity roundness ts 1 0.9 0.7 ts11 0.6 0.8 ts 2 0.8 0.8 ts12 0.5 0.7 ts 3 0.8 0.6 ts13 0.8 0.7 ts 4 0.9 0.6 ts14 0.6 0.8 ts 5 0.7 0.7 ts15 0.7 0.8 ts 6 0.6 0.8 ts16 0.7 0.6 ts 7 0.5 0.5 ts17 0.5 0.8 ts 8 0.9 0.8 ts18 0.9 0.7 ts 9 0.7 0.7 ts19 0.8 0.6 ts 10 0.6 0.7 ts20 0.5 0.6 table 5—average sphericity and roundness for quartz and topaz sand. parameters quartz sand topaz sand sphericity 0.7 0.7 roundness 0.7 0.7 improved oil and gas recovery 10 turbidity result. table 6 shows that the turbidity for quartz sand was 2.8 ntu, while for topaz sand was 3.83 ntu. although liang et al. (2016) reported a slightly higher turbidity value of 7.45 ntu, which exceeds the values found in the present work, all results meet the accepted limit set by api rp 56 and iso 13503-2 (<250 ntu). both quartz and topaz sand recorded a small number of suspended particles making them suitable for use as proppants. table 6—turbidity of quartz and topaz sand. sample turbidity (ntu) sample turbidity (ntu) distilled water 0.42 distilled water 0.42 distilled water + quartz sand 3.22 distilled water + topaz sand 4.25 quartz sand 2.80 topaz sand 3.83 bulk density result. table 7 presents the bulk density results, which are 1.24 ( 𝑔 𝑐𝑚3) and 1.28 ( 𝑔 𝑐𝑚3) for the two sands. these results indicate that both sands comply with the iso 13503−2 standard, which requires a bulk density of less than 2.0 ( 𝑔 𝑐𝑚3). moreover, the work of zwalatha et al. (2024) reported that proppants with high bulk density are not easily transported with fracturing fluids. the proppants could be prone to settle in the wellbore even before reaching into hydraulic fractures. however, the good thing about the quartz sand and topaz sand is the low bulk density value which makes them suitable for hydraulic fracturing operation. table 7—bulk density result. sample code number bulk mass (g) bulk volume (cm3) bulk density (g/cm3) qs 560.96 452.50 1.24 ts 483.51 378.94 1.28 acid solubility result. table 8 shows the results of the acid solubility test. quartz sand and topaz sand recorded solubility percentages of 1.50% and 1.72%, respectively. according to the api rp 19c standard, proppant materials should exhibit acid solubility values of < 2% to be considered suitable for hydraulic fracturing operations. both quartz and topaz sands fall within this acceptable range, demonstrating their potential suitability for use as proppants. the findings in this work align with other studies that have emphasized the importance of low acid solubility for proppant materials. for example, xu et al. (2022) found that proppants with acid solubility values below 2% maintained structural integrity under reservoir conditions, thus enhancing the overall efficiency of hydraulic fracturing operations. they also highlighted that proppants with low solubility in acidic environments are less likely to degrade, ensuring better performance and longer service life in fracturing applications. the slight difference in solubility values between quartz and topaz sands may reflect differences in their mineralogical compositions, yet both remain well within industry-accepted standards, supporting their potential applicability as effective proppants in hydraulic fracturing jobs. improved oil and gas recovery 11 table 8—acid solubility result. samples weight before (g) weight after (g) solubility (%) quartz sand 5.00 4.925 1.50 topaz sand 5.00 4.914 1.72 crush resistance result. figure 7 displays the percentage of crushed material at varying stress levels for the uncoated sand samples. at 1000 psi the percentage of fines generated for quartz is 4.65% while for topaz is 4.12%. after increasing the pressure to 2000 psi, the percentage of fines increases to 7.73% for quartz and 7.24% for topaz sand. the maximum closure stress level was reached at 3000 psi with a percentage of fines generated to be 10.89% for quartz sand and 10.33% for topaz sand. based on api rp 56, frac sand should generate <10% fines at a given closure stress level to be suitable for use at that stress level. the test results show that the strength of the uncoated sands varies from 1000 psi 3000 psi. however, for wells with closure stress greater than 3000 psi, the quartz and topaz sands will not be used at such pressures and will generate fines (> 10%), hence, there is need to coat the sand to improve its strength. figure 7— crush resistance result for 20/40 mesh size quartz and topaz sand (uncoated sand). figure 8 clearly indicates that the epoxy coating significantly enhanced the crush resistance of both topaz and quartz sands. the test results show that the strength of the sand varies from 1000 psi 4000 psi. both resin-coated quartz sand and topaz sand can withstand crush resistance at closure stress level of up to 4000 psi. at lower closure stress levels such as between 2000 psi to 3000 psi, the percentage of crushed material was significantly reduced in the coated samples compared to the uncoated ones. moreover, the coated samples maintained much lower crushing percentages as seen in figure 8 with a value of 7.51% and 7.10% at 3000 psi for quartz and topaz sand respectively. this indicates that the coating effectively protected the sand grains from breaking down under higher stress level. the result is in line with the work of zoveidavianpoor and gharibi (2015) who found that proppants with polymer coatings exhibited enhanced resistance to crushing particularly at higher stress levels. 0 2 4 6 8 10 12 0 500 1000 1500 2000 2500 3000 3500 p er ce n t c ru sh ed ( % ) pressure (psi) topaz sand quartz sand improved oil and gas recovery 12 figure 8— crush resistance result for resin-coated quartz and topaz sand. loss on ignition (loi) result. table 9 is the results of loss on ignition which showed that before heating the sample at 900ºc, it was twelve grams for both quartz and topaz samples. however, after subjecting the sands to heat, the values obtained were 11.80 and 11.83 grams for quartz and topaz sand respectively. this indicates that both quartz and topaz sands have low loss on ignition values, with quartz sand showing a 1.67% loss and topaz sand a 1.42% loss. this result aligns with studies by haque et al. (2019), who reported that proppants with loi values below 2% are considered suitable for hydraulic fracturing applications, as they have minimal impurities that could affect performance. according to the api rp 19c, lower loi values are desirable in proppants as they correlate with better thermal stability and reduced risk of chemical reactions during hydraulic fracturing operations. table 9—loss on ignition for quartz and topaz sand. @ 900ºc quartz sand topaz sand mass before heating (g) 12 12 mass after heating (g) 11.80 11.83 loss on ignition (%) 1.67 1.42 hardness result. the hardness was observed to be seven for quartz sand and eight for topaz sand, as shown in table 10. this means that the quartz sand sample can scratch minerals with mohs hardness values from 1 to 6 but cannot scratch those rated above 7. similarly, the topaz sand can scratch minerals rated from 1 to 7 on the mohs scale but not those rated eight or higher. 0 2 4 6 8 10 12 0 1000 2000 3000 4000 5000 p er ce n t cr u sh ed ( % ) pressure (psi) resin-coated sand (topaz) resin-coated sand (quartz) improved oil and gas recovery 13 table 10—hardness test for quartz and topaz sand. minerals number quartz topaz talc 1 scratched scratched gypsum 2 calcite 3 fluorite 4 apatite 5 orthoclase 6 quartz 7 7 topaz 8 not scratched 8 corundum 9 not scratched diamond 10 note: the hardness of the quartz and topaz are 7 and 8 respectively. table 11 presents a comparison of the results for quartz sand, topaz sand, and the api and iso standards. the xrf values were 79% for quartz sand and 72% for topaz sand, while ottawa sand recorded a higher value of 82% which is likely attributed to its formation. the bulk density was 1.24 g/cm3 for quartz sand and 1.28 g/cm3 for topaz sand, compared to 1.53 g/cm3 for ottawa sand. the crush resistance and loss on ignition values are consistent with the findings of kamel et al. (2019). overall, the results meet the required specifications. table 11—comparison of results with standard method. properties ottawa sand this study api/iso standard xrf (silicon oxide) ottawa sand 79% for quartz sand; 72% for topaz; ≥ 70 % particle sand size 82% 100% for quartz and topaz sand; > 90 % (850-425μm) roundness and sphericity 0.80 0.7 for both quartz and topaz sand; ≥ 0.6 turbidity 10.0 ntu 2.80 ntu for quartz; 3.83 ntu for topaz; < 250 ntu bulk density 1.53 (g/cm3) 1.24 (g/cm3) for quarts; 1.28 (g/cm3) for topaz sand; < 2.0 (g/cm3) acid solubility 1.00 1.50 % for quartz; 1.72% for topaz; < 2.0 % crush resistance 9.5% < 10% fines generated @ 2500 psi for quartz and topaz sand (uncoated sand); < 10% fines generated @ 4000 psi for quartz and topaz sand (resin coated sand) < 10 % fines loss on ignition 2.5% 1.67 % for quartz sand; 1.42% for topaz sand; < 2.0% improved oil and gas recovery 14 economic analysis. the economy analysis was used to investigate the potential of the proppant in hydraulic operations, and to examine the feasibility of the proppants for use in the niger delta oil fields. tables 12 and 13 show the parameters used for economic analysis. table 12—parameters used for the economic analysis (capital expenditure). s/no parameters quality/price 1 quartz sand $ 570 per ton 2 topaz sand $ 680 per ton total capex $1250 table 13—operating expenses (opex). parameters case a (topaz sand) case b (quartz sand) transportation cost $400 per ton $ 300 per ton labor assumed two workers $200 $200 maintenance/repair expenses $500 $500 miscellaneous expenses $300 $300 total opex $1400 $1300 the following assumptions were made. i. discount rate of 10%, ii. each ton of sand generates $2,000 in revenue, iii. the operation uses 1 ton of sand per year, iv. project duration will last for ten years. the following equations were used in the economic analysis. 𝑁𝑒𝑡 𝑐𝑎𝑠ℎ 𝑓𝑙𝑜𝑤 (𝐹𝑉) = 𝑅𝑒𝑣𝑒𝑛𝑢𝑒 − 𝑇𝑜𝑡𝑎𝑙 𝑂𝑃𝐸𝑋....................................................................................(4) 𝑃𝑉 = 𝐹𝑉 (1+𝑖)𝑛 ..................................................................................................................................................(5) 𝑁𝑃𝑉 = 𝑇𝑜𝑡𝑎𝑙 𝑃𝑉 − 𝐼𝑛𝑖𝑡𝑖𝑎𝑙 𝐶𝐴𝑃𝐸𝑋...............................................................................................................(6) where fv is the future value (cash flow per year), $; pv is the present value , $; i is the discount rate, %; n is the number of years. improved oil and gas recovery 15 figure 9—pv of cash flows over time for topaz and quartz sand. figure 9 provides valuable insights into the profitability of using quartz and topaz sand as proppants in niger delta oil field. for the project utilizing topaz sand, the pv starts at $545.45 in the first year. over the course of 10 years, it gradually decreased due to the discounting effect of 10%, reaching $231.32 in the 10th year. the total pv of net cash flows accumulated over the period is $3,686.71. this positive pv indicates that using topaz sand is economically viable and should generate a profitable return over its duration. similarly, using quartz sand also demonstrates profitability over the 10-year period. it starts with a present value of $636.36 in the first year and shows a consistent decline because of the time value of money. by the 10th year, the value became $270.99. the cumulative pv over the entire project duration amounts to $4,301.60. this indicates that the project will yield a profitable return, confirming its economic viability. these values reflect the fact that the net cash flows generated by each project is sufficient to cover initial investments and still produce a positive return. this supports the conclusion that both projects are economically feasible and will likely contribute positively to the financial goals of the hydraulic fracturing operations in niger delta. figure 10 shows the comparison of npv for quartz and topaz sand projects. the higher npv for quartz sand is attributed to its lower initial capital expenditure and slightly reduced operating expenses compared to topaz sand. this result clearly shows the superior financial performance of quartz sand over topaz. figure 10—comparison of net present value (npv) for quartz and topaz sand. 0 1000 2000 3000 4000 5000 0 2 4 6 8 10 12 p re se n t v al u e ($ ) time (years) quartz sand topaz sand 3731.2 3006.73 0 1000 2000 3000 4000 quartz sand ($) topaz sand ($) n p v ( $ ) improved oil and gas recovery 16 conclusions this research study investigated the use of quartz sand, topaz sand and resin coated sand based on the physical, chemical, and mechanical properties and compared them with the standards outlined in api rp/iso 13503-2. the study evaluated the performance of the sands as proppants. quartz sand and topaz sand exhibited excellent quality based on the parameters considered for commercial proppants. high silicon content makes sand the top choice for natural sand proppant. these sands are abundant at mining sites and very affordable. using quartz sand and topaz sand as proppants can reduce the costs associated with using high-priced ottawa sands in hydraulic fracturing operations. the following conclusions can be drawn from the experimental study: i. the x-ray fluorescence (xrf) test on the sand indicates that quartz sand contains a high percentage of silicon oxide, at 79.93%, while topaz sand contains 72.81%. ii. the sieve test analysis results showed that both quartz sand and topaz sand are 100% compliant in terms of particle size distribution. the crush resistance test results were 8.67% and 8.90%, respectively. iii. the roundness and sphericity test results were 0.7 and 0.8 respectively. the turbidity of the sand was observed to be 2.80 ntu and 3.83 ntu, while the bulk density of the quartz and topaz sand was 1.24 and 1.28 ( 𝑔 𝑐𝑚 3 ). iv. the economic analysis carried out showed that quartz had net presence value of 3731.2 ($) while that of topaz sand had 3006.73 ($) respectively. the results indicate that the quartz and topaz sands were profitable for use in hydraulic fracturing operations. v. the results of the study also showed that the quartz and topaz sands meet the recommended international standard organization and american petroleum institute methods and thus, a good candidate for use in hydraulic fracturing operations. recommendations the following are the recommendations from the study. i. quartz and topaz sand are recommended for use as proppants in hydraulic fracturing operations. ii. a conductivity test should be conducted to determine the amount of flow that the sand will allow and to assess the influence of the sand on the crush resistance potential of the reservoir. acknowledgments the authors express their gratitude to the management of the federal university of technology, owerri, for providing the laboratory facilities essential for this research. special thanks are extended to the federal government of nigeria and the petroleum technology development trust fund (ptdf) for their financial support in making this project possible. conflict of interest the authors declare that there are no conflicts of interest regarding the publication of this research. references agrawal, s. and gernand, j.m. 2020. quantifying the economic impact of hydraulic fracturing proppant selection in light of occupational exposure risk and functional requirements. risk analysis 40(2): 319-335. api std 19c, measurement of and specifications for proppants used in hydraulic fracturing and gravelpacking operations, 2nd edition. 2018. washington, dc: api. improved oil and gas recovery 17 bandara, a.p.g., ranjith, w., zheng, w., et al. 2022. grain-scale analysis of proppant crushing and embedment using calibrated discrete element models. acta geotechnica 17(12): 1-28. curimbaba, s., kerr de paiva cortes, g.w., and de paiva cortes, 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engineering 24(1): 24-34. zwalatha, m.r., mohammed, b.a., garba, k., et al. 2024. appraisal of the propping potential of luwa sand in nigeria for hydraulic fracturing applications. abuad journal of engineering and applied sciences 2(1): 1019. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1349 received january 5, 2025; revised march 1, 2025; accepted may 2, 2025. *corresponding author: christian.okalla@futo.edu.ng 1 technical evaluation of formation damage remediation in niger delta clastic reservoirs anthony ogbaegbe chikwe, christian emelu okalla*, and prayer samuel diovu, federal university of technology owerri, owerri, nigeria abstract formation damage continues to pose a significant challenge in hydrocarbon extraction, substantially hindering the productivity of reservoirs by diminishing the inherent permeability of the rock formations. this issue, which arises during drilling, production, or workover activities, results in subpar recovery efficiencies and considerable financial repercussions. the present investigation undertook a thorough technical assessment of formation damage and its remedial approaches for a well situated in the niger delta. in this study, pressure transient analyses were conducted on the buildup tests of well p, both prior to and following acidization treatment.the pta of well p before acidizing revealed a positive skin value of +6.11 and a permeability of 3.15 md, confirming the presence of considerable formation damage in the vicinity of the wellbore. to counteract this damage, a matrix acidizing treatment was executed, aimed at dissolving materials obstructing the pores and reinstating permeability. posttreatment analysis indicated a skin factor of -0.658 and an improved permeability of 11.9 md, signifying successful well stimulation and enhanced inflow performance. this research highlights the effectiveness of acidizing as a remedial measure in the clastic reservoirs of the niger delta, while also stressing the importance of combining technical diagnostics with economic assessments to enhance production efficiency and maximize asset value. introduction formation damage, a pivotal concept within the petroleum industry, pertains to the detrimental interplay between drilling activities and the productive formation. such interplay results in a diminishment of permeability in the vicinity of the wellbore, thereby ultimately diminishing the productivity of the well. this phenomenon represents a widespread challenge encountered throughout the processes of well-drilling, completion, production, and workover within the petroleum sector. bennion (2002) posits that formation damage refers to any process that degrades the inherent productivity of an oil or gas reservoir or the injectivity of a water or gas injection well. this study adopts the niger delta as a case in point. klungtvedt and saasen (2022) indicate that during drilling activities, interaction with drilling fluids can impair the formation's capacity for production or fluid flow. dake (1978) describes the incursion of foreign fluids into the reservoir rock as creating a zone of diminished permeability within the wellbore, termed the "skin." it is important to note that formation damage is not exclusively a consequence of drilling or completion activities; rather, it arises from a multitude of intricate reservoir processes (clifford 2019). in the development process, when the formation interacts with external fluids, physical and chemical reactions may occur if these fluids are incompatible with the reservoir fluids or mineral properties. these reactions can significantly impact the formation's productivity. the niger delta formation consists mainly of sandstone. as mailto:christian.okalla@futo.edu.ng improved oil and gas recovery 2 reported, the porosity of sandstone formations ranges from 10% to 35% due to the loose packing of individual sand or mineral grains. raza et al. (2015) have shown that the permeability of sandstone reservoirs typically ranges between 0.4 md and 60 md. however, fatt (1953) demonstrated that the application of overburden pressure decreases the permeability and porosity of sandstone reservoirs. consequently, the niger delta region is characterized by relatively good porosity and permeability properties. formation damage can be triggered by various factors and can occur at any stage of a well’s life. these factors affect the permeability of reservoir rocks, thereby reducing the natural productivity of the reservoir. to effectively evaluate formation damage, it is essential to investigate its root causes. this investigation is crucial for making informed decisions regarding the remedial actions to be taken on the well. factors contributing to formation damage include erosion, chemical weathering, fluid injection, and overburden pressure. the technical evaluation of formation damage demands a multidisciplinary approach due to its complexity. engineers can employ different strategies to address the problem of a damaged formation. a professional and indepth understanding of formation damage is required to analyze data and solve problems accurately and comprehensively. formation damage can result in substantial costs for remediation and deferred production (oseh et al. 2015). economic evaluation involves conducting a cost-benefit analysis of the financial impact. this includes assessing the lost revenue due to the reduced production rate caused by formation damage and the revenue generated from hydrocarbon production in the reservoir. once formation damage occurs, the reservoir generally cannot return to its original state. the phenomenon where substances that enter the porous media do not easily exit is known as the reverse funnel effect (porter 1989). well testing is an effective method for determining whether a formation is damaged. by analyzing transient well-test data, the skin factor can be obtained (renpu 2011). pressure transient analysis, which involves the analysis of pressure and flow data sets, extracts information from pressure and rate data measured in a producing well (alain 2018). well testing can directly assess the degree of damage by matching a model (either analytical or numerical) of the well and reservoir to the data (zarrouk and mclean 2019). pressure transient analysis is one of the most valuable tools for evaluating formation damage (denson et al. 2015). well testing is primarily conducted to obtain information on the formation's permeability and skin factor, which helps in assessing well conditions and estimating reservoir parameters. methodology the methodology employed in this study is well testing, a fundamental technique in petroleum engineering that involves measuring flow rates and pressure changes during production or injection tests. among the various types of well-testing methods, this research focuses specifically on the pressure buildup well test. a pressure buildup test entails the measurement and analysis of bottom-hole pressure data after a producing well is shut in. in this study, pressure transient analysis was performed using kappa saphirtm (developed by kappa engineering), a reservoir modeling software, to characterize reservoir parameters, including permeability and skin factor. the data required for the analysis is stored in a spreadsheet, typically in microsoft excel format. this spreadsheet contains detailed information such as the pressure and time data collected during the test, along with other essential parameters necessary for a comprehensive analysis. additionally, it includes the flow-rate data of the well and the pressures recorded with respect to time before the well was shut in. the process of loading data into the kappa saphirtm software for pressure transient analysis involves two key aspects: loading flow-rate data and loading pressure data. loading flow-rate data. for the flow-rate data, which is measured in standard barrels per day (stb/d), it is sourced from a spreadsheet, usually in microsoft excel format. once the software is set up with the correct data types and units, the “free” option is chosen in the format region. after specifying the appropriate time format for improved oil and gas recovery 3 the flow-rate data, it is imported into the kappa saphir software. once loaded, the flow-rate data is presented in a history plot, enabling a visual representation of how the flow rate changes over time. loading pressure data. regarding the pressure data, it is also retrieved from an excel spreadsheet. the data is organized in a two-column layout, with the first column showing time in hours and the second column presenting pressure in pounds per square inch absolute (psia). in the software, the relevant field is selected, and the correct data types and units are specified. the appropriate time format for the pressure data is then chosen. after importing the pressure data, a history plot is generated, plotting the pressure change against time. this plot helps in observing the pressure behavior during the test. after successfully importing the data into the software, several plots are generated, including the history plot, the horner plot, and the log-log plot. these plots are invaluable for extracting the required reservoir parameters, such as permeability and skin factor. the permeability value provides insights into the state of the permeable spaces within the reservoir, while the skin factor serves as an indicator of well damage. a skin factor of zero indicates no damage, a negative value suggests well stimulation, and a positive value implies formation damage. by analyzing these values, it is possible to quantify the extent of damage inflicted on the formation. results and discussions pressure transient analysis on well p. the reservoir rock, fluid, and wellbore parameters for well p (table 1) provide foundational insights into the reservoir’s physical characteristics and fluid behavior, critical for interpreting pressure transient analysis. the reservoir thickness (h=200 ft) and porosity (φ=0.30) define a volumetrically significant formation with substantial hydrocarbon storage potential, given the high porosity— indicating 30% of the rock volume is pore space. this porosity, combined with the oil viscosity (µ = 0.8 cp), suggests favorable fluid mobility, as low viscosity reduces resistance to flow through the reservoir. the total compressibility (cₜ=3×10⁻⁶ psi⁻¹) reflects minimal fluid and rock compression under pressure, which influences pressure propagation during transient tests. the oil formation volume factor (b₀=1.136 rb/stb) quantifies the expansion of oil from reservoir to surface conditions, aiding in converting subsurface volumes to stock-tank barrels for production calculations. additionally, the wellbore radius (rᵢ=0.345 ft) directly impacts near-wellbore flow dynamics and skin effect calculations, which are essential for evaluating formation damage or stimulation efficiency. together, these parameters underpin the reservoir’s storage capacity (φ∙h), fluid mobility (µ), and transient pressure response (governed by compressibility and viscosity), forming the basis for modeling well performance and optimizing acidizing interventions to enhance productivity. table 1—parameters used for pressure transient analysis. reservoir rock parameters for well p reservoir thickness (h) 200ft reservoir porosity (ϕ) 0.30 the pvt parameters for well p oil viscosity (µ) 0.8cp total compressibility of fluid (ct) 3e-6ps-1 oil formation volume factor (bo) 1.136rb/stb the wellbore parameters wellbore radius (rw) 0.345ft improved oil and gas recovery 4 the chosen interpretation models for pressure transient analysis (pta) of well p (table 2) reflect a streamlined, conventional approach tailored to the well’s characteristics. the standard model was selected, indicating reliance on established methodologies for vertical wells in a homogeneous reservoir with finite boundaries, simplifying the analysis by assuming uniform reservoir properties and a defined spatial extent. the single-phase oil flow assumption aligns with the reservoir’s fluid phase, allowing straightforward interpretation of pressure responses without complexities from multiphase interactions. a single flow rate during testing further reduces variables, enabling consistent analysis of transient data under steady production conditions. the assumption of constant wellbore storage and skin implies stable near-wellbore dynamics during the test, which simplifies early-time pressure data interpretation but may overlook transient changes in formation damage or stimulation effects over longer durations. together, these choices prioritize analytical simplicity and clarity, ideal for assessing baseline reservoir performance and evaluating acidizing impacts. however, homogeneity and finite boundary assumptions may limit the model’s ability to capture reservoir heterogeneities or long-term boundary effects, underscoring the need for complementary analyses if complex behaviors emerge post-acidizing. table 2—interpretation model for pta of well p before and after acidizing. interpretation models chosen interpretation models model option standard model well type vertical reservoir homogenous boundary finite fluid phase oil fluid flow rate single flowrate wellbore storage and skin constant table a within the appendix furnishes the detailed pressure buildup test data acquired from well p prior to the acidization procedure. the pressure buildup tests conducted on well p prior to and after acidization (table 3) elucidate significant operational and performance disparities.before acidizing, the test spanned 57 hours (july 1114, 2022) with a liquid rate of 1,000 stb/d at shut-in, reflecting a prolonged period likely required to assess pressure recovery in a damaged well with restricted flow. post-acidizing, the test duration shortened dramatically to 10 hours (october 22, 2022) under a higher liquid rate of 1,100 stb/d, signaling improved near-wellbore permeability and faster pressure stabilization due to reduced formation damage. the zero-rate shut-in during both tests ensured accurate measurement of reservoir pressure response, while the use of a single gauge-maintained data consistency. the shorter test duration post-acidizing underscores the treatment’s success in mitigating skin effects, enabling quicker reservoir evaluation and aligning with the increased production rate—a direct indicator of enhanced well productivity. these results highlight the acidizing intervention’s effectiveness in optimizing both operational efficiency and reservoir performance. improved oil and gas recovery 5 table 3—history listings of the pressure buildup test before and after acidizing before acidizing after acidizing name of well well p well p name of test buildup test buildup test start date of buildup test 07/11/2022 10/22/2022 end date of buildup test 07/14/2022 10/22/2022 time at start date of buildup test 03:00:17 12:00:00 liquid rate at start time (stb/d) 1000 1100 liquid rate at shut-in time 0 0 duration of buildup test 57.0277 10.00 no of gauges used for the test single gauge single gauge pta result analysis on well p before acidizing. figure 1 presents a historical plot of pressure (measured in psia) and liquid rate (in stb/d) against time (in hours) prior to acidizing. this plot effectively depicts two key aspects: the relationship between pressure and time, as well as the flowrate of the test over time. when examining the flow-rate plot, a distinct pattern emerges. during the initial flowing period, which lasts approximately 75 hours, there is a noticeable decline in pressure. this pressure decline is a characteristic phenomenon associated with the production of crude oil from the reservoir. as the oil is being extracted, the reservoir pressure gradually drops, which is a natural consequence of the reduction in the fluid volume within the reservoir. after the 75-hour flowing period, the well is shut in. subsequently, a pressure build up occurs over a period of 57 hours, which is the duration of the shut-in period. this process of pressure build up after shutting in the well is the basis for what is known as a pressure buildup test. this test is crucial in petroleum engineering as it provides valuable insights into the reservoir's properties, such as permeability and the presence of boundaries. in summary, the figure offers a clear visual representation of the reservoir's behavior during the production phase (pressure decline) and the subsequent shut in phase (pressure build up), highlighting the key stages of a pressure buildup test before acidizing the well. figure 1—the history plot of pressure (psia), liquid rate (stb/d) vs time (hrs) before acidizing. figure 2 illustrates a horner plot delineating the correlation between bottom-hole pressure (expressed in psia) and the logarithmic function of (tp+dt)/dt. the alignment of the data points on this plot with the derivative curve improved oil and gas recovery 6 is a critical indicator. this congruence substantiates the robustness of the model, offering a firm basis for conducting thorough and dependable analyses. consequently, we can exhibit a high degree of confidence in the precision of the outcomes yielded by this model. the horner plot serves a fundamental purpose in facilitating the computation of critical reservoir parameters. through the examination of the curve's slope on the plot, engineers can precisely ascertain the permeability of the reservoir. permeability, a crucial attribute, characterizes the ease with which fluids traverse the rock formation and is imperative for comprehending reservoir productivity. furthermore, the plot allows for the determination of the skin factor, which quantifies the extent of damage or improvement in the vicinity of the wellbore, exerting a substantial influence on well performance. furthermore, the horner plot constitutes a valuable instrument for the identification of various flow regimes encountered during well testing. these flow regimes, encompassing the early transient, transient, late transient, and pseudo-steady-state periods, each exhibit unique characteristics indicative of the fluid flow behavior within the reservoir. the recognition of these flow regimes is imperative for reservoir engineers, as it facilitates the optimization of well production strategies, the prediction of reservoir performance, and the making of informed decisions pertaining to reservoir management. figure 2—horner plot of bottomhole pressure vs log (tp+dt/dt) before acidizing. figure 3 illustrates a logarithmic scale graph depicting the correlation between differential pressure, pressure derivatives, and time (measured in hours). the curve positioned at the top of the graph signifies the pressure derivative (dp) plotted against time, whereas the curve located at the bottom corresponds to an additional pressure derivative (dp’) also plotted against time. within the domain of petroleum engineering, the log-log plot is of paramount importance in ascertaining the wellbore storage constant (c). the concept of wellbore storage, which pertains to the retention and subsequent release of fluids within the wellbore under transient flow conditions, is fundamental. through the examination of the curve characteristics on this log-log plot, engineers can precisely determine the value of c, a critical factor for comprehending well behavior and forecasting reservoir performance. additionally, the vertical divergence between the two curves on the logarithmic scale plot has substantial implications for the skin factor. the skin factor is a quantifiable parameter that characterizes alterations in the vicinity of the wellbore resulting from factors such as formation damage or stimulation. a more pronounced vertical divergence between the two curves signifies a greater value of the skin factor. this correlation enables engineers to evaluate the extent of near-wellbore damage or improvement, which subsequently affects well productivity and the efficacy of reservoir management strategies. thus, the log-log plot depicted in figure 3 offers significant insights into wellbore storage and conditions in the vicinity of the wellbore, facilitating more precise reservoir characterization and optimization of well performance. improved oil and gas recovery 7 figure 3—log-log plot of differential pressure (dp) and pressure derivative (dp’) vs dt (hrs) before acidizing. the results from the pressure transient analysis before acidizing reveal critical insights into the well’s performance and reservoir characteristics (table 4). the total skin factor of 6.11 indicates significant nearwellbore formation damage, which directly contributes to a pressure drop (δp) of 1,243.59 psi due to restricted flow efficiency. this damage underscores the necessity of acidizing to mitigate productivity losses. the reservoir’ s low permeability (3.15 md) and moderate permeability-thickness product (kh= 631 md·ft) suggest a thick but tight formation (~200 ft net pay), inherently limiting fluid flow despite the high initial reservoir pressure of 6,417.58 psia, which signals strong reservoir potential if damage is alleviated. the drainage radius of 214 ft and tested volume of 7.05 mmb further define the accessible reservoir volume, emphasizing the scale of recoverable resources. combined, these parameters highlight a reservoir constrained by both natural tightness and induced damage, positioning acidizing as a critical intervention to enhance connectivity, reduce skin, and unlock the well’ s productivity aligned with the reservoir’s high-pressure potential. table 4—results of pressure transient analysis before acidizing. model parameters values units tmatch 31.7 [hr]-1 pmatch 0.00492 [psia]-1 c 0.00734 bbl/psi total skin 6.11 kh 631 md×ft pi 6417.58 psia wellbore parameters (tested well) c 0.00734 bbl/psi skin (s) 6.11 reservoir and boundary parameters initial reservoir pressure 6417.58 psia permeability thickness product (k*h) 631 md×ft permeability (k) 3.15 md derived and secondary parameters drainage radius (re) 214 ft tested volume 7.0514 mmb delta p (total skin) 1243.59 psi improved oil and gas recovery 8 pta result analysis on well p after acidizing. figure 5 depicts a dual-axis graph illustrating the relationship between bottom-hole pressure (in psia) and liquid flow rate (in stb/d) over time (in hours) during a well test. the analysis of the pressure transient reveals a 14-hour shut-in phase, wherein the well was sealed, resulting in a distinctive pressure buildup curve—a defining feature of a pressure buildup (pbu) test. the evaluation of nearwellbore conditions, reservoir permeability, and skin effects is critically dependent on this test, which analyzes the pressure recovery response subsequent to the cessation of production. the flow rate axis corroborates the shut-in event (0 stb/d) and offers context for the production rate prior to shut-in. the pressure buildup observed over a 14-hour period equips engineers with the means to ascertain crucial reservoir parameters, including formation transmissibility and initial reservoir pressure, which are indispensable for the optimization of subsequent interventions such as acidizing. this analysis highlights the pivotal role of the pbu test in diagnosing well performance and in guiding strategies for reservoir management. figure 5—the history plot of pressure, liquid rate vs time after acidizing. figure 6, which depicts a horner plot, is evident that the data points correspond well with the derivative curve, indicating that the model is robust and suitable for our analysis. this facilitates the derivation of reliable results. the plot is instrumental in determining parameters such as permeability from its slope and the skin factor. furthermore, the horner plot enables the identification of various flow regimes pertinent to well testing, encompassing the early transient, transient, late transient, and pseudo-steady state periods. figure 6—semilog plot of bottomhole pressure vs. log (tp+dt/dt) after acidizing. improved oil and gas recovery 9 figure 7 illustrates the differential pressure and pressure derivative as a function of time in hours. the upper curve corresponds to the pressure derivative (dp) plotted against time (hrs), whereas the lower curve represents the pressure derivative (dp') as a function of time (hrs). the log-log plot facilitates the calculation of the well bore storage constant (c). additionally, it is understood that the vertical separation between the two plots is indicative of the skin factor, with a greater separation corresponding to a higher value of the skin factor. figure 7—log-log plot of differential pressure and pressure derivative vs. dt after acidizing. table 5 provides a detailed analysis of the permeability results following the acidification treatment of well p. the data presented in this table indicates that the permeability of the well has been measured to be 11.9 millidarcies (md). this value represents the ease with which fluids can flow through the rock formations surrounding the wellbore. additionally, the initial reservoir pressure was recorded at an impressive 2667.83 pounds per square inch absolute (psia), reflecting the high energy status of the reservoir before any production activities commenced. furthermore, the skin factor, a dimensionless parameter used to evaluate the condition of the wellbore and the near-wellbore formation, was calculated to be -0.658. a negative skin factor suggests that the acidification treatment has been successful in improving the permeability around the wellbore by removing or reducing damage caused by drilling muds, scales, or other factors that might have impeded fluid flow. this indicates an overall improvement in the well’s performance due to the treatment. lastly, the wellbore storage coefficient was estimated to be 1.23 barrels per psi (bbl/psi). this coefficient quantifies the volume of fluid that the wellbore can store per unit of pressure change and is crucial for understanding the well's response to pressure changes during production or injection operations. a lower value of this coefficient implies that the wellbore is more efficient in transmitting reservoir pressure changes to the formation, which is generally a favorable characteristic for well performance. improved oil and gas recovery 10 table 5—results of pressure transient analysis from saphir after acidizing. model parameters values units tmatch 0.71 [hr]-1 pmatch 0.0181 [psia]-1 c 1.23 bbl/psi total skin -0.658 kh 2390 md×ft pi 2667.83 psia wellbore parameters (tested well) c 1.23 bbl/psi skin (s) -0.658 reservoir and boundary parameters initial reservoir pressure 2667.83 psia permeability thickness product (kh) 2390 md×ft permeability (k) 11.9 md derived and secondary parameters drainage radius (re) 214 ft tested volume 7.0514 mmb pta result comparison. table 6 provides a detailed summary and comparison of three crucial parameters— permeability, skin factor, and wellbore storage coefficient—derived from the pressure transient analysis (pta) conducted on well p both before and after the acidizing treatment. the data presented in this table clearly illustrate that the acidizing process has significantly improved the fluid flow characteristics in the vicinity of the wellbore. specifically, there is a notable enhancement in permeability, which indicates a greater ease of fluid movement through the reservoir rock. additionally, the skin factor, which is a measure of the near-wellbore damage or improvement, has decreased substantially, suggesting that the acidizing treatment has effectively reduced any damage and improved the well's productivity. furthermore, the wellbore storage coefficient, which reflects the ability of the wellbore to store fluids, has also been positively impacted by the treatment. overall, these findings unequivocally demonstrate that the acidizing treatment has successfully enhanced the production capacity of well p by improving the fluid flow conditions near the wellbore. table 6—results of reservoir and wellbore parameters from saphir before and after acidizing well p. parameters before acidizing after acidizing units permeability (k) 3.15 11.9 md skin factor (s) 6.11 -0.658 wellbore storage coefficient (c) 0.00734 1.23 bbl/psi improved oil and gas recovery 11 conclusion formation damage has been identified as the blockage of the permeable spaces of a reservoir. technical evaluation has given room to professionally analyze a niger delta well from this project having a deep knowledge of what formation damage is and the properties of a niger delta formation which gave guide in validation of the results obtained during the analysis. the skin factor obtained before acidizing the well and permeability value proved that the well was damaged. from the results obtained after acidizing the well, it has shown that acidization is one of the effective remedial actions that can be carried out on a sandstone formation to improve permeability and productivity of a well. conflicting interests the author(s) declare that they have no conflicting interests. references alain, c.g. 2018. everything you always wanted to know about well test analysis but were afraid to ask. https://docslib.org/doc/1413322/everything-you-always-wanted-to-know-about-well-test-analysis-but-were-afraid-toask. bennion, b.d. 2002. an overview of formation damage mechanisms causing a reduction in the productivity and injectivity of oil and gas producing formations. j can pet technol 41(11):126-150. petsoc-02-11-das dake, l.p. 1978. fundamentals of reservoir engineering. amsterdam, netherlands: elsevier. denson, a.h., smith, j.t., and cobbt, w.m. 2015. determining well drainage pore volume and porosity from pressure buildup tests. spe j. 16(4): 209-216. spe-5595-pa fatt. 1953. the effect of overburden pressure on relative permeability. j pet technol 5(10): 15-16. spe-953325-g clifford, m. 2019. numerical evaluation of formation damage models for application in niger delta oil reservoirs. international journal of advanced engineering research and science 6(5): 136-149. klungtvedt, k.r. and saasen, a. 2022. a method for assessing drilling fluid induced formation damage in permeable formations using ceramic discs. journal of petroleum science and engineering 213(1):1-15. oluwagbenga, o. o., oseh, j., oguamah, i.a., et al. 2015. evaluation of formation damage and assessment of well productivity of oredo field, edo state, nigeria. american journal of engineering research 4(3):1-10. porter, k.e. 1989. an overview of formation damage. raza, a., bing, c.h., nagarajan, r., and hamid, m.a. 2015. experimental investigation on sandstone rock permeability of pakistan gas fields. iop conference series: materials science and engineering 78(1):1-12. renpu, w. 2011. advanced well completion engineering. amsterdam, netherlands: elsevier. zarrouk, s.j. and mclean, k. 2019. geothermal well test analysis. amsterdam, netherlands: elsevier. christian emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri, owerri, nigeria. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, natural gas, and reservoir simulation. https://docslib.org/doc/1413322/everything-you-always-wanted-to-know-about-well-test-analysis-but-were-afraid-to-ask https://docslib.org/doc/1413322/everything-you-always-wanted-to-know-about-well-test-analysis-but-were-afraid-to-ask improved oil and gas recovery 12 appendix table a—field data obtained from well p before acidizing. ∆t (hrs) pws (psia) tp+∆t/∆t q (stb/d) 0 6363.499 1000 0.00462 6342.726 16452.21212 1000 0.00924 6322.22 8226.606061 1000 0.01386 6301.943 5484.737374 1000 0.01848 6281.922 4113.80303 1000 0.0231 6262.127 3291.242424 1000 0.02772 6242.543 2742.868687 1000 0.03234 6223.182 2351.17316 1000 0.03696 6204.043 2057.401515 1000 0.04158 6185.135 1828.912458 1000 0.046654 6164.6 1630.128704 1000 0.052346 6141.827 1452.962465 1000 0.058733 6116.618 1295.062921 1000 0.0659 6088.786 1154.334789 1000 0.073941 6058.109 1028.910712 1000 0.082963 6024.368 917.1263887 1000 0.093086 5987.331 817.4985023 1000 0.104444 5946.758 728.7050554 1000 0.117188 5902.442 649.567816 1000 0.131488 5854.136 579.0366735 1000 0.147531 5801.723 516.175728 1000 0.165533 5745.04 460.1508488 1000 1.044442 4453.707 73.77050568 1000 1.171884 4383.539 65.85678143 1000 1.314875 4319.707 58.80366731 1000 89.75314 6175.142 1.846818277 1000 91.5533 6184.132 1.830167817 1000 improved oil and gas recovery 13 93.5731 6192.292 1.812248359 1000 95.83937 6199.78 1.793041564 1000 98.14937 6206.715 1.774376888 1000 100.4594 6213.18 1.756570578 1000 102.7694 6219.24 1.739564751 1000 105.0794 6224.957 1.723306615 1000 107.3894 6230.368 1.707747921 1000 109.6994 6235.504 1.692844483 1000 112.0094 6240.396 1.678555761 1000 114.3194 6245.07 1.66484449 1000 116.6294 6249.548 1.651676358 1000 118.9394 6253.84 1.639019721 1000 121.2494 6257.961 1.626845344 1000 123.5594 6261.924 1.615126177 1000 125.8694 6265.742 1.60383716 1000 128.1794 6269.428 1.592955035 1000 130.4894 6272.985 1.582458194 1000 131.2447 6276.422 1.579106128 1000 132.0000 6279.745 1.575792424 1000 132.0046 6282.961 1.575772272 1000 132.0092 6286.076 1.575752122 1000 132.0139 6289.097 1.575731972 1000 132.0185 6292.03 1.575711825 1000 132.0231 6294.876 1.575691678 1000 132.0277 6297.639 1.575671533 1000 132.0323 6300.324 1.57565139 1000 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1358 received january 10, 2025; revised march 1, 2025; accepted april 14, 2024. *corresponding author email: mmrm4@pme.suezuni.edu.eg 1 gas recycling optimization in gas condensate reservoirs using 3d compositional modeling mohamed r. kasem*, petronefertiti oil company, cairo, egypt; hamid m. khattab, and ali m. wahba, suez university, suez, egypt abstract gas condensate reservoirs undergo a decline in productivity due to retrograde condensation when the bottomhole flowing pressure falls below the dew point, leading to the formation of liquid droplets and subsequent obstruction near the wellbore. utilizing dry gas reinjection serves as an established method for enhanced recovery, as it sustains reservoir pressure above the dew point, thereby facilitating the revaporization of the trapped condensate. this research employs a three-dimensional compositional reservoir simulator to meticulously optimize the efficiency of gas cycling under varying conditions of reservoir quality, fluid compositions, and well configurations. a sector model was developed using the peng-robinson equation of state (pr-eos) calibrated to pvt data, which includes dual-permeability porous media to accurately capture the flow dynamics near the critical point. the foundational scenario simulated natural depletion through the utilization of five vertical producers. subsequent simulations assessed crestal gas injection methodologies by transforming one of the producers into a dry gas injector, calibrating injection rates to attain recycle ratios ranging from 0 to 1. the performance of horizontal wells was compared with that of vertical completions to evaluate recovery mechanisms dependent on geometry. notable outcomes indicate a direct correlation between the optimal recycle ratio (ropt) and condensate yield. for lean gases (20 stb/mmscf), a ropt of 50% is required to optimize recovery, whereas for richer fluids (60 stb/mmscf), a ropt of 75% is necessary to counteract vaporization hysteresis. reservoir quality dictates the efficacy of well type. horizontal wells in high-kh formations achieve 18-22% greater recovery than vertical wells for high-yield fluids, a result of improved contact with undersaturated zones. in contrast, in low-kh reservoirs, vertical injector-producer pairs exhibit superior performance due to enhanced vertical sweep efficiency and reduced coning risks. the present study constructs a decision matrix pertinent to gas cycling projects, encompassing fluid richness, formation deliverability, and completion design. the outcomes furnish actionable insights for the optimization of injection strategies within retrograde condensate systems, especially in the context of heterogeneous or liquidrich shale-condensate formations. introduction gas condensate reservoirs occupy a critical position within the oil and gas sector, serving as significant contributors to hydrocarbon production and meeting the increasingly demanding global energy needs. initially, these reservoirs exist in a single-phase state. however, when the reservoir pressure falls below the dewpoint pressure, a phenomenon known as retrograde condensation ensues, resulting in the accumulation of condensate within the reservoir pores (gao et al. 2020; li et al. 2005). as illustrated in figure 1 (behmanesh et al. 2018), mailto:mohammedhussein51@yahoo.com improved oil and gas recovery 2 the condensate dropout around the wellbore can lead to the formation of three distinct flow regions. this accumulation of condensate causes the obstruction of reservoir pores, thereby reducing the recovery of both gas and condensate (hailong et al. 2024; al-marhoon and al-shidhani 2003; zhao et al. 2024; wang et al. 2018; okporiri and idigbe 2014; aaditya 2014; whitson and whitson 2005). upon the reduction of the flowing bottomhole pressure in gas condensate wells below the dewpoint pressure, a marked decrease in productivity is noted. a region of elevated condensate saturation emerges proximate to the wellbore, subsequently diminishing gas permeability and deliverability (shi et al. 2006; ahmed et al. 1998; bennion et al. 2001). empirical data from the industry suggests that under depletion drive conditions, gas condensate reservoirs generally achieve gas recovery factors between 40% and 60%, and condensate recovery factors ranging from 10% to 30%. to enhance the recovery of condensate from gas condensate reservoirs, an array of secondary and tertiary recovery methods is implemented. these methods encompass the displacement of gas and condensate through the utilization of various injection gases, including nitrogen, carbon dioxide, dry gas, or gas mixtures (seah et al., 2014; esmaeili et al 2023). the efficacy of these technologies is contingent upon a multitude of factors, such as the volume of residual gas and condensate reserves, the accessibility of the injected gas, the complexity and capacity of surface facilities, the geological and structural characteristics of the field, reservoir depths, and economic factors, including payback periods and production agreements. dry gas recycling emerges as the predominant method for enhanced recovery in gas condensate reservoirs. it functions to sustain reservoir pressure above the dewpoint, diminishes the dewpoint pressure of the newly formed gas mixture, and vaporizes the heavy components that have precipitated in the reservoir. this methodology has the potential to enhance gas recovery rates to 65%-80% and condensate recovery rates to 40%-60% (el aily et al. 2016; zhang et al. 2024; serhii 2023). critical factors that influence gas and condensate recovery during dry gas recycling encompass the variance between the reservoir pressure and the dew point pressure, the content of condensate, reservoir quality, and the production and injection patterns (kerunwa, 2015; izuwa et al. 2014; cobanoglu et al. 2014; rasoul et al. 2014; nasiri et al. 2015). the principal difficulty in the development of gas condensate reservoirs is the determination of an optimal scenario that maximizes recovery and minimizes investment risks to attract stakeholders. this study aims to determine the optimal gas-recycling ratio to maximize gas and condensate recovery while ensuring that the reservoir pressure remains above the dewpoint. a three-dimensional compositional simulation model, constructed using petrel software, will be utilized to optimize the gas recycling ratio (angang et al. 2020; larry 2022). the study will evaluate reservoirs with varying condensate contents and quality levels, incorporating both vertical and horizontal well configurations. simulations will be conducted using eclipse software to identify the most effective production and injection strategies. improved oil and gas recovery 3 figure 1—flow regime depiction for a radial well from a gas condensate reservoir. materials and methods the research methodology initiates with the development of three-dimensional static reservoir models employing petrel software. these models are engineered to depict reservoirs of varying qualities, distinguished by disparate porosity and permeability characteristics. the determination of these attributes is pivotal, as they substantially affect fluid movement and containment within the reservoir. simultaneously, pressure-volume-temperature (pvt) compositional models have been developed for three distinct gas condensate fluid samples. these samples exhibit condensate contents of 20, 40, and 60 stb/mmscf, respectively, and were created utilizing pvt software. the pvt models precisely capture the intricate phase behavior of the gas condensate fluids across varying pressure and temperature conditions. subsequently, these pvt models are transferred from pvt to petrel, thereby enabling the integration of fluid properties into the static reservoir models. the research methodology initiates with the creation of three-dimensional static reservoir models, which encompass a spectrum of reservoir quality attributes, such as porosity and permeability characteristics, utilizing petrel software (calvin and mattax, 1990). furthermore, pressure-volume-temperature (pvt) compositional models are developed for three gas condensate fluid samples, each with differing condensate contents of 20, 40, and 60 stb/mmscf, employing pvt software. subsequently, these models are transferred from pvt to petrel (wood and young, 1988; akpabio et al., 2015; curtis et al., 1999). subsequently, the creation of three-dimensional dynamic models is executed by integrating each static reservoir model with each of the three gas condensate models, culminating in a total of nine dynamic models. these models are meticulously constructed within the petrel software environment (yang et al. 2024). initially, the models undergo simulation under depletion drive conditions, (which involves gas production without the implementation of gas injection, to ascertain the ultimate recovery of gas and condensate. these outcomes are established as the foundational benchmarks for assessing the supplementary recovery facilitated by gas recycling, which is subsequently modeled using the eclipse software (akinsete et al. 2021; spivak and dixon 1973; pal 2013; amini et al. 2011). the study subsequently assesses the nine models across various dry gas recycling (ratios, specifically 0.9, 0.75, 0.5, and 0.25, initially employing vertical production wells. the procedure is replicated with horizontal production wells substituting the vertical ones. ultimately, the outcomes from the distinct development scenarios are scrutinized for each reservoir quality and gas model combination. the scenarios are graded in accordance with condensate recovery to ascertain the optimal gas recycling ratio that maximizes condensate recovery. three-dimensional reservoir static model. the subject reservoir is a faulted anticline sandstone formation. it is overlain by shale and delineated by major faults to the northeast and southeast. the structure exhibits a dip from the northeast to the southwest. the reservoir comprises two vertically communicating zones within a depth range of 3500 ft to 4900 ft true vertical depth subsea (tvdss), featuring a distinct gas-water contact (gwc) at 4700 ft tvdss. five wells traverse the reservoir, as depicted in figure 2. a three-dimensional structural model has been constructed employing four seismic horizons: 1) the uppermost shale's summit; 2) the apex of sand a; 3) the crest of sand b; and 4) the nadir of the lowermost shale. additionally, the model incorporates two major faults. the model’s grid dimensions are 39×37 cells in the x and y directions, respectively, with a 100 m spacing, subdivided vertically into 61 layers, resulting in a total of 88,023 cells. a facies model was constructed based on facies logs from the five wells. subsequently, porosity and permeability models were developed to represent three reservoir quality scenarios: • low quality reservoir (average porosity = 10%, & average permeability = 100 md) • mid quality reservoir (average porosity = 15%, & average permeability = 1000 md) improved oil and gas recovery 4 • high quality reservoir (average porosity = 20%, & average permeability = 5000 md) the reservoir's production strategy incorporates four wells designated as producers situated in the down-dip area and one injector well positioned at the crest for peripheral injection. given the aquifer's weakness, an aquifer model was not integrated into the simulation. figure 3 offers a depiction of the constructed three-dimensional reservoir model, emphasizing its structural and property distributions. figure 2—reservoir structure contour map with penetrating wells. figure 3—reservoir three-dimensional model with penetrating wells. pvt model. three samples of gas were procured from separate gas condensate reservoirs, each exhibiting condensate yields of 20, 40, and 60 stb/mmscf. calibrated models were constructed for each sample employing the peng-robinson equation of state (eos) within the pvt software. these eos models were meticulously customized to precisely emulate the behavior of the reservoir fluids, considering their pressure, volume, and temperature (pvt) characteristics. the methodology for the development of these equations of state models encompassed the subsequent stages: • select equation of state type (akpabio et al. 2014; soave 1972; peng and robinson 1976; jaubert and mutelet 2004). • splitting pseudo component (whitson 1984; robinson and peng 1978). improved oil and gas recovery 5 • match dewpoint pressure with binary interaction coefficients. • match constant composition expansion (cce), constant volume depletion cvd and separator tests available data using different eos parameters (coats and smart 1986; merrill et al. 1994). • match gas viscosity. • lump the composition into 8 compositions and rematch again if needed. • export pvt data as compositional model (eos with its related parameters). figures 4 through 6 delineate the phase diagrams corresponding to the three gas samples, elucidating the unique characteristics of each reservoir fluid. additionally, table 1 delineates the aggregated compositions for the three calibrated equation of state (eos) models. figure 4—phase diagram of gas with condensate yield of 20 stb/mmscf. figure 5—phase diagram of gas with condensate yield of 40 stb/mmscf. improved oil and gas recovery 6 figure 6—phase diagram of gas with condensate yield of 60 stb/mmscf. improved oil and gas recovery 7 table 1—lumped compositions of the three calibrated gas pvt models. components gas composition with condensate yield of 20 stb/mmscf gas composition with condensate yield of 40 stb/mmscf gas composition with condensate yield of 60 stb/mmscf mole percent, % mole percent, % mole percent, % n2 0.23 0.23 0.22 co2 0.13 0.13 0.12 c1 80.04 78.15 76.37 c2 8.41 8.22 8.04 c3, ic4 & nc4 7.63 7.68 7.71 ic5, nc5 & c6 1.96 2.71 3.38 c7, c8 & c9 1.25 2.23 3.18 c10 & c11+ 0.34 0.65 0.96 total 100 100 100 dynamic model initialization. the establishment of the reservoir model necessitates the determination of pressure and fluid saturations within each grid cell at the outset of the simulation period, preceding the commencement of production or injection activities. the subsequent parameters and methodologies were utilized during the initialization process: • datum pressure. the pressure within the reservoir at a true vertical depth of 4200 feet tvdss served as the reference point for delineating the three-dimensional pressure profile. • gas-water contact (gwc). the gas-water contact was delineated at a true vertical depth of 4700 feet tvdss to determine fluid saturation. • scal data. the special core analysis (scal) data was derived from log analysis and relative permeability data originating from an offset field. the initial water saturation (swi) was established at 11%. the capillary pressure between gas and water (pcgw) was determined to be 0. • pvt models. three distinct compositional pvt models were utilized, corresponding to condensate yields of 20, 40, and 60 stb/mmscf, respectively. table 2 provides an overview of the initial conditions pertinent to the compositional models utilized for predictive simulations in scenarios involving depletion and gas recycling. initially, simulations are executed to confirm the stability of the models and to determine the initial quantities of gas and condensate reserves, in the absence of production or injection activities. table 3 delineates the initial quantities of gas and condensate for the nine models under consideration. table 2—initialized compositional models conditions. items gas reservoir condensate yield of 20 stb/mmscf condensate yield of 40 stb/mmscf condensate yield of 60 stb/mmscf initial pressure, psi 2400 2935 3225 datum, ft tvdss -4200 -4200 -4200 dewpoint pressure, psi 1900 2435 2725 gas water contact (gwc), ft tvdss -4700 -4700 -4700 capillary pressure @gwc 0 0 0 reservoir temperature, f 183.1 183.1 183.1 improved oil and gas recovery 8 table 3—gas and condensate initially in place for the nine models. model reservoir quality gas condensate yield, stb/mmscf initial gas in place, bscf initial condensate in place, mmstb 1 low 20 439 9 2 low 40 541 22 3 low 60 586 35 4 mid 20 659 13 5 mid 40 811 32 6 mid 60 879 53 7 high 20 834 17 8 high 40 1033 41 9 high 60 1120 67 base case operations. utilization of five wells, comprising one crestal well and four wells positioned downdip, is undertaken to establish the depletion scenario (without gas recycling), serving as the foundational case for the nine models. to investigate the impact of well geometry on condensate recovery, two foundational cases have been established. the initial foundational case is formulated with four down-dip vertical wells and a single vertical crestal well, while the second foundational case employs four down-dip horizontal wells alongside a single vertical crestal well. the production controls and constraints can be delineated as follows: • the field control production amounts to 60 mmscfd. • the maximum production capacity of the well is 20 mmscfd. • the well's constrained bottom-hole flowing pressure is 650 psi. • the economic gas and oil production rates for the well are 1 mmscfd and 20 stbd, respectively. • two stages of separation are utilized, with the first stage operating at 250 psi and 100 of, and the second at 14.7 psi and 60 of. • the forecasted production period spans 40 years, from 2024 to 2064. figures 7 to 9 depict the reservoir pressure performance and cumulative condensate production outcomes for the three gas models, which are characterized by low, intermediate, and high condensate content (20, 40, and 60 stb/mmscf, respectively), in the context of vertical and horizontal producing wells under depletion conditions. during primary production, the reservoir pressure experiences a rapid decline. condensate dropout occurs proximate to the production wells and within the reservoir pores where the pressure falls below the dew point pressure. as condensate is an immobile phase, it precipitates and results in a marked decrease in well productivity. the outcomes indicate that with an improvement in reservoir quality, cumulative condensate production increases for a given gas type (equivalent condensate yield), due to a lesser pressure drop and diminished impact of condensate blockage in reservoirs of superior quality. for reservoirs of equal quality, an escalation in gas condensate content results in elevated cumulative condensate production, ascribed to the larger volume of condensate. additionally, for identical reservoir types, the recovery of condensate from horizontal and vertical wells is equivalent, thereby affirming that well geometry does not affect condensate recovery. improved oil and gas recovery 9 figure 7—cumulative condensate production and reservoir pressure in the depletion scenario for a low-quality reservoir. figure 8—cumulative condensate production and reservoir pressure in the depletion scenario for a mid-quality reservoir. figure 9—cumulative condensate production and reservoir pressure in the depletion scenario for a for highquality reservoir. improved oil and gas recovery 10 gas recycling sensitivity analysis. utilizing a single crest well as an injector and four wells positioned down dip as producers, various gas recycling scenarios with differing proportions of dry gas injection were constructed. the dry gas composition is predominantly methane, constituting 98%, with the remaining 2% being ethane. it is presumed that 10% of the field's output is allocated for fueling generators and other equipment. consequently, 90% of the produced dry gas will be utilized for a comprehensive injection scenario. four distinct injection ratios for dry gas recycling—0.9, 0.75, 0.5, and 0.25—were employed to ascertain the optimal ratio for dry gas recycling, with two separate cases considered: one involving four vertical producing wells and the other involving four horizontal wells. the production controls and constraints can be encapsulated as follows: • the field control production amounts to 60 mmscfd. • the maximum production capacity of the well is 15 mmscfd. • the well's constrained bottom-hole flowing pressure is 650 psi. • the economic gas and oil production rates for the well are 1 mmscfd and 20 stbd, respectively. • two stages of separation are utilized, with the first stage operating at 250 psi and 100of, and the second at 14.7 psi and 60of. • the field gas re-injection ratios are 0.9, 0.75, 0.5, and 0.25, respectively. • the constrained bottom-hole injection pressure for the well is 4000 psi. • the forecasted duration of production is 40 years, spanning from 2024 to 2064. utilization of gas recycling results in greater cumulative condensate production compared to the depletion scenario, attributable to the following factors: • the preservation of reservoir pressure through gas recycling, or a reduction in the rate of pressure depletion, which subsequently diminishes the condensate dropout phenomenon; the altered composition of the reservoir fluid after the injection of dry gas, which exhibits a reduced dew point pressure; • and the vaporization of certain heavy components that precipitated out during gas extraction proximal to the wellbore. the findings indicate that as reservoir quality improves, condensate production recovery increases with the same gas type when dry gas recycling is implemented. this is attributed to a reduced pressure drop near the wellbore and a diminished impact of condensate blockage, as evidenced by figure 10. conversely, with consistent reservoir quality, an increase in the gas condensate content results in higher cumulative condensate production, as depicted in figure 11. regarding the influence of well geometry, the horizontal well presents a longer production exposure area compared to the vertical well, leading to the subsequent effects: • the pressure differential proximate to the wellbore of a horizontal well is diminished in comparison to that of a vertical well. consequently, the condensate accumulation around the horizontal wellbore is reduced, which enhances both the gas and condensate production rates. • the exposed production zone in horizontal producing wells is larger than that in vertical producing wells, leading to an earlier breakthrough of injected gas and a reduction in the condensate production rate. consequently, the production profile of condensate from horizontal wells exceeds that of vertical wells during the initial phase of production, followed by a decline over time. figure 12 illustrates the gas and condensate production profiles for horizontal and vertical wells within high-quality reservoirs, considering three gas models (20, 40, 60 stb/mmscfd condensate yield). improved oil and gas recovery 11 figure 10—cumulative condensate production and reservoir pressure under 0.9 dry gas recycling case for gas 40 stb/mmscf condensate yield. figure 11—cumulative condensate production and reservoir pressure under 0.9 dry gas recycling case for midquality reservoir. figure 12—gas and condensate production rate of horizontal and vertical wells for high-quality reservoir with the three gas models. improved oil and gas recovery 12 results four distinct dry gas recycling ratios (0.9, 0.75, 0.5, and 0.25) were employed to ascertain the optimal dry gas injection ratio for each of the nine models featuring either vertical or horizontal production wells. the findings indicate that cumulative condensate production throughout the recycling process is subject to two counteracting influences. the initial influence pertains to the maintenance of pressure and the vaporization of residual condensate resulting from dry gas recycling, which tends to augment condensate production as the injection ratio escalates. the subsequent influence is attributed to the phenomenon of dry gas breakthrough at the production sites, which tends to diminish condensate recovery as the injection ratio intensifies. consequently, the outcomes derived from the compositional models reveal varying optimal injection ratios for each gas reservoir. figure 13 depicts the relationship between cumulative condensate production and the injection ratio of dry gas in a low-quality gas reservoir, considering both vertical and horizontal production wells. in the case of vertical wells, a gas condensate yield of 20 stb/mmscf yields an optimal injection ratio of 0.5, resulting in a cumulative condensate production of 4.56 mmstb, marginally higher than the 4.53 mmstb achieved with an injection ratio of 0.75. for gas with a condensate yield of 40 stb/mmscf, the optimal injection ratio is 0.75, resulting in a cumulative condensate production of 13.23 mmstb, which is greater than the 12.61 mmstb produced with an injection ratio of 0.9. similarly, gas with a condensate yield of 60 stb/mmscf reaches its optimal injection ratio at 0.75, producing a cumulative condensate of 22.2 mmstb, exceeding the 21.44 mmstb produced with a 0.9 injection ratio. these outcomes suggest that as the condensate content rises, the optimal injection ratio also increases, a trend observed even in reservoirs of identical quality. in the context of horizontal production wells, the optimal injection ratios remain consistent with those applicable to vertical wells. nevertheless, vertical production wells exhibit superior condensate recovery in comparison to horizontal production wells when dealing with gases that yield condensate at rates of 40 and 60 stb/mmscf. this disparity can be attributed to the diminished condensate loss proximate to the wellbore in vertical wells, which are less susceptible to the incursion of dry injected gas. figure 13—accumulative condensate yield in relation to the injection ratio of dry gas for horizontal and vertical wells in a low-quality reservoir, utilizing three different gas models. the outcomes for medium-quality reservoirs suggest that they exhibit the same optimal injection ratio as their low-quality counterparts, as depicted in figure 14. in instance of gas possessing a condensate yield of 20 stb/mmscf, an injection ratio of 0.5 facilitated a cumulative condensate recovery of 7.04 mmstb. for gases with condensate yields of 40 and 60 stb/mmscf, the optimal injection ratio was determined to be 0.75, resulting in cumulative condensate recoveries of 18.24 mmstb and 29.89 mmstb, respectively. these results indicate that condensate recovery in medium-quality reservoirs surpasses that in low-quality reservoirs, attributable to improved oil and gas recovery 13 diminished pressure loss and condensate dropout. additionally, scenarios involving horizontal production wells exhibited identical optimal injection ratios and condensate recoveries to those with vertical production wells. figure 14—accumulative condensate yield in relation to the injection ratio of dry gas for horizontal and vertical wells in a mid-quality reservoir, utilizing three different gas models. figure 15 delineates the relationship between cumulative condensate production and the injection ratio of dry gas within high-quality reservoirs, substantiating that the optimal injection ratios remain uniform across reservoirs of varying quality. specifically, for gas exhibiting a condensate yield of 20 stb/mmscf, the optimal injection ratio is established at 0.5, whereas for gases with condensate yields of 40 and 60 stb/mmscf, the optimal injection ratio is determined to be 0.75. in the context of horizontal production wells, the optimal injection ratios are analogous to those observed in vertical production wells. nevertheless, horizontal wells exhibit a superior condensate recovery rate relative to vertical wells when dealing with gases that yield condensate at rates of 40 and 60 stb/mmscf. this phenomenon can be attributed to the fact that condensate losses in proximity to the wellbore are more pronounced than those resulting from the penetration of injected dry gas in such scenarios. figure 15—cumulative condensate yield in relation to the injection ratio of dry gas for both horizontal and vertical wells within a high-quality reservoir, as modeled by three distinct gas models. furthermore, the findings across all reservoir qualities indicate that condensate recovery enhances with escalating injection ratios, particularly in the case of gas exhibiting a condensate yield of 60 stb/mmscf in contrast to those with yields of 40 and 20 stb/mmscf. this enhancement is attributed to the elevated condensate improved oil and gas recovery 14 recovery attained when the reservoir pressure is sustained above the dew point, as well as to the augmented recovery of vaporized condensate. conclusions gas condensate reservoirs are of paramount importance in the oil and gas industry due to their intricate characteristics and substantial economic ramifications. a principal obstacle encountered in these reservoirs is the precipitation of heavier hydrocarbon components from the produced gas when the pressure falls beneath the dew point, which can occur proximate to the wellbore or within the reservoir's pores. this phenomenon results in diminished production efficiency. dry gas recycling stands out as one of the most economically viable and efficacious strategies to address this challenge. the present study utilized a three-dimensional compositional model to optimize the injection ratio of dry gas, with the aim of maximizing condensate recovery and net production. the model conducted a separate analysis of horizontal and vertical producing wells to assess the influence of well geometry on the optimal dry gas injection ratio and condensate recovery. the modeling outcomes suggest that the cumulative production of condensate with the implementation of dry gas recycling surpasses that are observed under depletion conditions. in the case of reservoirs characterized by varying condensate content, the cumulative recovery of condensate exhibits an increase in correlation with reservoir quality when dry gas recycling is utilized. the optimal dry gas injection ratio for low-condensate-yield gas reservoirs, (characterized by a yield of 20 stb/mmscfd, is established at 0.5 of the produced gas. conversely, for gas reservoirs with mediumand highcondensate yields, at 40 and 60 stb/mmscfd respectively, the optimal injection ratio is determined to be 0.75 of the produced gas. in reservoirs of high quality, horizontal wells exhibit a greater capacity for condensate recovery compared to vertical wells, particularly in gas reservoirs characterized by medium to high condensate yields, ranging from 40 to 60 stb/mmscfd. in contrast, within reservoirs of low quality, vertical wells demonstrate superior performance in condensate recovery relative to horizontal wells. in reservoirs of moderate quality, the efficacy of condensate recovery is comparable between horizontal and vertical wells. the results of this study offer preliminary guidelines for enhancing the optimization of gas-recycling ratios and may serve as a basis for subsequent research that integrates actual reservoir characteristics, operational parameters, and economic factors. abbreviations 3d three dimensions. stb stock tank barrel. mmscf million standard cubic feet. pvt pressure volume temperature. gwc gas water contact. tvdss true vertical depth sub sea. ft feet. md mile darcy. eos equation of state. cce constant composition expansion. cvd constant volume depletion. scal special core analysis log. improved oil and gas recovery 15 conflicting interests the author(s) declare that they have no conflicting interests. references aaditya, k. 2014. effect of reservoir and completion parameters on production performance in gas condensate reservoirs. master thesis,university of houston, houston, texas, usa. 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characterization on equations of state predictions. spe journal 24(6):685696. improved oil and gas recovery 17 wood, a.r.o. and young, m.s. 1988. the role of reservoir simulation in the development of some major north sea fields. paper presented at the international meeting on petroleum engineering, tianjin, china, 1-3 november. spe-17613-ms. yang, y., lun, z., wang, r., et al. 2024. a new model simulating the development of gas condensate reservoirs. energy geoscience 5(1):100149. zhao, h., zhang, x., gao, x., et al. 2024. a novel method for the quantitative evaluation of retrograde condensate pollution in condensate gas reservoirs. processes 12(1):522-538. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1346 received december 10, 2024; revised february 10, 2025; accepted february 23, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 investigation of oryza glaberrima nanoparticle-assisted fluid loss control in water-based drilling mud anthony kerunwa, bright udochi k. emenike, azunna i.b. ekejiuba, nnaemeka uwaezuoke, christain emelu okalla, chukwuebuka francis dike*, federal university of technology owerri, owerri, nigeria abstract drilling mud (dm) serves critical functions in wellbore operations, including drill cuttings removal, borehole stability maintenance, bit cooling, drillstring lubrication, hydraulic energy transmission, and formation of lowpermeability filter cakes to mitigate fluid loss. while conventional additives like carboxymethyl cellulose (cmc) and polyanionic cellulose (pac) are widely used for filtration control, their high cost and environmental drawbacks necessitate sustainable alternatives. this study evaluates the efficacy of oryza glaberrima (african rice husk, rh)-nanosilica (ns) composites as fluid loss control agents in water-based drilling mud (wbm). comparative analyses with cmc and pac were conducted using fourier transform infrared spectroscopy (ftir), x-ray diffraction (xrd), fluid loss tests, and mud cake characterization. results demonstrate that the rh-ns blend achieved superior fluid loss reduction (7.5 ml) compared to cmc (9.8 ml) and pac (8 ml). additionally, rh-ns exhibited favorable mud cake properties, with a thickness of 0.4 mm and permeability of 0.00068 md, outperforming standalone rh (12 ml, 0.4 mm, 0.00061 md) and ns (16 ml, 0.8 mm, 0.00271 md). the synergistic interaction between rh-derived cellulose and ns nanoparticles highlights the potential of eco-friendly, cost-effective alternatives for optimizing wbm performance. introduction drilling fluid, commonly referred to as "drilling mud," plays a pivotal role in oil and gas drilling operations (finger and blankenship 2010). its primary functions include removing drill cuttings, preventing the influx of formation fluids into the wellbore, cooling and lubricating the drill bit and drillstring, transmitting hydraulic energy to the bit, maintaining wellbore stability, and forming a thin, low-permeability filter cake to minimize fluid loss (kerunwa and gbaranbiri 2018). drilling mud is broadly categorized into water-based drilling mud (wb-dm), oil-based drilling mud (ob-dm), and pneumatic-based drilling mud (pb-dm). among these, wbdm is predominantly favored due to its lower environmental impact (kerunwa 2020). the design of effective drilling mud requires careful consideration of its key properties, including density (weight), rheology (viscosity and gel strength), and filtration control. additional parameters such as ph (alkalinity and acidity), chloride content, calcium content (hard water), and sand content also play critical roles in optimizing mud performance (igwillo 2000). among these properties, filtration control has garnered significant global attention due to its critical role in maintaining wellbore integrity during circulation. filtration loss, defined as the loss of the continuous phase of the drilling mud into the formation, remains a major challenge in drilling operations, particularly in deeper wells. severe filtration loss can lead to detrimental consequences such as lost circulation, differential pipe sticking, formation damage, mud weight reduction, reduced formation flow rates, and even well control issues like kicks and blowouts (igbani et al. 2015). mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 to mitigate filtration loss, various additives are incorporated into drilling mud formulations (azar and samuel 2007). these additives aim to form a low-permeability filter cake, a phenomenon known as filtration loss control (feng et al. 2009; agwu and akpabio 2018). conventional fluid loss control additives, such as polyanionic cellulose (pac) and carboxymethyl cellulose (cmc), have been widely used (caenn and chillinger 1996). however, their environmental impact and cost inefficiency have driven the search for more sustainable and costeffective alternatives, particularly locally sourced materials (kerunwa et al. 2024). several studies have explored the use of natural materials as fluid loss control additives. for instance, olatunde et al. (2012) investigated gum arabic, reporting a fluid loss of 17 ml. okon et al. (2014) evaluated rice husk (125 µm) and observed fluid losses ranging from 16 to 42.5 ml at concentrations of 5-20 grams. nmegbu and bariagara (2014) tested corn cob cellulose, achieving fluid losses of 5.8 ml at 2-3 grams. chinwuba et al. (2016) studied pleurotus tuber-regium, recording fluid losses of 8-10.8 ml at 5-6 grams. okon et al. (2020) compared rice husk (rh), detarium microcarpum (dm), brachystegia eurycoma (be), and cmc, with rh demonstrating the best performance at 2.8 ml, compared to 4.5 ml, 7.3 ml, and 4.2 ml for dm, be, and cmc, respectively. chinwuba et al. (2021) further evaluated a blend of local bentonite with periwinkle shell and mucuna solannie, achieving a fluid loss of 12 ml. ikram et al. (2021) tested okra and starch, with okra yielding fluid losses of 20.8 ml, 17.6 ml, and 17 ml at concentrations of 0.25%, 0.5%, and 1% by weight, respectively, while starch recorded 18.8 ml at 0.25% concentration. kerunwa et al. (2023) investigated coconut fiber (cf) and corn cobs (cc), with a cf-cc blend achieving the best performance at 8 ml, compared to 8.6 ml, 14 ml, and 10.2 ml for cmc, cf, and cc, respectively. in recent years, nanoparticles have emerged as promising fluid loss control additives due to their unique properties, such as high surface area and tunable surface chemistry (uwaezuoke 2022). ismail (2016) demonstrated the effectiveness of nanosilica, achieving a fluid loss of 7 ml and a gel strength of 7 pa. dejtaradon et al. (2019) evaluated zinc oxide (zno) nanoparticles, reporting a fluid loss of 14 ml and gel strengths of 15-37 pa. cheraghian et al. (2019) studied silica nanoparticles, achieving a fluid loss of 10 ml and gel strengths of 13– 32 pa. gbadamosi et al. (2019) further confirmed the efficacy of silica nanoparticles, with a fluid loss of 5.1 ml and gel strengths of 7-8 pa. this study investigates the fluid loss control performance of oryza glaberrima-derived nanoparticles blended with silica oxide, comparing their efficacy with conventional additives such as carboxymethyl cellulose (cmc) and polyanionic cellulose (pac). the evaluation is based on fourier transform infrared spectroscopy (ftir), x-ray diffraction (xrd), and low pressure-low temperature (lplt) fluid loss tests. the findings aim to provide insights into the potential of oryza glaberrima nanoparticles as a sustainable and efficient alternative for fluid loss control in water-based drilling muds. materials and methods the materials used in this study include: 1. fluid loss control additives: rice husk (rh) (local fluid loss control additive), nanosilica, conventional fluid loss control additives, such as polyanionic cellulose (pac-r) and carboxymethyl cellulose (cmc). 2. drilling fluid components: barite (density control), bentonite (viscosifier), calcium carbonate, sodium hydroxide (ph control agent), water (continuous phase). 3. laboratory equipment and tools: buck 530 ir-spectrophotometer, mud balance, rotary viscometer, agitator, spatula, small teaspoon, sand content tube, sieve and sieve shaker, weighing balance, washing bucket, gas oven, tray pan, measuring cylinder, stopwatch, mixer, grinding machine, ph paper, metre rule, low temperature low pressure (ltlp) api filter press. sourcing and preparation of fluid loss control additives. sourcing of materials. cmc, pac-r, and nanosilica were produced from an industrial chemical store. rice husk (rh) sourced from a milling factory in abakaliki, ebonyi state, nigeria, and transported to the laboratory for processing. improved oil and gas recovery 3 preparation of rice husk (rh): in the laboratory, unwanted particles and debris were manually removed from the rh to ensure purity. the cleaned rh was dried in a laboratory oven at 50°c for 72 hours to reduce its moisture content. the dried rh was ground into fine particles using an industrial blender. the pulverized rh was sieved using a us 250-mesh sieve to obtain uniformly sized particles. finally, the uniform rh particles were collected in airtight bottles and stored at room temperature for further use. figure 1 illustrates the rh before and after the treatment process, highlighting the transformation from raw material to a refined fluid loss control additive. (a)natural rh (before) (b)pulverized rh (after) figure 1--rh before and after treatment. fourier transform infrared spectroscopy. fourier transform infrared (ftir) analysis was conducted using an ir-spectrophotometer to characterize the molecular structure and chemical bonds of the selected materials, including rice husk (rh), nanosilica (ns), rice husk-nanosilica blend (rh-ns), polyanionic cellulose (pacr), and carboxymethyl cellulose (cmc). the ftir analysis generated absorbance spectra plots, which reveal the unique molecular arrangements and chemical bonds present in each material. the spectra exhibit distinct peaks corresponding to specific functional groups, such as alkanes, ketones, chlorides, and carboxylic acids. these functional groups absorb infrared radiation at characteristic wavelengths, allowing for their identification. the obtained spectra were cross-referenced with a standard reference library to determine the functional groups present in each material. x-ray diffraction. x-ray diffraction (xrd) was employed to analyze the chemical composition and physical properties of the test samples. the xrd analysis was performed as follows: instrument setup. the xrd device was powered on, and the operating parameters were set to a voltage of 45 kv, a current of 40 ma, and a temperature of 21 ± 2°c. software initialization. the computer system was switched on, and the xrd software was launched to initiate the analysis. sample preparation. the rh sample was ground into a fine powder and placed into the sample holder, which was then positioned in the sample chamber column. measurement settings. the scan axis was set to gonio, and the start and end positions, scan angle, and scan time were configured. analysis execution. the scan was initiated and allowed to run for the specified duration. upon completion, the results were saved for further analysis. mud formulation. for the fluid loss experimental evaluation, five distinct water-based mud (wbm) samples were formulated: (1) rh-wbm: containing rice husk as the fluid loss control additive. (2) ns-wbm: containing nanosilica as the fluid loss control additive. (3) cmc-wbm: containing carboxymethyl cellulose as the fluid loss control additive. (4) pac-r-wbm: containing polyanionic cellulose as the fluid loss control additive. improved oil and gas recovery 4 (5) rh-ns-wbm: containing a blend of rice husk and nanosilica as the fluid loss control additive. the detailed formulation of each mud sample, including the concentrations of additives and base components, is provided in table 1. table 1—fluid loss control additive formulation utilized for the study. s/n mud-type pac-r cmc rh ns 1 pac-r 0.5g, 1g, 1.5g, 2g nil nil nil 2 cmc nil 0.5g, 1g, 1.5g, 2g nil nil 3 rh nil nil 2g, 4g, 6g, 8g nil 4 ns nil nil nil 2g, 4g, 6g, 8g 5 rh-ns nil nil 7.5g 0.5g 6 rh-ns nil nil 7.0g 1.0g 7 rh-ns nil nil 6.5g 1.5g 8 rh-ns nil nil 6.0g 2.0g mixing procedure of mud sample formulation. the mud samples were prepared following a standardized mixing procedure to ensure consistency and reproducibility. first, the required quantities of additives, as specified in table 1, were accurately weighed using a precision weighing balance. next, 300 ml of distilled water, as detailed in table 2, was measured using a scientific measuring cylinder. the measured distilled water was then poured into a mud cup and placed on a hamilton beach mixer, which was activated to agitate the water at a consistent speed. to begin the formulation, 25 grams of bentonite were gradually added to the agitated water, and the mixture was allowed to mix thoroughly for 5 minutes to ensure complete hydration of the bentonite. following this, 0.5 grams of sodium hydroxide (naoh) and 10 grams of calcium carbonate (caco3) were added to the slurry, and the mixture was agitated for an additional 2 minutes to achieve homogeneity. for the incorporation of fluid loss control additives, 0.5 grams of polyanionic cellulose (pac-r) were introduced to the slurry, and the mixture was agitated for 3 minutes to ensure uniform dispersion of the additive. this procedure was repeated for the preparation of mud samples containing other fluid loss control additives, including carboxymethyl cellulose (cmc), rice husk (rh), nanosilica (ns), and the rice husk-nanosilica blend (rh-ns), as outlined in table 1. table 2—composition of other additives utilized for wbm formulation. s/n additives function concentration 1 water (ml) base fluid 300ml 2 bentonite viscosifier 25g 3 caco3 bridging agent 10g 4 naoh ph enhancer 0.5g mud filtration test. the mud filtration analysis was conducted under lplt conditions using api filter press depicted in figure 1. the filter press is utilized for the experiment and consists of 6 independent filter cells, placed on a system. the cells were cleaned and dried to remove unwanted particles, while the rubber gasket was inspected to ensure compliance. the dried cells were coupled-up using the following sequence base-cup, followed by rubber-gasket, followed by screen, followed by filter paper, followed by rubber gasket and finally the cell body. 130ml of the formulated dm with additives from table 1 and 2 was introduced to the cell before being improved oil and gas recovery 5 placed into the base and tightened to ensure closure. 50ml measuring cylinder was placed at the bottom of the cell to recover filtration. the cell was pressurized to 100psi before the filtrate volume was derived after 30 minutes. figure 2—api filter press. filter cake analysis. the formulated mud on the filter paper on the mud after the filtration loss experiment was qualitatively and quantitatively evaluated using api concepts. the qualitative approach for the filter cake was conducted by viewing and touching the mud cake to determine its nature, while the quantitative approach was conducted by deriving the thickness of the mud cake in mm. mud cake permeability test. the mud cake was derived using lomba (2010) formulation for wbm. k = 8.95 ∗ 10−5qwμε,.....................................................................................................................................(1) whrer k, qw, μ and ε represents mud cake permeability (md), mud filtrate volume (cm3), mud filtrate viscosity (cp) and mud cake thickness (mm). results and discussion ftir characterization analysis. the fourier transform infrared (ftir) spectra for carboxymethyl cellulose (cmc), polyanionic cellulose (pac-r), rice husk (rh), nanosilica (ns), and the rice husk-nanosilica blend (rh-ns) in water-based mud (wbm) are presented in figures 3 to 7. the ftir analysis revealed the presence of distinct functional groups in each material, which are critical for understanding their chemical interactions and fluid loss control mechanisms. the ftir spectrum of cmc (figure 3) exhibited characteristic peaks corresponding to functional groups such as carboxyl (–cooh), hydroxyl (–oh), sp hybridizing carbon (c≡c or c≡n), aromatic rings (c=c), and carbonyl (c=o) bonds. these groups are indicative of cmc's polymeric structure and its ability to form hydrogen bonds, which contribute to its effectiveness as a fluid loss control additive. similarly, the spectrum of pac-r (figure 4) showed the presence of carboxyl (–cooh), sp hybridizing carbon (c≡c or c≡n), aromatic rings (c=c), and hydroxyl (–oh) groups. these functional groups are consistent with the chemical structure of pacr, enabling it to interact effectively with clay particles and form a stable filter cake. improved oil and gas recovery 6 figure 3—ftir spectra for cmc wbm sample. figure 4—ftir spectra for pac-r wbm sample. the ftir analysis of rh (figure 5) revealed the presence of carboxyl (–cooh), sp hybridizing carbon (c≡ c or c≡n), and hydroxyl (–oh) groups. these functional groups are attributed to the organic components of rice husk, such as cellulose, hemicellulose, and lignin, which contribute to its fluid loss control properties. in the case of ns (figure 6), the spectrum displayed peaks corresponding to hydroxyl (–oh), sp hybridizing carbon (c ≡c or c≡n), and carboxyl (–cooh) groups. these groups are associated with the surface chemistry of nanosilica, which enhances its ability to adsorb clay particles and reduce fluid loss. the ftir spectrum of the rh-ns blend (figure 7) showed the presence of carboxyl (–cooh), hydroxyl (– oh), sp hybridizing carbon (c≡c or c≡n), and aromatic rings (c=c). the presence of these functional groups, which are also found in cmc and pac-r, suggests that the rh-ns blend exhibits similar chemical interactions and bonding mechanisms. this similarity likely contributes to its competitive performance as a fluid loss control additive. key observations from the ftir analysis include the identification of functional groups such as carboxyl, hydroxyl, and sp hybridizing carbon in rh, ns, and rh-ns, which are also present in cmc and pac-r. this indicates that these materials share similar chemical properties, essential for effective fluid loss control. the presence of hydroxyl and carboxyl groups in all materials suggests their ability to form hydrogen bonds with water molecules and clay particles, enhancing their ability to stabilize the drilling fluid and reduce fluid loss. additionally, the aromatic and sp hybridizing carbon groups observed in cmc, pac-r, and rh-ns further improved oil and gas recovery 7 highlight their potential for forming strong intermolecular interactions, which are critical for maintaining wellbore stability and minimizing fluid invasion into the formation. figure 5—ftir spectra for rh wbm sample. figure 6—ftir spectra for ns wbm sample. figure 7—ftir spectra for rh assisted ns wbm sample. improved oil and gas recovery 8 as observed, the ftir analysis provides valuable insights into the chemical composition and functional groups of the tested materials, demonstrating that rh-ns exhibits chemical properties comparable to conventional additives like cmc and pac-r. this supports its potential as a sustainable and effective alternative for fluid loss control in water-based drilling fluids. x-ray diffraction (xrd) analysis. table 3 presents the x-ray diffraction (xrd) results for carboxymethyl cellulose (cmc), polyanionic cellulose (pac), and the nanosilica-rice husk blend (ns-rh) in water-based mud (wbm). the xrd analysis provides insights into the mineralogical composition and crystalline structure of these materials, which are critical for understanding their performance as fluid loss control additives. cmc exhibited a diverse mineral composition, including quartz (42%), muscovite (11.1%), anorthite (5.8%), anthophyllite (3.14%), calcite (10.4%), orthoclase (11.3%), vermiculite (9.5%), and garnet (3.9%). the high percentage of quartz and the presence of minerals such as muscovite and orthoclase indicate a well-defined crystalline structure, which contributes to cmc's stability and effectiveness in fluid loss control. similarly, pac showed a mineral composition dominating by quartz (48%), with significant amounts of orthoclase (23%) and calcite (8%). other minerals, such as muscovite (3%), anorthite (5%), anthophyllite (5%), vermiculite (6%), and garnet (0.1%), were also present. the high quartz content and the presence of orthoclase suggest a robust crystalline framework, which enhances pac's ability to form a stable filter cake. table 3—xrd analysis of the materials utilized for the study. cmc-wbm pac(r)-wbm rh+ns-wbm mineral composition (%) mineral composition (%) mineral composition (%) quartz 42(3) quartz 48(106) quartz 42(3) muscovite 11.1(7) muscovite 3(6) muscovite 4.7(7) anorthite 5.8(6) anorthite 5(10) anorthite 8(2) anthophyllite 3.14(19) anthophyllite 5(19) anthophyllite 3.0(4) calcite 10.4(12) calcite 8(17) calcite 19(2) orthoclase 11.3(7) orthoclase 23(80) orthoclase 7.3(10) vermiculite 9.5(7) vermiculite 6(11) clinochlore 3. 8(11) osumilite 3.12(16) osumilite 3(6) osumilite 1.5(5) garnet 3.9(10) garnet 0.1(2) garnet 10.3(12) the ns-rh blend recorded a mineral composition of quartz (42%), muscovite (4.7%), anorthite (8%), anthophyllite (3%), calcite (19%), orthoclase (7.3%), vermiculite (3.8%), and garnet (10.3%). notably, nsrh exhibited a similar percentage of quartz (42%) and anthophyllite (3%) as cmc, along with comparable amounts of other minerals such as calcite and orthoclase. this indicates that ns-rh shares a similar crystalline structure with cmc and pac, which is essential for effective fluid loss control. the presence of well-defined crystalline minerals such as quartz, orthoclase, and calcite in all three materials (cmc, pac, and ns-rh) improved oil and gas recovery 9 indicates a strong and stable crystal composition. this is critical for maintaining the integrity of the filter cake and minimizing fluid loss during drilling operations. the similarity in mineral composition between ns-rh and conventional additives like cmc and pac highlights its potential as a sustainable and effective alternative for fluid loss control. the presence of calcite (19%) in ns-rh, which is higher than in cmc (10.4%) and pac (8%), may further enhance its ability to interact with carbonate formations, improving its performance in specific drilling environments. the xrd analysis confirms that cmc, pac, and ns-rh exhibit good crystalline compositions, with ns-rh showing a mineralogical profile like that of conventional additives. this similarity, combined with the unique mineral composition of ns-rh, supports its potential as a viable and sustainable alternative for fluid loss control in waterbased drilling fluids. the findings underscore the importance of mineralogical composition in designing effective drilling fluid additives and highlight the promising role of ns-rh in advancing environmentally friendly drilling practices. filtration loss analysis. figure 8 illustrates the fluid loss control performance of rice husk (rh), nanosilica (ns), polyanionic cellulose (pac-r), and carboxymethyl cellulose (cmc) in water-based mud (wbm). the initial fluid loss volume of the drilling mud was 40 ml, which was significantly reduced upon the addition of the tested additives. for cmc-wbm, the fluid loss volume decreased to 12 ml, 10.5 ml, 10 ml, and 9.8 ml when 0.5 g, 1.0 g, 1.5 g, and 2 g of cmc were introduced, respectively. similarly, pac-r-wbm demonstrated a reduction in fluid loss volume to 18 ml, 11 ml, 9 ml, and 8 ml at the same concentrations. in the case of ns-wbm, the fluid loss volume was reduced to 20 ml, 18.9 ml, 17 ml, and 16 ml at 2 g, 4 g, 6 g, and 8 g, respectively. rh-wbm also showed a notable reduction in fluid loss volume, achieving 19.5 ml, 17 ml, 15.8 ml, and 12 ml at 2 g, 4 g, 6 g, and 8 g, respectively. as observed in figure 8, pac-r-wbm recorded the best fluid loss control performance, achieving the lowest fluid loss volume of 8 ml at 2 g. in comparison, cmc-wbm, ns-wbm, and rh-wbm recorded fluid loss volumes of 9.8 ml, 16 ml, and 12 ml, respectively, at their optimal concentrations. the superior performance of pac-r-wbm can be attributed to the ability of pac to form a higher cellulose content when used as an additive, which enhances its ability to create a low-permeability filter cake and effectively reduce fluid loss (agwu et al. 2019). figure 8—fluid loss control performance of rh, ns, pac-r and cmc. figure 9 demonstrates the fluid loss control performance of rice husk (rh) water-based mud (wbm) when partially replaced by nanosilica (ns) at varying concentrations. the replacement of 0.5 g of rh with 0.5 g of ns 0 5 10 15 20 25 30 35 40 45 cmc pac-r control mud n.s rh filtrate volume (ml) f lu id l o ss c o n tr o l a d d it v e 8g 6g 4g 2g 1.5g 1g 0.5g 0g improved oil and gas recovery 10 resulted in a reduction of fluid loss volume from 12 ml to 11.2 ml. further replacement studies using 1 g, 1.5 g, and 2 g of ns showed a progressive decrease in fluid loss volume to 10 ml, 9.8 ml, and 7.5 ml, respectively. when compared to the fluid loss volumes of rh, pac, and cmc, the rh-ns blends consistently recorded lower fluid loss volumes. this enhanced performance can be attributed to the synergistic combination of the cellulose effect of rh and the sealing effect of ns. the cellulose content in rh contributes to the formation of a stable filter cake, while the nanosilica particles effectively seal micro-fractures and pores in the formation, reducing the volume of the continuous phase lost to the formation. the optimal proportion of rh and ns in the blend ensures a balanced interaction between these mechanisms, resulting in superior fluid loss control performance. figure 9—fluid loss control performance of various rh assisted ns at various concentration. mud cake thickness analysis. figure 10 illustrates the mud cake thickness for cmc, pac, rh, ns, and rhns at varying concentrations. the results highlight the influence of additive type and concentration on the formation and thickness of the mud cake, which is critical for effective fluid loss control. for cmc, the mud cake thickness decreased from 0.6 mm at 0.5 g to 0.4 mm, 0.4 mm, and 0.3 mm at 1 g, 1.5 g, and 2 g, respectively. similarly, pac exhibited a reduction in mud cake thickness from 0.8 mm at 0.5 g to 0.6 mm, 0.4 mm, and 0.3 mm at 1 g, 1.5 g, and 2 g, respectively. these results indicate that both cmc and pac are effective in forming thin and stable mud cakes at higher concentrations, which is essential for minimizing fluid loss. in the case of rh, the mud cake thickness decreased from 0.8 mm at 2 g to 0.7 mm, 0.6 mm, and 0.4 mm at 4 g, 6 g, and 8 g, respectively. this demonstrates that increasing the concentration of rh leads to the formation of thinner mud cakes, enhancing its fluid loss control performance. conversely, ns showed a different trend, with the mud cake thickness remaining constant at 0.8 mm from 2 g to 4 g, before increasing to 1 mm and 1.1 mm at 6 g and 8 g, respectively. this increase in thickness at higher concentrations may be attributed to the agglomeration of nanosilica particles, which can hinder the formation of a compact filter cake. the rh-ns blend exhibited a mud cake thickness of 1.1 mm at a concentration ratio of 7.5 g rh to 0.5 g ns, which remained constant at 7.0 g rh to 1.0 g ns. however, the thickness decreased to 0.6 mm and 0.4 mm at concentration ratios of 6.5 g rh to 1.5 g ns and 6.0 g rh to 2.0 g ns, respectively. this suggests that the optimal proportion of rh and ns in the blend is crucial for achieving a thin and effective mud cake. the consistent formation of thinner mud cakes by cmc and pac at higher concentrations was observed, demonstrating their effectiveness as fluid loss control additives. rh also showed a reduction in mud cake thickness with increasing concentration, highlighting its potential as a sustainable alternative. however, ns exhibited an increase in mud cake thickness at higher concentrations, likely due to particle agglomeration, which may limit its effectiveness. the rh-ns blend achieved the thinnest mud cake (0.4 mm) at a concentration ratio 0 2 4 6 8 10 12 7.5g:0.5g 7.0g:1.0g 6.5g:1.5g 6.0g:2.0g f lu id v o lu m e (m l) rh:ns concentration improved oil and gas recovery 11 of 6.0 g rh to 2.0 g ns, indicating that the synergistic combination of rh and ns can enhance fluid loss control performance. the mud cake thickness analysis underscores the importance of additive type and concentration in optimizing fluid loss control. the rh-ns blend demonstrates promising potential as a sustainable and effective alternative to conventional additives like cmc and pac. figure 10—mud cake thickness of cmc, pac, rh-ns, rh and ns. combining figures 8 to 10, cmc, pac, rh-ns and rh recorded continuous reduction in mud cake thickness and fluid volume with increase in concentration. the reduction in mud cake thickness can be attributed to the ability of the mud to form thin filter cake to prevent loss of the continuous phase of the formation and is in-line with kerunwa et al. (2024) study. ns however recorded an increase in mud cake thickness and reduction in fluid loss volume with increase in concentration. this can be attributed to depositional effects of the nanoparticles which reduce fluid volume but stacks up to form thicker filter cake. mud cake permeability. figure 11 illustrates the mud cake permeability of rice husk (rh), nanosilica (ns), and the rice husk-nanosilica blend (rh-ns) in water-based mud (wbm). as shown in the figure, rh exhibited a permeability of 0.002 md at 2 g. increasing the concentration to 4 g, 6 g, and 8 g resulted in a progressive reduction in permeability to 0.0015 md, 0.0012 md, and 0.00061 md, respectively. similarly, ns recorded a permeability of 0.00286 md at 2 g. when the concentration was increased to 4 g, the permeability decreased slightly to 0.00271 md. however, further increases to 6 g and 8 g led to an inconsistent trend, with permeability rising to 0.00304 md at 6 g before decreasing to 0.00295 md at 8 g. in contrast, the rh-ns blend demonstrated a more consistent reduction in permeability with increasing concentration. at a concentration ratio of 7.5 g rh to 0.5 g ns, the permeability was 0.00278 md. this value decreased to 0.0025 md, 0.00133 md, and 0.00068 md at concentration ratios of 7.0 g rh to 1.0 g ns, 6.5 g rh to 1.5 g ns, and 6.0 g rh to 2.0 g ns, respectively. the continuous reduction in mud cake permeability for rh and rh-ns can be attributed to the formation of a compact and low-permeability filter cake, which effectively inhibits the flow of the continuous phase into the formation. this is critical for minimizing fluid loss and preventing issues such as reduced oil productivity and formation damage (kosynkin et al. 2012). on the other hand, the inconsistent permeability values observed for ns are likely due to the nature and stacking behavior of the nanoparticles, which can lead to uneven particle distribution and agglomeration at higher concentrations. comparing the results from figures 8 through 11, the reduction in fluid loss volume for rh and rh-ns is closely linked to the formation of thin, low-permeability filter cakes. these filter cakes act as effective barriers, 0 0.2 0.4 0.6 0.8 1 1.2 cmc pac rh-ns rh ns m u d c a k e t h ic k n es s (m m ) fluid loss control additive 0.5g 1.0g 1.5g 2g 4g 6g 8.0g 7.5g + 0.5g 7.0g + 1.0g 6.5g + 1.5g 6.0g + 2.0g improved oil and gas recovery 12 preventing the continuous phase from invading the formation and thereby mitigating potential drilling challenges. the superior performance of rh-ns, in particular, highlights its potential as a sustainable and efficient alternative for fluid loss control in water-based drilling fluids. figure 11—mud cake permeability of rh, ns and rh-assisted-ns. conclusion based on the experimental study conducted with the selected materials, the following conclusions can be drawn: 1. the incorporation of nanosilica (ns) into rice husk (rh) significantly improved its fluid loss control capabilities, enabling it to compete effectively with conventional additives such as polyanionic cellulose (pac) and carboxymethyl cellulose (cmc). 2. the fourier transform infrared spectroscopy (ftir) study revealed that the rh-ns blend exhibited functional groups such as carboxyl, hydroxyl, and sp hybridizing carbon, which are also present in cmc and pac-r. this indicates similar chemical bonding and molecular interactions, contributing to its effectiveness as a fluid loss control additive. 3. the x-ray diffraction (xrd) study demonstrated that cmc, pac, and rh-ns possess well-defined crystalline structures, confirming their stable and effective chemical compositions. 4. the fluid loss study showed that the rh-ns blend outperformed other additives, reducing fluid loss to 7.5 ml. in comparison, rh, ns, pac, and cmc recorded fluid losses of 12 ml, 16 ml, 8 ml, and 9.8 ml, respectively. 5. the study of mud cake thickness indicated that cmc and pac formed thinner mud cakes (0.3 mm), while rh-ns, rh, and ns produced slightly thicker mud cakes of 0.4 mm, 0.4 mm, and 0.8 mm, respectively. 6. the permeability study of the mud cakes revealed that rh, ns, and rh-ns exhibited low permeability values of 0.00061 md, 0.00271 md, and 0.00068 md, respectively. these results suggest that the rh-ns blend effectively forms a low-permeability filter cake, further enhancing its fluid loss control performance. in summary, the rh-ns blend demonstrated superior fluid loss control performance, comparable chemical properties to conventional additives, and the ability to form a low-permeability filter cake. these findings highlight its potential as a sustainable and efficient alternative to traditional fluid loss control additives in waterbased drilling fluids. conflicting interests the author(s) declare that they have no conflicting interests. 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 rh ns rh-ns p er m ea b il it y ( m d ) fluid loss control additive 2g 4g 6g 8g 8g(7.5:0.5) 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the locally sourced materials as fluid loss control additives in water-based drilling fluid. heliyon 6(5):201-215. olatunde, a.o., usman, m.a., olafadehan, o.a., et al. 2012. improvement of rheological properties of drilling fluid using locally based materials. j. petroleum coal 54(1): 65-75. uwaezuoke, n. 2022. polymeric nanoparticles in drilling fluid technology. in drilling engineering and technologyrecent advances, new perspectives and applications, ed. zoveidavianpoo, m., chap. 1, 1-15. london: intechopen. anthony kerunwa is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum improved oil and gas recovery 14 economics. dr. kerunwa holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, a master’s degree in petroleum engineering from federal university of technology owerri, and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. bright udochi k. emenike is a master’s candidate at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluid technology. emenike holds a bachelor’s degree in petroleum engineering from federal university of technology owerri. azunna i.b. ekejiuba is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling optimization, fluid hydraulics, enhanced production & optimization, multiphase flow modeling and natural gas processing for domestic and industrial application. dr. ekejiuba has bachelor’s degree in petroleum engineering from university of ibadan, master’s degree in petroleum engineering from university of port harcourt, and phd degree in petroleum and gas engineering from university of port harcourt. nnaemeka uwaezuoke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling and well engineering. dr. uwaezuoke holds a bachelor’s degree in petroleum engineering from federal university of technology owerri, nigeria, master’s degree in petroleum engineering from university of stavanger, norway, and a phd degree in petroleum engineering from federal university of technology owerri, nigeria. christain emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri, with research interest in drilling, production, natural gas and reservoir simulation. he holds a bachelor’s degree in petroleum engineering and master’s degree in petroleum engineering from federal university of technology owerri. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri. he has research interest in drilling, drilling fluids technology, reservoir engineering, enhanced oil recovery and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1374 received march 8, 2025; revised april 10, 2025; accepted july 23, 2025. *corresponding author: lnhnam@hcmut.edu.vn 1 evaluation of orange peel as eco-friendly additive: impact of concentration, particle size, and temperature on drilling fluid performance nam nguyen hai le*, le nguyen hoang duy, and pham thi van phung, ho chi minh city university of technology, vietnam national university ho chi minh city, ho chi minh city, vietnam abstract drilling fluids play a crucial role in petroleum drilling operations, serving to maintain wellbore pressure, cleanse the wellbore by transporting cuttings to the surface, cool the drill bit while reducing friction, and stabilize the geological formation. despite their superior lubricity, salt tolerance, thermal stability, and shale inhibition properties, oil-based muds are subject to stringent regulatory constraints due to their environmental and health risks. consequently, the industry is actively pursuing more environmentally friendly alternatives. this paper presents the utilization of orange peel powder (opp) as a biodegradable additive in water-based mud to improve rheological and filtration properties. opp was tested in three particle sizes at 1%wt and in five concentrations (0.5-1.5%wt). rheological experiments at three different temperatures employed bingham plastic, power law, and hershel-bulkley models. smaller opp particles reduced fluid volume by approximately 3% and fluid loss by up to 11% compared to the base sample. the hershel-bulkley model provided the best fit, indicating that higher additive concentrations (>1%wt) increased viscosity but improved fluid loss by up to 20% at 1.5%wt. elevating temperature decreased viscosity but increased yield stress, enhancing cuttings transport. consequently, higher flow index (n) values at elevated temperatures suggested a transition toward more newtonian-like fluid behavior. the study highlights the potential of opp as a sustainable alternative to conventional chemical additives, contributing to reduced environmental impact in drilling operations. the comprehensive evaluation of opp's performance across varying particle sizes and concentrations, combined with temperature effects, provides insights into its optimization for specific drilling conditions. future work could explore the long-term stability of opp-modified muds and their compatibility with other drilling fluid components, further solidifying the practical application of this green technology. introduction drilling fluids are critical to petroleum drilling, where they maintain wellbore pressure, clean the well hole by transport cuttings up to surface, cool and mitigate the friction applied on drill bit, and stabilize the formation (sehly et al. 2015; baltoiu et al. 2008). these muds are typically classified into water-based muds (wbms) and oil-based muds (obms). currently, about 80% of drilled wells use wbms, whereas only 15% rely on obms composed of mineral oil or diesel suspended with polymers (caenn et al. 2011). although obms excel in lubricity, salt tolerance, thermal stability, and shale inhibition (fornasier et al. 2017), their environmental and health hazards (almudhhi 2016; okoro et al. 2022; pilgun and aramelev 2013; fornasier et al. 2017) have prompted strict regulatory limitations, motivating the industry to seek greener alternatives. mailto:lnhnam@hcmut.edu.vn improved oil and gas recovery 2 wbms are considered cost-effective and more environmentally benign. however, they often struggle in hightemperature or reactive shale environments and can lack sufficient cuttings suspension (aftab et al. 2017). conventional chemical additives—such as polyamines, chromium compounds, potassium-based salts, and other fluid-loss agents are typically expensive and pose environmental risks if not managed properly (nguyen et al. 2023). consequently, there is a growing focus on replacing these additives with sustainable bioproducts or wastebased materials to minimize ecological impact (shafiq et al. 2024). table 1 summarizes recent research on natural additives for drilling fluids, including okra mucilage, banana peel, and potato peel. these studies highlight improvements in rheological measurement parameters, to some extent, in filtration and friction reduction. among these additives, orange peel powder has shown promise in enhancing rheological properties and reducing fluid loss. with global orange production exceeding 60 million tons annually—and approximately 32 million tons of peel waste generated—orange peel presents a plentiful, low-cost resource. nevertheless, previous investigations have not thoroughly examined how op particle size and varying temperatures influence drilling fluid properties. temperature stability is critical for hightemperature drilling, where polymer degradation can compromise fluid performance (ali et al. 2022). this gap is especially pertinent for bentonite-based systems, where the interaction of op and temperature on rheological behavior remains underexplored. as drilling extends into deeper, hotter formations, understanding op’s performance under such conditions becomes essential for maintaining fluid stability and efficiency. table 1— current studies on natural additives for drilling fluid. additives findings limitations okra mucilage powder (murtaza et al. 2021 and 2022) acts as a shale swelling inhibitor. reduces bentonite swelling. improves viscosities. partially reduces filtration loss. no mention of particle size or temperature effects on mud properties. banana peel powder (al-saba et al. 2018) improves rheological properties (pv and yp). partially reduces filtration. potato peel powder (al-hameedi et al. 2019) increases pv while reducing yp. reduces filtration loss. citrus peel powder (michael-igolima et al. 2023; le et al. 2023; boruah et al. 2023; idress and hasan 2020; dinh et al. 2024) improves rheological properties. reduces fluid loss. this work explores the feasibility of utilizing orange peel as a sustainable additive in water-based mud. it details the preparation process of orange peel powder (opp) and systematically evaluates its effects on drilling fluid performance. specifically, the research investigates the effect of op concentration, particle size, and temperature on rheological and filtration properties. materials and method materials. figure 1 illustrates the step-by-step preparation of orange peel powder (opp) and the subsequent particle size classification process. raw orange peels were collected locally and thoroughly washed with distilled water to remove surface contaminants. the washed peels were dehydrated at 80 °c for 48 hours to ensure complete moisture removal. after drying, they were pulverized using a high-speed grinder. the resulting material was sieved to classify the opp into three distinct particle size ranges: 100-150 µm, 45-100 µm, and particles smaller than 45 µm. these classified opp particles were then used in further testing to assess their effects on drilling fluid performance. improved oil and gas recovery 3 figure 1— preparation process and particle size classification of orange waste peel (opp) powder. drilling mud preparation. 12 drilling fluid samples were prepared for this study. one base sample and eleven additional samples (labeled mud 1 to mud 11). bentonite and distilled water were used as the base fluid, providing viscosity and suspension properties for the control sample. opp was incorporated at specific concentrations and particle sizes, as detailed in table 2. to investigate the effect of particle size, three samples (mud 1, mud 2, and mud 3) were prepared with a fixed opp concentration of 1%wt, using particle sizes of <45 µm, 45-100 µm, and 100-150 µm respectively. five additional samples (mud 4 to mud 8) were formulated to examine the impact of varying opp concentrations (0.5-1.5%wt) using a particle size of <45 µm. lastly, three samples (mud 9, mud 10, and mud 11) were prepared with 1%wt opp (<45 µm) to evaluate the effects of various temperature at 25 oc, 50 oc, and 75 oc. table 2— samples with various opp concentrations, temperature and particle size. all mud samples were prepared following a standardized procedure to ensure consistency. first, bentonite and distilled water were mixed using a high-speed mixer for approximately five minutes to form a uniform base fluid. sample opp (%wt) temperature (oc) partical size (µm) base 0 50 mud 1 1 50 100-150 mud 2 1 50 45-100 mud 3 1 50 < 45 mud 4 0.5 50 < 45 mud 5 0.75 50 < 45 mud 6 1 50 < 45 mud 7 1.25 50 < 45 mud 8 1.5 50 < 45 mud 9 1 25 < 45 mud 10 1 50 < 45 mud 11 1 75 < 45 improved oil and gas recovery 4 next, a precise mass of opp was gradually introduced under continuous mixing for an additional 25 minutes to ensure even dispersion. finally, a few drops of defoamer were added as needed to control foam formation. after preparation, the rheological and filtration properties of each mud sample were determined. this systematic approach ensured reliable comparisons of the effects of opp particle size, concentration, and temperature on drilling fluid performance. mud density and ph measurement. mud density is an essential characteristic of drilling fluids, crucial for maintaining wellbore stability and regulating formation pressure. in this study, mud density and ph value were measured using a mud balance (figure 3) and the inolab equipment (figure 4), respectively. these measurements ensured accurate assessment of the fluid’s ability to maintain well integrity and drilling efficiency. figure 3— mud balance. figure 4—inolab ph7110. rheological measurement. twelve fluid samples were analyzed using an eight-speed rotational viscometer (figure 5) to evaluate their rheological properties at different shear rates. gel strength value was recorded at 10 seconds and 10 minutes to assess the interparticle forces that develop when circulation stops. to maintain consistent test conditions, a cup heater (figure 6) was used to regulate the temperature at 25 °c, 50 °c, and 75 °c. the bellow equations were applied to estimate the rheological parameters (r600: reading at 600; r300: reading at 300 rpm,). 𝐴𝑝𝑝𝑎𝑟𝑒𝑛𝑡 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 (av − cp) = r600/2,...................................................................................................(1) 𝑃𝑙𝑎𝑠𝑡𝑖𝑐 𝑉𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 (𝑃𝑉 − 𝑐𝑃) = 𝑅600 − 𝑅300,..............................................................................................(2) 𝑌𝑖𝑒𝑙𝑑 𝑃𝑜𝑖𝑛𝑡 (𝑌𝑃 − 𝑙𝑏 100𝑓𝑡2) = 𝑅300 − 𝑃𝑉,.......................................................................................................(3) improved oil and gas recovery 5 figure 5—8-speed rotational viscometer (ofite). figure 6—cup heater. rheological models. rheological models establish mathematical relationships between shear stress (𝜏) and shear rate (𝛾), providing insights into the flow rheological characteristic of drilling mud. in this study, three models were employed to interpret experimental data. bingham plastic model. a linear relationship between shear rate and shear stress is modeled once the fluid surpasses a critical yield point (𝜏0). the plastic viscosity (𝜇𝑝) is derived from the slope of this relationship, while the intercept represents the yield stress, 𝜏 = 𝜏0 + 𝜇𝑝𝛾,....................................................................................................................................................(4) where 𝜏 is shear stress, 𝜏0 is the yield point, 𝜇𝑝 is plastic viscosity, 𝛾 is shear rate power law model. it describes the non-newtonian behavior using two parameters model, consistency (k) and flow behavior (𝑛). the equation governing this model is, 𝜏 = k𝛾𝑛,............................................................................................................................................................(5) where 𝑛 indicates the degree of flow behavior; and k reflects the fluid’s consistency. herschel-bulkley model. it incorporates elements from both the bingham plastic and power law models. it accounts for both yield stress and non-newtonian behavior, providing a more accurate representation of drilling fluid flow properties, 𝜏 = 𝜏0 + k𝛾𝑛,...................................................................................................................................................(6) where 𝜏 represents shear stress; 𝜏0 is the yield stress; 𝛾 is shear rate; 𝑛 indicates the degree of flow behavior; and k reflects the fluid’s consistency. statistical evaluation of rheological model accuracy. to assess the accuracy of the predictive rheological models, two statistical metrics were used: the coefficient of determination (𝑅2) and the root mean square error (rmse). these metrics quantify the degree of agreement between measured shear stress values and modelimproved oil and gas recovery 6 predicted values. the 𝑅2 value represents the proportion of variance in measured shear stress (𝜏measured) that is explained by the model. 𝑅2 = 1 − ∑(𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑−𝜏𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑)2 ∑(𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑−(𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒)𝑎𝑣𝑒)2,.................................................................................................................(7) root mean square error (rmse) estimates the mean deviation between the predicted and actual shear stress values, providing an overall measure of model accuracy. 𝑅𝑀𝑆𝐸 = √ ∑(𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑−𝜏𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑) 2 𝑁 ,....................................................................................................................(8) where 𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑 is measured value; 𝜏𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 is calculated from model; (𝜏𝑚𝑒𝑎𝑠𝑢𝑟𝑒)𝑎𝑣𝑒 is the mean of measured value, 𝑁 is the number of observations filtration fluid loss measurement. filtrate loss, or fluid loss, refers to the separation of water from the drilling mud and its infiltration into fractures and pores of the formation rock near the wellbore due to differential pressure (novrianti et al. 2019). this process leads to the formation of a mud cake on the wellbore walls, which is essential for stabilizing the wellbore and preventing collapse or sloughing during drilling. however, excessive fluid loss can result in a thick, porous, and brittle mud cake, which may narrow the wellbore and increase the risk of drill string jamming. additionally, excessive filtrate loss can destabilize the formation by inducing swelling and potentially damaging the reservoir zone (dejtaradon et al. 2019). to mitigate these risks, it is crucial to maintain low filtrate loss while ensuring the formation of a thin, durable mud cake which contributes to hole stability and optimal drilling performance (ali et al. 2020). the fluid loss characteristics were assessed using a 100 psi filter press (figure 7) in accordance with api standards (american petroleum institute 2017). this test quantifies the volume of water lost from the bentonite mud, replicating potential water invasion into the formation. to perform the test, mud sample was placed into a cylinderal chamber, and a pressure of 100 psi was applied. fluid loss was recorded at multiple time intervals within 30 minutes. these measurements provided valuable insights into the fluid’s ability to control filtration, ensuring minimal fluid invasion while facilitating the development of a stable mud cake (le et al. 2023). figure 7—api filter press. results and discussions effect of opp particle size. figure 8a illustrates the influence of opp particle size on pv and yp for three tested mud samples (mud 1, mud 2, and mud 3). the results shows that particle size 100-150 µm, 45-100 µm, and improved oil and gas recovery 7 <45 µm do not siginificantly impact pv or yp. across 3 samples, pv remains constant at 6 cp, while yp fluctuates slightly between 5 and 6 lb/100 ft2. this suggests that within the tested size range, opp particle size has a minimal effect on flow resistance and cuttings suspension capability in the drilling fluid. figure 8b presents the effect of particle size on gel strength values at two times of 10 seconds and 10 minutes. a slight reduction in gel strength values is recorded as particle size decreases. in mud 1 (100-150 µm), gel 10s and gel 10m are recorded at 6 and 25 lb/100 ft2, respectively. in mud 3 (<45 µm), these values decrease slightly to 5 and 22 lb/100 ft2. despite this reduction, gel strength remains within the recommended range, ensuring effective cuttings suspension during static conditions.these findings suggest that smaller opp particles (<45 µm) maintain adequate suspension capabilities while slightly improving flow characteristics, making them optimal for further evaluation of drilling fluid performance. figure 8—influence of opp particle size on (a) rheology parameters, (b) gel strength characteristic. figure 9a illustrates the fluid loss volume over time for the mud samples containing different opp particle sizes (100-150 µm, 45-100 µm, and <45 µm). the data reveal that as the particle size decreases, the fluid loss volume slightly reduces. specifically, the mud sample with the smallest particle size (<45 µm, mud 3) exhibits the lowest fluid loss volume, reaching approximately 12.6 ml at 30 minutes, compared to 13.0 ml for the larger particle size samples (mud 1 and mud 2). the reduction in fluid loss with smaller particles is attributed to improved particle packing and reduced permeability of the filter cake, limiting water seepage into the formation. the images of mud cakes corresponding to the different particle sizes show that the thickness and visual distribution of the mud cakes are similar across all samples, with an average thickness of 2 mm (table 3). despite the slight reduction in fluid loss, the particle size does not significantly influence the mud cake structure. the mud cakes remain uniform and well-distributed, indicating effective particle bridging and filtration control across the tested particle sizes. table 3—effect of opp particle size on mud weight, fluid loss, ph and mudcake thickness. properties 100-150 µm 45-100 µm < 45 µm mud 1 mud 2 mud 3 mud weight (ppg) 8.6 8.6 8.6 filtration volume (ml) 13.0 13.0 12.6 ph 8.7 8.5 8.4 mud cake (mm) 2 2 2 improved oil and gas recovery 8 figure 9—fluid losses volume and mud cakes of different particle size samples. these results indicate that opp particles smaller than 45 µm provide the most effective reduction in fluid loss without while maintaining the structural integrity of the mud cake. therefore, this particle size was selected for further investigation into opp impact on drilling fluid performance. effect of opp concentrations. figure 10a shows the variation in plastic viscosity pv and yp with increasing opp concentration from 0.5%wt (mud 4) to 1.5%wt (mud 8). compared to the base fluid, yp decreased significantly from 12 lb/100ft² to 6 lb/100ft² at mud 5 (0.75%wt opp). as the concentration increased to 1.5%wt, yp gradually recovered but remained lower than the base sample. pv initially increased slightly between mud 4 and mud 6, peaking at 7 cp before declining at higher concentrations. the drop in yp, coupled with minimal pv changes, suggests that opp disrupts the fluid’s initial structural integrity, but higher concentrations help stabilize suspension capabilities. figure 10b illustrates the effect of opp concentration on both gel strength values. as opp concentration increased, gel strength showed a noticeable reduction. gel 10s decreased by half, while gel 10m dropped from 33 lb/100 ft² (base sample) to 23 lb/100 ft² at mud 8 (1.5%wt opp). the most significant drop occurred between the base sample and mud 4 (0.5%wt opp), with further increases in concentration having minimal additional impact. despite these reductions, gel strength values across all opp-modified samples remained within recommended limits, ensuring adequate cuttings suspension and wellbore stability during drilling operations. improved oil and gas recovery 9 figure 10—influence of opp concentrations on (a) rheology parameters (b) gel strength characteristic. the rheological parameters for the three models are presented in table 4. among the models, the bingham plastic model exhibited the least accurate fit. the r2 values ranged from 0.92 to 0.97, while rmse values remained relatively high (1.2674-1.6799), indicating lower predictive accuracy. the power law model proved improved performance, with r2 values between 0.9747 and 0.9878, and lower rmse values compared to the bingham model. however, this model did not entirely account for the nonlinear flow behavior of the fluid. among the three models, the herschel-bulkley model provided the most precise fit, achieving r² values above 0.99 in most cases and rmse values within an acceptable range. the flow behavior index (𝑛) remained below 1, confirming that the fluid exhibited shear-thinning characteristics. the incorporation of opp led to an increase in 𝑛 up to 1%wt (mud 6), but further increasing the concentration (mud 7 and mud 8) resulted in a decline, suggesting that excessive opp slightly diminished the shear-thinning effect. table 4—parameters of rheological models. model parameters base mud 4 (0.5% opp) mud 5 (0.75% opp) mud 6 (1% opp) mud 7 (1.25% opp) mud 8 (1.5% opp) hershel bulkley k 0.5995 0.4357 0.1327 0.1841 0.5663 0.5009 n 0.5051 0.5497 0.7137 0.6710 0.5133 0.5314 τ0 3.7431 1.8478 2.6059 2.2669 1.5607 1.9745 rmse 0.2939 0.4588 0.3758 0.7897 0.6528 0.6185 r2 0.9976 0.9941 0.9959 0.9830 0.9882 0.9896 power law k 2.2079 0.9904 0.6457 0.6506 1.0800 1.1368 n 0.3365 0.4410 0.4987 0.5005 0.4285 0.4237 rmse 0.8899 0.6619 0.9340 1.0784 0.7530 0.7921 r2 0.9824 0.9878 0.9747 0.9683 0.9843 0.9829 bingham plastic µp 0.0176 0.0178 0.0178 0.0181 0.0177 0.0178 τ0 7.2698 4.8131 4.0222 4.0507 4.9833 5.2021 rmse 1.2674 1.4985 0.8985 1.2857 1.6844 1.6799 r2 0.9274 0.9376 0.9765 0.9550 0.9214 0.923 1 figure 11 presents the fluid loss volume after 30 minutes for drilling fluid samples with varying opp concentrations. the finding shows a notable decrease in fluid loss as opp concentration increases, with the most improved oil and gas recovery 10 substantial decrease observed at 1.5%wt (mud 8). the fluid loss volume dropped from 14.2 ml (base sample) to 11.4 ml, representing an overall 20% reduction. this suggests that opp particles enhance cross-linking within the bentonite matrix, effectively lowering fluid permeability. table 5 shows that mud weight remained constant across all samples, indicating that opp had no impact on overall density. however, ph levels gradually decreased from 9.1 to 8.2 as opp concentration increased, though values remained within the acceptable range (8-12) for drilling operations. figure 11—fluid losses after 30 minutes for different opp concentrations. the formation of mud cakes, illustrated in figure 12, confirms that mud cake thickness remained unchanged at 2 mm for all samples, irrespective of opp concentration (table 5). this demonstrates that while opp effectively reduces fluid loss, it does not compromise mud cake structure or integrity. a thin, low-permeability mud cake is essential for preventing differential sticking and maintaining wellbore stability, making opp a promising additive for filtration control in drilling fluids. table 5—effect of opp concentrations on mud weight, fluid loss, ph and mudcake thickness. properties base mud 4 (0.5% opp) mud 5 (0.75% opp) mud 6 (1% opp) mud 7 (1.25% opp) mud 8 (1.5% opp) mud weight (ppg) 8.5 8.6 8.6 8.6 8.6 8.6 filtration volume (ml) 14.2 13.8 13.5 12.6 12.2 11.4 ph 9.1 8.7 8.5 8.4 8.3 8.2 mud cake (mm) 2 2 2 2 2 2 improved oil and gas recovery 11 figure 12—mud cake formation for different opp concentrations. effect of temperature. when temperature increases, the primary chains of polymeric molecules break down, leading to a reduction in the network structure and a decline in the rheology of mud (amani and al-jubouri 2012). however, the presence of additional additives such as opp helps manage and mitigate these detrimental effects, making it essential to assess how temperature impacts opp-modified drilling fluids (quan et al. 2014). figure 13a shows the impact of temperature on the apparent viscosity (av) of the 1% opp sample (mud 9) at a 600 rpm shear rate using an eight-speed rotational viscometer. the temperature gradually rose from 25oc to 75oc in 5oc increments. as indicated by eq. 9, av exhibited a consistent decline with rising temperatures. this relationship is quantified by an interpolation equation, which yields an r-squared value of 0.9929. av = 48.978×t0.463...........................................................................................................................................(9) this strong correlation highlights the inverse relationship between av and temperature, suggesting that the fluid becomes less viscous at higher temperatures due to thermal breakdown of its internal structure. figure 13b presents the variation in herschel-bulkley parameters, 𝐾, 𝑛, and 𝜏0 for the opp-modified drilling mud at 25, 50, and 75°c. the following trends were observed: yield stress (𝜏0) increased significantly from 0.7461 lb/100ft2 at 25°c to 2.5967 lb/100ft2 at 75°c—an increase of 2.5 times. this rise suggests enhanced cuttings suspension capacity at high temperatures, which is crucial for maintaining efficient drilling in deep wells. however, the elevated yield stress could also increase pressure losses, requiring careful monitoring. the flow behavior index, 𝑛, increased with temperature, indicating a reduction in the fluid’s non-newtonian characteristics. as temperature rose, the fluid became more newtonian, suggesting lower resistance to flow under high shear conditions, which is beneficial for minimizing pressure losses during fluid circulation. the consistency index 𝐾 decreased by 80%, from 0.5617 lb·s/100ft2 at 25°c to 0.0995 lb·s/100ft2 at 75°c. this decline implies reduced viscosity at high temperatures, contributing to improved flowability and reduced pumping effort. improved oil and gas recovery 12 figure 13—impact of temperature on rheology behavior. conclusions this study underscores the potential of opp as a sustainable additive for water-based mud, demonstrating its efficacy in controlling fluid loss and enhancing overall drilling fluid performance. the integration of opp markedly diminishes fluid loss, particularly when the particle size is less than 45 µm, thereby alleviating issues such as kick and formation contamination. opp also reduces viscosity and gel strength, while ensuring that these parameters remain within the recommended ranges for effective cuttings suspension and wellbore stability. furthermore, the study elucidates the influence of temperature in the presence of opp. as drilling depth increases, temperature-induced alterations in the apparent viscosity were successfully modeled, offering a predictive framework for evaluating the behavior of drilling mud under bottom hole conditions. in summary, the findings corroborate the viability of opp as a viable and cost-effective alternative to traditional chemical additives, contributing to environmentally responsible drilling practices. acknowledgements this research is funded by vietnam national university ho chi minh city (vnu-hcm) under grant number c2024-20-28. we acknowledge ho chi minh city university of technology, vnu-hcm for supporting this 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presented at the spe arctic and extreme environments technical conference and exhibition, moscow, russia, 15-17 october. spe-166847-ms. quan, h., li, h., huang, z., et al. 2014. copolymer sj-1 as a fluid loss additive for drilling fluid with high content of salt and calcium. international journal of polymer science 2014:1-15. sehly, k., chiew, h., li, h., et al. 2015. stability and ageing behaviour and the formulation of potassium-based drilling muds. applied clay science 104(1):309-17. improved oil and gas recovery 14 shafiq, m. u., vivegananthan, d. n. khan, m., et al. 2024. experimental investigation of agricultural wastes effect on drilling mud properties. improved oil and gas recovery 8(1):1-18. nam nguyen hai le is a lecturer in the department of geology and petroleum engineering at ho chi minh city university of technology, vnu-hcmc, ho chi minh city, vietnam. he obtained both his b. eng. and m. eng. degrees in petroleum engineering from the same institution and earned his ph.d. in earth resources engineering from kyushu university, japan. his research focuses on drilling engineering, reservoir engineering, and enhanced oil recovery. le nguyen hoang duy is currently an undergraduate student in department of geology and petroleum engineering, ho chi minh city university of technology, vnu-hcmc, ho chi minh city, vietnam. his research interests include hole cleaning in wells, drilling optimization, and drilling fluid materials, with a focus on enhancing wellbore stability and improving drilling efficiency. pham thi van phung is currently an undergraduate student in department of geology and petroleum engineering, ho chi minh city university of technology, vnu-hcmc, ho chi minh city, vietnam. her research interests focus on eco-friendly materials and shale inhibitor agents in drilling fluids, aiming to enhance drilling performance while promoting environmental sustainability. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1355 received january 2, 2025; revised march 27, 2025; accepted may 27, 2025. *corresponding author: dike.chukwuebuka@futo.edu.ng 1 study on hydrate formation potential in natural gas pipeline anthony ogbaegbe chikwe, chukwudozie ian awah, and chukwuebuka francis dike*, federal university of technology owerri, owerri, nigeria abstract the formation of hydrates within the natural gas pipeline poses a significant challenge that requires careful attention and management. this research endeavor is focused on predicting and forecasting the specific conditions under which hydrate formation is likely to occur within the natural gas pipeline infrastructure. by understanding these conditions, it becomes possible to implement preventive measures and strategies to mitigate the risks associated with hydrate formation. the work aims to ascertain the precise temperatures and pressures at which hydrocarbon and water dew points are reached within gas streams. determining these dew points is crucial because it allows for the optimization of pipeline operations, ensuring that the gas remains in a stable state and does not precipitate into hydrates or condense into liquid form, which could lead to blockages and operational inefficiencies. the study examined the formation of hydrates and the deposition of hydrocarbon slugs, which are primary concerns in gas pipelines that can lead to significant environmental damage and substantial financial repercussions. the prediction of hydrate formation conditions and the pipeline segments where these conditions are likely to occur was conducted to provide a basis for designing a cost-effective hydrate prevention strategy. additionally, the prediction of the hydrocarbon and water dew points of a gas stream was accomplished using two equations of state within the aspen hysys simulation software. this analysis confirms that under specific conditions of elevated pressure and reduced temperature, hydrate formation is promoted or favored, and water condenses out prior to hydrocarbons in natural gas streams. this paper serves as a guide for forecasting the conditions conducive to gas hydrate and hydrocarbon liquid formation, as well as identifying pipeline sections prone to hydrate formation in long-distance pipelines. in essence, this research seeks to enhance the safety, reliability, and efficiency of natural gas transportation by providing a comprehensive understanding of the thermodynamic conditions that govern the behavior of gas streams within pipelines. introduction fossil fuels recorded major contributions to global energy consumption with an estimated 87 million barrels/day (bpd) and this has raised the stakes for oil production despite obvious productivity decline (kerunwa et al. 2024). fossil fuels could be solid (coal and/or tar sand), liquid (crude oil) or gaseous (natural gas) in nature (meyers 2002), but gaseous based fossil fuel has recorded significant global attention from several countries (ikoku 1992) due to its excellent eco-properties compared to other fossil fuel forms (mohammad 2009). natural gas is a gas derived conventional underground formation either as gas associated with crude oil or free water (anyadiegwu et al. 2014), and comprises predominantly of methane, significant quantities of ethane, propane, butane and pentane (abdel et al. 2003), and other impurities such as water vapour, carbon (iv) oxide and hydrogen sulphide. the study of hydrates (also known as “gas hydrates”) has captured the attention of the industry and the economy because of the identification of its vast deposits (as new energy source), concurrent lack of traditional fossil fuels (guimin et al. 2022) and its adverse effects in pipelines and process equipment. gas hydrates are structured crystalline materials with an organized structure in which methane and other guest molecules are enclosed in cages made of water molecules and held in place by hydrogen bonds. since an empty cage lacks thermodynamic stability, these guest molecules are essential for stabilizing the cages (naser and brandstatter 2011). hydrates fobendsh pressures and low temperatures, in the presence of free water especially near regions with significant agitation and turbulence like valves mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 and bends and can impede pipelines in deep sea or permafrost conditions. due to this clogging, dangerous working conditions, high operational costs, and even the possibility of fatal accidents are all created. predicting the critical sections of the natural gas pipeline at which hydrates form is very crucial for pipeline operation optimization and for a better pipeline cost optimized hydrate prevention methods. however, since it is not feasible, to empirically determine segmental variations in pressure, temperature, density, viscosity, etc., along a transmission pipeline, these parameters are determined by applying thermodynamic and conservation principles (carroll 2003). also, precise measurement of hydrocarbon dew points is vital in achieving safe and efficient transportation through natural gas pipelines specific for single phase fluids (shoaib et al. 2018). the conditions (pressure and temperature) at which the heavier elements condense out of the gas stream and turn into liquids are known as the hydrocarbon dew point (hcdp). in some regions, ambient temperatures regularly cause natural gas streams to cool to their hydrocarbon dew points, resulting in condensation taking place in transmission pipelines. if these condensed liquids are not recovered, the stream will lose the heating value they represent, and the liquids themselves could cause equipment in the natural gas delivery system to malfunction, (george et al. 2005). from an analytical gas composition, various techniques can be used to predict hydrocarbon dew point using chilled mirror apparatus, various software programs and equations of state. industry experience, however, suggested that these various approaches would yield noticeably different outcomes, particularly when the proportions of heavier and hexane (c6)-containing substances are significant (galatro and marin-cordero 2014). methodology hydrate formation prediction. hysys simulation package was used to simulate the thermodynamic environment that will suit transportation of the natural gas stream through a gas pipeline. with the peng robinson’s equation of state (pr eos) as the fluid package, the temperature and pressure variations at varying sections of the pipeline were determined. for each pipeline section, hysys calculates the hydrate formation temperature at the prevalent section’s pressure, for which a careful comparison with the section’s prevalent temperature determines the pipeline section’s susceptibility to hydrate formation. hammerschmidt correlation for hydrate formation temperatures used to validate the formation temperatures obtained at each pipe section’s pressure. 𝑇 = 8.9𝑃0.285 ,..................................................................................................................................................................(1) where t is the hydrate formation temperature, fahrenheit; and p is the pressure, psi. table 1 displays the detailed composition of the natural gas that is utilized for the purpose of predicting the formation of gas hydrates. the primary constituent found within this natural gas is methane, which plays a crucial role in the overall analysis and understanding of hydrate behavior. table 1—composition of the natural gas for hydrate prediction. mole fraction methane 0.7120 ethane 0.1040 propane 0.0644 i-butane 0.0090 n-butane 0.0196 i-pentane 0.0051 n-pentane 0.0056 n-hexane 0.0024 n-octane 0.0001 h2s 0.0200 nitrogen 0.0190 co2 0.0380 n-heptane 0.0008 improved oil and gas recovery 3 dew point prediction. two equations of states, namely the peng-robinson and the soave-redlich-kwong are used as the fluid packages in hysys to predict the hydrocarbon and water dew points of a natural gas stream at designated pressure points and produce a phase envelope for the gas stream. table 2 presents the gas composition utilized for the prediction of the dew point. a careful comparison analysis between the hydrocarbon and water dew point with each equation of state confirms the behavior of gas streams, where the heavier components condense out first. table 2—gas composition for dew point prediction. mole fractions nitrogen 0.0569 co2 0.0020 methane 0.8274 ethane 0.0790 propane 0.0214 i-butane 0.0034 n-butane 0.0053 i-pentane 0.0012 n-pentane 0.0014 n-hexane 0.0012 n-heptane 0.0005 n-octane 0.0001 n-nonane 0.0000 n-decane 0.0000 n-c11 0.0000 n-c12 0.0000 h2o 0.0001 results and discussion to ascertain which sections of the pipeline are most vulnerable to the formation of hydrates, a meticulous comparison was conducted between the prevailing temperatures of each section of the pipeline and the corresponding temperatures at which hydrates are known to form. this process involved a detailed analysis to identify any potential discrepancies or areas where the pipeline's temperature might drop below the threshold required for hydrate formation. furthermore, to ensure the accuracy and reliability of the determined hydrate formation temperatures, a validation process was undertaken using the well-established hammerschmidt correlation. this correlation, which is widely recognized in the industry, provides a means to predict hydrate formation temperatures based on the specific conditions within the pipeline. the results of this validation process, which confirmed the accuracy of the calculated hydrate formation temperatures, are presented and illustrated in appendix a1. this table serves as a crucial reference, offering a comprehensive overview of how the calculated temperatures align with the established hammerschmidt correlation, thereby providing a robust foundation for further analysis and decision-making regarding the management and mitigation of hydrate formation risks within the pipeline system. it indicates that within section 10 of the pipeline and in areas below, the temperature at which hydrates form exceeds the prevailing temperature of the pipeline, rendering these sections prone to hydrate formation. figure 1 shows that pressure and temperature slowly decline as we move down the pipeline section. it is worthy to note that the pressure decline with increasing pipe length is uniform, while a steep temperature decline is observed at the beginning of the pipeline and a more gradual decline with increasing length of the pipeline. figure 2 shows the relationship between the pipeline pressure, pipeline temperature, hysys hydrate formation temperature and the hammerschmidt hydrate formation temperature. the region below the pipeline temperature and the hysys hydrate formation temperature depicts the hydrate formation region. an acceptable difference of 4.35% exists between the hammerschmidt and hysys hft due to the presence of hydrogen sulphide in the gas stream, as hammerschimdt correlation was developed mainly for sweet gases. improved oil and gas recovery 4 figure 1—pressure and temperature change against pipeline length. figure 2—pipeline temperature, hysys hft and hammerschmidt hft. appendix a2 presents the outcomes of the simulated water and hydrocarbon dew points employing the peng-robinson and soave-redlich-kwong equations of state. a meticulous examination reveals an average disparity of approximately 0.8% and 0.12% for the hydrocarbon and water dew points, respectively, between the dew point temperatures simulated by the peng-robinson and those by the soave-redlich-kwong at each specified pressure point. this discrepancy is attributed to the greater complexity of the peng-robinson equation of state, which accounts for molecular shape and the presence of associating molecules—those capable of forming weak associations, such as hydrogen bonds—whereas the soave-redlichkwong equation does not. regardless of the type of equilibrium oil saturation (eos) that is employed in the analysis, a comparison between the water dew points as depicted in figure 3 and the hydrocarbon dew point as shown in figure 4 reveals a significant observation. specifically, it becomes evident that the temperature at which the water dew point is reached occurs earlier than the temperature at which the hydrocarbon dew point is attained under certain pressure conditions. this sequence of condensation events can be explained by the inherent properties of the components involved. in this scenario, water, being the heavier component, tends to condense out of the gas stream prior to the hydrocarbon, which is lighter in molecular weight. this behavior is consistent with the general principle that in a gas mixture, the component with a higher molecular weight and a greater affinity for condensation will precipitate out of the gas phase before the lighter components do. improved oil and gas recovery 5 figure 3—comparison between the pr and srk water dew points. figure 4—comparison between the pr and srk hydrocarbon dew points. in figure 5, a detailed comparison has been conducted to illustrate the differences between the hydrocarbon dew point and the water dew point, utilizing the pr eos as the analytical framework. this comparison reveals a consistent trend where, across a range of different pressures, the hydrocarbon dew point invariably exceeds the water dew point. figure 5—comparison between hydrocarbon dew point and water dew point using pr eos. improved oil and gas recovery 6 conclusion long-distance pipelines can use the study done on the sample gas pipeline above as a reference for forecasting gas-hydrate formation conditions and anticipated hydrate formation locations. it also provides an insight into designing and costoptimizing hydrate prevention schemes, like stating the pipeline section to insulate or to inject inhibitors. for this specific pipeline, the remediation methods should be implemented at the beginning sections of the pipeline, as the hydrate formation conditions are most likely to be met at these points. furthermore, hysys can be used to determine the temperature and pressure at which liquid hydrocarbon and water will condense out of the gas stream with reasonable accuracy especially with the peng-robinson’s and soave-redlich-kwong’s equation of state. conflicting interests the author(s) declare that they have no conflicting interests. references abdel, a.h.k., mohamed, e. and fahim, m.a. 2003. petroleum and gas field processing. new york: marcel dekker inc. anyadiegwu, c.i.c., kerunwa, a. and oviawele, p. 2014. natural gas dehydration using triethylene glycol (teg). petroleum and coal 56(4): 407-417. caroll, j., 2003. natural gas hydrates a guide for engineers. elsevier. galatro, d., and marín-cordero, f. 2014. considerations for the dew point calculation in rich natural gas. journal of natural gas science and engineering 18: 112-119. george, d. l., barajas, a. m., and burkey, r. c. 2005. the need for accurate hydrocarbon dew point determination. pipeline & gas journal 232(9), 32-34. guimin, y., hao, j., and qingwen, k. 2022. study on hydrate risk in the water drainage pipeline for offshore natural gas hydrate pilot production. frontiers in earth science 9(1):1-12. ikoku, c. i. 1992. natural gas production engineering. boca raton, usa: krieger publishing company. kerunwa, a., izuwa, n.c., dike, c.f., et al. 2024. review on the utilization of local asp in the niger-delta for enhanced oil recovery. petroleum and coal 66(1): 256-275. meyers, r.a. 2002. encyclopedia of physical science and technology. academic press. naseer, m. and brandstätter, w. 2011. hydrate formation in natural gas pipelines. wit transactions on engineering sciences 70: 261–269. shoaib, a.m., bhran, a.a., awad, m.e., et al. 2018. optimum operating conditions for improving natural gas dew point and condensate throughput. journal of natural gas science and engineering 49(1): 324-330. anthony ogbaegbe chikwe is a senior lecturer at the department of petroleum, federal university of technology with research interest in production, and reservoir & gas engineering. he holds bachelor’s degree and master’s degree in petrochemical engineering from university of oil and gas, moscow, russia, and phd degree in petroleum engineering from federal university of technology owerri, owerri, nigeria. chukwudozie ian awah is a graduate candidate at the department of petroleum engineering, federal university of technology owerri, with research interest in natural gas engineering. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology owerri, owerri, nigeria. he has research interest in drilling, drilling fluids technology, reservoir engineering, enhanced oil recovery and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering. improved oil and gas recovery 7 appendix appendix a1—pipeline temperature and pressure variations with hydrate formation temperature. pipe sections axial length (ft) pressure (psi) temperature (f) hysys hft (f) hammerschmidt hft (f) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 0.000 546.810 1640.420 2734.030 3827.650 4921.260 6014.870 7108.490 8202.100 9295.710 10389.330 11482.940 12576.550 13670.170 14763.780 15857.390 16951.010 18044.620 19138.230 20231.850 21325.460 22419.070 23512.690 24606.300 25699.910 26793.530 27887.140 28980.750 30074.370 31167.980 32261.590 32808.400 2139.310 2137.900 2135.120 2132.390 2129.700 2127.050 2124.420 2121.810 2119.220 2116.640 2114.070 2111.520 2108.960 2106.420 2103.870 2101.330 2098.790 2096.250 2093.710 2091.170 2088.630 2086.090 2083.550 2081.000 2078.450 2075.900 2073.350 2070.790 2068.230 2065.670 2063.110 2061.820 140.000 132.850 119.820 109.090 100.250 92.970 86.980 82.040 77.970 74.630 71.870 69.600 67.730 66.190 64.920 63.870 63.010 62.310 61.720 61.240 60.850 60.520 60.250 60.030 59.850 59.700 59.580 59.470 59.390 59.320 59.260 59.240 75.419 75.416 75.409 75.401 75.394 75.387 75.380 75.373 75.366 75.360 75.353 75.346 75.339 75.333 75.326 75.319 75.312 75.306 75.299 75.292 75.285 75.279 75.272 75.265 75.258 75.252 75.245 75.238 75.231 75.223 75.218 75.214 79.162 79.147 79.118 79.089 79.061 79.033 79.005 78.977 78.950 78.922 78.895 78.868 78.841 78.813 78.786 78.759 78.732 78.705 78.678 78.650 78.623 78.596 78.569 78.541 78.514 78.486 78.459 78.431 78.404 78.376 78.348 78.334 improved oil and gas recovery 8 appendix a2—hydrocarbon and water dew point temperatures using the pr and srk eos. pressure (bar) wdp (k)-srk wdp (k)-pr hcdp (k)-srk hcdp (k)-pr 2.20 2.60 3.90 4.70 5.90 7.30 8.00 9.70 10.60 11.20 12.90 14.10 15.60 16.50 17.70 18.90 20.40 21.30 22.30 23.40 24.80 26.00 27.20 28.50 29.70 31.40 33.30 35.20 36.80 38.70 41.10 42.40 44.00 45.40 46.80 48.50 50.90 53.90 56.90 59.50 61.60 235.14 236.74 240.71 242.58 244.88 247.06 248.00 250.00 250.93 251.50 252.98 253.91 254.97 255.55 256.28 256.97 257.76 258.21 258.68 259.18 259.77 260.25 260.71 261.18 261.60 262.15 262.73 263.27 263.70 264.18 264.74 265.03 265.37 265.66 265.93 266.25 266.67 267.15 267.60 267.96 268.23 234.85 236.46 240.44 242.31 244.61 246.80 247.74 247.75 250.67 251.25 252.73 253.66 254.71 255.30 256.03 256.71 257.51 257.95 258.43 258.92 259.52 260.00 260.45 260.92 261.33 261.89 262.46 263.00 263.43 263.91 264.47 264.76 265.10 265.38 265.65 265.70 266.39 266.87 267.31 267.67 267.94 258.30 260.07 264.94 267.10 269.95 272.30 273.48 275.84 276.58 277.17 278.79 279.97 281.00 281.43 282.03 282.47 283.21 283.60 284.09 284.53 284.98 285.12 285.27 285.42 285.57 285.86 286.10 286.30 286.45 286.60 286.30 286.15 286.00 285.90 285.71 285.57 285.36 284.98 284.09 283.35 282.32 256.13 257.86 262.83 265.05 267.89 270.24 271.42 273.78 274.64 275.10 276.87 277.90 278.90 279.23 279.82 280.40 281.00 281.86 281.88 282.30 282.52 282.85 283.00 283.20 283.35 283.50 283.65 284.00 284.02 283.94 283.70 283.60 283.50 283.35 283.21 282.76 282.32 281.80 281.00 280.11 279.37 copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1366 received february 3, 2025; revised june 21, 2025; accepted july 23, 2025. *corresponding author: ahmed.noori203@aut.ac.ir 1 effect of residual oil saturation on oil recovery and reservoir performance for mishrif formation in southern iraqi oil field abdulkareem abbas khalil，kerbala university, kerbala city, iraq; hussein ali baqer, almaaqal university, basrah, iraq; hiba alaa naseef, university of baghdad, baghdad, iraq; ahmed n. aldujaili*, amirkabir university of technology, tehran, iran abstract the determination of the residual oil saturation (sor) is an essential parameter for reserve assessment and recovery estimates. moreover, reliable sor data is crucial for potential incremental analysis under enhanced oil recovery (eor) methods. the objective of this study is to construct a reservoir model for the buzurgan field in southeastern iraq that aligns with actual field data measurements, predicts reservoir performance from 2007 to 2032, and determines the effect of the sor on oil recovery using petreltm. the matching percentage results were 100% after modifying the permeability and multiplying by 1.5, considering a weak aquifer that had not been considered previously. the predicted performance indicated a decrease in production rate and an increase in water cuts due to a significant decline in pressure. the proposed prediction strategy involves developing the capacity of surface facilities. the simulation model was executed to estimate the cumulative oil production and oil recovery for various sor values (0.16, 0.23, 0.20, and 0.28), which results in a decline in recovery as sor increases, due to changes in relative permeability. the secondary mechanism, implemented through injection, is used to enhance the recovery factor, increase productivity, and maintain pressure above the saturated pressure. introduction the reservoir requires exploration and development to enhance recovery rates and reduce costs. exploration will be conducted by geologists to gather data, while development may involve increasing the number of drilling wells or enhancing recovery through fracturing, acidizing, and injection (satter and iqbal 2015). the integration of reservoir studies encompasses defining and describing the reservoir structure, rock properties, fluid properties, and creating a reservoir simulation model (al-dujaili et al. 2024). carbonate reservoirs pose greater challenges in estimating petrophysical properties and understanding fluid flow mechanisms and production performance compared to most sandstone reservoirs, due to their heterogeneous porosity and permeability distributions (hurley et al. 1998). these reservoirs are highly complex, and proposing the correct reservoir model involves significant difficulties; thus, only limited success can be achieved with available and suitable reservoir simulation techniques. field development planning is one of the most critical activities in reservoir engineering. the recovery strategy primarily depends on the geological characteristics of the reservoir and the operational schedule for the field (aldujaili 2023). however, evaluating all possible combinations is not feasible due to the multitude of parameters influencing the decision-making process. therefore, it is necessary to assess the most critical parameters related to the problem and develop an approach to achieve a satisfactory outcome (cao et al. 2024). a reservoir model represents the physical space of the reservoir through an array of discrete cells, defined by a grid that can be regular or irregular (ugwu et al. 2023). typically, this array of cells is three-dimensional, although one-dimensional and two-dimensional models are sometimes utilized. each cell is associated with values mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 for attributes such as porosity, permeability, and water saturation (ugwu et al. 2023). the value of each attribute is assumed to be uniformly distributed throughout the volume of the reservoir represented by the cell. geological models are constructed by geologists and geophysicists to provide a static description of the reservoir before production begins. reservoir simulation models are developed by reservoir engineers and employ finite difference methods to simulate fluid flow within the reservoir throughout its production lifecycle (aljawad et al. 2017). effective attribute values for the simulation model are derived from the geological model through a process known as "upscaling." alternatively, if a geological model is unavailable, attribute values for the simulation model can be determined by sampling geological maps (hamdan 2011). the term "reservoir characterization" is sometimes used to describe reservoir modeling activities up until the point when a simulation model is prepared to simulate fluid flow. commercial software is utilized in the construction, simulation, and analysis of reservoir models (natvig et al. 2023). the residual oil saturation (sor) is the level of oil saturation above which the oil becomes movable. in petroleum reservoirs, only a small fraction of the original oil-in-place is economically recoverable through primary, secondary, and tertiary recovery methods. the oil that remains in the porous media after waterflooding is referred to as the remaining oil saturation (ros), which is higher than the relative permeability residual oil saturation (sorw or simply sor). this residual oil saturation varies based on factors such as lithology, pore size distribution, permeability, wettability, fluid characteristics, recovery method, and production scheme. (teklu et al. 2013) the determination of a reservoir's residual oil saturation is a critical parameter for reserve assessment and recovery predictions (chen et al. 2023). moreover, reliable sor data is essential for evaluating potential incremental recovery through enhanced oil recovery (eor) techniques (vishnumolakala et al. 2020). core analysis offers direct measurement of reservoir properties. the laboratory-measured residual oil saturation from cores is contingent upon the method of core recovery and handling, including conventional coring, pressure coring, or sponge coring (al-dujaili et al. 2021a). special core analysis (scal) encompasses all core analysis techniques beyond porosity and permeability measurements (al-dujaili et al. 2021b). cutoffs are limiting points at which the flow of fluid is halted. each layer has specific cutoffs for petrophysical properties, including porosity, permeability, and water saturation (zeyghami and taghizadeh, 2023). reservoirs with higher porosity and permeability can produce fluids (oil, gas, or water) with commercial productivity. in contrast, reservoirs with porosity and permeability values below the cutoff will not yield fluids of commercial value. the cutoff is crucial for estimating the volume of rocks that do not significantly contribute to the reservoir's evaluation (worthington and cosentino 2005) (figure 1). the properties of the production zone should meet the following criteria: porosity > cutoff, permeability > cutoff, and water saturation < cutoff. gross thickness is defined as the interval from the top to the bottom of the reservoir, encompassing all non-reservoir rocks such as shales, anhydrites, and salts. net sand refers to the fraction of the gross sand that is porous, permeable, and contains hydrocarbons and water, subject to a defined or arbitrary porosity cutoff (cobb and marek 1998). net pay is the component of the net sand that contains only hydrocarbons, subject to a water saturation cutoff. in addition to volumetric analysis, estimating net pay is useful for determining the total reservoir energy, which must account for both movable and non-movable hydrocarbons. the selection of net pay favors intervals with favorable relative permeability to injection fluids (qassamipour et al. 2020). improved oil and gas recovery 3 figure 1—reservoir interval pattern (worthington and cosentino 2005). in water-wet rock, a layer of water coats the rock surface, acting as a lubricant for oil residing in the central parts of the pores. swc represents the connate or irreducible water saturation, which is the minimum water saturation at which water remains immobile due to capillary forces. the relative permeability of water at saturations below swc is zero. sorw denotes the residual oil saturation or critical oil saturation, which is the minimum oil saturation at which the oil becomes immobile, meaning its relative permeability is zero, as depicted in figure 2 (geffen et al. 1951; eliebid et al. 2024). figure 2—oil-water relative permeability curves (geffen et al. 1951). capillary pressures arise at the interfaces between two immiscible fluids within the pores (capillaries) of reservoir rock (tsuji et al. 2016). typically, one fluid phase is considered the wetting phase, while the other is the non-wetting phase. consequently, drainage data can often be employed to forecast the saturation of nonwetting fluids at various points within a reservoir. in contrast, imbibition data can be valuable for evaluating the relative influences of capillary and viscous forces in dynamic systems (muskat 1949). the leverett 'j' function aims to correlate capillary pressure with pore structure, which is defined by porosity and permeability. the fundamental capillary model suggests that displacing a wetting phase with a non-wetting phase is predictable (leverett and lewis 1941). improved oil and gas recovery 4 j (sw) = 0.21645 pc/σ/ (√k∅),.....................................................................................................................(1) where j(sw) is the dimensionless j-function; pc is the capillary pressure, in psi; σ represents the interfacial tension, in dynes/cm; k is the permeability, in md; and ∅ is the porosity, as a fraction. geological setting the buzurgan oil field is situated in southeastern iraq, close to the iraqi-iranian border, approximately 60 kilometers southeast of amara city, the capital of maysan governorate. structural contour maps of the mishrif formation indicate that buzurgan is an anticline fold with a length of 60 kilometers and a width of 8 kilometers (figure 3) (al-mimar et al. 2015). discovered in 1969, the field commenced production from the mishrif reservoir in november 1976, utilizing a regular well pattern with large spacing (over 800 meters) (seismic study for buzergun and fauqa oil field, 1980). the buzurgan field comprises three primary formations: the mishrif, khasib, and rumaila formations. the mishrif formation, dating back to the cretaceous period, is a key carbonate reservoir in southern iraqi oil fields, recognized for its varied and complex features. within this formation, six distinct facies have been identified, ranging from mid-decline to peripheral facies (al-dujaili et al. 2023a). overlying the mishrif formation is the khasib formation, which acts as a cap rock for the mishrif, and underlying it is the rumaila formation (al ibrahim et al. 2022). the mishrif structure is segmented into three parts: the north dome, south dome, and saddle. the mishrif formation consists of six units, ma, mb11, mb12, mb21, mc1, and mc2, owing to differences in composition, petrophysical properties, and fluid properties among them (al-mimar et al. 2018). figure 3—location maps of the buzurgan oilfield (al ibrahim et al. 2022). methodology the data used included the final well report, which detailed the hole size, casing size, location, type of drilling mud, type of cementing, type of completion, and total depth for all wells. additionally, the final geological report provided depth and thickness of formations for all wells. the cpi report, which stands for computer processing interpretation, encompassed log files for porosity and saturation data for wells bu-1, 6, 7, 12, 14, 15, and bu-16. the core analysis report included porosity and permeability core data for wells bu-1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 14, 15, and bu-18. the special core analysis report detailed relative permeability and capillary pressure curves improved oil and gas recovery 5 for wells bu-3 and bu-4. pvt data, including pressure, formation volume factor, viscosity, density, and gas oil ratio (gor), was provided for wells bu-1, 3, 4, 6, 10, 12, 15, and bu-16. lastly, daily production data from 1978 to 2007 was also included. the general methodology for creating an adequate geological and reservoir model for the mishrif formation/buzurgan oilfield is organized as follows: 1. the static model is based on field data analysis to determine the original oil in place (ooip). 2. a dynamic model, developed to enhance a tool for predicting hydrocarbon reservoir performance under various operating strategies (aziz, 1979), was constructed using dynamic data, such as pvt (pressurevolume-temperature) and scal (special core analysis) data, and subsequently simulated by the reservoir engineer. 3. initial conditions, (including initial reservoir pressure, datum pressure, fluid contact, and aquifer properties, were used to solve the simulation model. sor (solution gas-oil ratio) estimation was conducted using relative permeability curves for all cores. following this, the simulation case must be executed for each sor value to calculate cumulative production and recovery. initialization of saturation and pressure. initialization involves assigning initial saturation and pressure values to each grid block within a reservoir, whether it contains hydrocarbons or not. the initial phase distribution is established based on the equilibrium between capillary pressure and gravitational force (siripatrachai et al. 2017). the subsequent step may illustrate the workflow of the equilibrium method for an oil-water reservoir system, with the pressure datum depth situated in the oil zone. this workflow utilizes the eclipse simulator (alkhateeb 2019). 1. identification the water pressure at reference point (owc), pw = pw, owc @ z = owc ,........................................................................................................................(2) 2. at the owc, pc=pd (the capillary enters pressure) po=pw, woc+pd 3. estimation the hydrostatic head, poi = po, owc + ρo g (zi – zwoc),..................................................................................................................(3) pwi= pw, owc + ρw g (zi– zwoc),...................................................................................................................(4) 4. estimation the pc at all depths, pci = poi − pwi ,.........................................................................................................................................(5) 5. using the pc values and curve to estimate saturation at each depth, pci = f (siw),.....................................................................................................................................................(6) where pw is water pressure; pw (owc) is reference water pressure at water oil contact depth (owc); po is oil pressure; ρw is water density; ρo is oil density; and pc is capillary pressure. the workflow depicted in figure 4 shows the initialization of pressure and saturation. improved oil and gas recovery 6 figure 4—initialization of pressure and saturation. (alkhateeb 2019). capillary pressure. capillary pressure is crucial in reservoir engineering for controlling fluid distribution within reservoir rock (ji et al. 2023). the small pores in reservoir rock act like capillary tubes and typically contain two immiscible fluid phases in contact (deng et al. 2023; al-dujaili et al. 2023c). numerous curves are involved in the calculation of capillary pressure for (bu-3 and bu-4), which arise from measuring capillary pressure using the restored state method (table 1). estimating the capillary pressure curve is essential for all reservoirs, as the core sample represents only a small portion of the reservoir. the leverett j-function combines these curves. the leverett j-function method can be estimated using the j-function method and plotted against water saturation to find the best-fit curve and subsequently calculate pc for each (jsw) (tohidi et al. 2024). table 1—core samples information for capillary pressure. sample no. well name depth (m) porosity % permeability (m.d) 1 bu-3 12560 16.9 9.2 2 bu-3 12593 17.3 1.6 3 bu-3 12639 19.6 4.5 4 bu-3 12662 15.3 7.5 5 bu-3 12677 14.4 5.4 6 bu-4 12655 18.1 15.8 7 bu-4 12661 16.2 11.4 8 bu-4 12687 15.9 3.0 9 bu-4 12708 15.7 2.6 10 bu-4 12717 14.4 2.7 improved oil and gas recovery 7 figure 5—a)relationship between sw vs j-function for all cores; b) rightsw vs pc for all cores. jsw is calculated using eq. 1 at each water saturation (sw), incorporating core sample properties such as porosity and permeability (sugiharto et al. 2020). figure 5a illustrates the scatter plot of jsw against water saturation, along with the best-fit curve, which is drawn in black. subsequently, eq. 1 was applied using reservoir properties, including porosity and permeability, to determine pc for each corresponding value of jsw at a specific sw (figure 5b). fluid pvt properties. eight pvt samples were collected from wells (bu1, bu3, bu4, bu6, bu10, bu12, bu15, and bu16) at various depths, each with corresponding bottom-hole pressure values. to construct a pvt model, it is necessary to utilize a pvt program that employs standing correlations to track the average properties of the oil reservoir (tariq and abdulraheem 2021). table 2 presents the average properties of the pvt fluid. table 2—average properties of pvt fluid. pressure (kg/cm2) bo (rb/stb) gor (m3/ m3) viscosity (cp) 56.9 1.13844 11.8633 3.06774 761.74 1.20105 37.4134 2.08431 1465.58 1.27351 64.2003 1.51324 2171.435 1.35981 94.3236 1.12725 2876.273 1.38005 105.403 1.0452 3581.125 1.38126 105.403 1.0884 results and discussion static and dynamic geological models. petreltm comprises a suite of modules that derive their intrinsic capability to precisely characterize the reservoir by segmenting it into three-dimensional rock cells (al-dujaili et al. 2023c). the geo-modeling process has been developed in accordance with the petrel workflow from schlumberger company, which integrates data to enhance 3d models of porosity, water saturation, and permeability estimates. this is achieved by incorporating well-bore petrophysical calculations and assigning properties through the appropriate application of deterministic, stochastic, and object modeling techniques (mohammed et al. 2022) (figure 6). improved oil and gas recovery 8 figure 6—skelton grid for the studied reservoir. stratigraphy. stratigraphy seeks to ascertain the depth and thickness of reservoir units to facilitate correlation between wells (mahmud et al. 2020). the stratigraphy of the mishrif formation in the buzurgan oil field has been subdivided into six units (ma, mb11, mb12, mb21, mc1, and mc2) based on previous studies and well reports. the boundaries of each unit were established through well-to-well correlation using petrel software, which analyzed well logs and geological reports. figures 7 and 8 illustrate the well sections for wells bu-1, 3, 5, 6, 7, 10, 11, 14, 15, and bu-16. the geological model was constructed using petrel software, which performed the processes of horizon zoning and layering. figure 9 presents a 3d view of the subsurface units/mishrif formation, while table 3 details the average thickness and layer count for each reservoir unit. table 3—division of vertical direction of 3d grid reservoir. no. of layers thickness(m) unit zone 5 20 ma-mb11 zone 1 25 19-24 mb11-mb12 zone 2 25 42-59 mb12-mb21 zone 3 20 8-20 mb21-mc1 zone 4 25 4-16 mc1-mc2 zone 5 figure 7—well section no.1 of mishrif zones and layers. improved oil and gas recovery 9 figure 8—well section no.2 of mishrif zones and layers. figure 9—3d-view of subsurface units/ mishrif formation. property modeling by conventional up-scaling. the property modeling aims to distribute reservoir properties among wells to realistically describe the reservoir heterogeneity, matching the well data (hamdi et al. 2014). the geological model must be upscaled for use in the reservoir simulator (al-janaee and al-shahwan 2019). upscaling, or homogenization, is the final stage of the geological model, involving the process of mathematically extrapolating fine-scale reservoir data to coarser scales to populate reservoir grid cells, which can be up to dozens of meters in size. improved oil and gas recovery 10 figure 10—top) water saturation and porosity models of mb21 unit; bottom) water saturation and porosity histograms for all cells. static models for water saturation, porosity, and permeability were constructed using petreltm, based on the cpi log data from wells bu-1, 6, 7, 12, 14, 15, and 16 in the buzurgan oil field. the distribution of water saturation is used to estimate the original oil in place (ooip), which is influenced by the capillary pressure curve (alhusseini and hamd-allah 2022). the water saturation distribution is also affected by the oil-water contact, which is located 3860 feet below sea level (sl). the oil-water contact (owc) value and two zones—the oil and water zones-were estimated in petreltm. figure 10 illustrates the water saturation and porosity distribution maps for mb21, as well as histograms. the results indicate that porosity distribution values range from 0.012 to 0.1842 (table 4), with water saturation values between 0.9 and 1.0 covering 45% of the cells, while the remaining 55% range from zero to 0.9 (figure 10). improved oil and gas recovery 11 table 4—summary of statistical results of porosity distribution unit type min. max. delta mean std. zone 1 property upscale 0.0325 0.0325 0.1842 0.1842 0.1516 0.1516 0.1350 0.1350 0.319 0.316 zone 2 property upscale 0.0121 0.0120 0.1523 0.1523 0.1401 0.1401 0.0559 0.0547 0.0322 0.0330 zone 3 property upscale 0.0410 0.0410 0.1659 0.1659 0.1249 0.1249 0.0989 0.1043 0.0360 0.0370 zone 4 property upscale 0.0310 0.0306 0.1432 0.1459 0.1122 0.1109 0.0867 0.0913 0.0370 0.0380 zone 5 property upscale 0.0223 0.0226 0.1460 0.1406 0.118 0.118 0.127 0.109 0.0298 0.0288 the classic method was used as the basis for estimating permeability values, employing a cross plot between core porosity and permeability, based on conventional core analysis data. porosity logs were used to set a permeability cut-off at 0.1 (farouk et al. 2021). the unit mb21 is particularly crucial as it represents the reservoir units and has a significant impact on the dynamic model well-log interpretation. mb21 is characterized as sandstone, while the mc1 and mc2 units are predominantly shale sand and exhibit better porosity and permeability (figure 11). due to the discrepancy between core and log porosity, a mathematical correlation can be established to correct porosity values. consequently, corrected porosity values, in conjunction with core permeability at a permeability cut-off of 0.1, can be depicted (figure 12 and table 5). figure 11—scatter plot of porosity versus permeability for cores from the mb21, mc1, and mc2 units. improved oil and gas recovery 12 table 5—properties cut-off value for each unit. unit permeability porosity mb21 0.1 8.2 mc1 0.1 6 mc2 0.1 7.5 figure 12—scatter plot of porosity log versus porosity core for mb21, mc1, and mc2 units. reservoir interval calculation. the reservoir interval encompasses all layers, both hydrocarbon-bearing and non-hydrocarbon-bearing, such as shale, anhydrites, salts, etc. (liu et al. 2023). net pay is crucial for assessing the total reservoir energy, which includes both mobile and immobile hydrocarbons. it can be estimated by considering the net-to-gross ratio, based on the threshold values for porosity and water saturation, while disregarding values that fall below these thresholds (ebraheem et al. 2022). the reservoir interval can be delineated by the upper and lower boundaries of each layer, as identified by ip tm. table 6 presents the results of the reservoir interval analysis for each well. improved oil and gas recovery 13 table 6—reservoir interval calculation. bu-1 n/g net gross bottom top bu-3 n/g net gross bottom top 1 77 77 3954.3 3877.3 0.988 83 84 3910.5 3826.5 0.657 40.2 61.2 4015.5 3954.4 0.478 44 92.1 4002.6 3910.5 0.965 42.5 45.5 4061 4015.5 0.945 32.5 34.4 4037 4002.6 bu-5 n/g net gross bottom top bu-6 n/g net gross bottom top 0.973 84.61 87 3912 3825 0.39 30.39 78 3990 3912 0.602 72 116.9 3878.5 3795.5 0.7 26.61 38 4028 3990 0.602 72 116.9 4960 3878.5 bu-7 n/g net gross bottom top bu-10 n/g net gross bottom top 0.963 68 70.95 3926.5 3840.5 0.963 80 81.5 3903 3821.5 0 0 0 4017.8 3926.5 0.509 43.55 85.5 3988.5 3903 0 0 0 4065 4017.8 0.965 28 29 4017.5 3988.5 bu-11 n/g net gross bottom top bu-12 n/g net gross bottom top 0.978 89.51 91.5 3916.5 3825 0.976 73.2 75 3916 0.311 28 90 4006.5 3916.5 0.439 31 70.5 3986.5 3916 0.97 32.49 33.5 4040 4006.5 0.969 32 33 4019.5 3986.5 bu-13 n/g net gross bottom top bu-14 n/g net gross bottom top 0.677 58.21 86 3887.5 3801.5 0.988 85.2 86.5 3893.5 3807 0.525 42.79 81.5 3969 3887.5 0.89 60.1 67.5 3961 3893.5 0.568 22.71 40 4009 3969 0.967 47.4 49 4010 3961 bu-15 n/g net gross bottom top bu-16 n/g net gross bottom top 0.972 83.64 86 3889 3803 0.951 79.43 83.5 3889.5 3806 0.651 53.44 82 3971 3889 0.627 53.57 85.5 3975 3889.5 0.989 35.52 36 4007 3971 1 34.5 34.5 4009 3975 improved oil and gas recovery 14 based on the porosity distribution maps for each unit, unit ma exhibits low porosity due to the lithological heterogeneity between shale and sand. the mb21 unit, however, demonstrates excellent porosity values, while the mc unit has good porosity values. the net pay and net-to-gross models were constructed using petrel™ (figure 13). figure 13—top) net to gross map distribution; bottom) net pay map distribution for mb21 unit. dynamic model. the dynamic model constitutes the second phase of this study, representing time-dependent elements. petrel tm was utilized to construct this model, incorporating the oil-water relative permeability curve, the pc curve, pvt data, and production data. improved oil and gas recovery 15 relative permeability. in this study, numerous relative permeability curves are presented for wells bu-3 and bu-4. each well has multiple samples, with each sample possessing distinct porosity and permeability values. the average relative permeability for the water–oil system can be estimated (figure 14). figure 14—average oil -water relative permeability curve. importing the pvt data into petrel™ leads to the establishment and development of pvt and dynamic simulation models. figure 15 illustrates the correlations of (bo, gor, density, and viscosity) with pressure. figure 15—averaging model for the formation volume factor, viscosity, density, and rs. improved oil and gas recovery 16 residual oil saturation calculation. the residual oil saturation for wells bu-3 and bu-4 can be estimated through special core analysis tests. by utilizing the relative permeability curve from numerous samples, an average curve can be derived to estimate the relative permeabilities to oil (kro) and water (krw) at various water saturation levels (figure 16). given that the sor (residual oil saturation) is 0.2, these results can then be applied to a simulation to project the accumulative production. figure 16—relative permeability curve for estimating sor. the relationship between the recovery factor and the sor can be summarized by altering the sor values and adjusting the average curve at the sw cutoff to 0.84. subsequently, kro and krw are estimated at various water saturation levels. these estimates are then utilized to conduct another simulation run to calculate the accumulative production. table 7 presents the assumed sor values, which are based on eq. 7, sor = 1 − sw cutoff,.....................................................................................................................................(7) table 7—residual oil saturation value. sw cutoff sor 0.8 0.2 0.77 0.23 0.72 0.28 simulation model. reservoir simulation is one of the most effective techniques currently available to reservoir engineers. the model requires that the field under study be described by a grid system, usually referred to (s cells or grid blocks. each cell must be assigned to represent the reservoir properties. the simulation allows for the description of a fully heterogeneous reservoir, including varied well performance and studying different recovery mechanisms. history matching. the observed oil production rates (monthly measurements) were honored, along with the reservoir pressure measurements from static gradient surveys (a single value for each well's entire production history). however, the production history data (spanning a long period from 1976 to 2007) is available for wells bu-1, bu-3, bu-4, bu-5, bu-6, bu-7, bu-9, bu-10, bu-11, bu-12, bu-13, bu-14, bu-15, bu-16, bu-17, bu-18, bu-19, and bu-20 (refer to table 8). the history matching, which encompasses both pressure and production history, was achieved by running the numerical model, iteratively adjusting the permeability distribution (multiplying permeability by a specific factor for all the reservoirs under study) until a satisfactory match was found between the measured and calculated production histories, while the porosity distribution was improved oil and gas recovery 17 derived from the geological model. figure 17 illustrates the matching of cumulative field oil production and field pressure, as calculated by petreltm, along with the field recovery factor and pressure. figures 18 to 21 depict the historical matching of oil production rates for wells within the reservoir under study. the buzurgan oil field commenced production in 1976 and continued until 1980, when production ceased in the field due to the iraqiiran war. production resumed in 1998 and has continued to the present day. table 8—date of well history production data. well no. history of oil production period (months) oil rate (bbl/day) from to bu-1 1/11/1976 1/1/1980 49 2750 1/1/2000 26/9/2004 57 2590 bu-4 1/2/1976 1/2/1980 48 8000 1/7/2004 31/7/2004 1 2350 bu-5 1/5/1976 1/1/1980 44 9050 3/2/1999 5/4/2003 50 6400.3 bu-6 1/1/2002 1/7/2002 7 4409 bu-7 1/2/1977 1/1/1981 47 5120.6 bu-9 1/1/1977 23/6/1979 30 2500 1/1/2000 15/1/2003 36 4600 bu-10 3/1/1978 11/1/1981 38 3800 1/8/1998 14/7/2002 61 3450 bu-11 1/8/1980 2/11/1980 3 4450 1/8/1998 14/7/2002 23 4000 bu-12 1/2/1999 12/11/2002 43 3400 bu-13 1/3/2000 1/1/2001 10 4900 1/1/2002 1/9/2002 9 5250 bu-14 1/6/1980 1/11/1980 5 2200 1/4/1999 1/6/2002 38 4050 bu-15 1/1/2003 1/1/2007 48 2350 bu-16 1/1/2000 1/7/2007 31 4450 bu-17 1/10/1980 31/10/1980 1 2780 1/7/1998 1/7/2002 48 3080 bu-18 1/1/2003 1/1/2007 48 3300 bu-19 1/1/2001 1/10/2002 22 2600 bu-20 1/1/2000 1/1/2001 12 2350 1/1/2002 1/6/2002 60 2550 improved oil and gas recovery 18 figure 17—field oil production rate (calculated vs. observed) with corresponding field pressure. figure 18—oil production rate (calculated and observed) for wells bu-1, 3, 4, and 5. improved oil and gas recovery 19 figure 19—oil production rate (calculated and observed) for the wells bu-6, 7, 9, 10, 11, and 12. figure 20—oil production rate (calculated and observed) for the wells bu-13, 14, 15, 16, 17, and 18. improved oil and gas recovery 20 figure 21—oil production rate (calculated and observed) for the wells bu-19 and bu-20, calculated field pressure, and field pressure for the well bu-1. geological structure. the geological structure of the buzurgan oil field extends from the northwest to the southeast and comprises two domes. the southern dome is larger and higher than the northern dome. the primary producing reservoir within the mishrif formation is the mb21 unit, which is the thickest and accounts for over 90% of production. it is more significant than the other units due to its favorable porosity (exceeding 6%) and low water saturation (below 60%), indicating economically viable oil reserves. wells in this field produce naturally. prior to 2003, 18 wells were drilled. after 2003, 44 directional wells were drilled primarily in the southern dome of the mishrif structure to enhance productivity. no wells have been drilled in the area between the two domes, as it is a water saddle. moreover, the southern dome's proximity to the surface suggests a greater potential for recovery. the three units (mb21, mc1, and mc2) are more considerable in petrophysical properties. as compared between the three units in these properties for porosity cut-off (table 9). these values show that unit mc1 has more recoverable volumes. but these values are not absolute as compared to thickness, unit mb21 still gives more recoverable volumes. table 9—porosity cut-off for mishrif units. unit mb21 mc1 mc2 porosity cut off 8.2 6 7.5 volume calculations. volume calculation involves estimating pore volume and determining the stock tank's original oil in place (stooip). the pore volume for each grid cell is calculated by multiplying the cell's volume (bulk volume) by its porosity. the (tooip is determined by multiplying the pore volume by the oil saturation and then dividing by the oil formation volume factor (bo) for each grid cell. the total stooip is the sum of the stooip values across all the reservoir grid cells. the following equation illustrates these calculations. stooip= vp∗(1−sw) bo ,........................................................................................................................................... (8) vp =∅ ∗ vb,..........................................................................................................................................................(9) improved oil and gas recovery 21 where vp is pore volume; vb is bulk volume; ø is porosity; sw is water saturation; and bo is formation volume factor. the static and dynamic models estimate the initial oil in place. there were differences between the two values according to the method used in the cell porosity and saturation estimation, in addition to the bo. calculation with a static model depends on the cell value of the petrophysical model that was estimated from well logs and distributed overall reservoir with geo-statistics methods. the result value of stooip is (3.2 billion cubic meters) according to bo value used. for the dynamic model, the porosity differs from that of static because of the effect of rock compaction considering the rock compressibility effect represented by the pore volume at the reservoir pressure condition using the following equation: vpore (p) = vpore (pref) [1 + c (p − pref)],..........................................................................................(10) where vpore (p) is the pore volume at cell pressure; vpore (pref) is the pore volume at reference pressure; c is the rock compressibility; p is cell pressure; and pref is reference pressure. the method for distributing water saturation in the dynamic model differs from that in the static model. in the dynamic model, water saturation distribution relies on the capillary pressure curve. the oil formation volume factor (bo) in the dynamic model is defined in relation to cell pressure and in accordance with the oil pvt table. the dynamic model's estimate of stooip is 2.1 billion cubic meters, which varies from the static model's estimate. history matching. aafter constructing the reservoir model, the reservoir simulation model was executed to match the production and pressure history and to validate the constructed model. there are numerous simulation models that can be used to reach the match point. each simulation model varies by altering the variables, including the reservoir characteristics (figure 22). the blue solid line represents the calculated oil production rate by the simulation model operating in oil rate mode, alongside the observed production rate and without any alterations to the variables. the estimated rate did not align with the measured historical production data (depicted by the dotted red line) because of the declining bottom hole pressure (bhp). the significant drop in bottom hole pressure (bhp) depicted in figure 22 results in alterations to the wellcontrol mode. the bhp control mode reduces the production rate to maintain bhp above the saturation pressure. there are several reasons for the high pressure decline, including the neglect of the aquifer effect (assuming the reservoir lacks aquifer support), its weakness, the absence of data, or uncertainties regarding reservoir permeability. generally, history matching is an inverse problem that entails adjusting model parameters until the simulation output from the reservoir model aligns with observed data. there are discrepancies between the observed and calculated values due to the significant decrease in bottom hole pressure (bhp) (refer to figure 22). the additional aquifer increases the reservoir pressure at the measurement point, yet it fails to achieve a satisfactory match. on the other hand, reservoir properties are the primary factor influencing the production rate, with reservoir pressure being indicative of permeability. this is because increased permeability raises the flowing bottom hole pressure (fbhp), allowing the well to continue producing under oil rate control, while the decline in reservoir pressure diminishes. consequently, the horizontal permeability has been adjusted using a multiplier of 1.5. this adjustment falls within the range of uncertainty. improved oil and gas recovery 22 figure 22—field pressure calculated by petreltm. reservoir performance. after history matching has been completed for the reservoir model, the subsequent step involves predicting the reservoir performance. the aim of performance prediction is to manage the field effectively and strive to maximize the recovery factor. numerous wells in the buzurgan oil field were drilled post-2003, a consequence of the iraqi-iranian war. these wells, along with others, were included in the history matching process. however, for the current study, there was insufficient data available for these wells. the performance of the mishrif formation was predicted from 2007 to 2032 across various scenarios, which are summarized in table 10 for cumulative production and recovery. table 10—0il production rate and recovery for prediction performance. case cum-prod. mmstb recovery 1 2750 0.5 2 2090 0.38 3 1650 0.3 4 2400 0.43 the base case, which serves as the foundation, was governed by the historical matching of the oil production rate, with additional control exerted by maintaining the bottom-hole pressure above the saturation pressure. the outcomes of this run, including the production rate and reservoir pressure, are depicted by the red figures (figures 23 and 24), while the green curve represents the predictive performance of the reservoir when controlled by the water cut. it indicates a significant decline in production rate and a high water cut due to the decrease in bottomhole pressure. consequently, there is a need for high-capacity surface facilities and an injection process to mitigate the high pressure drop and enhance productivity and the recovery factor. improved oil and gas recovery 23 figure 23—prediction performance for the field oil production cases. figure 24—prediction performance for the field oil production cases. sor calculation. the reservoir simulation model was executed to estimate the cumulative oil production and oil recovery for various sor (solution gas-oil ratio) values, based on the special core analysis reports for bu3 and bu-4. these reports include oil-water relative permeability curves, each characterized by specific porosity and permeability values. by averaging these curves into a single curve, the relative permeability for oil and water was adjusted according to the changes in sor. this process involved running simulations to study reservoir performance, with the aim of enhancing productivity and sustaining reservoir pressure above the saturation pressure. figure 16 illustrates the average oil-water relative permeability curve derived from bu-3 and bu-4, where the oil relative permeability is zero. at this point, sw (water saturation) equals the cut-off value, and the sor can be estimated using eq. 7. figure 16 indicates that the cut-off for sw is 0.8, hence sor equals 0.2. the relative permeability values were input into petrel to conduct the simulation (table 11). to obtain other sor values, one can adjust the average curve in figure 16 to a different sw cut-off (hypothetical) and perform a new simulation run. improved oil and gas recovery 24 table 11—oil production and recovery for each sor. sor cumulative production (mmstb) sor 0.15 1375 0.25 0.23 1045 0.19 0.28 825 0.15 average (0.2) 1100 0.20 in the initial simulation run, with a water-oil ratio (sor) of 0.15 and a water saturation (sw) cut-off of 0.85, achieving a good history match for the reservoir in question, the cumulative oil production amounted to 1,375 million stock tank barrels (mmstb), and the recovery factor was 25% without any injection process. during the second simulation, with the sor increased to 0.23 and the sw cut-off set at 0.77, the cumulative production decreased to 1,045 mmstb, and the recovery factor was 19%. in the third simulation run, with an sor of 0.28 and a sw cut-off of 0.72, the cumulative production further decreased to 825 mmstb, and the recovery factor was 15% (table 11). when these three scenarios were plotted on a single graph, the cumulative production was 1,100 mmstb, and the recovery factor was 20%. from the results, it is evident that recovery values decrease with an increase in sor, and this decline correlates with changes in relative permeability at each sor increment. relative permeability to oil is higher in water-wet rock, which may lead to a higher ultimate oil recovery in mixed-wet and oil-wet rock. consequently, as the sor increases (indicating a decrease in water saturation), the rock becomes less water-wet, which lowers the relative permeability of oil and increases the relative permeability of water, thereby decreasing oil recovery. conclusions static and dynamic models for the mishrif formation of the buzurgan field have been constructed using commercial software, followed by history matching. subsequently, predictions of future reservoir performance have been made. some important conclusions can be drawn as follows. 1. the mishrif reservoir, characterized by its carbonate composition and heterogeneity, is considered the best due to its excellent petrophysical properties. it is the primary reservoir, with the mb21 unit contributing 90% of the total production from the mishrif formation. 2. the carbonate rock exhibits scattering with a reasonable correlation on the permeability versus porosity plot. consequently, this correlation was utilized in the simulation model for calculating permeability, as it provided good history matching when multiplied by a specific factor. 3. the initial oil in place is calculated using both static and dynamic models. there are differences between them regarding the values of porosity and saturation. in the static model, the calculation relies on porosity and water saturation data from well logs. in contrast, the dynamic model considers the effects of rock compaction, compressibility, and capillary pressure. 4. the oil-in-place in the static model is approximately 3.2 billion cubic meters, whereas in the dynamic model, it is about 2.1 billion cubic meters. 5. the value of recovery declines with an increased sor, and this decline correlates with changes in relative permeability at each shift in sor. therefore, it is recommended to enhance the recovery factor through secondary mechanisms, utilizing injections to maximize productivity and maintain pressure above the saturation pressure. improved oil and gas recovery 25 nomenclature  = interfacial tension, dyne/cm o = oil density w = water density 𝑉𝑝 = pore volume ∅ = porosity bhp = bottom hole pressure bo = oil formation factor bu = buzurgan c = rock compressibility cp = centipoise cpi = computer-processed interpretation cum. = cumulative eor = enhanced oil recovery fbhp = flowing bottom hole pressure gm = gamma ray gor = gas oil ratio ip = interactive petrophysics software j(sw) = j-function dimensionless k = permeability, md kro = oil relative permeability krw = water relative permeability md = millidarcy n/g = net to gross ooip = original oil in place owc = oil water contact pref = reference pressure p = cell pressure pc = capillary pressure, psi phi = porosity po = oil pressure prod. = production pvt = pressure-volume-temperature pw = water pressure pw (owc) = reference water pressure at water oil contact ros = remaining oil saturation rs = solution gas oil ratio, scf/ stb scal = special core analysis scf = standard cubic feet sor = residual oil saturation sorw = residual oil saturation or critical oil saturation sp = spontaneous potential sstvd = sub sea true vertical depth stb = stock tank barrel std = standard deviation stooip = stock tank original oil in place sw = water saturation swc = connate or irreducible water saturation tm = trade mark tvd = true vertical depth vb = bulk volume (cell volume) improved oil and gas recovery 26 vpore (p) = pore volume at cell pressure vpore (pref) = pore volume at reference pressure vsh = shale volume conflicting interests the author(s) declare that they have no conflicting 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exploration and production technology 13(7):1551-1573. abdulkareem abbas khalil is an assistant professor at the university of kerbala. he holds a phd in petroleum engineering from baghdad university (2007), with msc (1990) and bsc (1987) degrees in the same field from the same university. his research interests focus on petroleum engineering, including oil well drilling operations, horizontal and directional drilling, oil well control, and well logging. hussain ali baker serves as an assistant professor at almaaqal university in basrah, iraq. he obtained his phd in petroleum engineering from baghdad university (2000), complemented by an msc (1989) and a bsc (1981) in petroleum engineering from the same institution. his key research areas include phase behaviour, well testing, applied reservoir engineering, and enhanced oil recovery (eor). hiba alaa naseef is affiliated with the petroleum engineering department at the university of baghdad. she earned her msc in petroleum engineering from baghdad university (2020) and a bsc in the same field from the university (2016). her research focuses on reservoir engineering and enhanced oil recovery. ahmed n. aldujaili is an assistant professor at amirkabir university of technology in tehran, iran, and a visiting professor at kerbala university. he holds a phd in petroleum engineering from amirkabir university of technology (2022), with an msc (2015) and a bsc (1992) in petroleum engineering from baghdad university. his broad research interests include petroleum exploration, reservoir engineering, drilling engineering, petroleum geology, eor, and water resources. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1352 received december 23, 2024; revised february 12, 2025; accepted may 25, 2025. *corresponding author: christian.okalla@futo.edu.ng 1 a comparative study of the rheological properties under hpht conditions anthony ogbaegbe chikwe, christian emelu okalla*, federal university of technology owerri, owerri, nigeria; oluwasanmi olabode, and abigail lnemesit uduak, covenant university abstract well drilling and the extraction of hydrocarbons from the wellbore depend significantly on drilling fluid. they have a variety of functions, including removing debris, regulating pressures to safeguard the well, ensuring the stability of the well, and reducing environmental effect. water-based muds (wbms) and oil-based muds (obms), are the predominant choices of drilling muds and they encounter some limitations in maintaining optimal rheological properties under such extreme conditions, necessitating advanced formulations. wbms struggle with stability, obms raise environmental concerns under high temperature-high pressure (hthp) conditions in subsurface drilling. this project research is on comparative study of the rheological properties of formulated water-based mud (wbm) using nano particles and almond base oil under hthp conditions. this study aims to investigate the rheological properties and performance of both nanoparticles incorporating water-based mud and almond oil-based mud, incorporating varying concentrations of silica oxide nanoparticles (0.1%, 1%, 5%, and 10%). the focus is on assessing the mud's density, gel strength, dial readings, plastic viscosity (pv), yield point (yp), apparent viscosity (av), fluid loss, and mud cake thickness. results demonstrate that the addition of silica oxide nanoparticles significantly enhances the mud's rheological properties, with optimal performance observed at a 5% concentration for both mud types. cost-effectiveness, environmental impact, and ease of use were also evaluated, with silica nanoparticles in water-based mud having good rheological properties compared to normal water-based mud and almond oil-based muds offering superior environmental benefits, while diesel-based muds provided better cost efficiency and handling. introduction drilling fluids constitute for 15% to 18% of the overall cost of petroleum well drilling and they must typically meet these essential criteria: they must be: easy to use; cost-effective; and environmentally friendly (khodja et al. 2010). well drilling and the extraction of hydrocarbons from the wellbore depend significantly on drilling fluid (vishnyakov et al. 2020). they have a variety of functions, including removing debris from the well, regulating formation pressures to safeguard the well, ensuring the stability of the well, supporting, lubricating, and cooling the drill string and drill bit and reducing environmental effect (almotasim et al. 2023). the rheological characteristics of drilling muds, particularly in the context of severe conditions such as those encountered in high temperature and high pressure (hthp) environments, play a pivotal role in determining the success of drilling operations. the viscosity and flow behavior of these muds under such extreme conditions are essential parameters that can significantly impact the efficiency and effectiveness of the drilling process. among the various types of drilling fluids available, water-based muds (wbms) and oil-based muds (obms) have traditionally been the primary options that drillers rely on (agwu, 2021). these muds are specifically formulated to provide optimal performance in terms of cooling the drill bit, lubricating the drill string, and maintaining stability in the borehole. the choice between wbm and obm often depends on the specific requirements of the drilling operation, such mailto:christian.okalla@futo.edu.ng improved oil and gas recovery 2 as the type of formation being drilled, the temperature and pressure conditions, and environmental regulations. in addition to these conventional options, ongoing research and development have led to the exploration of alternative drilling fluids, such as synthetic-based muds and various types of invert emulsion fluids, which offer improved performance in certain scenarios. the summary of other related work in this field is presented in table 1, which provides a comprehensive overview of the various studies and findings that have contributed to the understanding and advancement of drilling mud technology, particularly concerning their rheological properties under extreme conditions. table 1—review study. authors (year) materials used base fluid modified properties summary of result gaps identified ananwe et. al. (2014) jatropha oil groundnut oil oil viscosity the obm made with groundnut and jatropha oils were respectively 2.7 and 3 times more viscous than the mud based on diesel oils accounted for just jatropha oil chikwe et al. (2019) almond oil castor oil groundnut oil oil rheological properties and environment friendly using almond oil is less toxic than diesel and has better cleaning hole capacity. did not account for different temperature ranges for the rheological properties. hassani et al. (2016) sio2 zno carbon nanotubes water rheological properties using 2.0wt% for all the nanoparticles showed twice the improvement in rheological properties with the most improvement from sio2 need for comprehensive studies on the long-term effects and environmental impacts of nanoparticles methodology the materials used in this research project include bentonites, barite, nanoparticles (sio2 0.1wt%, 1wt%, 5 wt% and 10% wt): nanoparticles particles are a particle with a diameter smaller than 100 nm. the components of silica dioxide nanoparticles are made of silicon and oxygen. in this project, four different concentrations were used (sio2 0.1 wt%, 1 wt%, 5 wt% and 10% wt). deionized water, carboxy methyl cellulose (cmc), almond oil. to create the formulation for a water-based mud, the subsequent procedure was meticulously carried out to ensure the desired properties and consistency were achieved. 1. 400ml of deionized water was accurately measured into a measuring cylinder. 2. the above quantity of water was emptied into the hamilton beak mud mixer and fixed to the mixer. 3. the mixer is plugged into a power supply. 4. bentonite of about (25g) was measured using an electric weighing balance and is poured into the hamilton mixer then stirred for 5 minutes to ensure mixing is done evenly and absence of lumps. 5. 15g of barite was added to this mixture and stirred for 5 minutes. 6. 0.3g of the cmc was measured and on the electric chemical balance and poured inside the mud mixer which already contains the evenly mixed water 7. for water-based mud with nanoparticles incorporated in it, 4 different concentrations of silica oxide nanoparticles were used (0.1wt%, 1wt%,5 wt% and 10%wt). 8. it was stirred for 15 minutes to ensure evenly mixed and absence of lumps. the specific methodology that was employed to derive the formulation for an oil-based mud involved several detailed steps. 1. 300ml of almond oil was accurately measured into a measuring cylinder. 2. the above quantity of oil was emptied into the hamilton mud mixer and fixed to the mixer. improved oil and gas recovery 3 3. the mixer was then plugged into a power supply. 4. bentonite of about (25g) was measured using an electric weighing balance and was poured into the hamilton mixer then stirred for 5 minutes to ensure mixing was done evenly and absence of lumps. 5. 15g of barite was added to this mixture and stirred for 5 minutes. 6. 0.3g of the cmc was measured and on the electric chemical balance and poured inside the mud mixer which already contains the evenly mixed oil. 7. it was stirred for 15 minutes to ensure evenly mixed and absence of lumps. procedure for measuring mud weight. the prepared mud mixture was introduced into the stationary mud cup and subsequently sealed with its lid. any air bubbles and extraneous mud emerging from the aperture in the lid were meticulously removed. the stationary mud cup was then positioned within its holder. the sliding weight rider was adjusted until the balance achieved a stable state, with the level bubble centered. the mud density corresponding to each mud formulation was duly recorded. rotational viscometer measurement. the viscosity of a material and its yield point can be determined with the help of this apparatus, amongst other things. an inner bob and a spinning outer sleeve are two of the components that are included in this device. these components work together to shear and rotate the mud sample at a consistent rate. the test was carried out at a range of different speeds, such as 600, 300, 100, and so on. after placing the sample of mud in a cup (preferably, one designed to hold slurries), readings are obtained by rotating the cup containing the mud. after these components have been converted into a plastic viscosity, the point of yield is then attained. protocol for the measurement of rheological characteristics. the mud specimen was introduced into the warm cup until it attained the designated mark on the cup's surface. subsequently, the warm cup was positioned atop the viscometer's stand. the cup was elevated and maintained in place until the rotating sleeve was fully submerged, aligning with the recording device. securement was achieved by engaging the locking mechanism, ensuring the cup was properly affixed. a mixing protocol was then initiated, involving a 10-second agitation period, followed by sequential adjustments of the handle to various rotational speeds. at the point where the dial reading balances out, values were obtained. plastic viscosity (pv) (cp) =600 rpm readings-300 rpm readings,................................................................(1) yield point (yp) (lb/100ft2)=300 rpm readings-plastic viscosity,....................................................................(2) apparent viscosity (av) (cp) = = 600rpm readings 2 .............................................................................................(3) it is important to note that the gel strength at 10 seconds, denoted in pounds per 100 square feet (lb/100ft²), refers to the peak dial deflection occurring after a duration of 10 seconds. conversely, the gel strength at 10 minutes, also measured in pounds per 100 square feet (lb/100ft²), signifies the peak dial deflection observed after a period of 10 minutes. steps for the measurement of ph. activate the ph meter and proceed to rinse the electrode with distilled water, subsequently drying it with a clean tissue. calibrate the ph meter employing deionized water (calibrated to a ph of 7.0). procure a sample of the drilling fluid within a clean beaker. thoroughly agitate the drilling fluid sample using a stirring rod or magnetic stirrer to guarantee homogeneity. submerge the electrode into the drilling fluid sample, ensuring complete immersion without allowing contact with the container's base. allow the ph meter to reach equilibrium and subsequently display the ph value. document the ph value. the electrode should be rinsed with distilled water subsequent to the measurement process. the procedure for evaluating high-temperature high-pressure (hthp) fluid loss control involves utilizing a filtration assembly designed for hthp filtration tests. the drilling fluid sample is prepared within the filtration cell, and thereafter, improved oil and gas recovery 4 the requisite pressure is applied to the sample. the temperature is consistently maintained throughout the duration of the test. the filtrate that permeates through the filter medium is collected, and the volume of this filtrate is quantified over a predetermined time interval. subsequently, the thickness of the filter cake is documented. results this section presents the detailed outcomes of the experiments and analyses conducted to fulfill the objectives of the current study. the drilling segment delineates the results, which elucidate the influence on the rheological properties and characteristics of the mud subsequent to the addition of nanoparticles to water-based mud and the utilization of almond oil in the formulation of oil-based mud. silica oxide nanoparticles ftir analysis. figure 1 shows the results of a fourier transform infrared (ftir) spectroscopy analysis of silica oxide nanoparticles. ftir spectroscopy is a technique used to obtain an infrared spectrum of absorption or emission of a sample. it provides information about the molecular composition and structure of the sample by measuring how different wavelengths of infrared light are absorbed by the sample. figure 1—ftir analysis. analysis of the ftir spectrum. the x-axis represents the wavenumber in cm⁻¹, which is the reciprocal of the wavelength and is directly proportional to the energy of the vibrations. the range typically extends from 4000 cm⁻¹ to 400 cm⁻¹. the y-axis represents the transmittance (%), which indicates how much light passes through the sample. a lower transmittance at a specific wavenumber means higher absorption, corresponding to the presence of specific chemical bonds. four significant peaks are identified in the spectrum, each corresponding to specific vibrational modes of the silica oxide nanoparticles (table 2): peak 1: this peak is likely associated with the bending vibrations of si-o-si bonds in the silica network having a wavenumber of 693.28484 cm⁻¹ and intensity of 66.99708; peak 2: this peak is typically attributed to symmetric stretching vibrations of the si-o-si bonds having a wavenumber of 775.28627 cm⁻¹ and intensity of 43.64883; peak 3: this peak corresponds to the asymmetric stretching vibrations of the si-o-si bonds, which is a characteristic peak for silica materials having a wavenumber of 1051.10927 cm⁻¹ and intensity of 34.76249; improved oil and gas recovery 5 peak 4: this peak is often associated with the asymmetric stretching vibrations of si-o bonds, indicating the presence of silica having a wavenumber of 1162.92941 cm⁻¹ and intensity of 72.06705. table 2—ftir readings. peak number wavenumber (cm-1) intensity 1 693.28484 66.99708 2 775.28627 43.64883 3 1051.10927 34.76249 4 1162.92941 72.06705 water based mud formulation. five distinct formulations of water-based mud were carefully prepared and meticulously measured for their properties. sample a serves as the foundational fluid mixture, comprising 25 grams of bentonite, 400 milliliters of deionized water, 10 grams of barite, and a precise amount of 0.3 grams of carboxymethyl cellulose (cmc). following the creation of this baseline sample, samples b through e were crafted by introducing varying concentrations of silicon dioxide (sio2) into the mixtures. each subsequent sample was engineered to include a different amount of sio2, allowing for a comparative analysis of how this additive influences the properties of the water-based mud. sample a: 25g bentonite + 400 ml deionized water + 10g barite + 0.3 cmc,................................................(4) sample b: 25g bentonite + 400 ml deionized water + 10g barite + 0.3 cmc + 0.1wt% sio2,.......................(5) sample c: 25g bentonite + 400 ml deionized water + 10g barite + 0.3 cmc + 1wt% sio2,..........................(6) sample d: 25g bentonite + 400 ml deionized water + 10g barite + 0.3 cmc + 5wt% sio2,..........................(7) sample e: 25g bentonite + 400 ml deionized water + 10g barite + 0.3 cmc + 10wt% sio2,........................(8) to thoroughly evaluate and compare the performance of all the different formulations of water-based mud, a series of comprehensive measurements were meticulously carried out. these measurements encompassed a variety of critical parameters, such as the determination of density, the assessment of ph levels, and the evaluation of gel strength, among other essential tests. each of these measurements was crucial in understanding the unique characteristics and behaviors exhibited by the various mud formulations under investigation. the meticulous data collected from these tests were then systematically organized and presented in a clear and structured manner within tables 3 through 7, providing a detailed comparative analysis of the results obtained from each formulation. upon conducting a thorough examination of the densities of all the samples under consideration, it has been observed that their values are remarkably similar, with a very tight clustering around the range of 8.65 to 8.8 ppg. this consistency is clear in the data presented in table 3. similarly, when analyzing the ph values of these samples, it becomes apparent that they also exhibit a high degree of similarity, with their values closely grouped around a range of 8.0 to 8.53 (table 4). table 3—density reading of the samples. sample a base fluid, ppg sample b 0.1wt% sio2, ppg sample c 1wt%wt sio2, ppg sample d 5wt% sio2, ppg sample e 10wt% sio2, ppg 8.7 8.8 8.8 8.65 8.8 improved oil and gas recovery 6 table 4—ph readings of the samples for water-based mud. table 5—gel strength on different fluid samples for water-based mud. sample a base fluid sample b 0.1wt% sio2 sample c 1wt%wt sio2 sample d 5wt% sio2 sample e 10wt% sio2 gel strength (10 secs) 3 2 3 6 4 gel strength (10 mins) 12 9 12 17 15 table 6 provides a detailed overview of the dial readings recorded for the five distinct mud samples, spanning a comprehensive spectrum from 6 rpm up to 600 rpm. it is evident that the presence of sio2 within these samples has a notable impact on the dial readings. specifically, as the concentration of sio2 within the samples is incrementally increased from 1wt% to 10wt%, there is a corresponding and noticeable rise in the dial readings, indicating a direct correlation between higher sio2 content and increased dial readings. conversely, when the concentration of sio2 is reduced to a minimal level of just 0.1wt%, the dial readings exhibit a decline, suggesting that lower concentrations of sio2 result in lower dial readings. this pattern underscores the significant influence that sio2 concentration has on the dial readings of mud samples under varying rotational speeds. table 6—dial readings on different fluid samples for water-based mud. dial readings sample a base fluid sample b 0.1wt% sio2 sample c 1wt%wt sio2 sample d 5wt% sio2 sample e 10wt% sio2 600rpm 22 17 23 23 28 300rpm 16 13 17 17 18 200rpm 12 11 13 13 14 100rpm 7 6 8 8 10 60rpm 5 4 5 5 6 30rpm 4 3 3 3 5 6rpm 1 1 1 1 2 as the concentration of silicon dioxide (sio2) within the base fluid is progressively elevated, it becomes increasingly apparent that there is a corresponding reduction in both the fluid loss and the thickness of the mud (table 7). this phenomenon can be attributed to enhanced structural integrity and improved rheological properties that silicon dioxide imparts to the fluid. the addition of sio2 particles increases the viscosity and creates a more stable suspension, which in turn helps to reduce the escape of fluid from the mud system. additionally, the presence of these particles contributes to the formation of a stronger filter cake on the wellbore walls, further minimizing fluid loss. the overall effect is a more controlled and efficient drilling operation, as the mud retains its desired consistency and thickness, ensuring better lubrication and cooling of the drill bit, as well sample a base fluid sample b 0.1wt% sio2 sample c 1wt%wt sio2 sample d 5wt% sio2 sample e 10wt% sio2 8.35 8.0 8.49 8.53 8.39 improved oil and gas recovery 7 as improved suspension of cuttings. this allows for more effective drilling and reduces the risk of wellbore instability, ultimately leading to cost savings and enhanced operational safety. table 7—fluid loss and fluid thickness of the sample for water-based mud sample a base fluid sample b 0.1wt% sio2 sample c 1wt%wt sio2 sample d 5wt% sio2 sample e 10wt% sio2 fluid loss, ml 21 18 16 13 14 mud thickness, mm 2.0 1.8 1.7 1.2 1.4 oil based mud formulations. in the realm of oil-based mud formulations, we have two distinct samples, designated as sample f and sample g. sample f is meticulously crafted using a blend of components. it consists of 25 grams of bentonite, a versatile clay mineral known for its excellent rheological properties, which are crucial for mud formulations. this is then mixed with 300 milliliters of almond oil, chosen for its lubricating qualities and ability to reduce friction in drilling operations. to enhance the density and provide weight to the mud, 10 grams of barite are added; barite is a dense mineral commonly used in drilling fluids for its high specific gravity. completing the formulation, 0.3 grams of carboxymethyl cellulose (cmc) are included; cmc acts as a viscosifier, helping to maintain the desired viscosity of the mud. this combination is carefully mixed to ensure homogeneity and optimal performance in oil-based mud applications. the specific formulation is represented as follows: 25g bentonite + 300 ml almond oil + 10g barite + 0.3 cmc............................................................................(9) sample g, on the other hand, shares some similarities with sample f but differs in key aspects. it also comprises 25 grams of bentonite, providing the foundational rheological properties. however, instead of almond oil, this formulation uses 300 milliliters of diesel oil, selected for its superior ability to dissolve organic compounds and its cost-effectiveness. like sample f, it includes 10 grams of barite for increased density and 0.3 grams of cmc for viscosity control. the formulation is represented as follows: 25g bentonite + 300 ml diesel oil + 10g barite + 0.3 cmc.............................................................................(10) to evaluate the effectiveness of these formulations, the density of both sample f and sample g was measured. the density of sample f was determined to be 9.1, indicating a relatively lightweight yet effective composition suitable for certain drilling conditions. in contrast, sample g exhibited a slightly higher density of 9.3, suggesting a formulation that is better suited for scenarios requiring a denser mud to manage wellbore pressures more effectively. these measurements are crucial in determining the suitability of each formulation for specific drilling environments and objectives. the ph values of sample f and sample g were measured to be 7.7 and 6.8, respectively, indicating that sample f is slightly alkaline while sample g is mildly acidic. table 8 provides a detailed examination of the dial readings for the two oil-based mud samples, encompassing a range from 6 rpm to 600 rpm. it is apparent that the oil component within both samples significantly influences the dial readings in comparison to the base mud sample (sample a). notably, sample g, which contains diesel oil, exhibits a corresponding and significant increase in dial readings. improved oil and gas recovery 8 table 8—dial reading on the oil formulations. dial readings sample a base fluid sample f (with almond oil) sample g (with diesel oil) 600rpm 22 30 38 300rpm 16 23 26 200rpm 12 15 16 100rpm 7 12 14 60rpm 5 10 12 30rpm 4 8 9 6rpm 1 4 3 the gel strength measurements, taken at both 10 seconds and 10 minutes, for the two types of oil-based mud are detailed in table 9. upon examination of the data, it becomes evident that sample f exhibits a significantly lower gel strength compared to sample g at both time intervals. the fluid loss and mud thickness for the two oilbased mud are presented (table 10). specifically, sample f, which incorporates almond oil, exhibits a significantly higher level of fluid loss and a thicker mud thickness compared to sample g. table 9—gel strength of the mud formulations. sample f: almond oil sample g: diesel oil gel strength (10 secs) 3 4 gel strength (10 mins) 12 15 table 10—fluid loss and mud thickness of the mud formulation. sample f: almond oil sample g: diesel oil fluid loss, ml 21 19 mud thickness, mm 2.0 1.5 comparison of both mud formulation. table 14 provides a comprehensive review and summary of the rheological characteristics exhibited by each of the seven different mud samples under examination. this table meticulously details various essential parameters that are crucial for evaluating the performance and behavior of drilling fluids in various conditions. in particular, samples c through g exhibit elevated plastic and apparent viscosity values compared to the base mud sample, indicative of a greater resistance to flow attributable to the presence of solid particles within the fluid. the yield point is also covered, representing the in the mud sample. oil-based mud samples (designated as sample f and sample g) exhibit a greater yield point, suggesting that the presence of an oil component within the mud necessitates a higher minimum applied force to initiate flow. furthermore, the gel strength at two distinct intervals—10 seconds and 10 minutes—is provided. this aspect is particularly important as it indicates the mud's ability to suspend drilled solids when circulation is stopped, such as during tripping operations. by examining these properties, one can gain valuable insights into the mud samples’ overall performance and suitability for specific drilling applications. improved oil and gas recovery 9 table 14— rheology properties of the mud formulations. properties sample a base fluid sample b 0.1wt% sio2 sample c 1wt%wt sio2 sample d 5wt% sio2 sample e 10wt% sio2 sample f almond oil sample g diesel oil plastic viscosity 6 4 6 10 7 7 12 yield point 10 9 11 8 10 16 14 apparent viscosity 11 9.5 11.5 14 12 15 19 gel strength (10 secs) 3 2 3 6 4 3 4 gel strength (10 mins) 12 9 12 17 15 12 15 discussion the identified peaks and their wavenumbers are consistent with the characteristic vibrational modes of silica (sio₂) bonds as seen in figure 1. the variations in peak intensities suggest differences in the concentration or environment of the chemical bonds in the sample. the presence of these peaks confirms the silica structure and provides insights into the specific bonding and arrangement of the sio₂ network in the nanoparticles. the analysis of the rheological properties of the samples, including the base fluid, sio₂ nanoparticle suspensions in waterbased mud, almond oil-based mud, and diesel oilbased mud, reveals significant insights into their potential applications and suitability for various industrial purposes. the data indicate that all samples exhibit shear-thinning behavior, where viscosity decreases with an increasing shear rate. this characteristic is advantageous for applications requiring ease of pumping and spreading at high shear rates while maintaining sufficient thickness at low shear rates. the addition of sio₂ nanoparticles to the base fluid generally increases its viscosity, with the effect being more pronounced at higher concentrations. specifically, at 5 wt% sio₂, the sample exhibits the highest viscosity, which could be beneficial for applications needing thicker lubricants. however, beyond this concentration, the viscosity increases likely due to particle-particle interactions or aggregation, suggesting an optimal concentration threshold for enhancing viscosity without causing stability issues. from a cost perspective, the inclusion of sio₂ nanoparticles must be carefully evaluated. while nanoparticles can improve the rheological properties of fluids, they also add to the overall cost of the formulation. the price of sio₂ nanoparticles is relatively high, especially for high-purity or specially treated particles. thus, the cost-benefit ratio must be assessed, particularly in comparison to more readily available and potentially cheaper alternatives like diesel oil. almond oil, though exhibiting higher viscosity, is more expensive compared to using diesel oil or silica oxide incorporated water-based mud due to its sourcing and production process, which is typically more expensive than synthetic or mineral oils. diesel oil, while providing high viscosity, is generally more affordable and widely available, making it a practical choice for heavy-duty applications where cost constraints are critical. improved oil and gas recovery 10 environmental considerations play a crucial role in selecting suitable fluids for industrial applications. sio₂ nanoparticles, while enhancing rheological properties, must be evaluated for their environmental impact during production, usage, and disposal. nanoparticles can pose risks to ecosystems if not managed properly, necessitating the implementation of stringent environmental and safety protocols. almond oil, being a natural and biodegradable product, offers a more environmentally friendly alternative, though its production must be sustainable to avoid negative ecological impacts. diesel oil, despite its effectiveness and low cost, poses significant environmental concerns due to its petroleum-based nature and associated pollution risks. therefore, its use should be carefully managed to minimize environmental damage, and alternatives should be considered where feasible. the choice of fluid should balance rheological performance, cost-efficiency, and environmental impact. sio₂ nanoparticles can enhance viscosity but come with higher costs and environmental considerations. almond oil provides a natural and biodegradable option but at a higher price, while diesel oil, despite its cost-effectiveness, raises significant environmental concerns. the decision should align with the specific requirements of the application, budget constraints, and sustainability goals. conclusions this study presents a comprehensive comparative analysis of the rheological properties of formulated water-based mud (wbm) enhanced with sio₂ nanoparticles and oil-based mud (obm) using almond oil under high-pressure high-temperature (hpht) conditions. the primary objective was to investigate the effect of sio₂ nanoparticles on the rheological behavior of wbm and compare it with obm, specifically almond oil-based mud, to determine their suitability for hpht drilling applications. the rheological analysis revealed that both nanoparticle-enhanced wbms and almond oil-based obms exhibit shear-thinning behavior, characterized by a decrease in viscosity with increasing shear rate. this property is crucial for effective mud circulation during drilling operations. the inclusion of sio₂ nanoparticles in the wbm significantly altered its viscosity, with higher concentrations (up to 5 wt%) resulting in notable increases in viscosity. however, the increase in viscosity plateaued beyond this concentration, likely due to particle aggregation or saturation effects. almond oil-based obm demonstrated higher viscosity across all shear rates compared to the base fluid and sio₂enhanced wbm. this suggests that almond oil could provide better hole cleaning and cuttings suspension, particularly in low shear rate conditions common in deep well drilling. despite this, the cost and environmental considerations associated with almond oil and sio₂ nanoparticles must be factored into their practical application. in summary, the study concludes that while sio₂ nanoparticles effectively enhance the viscosity of wbm, the optimal concentration must be carefully controlled to avoid stability issues. almond oil based obm, although exhibiting superior rheological properties, requires careful cost and environmental impact assessments. recommendations based on this study, the following recommendations are proposed: 1. it is recommended to use sio₂ nanoparticles at an optimal concentration of around 5 wt% in wbm. this concentration maximizes viscosity enhancement without causing significant particle aggregation or stability issues. 2. conduct a thorough cost-benefit analysis when considering the use of sio₂ nanoparticles and almond oil for mud formulation. while nanoparticles improve rheological properties, their cost must be justified by the performance benefits they offer. similarly, the use of almond oil should be evaluated for its overall cost implications, especially in large-scale drilling operations. 3. implement stringent environmental impact assessments for the use of sio₂ nanoparticles and almond oil in drilling fluids. ensure that the production, usage, and disposal of these materials adhere to environmental improved oil and gas recovery 11 regulations and minimize ecological risks. explore the development of biodegradable and environmentally friendly alternatives to conventional drilling fluids, aiming to reduce the ecological footprint of drilling operations. 4. for future research purposes, extend the research to evaluate the long-term stability and performance of sio₂enhanced wbms and almond oil-based obms under varying hpht conditions. investigate the interaction mechanisms of nanoparticles at higher concentrations to optimize their dispersion and effectiveness. explore the potential of other nanoparticles and natural oils to further enhance the rheological properties of drilling muds, aiming for improved performance and sustainability. 5. conduct field analysis to validate the laboratory findings and assess the practical performance of sio₂enhanced wbms and almond oil-based obms in real drilling scenarios. field trials will provide critical data on the operational feasibility and economic viability of these formulations. conflicting interests the author(s) declare that they have no conflicting interests. refereneces agwu, o. e., akpabio, j. u., ekpenyong, m. e., et al. 2021. a critical review of drilling mud rheological models. journal of petroleum science and engineering 203(1):108659. almotasim, a. k., chala, g.t., and alkalbani, g. t. 2023. experimental investigation of the rheological properties of water base mud with silica nanoparticles for deep well application. ain shams engineering journal 14(10): 102147. ananwe, a.l., efeovbokhan, v.e, ayoola a.a., et al. 2014. investigating alternatives to diesel in oil based drilling mud formulations used in the oil industry. journal of environment and earth science 4(14):1-12. chikwe, a.o., onuh, c.h., ajugwe, u.j., et al. 2019. development of environmentally friendly oil based mud using almond oil, castor oil and groundnut oil. american journal of engineering research 4(2): 88-98. hassani, s.s., amrollahi, a., rashidi, a., et al., 2016. the effect of nanoparticles on the heat transfer properties of drilling fluids. j. pet. sci. eng. 146 :183-190. khodja, m. k.s. 2010. drilling fluid technology: performances and environmental considerations. r&d to final solutions 5(2): 227-256. vishnyakov, v., suleimanov, b., salmanov a. et al. 2020. introduction to well technology, primer on enhanced oil recovery. houstion, usa: gulf professional publishing. christian emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri, owerri, nigeria. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, natural gas, and reservoir simulation. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1329 received december 11, 2024; revised january 22, 2025; accepted february 10, 2025. *corresponding author: mjawwad_khan@yahoo.com 1 investigating the impact of water and polymer flooding techniques on reservoir performance in heterogeneous unconsolidated formations sajjad aziz, nfc-institute of engineering and technology, multan, pakistan; muhammad jawad khan*, universiti teknologi petronas, perak, malaysia; muhammad asad, and farzain ud din kirmani, nfcinstitute of engineering and technology, multan, pakistan; hassan aziz, dawood university of engineering and technology, karachi, pakistan, and mehran university of engineering and technology, jamshoro, pakistan; fahd saeed alakbari, universiti teknologi petronas, perak, malaysia abstract the global oil and gas industry increasingly leverages advanced enhanced oil recovery (eor) methods to optimize hydrocarbon extraction from mature reservoirs. among these, water flooding remains a widely adopted technique, typically achieving recovery rates ranging from 10% to 40% of the original oil in place (ooip). polymer flooding, a prominent eor strategy, enhances recovery by introducing water-soluble polymers to increase the viscosity of the injected water, thereby improving the mobility ratio and vertical sweep efficiency compared to conventional waterflooding. this study evaluates the comparative performance of water flooding and polymer flooding with respect to oil production rates, cumulative production, recovery factors, and the timing of water breakthrough. a threedimensional, two-phase (oil and water) reservoir model was developed using a black-oil simulator. the investigation incorporated the injection of a flexible biopolymer, such as xanthan gum, into a heterogeneous and unconsolidated reservoir using a direct-line drive method. the study further conducted a sensitivity analysis of polymer flooding, focusing on various injection well configurations, with an emphasis on the five-spot pattern, to identify the optimal injection strategy. the results demonstrate that polymer flooding using a direct-line drive achieves a recovery factor of approximately 44%. in contrast, employing a five-spot injection pattern significantly enhances recovery efficiency to 52% while substantially delaying water breakthrough. these findings underscore the effectiveness of integrating polymer flooding with a five-spot injection pattern to maximize oil recovery from heterogeneous reservoirs. introduction as global energy demand continues to rise, oil remains a critical primary energy source. currently, global daily oil consumption has increased by 0.8 million barrels, reaching approximately 101 million barrels per day, while daily oil production has grown by 2.1 million barrels, reflecting a growth rate of 2.3%. the recovery factor (rf) in oil fields is typically categorized into three phases: primary, secondary, and tertiary recovery (ragab and mansour 2021). mailto:mjawwad_khan@yahoo.com improved oil and gas recovery 2 the primary recovery phase relies on natural reservoir energy, such as solution gas drive, gas cap drive, and aquifer influx, to extract oil, achieving recovery rates of 5% to 15% (thomas 2016). as the natural energy depletes, secondary recovery methods, including water flooding and gas injection, are employed to maintain reservoir pressure and sustain production. the combined recovery factor from primary and secondary recovery methods typically reaches 32%. tertiary recovery, commonly referred to as enhanced oil recovery (eor), employs advanced techniques such as chemical flooding, gas injection, and thermal recovery to mobilize remaining oil. these methods significantly enhance recovery efficiency, achieving recovery factors of 30% to 60% of the original oil in place (ooip), substantially exceeding the 20% to 40% recovery typically realized with primary and secondary recovery methods (gbadamosi et al. 2019; li et al. 2017). chemical flooding, a prominent eor method, involves injecting water mixed with tailored chemicals, such as surfactants and polymers, to improve oil displacement efficiency. even after secondary recovery methods like water or gas injection, significant volumes of oil remain trapped in the reservoir due to unfavorable mobility control, as depicted in figure 1(a). according to glatz, an unfavorable mobility ratio is a major contributor to this inefficiency. the mobility ratio, defined as the ratio of the displacing fluid's mobility (permeability divided by viscosity) to that of the displaced fluid, directly influences the efficiency of the displacement process (jang et al. 2015; kossack 2012; khan et al. 2021). an inverse relationship exists between volumetric sweep efficiency and the mobility ratio. when the mobility ratio (m>1) exceeds unity, the displacement process becomes unstable, resulting in viscous fingering. over time, this instability allows the displacing fluid to prematurely breakthrough to the production well, significantly reducing overall recovery efficiency. this phenomenon underscores the importance of achieving a favorable mobility ratio to optimize reservoir performance and enhance recovery outcomes. 𝑀 = λ 𝑤𝑎𝑡𝑒𝑟 λ 𝑜𝑖𝑙 = κ 𝑤𝑎𝑡𝑒𝑟 μ 𝑤𝑎𝑡𝑒𝑟⁄ κ 𝑜𝑖𝑙 μ 𝑜𝑖𝑙⁄ ,..........................................................................................................................(1) to address the challenge of an unfavorable mobility ratio, polymer flooding is employed to reduce the mobility ratio and enhance displacement stability. by increasing the viscosity of the displacing fluid, this method mitigates the fingering effect, stabilizes water movement, and significantly improves oil recovery efficiency, as illustrated in figure 1(b). first introduced as a tertiary recovery method in the early 1960s, polymer flooding has since gained widespread recognition as a highly effective enhanced oil recovery (eor) technique (thomas 2016; li et al. 2017). (a) fingering effect promoted by the unfavorable m (b) oil recovery facilitated using polymer flooding figure 1—chemical flooding mechanism (ragab and mansour 2021). improved oil and gas recovery 3 polymer flooding has been extensively studied over the past four decades, demonstrating its capability to recover up to 30% of the original oil in place (ooip) across diverse reservoir conditions. this method is also cost-effective compared to conventional waterflooding, as it not only enhances oil production but also reduces excessive water production. typically, the efficiency of polymer flooding requires the injection of 0.7 to 1.75 pounds of polymer per barrel of additional oil recovered. the addition of polymers to water increases the viscosity of the displacing fluid, effectively reducing its relative permeability and improving the mobility ratio. the process begins with the injection of water containing surfactants, which lowers the interfacial tension between oil and water and alters the wettability of the reservoir rock. following this preconditioning step, a polymer-water solution is injected continuously over a period of several years. once approximately 30% to 50% of the reservoir’s pore volume has been injected with the polymer solution, the injection is terminated, and drive water is subsequently used to push the polymer slug and the resulting oil bank toward production wells (figure 2). ideal mobility control agents for polymer flooding should exhibit a combination of cost-effectiveness and high injectivity, while maintaining stability and performance under challenging reservoir conditions. these agents must resist mechanical and microbial degradation, tolerate high reservoir temperatures (up to 200°c), and perform effectively in the presence of reservoir brines and oilfield chemicals. additionally, they should demonstrate low retention within porous media, ensuring minimal loss during injection. the agents must also be resilient to variations in acidity (ph) and remain unaffected by the presence of hydrocarbons to maximize their effectiveness in diverse reservoir environments (ahmed 2006). figure 2—schematic of polymer flooding (ragab and mansour 2021). polymer types. polymers employed in enhanced oil recovery (eor) are broadly categorized into synthetic polymers and biopolymers. commonly utilized synthetic polymers include polyacrylamide (pam) and partially hydrolyzed polyacrylamide (hpam), whereas biopolymers encompass xanthan gum and modified natural polymers such as hydroxyethyl cellulose (hec), guar gum, sodium carboxymethyl cellulose, and carboxy ethoxy improved oil and gas recovery 4 hydroxyethyl cellulose (li et al. 2017). each polymer type offers unique advantages and limitations, necessitating a selection process tailored to specific reservoir conditions. pam, characterized by a high molecular weight (>1.0×10⁶ g/mol), was among the earliest thickening agents used in aqueous solutions for eor. however, its application is constrained by its thermal stability, which is limited to temperatures of up to 90°c under normal salinity conditions and 62°c in seawater salinity. these temperature restrictions have primarily confined its usage to onshore operations. additionally, high salinity environments can significantly reduce the viscosity of pam solutions, further limiting its effectiveness (khan et al. 2021). hpam, derived either through the partial hydrolysis of polyacrylamide (pam) or the copolymerization of sodium acrylate with acrylamide, is one of the most widely utilized polymers in contemporary enhanced oil recovery (eor) applications. it offers numerous advantages, including high mechanical stability during polymer flooding, resistance to bacterial degradation, and cost-effectiveness. hpam exhibits thermal stability up to 99°c, with certain modifications extending its performance range to even higher temperatures-104°c for hpam and up to 120°c for sulfonated polyacrylamide. despite these benefits, its effectiveness diminishes in saline reservoirs due to its high sensitivity to brine salinity, water hardness, and interactions with surfactants or other chemicals, which can adversely impact its viscosity and performance (khan et al. 2021; ahmed 2016; littmann 1988). xanthan gum, a polysaccharide produced by the bacterium xanthomonas campestris through the fermentation of glucose or fructose, is notable for its exceptionally high molecular weight (2-50×106 g/mol) and rigid polymer chains. this structural rigidity imparts xanthan gum with a remarkable tolerance to high salinity and water hardness, making it compatible with most surfactants and additives commonly used in tertiary oil recovery formulations. its thermal stability ranges from 70oc to 90°c, although it is prone to bacterial degradation in lowertemperature regions of the reservoir. furthermore, the presence of cellular debris in xanthan gum solutions may lead to plugging issues, potentially impacting injectivity and flow efficiency during application (khan et al. 2021; ahmed 2016; thang 2005). recent research has highlighted the potential of xanthan gum in polymer flooding as an effective means of enhancing oil recovery. biopolymers such as xanthan gum and guar gum are increasingly favored in polymer flooding applications due to their biodegradability, shear-thinning behavior, cost-effectiveness, low adsorption tendencies, and superior compatibility with brine. the selection of an appropriate polymer is primarily dictated by specific reservoir conditions and the desired recovery efficiency. while synthetic polymers and polysaccharides offer distinct advantages, their applicability is often constrained by reservoir-specific challenges, such as salinity, temperature, and chemical interactions, underscoring the need for tailored polymer solutions to optimize recovery performance. previous studies have often underestimated the potential of polymer flooding to enhance oil recovery in heavy oil reservoirs with unconsolidated formations. xanthan gum, however, demonstrates significant promise for application in heterogeneous, unconsolidated sedimentary rock formations. its use in polymer flooding offers notable advantages over conventional water flooding in addressing the challenges posed by these complex environments. in general, polymers outperform water flooding by effectively mitigating the impact of reservoir heterogeneity. nonetheless, a comparative analysis of polymer flooding and conventional methods in such reservoirs remains critical. this study aims to evaluate the synergistic effects of combining polymers with water flooding on the performance of heavy oil reservoirs, with a particular emphasis on improving water mobility. furthermore, it investigates various injection well patterns, including the five-spot pattern, to identify the most efficient flooding strategy for optimizing polymer application in heterogeneous reservoirs. improved oil and gas recovery 5 literature review extensive research by scholars and industry professionals has focused on improving the recovery of hydrocarbons that are otherwise unrecoverable using conventional methods. hydrocarbon production from oil and gas reservoirs progresses through distinct recovery phases. during the primary recovery phase, approximately 20-35% of the original oil in place (ooip) is extracted, driven by the reservoir's natural energy mechanisms (tunio et al. 2011). secondary recovery techniques involve injecting fluids such as water or gas through injection wells to displace hydrocarbons toward production wells. the primary objective of secondary recovery is to maintain reservoir pressure; gas injection is typically applied in reservoirs with gas caps, while water injection is preferred in reservoirs with aquifers (ramero-zaron 2012). the tertiary recovery phase, or enhanced oil recovery (eor), employs advanced methods such as gas injection (miscible or immiscible), chemical injection, thermal recovery, and microbial processes (samantha et al. 2012). eor techniques have been shown to significantly enhance recovery efficiency, with kamal et al. reporting recovery factors (rf) reaching up to 65%. in the context of polymer flooding, several factors, including polymer viscosity, mobility ratio, and polymer slug size, play a critical role in determining recovery efficiency (kamal et al. 2015). recovery from heavy oil reservoirs is typically low when employing primary and secondary methods, primarily due to the high viscosity of heavy oil, which significantly impedes its flow toward production wells. global reservoir data indicate that the recovery efficiency for low-permeability or heavy oil reservoirs using primary and secondary recovery techniques ranges between only 5% and 10%, highlighting the limitations of conventional approaches in such challenging environments (tunio et al. 2011; ramero-zaron 2012; standnes and skjevrak 2014). a simulation study conducted on a mature oil field demonstrated that polymer flooding can be economically viable by converting production wells into injection wells, resulting in an increase in recovery factor and net present value (npv) by up to 46% (lamas et al. 2021). the viscosity of the polymer plays a critical role in this process, as it modifies the mobility ratio and reduces the mobility of the displacing fluid during flooding. another study highlighted those enhancements in polymer viscosity, sweep efficiency, and breakthrough time significantly contribute to higher recovery rates (juarez et al. 2020). polymer flooding is particularly effective in reservoirs with pronounced permeability variations across layers. furthermore, as the molecular weight of the polymer increases, its viscosity also rises, directly influencing the efficiency of the flooding process (li et al. 2021; zhu et al. 2016). a study analyzing the effects of polymer solutions with varying molecular weights across different reservoir layers concluded that utilizing polymers with tailored molecular weights can enhance the injection profile and improve overall reservoir development (liang et al. 2010). polymer retention is another critical factor, particularly in heavy oil reservoirs. wang et al. (2000) conducted laboratory experiments to investigate polymer retention and effluent viscosity. their findings emphasized that polymer retention may be overestimated if the relationship between polymer concentration and viscosity is not accurately accounted for. additionally, a separate study explored polymer retention by considering oil saturation in two-phase flow conditions. the results indicated that polymer retention increases with polymer concentration and that higher retention values are observed under oil-saturated conditions. these findings highlight the importance of understanding polymer retention dynamics in the presence of oil to optimize polymer flooding performance in heavy oil reservoirs (yoo et al. 2020). injection rates play a significant role in recovery from viscous oil reservoirs. in polymer flooding, injection rates are generally lower than in water flooding due to the higher viscosity of polymer solutions. a numerical simulation study optimized polymer solution injection rates and viscosities, revealing that coarse grid simulations tend to overestimate injection pressures (aitkulov et al. 2021). this technique has also been shown to be effective in sandstone and shale reservoirs with thin layers and low-permeability sequences, as polymers with tailored molecular weights and viscosities enhance oil recovery in these challenging formations. notably, medium improved oil and gas recovery 6 molecular weight polymers have demonstrated the ability to improve displacement profiles, resulting in increased oil production while reducing water production, all without causing pore throat blockage (wang et al. 2000). a simulation study on polymer flooding in multilayer heterogeneous reservoirs revealed that using polymers with varying molecular weights is more efficient than commingled or zonal polymer flooding approaches (liu et al. 2018). research into the effect of extensional viscosity found that extremely high extensional viscosity significantly enhances microscopic displacement efficiency and overall recovery (zhu et al. 2016). additionally, a study on hydrophobically modified polyacrylamide polymers demonstrated that incorporating sodium dodecyl sulfate increased the apparent viscosity of the polymer solution, leading to a 24.4% improvement in heavy oil recovery by optimizing the mobility ratio (ji et al. 2016). furthermore, functional polymers specifically designed for viscosity reduction in heavy oil reservoirs showed superior performance, effectively reducing viscosity and broadening the oil-water ratio, thereby improving recovery efficiency (li et al. 2021). ultra-high molecular weight polymers are widely utilized in natural gas liquid (ngl) miscible enhanced oil recovery (eor) processes. the low molecular weight and viscosity of ngls, such as ethane, propane, and butane, often result in fingering through the reservoir oil, leading to early breakthrough and reduced oil recovery. experimental studies have demonstrated that the addition of ultra-high molecular weight polymers to ngl mixtures enhances recovery by increasing the density and viscosity of the ngl phase. this adjustment improves the mobility ratio, thereby promoting a more stable displacement front and improving overall oil recovery efficiency (dhuwe et al. 2016). methodology this study investigates reservoir performance by comparing waterflooding and polymer flooding techniques. a comprehensive literature review provided the foundational data necessary to develop a three-dimensional (3d) reservoir model using a commercial simulation software. the base case scenario was established, employing a direct-line drive configuration for both water and polymer flooding to evaluate and compare the effectiveness of these injection methods. furthermore, a sensitivity analysis was conducted to assess the impact of various injection well patterns, with a particular emphasis on the five-spot pattern, to determine its influence on reservoir behavior. the final phase of the study identified the optimal injection pattern based on key technical parameters, including oil production rates, cumulative oil recovery, water breakthrough timing, and overall recovery efficiency. a detailed visual representation of the methodology and workflow utilized in this study is provided in figure 3. reservoir characteristics. a three-dimensional (3d) reservoir model with dimensions of 500 feet in length, 500 feet in width, and 50 feet in thickness was constructed and simulated. the model is discretized into 7 grid blocks along the x-direction, 7 grid blocks along the y-direction, and 3 grid blocks along the z-direction, resulting in a total of 147 grid cells. the reservoir is characterized by two active phases—oil and water—and comprises three vertically stacked layers with permeabilities ranging from 20 to 1000 md. the porosity is uniformly set at 20%. the simulation spans a 12-year period, with table 1 detailing the reservoir and fluid properties used in the base case model. improved oil and gas recovery 7 figure 3—methodology workflow diagram. table 1—reservoir and fluid properties (tunio et al. 2011). parameters values parameters values type of simulator black oil datum depth 8,074 ft geometry option blockcentered water fvf 1.02 rbbl/stb reservoir length 500 ft density of water 63.0 lb/ft3 reservoir width 500 ft density of oil 49.0 lb/ft3 reservoir thickness 50 ft viscosity of water 0.5 cp porosity 20 % viscosity of oil 0.8 cp permeability range 20-1000 md compressibility of rock 4.0×10-6 psi-1 reservoir pressure 4500 psi compressibility of water 3.0×10-6 psi-1 two wells are positioned at opposite corners of the base model. the well labeled ‘inj1’ functions as the injector, while the well designated ‘prod’ is used for production, as depicted in figure 4. improved oil and gas recovery 8 figure 4—a three-dimensional reservoir model featuring inj1 and prod. results and discussion this section presents the results of the simulation and analyzes the performance of both water and polymer flooding techniques. the effect of different injection patterns on key performance indicators such as oil production rate, recovery efficiency, water cut, and reservoir pressure are discussed in detail. comparison of water flooding and polymer flooding performance using direct line drive. the base model employs water flooding techniques with a single injector and producer well. a polymer solution with a concentration of 2.2 wt% is introduced into the water and injected into the reservoir. the results from the polymer flooding scenario are then compared to the base case model. the reservoir models demonstrate variations in oil saturation within the reservoir grid block, showing the impacts of water flooding and polymer flooding techniques, as shown in figure 5. figure 5(a) shows the oil saturation distribution in the reservoir following water injection. high oil saturation remains in several areas, suggesting that waterflooding alone didn't fully sweep these zones. figure 5(b) presents the oil saturation distribution after polymer flooding. the oil saturation decreases significantly in certain areas, highlighting improved displacement of oil by the polymer solution. polymer flooding generally enhances the sweep efficiency by increasing water viscosity, thus reducing fingering and improving oil displacement. (a) after waterflooding (b) followed by polymer flooding figure 5—oil saturation distribution. improved oil and gas recovery 9 figure 6 illustrates changes in water saturation within a reservoir grid, exhibiting the effects of water flooding and polymer flooding techniques. figure 6(a) depicts water saturation after water flooding. the relatively uniform blue shades indicate higher water saturation, but some oil-rich areas might still be left upswept in the pores. figure 6(b) shows water saturation following polymer flooding, where the water saturation is more uniformly distributed, reflecting the improved efficiency of polymer flooding. this technique leads to more effective oil displacement, reducing oil saturation and enhancing overall water sweep. (a) after waterflooding (b) followed by polymer flooding figure 6—water saturation distribution. figure 7 illustrates that polymer flooding achieves a higher oil production rate compared to water flooding. in the beginning, waterflooding reaches a peak oil production rate of 2,560 stb/d in the first year, but this rate declines throughout the simulation period. in contrast, the oil production rate for polymer flooding rises consistently during the first year, reaching a peak of around 5,000 stb/d. it then stabilizes around this level for the next 12 years of production. these results highlight that polymer flooding outperforms waterflooding in terms of sustained oil production rate. figure 7—oil production rate. as shown in figure 8, waterflooding exhibits a slight increase in total oil production, while polymer flooding demonstrates a steady and consistent rise throughout the production period. the higher mobility of water in waterflooding results in early water breakthrough, which leads to a decline in oil production over time. in contrast, 0 1000 2000 3000 4000 5000 6000 0 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld o il p ro d u ct io n r at e (s t b /d ) time (years) water flooding polymer flooding improved oil and gas recovery 10 the addition of polymers to the water in polymer flooding reduces its mobility, improving the displacement efficiency and enhancing oil recovery. by the end of the production period, total oil production reaches 6.2 mmstb for waterflooding and 21 mmstb for polymer flooding, highlighting the superior efficiency of polymer flooding. the increased viscosity of the water in polymer flooding delays the onset of water cut, which is directly correlated with a higher oil production rate and an overall increase in total oil production. figure 8—total field oil production. as shown in figure 9, both water flooding and polymer flooding begin with an oil recovery efficiency of 3% in the first year. while waterflooding observes a gradual increase in recovery efficiency over time, polymer flooding demonstrates a more pronounced and rapid increase in recovery factors. by the end of the production period, waterflooding achieves a recovery efficiency of 13%, whereas polymer flooding attains a much higher recovery rate of 44%, indicating superior sweep efficiency over water flooding. figure 9—field oil recovery. figure 10 depicts the initial reservoir pressure at 4500 psi. with water flooding, there is a sharp increase in pressure within the first year, reaching approximately 9930 psi. however, when the polymer is introduced along with water during polymer flooding, the initial pressure reaches a comparatively lower value of 5964 psi. in this 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld t o ta l o il p ro d u ct io n (m m s t b ) time (years) waterflooding polymer flooding 0 10 20 30 40 50 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld o il e ff ic ie n cy ( % ) time (years) water flooding polymer flooding improved oil and gas recovery 11 case, waterflooding maintains higher reservoir pressure due to effective voidage replacement, while polymer flooding with its increased water viscosity, improves sweep efficiency. by the end of the simulation period, waterflooding results in an average reservoir pressure of 10,445 psi, whereas polymer flooding maintains a lower reservoir pressure of 6,143 psi, demonstrating improved pressure control with polymer flooding. figure 10—field pressure. as shown in figure 11, waterflooding results in increased field water production, primarily due to water breakthrough in the first year. polymer flooding, however, experiences its breakthrough in the second year, leading to lower overall water production. the delay is attributed to the enhanced water viscosity in polymer flooding, which helps maintain reduced water production rates. over a 12-year simulation period, waterflooding generates a total water production of 37 mmstb, while polymer flooding produces only 3.1 mmstb. figure 11—field total water production. the results suggest that polymer flooding is a more effective method than water flooding for improving oil recovery efficiency in unconsolidated heavy oil reservoirs. polymer flooding enhances oil recovery and delays water breakthrough, significantly reducing water production. these findings indicate that polymer flooding is a more efficient and feasible approach for enhancing oil recovery in comparison to conventional methods. 0 2000 4000 6000 8000 10000 12000 0 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld p re ss u re ( p si ) time (years) waterflooding polymer flooding 0 5 10 15 20 25 30 35 40 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld t o ta l w at er p ro d u ct io n (m m s t b ) time (years) water flooding polymer flooding improved oil and gas recovery 12 performance analysis. a sensitivity analysis was performed to compare oil saturation and water saturation under two different flooding configurations, such as direct line drive and five-spot injection pattern. figure 12(a) shows oil saturation after applying a direct line drive pattern. high oil saturation is concentrated in certain regions, suggesting that this configuration might have left upswept zones with significant remaining oil. the line drive pattern can sometimes result in channeling, where injected water or polymer solution flows along highpermeability paths, leaving pockets of oil behind. figure 12(b) illustrates the oil saturation distribution following polymer flooding in a five-spot pattern, where four injector wells are positioned at the corners with a producer well at the center. compared to the direct line drive, the five-spot pattern shows lower oil saturation throughout the grid block, indicating more uniform oil displacement and less residual oil. this pattern typically enhances the sweep efficiency by providing multiple injection and production points, allowing for a more effective flood front. (a) direct line drive (b) five-spot pattern after polymer flooding figure 12—comparison of oil saturation. figure 13(a) shows water saturation using the direct line drive configuration. the overall water saturation appears uneven, and some areas might have relatively low water saturation, indicating an incomplete sweep. on the other hand, figure 13(b) illustrates water saturation with the five-spot pattern after polymer flooding. there is a more uniform distribution of water saturation, suggesting that the five-spot pattern has a better areal sweep, distributing water more effectively and reducing bypassed oil zones. the comparison between the five-spot pattern and the direct-line-drive method offers valuable insights into the performance differences between these two injection techniques. (a) direct line drive (b) five-spot pattern after polymer flooding figure 13—comparison of water saturation. improved oil and gas recovery 13 figure 14 shows that both configurations experience an initial rise in oil production rates, with the five-spot pattern sustaining a higher rate throughout the first year. the direct-line drive achieves an initial rate of 4,973 stb/d, while the five-spot pattern reaches 7,068 stb/d. after the first year, however, the five-spot pattern’s production rate gradually declines, whereas the direct-line drive maintains a stable rate for the entire simulation period. the five-spot pattern’s high initial rates are achieved by injecting a large water-polymer mixture, which, however, also results in a higher water-to-oil ratio. by the end of the production period, the direct-line drive records a field oil production rate of 4,365 stb/d, compared to 3,638 stb/d for the five-spot pattern. figure14—field oil production rate. in figure 15, both configurations exhibit increased total oil production, directly influenced by their production rates. the direct-line drive yields 2 mmstb in the first year, while the five-spot pattern achieves 3 mmstb, indicating the greater initial efficiency of the five-spot pattern. by the end of the production period, the directline drive produces a cumulative total of 21 mmstb, whereas the five-spot pattern achieves 25 mmstb, confirming the superior production capability of the five-spot pattern in polymer flooding applications. figure 15—total field oil production. 0 1000 2000 3000 4000 5000 6000 7000 8000 0 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld o il p ro d u ct io n r at e (s t b /d ) time (years) direct line polymer 5 spot polymer 0 5 10 15 20 25 30 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld o il p ro d u ct io n t o ta l (m m s t b ) time (years) direct line polymer 5 spot polymer improved oil and gas recovery 14 figure 16 indicates that polymer flooding enhances oil recovery efficiency in both configurations. higher cumulative oil production significantly improves the recovery factor, with initial recovery efficiency values of 3% for the direct-line drive and 5% for the five-spot pattern. over the 12-year simulation, the direct-line drive’s recovery efficiency rises to approximately 44%, while the five-spot pattern reaches 52%, showing the higher effectiveness of the five-spot pattern in enhancing the recovery factor. figure 16—field oil recovery. as shown in figure 17, both flooding patterns begin with an initial reservoir pressure of 4,500 psi, with pressure increases observed as production progresses. after eight months, both the five-spot pattern and directline drive reach an average reservoir pressure of around 5,717 psi. the five-spot pattern maintains a slightly higher average pressure due to its larger injected water volume, which provides better reservoir support. over the 12 years, the five-spot pattern and direct-line drive configurations exhibit minimal differences in pressure maintenance, with average pressures of 6,143 psi for the five-spot pattern and 5881 psi for the direct-line drive, reflecting a minor (4.4%) difference. figure 17—field pressure over time. 0 10 20 30 40 50 60 1 2 3 4 5 6 7 8 9 10 11 12 f il ed o il r ec o v er y (% ) time (years) direct line polymer 5 spot polymer 0 1000 2000 3000 4000 5000 6000 7000 0 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld p re ss u re ( p si ) time (years) direct line polymer 5 spot polymer improved oil and gas recovery 15 figure 18 indicates a steady increase in water production over time, which is directly correlated to cumulative water production levels. the five-spot pattern configuration shows higher water production from the start, reaching 0.1 mmstb in the first year, as it relies on large volumes of water-polymer injection to sustain reservoir pressure. by the end of the simulation, the direct-line drive configuration produces 3 mmstb of water, whereas the five-spot pattern generates a higher total of 5 mmstb due to its enhanced injection scheme. figure 18—field water production over time. the simulation results highlight the critical role of waterflooding in maintaining reservoir pressure, while polymer flooding emerges as a highly effective method to enhance hydrocarbon recovery. the increased viscosity of water due to polymer injection mitigates the fingering effect, reducing water cuts and delaying water breakthrough, which ultimately leads to a significant increase in oil recovery efficiency. addressing the fingering phenomenon, which is particularly pronounced in conventional waterflooding, is essential for optimizing oil production rates. the sensitivity analysis identified the five-spot pattern as the optimal injection strategy for this reservoir, demonstrating superior oil recovery efficiency and maximizing total oil production. this pattern thus represents the preferred choice for optimizing reservoir performance in heterogeneous, unconsolidated formations. conclusion this study examines the impacts of waterflooding and polymer flooding on reservoir performance in heterogeneous, unconsolidated formations. additionally, a sensitivity analysis was conducted to determine the optimal injection pattern, comparing direct-line drive and five-spot patterns. the key findings from the simulation are summarized as follows: 1. polymer flooding proved to be significantly more effective than conventional water flooding, enhancing oil recovery efficiency to approximately 44%, compared to just 13% achieved by waterflooding. 2. cumulative oil production was substantially higher with polymer flooding, reaching 21 mmstb by the end of the simulation, compared to 6.2 mmstb for waterflooding. 3. water breakthrough occurred early during waterflooding, while the development of water cut was successfully delayed for a considerable period with polymer flooding, extending the production phase. 4. the sensitivity analysis identified the five-spot injection pattern as the most effective approach for this specific reservoir. however, its efficiency can vary depending on the characteristics of different reservoirs. 5. furthermore, the five-spot pattern achieved a higher oil recovery efficiency of approximately 52%, with greater cumulative oil production, reaching 24 mmstb, surpassing the 21 mmstb produced using the direct-line drive technique. 0 1 2 3 4 5 6 1 2 3 4 5 6 7 8 9 10 11 12 f ie ld t o ta l w at er p ro d u ct io n (m m s t b ) time (years) direct line polymer 5 spot polymer improved oil and gas recovery 16 acknowledgment we want to acknowledge nfc-institute of engineering and technology multan, punjab, pakistan, for their support and permission to publish this significant research work. nomenclature ceor = chemical enhanced oil recovery mior = microbial improved oil recovery ooip = original oil in place sor = residual oil saturation conflicting of interest the author(s) declare that they have no conflicting interests. references ahmed, t. 2006. reservoir 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2005. enhanced oil recovery in basement rock of the white tiger field in offshore southern vietnam. m.s. thesis, asian institute of technology, pathum thani, thailand. thomas, a. 2016. polymer flooding. in chemical enhanced oil recovery (ceor) a practical overview, ed. romerozeron, l., chap. 2, 55-99. tunio, s.o., tunio, a.h., ghirano, n.a., et al. 2011. comparison of different enhanced oil recovery techniques for better oil productivity. int. j. appl. sci. technol. 1(5):143-153. wang, et al., cheng, j., yang, q., et al. 2000. viscous-elastic polymer can increase microscale displacement efficiency in cores. paper presented at the spe annual technical conference and exhibition, dallas, texas, 1-3 october. spe63227-ms. yoo, h., kim, h., sung, w., et al. 2020. an experimental study on retention characteristics under two-phase flow considering oil saturation in polymer flooding. journal of industrial and engineering chemistry 87 (1):120-129. zhu, h., luo, j., klaus, o., et al. 2016. the impact of extensional viscosity on oil displacement efficiency in polymer flooding. colloids and surfaces a: physicochemical and engineering aspects 414(1):498-503. sajjad aziz is a master candidate in the petroleum and gas engineering department at the university of engineering and technology, lahore, pakistan. his research interests include enhanced oil recovery (eor), fluid flow in porous media, and carbon capture, utilization, and storage (ccus). he holds a bachelor’s degree from the nfc-institute of engineering and technology, multan, pakistan. muhammad jawad khan is a ph.d. scholar in the petroleum engineering department at universiti teknologi petronas, malaysia. his research interests include co2 sequestration, caprock integrity, eor/ior, production optimization, and modeling flow and transport in porous media. he holds a master’s degree in petroleum engineering and a bachelor’s degree in petroleum and natural gas engineering from mehran university of engineering and technology, jamshoro, pakistan. farzain ud din kirmani is a lecturer in petroleum and gas engineering department at the nfc-institute of engineering and technology, multan, pakistan. his research interests include the application of simulators to quantify the behaviour of unconventional reservoirs, eor, co2 storage, and underground hydrogen storage. he holds a master’s degree in energy and environment from punjab university, lahore, and a bachelor’s degree in petroleum engineering from the university of engineering and technology, lahore, pakistan. hassan aziz is an assistant professor in the petroleum and gas engineering department at dawood university of engineering and technology, where he has been a faculty member for six years. his research focuses on nanoparticles, polymers, and water flooding. he holds a master’s degree in petroleum engineering and a bachelor’s degree in petroleum and natural gas engineering from mehran university of engineering and technology, jamshoro, pakistan. he is currently pursuing a ph.d. in petroleum engineering from the same institution. fahd saeed alakbari is a postdoctoral researcher at the institute of subsurface resources, universiti teknologi petronas, malaysia. his research focuses on the application of machine learning, artificial intelligence, sand improved oil and gas recovery 18 production, and nanotechnology. he holds a ph.d. degree in petroleum engineering from universiti teknologi petronas, malaysia. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1367 received february 8, 2025; revised march 10, 2025; accepted may 27, 2025. *corresponding author: nnaemeka.uwaezuoke@futo.edu.ng 1 causticized application of low-carbon lignite for ph and fluid loss control in an aqueous mud system nnaemeka uwaezuoke*, eruchalu henry onyedikachi, anuforo joseph uchenna, emmanuel nmesoma noble, iroagba chibueze valentine, nzenwa daniel enyioko, nwanwe ivan onyebuchi, federal university of technology,owerri, nigeria abstract lignite, a low-carbon coal variety, is prevalent in numerous global locations. its application in the oil and gas drilling industry, particularly for controlling ph and fluid loss in aqueous mud systems, has garnered significant attention. through causticization, lignite can be modified to enhance its performance in these systems. the present study undertakes an assessment of the efficacy of nigerian lignite in mitigating fluid loss within water-based mud systems. laboratory analyses were executed in accordance with american petroleum institute standards to ascertain the rheological attributes and filtration properties of the developed drilling muds, which contained varying levels of lignite. furthermore, the performance of the lignite was juxtaposed with that of carboxymethylcellulose (cmc), a traditional fluid loss reduction agent, to elucidate its potential advantages. it was noted that as the lignite concentration escalated from 0.5g to 5g, there was a corresponding reduction in fluid loss, ranging from 0.3ml to 7ml, in contrast to the conventional additive (cmc). nigerian lignite emerges as an exceptional fluid loss control agent, effectively diminishing the thickness of the mud cake. the integration of nigerian lignite into water-based drilling fluids led to a significant reduction in both filtrate loss volume and mud cake thickness during drilling activities. the mud cake generated within the water-based mud system incorporating the nigerian lignite sample was characterized by its thinness and smoothness. progressive gelation was observed in the mud formulations. additionally, it is inferred that causticized lignite functions as mud thinner. with increasing lignite concentration, mud viscosities exhibited a decline. lignite also contributed to the stabilization of the drilling muds’ ph across various concentrations. the mud's ph remained constant at 13. therefore, it is affirmed that nigerian lignite possesses the potential to serve as a ph modifier for water-based mud. this research underscores the viability of utilizing locally sourced lignite, fostering sustainable methodologies within the oil and gas sector and potentially diminishing operational expenditures. introduction drilling fluids cool and lubricate the drill bit, carry and float cuttings from the hole to the surface, release the cuttings at the shale shaker, minimize formation damage, and wall the wellbore with an impermeable filter cake. drilling fluid loss is the most notable technical challenge in drilling, and static and dynamic filtration are regulated by the permeability of the filter cake and should be managed for efficient drilling (herzraft et al. 2001; oleas et al. 2008). fluid loss control is the process of preventing or minimizing the loss of drilling or completion fluids to the formation during well operations. fluid loss can cause various problems, such as formation damage, reduced productivity, increased operational costs, and compromised well control (bourgoyne et al. 1991; caenn et al. 2011). various forms of materials are used as fluid loss control additives. they include polymers or gels, particles mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 or fibers (uwaezuoke et al. 2022), nanoparticles (uwaezuoke 2022; al-awadhi 2019), and biopolymers (uwaezuoke et al. 2017) both in water-based and oil-based muds. but they must conform to standards such as the american petroleum institute specifications. however, nigerian lignite is a type of coal that has been proposed as a potential fluid loss control additive in water-based drilling mud. lignite is the lowest coal grade and has the least concentration of carbon. it can control fluid loss, stabilize shale, and improve hole cleaning. its application in drilling muds can be done in a variety of techniques. in dry application, lignite is added directly to the drilling mud formulation. it can also be pre-solubilized; where it is dissolved in another solution before addition to the mud formulation. also, in a causticized form of application, the addition of caustic soda or any alkaline solution to lignite to maintain consistent ph is achieved. causticization releases the humic acid content in lignite to serve better as fluid loss control agents (apostolidou 2020). in causticized lignite, impurities are removed, and reactivity is improved. this technique yields a lignite that can function as thinner. research findings have been presented on the suitability of nigerian lignite and other alternatives as fluid loss control materials in drilling fluid formulations. al-hameedi et al. (2019) examined the effect of adding lignite nanoparticles to water-based drilling fluid. they showed that lignite nanoparticles can significantly reduce fluid loss and increase the temperature stability of the drilling fluid. they also suggested that lignite nanoparticles can be used as a cost-effective and environmentally friendly additive. a comparison of nigerian lignite as a fluid loss control additive in water-based drilling mud to conventional additives has been presented. okon et al. (2020) compared the performance of nigerian lignite with cmc, an organic polymer. the fluid loss was reduced by nigerian lignite by 64.89% at 20g per 350ml mud concentration. nigerian lignite had a lower filter cake thickness, higher resistance to water penetration, and good thermal stability. they concluded that nigerian lignite could be a viable and environmentally friendly alternative to cmc in aqueous mud systems. onuh, et al. (2017), compared nigerian lignite with coconut shell and corn cob biowastes. it was observed that the mixture of nigerian lignite and corn cobs had a lower fluid loss than the corn cobs and lignite considered separately. it was also more effective than coconut shells. materials and methods sample collection. the lignite was obtained from kaduna state, northern nigeria, and stored in a clean and airtight glass container to avoid moisture and contamination. the lignite sample was further processed by crushing with glass mortar, ground using a hamilton beach blender and sieved with a no. 200 mesh to get the fine grain size of 74 µm. it was stored in an airtight glass bottle for use. the materials and laboratory apparatus used are presented in tables 1 and 2. table 1—mud composition and function(s). product density (g/cc) function(s) water 1 base fluid bentonite 2.6 mud viscosifier naoh 2.13 ph control cmc 1.6 fluid loss control pac-r 1.5 viscosifier and mild fluid loss control lignite 1.5 fluid loss and ph control caco3 2.5 densifier barite 4.48 densifier improved oil and gas recovery 3 table 2—laboratory apparatus/equipment used. laboratory apparatus/equipment function(s) baroid mud balance measurement of mud density meter rule measurement of filter cake thickness hamilton beach blender blending of the lignite hamilton beach mixer mixing of the mud compositions fann v-g meter measurement of viscosity and gel strength api lt/lp filter press with 2.7m pore size api filter paper fluid loss control test ph meter ph measurement sem-eds surface morphology and elemental composition tga/dta measures weight changes due to temperature change characterization of the lignite. the lignite was characterized to obtain the elemental composition, surface morphology, and weight changes due to temperature variation. sem/eds. the scanning electron microscope – energy dispersion spectroscopy (sem) phenom prox (by phenom-world eindhoven) was used to carry out the morphology and elemental analyses. with sticky carbon tape, the sample was placed in the aluminium stub. the sample was insulated using gold and then grounded electrically. each sample was then labeled on its stub and then dried in the oven at 140 of for 3 hours. the nitrogen line was opened at 50 psi and the vent button was pressed to fill the area with nitrogen for proper purging of the chamber. the sample holder stub was then placed in the sample chamber holes, the door was shut, and the rotary pump was picked. at about 35 minutes, the vacuum of 5 x 10-5 pa was created. the filament light was switched on and the monitor automatically switched on. at this stage, the peak accelerator voltage read 15kv and the filament burned out. specific wavelengths of x-rays are emitted when electron beams excite surface atoms which characterize the element's atomic structures. a dispersive energy detector analyzes the emissions, assigning elements, which yields atomic composition. the lowest scan mode of 10x was picked and the tv scan clicked. the magnification was then taken to 1000x at a slow scan, 2000, 3000 to 10,000. the image was then saved. this is known as energy-dispersive x-ray spectroscopy (eds), and it is used for specimen surface composition analyses. tga/dta analyzer.tga of the biomass residues was performed using a tg analyzer (tga-q500 series, ta instruments) at standard pressure. the sample was first dried to a constant weight at 103°c to remove all moisture present then pulverized and silver to 50 microns size before the analysis. about 10.0 mg of each sample was placed in platinum crucibles in the furnace chamber of the tga and heated linearly at given heating rates, (5, 10, 15, 20, 25, or 30 °c/min) from ambient room temperature to 950 °c. nitrogen gas was opened and allowed to flow throughout the chamber of the furnace at a flow rate of 30 ml/min. this was used to purge the system and provide an inert atmosphere for the experiments. the thermogravimetric analysis then produced a curve, that shows the effect of temperature (or time), presented on the x-axis, on the weight of the sample (the y-axis). the weight is usually expressed in terms of the percentage of the sample that remains, versus the weight at the start of the experiment, at a given temperature/time. the results also include a second y-axis on the graph which presents the data for the first derivative of the tga curve. this is known as the derivative thermogravimetric analysis (dta) curve and represents the rate of change of mass concerning temperature. the dta curve often allows for easier visual interpretation of the data, as periods of large mass change can be seen with more clarity. improved oil and gas recovery 4 causticizing of the lignite. the purpose of the sieved and ground lignite was to expose the surface area. the sieved lignite was causticized using naoh of about 11% concentration in water to facilitate the reaction. it was an allowed time of 45 minutes since naoh was designed to be a composition of mud for ph control. a waiting time of 2-4 hours is normally allowed for other applications. it was not added directly in the formulation; so, impurities were also removed in the process. the reaction was done in a glass vessel by agitating the powder in a glass with naoh solution using a magnetic stirrer, while ambient temperature was maintained. it was later filtered and allowed some time to dry at ambient temperature. using the api specifications for water-based muds, the formulations were prepared by mixing with the hamilton beach mixer using the mixing order (table 3) for testing in the viscometer and the api lt/lp filter press. table 3—mixing order and time. product density g/cc unit mixing order mixing time mins grams mls water 1 bbl 1 4 341.51 bentonite 2.6 2 5 15 5.769 naoh 2.13 3 3 0.5 0.235 cmc 1.6 4 2 1.5 0.938 pac-r 1.5 5 3 0.2 0.133 lignite 1.5 6 2 0.5, 1, 3, 5 0.333 caco3 2.5 7 2 1.5 0.6 barite 4.48 8 5 28 6.25 350 results it has been noted through careful observation and analysis that lignite, as depicted in figures 1 and 2, exhibits characteristics of a low-carbon fuel. additionally, the particles of lignite are found to be highly inhomogeneous, displaying a tendency to clump together because of being wetted by moisture content. this agglomeration is further influenced by the particles' varying sizes, which contribute to bridging effects. these bridging tendencies are a direct consequence of the heterogeneous nature of the particle sizes present in lignite, leading to a complex structure that can pose challenges in handling and processing. improved oil and gas recovery 5 figure 1—sem/eds spectroscopy of the lignite showing the elemental composition. figure 2—sem/eds result showing dominant elements. there are three weight loss steps due to moisture, volatiles, and fixed carbon respectively (figure 3). the first observable weight change occurred between 25.56oc to 100oc. that represents a change due to the evaporation of moisture in the lignite. the second stage of weight change is due to the material decomposition of the volatile components due to temperature from around 200oc to about 350oc. the third stage occurred from about 400oc to a peak value of around 470oc. all impurities would have decomposed as well. it is deduced that the lignite can withstand a temperature of up to 200oc while in use as a mud additive, with the volatile components being retained. hence, it can also be used in high-pressure high-temperature (hpht) wells. improved oil and gas recovery 6 figure 3—tga/dta test result. physical properties.the fundamental fluid characteristics are explicitly presented in table 4. it is evident that the addition of lignite played a significant role in maintaining the ph stability of the drilling mud across a range of different concentrations, as detailed in table 5. from the data presented, one can infer that the causticized lignite functioned effectively as a mud thinner, as indicated in table 6. as the concentration levels of the lignite were elevated, a corresponding reduction in mud viscosities was observed. this phenomenon was analogous to the behavior exhibited by the control mud sample. nevertheless, it was noted that at the higher concentration of 5 grams, the effect was less pronounced compared to the results obtained at 0.5 grams, 1 gram, and 3 grams, respectively. consequently, this could necessitate an increase in pump pressure to facilitate the circulation of the mud that was formulated using lignite, as outlined in table 7. to manage this behavior, it might be essential to incorporate additional thinning agents into the mixture. table 4—properties of the control mud. physical properties value api specifications ph 13 9.1-12 mud density (ppg) 9 filtrate volume (ml) 6.9 <12 mud cake thickness (mm) 0.0625 <2mm temperature (℃) 28 improved oil and gas recovery 7 table 5—properties of the formulations with lignite. physical properties concentration of lignite api specifications 0.5g 1g 3g 5g ph 13 13 13 13 9.1-12 mud density (ppg) 9.1 9.1 9.1 9.1 filtrate volume (ml) 9.3 8.9 8.8 7 <12 mud cake thickness (mm) 0.0625 0.0625 0.0625 0.0625 <2mm temperature (℃) 28 28 28 28 table 6—rheological behavior of the formulations at lt/lp. rpm concentration of lignite control 0.5g 1g 3g 5g 3 2.5 4 6.5 3.5 2.5 6 3.5 4 7 3.5 4 30 7.5 6 9.5 6.5 5 60 11 8.5 10 7.5 6.5 100 15 10 12 10 8 200 24 13.5 17.5 15 12 300 31.5 15.5 21 19 15 600 49.5 24 30 29.5 24.5 table 7—gel strength measurement. concentration of lignite sample time control 0.5g 1g 3g 5g @10secs. 5 7 10 7 7 @10mins. 13 12 21 14 10 conclusions this study has brought out different perspectives on the behavior of nigerian lignite in drilling fluids. the data generated from the different experiments highlights the physical properties of mud samples with the lignite as a fluid loss agent. the ph obtained and maintained in the formulations closely matches the acceptable range of api limits for drilling fluids between 9.1 to 12. knowing the ph of the mud is critical because it affects the solubility of the organic materials like thinners and the dispersion of clays present in the drilling fluid. an increase from 0.5g to 5g of the lignite sample shows a decrease in the fluid loss volume respectively. the fluid loss volumes are also within the api specifications. the thickness of the mud cake and its integrity can reveal that the lignite sample deposited on the cake with optimum concentration established an effective seal with all values within far less than the api specifications. the lignite did not inhibit the gelling of the mud. however, the progressive gel, which is the situation where the 10secs gel strength and the 10mins gel strength have dissimilar values might not be favorable to the circulating system. the reason is that the pressure of the pump might be increasingly altered to be able to push the mud. this might require changing the piston to a smaller area for an increase in pressure to improved oil and gas recovery 8 be achieved. this might happen at the expense of the adequate flow rate requirements which are achieved with larger pistons. hence, alternative thinners might be incorporated in the mud as a requirement. nomenclature ansi = american national standards institute api = american petroleum institute cmc = carboxymethyl cellulose hpht = high-pressure high-temperature lt/lp = low-temperature low-pressure sem-eds = scanning electron microscopy/energy dispersive spectroscopy tga/dta = thermogravimetric analysis and differential thermal analysis acknowledgment the authors acknowledge the support of the laboratory staff of the department of petroleum engineering, federal university of technology, owerri nigeria. conflict of interest the author(s) declare that they have no conflicting interests. references al-awadhi, a. 2019. investigation of the mitigation of lost circulation in oil-based drilling fluids using nanoparticles. j. petrol. expl. and prod. tech. 9(4): 2897-2907 al-hameedi, a.t., alkinani, h.h., dunn-norman, s., et al. 2019. improving the performance of drilling fluid using lignite nano particles. j. of al-qadisiyah for eng. sci. 12(3): 1-10. apostolidou, c. 2020. investigation of lignite effect on rheological and filtration properties of water-based drilling muds. master thesis, aristotle university of thessaloniki, greece. bourgoyne, a.t., chenevert, m.e., young, f. s., et al. 1991. applied drilling engineering. society of petroleum engineers textbook. caenn, r., darley, h. c. h., gray, g. r. 2011. composition and properties of drilling and completion fluids (6th ed.). houston, usa: gulf professional publishing. herzraft, b., rousseau, l., neau, l., et al. 2001. influence of temperature and clay/emulsion microstructure on oil-based mud low shear rate rheology. soc. petrol. eng. j. 8(1): 211-217 okon, a. n., udoh, f. d., and bassey, p. g. 2020. evaluating the locally sourced materials as fluid loss control additives in water-based drilling fluid. journal of petroleum exploration and production technology 10(4): 1569-15771 oleas, a., osuji, c.e., chenevert, m.e., et al. 2008. entrance pressure of oil-based mud into shale: effect of shale water activity and mud properties. paper presented at annual technical conference and exhibition, denver, colorado, usa, 21-24 august. spe-116364-ms. onuh, c. y., igwilo, k. c., anawe, p. a. l., et al. 2017. development of high temperature high pressure (hthp) water based drilling fluid using coconut shell and corncob. international journal of engineering research in africa 32(2): 70-92 uwaezuoke, n. 2022. polymeric nanoparticles in drilling fluid technology. in drilling engineering and technology-recent advances, new perspectives and applications, ed. m. zoveidavianpoo, chap. 1, 1-15. london: intechopen. improved oil and gas recovery 9 uwaezuoke, n., onwukwe, s.i., igwilo, k.c., et al. 2017. biopolymer substitution and impact on cuttings transport of a lightweight water-based drilling fluid. j petrol. eng. technol 7(2):54-64 uwaezuoke, n., okoro, v., igwilo, k.c., et al. 2022. characterization of amuda-isuochi nigerian clay deposit for potential industrial applications. international journal of engineering research in africa 62(1):1-18. nnaemeka uwaezuoke is a senior lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in drilling and well engineering. uwaezuoke holds a bachelor’s degree in petroleum engineering from the federal university of technology owerri, nigeria, master’s degree in petroleum engineering from the university of stavanger. eruchalu henry onyedikachi, is a recent graduate of the department of petroleum engineering, federal university of technology, owerri, with research interests in drilling fluid technology. anuforo joseph uchenna, is a recent graduate of the department of petroleum engineering, federal university of technology, owerri, with research interests in drilling fluid technology. emmanuel nmesoma noble, is a recent graduate of the department of petroleum engineering, federal university of technology, owerri, with research interests in drilling fluid technology. iroagba chibueze valentine, is a recent graduate of the department of petroleum engineering, federal university of technology, owerri, with research interests in drilling fluid technology. nzenwa daniel enyioko is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids and enhanced oil recovery. enyioko holds a bachelor’s degree and master's in geology from federal university of technology owerri, nigeria. nwanwe ivan onyebuchi is a lecturer at the department of petroleum engineering, federal university of technology owerri with research interest in reservoir and production engineering. ivan holds a bachelor’s degree in petroleum engineering from university of benin, nigeria, master’s degree in petroleum engineering from t.u clausthal, germany and a ph.d in petroleum engineering from the federal university of technology owerri, owerri. https://www.google.com/search?sca_esv=aac09e88d3bc5d88&rlz=1c1fhfk_enng994ng994&q=t.u+clausthal&spell=1&sa=x&ved=2ahukewiehqfewrslaxu0rqqehd5npv4qkeeckab6bagleae copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1314 received august 17, 2024; revised september 1, 2024; accepted september 19, 2024. *corresponding author: weirong.li@xsyu.edu.cn 1 effect of surfactants on the minimum miscible pressure of co2 with crude oil from the chang-8 oilfield using molecular dynamics simulation zhenzhen dong, tong hou, zhanrong yang, lu zou，weirong li*, xi’an shiyou university, xi’an, china; keze lin, china university of petroleum (beijing), beijing, china; hongliang yi, petrochina liaohe oilfield company, panjin, china; zhilong liu, enertech-drilling & production co., cnooc energy technology & services ltd abstract co2 flooding represents a promising approach for enhancing the recovery of tight reservoirs, facilitating the efficient development of unconventional oil and gas resources while concurrently contributing to co2 reduction. this method is of significant importance for the sustainable advancement of energy in china. both theoretical and empirical evidence indicate that the oil recovery efficiency associated with co2 miscible-phase processes markedly exceeds that of non-miscible-phase processes. however, current co2 injection technologies often struggle to achieve miscible-phase conditions in various contexts, thus limiting their effectiveness in enhancing recovery from tight reservoirs. the composite system formed by co2 and surfactants presents a novel avenue for optimizing co2 flooding technology aimed at improving recovery of tight reservoirs. in this study, a molecular system model was established to characterize the interaction between co2 and crude oil specific to the chang 8 tight reservoir. molecular dynamics simulations were employed to estimate the miscibility pressure. the surfactant c12po6 was introduced to investigate its impact on physical parameters, including intermolecular forces, interfacial tension, and miscible pressure, within the co2-crude oil-surfactant system. the findings demonstrate that the incorporation of surfactants enhances molecular interactions between co2 and crude oil, resulting in a reduction of minimum miscibility pressure by 9.36% at a temperature of 344 k. furthermore, the extent of this reduction is temperature-dependent, with a 10% increase in surfactant efficacy observed as the temperature rises from 323 k to 363 k. this research elucidates the interactions among multiple fluid molecules at the molecular level, revealing the microscopic mechanisms by which the co2-surfactant composite system reduces miscibility pressure in tight reservoirs. these insights are poised to advance the development of co2 enhanced recovery technologies within china’s tight oil and gas sector. introduction the greenhouse effect and the increasing global energy demand have emerged as critical issues. in this context, co2 gas flooding has gained considerable attention for its dual benefits (gozalpour et al. 2005; peng et al. 2022). it not only enhances the recovery of oil and gas resources, thereby extending the lifespan of limited energy supplies, but also aids in co2 sequestration, contributing to the reduction of atmospheric co2 emissions and mitigating the greenhouse effect on earth’s climate (ju et al. 2012). mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 the mechanisms by which co2 increases oil and gas recovery primarily involve two processes: immiscible flooding and miscible flooding. in immiscible flooding, the reservoir pressure is below the minimum miscibility pressure (mmp), preventing co2 from fully mixing with the oil and resulting in a phase interface. in contrast, miscible flooding occurs when the reservoir pressure exceeds the mmp, allowing complete mixing of oil and gas, thus enhancing the efficiency of co2 flooding for improved oil recovery. studies indicate that recovery rates from miscible flooding are significantly higher than those from immiscible flooding (mian et al. 2018; fath and pouranfard 2014). however, many oil reservoirs in china exhibit relatively low formation pressures, and the crude oil often has high viscosity and a substantial content of heavy components, posing challenges to achieving the mmp necessary for co2 miscible flooding. consequently, realizing miscible co2 flooding presents a significant challenge. to facilitate co2 miscible flooding, one strategy is to increase formation pressure through gas or water injection until it reaches or surpasses the mmp. however, this approach may lead to reservoir fracturing. therefore, researchers have started investigating the use of specific chemical additives to modify the phase behavior of co2 and crude oil, thereby reducing the mmp and promoting the miscible flooding process. notable chemical additives include alcohols, fatty acids, and surfactants (almobarak et al. 2021). alcohols, as nonpolar solvents, can enhance the viscosity and density of co2while simultaneously reducing the viscosity and density of crude oil (li et al. 2003), lowering interfacial tension between co2 and crude oil, which aids in their mixing and promotes miscibility (djabbarah et al. 1988). yang et al. (2019) employed the interfacial tension disappearance method to study the impact of adding 5 wt% primary alcohols (1-butanol, 1pentanol, and 1-hexanol) on co2 solubility in the co2-crude oil system. their results indicated that the solubility of co2 increased with pressure, and the addition of alcohols improved co2 solubility in heavy crude oil components. additionally, the introduction of a mixed alcohol led to a 9.21% reduction in minimum miscibility pressure compared to the absence of alcohol (rudyk et al. 2013). fatty acids, characterized by a hydrophobic hydrocarbon chain and a polar carboxyl tail (voon and awang 2014), also enhance co2 solubility in crude oil due to the presence of polar functional groups. qayyimah et al. (2016) utilized the slim tube method to assess the effects of fatty acid methyl esters (fame) on mmp in co2oil systems. their experiments revealed a 4% reduction in mmp with the addition of 5 vol% fame at pressures ranging from 18 to 31 mpa. however, the emulsifying capacity of fatty acids remains suboptimal, even at high concentrations. surfactants are amphiphilic compounds with a hydrophilic head and a hydrophobic tail. they reduce mmp in co2 flooding through several mechanisms: (1) enhancing co2's interaction with heavy components, thereby increasing co2 solubility in crude oil (qi et al. 2016); (2) disrupting the equilibrium between liquid and gas phases to enhance co2 extraction from crude oil; (3) adsorbing onto crude oil surfaces, thereby decreasing intermolecular forces and viscosity (yang et al. 2015); and (4) interacting with both crude oil and co2 to reduce interfacial tension and promote miscibility (miao et al. 2013). surfactants can be categorized based on their hydrophilic heads into anionic, cationic, nonionic, and amphoteric types. traditional anionic and cationic surfactants exhibit poor solubility in supercritical co2, hindering micelle formation. guo et al. (2017) investigated the influence of a synthesized oil-soluble surfactant (cae) on mmp using the slim tube method at pressures of 18-30 mpa and 85°c, finding a 6.1 mpa (22%) reduction in mmp with a preslug of 0.2 wt%. lou et al. (2018) examined the effects of nonionic surfactants in a co2 flooding system, reporting a reduction in mmp from 19.1 mpa to 13.8 mpa (27.7%) with 0.6 wt% of a propoxylated surfactant. wang et al. (2016) demonstrated that fatty alcohol polyoxypropylene ethers effectively reduce miscibility pressure, achieving a significant reduction when the hydrophobic chain length was 12 and the hydrophilic functional group had a degree of polymerization of 6 (c12po6). under specific conditions (0.6 wt% c12po6, 0.7 wt% ethanol, and 333.15 k), mmp was reduced from 17.79 mpa to 13.22 mpa, indicating a decrease of over 26%. in summary, among various chemical additives, nonionic surfactants, particularly c12po6, have shown notable efficacy in lowering mmp. however, the exact mechanisms by which c12po6 reduces interfacial improved oil and gas recovery 3 tension remain inadequately understood. this study employs molecular dynamics simulations to explore the mechanisms through which c12po6 reduces interfacial tension, comparing mmp and interfacial properties before and after its addition, with a focus on molecular structure and fundamental force fields. the paper is structured as follows: the introduction reviews methods and the current state of research on reducing miscibility pressure between co2 and crude oil; the second section outlines fundamental theories and research methods; the third section delves into surfactants’ mechanisms affecting co2 and crude oil miscibility; and the final section presents discussion and conclusions. methodology this study utilized molecular dynamics simulations conducted with the lammps (large-scale atomic/molecular massively parallel simulator) software, originally developed by sandia national laboratories in 1984. lammps is an open-source package specifically designed for large-scale atomic and molecular parallel simulations. the motion trajectories and instantaneous structural representations of all models were visualized and analyzed using the ovito software. molecular model. to accurately replicate the miscibility process between crude oil and co₂ , the molecular dynamics model of crude oil was developed based on the actual composition of reservoir components. the composition consists of 24.90% c1, 30.93% c2, 9.54% c8+, 19.59% c11+, and 15.05% c23+. this study focuses on linear aliphatic structures, excluding the consideration of their complex isomeric forms. all alkanes are constructed using a united-atom model, where hydrogen atoms are combined with their adjacent carbon atoms to form unified atoms. this simplification in the force field model balances model efficiency with the accurate representation of molecular structure and properties (dong et al. 2022; qu et al. 2022). the molecular models of each component are depicted in figure 1. co2 methane (c1) ethane (c2) hexane (c6) undecane (c11) tricosane (c23) oil the molecular formula of c12po6 c12po6 figure 1—each individual molecular model/crude oil model. the selection of an appropriate molecular force field is a critical step in molecular simulations, as it directly influences the accuracy of the results. in constructing this model, co2 molecules were represented using the zhu force field (zhu et al. 2009), a flexible and computationally efficient model particularly suitable for systems involving supercritical co2. the ch4 molecules in the crude oil were modeled with the trappe-ua (transport properties of pure and polymeric compounds) force field (nath et al. 1998; martin and siepmann 1998). surfactant molecules were described using the opls-ua (optimized potential for liquid simulationsimproved oil and gas recovery 4 united atoms) force field (jorgensen et al. 1996), while the remaining crude oil components (c2, c8, c11, c23) were modeled using the nerd force field (wang et al. 2018; nath et al. 1998). ,..............................................................................................................(1) where, εij represents the depth of the potential well; σij represents the distance at which the interaction energy between two particles is minimal; rij is the distance between particles i and j; while qi and qj denote the partial charges for particles i and j, respectively. by employing mixing rules, lennard-jones (lennard-jones 1931) parameters for various atomic interactions can be calculated. in this simulation, the commonly employed lorentz-berthelot combination rule is utilized (stanishneva-konovalova and sokolova 2015), ,..........................................................................................................................................................(2) ,..........................................................................................................................................................(3) the force field parameters used for the simulations in this paper are outlined in table 1(qian et al. 2024). table 1—molecular force field parameters. molecular atom σij (nm) ɛij (kj•mol-1) change(e) model co2 c 0.2757 0.2339 0.6512 zhu o 0.3 0.6690 -0.3256 n-decane ch3 0.3910 0.8647 0 nerd ch2 0.3930 0.3808 0 ch4 ch4 0.3730 1.2300 0 trappe-ua fatty alcohol ether c12po6 c(in ch-or bond) 0.35 0.2761 0.17 opls-ua c(in c-oh bond) 0.35 0.2761 0.205 ch2(in ch2-or bond) 0.38 0.4937 0.25 ch2(in c-c bond) 0.3905 0.4937 0 ch3(in c-c bond) 0.3905 0.7322 0 o(in c-oh bond) 0.312 0.7114 -0.683 o(in c-o-c bond) 0.3 0.7113 -0.5 h(in o-h bond) 0 0 0.418 improved oil and gas recovery 5 simulation details and analysis methods. all simulation units established in this study were configured using periodic boundary conditions in the x, y, and z directions. to replicate reservoir conditions, the simulation temperature was controlled within the range of 50 to 90 degrees celsius. the simulation box dimensions automatically adjusted to their optimal sizes under varying temperature and pressure conditions through molecular simulations. as initial molecular models often deviate significantly from equilibrium, a series of preparatory steps was performed before the simulations. first, the models underwent energy minimization using the conjugate gradient method to achieve minimal energy and optimized configurations. subsequently, initial velocities were randomly assigned to the atoms according to the maxwell-boltzmann distribution. the equations of motion were solved using the verlet integration method (li et al. 2023). thermodynamic ensembles are essential in molecular dynamics, enabling the study of macroscopic system properties by conducting multiple simulations under varying conditions to gather data. the most common ensembles include the microcanonical ensemble (nve), canonical ensemble (nvt), isothermal-isobaric ensemble (npt), and isobaric-isenthalpic ensemble (nph). in this study, both the nvt and npt ensembles were employed. the npt ensemble maintains a constant number of particles (n), pressure (p), and temperature (t) during the simulation. similarly, in the nvt ensemble, the number of particles (n) and temperature (t) remain constant, while the volume (v) is held fixed. the simulation process began with npt simulations to equilibrate the system's properties, ensuring a stable state of energy, temperature, and pressure. this was followed by control over the system using the nvt ensemble. trajectory data was recorded at 1 ps intervals, and data points were generated every 1 fs for further analysis. in npt simulations, temperature control was achieved via the nosé-hoover thermostat with a relaxation time of 200 fs (hoover et al. 1982; nosé 1984). for systems involving co2, long-range electrostatic interactions were calculated using the particle-particle particle-mesh (pppm) method (hockney et al. 1989), with an accuracy of 10-5. a cutoff radius of 20 å was employed, and the time step was fixed at 1 fs. the results from molecular dynamics simulations were analyzed by observing trajectories, generating radial distribution functions, density distribution curves, and measuring interfacial tension. trajectories analysis. trajectory analysis entails capturing the positions and velocities of each atom in the system at every time step during molecular simulations. this data is subsequently processed using software tools such as ovito, which generates visualizations of instantaneous trajectories, providing an intuitive representation of particle motion throughout the simulation. this method is crucial for gaining insights into the dynamic behavior, energy, and thermodynamic properties of the system's individual particles (stukowski et al. 2009). radial distribution function (rdf). the rdf is a key metric for describing the spatial distribution relationships between different atoms or molecules in a system. it is defined as the ratio of the probability of finding a particular atom or molecule within a given spatial volume at a distance 'r' to the probability of finding the same atom or molecule in a randomly distributed system within the same volume. rdf is an invaluable tool for exploring intermolecular forces and interactions between atoms or molecules (mo et al. 2014). drr dnrg 24 )(   ,................................................................................................................................................(4) where n represents the number of particles in the system; ρ denotes the particle density within the system, measured in units of g/cm3; and r represents the distance between two particles, measured in ångströms (å). density distribution curve. the density distribution curve provides a visual representation of particle aggregation across different positions within the system, accurately illustrating particle distribution at various time intervals. it is particularly useful in reducing inaccuracies caused by sampling and measurement errors, ensuring a more reliable depiction of particle behavior within the simulated environment. interfacial tension (ift). interfacial tension is a critical parameter used to describe the properties of an interface between two phases (rao 1997). in molecular simulations, the pressure tensor is calculated in different directions within the system, and the ift is subsequently derived by integrating the appropriate equation (e.g., improved oil and gas recovery 6 eq. 5). this method enables a precise estimation of the system's interfacial tension, offering insight into phase behavior and surface properties.      z yyxx zz l tn l pp pdzzpzpz          22 12 1 0  ,.............................................................................................(5) where γ represents the interfacial tension; pn(z) and pt(z) denote the normal and tangential pressures, respectively.  zyxp ,, is the quantity along the diagonal of the pressure tensor, and lz is the length in the z direction of the simulated system. results molecular dynamics simulation of the co2 and crude oil system. as shown in figure 2(a), the initial setup of the simulation consists of 1000 co2 molecules positioned on both sides, with 800 crude oil molecules centered between them. the co2-crude oil system is examined under two pressure conditions: 13.5 mpa (nonmiscible) and 19.5 mpa (miscible). the system’s structural evolution is analyzed at different time intervals during the simulation. a)0ns 13.5mpa/19.5mpa b)1ns 13.5mpa 19.5mpa c)10ns 13.5mpa 19.5mpa figure 2—instantaneous structures of the co2-crude oil system at various time steps (13.5mpa/19.5mpa). improved oil and gas recovery 7 at 13.5 mpa, the initial configuration reveals co2 molecules occupying the outer regions, with crude oil components located centrally, forming a distinct oil-gas interface. after 1 ns, the crude oil begins to diffuse outward, while co2 starts dissolving into the oil. however, due to the pressure being significantly lower than the miscibility threshold, the diffusion of both co2 and crude oil remains limited over time, resulting in minimal co2 dissolution within the system. in contrast, at 19.5 mpa, the system exhibits a different progression. as time advances, co2 molecules from the outer regions infiltrate the central zone containing crude oil. this interaction leads to co2 enveloping the crude oil molecules, and the oil diffuses towards the system's periphery, broadening the phase interface. with prolonged simulation time, the solubility of co2 in crude oil increases, resulting in the formation of co2 clusters around crude oil molecules. this ultimately causes the phase interface to vanish, indicating that the system has reached miscibility. a comparison of the structural snapshots at both pressure conditions highlights a significant difference. at 1 ns, the oil-gas interface at 19.5 mpa is broader than that at 13.5 mpa, primarily due to the higher pressure enhancing co2 solubility within the crude oil system. the stronger interactions between co2 and crude oil at 19.5 mpa result in faster diffusion. by 10 ns, the interface in the lower-pressure system remains largely unchanged, whereas in the higher-pressure system, the oil and gas have become fully miscible. figure 3—the variation of interfacial tension in co2-crude oil systems with pressure. minimum miscibility pressure determination. the minimum miscibility pressure (mmp) between co2 and crude oil at a temperature of 344 k was established using the interfacial tension (ift) disappearance method. by calculating the ift at varying pressure levels, a relationship between interfacial tension and pressure was plotted, as shown in figure 3. the graph clearly indicates a linear relationship between ift and pressure, where the interfacial tension decreases as the pressure increases. through linear regression analysis, the following equation was obtained to describe this relationship, ift=−1.22p+22.67,............................................................................................................................................(6) where ift is the interfacial tension in mn/m; p is the pressure in mpa. according to this linear model, when the interfacial tension reaches zero, the minimum miscibility pressure (mmp) is determined. setting ift to 0 in the equation yields, 0=−1.22p+22.67.................................................................................................................................................(7) solving for p, the mmp is found to be 18.65 mpa. this value signifies the pressure at which co2 and crude oil become miscible, a critical parameter for processes such as enhanced oil recovery (eor). improved oil and gas recovery 8 molecular dynamics simulation of surfactant-mediated reduction in co2 flooding miscibility pressure. this study employs c12po6 as the selected surfactant for molecular dynamics simulations, aiming to investigate the variations in minimum miscibility pressure of the co2 and crude oil system before and after the surfactant's incorporation. the objective is to elucidate the mechanisms that contribute to the reduction of minimum miscibility pressure. in this section, the simulation framework consists of crude oil situated at the center, flanked by co2 molecules on either side, with a monolayer of surfactant molecules bridging the oil and gas phases. the oil components comprise a total of 800 molecules, consistent with the specifications outlined in the preceding section. each monolayer is composed of eight c12po6 molecules, while the system contains a total of 2000 co2 molecules, with 1000 positioned on each side. initially, within the npt ensemble, the system's density is gradually equilibrated to a stable state over a total simulation duration of 25 ns. subsequently, the simulation transitions to the nvt ensemble for a 10 ns equilibrium sampling period, during which data is collected once the system attains equilibrium in both energy and temperature. (a)0ns co2-oil co2-oil-c12po6 (b)1ns co2-oil co2-oil-c12po6 (c)10ns co2-oil co2-oil-c12po6 figure 4—instantaneous structure of the co2/crude oil/c12po6 system at various time steps (@19.5 mpa). improved oil and gas recovery 9 at a pressure of 19.5 mpa, comparisons are made of the instantaneous structural snapshots of the simulation system at various time points before and after the addition of the surfactant. figure 4(a) illustrates the initial configurations of both systems. over time, co2 molecules are observed to dissolve into the crude oil at the center of the system, while crude oil molecules migrate towards the periphery (figure 4(b)). it is evident that following the addition of the surfactant, the interface between the oil and gas phases becomes significantly wider compared to the scenario without the surfactant. this observation can be attributed to the surfactant's enhancement of co2 dissolution rates, facilitating a more rapid and complete mutual dissolution of the two phases. by the 10 ns mark (figure 4(c)), both systems are observed to have reached a state of miscibility. using the interface disappearance method, a series of simulations were conducted on the co2-crude oil system following the incorporation of the surfactant, with a constant temperature maintained while varying the pressure. as illustrated in figure 5, the introduction of c12po6 results in a reduction of interfacial tension within the co2-crude oil system. this finding indicates that the c12po6 surfactant plays a significant role in enhancing the miscibility of co2 with crude oil. the linear relationship between pressure and interfacial tension can be expressed by the fitted equation, ift = -1.42p+24.01...........................................................................................................................................(8) based on this relationship, it can be inferred that the system's minimum miscibility pressure is 16.9 mpa when the interfacial tension approaches zero. this signifies a reduction of 9.36% in the minimum miscibility pressure. figure 5—changes in interfacial tension in the co2-crude oil system before and after surfactant addition. figure 6 illustrates the density distribution of various substances at the specified temperature and pressure. the density distribution curves for c1, c2, c8, and co2 exhibit relative uniformity across the system. in contrast, the curves for c11, c23, and c12po6 display a uniform central region with a declining trend toward both ends, resulting in a distribution that is slightly narrower than the overall width of the system. this behavior can be attributed to the achievement of miscibility throughout the system; lighter components such as c1, c2, c8, and co2 are evenly distributed due to sufficient dissolution, thereby occupying the entire available space. improved oil and gas recovery 10 figure 6—density distribution curves before and after the addition of c12po6. conversely, heavier components like c11 and c23 possess higher viscosity and density, which hinders the dissolution of co2 within them. as a result, during the phase-mixing process, these heavier components struggle to permeate the entire system uniformly. figure 7 presents the density distribution of the heavier components under two conditions: with and without the surfactant. at the miscibility pressure, neither scenario achieves a completely uniform distribution of c11 and c23 within the system. however, a comparative analysis reveals that the presence of the surfactant facilitates a more favorable distribution and diffusion of c11 relative to c23. this observation is attributed to the lighter mass of c11, which enhances its diffusion under the influence of the surfactant. figure 7—the density distribution of heavy components before and after the addition of surfactant. molecular dynamics simulations provide a detailed characterization of the phase interface properties between co2 and the oil system, which are often difficult or impossible to observe using traditional experimental methods. due to the diversity of oil components and the significant variations in their concentrations, individual analyses may introduce considerable uncertainty. consequently, when assessing the density distribution of the oil and gas phases, all six oil phase components are grouped together and collectively referred to as 'oil' to ensure a consistent analysis of density distribution. improved oil and gas recovery 11 (a) co2 density distribution (b) crude oil density distribution figure 8—co2 and crude oil density distribution before and after the addition of surfactant (344k). figure 8 illustrates the density distribution curves of co2 and crude oil both before and after the addition of surfactant. under the same pressure conditions within the co2-crude oil system, the introduction of surfactant results in a decrease in the density of crude oil while simultaneously increasing the density of co2 within the oil phase. this expansion in oil volume indicates that co2 can dissolve more effectively in the crude oil, ultimately contributing to a reduction in the minimum miscibility pressure between the oil and gas. as pressure increases, the density of co2 in the oil gradually rises, suggesting that elevated pressure enhances the dissolution of co2 in the crude oil. concurrently, the density of crude oil in the central region of the system decreases due to the increased pressure causing crude oil to disperse towards the system's edges, which leads to an expansion of the volume occupied by the crude oil. (a) before and after the addition of c12po6 (13.5mpa, 344k) (b) the system after the addition of c12po6 (344k) figure 9—radial distribution functions of co2-oil before and after adding c12po6/radial distribution functions of co2-oil in the system after the addition of c12po6 as a function of pressure. improved oil and gas recovery 12 figure 9(a) presents the radial distribution functions of co2 and crude oil molecules, both with and without the surfactant, under conditions of 344 k and 13.5 mpa. this graphical representation provides insights into the interactions between these components. a comparative analysis of the two curves reveals that the introduction of surfactants under identical conditions results in a steeper distribution curve with higher peaks. this observation indicates a significant enhancement of the interaction forces between co2 and crude oil, facilitating increased co2 solubility in the crude oil. thus, the addition of surfactants alters the intermolecular forces between oil and gas molecules, subsequently affecting the solubility of co2 in crude oil. figure 9(b) depicts the radial distribution functions between co2 and crude oil molecules within the co2crude oil-c12po6 system at varying pressures of 11.5, 13.5, and 15.5 mpa. as pressure increases, the peaks of these radial distribution functions become more pronounced. this trend signifies that, at higher pressure levels, the intermolecular forces between co2 and crude oil molecules strengthen, leading to enhanced solubility of co2 in the crude oil. effect of temperature on the efficiency of surfactant. reservoir temperature is a critical determinant of the minimum miscibility pressure in co2 flooding processes. to encompass the temperature range observed in the examined reservoirs, this chapter performs molecular dynamics simulations on oil and gas systems at three distinct temperatures: 323 k, 344 k, and 363 k. the accompanying graph illustrates the variations in interfacial tension within the co2 and crude oil system as a function of temperature. it is evident that, at lower pressures, interfacial tension decreases with rising temperature, whereas at higher pressures, interfacial tension increases with temperature. by utilizing the linear relationship between pressure and interfacial tension, specific pressure-interfacial tension equations were formulated for different temperatures. ultimately, we calculated the minimum miscibility pressure, corresponding to the point at which interfacial tension approaches zero, as shown in figure 10. these results indicate that minimum miscibility pressure increases with rising temperature. without the addition of surfactant, the minimum miscibility pressure escalates from 12.808 mpa at 323 k to 18.65 mpa at 363 k. in contrast, with surfactant inclusion, it rises from 12.13 mpa to 18.06 mpa. (a) co2+oil system (b) co2+oil+ c12po6 system figure 10—variations in interfacial tension within the oil displacement system at different temperatures. in all three temperature conditions, an equal number of c12po6 surfactant molecules were introduced (16 molecules in total, with eight molecules on each side of the crude oil phase). the minimum miscibility pressure (mmp) values before and after the addition of surfactants at each temperature were compared, and the results improved oil and gas recovery 13 are presented in table 2. it is evident that an increase in temperature results in a greater reduction in the minimum miscibility pressure of the system. at 362k, the reduction is 10% higher compared to that at 323k. table 2—the minimum miscibility pressure for co2 flooding under different conditions. temperature, k minimum miscibility pressure, mpa reduction, % co2+oil co2+oil +c12po6 323 12.81 12.13 5.29 344 18.65 16.90 9.38 363 21.32 18.06 15.29 table 2 reveals that within the reservoir temperature range, the minimum miscibility pressure for co2 flooding increases as the temperature rises. however, the addition of surfactant demonstrates more effective performance. at a temperature of 363 k, the reduction in minimum miscibility pressure is notably higher compared to that at 323 k. therefore, within this temperature range, reservoirs with higher temperatures are better suited for utilizing surfactants as additives to enhance oil recovery. conclusions this study utilized molecular dynamics simulations to construct systems consisting of co2 and oil, as well as co2, oil, and a surfactant (c12po6). interface tensions were computed at different pressures under constant temperature for both systems. the minimum miscibility pressure was determined using the interface disappearance method, and the research focused on investigating how non-ionic surfactants reduce the minimum miscibility pressure. the investigation was primarily conducted by examining instantaneous phaseseparation trajectories, density distributions, and radial distribution functions. these analyses shed light on the mechanisms at play in the interactions between co2 and crude oil, as well as the impact of surfactants in co2oil systems. the key findings are as follows: (1)the addition of surfactants noticeably widens the oil-phase interface and increases its volume occupancy. surfactant molecules added to the system adsorb at the interface between crude oil and co2, forming a molecular film that enhances the interaction forces between the two, resulting in an expanded interface width. (2)surfactants can effectively reduce the minimum miscibility pressure (mmp) of the co2-crude oil system, facilitating the achievement of miscibility at lower reservoir pressures, thereby enhancing recovery (at a reservoir temperature of 344k, the reduction is increased by 9.36%). (3)temperature is a crucial factor affecting the effectiveness of recovery. with increasing reservoir temperature, the minimum miscibility pressure (mmp) for co2 and crude oil tends to rise, making it more difficult to achieve miscibility. however, at higher temperatures, the addition of surfactants leads to a more substantial reduction in mmp, enhancing their effectiveness in lowering mmp (at 363k, the decrease in temperature is enhanced by 10% compared to 323k). acknowledgments this research was funded by the open foundation of the shaanxi key laboratory of carbon dioxide sequestration and enhanced oil recovery. additionally, the work was supported by the petrochina innovation foundation (grant number 2022dq020201). the research also includes several specific projects: the study on improved oil and gas recovery 14 the mechanism of rod-tubing corrosion and wear in co₂ solution based on machine learning (project number yjsyzx23skf0002), the study on the optimization of flowback models and regimes for shale gas postfracturing (project number gsyky-b09-33), the evaluation of shale gas horizontal well productivity based on machine learning (project number riped-2022-js-1477), the evaluation methods and optimization of production regimes for two-phase flow in multi-stage fractured horizontal wells for shale gas (project number riped-2023-js-29), and the optimization of nozzle operating regimes for shale gas horizontal wells (project number pgwx-202401). conflicting interests the author(s) declare that they have no conflicting interests. references almobarak, m., wu, z., zhou, d., et al. 2021. a review of chemical-assisted minimum miscibility pressure reduction in co2 injection for enhanced oil recovery. petroleum 7(1):245-253. djabbarah, n.f. 1990. miscible oil recovery process using carbon dioxide and alcohol. us patent us4899817a. dong, z., ma, x., xu, h., et al. 2022. molecular dynamics study of interfacial properties for crude oil with pure and impure ch4. applied 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polyoxypropylene ether on the minimum miscibility pressure of carbon dioxide flooding. petroleum geology and oilfield development in daqing 35(1): 118-122. wang, r., peng, f., song, k., et al. 2018. molecular dynamics study of interfacial properties in co2 enhanced oil recovery. fluid phase equilibria 474(1): 176-183. yang, s.y., lian, l.m., yang, y.z., et al. 2015. molecular optimization design and evaluation of miscible processing aids applied to co2 flooding. xinjiang petroleum geology 36(5): 555-559. yang, z., wu, w., dong, z., et al. 2019. reducing the minimum miscibility pressure of co2 and crude oil using alcohols. colloids and surfaces a: physicochemical and engineering aspects 568(1):105-112. zhu, a., zhang, x., liu, q., et al. 2009. a fully flexible potential model for carbon dioxide. chinese journal of chemical engineering 17(1): 268-272. zhenzhen dong, is a professor in the petroleum engineering department at xi’an shiyou university. her research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dr. dong holds a bachelor’s degree in mathematics from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. tong hou, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focuses her research in areas involving molecular dynamic simulation and enhanced oil recovery. zhanrong yang, is a master candidate in petroleum engineering department at xi’an shiyou university. his research focuses on reservoir simulation and enhanced oil recovery. lu zou, is a master candidate in petroleum engineering department at xi’an shiyou university. his research involves machine learning, reservoir simulation,and enhanced oil recovery. https://doi.org/10.1016/j.fluid.2018.03.022 improved oil and gas recovery 16 weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. his research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dr. li holds a bachelor’s degree in petroleum engineering from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. keze lin, is a undergraduate student of china university of petroleum (beijing), beijing. he focuses on enhanced oil recovery and reservoir engineering. hongliang yi, is a senior reservoir engineer in liaohe oilfield company of petrochina. he specializes in enhanced oil recovery and production analysis. zhilong liu is a senior reservoir engineer in enertech-drilling & production co., cnooc energy technology & services ltd. his specialties include reservoir management and enhance oil recovery. abstract introduction methodology results conclusions acknowledgments conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1325 received october 11, 2024; revised november 25, 2024; accepted december 20, 2024. *corresponding author: nkemakolam.izuwa@covenantuniversity.edu.ng 1 application of thermochemical in removing condensate banking in gas condensate reservoirs ezeoke tobechukwu, covenant university, ota, nigeria; nkemakolam chinedu izuwa*,covenant university, ota, nigeria and federal university of technology, owerri, nigeria; adegoke amosu, igbereyivwe oghenetejiri, humphery dike, covenant university, ota, nigeria; placid anyanwu, and chukwuebuka francis dike, federal university of technology, owerri, nigeria abstract the accumulation of liquid near the wellbore, induced by condensate banking in gas condensate reservoirs, significantly impairs gas production rates, presenting a substantial challenge for hydrocarbon recovery. conventional methods such as co2 injection and produced gas cycling offer only temporary mitigation, requiring frequent reapplication, which results in high operational costs and logistical complexities. this study explores the potential of thermochemical fluids (tcfs) as a more durable and cost-efficient alternative to address condensate banking. the exothermic reaction between sodium nitrite (nano2) and ammonium chloride (nh4cl), catalyzed by acetic acid (ch3cooh), produces heat, generating temperatures of up to 84oc, and achieving a maximum recovery of 52% from four core samples. tcfs induce in-situ heating, the release of nitrogen gas, and the generation of pressure, which together create microcracks that facilitate the vaporization and mobilization of the trapped condensate. this approach also helps maintain reservoir pressure above the dew point and reduces capillary pressure in the pore spaces. the study investigates the influence of varying reactant and catalyst concentrations on the reaction kinetics, emphasizing the critical role of optimal stoichiometry to maximize heat generation. core flooding experiments were conducted using the huff-and-puff injection technique to compare the performance of tcfs injection with co2 injection. the results consistently showed superior condensate recovery with tcfs injection across all experiments. introduction retrograde gases represent a distinct category of gases that exhibit non-ideal behavior. unlike typical gases, which expand when pressure decreases in accordance with boyle’s law, retrograde gases undergo condensation into a liquid phase. as pressure decreases and approaches a critical point, intermolecular forces, particularly van der waals forces, become increasingly significant, leading to a reduction in volume and a phase transition from gas to liquid. this behavior deviates from the ideal gas law, where volume and pressure are inversely proportional at a constant temperature. condensate gas reservoirs, which exhibit retrograde gas behavior, have garnered considerable attention due to their unique and complex nature. with the increasing global demand for energy, including oil and gas, the simultaneous production of gas and condensate holds substantial economic value (izuwa et al. 2014; li et al. 2023). in particular, nigeria stands to benefit from condensate production, as it is not subject to opec production quotas (nwabueze 2000). furthermore, the pricing of condensates is comparable to that of naphtha, making it more profitable than crude oil on a per-volume basis. in alignment with this, on january 1st, 2024, the nigerian upstream petroleum regulatory commission (nuprc) set an mailto:modibbo.edu@gmail.com improved oil and gas recovery 2 ambitious target of producing 2.6 million barrels per day (bpd) of oil and condensates by 2026, a notable increase from the 1.6 million bpd achieved in 2023 (mishra 2024). nigeria's oil exports have been adversely affected by factors such as inadequate investment, crude theft, and pipeline vandalism, which have collectively diminished government revenues. consequently, there is a strong incentive to enhance condensate production through innovative methods. however, the efficient exploitation of these reservoirs requires a comprehensive understanding of their phase behavior to prevent condensate banking, a phenomenon that has substantial implications for hydrocarbon recovery (shariati et al. 2014). the phase envelope diagram in figure 1 depicts the reservoir’s behavior, with the system operating between the critical temperature and cricondentherm, as described by guo et al. (2020). the dashed lines within the envelope represent constant liquid volume fractions, ranging from 100% at the bubble point to 0% at the dew point. for the purpose of this experiment, assume the initial conditions are at pressure pi and temperature ti, where the reservoir temperature lies below the phase envelope’s cricondentherm but remains above the critical temperature (c). as the reservoir pressure is reduced at constant temperature, following the pathway denoted by the solid line abde, the phase behavior of the system can be analyzed. at point a along the dew point line, a liquid phase begins to form in the reservoir. as the pressure is reduced, additional liquid condenses, increasing the liquid phase volume until it accounts for 10% of the total reservoir volume at point b. with further pressure reduction, the liquid volume fraction rises to a maximum of approximately 12%. beyond this point, the liquid phase volume decreases as the pressure continues to decline, returning to 10% at point d. the liquid volume continues to decrease from point d to point e. at point e, corresponding to the lower dew point, the liquid phase completely disappears (ezekwe 2010). the liquid phase that has formed remains immobile until the condensate saturation exceeds the critical condensate saturation, at which point the oil phase becomes mobile and starts to flow (izuwa et al. 2015). figure 1—phase envelope of retrograde gas condensate (source: ezekwe 2010). the accumulation of condensate around the wellbore results in significant immobilization, leading to a marked reduction in effective gas permeability, which in turn decreases overall gas production (hassan et al. 2019a). asgari et al. (2014) demonstrated that condensate banking in carbonate reservoirs could reduce effective gas permeability by up to 80%. additionally, in a core flooding experiment conducted by kumar et al. (2006) on both reservoir and berea sandstone cores, condensate banking caused the relative permeability to gas improved oil and gas recovery 3 to decrease by 90% of its initial value during condensate accumulation. the impact of condensate banking on the gas relative permeability (krg) is illustrated in figure 2. as the distance from the borehole increases, condensate saturation (depicted by the green curve) decreases, while gas relative permeability (shown by the red curve) increases. this reduction in condensate saturation facilitates greater gas flow through the pore network. the issue is particularly pronounced in tight or lowpermeability reservoirs, where the accumulated condensate remains largely immobile, acting as a barrier to the movement of gas, potentially leading to a complete cessation of gas productivity (sayed and al-muntasheri, 2016). to address this challenge, various recovery techniques, such as chemical injection, horizontal well technology, gas cycling, and hydraulic fracturing, are commonly employed to mobilize the trapped condensate and enhance gas reservoir deliverability (kumar et al. 2006; evans et al. 2016; su et al. 2017; khan et al. 2010). the thermochemical enhanced oil recovery (eor) process introduces a novel approach by addressing both the fluid properties and the physical conditions required for pressure stabilization within gas condensate reservoirs, setting it apart from conventional methods that primarily focus on physical interventions. hydraulic fracturing creates new fluid flow pathways within reservoir rock formations but does not alter the properties of the fluids, such as oil, condensate, or water. gas cycling, which involves reinjecting gas to maintain reservoir pressure and mitigate condensate dropout, similarly does not modify interfacial tension or wettability. horizontal well drilling increases the reservoir volume and enhances wellbore contact with the formation; however, like hydraulic fracturing, it does not directly impact the fluid properties. figure 2—condensate blockage schematic with reflection to relative permeability curves (source: sayed and almuntasheri 2016). a novel thermochemical treatment has been developed to enhance formation productivity and mitigate condensate banking (sayed and al-muntasheri 2016). this approach utilizes reactive fluids to generate both pressure and heat, which not only creates multiple fractures but also modifies the behavior of the condensate (hassan et al. 2018). according to hassan et al. (2019a), the in-situ temperature and pressure generated during this process can exceed 500 ° f and 5000 psi, respectively. this treatment has demonstrated potential for reducing condensate-related damage and improving long-term formation deliverability (hassan et al. 2019b). hassan et al. (2018) further observed that the injection of thermochemical fluids can increase the reservoir pressure and temperature beyond the dew point curve, facilitating the transformation of liquid condensate into gas. their findings revealed that the thermochemical reaction could generate a pressure of 1300 psi under typical reservoir conditions. the mechanisms driving this recovery include the reduction of capillary forces, improved oil and gas recovery 4 immiscible displacement, modification of rock characteristics, and a decrease in viscosity (hassan et al. 2019a). under reservoir conditions, two chemicals that remain stable under surface conditions, ammonium chloride (nh4cl) and sodium nitrite (nano2), can produce in-situ nitrogen gas, steam, heat, and pressure when their reaction is triggered. the reaction products are only generated once the thermochemical reaction begins. thermochemical fluids (tcfs) are typically non-toxic, cost-effective, and environmentally friendly. the reaction can be initiated either by the natural reservoir temperature or by introducing a chemical activator. specifically, the injection of an acidic fluid, acting as a catalyst, lowers the ph and triggers exothermic reactions within the reservoir formation (hassan et al. 2019c; hassan et al. 2020). nh4cl + nano2 →nacl + 2h2o + n2 (gas) + δh (heat),...............................................................................(1) in an experiment conducted by hassan et al. (2019c), the huff-and-puff technique was applied to tight sandstone cores with a permeability of 0.9 md, resulting in a 63% recovery of the initial condensate through the injection of thermochemical fluids. this process led to an increase in the inlet pressure, reaching 2300 psi, which significantly altered the behavior of the condensate. as depicted in figure 3, the thermochemical treatment raised the temperature and partially restored the pressure within the system. the treatment moved the system to the point (3500 psi, 350 ° f), marked by the green triangle. this elevated temperature shifted the pressure-temperature (p-t) conditions back within the phase envelope, facilitating the redissolution of condensate liquid into the gas phase, thus enhancing flow efficiency and reducing liquid dropout. furthermore, the treatment affected the rock's properties, such as permeability and capillary forces, through the pressure pulses. the removal of condensate banking resulted in an increase in the effective gas permeability, improving the relative permeability to gas by a factor of 1.98. the treatment also reduced capillary forces by 90%, with capillary pressure decreasing to 1.36 psi and 90.4 psi, respectively (hassan et al. 2019c). figure 3—alterations of condensate behaviour due to thermochemical treatment (adapted from hassan et al. 2019b). in a separate study, hassan et al. (2019a) demonstrated that thermochemical fluids can effectively mitigate condensate damage in sandstone formations when applied using the huff-and-puff injection method. the study showed that, on average, 67% of condensate could be removed without causing any formation damage. it was observed that more permeable rocks experienced greater condensate removal after treatment, while tight sandstones exhibited more moderate levels of liquid removal. the thermochemical treatment works through a chemical reaction between the fluid and the minerals in the formation, generating heat or gas to mobilize the improved oil and gas recovery 5 condensate and remove it from the pore spaces. in permeable rocks, the larger pore throats facilitate easier penetration of the fluid, leading to more significant condensate removal. in contrast, tight sandstones, with their smaller pore throats, exhibited less pronounced condensate removal. the study concluded that, in general, three cycles of thermochemical treatment are sufficient to mitigate condensate damage in various sandstone formations. methodology this section will present both qualitative and quantitative analyses, including thin section analysis of various tight sandstone cores, determination of porosity and permeability, chemical reactions of aqueous solutions, and core flooding experiments. for the thin section analysis, a polarizing microscope will be utilized due to its ability to provide detailed insights into the mineralogical composition and structural characteristics of the sandstone cores. thin section analysis. in this study, thin section analysis was conducted on five tight sandstone cores with varying porosities using a polarizing microscope in the laboratory. the polarizing microscope is a specialized tool equipped with polarizing filters that allows for the detailed examination of mineral compositions in core samples. the process involves slicing the rock into extremely thin sections and then illuminating them with polarized light. by observing how the light interacts with the minerals, i was able to identify and quantify the different minerals present, such as quartz, plagioclase, and muscovite. the percentages of these minerals are presented in table 1. table 1—diagnostic features of minerals from thin section. mineral observed isotropic vs. anisotropic interference colours pleochroism quartz isotropic no variation in colour none (remains colourless) plagioclase feldspar anisotropic typically shows 1st order colours (low to moderate intensity): grey, white, yellow can exhibit weak pleochroism in some varieties (subtle colour changes) muscovite anisotropic high order interference colours: bright yellows, greens, or reds strong pleochroism: colourless to pale yellow/green depending on orientation microcline anisotropic like plagioclase: 1st order colours (grey, white, yellow) can exhibit weak to moderate pleochroism in some varieties improved oil and gas recovery 6 figure 4—thin section of cores on glass slides. reaction kinetics. reaction kinetics refers to the study of the rates at which reactants are consumed and products are formed over time. it is typically quantified in units such as concentration change per unit time (e.g., m/s). the investigation of reaction kinetics involves understanding how different factors influence the rate of a chemical reaction. these factors include: (i) concentration of reactants (ii) temperature (iii) presence of a catalyst (iv) reaction mechanism (the step-by-step process of the reaction) experimental design. a thermometer was placed within the vacuum tube of the compacted vacuum system to monitor any changes occurring during the experiment. the distinct thermochemical fluids were mixed in the vacuum jar after being dissolved in de-ionized water to create a soluble solution. the reaction was observed for five minutes before adding a catalyst (20 ml of acetic acid) to initiate the reaction. throughout the experiment, the generated pressure and temperature were recorded at 5-minute intervals, along with their relationship to time. key parameters such as the buildup, stability duration, and reaction rate were determined by observing the system ’s response. the experiment was conducted at various molar and catalyst concentrations, as outlined in tables 2 to 4. by tracking the reaction temperature and ph after the catalyst (acetic acid, ch3cooh) was introduced, the impact of different reactant concentrations on the reaction kinetics of the nano2/nh4cl system was evaluated. the results indicated that a molar concentration of 5m nano2 and 5m nh4cl produced the highest temperature yield and ph reduction, indicating a more efficient reaction. table 2—properties for 2m+2m solution + 20ml acetic acid. properties nano2 nh4cl product molar concentration, mol (g) 2m (138g) 2m (107g) ph 6 4 5 temperature (°c) 22 24 65 table 3—properties for 2m+2m solution + 30ml acetic acid. properties nano2 nh4cl product molar concentration, mol (g) 2m (138g) 2m (107g) ph 6 4 5 temperature (°c) 22 24 67 improved oil and gas recovery 7 table 4—properties for 5m+5m solution + 60ml acetic acid. properties nano2 nh4cl product molar concentration, mol (g) 5m (345g) 5m (267.5g) ph 6 4 3 temperature (°c) 18 20 84 result modal analysis of core samples. modal analysis utilizes data from the thin section to quantify the relative abundance of each mineral present in the rock. it determines the modal mineralogy, which refers to the volume percentage of each mineral in the rock sample. table 5 presents the modal analysis of the niger delta core plugs used in the experiment. the thin section analysis revealed a predominance of quartz in all five core samples, with concentrations ranging from 76.89% in sample 3 to 96.8% in sample 1. other identified minerals included microcline (a type of feldspar), plagioclase feldspar (present in samples 3 and 4), and muscovite (a clay mineral), which was only found in sample 3. these findings provide insight into the mineral composition of the core samples, which can be important for understanding their petrophysical properties and behavior under various experimental conditions. table 5—modal analysis of niger delta core samples. sample number quartz (%) microcline (%) plagioclase (%) muscovite (%) sample 1 96.8 3.2 sample 2 96 4 sample 3 76.89 13.2 6.6 3.3 sample 4 93.8 3.09 3.09 sample 5 95.77 4.22 potential impact of clay minerals on condensate recovery. the presence of clay minerals, particularly muscovite in sample 3, could potentially affect condensate recovery in the core flooding experiment through several mechanisms: reduced pore throat size. clay minerals often have a platy (plate-like) structure. these platy clays can coat pore surfaces and bridges between larger grains, effectively reducing the size of pore throats. this can hinder the flow of condensate through the rock, potentially impacting recovery during the production phase. wettability alteration. clay minerals can alter the wettability of the rock surface. in some cases, clays can promote a more water-wet condition. condensate, being a hydrocarbon liquid, prefers a more oil-wet environment. a shift towards water-wetness might lead to increased residual condensate saturation within the core, further reducing recoverable volumes. effect of reactant and catalyst concentration on the temperature generated. the reaction between sodium nitrite and ammonium chloride was evaluated by measuring the heat produced over time. additionally, the influence of temperature and concentration on the reaction was explored to better understand its kinetics. figures 5 to 7 illustrate how the concentration of the thermochemical fluids affects the temperature during the improved oil and gas recovery 8 reaction. these figures provide a visual representation of how varying concentrations of the reactants influence the thermal output, contributing to the overall understanding of the reaction dynamics and its potential for enhancing gas reservoir productivity. the study investigated the effects of varying concentrations of sodium nitrite (nano2) and ammonium chloride (nh4cl), at 2m and 5m, on the temperature generated during the reaction. additionally, the influence of catalyst concentration, specifically acetic acid (ch3cooh), was explored. a series of reaction kinetics experiments were conducted to examine the interaction between reactant and catalyst concentrations, and the resulting temperature profiles. in these experiments, identical initial concentrations of 2m sodium nitrite and 2m ammonium chloride were used, with varying volumes of acetic acid (figures 5 and 6). in another set of experiments (figure 7), the reactant concentrations were increased, and the catalyst volume was proportionally adjusted. temperature changes were monitored over time, from 5 to 80 minutes. the results indicate a significant interplay between reactant concentration, catalyst volume, and the heat generated, providing deeper insights into the kinetics of the thermochemical reaction. in figures 5 and 6, a modest temperature increase is observed with a slight increase in catalyst volume (30 ml vs. 20 ml). both scenarios show a peak temperature around the 10-minute mark, with figure 6 exhibiting a marginally higher peak (67°c vs. 65°c). however, the increase in temperature is minimal, and considering the additional cost of the catalyst, this may not be economically advantageous for field-scale applications. in contrast, figure 7 demonstrates a more substantial temperature increase. in this case, both reactant concentrations were increased fivefold (to 5m), and the catalyst volume was adjusted proportionally to 60 ml. this resulted in a significantly higher peak temperature of 84 oc compared to the previous scenarios. this finding highlights the critical role of reactant concentration in driving the heat evolution during the thermochemical reaction. a higher concentration of reactants provides more reacting molecules, amplifying the exothermic reaction and leading to a higher temperature rise, which is more favorable for optimizing reaction efficiency in larger-scale operations. these findings indicate that while catalyst concentration does have some influence on temperature, the concentration of reactants plays a more critical role in optimizing heat generation during the thermochemical reaction for condensate bank remediation. higher reactant concentrations lead to a greater number of reacting molecules, resulting in a more significant exothermic effect and a higher temperature increase. this insight is crucial for optimizing the thermochemical formulation for field applications, allowing for a balance between economic feasibility and the achievement of the desired temperature profile necessary for effective condensate recovery. by carefully adjusting reactant concentrations and catalyst volumes, it is possible to maximize the efficiency of the treatment while maintaining cost-effectiveness in field operations. figure 5—temperature yield analysis–2m+2m (20ml acetic acid). improved oil and gas recovery 9 figure 6—temperature yield analysis–2m+2m (30 ml acetic acid). figure 7—temperature yield analysis–5m+5m (60ml acetic acid). analysis of thermochemical injection vs co2 injection. building upon the insights from the reaction kinetics experiments, we proceeded with core flooding experiments to evaluate the performance of the most effective thermochemical formulation (5m+5m reactants with 60 ml catalyst) in comparison to co2 injection, a commonly utilized enhanced oil recovery (eor) technique. the huff-and-puff method was employed on four core samples (s4, s5, s6, s7), with their properties detailed in table 6. table 6—sandstone core properties. test no. diameter (cm) length (cm) dry weight (g) wet weight (g) bulk volume (vb) (cm3) porosity (%) pore volume (vp) (cm3) permeability (md) s4 3.7 3.3 68 77 35.48 13.24 9.00 285 s5 3.65 4.2 86 97 43.95 12.79 11.0 372 s6 3.8 5.0 121 129 56.71 6.61 8.0 409 s7 3.8 5.0 121 129 56.71 6.61 8.0 409 production data for each core sample are shown in figure 8. a consistent trend emerged across all four core samples: the highest condensate recovery occurred during the first injection cycle. specifically, figure 8(c) highlights sample s6, which achieved the highest initial recovery of 21.7%. this result demonstrates the improved oil and gas recovery 10 efficacy of the thermochemical treatment in improving condensate recovery during the initial stage of the process, with the potential for further optimization in subsequent cycles. (a)s4 (b)s5 (c) s6 (d)s7 figure 8—production comparative analysis. however, sample s6 also exhibited a significant decline in condensate recovery during the subsequent cycles, ultimately resulting in the lowest overall recovery of 47.1%. in contrast, sample s5, despite having the lowest initial recovery (figure 8(b)), demonstrated a more stable recovery profile across all cycles, ultimately achieving the highest cumulative recovery among all the samples. these observations suggest that factors beyond initial recovery, likely related to the structural or petrophysical properties of the core samples, can significantly influence long-term performance. the core flooding experiments also provided a valuable comparison between thermochemical fluid injection (tcfs) and co2 injection. while co2 injection typically stabilizes pressure and reduces condensate dropout, the thermochemical treatment showed superior performance in terms of both initial recovery and long-term improved oil and gas recovery 11 condensate mobilization, especially in cores with favorable petrophysical characteristics. these findings highlight the potential for thermochemical treatments to enhance recovery efficiency, particularly in challenging reservoirs with complex phase behavior. in all four core samples, the injection of thermochemical fluids (tcfs) consistently resulted in higher condensate recovery compared to co2 injection. these findings highlight the effectiveness of thermochemical fluids in mobilizing trapped condensate within the rock matrix. the enhanced recovery can likely be attributed to the synergistic effects of heat generation, gas evolution, and potential wettability alteration, which together facilitate the release and flow of condensate. overall, the core flooding experiments validated the potential of thermochemical fluids as a promising enhanced oil recovery (eor) technique for condensate bank remediation. the consistent trend of superior recovery with tcfs injection, in comparison to co2 injection, underscores the potential of this approach for improving gas production in condensate gas reservoirs. this indicates that thermochemical treatments could offer a more efficient and cost-effective solution for addressing condensate accumulation and enhancing production in such reservoirs. conclusions this study investigates the application of thermochemical fluids (tcfs) for enhanced oil recovery (eor) in condensate gas reservoirs, with a specific focus on their ability to remediate condensate banks. the results reveal several key findings that underscore the effectiveness of thermochemical treatments in improving condensate recovery and enhancing gas production. the following are the main conclusions drawn from the study. 1. the concentration of reactants plays a more significant role in temperature increase than catalyst concentration. higher reactant concentrations, particularly sodium nitrite and ammonium chloride, result in more pronounced heat generation, which is crucial for mobilizing trapped condensate. 2. core flooding experiments demonstrated that the injection of thermochemical fluids consistently led to higher condensate recovery than co2 injection across all tested core samples. this finding highlights the effectiveness of tcfs in mobilizing and vaporizing condensate within tight formations, making it a promising alternative to traditional gas injection methods. 3. the huff-and-puff injection method used in the experiments showed no significant decrease in condensate recovery after four cycles compared to three cycles. this suggests that multiple cycles of thermochemical injection may offer sustained benefits, though further investigation is needed to optimize the number of cycles and evaluate their economic feasibility. 4. the thermochemical reaction generates nitrogen gas, which acts as an inert carrier gas to displace reservoir fluids. this gas production contributes to maintaining pressure within the reservoir, 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in tight sandstone reservoirs. journal of petroleum science and engineering 133(1): 201207. ezeoke tobechukwu is a graduate of petroleum engineering, covenant university, ota. mr. tobechukwu holds bachelor’s degree in petroleum engineering. he is interested in enhancing/improving oil and gas recovery. nkemakolam chinedu izuwa is an associate professor at the department of petroleum engineering, federal university of technology, owerri. he also spent sabbatical leave at covenant university, ota and currently serving as a visiting associate professor. dr. izuwa holds a bachelor’s degree in petroleum engineering, master’s degree in natural gas engineering and ph.d in petroleum engineering. dr. izuwa involved in teaching, student development/mentorship and research. his research areas include but not limited to formation evaluation, enhanced oil recovery, drilling fluids engineering, geothermal engineering, surface active agents and gas engineering. currently, he is handling research on green hydrogen production. https://www.offshore-technology.com/news/nigeria-oil-production-target/ improved oil and gas recovery 13 adegoke amosu is a graduate of petroleum engineering, covenant university, ota. mr. adegoke holds bachelor’s degree in petroleum engineering. he is interested in enhancing /improving oil and gas recovery. igbereyivwe ogehenetejiri is a graduate of petroleum engineering, covenant university, ota. mr. oghenetejiri holds bachelor’s degree in petroleum engineering. he is interested in enhancing/improving oil and gas recovery. humphrey dike is currently a researcher and faculty member at the department of petroleum engineering, covenant university, ota. he holds a bachelor’s degree in petroleum engineering, master’s degree in gas engineering, and doctorate degree in petroleum and gas engineering with special interest in drilling fluids. dr. dike is a member of different research clusters, including drilling and drilling fluids engineering research cluster, business, energy and politics cluster, and currently driving blue hydrogen research at covenant university, nigeria. his areas of core competence are drilling fluids engineering, oilfield chemicals, natural gas engineering and processing, and surface production operations. placid ikechukwu anyanwu is a senior lecturer at the department of polymer engineering, federal university of technology, owerri. dr. anyanwu holds a ph.d in polymer science and engineering. he is involved in teaching and research. his research areas revolve around bioplastics and composite, coatings, corrosion and rubber. chukwuebuka francis dike is a research technologist at the department of petroleum engineering, federal university of technology, owerri. his research interest is drilling fluids, enhanced oil recovery, reservoir engineering, and flow assurance. dr. dike holds a bachelor degree and master’s degree in petroleum engineering. abstract introduction methodology result conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1341 received december 10, 2024; revised december 30, 2024; accepted january 20, 2025. *corresponding author: christian.okalla@futo.edu.ng 1 evaluation of wax inhibition in crude oil pipelines using extracts from moringa seeds and lime mathew chidubem udechukwu, christian emelu okalla*, anthony kerunwa, nzenwa dan enyioko, chidera prince ohanaga, and francis chukwuebuka dike, federal university of technology owerri, owerri, nigeria abstract wax deposition in crude oil pipelines is a significant operational challenge, particularly in low-temperature environments such as offshore installations, where wax crystallization hinders flow. traditional wax inhibitors, such as xylene, are effective but raise environmental concerns due to their hazardous nature. this study explores the use of moringa seed extract (mse) and lemon extract as eco-friendly, bio-based alternatives to conventional inhibitors. fourier-transform infrared (ftir) spectroscopy was utilized to characterize the functional groups in these inhibitors alongside xylene. the ftir analysis confirmed the presence of hydroxyl and carboxyl groups, which are critical for wax inhibition. both mse and lemon extract demonstrated functional similarities to xylene in their inhibitory capabilities. physicochemical analysis of the crude oil was conducted to establish a baseline for evaluating inhibitor performance, revealing a specific gravity of 0.860, api gravity of 33.035, kinematic viscosity of 8.14 cst, and dynamic viscosity of 7.01 cp. cloud and pour point tests, simulating sub-ambient offshore conditions, were used to assess wax inhibition. results showed that mse, at a 9 ml concentration, achieved a pour point of 17°c and a cloud point of 19°c, outperforming xylene, which recorded a pour point of 19°c and a cloud point of 20° c at the same concentration. lemon extract also proved effective, achieving a pour point of 22°c and a cloud point of 23°c, though its performance was slightly below that of mse and xylene. this study highlights the superior wax inhibition capability of mse over conventional inhibitors like xylene, presenting it as a sustainable and environmentally friendly alternative for pipeline transportation. the concentration-dependent effectiveness of mse underscores its potential for commercialization, with further optimization of concentration levels recommended for large-scale applications. additionally, a comprehensive environmental impact assessment is suggested to validate its safety. these findings provide valuable insights into bio-based wax control methods, encouraging the adoption of greener practices in the petroleum industry. introduction wax deposition in crude oil pipelines poses a critical challenge to the oil and gas industry, particularly in cold environments and deepwater fields. as crude oil flows through pipelines, its temperature often drops below the wax appearance temperature (wat), leading to the precipitation of paraffin waxes from the oil. these waxes adhere to the pipeline walls, forming deposits that progressively reduce the effective pipeline diameter. this deposition results in increased pressure drops, diminished flow rates, and, in severe cases, complete pipeline blockages (olajire 2021). the operational and economic implications of wax build-up are significant, as they mailto:christian.okalla@futo.edu.ng improved oil and gas recovery 2 necessitate frequent maintenance, the use of inhibitors, or remedial interventions to restore pipeline functionality (kiyingi et al. 2022). to ensure smooth operations, various methods of wax mitigation and control have been developed. methods for inhibiting wax buildup include physical techniques such as preheating pipelines (haj-shafiei et al. 2014; srivastava et al. 1992; cao et al. 2022; yang et al. 2022), applying internal pipeline coatings (lei et al. 2023; li et al. 2020; yang et al. 2021; goncalves et al. 2004; bingfan et al. 2019), using heated transportation (liu et al. 2022; bingfan et al. 2019) and dilution methods (tang et al. 2022). chemical approaches include adding coagulants (soedarmo et al. 2017; taheri-shakib et al. 2018; akinyemi et al. 2016) and drag-reducing agents (akinyemi et al. 2018; deka et al. 2020). however, both predictive models and inhibitors face limitations in universal application due to variations in crude oil composition, flow conditions, and fluid properties across different regions. pigging, though effective at removing wax deposits, can cause operational disruptions and is costly in deepwater or long-distance pipelines (singh et al. 2000). heating pipelines is energy-intensive and environmentally unsustainable. chemical inhibitors, while commonly used, pose significant environmental risks due to their non-biodegradable nature. furthermore, the continuous use of chemical inhibitors increases operational costs, making this approach less attractive for long-term solutions (lee 2008). a comprehensive wax management strategy typically involves a combination of these methods, depending on the specific characteristics of the crude oil, pipeline conditions, and environmental factors. the high cost and environmental impact of conventional wax inhibition methods have prompted a search for more sustainable alternatives. one promising solution is the use of natural, biodegradable wax inhibitors derived from locally available plant materials. natural inhibitors can potentially reduce the environmental footprint and provide a cost-effective means of addressing wax deposition. for example, plant-based materials like fatty acids and essential oils have shown promise in altering the crystallization behaviour of waxes, preventing their agglomeration, and reducing deposition on pipeline walls (alpandi et al. 2022). in this study, the use of locally sourced natural inhibitors, such as moringa oleifera (moringa) seed extracts and lime extracts, has emerged as a potentially viable solution. moringa seeds are rich in bioactive compounds, such as fatty acids and proteins, that exhibit surfactant and dispersant properties (chis et al. 2024). lime, on the other hand, contains citric acid and essential oils that can modify the surface properties of wax crystals, preventing their adhesion to pipeline walls (cruz-valenzuela et al. 2015). despite their potential, there is a notable lack of comprehensive research evaluating the effectiveness of these natural inhibitors in real-world pipeline conditions, particularly in regions like the niger delta, where wax deposition is a recurring issue. the primary problem addressed in this study is the lack of environmentally sustainable and cost-effective methods for controlling wax deposition in crude oil pipelines. given the environmental impact and economic burden associated with conventional wax inhibitors, there is an urgent need for alternative solutions that are both effective and eco-friendly. while natural inhibitors like moringa seed and lime extracts hold potential, their application in the oil and gas industry has not been extensively studied, and their effectiveness compared to conventional methods remains unclear. materials and method materials. table 1 outlines the materials used in the study and their specific functions. crude oil serves as the primary subject of the research, providing the medium for wax deposition and inhibition tests. xylene is employed as a solvent for dissolving and extracting wax components from crude oil samples, enabling further analysis. filter paper is used to separate solid impurities from extracted oils during the soxhlet extraction process. ice blocks are essential for maintaining low temperatures in wax deposition experiments, simulating sub-ambient conditions commonly encountered in offshore environments. finally, wax inhibitors, which include locally sourced and conventional options, function as surfactants to mitigate wax deposition in crude oil pipelines. figure 1 illustrates xylene, a conventional chemical solvent widely used in wax inhibition studies, known for its effectiveness in dissolving and extracting waxes from crude oil samples. these materials improved oil and gas recovery 3 represent the core components used in this study to evaluate the performance of locally sourced and conventional wax inhibitors. table 1—materials used and their functions. s/n materials functions 1 crude oil the primary subject of the study. 2 xylene serves as a solvent for dissolving and extracting wax from crude oil samples. 3 filter paper used to filter out solid particles and impurities while extracting the oil in the soxhlet extractor. 4 ice-block utilized to maintain low temperatures in the wax deposition experiments. 5 wax inhibitors acts as surfactant to prevent or reduce wax deposition. figure 1—xylene. table 2 categorizes the wax inhibitors used in the study into locally sourced and conventional types. the locally sourced inhibitors include lemon extract and moringa extract, both of which are bio-based alternatives investigated for their wax inhibition performance. the conventional inhibitor used is xylene (xy), a widely recognized industrial solvent for wax control. this classification highlights the comparative focus of the study on evaluating the effectiveness of wax inhibitors. table 2—wax inhibitors. s/n locally sourced inhibitor convention inhibitor 1 lemon extract xylene (xy) 2 moringa extract figure 2(a) depicts grinded moringa seed, which was prepared by cleaning, drying, and grinding the seeds into a fine powder to maximize the surface area for efficient extraction of bioactive compounds. figure 1(b) shows lemon peel, which was similarly processed by peeling, air-drying, and grinding to obtain a powdered form suitable for extraction. improved oil and gas recovery 4 (a)grinded moringa seed (b)lemon peel figure 2—locally sourced inhibitors. equipment. in this study, equipment used are as follows. 1. soxhlet extractor: a laboratory apparatus designed for the continuous extraction of a specific compound from a solid material. the soxhlet extractor is commonly used in oil analysis and other chemical extractions, utilizing a solvent that is heated, condensed, and cycled through the sample to maximize extraction efficiency (figure 3). figure 3—soxhlet extraction apparatus. 2. dry water-bath: a temperature-controlled laboratory instrument used for heating samples uniformly. it provides precise heating without direct contact with liquids, making it ideal for processes such as incubation, digestion, or chemical reactions. 3. standing clamp: a versatile support tool used in laboratory setups to hold equipment like glassware, thermometers, or tubing securely in place during experiments. it is essential for ensuring stability and safety in experimental procedures. 4. thermometer: an instrument used to measure temperature accurately in laboratory experiments. it is particularly critical for monitoring and maintaining precise temperature conditions during chemical processes or sample testing. 5. rotary evaporator: a sophisticated device used to remove solvents from samples through evaporation under reduced pressure. it is widely used in the concentration of solutions, solvent recovery, and sample purification in chemical and oil-related studies (figure 4). improved oil and gas recovery 5 figure 4—rotary evaporator. 6. pour point/cloud point base: a specialized instrument used to determine the pour point (the lowest temperature at which a liquid can flow) and cloud point (the temperature at which wax crystals first appear in oil). these parameters are crucial for assessing the flow properties of crude oil and petroleum products at low temperatures. 7. hydrometer: a device used to measure the specific gravity (density) of liquids. in petroleum studies, it is commonly employed to determine the density of crude oil or other petroleum-derived fluids, aiding in quality control and classification. 8. tubes: general-purpose laboratory tubes used for holding, mixing, or heating samples. they are essential for conducting small-scale chemical reactions, sample storage, or analysis in controlled environments. sourcing of materials. the moringa seeds and lemons used in this study were procured from a local market in owerri, imo state, ensuring accessibility and cost-effectiveness of the natural materials. the conventional inhibitor, used as a comparison in this study, was obtained from an industrial chemical store also located in owerri, imo state. this local sourcing approach aligns with the goal of exploring readily available and sustainable materials for enhanced oil recovery applications. extraction process for local inhibitor. the extraction of bioactive compounds from natural sources, such as lemon peels and moringa seeds, for use as wax inhibitors requires an efficient and effective method. the soxhlet extraction technique is a widely adopted process for isolating oils and other soluble compounds from plant materials due to its ability to maximize extraction efficiency. the procedure is outlined as follows: preparation of plant material. for the lemon extract, fresh lemons were peeled, and the peels were air-dried to eliminate residual moisture. for the moringa extract (figure 6), seeds were carefully removed from the pods and cleaned to ensure the absence of debris or contaminants. once dried, the lemon peels and moringa seeds were ground into a fine powder using a blender. this step increases the surface area of the plant material, facilitating more efficient extraction. loading soxhlet extractor. the ground plant material (lemon peels or moringa seeds) was placed into a thimble, which serves as a porous solid filter. the thimble ensures that the plant material remains contained while allowing the solvent to flow through. the thimble was then securely positioned in the main chamber of the soxhlet extractor. solvent addition. hexane (250 ml) was measured and poured into a round-bottom flask, which acts as the solvent reservoir. the round-bottom flask was then carefully attached to the base of the soxhlet extractor. improved oil and gas recovery 6 assembly the soxhlet extraction apparatus. the soxhlet apparatus was assembled by connecting the soxhlet extractor to a condenser at the top and the round-bottom flask containing the solvent at the bottom. the condenser was connected to a cold-water source to ensure continuous cooling and condensation of the solvent vapor during the extraction process. this setup allows the solvent to circulate through the plant material in a repetitive cycle, optimizing the extraction of bioactive compounds. heating and extraction. the extraction process begins with the assembly of the soxhlet apparatus on a water bath. the round-bottom flask containing the solvent is heated, typically to a temperature range of 60-70°c. as the solvent heats, it vaporizes and rises into the condenser at the top of the apparatus. in the condenser, the vapor cools and condenses into liquid form, dripping back onto the plant material contained within the thimble. the condensed solvent percolates through the plant material, extracting the bioactive compounds in the process. once the solvent becomes saturated with the extracted compounds, it flows back into the round-bottom flask through the siphon arm, completing one full extraction cycle. this cyclical process ensures efficient and continuous extraction of the desired bioactive components from the plant material. continuous extraction process. the process of continuous extraction involves the soxhlet extractor cycling the solvent through the plant material repeatedly over several hours. during this process, the bioactive compounds are gradually extracted, and the color of the solvent in the thimble fades. when the solvent becomes colorless, it indicates that the extraction is complete. to recover the extracted oil, a distillation apparatus is employed to separate the oil from the hexane solvent. the solvent-oil mixture is heated in the round-bottom flask, causing the hexane to evaporate due to its lower boiling point. the evaporated hexane is condensed and collected in a separate container for reuse in future extractions, ensuring minimal waste. the remaining oil, either moringa seed oil or lemon extract (figure 5), is retained in the flask as the final product. this method ensures an efficient and sustainable approach to extracting bioactive compounds. (a) moringa extract (b)lemon extract figure 5—extraction product of local inhibitor. method the method utilized for the study includes sample characterization, crude oil properties analysis and wax appearance evaluation. sample characterization. fourier transform infrared (ftir) spectroscopy is a powerful analytical technique used to identify functional groups and characterize the molecular composition of organic materials. in this study, ftir is employed to characterize both lemon extract and moringa seed oil, focusing on identifying specific bioactive compounds that contribute to their potential as wax inhibitors in crude oil pipelines. both extracts are prepared in their pure form for ftir analysis, ensuring that they are devoid of any impurities or remaining solvent that could interfere with the characterization process. the ftir spectra are recorded over the wavenumber range of 4000 cm⁻¹ to 400 cm⁻¹, covering the range where most functional groups show characteristic absorption peaks. improved oil and gas recovery 7 crude oil properties analysis. physiochemical analysis was carried out on the crude oil utilized for this study. the physiochemical properties analysed includes specific gravity, api gravity and viscosity. specific gravity. specific gravity (sg) is defined as the ratio of the density of crude oil to that of water, which serves as a universal reference. the procedure for determining the sg of crude oil is as follows: 1. a 250 ml sample of crude oil was poured into a clean, dry measuring cylinder. 2. a hydrometer, calibrated for the specific sg range of the crude oil, was gently placed into the measuring cylinder and allowed to stabilize for 10 minutes to ensure accurate reading. 3. as the hydrometer floated, the principle of buoyancy came into effect, generating an upward force that lifted the hydrometer to a specific level corresponding to the sg of the crude oil. 4. the sg was determined by reading the value indicated on the graduated scale of the hydrometer at the point where it intersected the liquid surface. 5. the temperature of the crude oil in the measuring cylinder was subsequently measured and recorded, as temperature variations can affect the sg reading. this procedure ensures accurate determination of the specific gravity, a critical parameter for characterizing crude oil properties in petroleum engineering applications. api gravity. api gravity is a globally recognized standard for classifying and characterizing crude oil based on its density. it is calculated using the following formula: ���� � = 141.5 ��@ � − 131.5,..............................................................................................................................(1) where sg is the specific gravity of the crude oil, determined at 60°f. this dimensionless parameter provides a measure of the oil's density relative to water. crude oils with higher api gravity are lighter and generally considered of higher quality, as they typically yield more valuable products such as gasoline and diesel during refining. conversely, lower api gravity indicates heavier crude, which is denser and requires more complex processing. api gravity is a critical property used in the petroleum industry for reservoir evaluation, refining processes, and transportation planning. viscosity. viscosity, a key property of crude oil, defines its resistance to flow or deformation under applied stress. to measure the viscosity of crude oil, a capillary tube viscometer (ostwald's viscometer) was employed, following the steps outlined below: 1. crude oil was carefully introduced into ostwald’s viscometer until the specified graduation level was reached. 2. the efflux time was recorded by measuring the average time required for the oil to flow between two designated graduations in the capillary tube. 3. the kinematic viscosity of the crude oil was calculated by multiplying the measured efflux time by the capillary constant specific to the viscometer. 4. the dynamic (or absolute) viscosity was then determined by multiplying the kinematic viscosity by the crude oil’s density. this procedure provides an accurate assessment of both kinematic and dynamic viscosity, which are critical parameters for understanding the flow behavior of crude oil in reservoirs, pipelines, and processing facilities. wax appearance test. the effectiveness of both locally formulated and conventional wax inhibitors in preventing wax formation was evaluated through cloud point and pour point tests. these tests determine the temperature at which the first wax crystals (cloud point) appear and the temperature at which crude oil ceases to flow (pour point). these parameters are crucial for simulating offshore conditions where temperatures can drop below ambient, potentially causing wax deposition. table 3 presents the inhibitor formulations used in this study, detailing the ratios of inhibitor to crude oil (ml) for three types of wax inhibitors: xylene (xy), moringa seed extract (mse), and lemon peel extract (lpe). each inhibitor was prepared at varying concentrations, with ratios ranging from 1:50 to 9:50, representing the volume of inhibitor relative to crude oil. these formulations were used to evaluate the effectiveness of each improved oil and gas recovery 8 inhibitor in reducing wax deposition under controlled experimental conditions. this systematic approach ensures a comprehensive comparison of conventional and bio-based inhibitors in terms of performance and efficiency. table 3—inhibitor formulation s/n inhibitors inhibitor: crude oil (ml) 1 xylene (xy) 1:50 3:50 5:50 7:50 9:50 2 moringa seed extract (mse) 1:50 3:50 5:50 7:50 9:50 3 lemon peel extract (lpe) 1:50 3:50 5:50 7:50 9:50 the experimental procedure is outlined as follows: 1. ice blocks were placed in the chamber of the pour and cloud point apparatus to create a controlled cooling environment. 2. six test tubes, each containing 50 ml of crude oil, were prepared. 3. inhibitor formulations, as specified in table 3, were added to five test tubes, while one test tube was left as a control without any inhibitors. 4. a thermometer was inserted into each test tube through a wooden cork, which was securely fastened to ensure isolation from room temperature. 5. the sealed test tubes were placed in the cooling chamber of the pour and cloud point apparatus. observations were made every three minutes to identify the cloud point (appearance of wax crystals) and the pour point (when the oil ceases to flow). 6. the wax inhibition performance of each inhibitor was calculated using a standard formula to quantify the effectiveness of the formulations in reducing wax formation. %wax temperature reduced = pour pointcontrol crude−pour pointinhibited crude pour pointcontrol crude ,.............................................. (2) 7. the procedure was repeated for each of the wax inhibitors. this methodology provides a reliable evaluation of wax inhibitors under controlled conditions, offering insights into their suitability for preventing wax deposition in crude oil under low-temperature environments. result and discussion the presented results offer an extensive analysis of the ftir characterization, physicochemical properties of the crude oil sample, and the performance of locally formulated and conventional inhibitors in reducing wax formation through pour and cloud point tests. each aspect of the data provides insights into the effectiveness of the inhibitors and highlights key molecular and physical characteristics that influence wax deposition tendencies in crude oil. ftir characterization. the ftir spectra for xylene (xy), moringa seed extract (mse), and lemon extract reveal critical functional groups responsible for the effectiveness of these compounds as wax inhibitors. functional group analysis is essential to understand the interactions between the inhibitors and the wax constituents in crude oil. sample a. table 4 presents the ftir spectra interpretation for sample a (xy), highlighting key functional groups and associated chemical compounds identified at specific wavelengths. this analysis provides critical insights into the molecular structure of the sample, which is essential for understanding its chemical properties and potential applications. each functional group corresponds to characteristic absorbance bands, indicating the presence of compounds such as alkyl halides, aromatics, carboxylic acids, and primary amines, among others. improved oil and gas recovery 9 the table further illustrates the diversity of functional groups, including hydroxyl (o-h), carbonyl (c=o), and amine (n-h) groups, which are significant in determining the reactivity and behavior of the sample under various conditions. these findings establish a foundation for further analysis and practical applications of the sample. xylene showed a diverse range of peaks, indicating the presence of functional groups such as alkyl halides (c-cl), aromatic compounds (c-h, c-c stretches), amines (n-h stretches), anhydrides (c=o stretch), thiocyanates (n=c=s stretch), carbon dioxide (o=c=o), and alcohols (o-h stretches) as seen in figure 8. these functional groups are characteristic of xylene, which has notable solvent properties, enabling it to dissolve wax components effectively. table 4—ftir spectra interpretation for sample a (xy). wavelength functional group compounds 777.8818 c-cl alkyl halides 852.4089 c-h aromatics 1287.615 c-h (-ch2x) alkyl halides 1415.616 c-c aromatics stretch (in ring) 1627.491 n-h 1 amines bend 1850.431 c=o anhydride stretch 2017.684 n=c=s isothiocyanate stretch 2171.732 s-c=n thiocyanate stretch 2454.658 o=c=o carbon dioxide stretch 2529.809 o-h carboxylic acid stretch 2623.411 o-h carboxylic acid stretch 2766.342 o-h alcohol stretch 2861.215 c-h alkane stretch 2988.119 n-h amine salt stretch 3118.272 o-h alcohol stretch 3263.587 n-h aliphatic primary amines stretch 3437.153 n-h primary amines stretch 3479.116 n-h primary amines stretch improved oil and gas recovery 10 figure 8—ftir spectra for sample a (xy) sample b. table 5 provides a detailed interpretation of the ftir spectra for sample b, derived from moringa oleifera seed extract. the table identifies key wavelengths corresponding to specific functional groups and their associated chemical vibrations, along with relevant descriptions. notable findings include the presence of -oh stretching vibrations (ester, alcohol, carboxylic acid, and ether groups) at 3433 cm-1 and 3452 cm-1, indicative of the extract's hydroxyl-rich structure. aromatic stretching vibrations related to bioactive compounds and proteins are observed at 1034 cm-1, while a characteristic absorption band for magnesium oxide (mgo particles) is detected at 442 cm-1 and 438 cm-1. these features highlight the chemical complexity and potential bioactivity of the extract. the accompanying ftir spectrum (figure 9) visually supports the above findings, showcasing transmittance as a function of frequency (cm-1). key absorption peaks, such as the broad band near 3420 cm-1 corresponding to -oh stretching, aligning with the data in the table. peaks at 3433 cm⁻¹ and 3452 cm⁻¹ indicate ester, alcohol, carboxylic acid, and ether groups, which provides polar functional sites capable of interacting with wax molecules. the presence of bioactive compounds and proteins, as seen in the aromatic stretching at 1034 cm⁻¹, contributes to mse's ability to act as a stabilizing agent for wax particles, effectively reducing wax aggregation. additional peaks, including those at 2923 cm-1 and 2852 cm-1, represent c-h stretching vibrations, while the peaks near 1600-1800 cm-1 are associated with carbonyl (c=o) stretching vibrations, signifying esters or carboxylic acids. the smaller peaks at lower frequencies confirm the presence of bioactive aromatic compounds and metal oxides. together, table 5 and figure 9 provide complementary insights into the functional groups and chemical constituents of the moringa oleifera seed extract, validating its potential application as a bio-based inhibitor in industrial processes. this detailed characterization lays the groundwork for further analysis of its efficacy and performance in practical scenarios. improved oil and gas recovery 11 figure 9—ftir spectra for sample b (moringa oleifera seed). table 5—ftir spectra interpretation for sample b (moringa oleifera seed). wavelength functional group description 3433 cm⁻¹ and 3452 cm⁻¹ –oh stretching vibrations (ester, alcohol, carboxylic acid, ether groups) these peaks correspond to –oh stretching, indicating the presence of ester, alcohol, carboxylic acid, and ether groups. 1636 cm⁻¹ –oh bending vibration attributed to the bending vibration of the hydroxyl group. 1034 cm⁻¹ aromatic stretching (bioactive compounds and proteins) related to the aromatic stretching of bioactive compounds and proteins. 442 cm⁻¹ and 438 cm⁻¹ metal oxide characteristic absorption band (mgo particle) assigned to the stretching mode of magnesium oxide (mgo). sample c. table 6 provides a detailed analysis of the functional groups identified in sample c, derived from lemon extract, using ftir spectroscopy. each row in the table lists the wavelength (in cm-1), corresponding bond type, and functional group detected. key findings include the presence of hydroxyl (-oh) groups associated with alcohols and phenols at 395.31 cm-1, c-h stretches indicating alkanes at 2931.80 cm-1 and 2862.36 cm-1, and c≡c stretching vibrations suggesting alkynes at 2222.00 cm-1. additional functional groups, such as carbonyl (c=o) indicative of α, β-unsaturated esters, and c-n stretches denoting aliphatic amines, were also identified. these results confirm the diverse chemical composition of the lemon extract, which may contribute to its wax inhibition properties. improved oil and gas recovery 12 table 6—functional groups present in sample c (lemon). wavelength (cm⁻¹) bond functional group 395.31 (s, sh) o-h stretch, h-bonded alcohols, phenols 2931.80 (m) c-h stretch alkanes 2862.36 (m) c-h stretch alkanes 2222.00 (w) c=c stretch alkynes 1728.22 (s) c=o stretch α, β-unsaturated ester 1319.31 (s) c-o stretch alcohols, carboxylic acid, esters 1242.16 (s) c-n stretch aliphatic amines 1149.57 (m) c-h wag (-ch2x) alkyl halides 1095.57 (m) c-n stretch aliphatic amines 1056.99 (m) c-n stretch aliphatic amines 1026.13 (m) c-n stretch aliphatic amines 804.97 (m) c-cl stretch alkyl halides 840.98 (m) c-cl stretch alkyl halides figure 10 complements table 6 by presenting the ftir spectra for sample c in graphical form. the spectrum illustrates transmittance as a function of frequency (wavenumber, cm-1), visually depicting the absorbance peaks corresponding to the functional groups detailed in table 6. prominent peaks, such as those near 395 cm-1, 2931 cm-1, and 1728 cm-1, align with the chemical bonds identified in the table. the spectrum also highlights minor peaks representing aliphatic amines and alkyl halides, reinforcing the complexity and multi-functionality of the extract. both table 6 and figure 10 provide a comprehensive chemical profile of the lemon extract, emphasizing its potential as a bio-based alternative to traditional wax inhibitors in the petroleum industry. these functional groups indicate a composition rich in organic acids and alcohols, providing both polar and non-polar functionalities that can interact with and inhibit wax crystallization. the ftir spectra demonstrate that each inhibitor possesses unique functional groups that enable different modes of interaction with wax molecules in crude oil, hence affecting the efficiency of wax inhibition. this characterization serves as a foundation for further exploration of its performance in pipeline flow assurance applications. improved oil and gas recovery 13 figure 10—ftir spectra for sample c (lemon). properties of the crude oil. table 7 outlines the specific gravity, api gravity, kinematic viscosity, and dynamic viscosity of the crude oil used in this study. with a specific gravity of 0.860 and api gravity of 33.035, the crude is classified as a light crude oil. light crude oils typically have lower viscosity and lower wax content, but they are still prone to wax precipitation at low temperatures. kinematic viscosity was measured at 8.14 cp, and dynamic viscosity was 7.01 cp. these values indicate that the crude oil has relatively low resistance to flow, consistent with its classification as a light crude. this viscosity data provides a baseline for assessing the performance of wax inhibitors by understanding how much the inhibitors can reduce flow resistance by preventing wax deposition. table 7—physicochemical analysis of the crude oil. s/n specific gravity api gravity crude type kinematic viscosity, cp dynamic viscosity, cp 1 0.860 33.035 light crude 8.14 7.01 pour and cloud point. the cloud and pour point data obtained for the control and treated samples with varying concentrations of inhibitors illustrate the temperature-dependent wax inhibition performance. the control sample (no inhibitor) reached the cloud point (cp) at 27°c and the pour point (pp) at 24°c (table 8 and figure 12). this indicates the onset of wax precipitation and solidification under cooling conditions, which can lead to pipeline blockages in the absence of inhibitors. improved oil and gas recovery 14 table 8—temperature vs time for control. time (mins) temperature (oc) 3 30 6 29 9 28 12 27 (cp) 15 26 18 24 (pp) 21 figure 12—temperature vs time for control. sample a. as shown in table 9 and figure 13, xylene was effective at delaying the cloud and pour points across concentrations. at 1 ml xy, the cloud point was delayed to 26°c, and the pour point to 23°c. higher concentrations of xylene (5 ml to 9 ml) further delayed the pour point to below 20oc. this demonstrates xylene's effectiveness as a conventional inhibitor, given its high solvent power, which dissolves wax crystals and reduces wax deposition. however, at higher concentrations, the inhibition effect tends to stabilize, suggesting an optimal concentration beyond which no further benefits are observed. pp cp improved oil and gas recovery 15 table 9—temperature vs time for sample a (xy). time control 1ml of xy 3ml of xy 5ml of xy 7ml of xy 9ml of xy 3 29 29 29 29 29 29 6 29 29 29 29 29 29 9 28 29 28 29 29 29 12 27 (cp) 28 28 28 29 28 15 26 27 26 27 28 28 18 24 (pp) 26 (cp) 25 (cp) 26 28 28 21 24 24 (pp) 24 (cp) 27 27 24 23 (pp) 21 (pp) 25 25 27 23 (cp) 24 30 22 22 (cp) 33 22 21 36 21 20 39 20 (pp) 20 42 19 (pp) 45 figure 13—temperature vs time for sample a. sample b. table 10 and figure 14 indicate mse’s effectiveness at various concentrations. at 1 ml mse, the cloud point was reduced to 23°c, with the pour point dropping to 20°c. higher concentrations (5 ml to 9 ml) further decreased the pour point to around 18°c. the presence of bioactive compounds and proteins in mse aids in dispersing wax crystals and reducing their tendency to aggregate. mse's natural composition provides eco-friendly advantages, while its molecular composition effectively inhibits wax formation at higher concentrations. improved oil and gas recovery 16 table 10—temperature vs time for sample b (moringa seed extract). time control 1ml of mse 3ml of mse 5ml of mse 7ml of mse 9ml of mse 3 29 28 28 29 29 29 6 29 28 28 29 29 29 9 28 27 28 28 29 29 12 27 (cp) 27 27 27 28 29 15 26 26 27 27 28 28 18 24 (pp) 25 26 26 27 28 21 24 25 25 26 27 24 23 (cp) 24 24 26 27 27 21 23 23 25 26 30 20 (pp) 22 (cp) 22 (cp) 24 25 33 21 21 23 25 36 20 20 22 24 39 19 (pp) 18(pp) 21 (cp) 22 42 20 21 45 19 20 (cp) 48 18 (pp) 19 51 19 54 18 57 17 (cp) 60 figure 14—temperature vs time for sample b. sample c. as seen in table 11 and figure 15, lemon extract performed similarly to mse. the cloud point and pour point were significantly reduced with increasing inhibitor concentration. at 3 ml lemon extract, the cloud point reached 23°c, with a pour point of 22°c, while 7 ml lemon extract reduced the pour point to 18°c. lemon extract's organic acids and alcohols interact with wax molecules to disrupt crystallization processes, confirming its potential as an environmentally friendly wax inhibitor. improved oil and gas recovery 17 table 11—temperature vs time for sample c (lemon extract) time control 1ml of xy 3ml of xy 5ml of xy 7ml of xy 9ml of xy 3 29 28 28 28 28 28 6 29 28 28 28 28 28 9 28 27 27 27 28 28 12 27 (cp) 27 27 27 27 27 15 26 26 27 27 27 27 18 24 (pp) 25 26 26 27 27 21 24 (cp) 25 25 26 26 24 23 (pp) 24 (cp) 24 (cp) 25 25 27 23 (pp) 23 (pp) 24 24 30 23 (cp) 23 (cp) 33 22 (pp) 22 (pp) 36 39 42 45 figure 15—temperature vs time for sample c. conclusion this study demonstrates the potential of locally sourced wax inhibitors, such as moringa seed extract and lemon extract, in reducing wax deposition in crude oil, with comparable efficacy to conventional inhibitors like xylene. both mse and lemon extract offer an environmentally sustainable solution for mitigating wax formation in crude oil, which is essential for operational efficiency in offshore and cold-weather oil production environments. these findings could drive further research into bio-based wax inhibitors, with a focus on improved oil and gas recovery 18 optimizing concentrations and improving the environmental profile of crude oil transport and production processes. conflicting interests the author(s) declare that they have no conflicting interests. references akinyemi, o. p., udonne, j. d., and oyedeko, k. f. 2018. study of effects of blend of plant seed oils on wax deposition tendencies of nigerian waxy crude oil. j. pet. sci. eng. 161(1):551-558. akinyemi, o. p., udonne, j. d., efeovbokhan, v. e., et al. 201). a study on the use of plant seed oils, triethanolamine and 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udechukwu is a senior lecturer at the department of petroleum engineering, federal university of technology owerri, with research interest in gas engineering and production engineering. udechukwu holds a bachelor’s degree, master’s degree and doctorate degree in petroleum engineering from federal university of technology owerri, owerri, nigeria. christian emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri, owerri, nigeria. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, natural gas, and reservoir simulation. anthony kerunwa is an associate professor at the department of petroleum engineering, federal university of technology owerri with research interest in drilling, production, reservoir engineering and petroleum economics. dr. kerunwa holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri, owerri, nigeria, and a phd degree in petroleum engineering from centre for oilfield chemicals research, ips, university of port harcourt. nzenwa dan enyioko is a seasoned petroleum/sedimentary geologist and research technologist at the department of petroleum engineering, federal university of technology owerri with a strong foundation in geoscience, he seeks to integrate cutting-edge technology into drilling fluids and flow assurance. enyioko holds a bachelor’s degree and master’s in geology from federal university of technology owerri, nigeria. chidera prince ohanaga is a graduate of the department of petroleum engineering, federal university of technology owerri. he holds a b.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, and reservoir engineering. francis chukwuebuka dike is a research technologist at the department of petroleum engineering, federal university of technology owerri with research interest in drilling fluids, enhanced oil recovery, reservoir engineering and flow assurance. dike holds a bachelor’s degree and master’s degree in petroleum engineering from federal university of technology owerri, owerri, nigeria. abstract introduction materials and method method result and discussion conclusion conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1348 received december 11, 2024; revised january 5, 2025; accepted march 1, 2025. *corresponding author: mr2509@msstate.edu 1 a capillary pressure-driven empirical model for permeability estimation in carbonate reservoirs mustafa rezaei*, mississippi state university, starkville, usa abstract permeability prediction is a crucial aspect of reservoir characterization, typically derived from core analysis. using mercury injection test data, permeability can also be predicted. various models have been proposed for permeability estimation, with their coefficients depending on the pore geometry, rock heterogeneity, and pore throat size. most existing models rely on a single saturation point or parameter, such as 35% or 25% mercury saturation, or the weighted geometric mean of pore throats and porosity. this study introduces a new empirical model that combines multiple effective parameters to estimate permeability. a total of 50 carbonate samples were used to develop the model, with 20 additional samples, and log data used for verification. in this study, permeability ranges from 0.01 to 450 md, and porosity ranges from 1% to 30%. multiple linear regression was employed to establish a relationship between permeability, porosity, r35 (the radius corresponding to 35% mercury saturation), and swanson’s parameter (the ratio of sb/pcmax, where pcmax is the capillary pressure). this model addresses potential errors in previous models by incorporating more comprehensive parameters. the model was verified using mercury injection test data from various wells and has demonstrated promising results. introduction the extraction of subsurface oil and gas resources depends on several essential factors, such as porosity, permeability, relative permeability (rp), capillary pressure, and wettability, among others (feng et al. 2021). the permeability of rock is closely associated with the distribution of pore throat sizes, making the mercury injection capillary pressure (micp) curve a reliable tool for predicting permeability. the rp curve illustrates the relationship between the permeabilities of various fluid phases, including oil and water, within a porous medium. this relationship governs the movement of these phases through the reservoir's porous structure and fracture networks, playing a crucial role in enhancing the precision of reservoir simulation models (wang et al. 2023). the rp curve plays a vital role in reservoir modeling, as it greatly influences history matching, the development and optimization of production strategies, and enhanced recovery. therefore, it is essential to develop efficient and precise techniques for obtaining rp curves. various techniques have been employed to obtain rp curves, generally classified into direct and indirect methods. the direct approach involves conducting laboratory experiments on rock cores using either steady-state or unsteady-state measurement techniques (swanson 1981; pittman 1992; dastidar et al. 2007; krevor et al. 2012; feng et al. 2018). one commonly used technique is mercury injection, where mercury is introduced into the microscopic pores of a porous medium under controlled pressure conditions, establishing a correlation between pressure and the volume of injected mercury. the rp curves derived from these experiments are influenced by the complex micro-pore structure of the medium. due to the ease of data acquisition and the ability to analyze relatively large sample sizes, numerous researchers have developed rp models based on capillary pressure experiments (purcell 1949; burdine 1953; corey 1954; brooks and corey 1966). purcell (1949) introduced a mailto:mr2509@msstate.edu improved oil and gas recovery 2 permeability model based on the capillary pressure curve, if water flows through smaller capillary tubes while gas moves through larger ones, leading to a straightforward rp model. expanding on purcell’s foundation, burdine (1953), corey (1954), and brooks and corey (1966) developed rp models that incorporate pore size distribution and tortuosity; however, these models do not account for the presence of an irreducible water film. the integration of percolation theory into rp calculations, first introduced by helba et al. (1992), has since been adopted and refined by several researchers, including salomao (1997), dixit et al. (1998), phirani et al. (2009), and kadet and galechyan (2014). one of the primary challenges in this approach is accurately determining coordination numbers and pore fractions within network models. currently, many permeability models rely on the micp curve, which can be categorized into two main types (comisky et al. 2007). the first category includes permeability models based on percolation theory, which assumes that flow paths in porous media can be represented by a single-scale aperture. notable examples within this category are the kozeny-carman model (schwartz et al. 1989; bernabé and maineult 2015), the katz-thompson models (katz and thompson 1986), and the revil-glover-pezard-zamora model (glover et al. 2006). the second category includes permeability models based on poiseuille's equation and darcy's law, which conceptualize flow paths in porous media as a collection of capillary tubes. notable models in this category include the purcell model (purcell 1949; zhang et al. 2017), the thomeer model (thomeer 1960 and 1983), the r35 model (initially proposed by winland and later reported by kolodzie (1980)), the swanson model (swanson 1981; kamath 1992), the r25 model (pittman 1992), the capillaryparachor model (guo et al. 2004; liu et al. 2016; xiao et al. 2017), the huet model (huet et al. 2005), the r50 model (rezaee et al. 2006; gao and hu 2013), and the rwgm model (dastidar et al. 2007), where rwgm represents the weighted geometric mean radius. zhou et al. (2023) applied the ensemble kalman method to predict rp curves using saturation data, while lanetc et al. (2024) developed a novel approach that integrates hybrid pore network and fluid volume methods for rp curve estimation. additionally, rezaei et al. (2020) focused on modifying permeability models initially designed for sandstones to enhance their applicability to carbonate reservoirs. while these studies have made notable progress in acquiring rp curves through various methodologies, each approach presents certain limitations. therefore, the development of a more efficient framework for obtaining rp curves remains a critical objective. various permeability models, including those developed by winland (1992), swanson (1981), and dastidar (2007), have utilized different parameters to predict permeability, often calibrated using clastic or carbonate rock samples. carbonate rocks, due to their diverse depositional environments and complex diagenetic processes, pose significant challenges for permeability modeling. earlier models, such as those by winland, pittman, and swanson, were designed for specific facies and diagenetic conditions, incorporating factors like pore throat size, porosity, and swanson’s parameter—the maximum ratio of sb/pcmax. although these models have contributed to permeability predictions, they have sometimes exhibited inaccuracies when applied to certain carbonate samples (nooruddin et al. 2014). to address these shortcomings, this study introduces a new model that integrates multiple key parameters to improve permeability estimation in carbonate rocks. the proposed model includes porosity, permeability, the pore-throat radius at 35% mercury saturation, and swanson’s parameter, offering a more comprehensive approach. by considering a wider range of influential factors, this model aims to enhance the accuracy and reliability of permeability predictions for complex carbonate reservoirs. materials and methods in this study, 70 core plug samples were used from three wells within a carbonate reservoir. all core plugs were one inch in diameter and two inches in length. during the mercury injection capillary pressure (micp) test, mercury is injected into a sample under increasing pressure, and mercury saturation is plotted against pressure. the resulting curve is used to determine key petrophysical properties. three well-established methods for permeability prediction, including the winland, pitman, and dastidar models, were evaluated. the results from each model were compared to laboratory-measured permeability values. extracted data include pore-throat sizes and porosity. improved oil and gas recovery 3 the micp test was conducted on all plug samples, with porosity calculated from the volume of mercury injection. permeability was measured using air, following darcy’s law, and ranged from 0.01 md to 450 md, with porosity values between 1% and 30%. a multiple linear modeling approach was applied to propose an empirical relationship between permeability and micp data. linear regression, combined with actual permeability data, was employed to refine permeability prediction models. this method quantifies the relationship between key variables and permeability, ensuring simplicity and interpretability of the model. incorporating multiple predictors and validating the model against real data enhances its accuracy and reliability. the predicted and actual permeability values were then compared using the linear modeling approach. additionally, a total of 1,367 thin sections were prepared to study the geological properties of the formations. a permeability log, generated from stoneley waves, and 20 modular formation dynamic tests (mdt) were also used to validate the results. results micp test. the mercury injection capillary pressure (micp) test was used to extract pore-throat size distribution (pstd), while also determining the porosity and permeability of the samples. petrographical analysis revealed that the samples predominantly consist of grainstone, with occasional occurrences of mudstone, wackestone, and rare packstone (figure 1). samples for the micp test were selected based on this distribution shown in figure 1. anhydrite observed in some samples; however, these were excluded from the study due to their lack of reservoir interest. figure 1—sedimentary facies in the studied carbonate reservoir. winland permeability model. winland established an empirical relationship between porosity, permeability, and the diameter of pore throats, expressed as follows (kolodzie 1980): log k = −(0.732− 0.864 (log φ)−(log 𝑅35)) 0.588 ..............................................................................................................(1) where r35 is the radius of the pore-throat in 35 % of mercury saturation, k is permeability (md), and 𝝋 is porosity (%). the correlation between predicted and measured permeabilities can be seen in figure 2(a). pittman permeability model. pitman permeability model has been constructed and calibrated based as follows (pittman et al. 1992): log 𝐾 = −1.221 + 1.415 (log φ) + 1.512 (log r25)....................................................................................(2) 13.18 6.66 41.68 1.46 28.2 0.8 7.98 wackestone packstone grainstone boundstone mudstone claystone anhydrite f re q u en cy , % improved oil and gas recovery 4 where r25 is the radius of the pore-throat in 25 % of mercury saturation, k is permeability (md), and 𝝋 is porosity (%). the correlation and coefficient of determination (r2) between the measured and predicted permeabilities are presented in figure 2(b). dastidar permeability model. dastidar permeability model uses rwgm (weighted geometric mean of the porethroat) and porosity (dastidar et al. 2007) according to the following model: log 𝑘 = −2.51 + 3.06 (log φ) + 1.641 (log 𝑅𝑊𝐺𝑀 ).....................................................................................(3) where k is permeability (md), 𝝋 is porosity (%), and rwgm is weighted geometric mean of the pore-throat radius (µm). the predicted and the measured permeabilities and their linear modeling are shown in figure 2(c). model development and validation. the development of the new permeability prediction model was guided by a thorough review of existing models, including those proposed by swanson (1981), pittman et al. (1992), and winland (kolodzie 980). key parameters, characterized by significant coefficients and substantial geological influence on permeability, were prioritized. after integrating these factors, the model underwent rigorous testing to optimize its accuracy. the result is the refined permeability prediction model presented in this study. proposed model. based on samples from carbonate formations and using multiple linear modeling analysis, a new model is introduced here. this model incorporates a comprehensive set of influential factors for permeability estimation in carbonate reservoirs, where grainstone predominates, along with the presence of mudstone. the model is calibrated for a permeability range up to 90 md. the advantage of this model lies in its integration of various criteria and factors, offering improvements over previously proposed models. the model was developed using multiple linear modeling analysis and is presented as follows: 𝐾 = 0.242 − 19.552 (log φ) − 17.432 (log 𝑅35) + 3.123 ( 𝑆𝑏 𝑃𝑐max ),..............................................................(4) where r35 is the radius of the pore-throat related to the 35 % of mercury saturation, k is permeability (md), 𝝋 is porosity (%), and sb/pcmax is the maximum value of sb/pc (a point is swanson’s parameter). the predicted values of permeability vs. the actual permeabilities and their linear modeling models are presented in figure 2(d). an r2 value of 0.92 in the linear regression model indicates that 92% of the variability in the dependent variable is explained by the independent variable. the equation y=1.46x−15.40 suggests a strong positive relationship between the variables. while this high r2 suggests a good fit, it's essential to also consider residual patterns and the statistical significance of coefficients to ensure model robustness and avoid potential overfitting. improved oil and gas recovery 5 figure 2—the measured permeabilities vs. their predicted values in winland (a), pitman (b), dastidar (c), and the proposed model (d). the r2 values and the slope of the lines and y-intercepts are also presented in each plot. verification of the model. micp data from two additional wells were used to verify the new model. the samples for verification were from the same carbonate formations. predicted permeability values were compared with the measured values, yielding satisfactory results. these results are presented in figure 3. figure 3—comparison of measured and predicted permeability values based on the new model. model verification using sonic log and stoneley permeability. permeabilities were also obtained using stoneley waves, extracted from a sonic scanner in the reservoir. the permeability values derived from stoneley waves showed a strong correlation with those obtained from modular formation dynamic tests (mdt). the results are presented in figure 4. improved oil and gas recovery 6 figure 4—comparison of the generated permeability from stoneley waves and mdt. the next step involved comparing the permeability log, confirmed by mdt, with the predicted permeability from the proposed model. the result was satisfactory, with a r2 value of 0.71, as shown in figure 5. figure 5—comparison of permeability derived from stoneley waves and predicted permeability from the proposed model. improved oil and gas recovery 7 discussion this study proposes a new empirical model for permeability prediction in carbonate rocks. by considering the heterogeneity of various carbonate facies, the model achieves more accurate permeability predictions. each experimental permeability model relies on core samples for calibration, and previous models, such as winland’s, used both carbonate and clastic formations for this process. due to the differing petrophysical properties between carbonate and clastic rocks, permeability predictions from these models may not be fully accurate. as shown in rezaei et al. (2024), variations in mg/ca concentrations were observed across parallel calcite crystal faces. crystallographic orientation appears may influence the incorporation of impurities into minerals, affecting their physical and chemical properties (rezaei 2023). due to the diverse depositional environments and complex diagenetic processes of carbonate rocks, permeability modeling remains a significant challenge. gabitov et al. (2022) emphasized the heterogeneous distribution of trace elements in carbonates, which impacts pore structure and complicates permeability estimation. these variations can affect calcite solubility, which in turn influences permeability, and adds complexity to reservoir prediction. winland's model, averaged petrophysical features from both rock types, leading to potential inaccuracies, as evidenced by the r2 values in figure 2. similarly, the pitman and dastidar models were primarily calibrated using clastic rocks, making them less reliable for carbonate reservoirs. in contrast, the proposed model accounts for the distinct characteristics of carbonate formations, considering the different facies and sedimentary environments that influence permeability. this approach is particularly important for carbonate reservoirs, where geological features can vary significantly. for example, grainstones and packstones dominate the facies in the studied carbonate formations, with dolomite and limestone as the primary lithologies. different facies exhibit varying petrophysical characteristics, which influence permeability prediction. however, the proposed model incorporates samples from a range of facies with diverse petrophysical properties. previous research (e.g., nooruddin et al. 2016) has demonstrated that earlier models sometimes yield significant errors. in the current model, the linear regression equation between predicted and measured permeability is characterized by a slope and an r2 value. a slope and r2 value of 1 indicate a close match between actual and predicted permeability. in the proposed model, the slope and r2 values are 1.4 and 0.91, respectively. the new model incorporates more effective parameters, reducing the impact of errors in varying conditions. key factors such as r35, porosity, and sb/pcmax were specifically considered and adjusted for carbonate rocks. other models were developed based on different formations, lithologies, and sedimentary environments. the permeability predictions from the proposed model, compared with actual permeability measurements, were reliable. although the predictions were satisfactory, the model was further verified using data from different wells. the verification results showed a slope of 1.3 and an r2 value of 0.85, indicating high accuracy in predicting permeability in these carbonate formations. the model also demonstrated good agreement with modular formation dynamic tests (mdt), which reflect dynamic permeability under natural reservoir conditions. the comparison between the predicted permeability from the new model and the permeability log derived from stoneley waves showed a strong correlation. these results indicate that accurate permeability data can be obtained under natural reservoir conditions. conclusions this study presents a new empirical correlation for estimating permeability in carbonate reservoirs. the proposed model, developed using data from various carbonate formations, incorporates more effective parameters, resulting in improved permeability prediction. the model was applied to new data from two additional wells, yielding satisfactory results during verification. in practical applications, this correlation proves useful for predicting permeability in similar geological reservoirs. future studies could explore the applicability of this model to other formations or investigate the effects of different parameter combinations. improved oil and gas recovery 8 conflicting interests the author(s) declare that they have no conflicting interests. references bernabé, y. and maineult, a. 2015. physics of porous media: fluid flow through porous media. treatise on geophysics 11(1): 19-41. brooks, r. h., corey, a. t. 1966. properties of porous media affecting fluid flow. journal of irrigation and drainage division, proceedings of the american society of civil engineers 92(2): 61-88. burdine, n. 1953. relative permeability calculations from pore size distribution 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relative permeability curves in reservoir rocks with ensemble kalman method. european physical journal e 46(6): 44-52. mustafa rezaei is a ph.d. candidate in geochemistry at mississippi state university, where he has conducted research and taught courses for the past several years. he is also a data scientist with expertise in applying advanced analytical techniques to geological and geochemical datasets. his work has been presented at international conferences, and he has authored multiple peer-reviewed publications. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1370 received january 17, 2025; revised february 1, 2025; accepted february 14, 2025. *corresponding author: weirong.li@hotmail.com 1 hydrogen storage optimization in the t gas field: numerical simulation insights from the ordos basin xueling ma, lu zou, zhanrong yang, tong hou, weirong li*, xi’an shiyou university, xi’an, china; keze lin, china university of petroleum, beijing, china; hongliang yi, liaohe oilfield, cnpc, china; zhilong liu, cnooc energy technology & services limited, tianjin, china abstract amidst the global acceleration of the energy transition and the widespread adoption of renewable energy, hydrogen has emerged as a cornerstone of future energy systems, owing to its zero-carbon emissions and high energy density. nevertheless, the pursuit of efficient large-scale hydrogen storage persists as a formidable challenge. this research employs numerical simulations to comprehensively analyze underground hydrogen storage (uhs) in the depleted t gas field within the ordos basin, china. a detailed geological model and a pvt (pressure-volume-temperature) fluid model encompassing hydrogen, methane, and other gases were meticulously developed. the study systematically investigated multiple factors, including hydrogen injection timing, injection rate, injection-production cycles, buffer gas type, and molecular diffusion, to assess their effects on hydrogen storage and recovery. the findings confirm that depleted gas reservoirs are highly suitable for ultra-highpressure hydrogen storage, with a remarkable hydrogen recovery rate reaching 92.15%. it was emphasized that residual gas saturation (linked to injection timing) and buffer gas type significantly influence hydrogen purity and the ultimate recovery rate. nitrogen, when used as a buffer gas, can enhance hydrogen recovery. additionally, molecular diffusion was found to cause a 3.3% reduction in hydrogen recovery at lower injection rates. the research also revealed that although higher injection rates may lead to a decrease in hydrogen recovery, the number of injection-production cycles has a negligible impact on recovery performance. this in-depth exploration of ultra-high-pressure hydrogen storage in depleted gas fields identifies key variables and offers valuable insights for optimizing the deployment and operational efficiency of this technology. introduction the global energy landscape is undergoing a paradigm shift driven by industrialization, urbanization, and escalating demand for sustainable solutions. while fossil fuels remain the primary energy source for most nations, concerns over energy security, greenhouse gas emissions, and environmental degradation have intensified efforts to transition toward renewable energy systems (zhu 2021). countries such as the united states, china, germany, and australia have implemented national strategies to prioritize investments in wind, solar, and hydropower technologies, aiming to reduce reliance on coal and nuclear energy (noussan et al. 2021; bauer et al. 2022). hydrogen, the most abundant element in the universe, has emerged as a cornerstone of decarbonization due to its high gravimetric energy density and zero-carbon emissions upon combustion (gabrielli et al. 2020). with declining costs of renewable electricity, electrolytic hydrogen production has become economically viable, positioning hydrogen as a versatile energy carrier for transportation, heating, and power generation (li et al. mailto:weirong.li@hotmail.com improved oil and gas recovery 2 2021; shao and yi 2019). however, the intermittent nature of renewable energy sources introduces supply volatility, necessitating large-scale storage solutions to ensure grid stability and seasonal energy security (shi et al. 2020; züttel 2003). conventional hydrogen storage methods— including high-pressure cylinders, cryogenic liquefaction, and adsorption via metal hydrides or nanomaterials—face limitations in cost, volumetric efficiency, and reversibility (zhou 2005; demirel 2012). for instance, compressed gas storage at 800 bar incurs high capital costs, while cryogenic systems require energy-intensive liquefaction at 21 k (züttel 2004). metal hydrides and chemisorption-based approaches suffer from low gravimetric capacity (<3 wt%) and kinetic constraints (hagemann et al. 2018). consequently, subsurface storage in geological formations, such as salt caverns, aquifers, and depleted hydrocarbon reservoirs, has gained traction as a scalable and cost-effective alternative (thoraval et al. 2015). salt caverns, though mature for hydrogen storage, demand specific halite deposits and multiyear development timelines for leaching (michalski et al. 2017; ozarslan, 2012). aquifers require structurally intact caprocks, high permeability, and hydrodynamic traps to mitigate buoyancy-driven hydrogen migration (kanaani et al. 2022). depleted gas reservoirs, by contrast, offer inherent advantages: pre-existing infrastructure, proven sealing mechanisms, and residual methane cushion gas to minimize hydrogen mixing and enhance recovery (zamehrian and sedaee 2022; tarkowski 2019). additionally, hydrogen ’ s lower solubility in natural gas compared to crude oil reduces operational losses, making gas reservoirs preferable to oil fields for storage (amid et al. 2016). recent numerical and experimental studies have advanced understanding of hydrogen behavior in subsurface systems. amid et al. (2016) demonstrated comparable working gas capacities for seasonal hydrogen and methane storage in depleted reservoirs. hemme and van berk (2018) quantified minimal hydrogen losses (<2%) from microbial activity and diffusion in sandstone reservoirs. lysyy et al. (2021) achieved 87% hydrogen recovery in the norne field via cyclic injection, highlighting the efficacy of residual methane as cushion gas. carchini et al. (2023) further validated low hydrogen adsorption on calcite and silica surfaces, confirming the suitability of carbonate and siliciclastic reservoirs for storage. despite these advances, no prior studies have evaluated hydrogen storage potential in the ordos basin, china ’ s second-largest sedimentary basin. the t gas field, located in the basin ’ s stable cratonic setting, features a gently monoclinal structure, well-connected pore networks, and high reservoir continuity—attributes critical for minimizing hydrogen leakage and ensuring operational integrity (mei 2011). seasonal surpluses of wind and solar energy in western china (1.213 billion kw installed capacity by 2022) further underscore the strategic value of converting excess electricity to hydrogen for subsurface storage, thereby mitigating grid intermittency (reuß et al. 2017; gabrielli et al. 2020). this study employs numerical simulation to assess the feasibility of hydrogen storage in the t gas field’s depleted reservoirs. section 2 details the simulation methodology, including reservoir characterization, fluid modeling, and operational constraints. section 3 evaluates hydrogen injectivity, withdrawal efficiency, and parametric sensitivities (injection rate, cycle duration, cushion gas composition, and diffusion effects). section 4 synthesizes key findings and implications for industrial deployment. establishment of numerical simulation model this study utilized the commercial numerical simulation software cmg to perform numerical simulations of an underground hydrogen storage system within a partially depleted natural gas reservoir in the t depleted gas field of the ordos basin, china. gem, a preeminent equation of state (eos) reservoir simulator, is well suited for simulating multi-component systems, chemical flooding processes, gas storage scenarios, and unconventional reservoirs. leveraging its advanced solver and parallel computing technology, gem can fully exploit the hardware's capabilities to expedite the completion of large scale, intricate simulation tasks. the fluid models were characterized using cmg's winprop software. improved oil and gas recovery 3 reservoir model. table 1 presents a comprehensive summary of the reservoir properties of the t gas field, encompassing parameters such as size, grid block dimensions, permeability, porosity, pressure, temperature, and saturation. the gas reservoir covers an area of approximately 1.8 km×1.9 km and was discretized into a 35× 36×46 grid cell system along the x, y, and z directions, respectively. a dual well system, consisting of one injection well and one production well, was adopted for several key reasons. firstly, it enables the coverage of a larger reservoir area. secondly, it allows for effective control of the pressure distribution within the reservoir, thereby preventing reservoir damage that could result from excessively high or low pressures. this approach also helps maintain reservoir integrity and optimal hydrogen storage performance while ensuring a distinct division of roles between the injection and production wells. the reservoir structure is depicted in figure 1, where different grid colors represent varying reservoir depths, with the depth gradually increasing from blue to red. at the onset of hydrogen storage operations, the average reservoir pressure was 7 mpa. the rock compressibility was measured at 1×10⁻⁵ kpa⁻¹ , and the reservoir is located at a depth of 2000 meters with a thickness of 430 meters. figure 2 illustrates the relative permeabilities of the water and gas phases within the reservoir matrix. figure 1—geologic model. table 1—the properties of reservoir model. parameters values number of grid blocks (i, j, k) (35, 36, 46) grid block size, m×m×m 20×20×9.35 reservoir depth, m 2000 initial reservoir temperature,℃ 80 initial reservoir pressure at the grid top, kpa 2000 mean permeability, md 1.3 porosity, % 20 initial gas saturation, % 70 initial water saturation, % 30 improved oil and gas recovery 4 figure 2—relative permeability curve. fluid model. in this research, only ch₄ was considered as the original fluid component in the t gas field. table 2 summarizes the fluid components, and their properties generated during the injection and production processes. the gem module in the cmg software already incorporates the basic properties of h₂, n₂, ch₄, and co₂. h₂ serves as the primary component of the injected gas. prior to h₂ injection, a combination of h₂, n₂, co₂, and ch₄ is used as cushion gas. the cushion gas fulfills two main functions. firstly, it pressurizes the reservoir to sustain the desired production rate. secondly, it acts as a barrier between h₂ and the natural fluids in the reservoir. therefore, meticulous consideration must be given to the type, volume, injection rate, and composition of the cushion gas, as the compatibility between the cushion gas and the existing fluids is critical in preventing unwanted chemical reactions. moreover, since some cushion gases are expected to co produce with h₂, the separation process also needs to be carefully considered. table 2—component fluid system and parameters. component specific gravity mole weight, g/mol pc, atm tc, k acentric factor composition, % h2 0.071 2.0159 12.9 33.19 0.214 0.0 n2 0.967 28.013 33.5 126.2 0.04 0.0 co2 1.519 44.01 72.8 304.2 0.225 0.0 ch4 0.553 16.043 45.4 190.6 0.008 1.0 hydrogen gas is characterized by its colorless, odorless, highly flammable nature and strong reducing properties. it has low solubility in water. compared to air, the relative molecular mass of h₂ is merely 0.069 times that of air, and it requires a compression capacity 14.5 times greater than that of air to achieve mass balance. at standard conditions, the density of h₂ (0.089 kg/m³) is approximately one fourteenth of the density of air (1.29 kg/m³). the dynamic viscosity of air at standard conditions is 18.448×10⁻³ mpa·s, which is twice the dynamic viscosity of h₂ at 8.915×10⁻³ mpa·s. table 3 presents a summary of the physical and chemical properties of h₂ gas at standard conditions. improved oil and gas recovery 5 table 3—physical and chemical properties of h2 at stp. properties unit values mole mass / 2.016 density (25°c, 1atm) kg/m3 0.08375 calorific value kj/g 120-142 the concentration range of combustion in air vol% 4-75 minimum ignition energy mj 0.02 self-ignition point °c 585 combustion heat kcal/g 34.2 diffusion coefficient in air (25°c, 1atm) m2/s 0.61×10-4 diffusion coefficient in pure water (25°c) m2/s 5.13×10-9 diffusion coefficient in clay saturated with water (25°c) m2/s 3.0×10-11 dynamic viscosity (50℃, 20mpa) mpa·s 0.00935 critical pressure mpa 1.28 critical temperature °c -239.95 the density of h₂ exhibits a sharp increase with rising pressure and a slight decrease with increasing temperature, as shown in figure 3(a). at a temperature of 298 k, when the pressure increases from 0.6 mpa to 16 mpa, the density of hydrogen gas rises from 0.5 kg/m³ to 12 kg/m³. at 30 mpa, as the temperature increases from 313 k to 373 k, the density of h₂ only decreases from 20 kg/m³ to 16 kg/m³. the viscosity of hydrogen gas is minimally influenced by temperature and pressure, as depicted in figure 3(b). at 373 k, when the pressure increases from 0.1 mpa to 50 mpa, the viscosity of h₂ increases from 10.4×10⁻³ mpa·s to 11.8×10⁻³ mpa·s. at 20 mpa, as the temperature rises from 313 k to 373 k, the viscosity of hydrogen gas increases from 9.32×10⁻³ mpa·s to 10.31×10⁻³ mpa·s. according to pan et al. (2021), high pressure reservoirs offer greater storage potential for h₂ compared to atmospheric pressure reservoirs when selecting geological spaces for hydrogen storage in depleted gas reservoirs. (a) density (b) viscosity figure 3—relationship between gas (h2) properties and pressure (pan et al. 2021). improved oil and gas recovery 6 the diffusion coefficient of hydrogen gas is significantly affected by temperature and pressure, depending on the diffusion medium type, as shown in figure 4. at 323 k, as the pressure increases from 0.35 mpa to 2.1 mpa, the diffusion coefficient of h₂ in ch₄ decreases from 1120 ×10⁻⁸ m²/s to 385 ×10⁻⁸ m²/s, nearly a threefold reduction. in water at 25 mpa, as the temperature increases from 650 k to 973 k, the diffusion coefficient of h₂ increases from 14.4×10⁻⁸ m²/s to 218.8×10⁻⁸ m²/s (pan et al. 2021). a. h2 diffusivity in water b. h2 diffusivity in ch4 figure 4—relationship between h2 diffusivity and pressure (pan et al. 2021). simulation settings for the underground hydrogen storage (uhs). table 4 provides a summary of the well-controlled conditions for the underground hydrogen storage simulation. throughout the entire production process, the depletion of gas production commences and continues until the average reservoir pressure drops to 7 mpa, corresponding to a maximum gas recovery of 65%. subsequently, the underground hydrogen storage process is initiated. table 4—simulation schemes. parameter uhs well control condition injection well max bhp, kpa 30000 gas injection rate, ×106m3/day 1 min bhp, kpa 5000 production well initial stage gas production rate, ×106m3/day 0.4 period gas production rate, ×106m3/day 2 cycle index/cycles 10 gas injection cycle number/month 6 gas production cycle number/month 3 improved oil and gas recovery 7 the total production period spans 30 years, with the first 16 years dedicated to depletion gas production, followed by 7 years of hydrogen storage, and the final 7 years serving as an extended production period. the number of underground hydrogen storage cycles was set to 10, with each cycle consisting of 6 months of gas injection and 3 months of gas production. the initial gas production rate is 0.4×10⁶ m³/day. drawing on previous research by lysyy et al. (2021) and mohammad et al. (2022), the gas injection time is designed to be twice the gas production time. consequently, the gas production rate in the subsequent cycles is also twice the injection rate. the injection rate for h₂ remains consistently at 1×10⁶ m³/day, while the gas production rate is 2×10⁶ m³/day. during the initial depletion production process, the bottom hole pressure (bhp) at the production well is set at 5000 kpa. additionally, a sensitivity analysis was conducted to evaluate the influence of injection timing, injection production cycles, injection rates, molecular diffusion, and various cushion gases on the underground hydrogen storage process. table 5 summarizes the range of values for different influencing factors. table 5—range of values for sensitivity analysis. influence factor range of values injection timing (pressure drops to, mpa) 7 10 13 16 19 injection-production cycles 5 10 15 20 injection rates, 106m3/day 0.5 1 1.5 2 2.5 molecular diffusion without diffusion with diffusion cushion gas without cushion gas h2 n2 ch4 co2 results and discussion base case underground hydrogen storage. after multiple simulations and sensitivity analyses, the underground hydrogen storage scheme was implemented as the gas reservoir pressure declined from 20mpa to 7mpa. ten injection-production cycles were simulated, followed by a 7-year extended production period. figure 6 illustrates the variations in reservoir pressure, hydrogen injection, and production during the hydrogen storage process. it's worth noting that the base case did not involve cushion gas injection. during the hydrogen storage process, the pressure gradually increases. as the initial reservoir pressure is relatively low (7 mpa), the volume of produced gas is significantly less than the amount of hydrogen injected. after each production cycle, the pressure does not return to its previous level. with subsequent alternating injections and production cycles, the pressure gradually increases, and the h2 production increment becomes larger after each cycle. since pure h2 is injected, the mixture of hydrogen and methane is produced. as shown in figure 7, the mole fraction of methane in the produced gas decreases after each cycle. until the h2 injection is stopped, the proportion of h2 in the produced gas decreases, while the proportion of methane increases. as shown in figure 5, at the first, fifth, and tenth cycles, the cumulative amount of h2 injected reached 3.62×108 m³, 18.2×108 m³, and 36.2×108 m³, respectively. over the first, fifth, and tenth cycles, a cumulative amount of 1.19×108 m³, 10.82×108 m³, and 26.92×108 m³ of h2 was recovered (table 6). finally, after a 7-year extended production period, the cumulative h2 production could reach 33.36×108 m3. due to the low energy in the early cycles, the reservoir pressure is insufficient, causing some h2 to remain trapped in the reservoir and not be effectively recovered. improved oil and gas recovery 8 figure 5—h2 injection/production and reservoir pressure profile during uhs (basic case). additionally, as shown in figure 6, the presence of methane further reduces the purity and recovery rate of h2, as these fluids mix with h2 or impede its flow. in each cycle, the trapped h2 provides additional energy to the reservoir, and as the number of cycles increases, the reservoir pressure gradually recovers, while the amount of methane in the reservoir decreases. this process improves the flow and recovery efficiency of h2, enhancing both its purity and recovery rate. however, once h2 injection stops, the purity of hydrogen begins to decline. figure 6—mole fraction of the produced gas. additionally, the presence of methane further reduces the purity and recovery rate of h2, as these fluids mix with h2 or impede its flow. in each cycle, the trapped h2 provides additional energy to the reservoir, and as the number of cycles increases, the reservoir pressure gradually recovers, while the amount of methane in the reservoir decreases. this process improves the flow and recovery efficiency of h2, enhancing both its purity and recovery rate. however, once h2 injection stops, the purity of hydrogen begins to decline. after the completion of 10 injection-production cycles, the recovery for h2 reaches 74.36%. the final recovery for h2 is 92.15%. the final recovery of h2 is determined by the extended production period because h2 injection has ceased. to maximize economic benefits, it is necessary to evaluate the duration of the extended production period. improved oil and gas recovery 9 table 6—h2 recovery of uhs in basic case. cycle index frist cycle 5th cycle 10th cycle ultimate time ch4 egr (%)chp (108m3) h2rf (%) chp (108m3) h2rf (%) chp (108m3) h2rf (%) chp (108m3) h2rf (%) value 1.19 32.87 10.82 59.45 26.92 74.36 33.36 92.15 6.34 (chp: cumulative h2 production; rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) injection time. the timing of implementing the underground hydrogen storage scheme is related to the degree of reservoir depletion. the longer the reservoir has been in production, the more depleted it becomes, resulting in lower reservoir pressure, which can affect the effectiveness of h2 storage. to investigate the impact of the timing of hydrogen injection on underground hydrogen storage, simulations were designed for five groups of reservoirs with varying degrees of depletion. the degree of reservoir depletion is characterized by the extent of pressure drop in the reservoir. figure 7 shows the changes in reservoir pressure during hydrogen injection across various degrees of depletion. it is evident that as the depletion level intensifies, the increase in pressure becomes less significant. when the reservoir is minimally depleted, early hydrogen injection leads to a higher final h2 recovery rate (table 7). this is primarily because the original fluids within the reservoir help maintain pressure. once these fluids are extracted, the reservoir loses some of its supportive pressure. therefore, in gas reservoirs where the pressure has already decreased to lower levels, the newly injected h2 struggles to attain the previously highpressure states due to a lack of sufficient initial pressure. moreover, as fluids are extracted, structural changes may occur in the reservoir, such as reduced porosity and the closure of fractures, further limiting the effective storage of h2. figure 7--effect of reservoir depletion degree on pressure profile during uhs. improved oil and gas recovery 10 table 7--effect of reservoir depletion degree on h2 recovery. pressure (mpa) 10th cycle ultimate time chp (108m3) rf (%) chp (108m3) rf (%) 7 26.92 74.36 33.36 92.15 10 31.12 76.49 35.12 97.02 13 31.55 82.40 35.65 98.48 16 30.84 83.12 35.82 98.95 19 30.62 80.97 35.89 99.14 (chp: cumulative h2 production; rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) figure 8 illustrates the molar fractions of methane within reservoirs at various depletion levels. the gas in the reservoir is a mixture of h2 and ch4. it is observed that higher reservoir pressures, corresponding to lower depletion levels, result in a larger amount of remaining ch4. as a result, the ch4 produced is of higher purity, while the purity of h2 is lower, which entails additional costs for h2 purification. therefore, the timing of h2 injection must balance between enhancing h2 recovery and maintaining its purity. (a) 19mpa (b)16mpa (c)13mpa (d)10mpa (e)7mpa figure 8—mole fraction of ch4 in different reservoirs pressure. improved oil and gas recovery 11 different cushion gas. injecting gas before injecting h2 into the gas reservoir will increase the reservoir pressure and can mitigate the influence of gravity, thereby improving h2 recovery. this study investigated the impact of injecting n2, ch4, h2, and co2 as cushion gas on hydrogen storage. each type of cushion gas was injected for 1 year at a rate of 1×106 m³/day. as shown in figure 9, using h2 as a cushion gas results in the highest increase in reservoir pressure, reaching up to 9.95 mpa, followed by n2 (9.75 mpa) and ch4 (9.49 mpa). when co2 is used as a cushion gas, the pressure increases up to 9.01 mpa. these variations are attributed to the differences in specific gravities of the gases, which affect their gravitational segregation and buoyancy effects in the reservoir. gases with high specific gravity, such as co2, tend to settle at the bottom of the reservoir, thereby reducing the height of the gas column and contributing less to the pressure increase. conversely, gases with low specific gravity, such as h2 and n2, distribute more evenly and fill the reservoir pore space more effectively, leading to a significant overall pressure increase. as the hydrogen storage cycles progress, hydrogen gradually becomes the dominant component in the reservoir, and the influence of cushion gas types diminishes. figure 9—effect of different cushion gas on reservoir pressure. figure 10 illustrates the impact of different cushion gases on the cumulative h2 injection and production volumes. the results indicate that when h2 is used as a cushion gas, the cumulative injection of h2 is the highest. however, the cumulative h2 production in the 10th cycle and the final cumulative production are relatively low, resulting in h2 recovery rates of only 76.49% and 92.87% respectively. this indicates that h₂ is not an ideal cushion gas because the h2 used as a cushion gas is also included in the cumulative injected volume, representing a waste of h2. therefore, selecting more cost-effective and readily available gases as cushion gases is more appropriate. when n2, ch4, or co2 is used as a cushion gas, both the 10th cycle and final cumulative h2 production increase, leading to significant improvements in h2 recovery rates. these results are like the performance of cushion gases in figure 10, indicating that n2 and ch4 are better suited as cushion gases for h2 storage (table 8). improved oil and gas recovery 12 figure 10—effect of different cushion gas on h2 cumulative injection and production. table 8—effect of different cushion gas on h2 recover. cushion gas type 10th cycle ultimate time chp (108m3) rf (%) chp (108m3) rf (%) no cushion gas 26.92 74.36 33.36 92.15 h2 cushion gas 33.92 76.49 40.25 92.87 n2 cushion gas 29.85 82.4 34.70 95.85 ch4 cushion gas 30.34 83.12 34.74 95.96 co2 cushion gas 29.31 80.97 34.52 95.36 (chp: cumulative h2 production; rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) injection rate. to investigate the effects of different injection rates on underground hydrogen storage, five sets of different scenarios were compared. to maintain a constant total volume of injected h2 (figure 11), injection rates were set at 0.5×106,1.0×106,1.5×106, 2.0×106, and 2.5×106 m3/day (with corresponding decreases in the injection-production cycle time). (a) cumulative h2 injection (b) cumulative h2 production figure 11—effect of different injection rates on h2 cumulative injection and production. improved oil and gas recovery 13 as shown in figure 12, an increase in injection rate leads to a corresponding rise in reservoir pressure. however, this results in a decrease in ch4 purity and an increase in h2 purity within the produced gas. when the injection rate reaches 2.5×106 m³/day, the reservoir pressure can hit 14 mpa. although the purity of produced h2 is high, the h2 recovery rate at the end of the cycle is low. this is primarily due to the dual-well, inject-produce model used, where rapid pressure increases caused by high-rate h2 injection led to h2 predominantly accumulating near the injection well, without sufficient time to disperse to the farther reaches of the reservoir. (a)injection rates vs. reservoir pressure (b)injection rates vs. mole fraction figure 12—effect of different injection rates additionally, while the pressure inside the reservoir quickly builds to a high level at high injection rates, the rapid pressure decline following cessation of injection is detrimental to effective h2 recovery. consequently, although reservoir pressure peaks and natural gas production quickly increases after stopping the injection, as production continues, reservoir pressure begins to decline, eventually stabilizing the h2 recovery rate at 92.15% (table 9). this demonstrates that while the injection and production rates do not affect the final h2 recovery in the storage process, they do influence the rate and efficiency of achieving this recovery. table 9—effect of different injection rates on h2 recovery. injection rate,（×106m3/day） 10th cycle ultimate time chp (108m3) h2rf (%) chp (108m3) h2rf (%) 0.5 29.10 80.38 33.36 92.15 1.0 26.92 74.36 33.36 92.15 1.5 24.31 67.15 33.36 92.15 2.0 22.73 67.15 33.36 92.15 2.5 21.92 60.55 33.36 92.15 (chp: cumulative h2 production; h2 rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) injection-production cycle. to investigate the impact of different h2 injection-production cycle counts on underground hydrogen storage efficiency, this study established four groups with varying cycle counts: 5, 10, 15, and 20 cycles. to maintain a consistent total volume of injected h2, the duration of each cycle was reduced as the number of cycles increased. improved oil and gas recovery 14 as shown in figure 13, fewer cycles result in a greater amount of h2 injected per cycle, thereby leading to higher reservoir pressures. figure 14 and table 10 display the cumulative volumes of h2 injected and produced under different cycle counts, along with the corresponding h2 recovery rates. the results indicate that although the variation in cycle counts has a minimal impact on the amount of h2 stored, higher cycle counts lead to relatively higher h2 recovery rates. figure 13—effect of different numbers of cycles on reservoir pressure. figure 14—effect of different numbers of cycles on h2 cumulative injection and production. table 10—effect of different numbers of cycles on h2 recovery. injection-production cycle （cycles） 10th cycle ultimate time chp (108m3) h2rf (%) chp (108m3) h2rf (%) 5 26.73 73.84 33.01 91.18 10 26.92 74.36 33.36 92.15 15 27.18 72.08 33.47 92.45 20 27.23 75.22 33.58 92.76 (chp: cumulative h2 production;rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) improved oil and gas recovery 15 figure 15 illustrates the molar fractions of in the gas produced under different cycle counts. with an increase in cycle counts, the purity of in the produced gas decreases, while the purity of h2 increases. this is because fewer cycles mean more h2 is injected per cycle, significantly increasing the initial reservoir pressure. this higher initial pressure leads to increased ch4 production, subsequently affecting the purity of h2. overall, these findings suggest that increasing the cycle count can optimize the purity and recovery rates of h2, which is crucial for enhancing the economic benefits and efficiency of underground hydrogen storage. figure 15—mole fraction of ch4 in different numbers of cycles. diffusion effect. to investigate the impact of h2 molecular diffusion on underground hydrogen storage, we established a control group for molecular diffusion simulation. figure 16 shows the influence of considering h2 molecular diffusion on the cumulative injection and production of h2 in the reservoir. the results indicate that molecular diffusion does have some effect on h2 storage, though the impact is not significant and is mainly due to the high injection rate. figure 16—effect of molecular diffusion on h2 cumulative injection and production. consequently, we simulated a control group with a lower rate of molecular diffusion. as shown in figure 17, molecular diffusion at lower rates does not have a beneficial effect on h2 recovery. compared to scenarios without diffusion, considering molecular diffusion can reduce h2 recovery by up to 3.3% (table 11). this is improved oil and gas recovery 16 because molecular diffusion is a fundamental mass transfer phenomenon where h2 is lost to the reservoir by diffusing into the water, leading to reduced h2 production and recovery. figure 17—effect of molecular diffusion on h2 cumulative injection and production with lower injection rate. table 11—effect of molecular diffusion on h2 recovery. diffusion 10th cycle ultimate time chp (108m3) h2rf (%) chp (108m3) h2rf (%) with diffusion 1.25 69.44 1.58 87.77 without diffusion 1.31 72.77 1.62 90.00 (chp: cumulative h2 production; rf: h2 recovery; ultimate time: 7-year depletion phase following the final cycle) furthermore, the impact of gas diffusion is not only evident in the loss of h2 to the reservoir but also affects the purity of the produced h2 due to its mixing with existing gases. as illustrated in figure 19, at lower h2 injection rates, the impact of molecular diffusion on the mole fraction of h2 in the produced gas is clearly visible. the results show that considering diffusion effects significantly decreases the purity of h2 in the produced gas. figure 19—effect of molecular diffusion on the mole fraction of h2 in the produced gas with lower injection rate. improved oil and gas recovery 17 figure 20 displays the distribution of h2 in the reservoir after the 10th cycle, including both scenarios with and without molecular diffusion. different colors represent different h2 concentrations, with white areas indicating rock media where h2 cannot be stored. clearly, the h2 concentration near the well is higher. furthermore, as shown in figure 20b, when molecular diffusion is considered, the distribution of h2 in the reservoir becomes more widespread, allowing it to further diffuse from the vicinity of the well, especially into areas with higher porosity and permeability. this diffusion is a key factor influencing underground hydrogen storage performance. therefore, the feasibility studies of underground hydrogen storage should fully consider the molecular diffusion of h2. (a)without diffusion (b)with diffusion figure 20—effect of molecular diffusion on h2 molar fraction in the reservoir. conclusions this study investigated the feasibility of underground hydrogen storage in depleted gas reservoirs. numerical simulations based on a pure methane fluid model were performed for the underground hydrogen storage process consisting of 16 years of depletion followed by 10 cycles (7 years) of h2 injection and production, with an additional 7-year extended production phase. furthermore, to analyze the influencing factors during the underground hydrogen storage process, sensitivity analyses were conducted on different injection timings, injection rates, injection-production cycles, cushion gas types, and molecular diffusion. the main conclusions drawn from this study are as follows: 1. depleted gas reservoirs prove to be a relatively ideal option for underground hydrogen storage. at the end of 10 injection-production cycles, the h2 recovery reaches 74.36%. the final h2 recovery can also reach 92.15% 2. the timing of h2 injection is crucial. injecting h2 earlier results in lower h2 purity in the produced gas, but a higher h2 recovery. 3. using n2 as cushion gas during the underground hydrogen storage process leads to higher reservoir pressure and increased h2 recovery. 4. the injection-production cycle has almost no impact on h2 recovery. higher injection rates result in lower h2 purity and lower recovery. 5. molecular diffusion is detrimental to underground hydrogen storage. at higher h2 injection rates, the impact of molecular diffusion on h2 storage is relatively low. however, reducing the h2 injection rate results in reduced h2 recovery and purity due to molecular diffusion. the findings of h2 storage in depleted gas reservoirs have certain limitations and may not be directly applicable to h2 storage in salt caverns or aquifers due to the significant differences in the physical properties and behavior of these reservoirs. furthermore, although this study has considered various engineering factors affecting h2 storage performance, it has not fully accounted for potential loss mechanisms during long-term storage. for instance, chemical reactions between h2 and reservoir rocks may lead to changes in porosity, while microbial activity could consume h2 or produce byproducts over extended periods. these long-term dynamic effects require further investigation to refine the storage model and enhance its practical applicability. improved oil and gas recovery 18 conflicting interests the author(s) declare that they have no conflicting interests. references zhu, y. 2021. scenario planning and environmental benefits study for china’s future energy system with high proportions of renewable energy. master’s thesis, huazhong university of science and technology, hefei, china. noussan, m., raimondi, p. p., scita, r., et al. 2021. the role of green and blue hydrogen in the energy transition-a technological and geopolitical 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at xi’an shiyou university. she has focused her research on areas involving ccus, reservoir simulation and enhance oil recovery. lu zou, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research on areas involving reservoir simulation and enhance oil recovery. zhanrong yang, is a master candidate in petroleum engineering department at xi’an shiyou university. he has focused his research in areas involving reservoir simulation and enhance oil recovery. tong hou, is a master candidate in petroleum engineering department at xi’an shiyou university. she has focused her research on areas involving reservoir simulation and enhance oil recovery. weirong li, is a professor in the petroleum engineering department at xi’an shiyou university. his research interests include unconventional resources/reserves estimates, reservoir simulation, well testing, and production analysis. dr. li holds a bachelor’s degree in petroleum engineering from northeast petroleum university, china; a master’s degree in petroleum engineering from research institute of petroleum exploration and development, china; and a phd degree in petroleum engineering from texas a&m university. keze lin, is an undergraduate student at china university of petroleum (beijing), majoring petroleum engineering. hongliang yi, is a senior reservoir engineer in liaohe oilfield company of petrochina. he specializes in enhanced oil recovery. zhilong liu, is a senior reservoir engineer in enertech-drilling & production co., cnooc energy technology & services limited, tianjin, china. he specializes in enhanced oil recovery. abstract introduction establishment of numerical simulation model results and discussion conclusions conflicting interests references copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1326 received october 15, 2024; revised november 18, 2024; accepted december 2, 2024. *corresponding author: christian.okalla@futo.edu.ng 1 modelling annual natural gas demand forecasting using non-linear autoregressive with exogenous input (narx) neural networks hussein mohammed and christian emelu okalla*, federal university of technology owerri, imo state, nigeria abstract accurate natural gas demand forecasting is critical for ensuring efficient resource allocation, infrastructure planning, and energy security. this study presents the implementation of a narx artificial neural network (ann) model using matlab (r2022b) to forecast nigeria’s natural gas demand. the narx model, known for its capability to handle nonlinear time series data with external inputs, was applied using key variables such as population, gdp per capita, natural gas reserves, and price, with the target output being natural gas demand. the methodology involved data sourcing, cleaning, and normalization, followed by model training with the levenberg-marquardt (lm) algorithm in matlab, validation, and testing. three different narx configurations (narx-1, narx-2, and narx-3) were tested, with sensitivity analyses conducted on the number of time delays and neurons to optimize the model's structure. performance was evaluated using metrics like mean squared error (mse) and coefficient of determination (r2), with results indicating that the narx-1 model with 20 neurons achieved the best performance, boasting an r2 of 0.988. the result showed that natural gas demand in nigeria has steadily increased over time, with fluctuations in response to global economic crises like the 2008 recession and the covid-19 pandemic. sensitivity analyses revealed that the narx-1 configuration, with 20 neurons, provided the most accurate forecasting results based on its low mse of 0.003396 and high r2 value of 0.988155, outperforming other models. these findings demonstrate the effectiveness of the narx model for forecasting natural gas demand, making it a valuable tool for energy planning and decisionmaking in nigeria. introduction energy plays a crucial role in the progress of societies and global economies, with its significance increasing due to factors such as economic growth, population expansion, and rapid urbanization worldwide (toren 2023). there is a greater emphasis on energy modelling and forecasting within the energy sectors due to the government’s strict energy production regulations and growing environmental concerns. a reliable and consistent energy supply is crucial for a nation's economic and societal advancement. therefore, policymakers need to understand the future energy needs to develop a plan for the country's energy provision (sharma et al. 2021). predicting energy consumption and demand, considering limitations such as resource availability, fuel costs, capacity needs, and investments, has become essential for managing the rising trend of energy use. mailto:christian.okalla@futo.edu.ng improved oil and gas recovery 2 natural gas has long been considered a “cleaner” alternative to traditional fossil fuels like crude oil and coal due to its lower carbon footprint (mohammad et al. 2021). it is often regarded as a more reliable power generation option compared to renewable sources such as solar and wind, owing to its consistent availability and ability to provide stable power output regardless of weather conditions (lehner et al. 2023). given its reliability and accessibility, natural gas is favoured for power generation, urban heating, public transportation, and manufacturing. as the global emphasis on decarbonization and sustainability grows, natural gas is expected to continue playing a significant role as an energy source. it is anticipated to play a pivotal part in the transition from fossil fuels to "green" and renewable energies, contributing significantly to the social and economic progress of nations and aligning with sustainable energy trends (kuzemko et al. 2020; zhukovskiy et al. 2021; zaytsev et al. 2022). the energy shortage in nigeria has been a longstanding concern for both the government and the populace (omidih and omotehinse 2020). various interventions at the community, state, and national levels have had limited impact on addressing the energy challenges (endurance et al. 2021). the federal government of nigeria has made efforts to diversify the energy mix to include conventional energy generation, renewable energy technologies (rets), and nuclear energy (diemuodeke et al. 2021). however, despite these initiatives, the issue of energy scarcity persists, with demand for electricity outpacing supply (bassey et al. 2022). the gas sub-sector, including power generation, petrochemicals, cement, and residential applications, has been identified as a critical area capable of driving the country's economic development (agbonifo 2016). natural gas is among nigeria's abundant indigenous energy sources, making it essential to grasp how its demand will change to support rapid economic growth (ekwueme et al. 2022). given the growing importance of natural gas in the global energy landscape, there exists an intriguing research opportunity in developing quantitative demand models for this essential energy source (cai et al. 2021; liu et al. 2023). forecasting natural gas demand holds immense importance in nigeria's energy policy and planning. an inaccurate estimation of natural gas consumption can have significant repercussions, leading to economic losses for end consumers and mismanagement of supplies and infrastructure. this misestimation can result in disruptions in natural gas supply, causing substantial economic costs. for instance, disruptions in natural gas supply have led to losses in productivity in manufacturing industries, with reported losses amounting to billions of dollars (duhalt 2022). moreover, the nexus between natural gas consumption and economic growth is non-linear, emphasizing the importance of accurate estimations to ensure sustainable economic development (sohail et al. 2021). natural gas demand forecasting is a crucial aspect of energy planning, particularly in an industry marked by risks and uncertainties. it involves utilizing models to analyse historical data and offer insights into future energy demand trends (petkovic et al. 2021). this process primarily deals with time-series forecasting, focusing on data points sampled at regular intervals (hurn et al. 2023). the classification of natural gas demand modelling involves criteria such as the forecasting horizon, tools used, data types, and the specific area of application (hong 2023). the forecasting horizon can range from hourly and daily to monthly, annually, or a combination of these periods. methods for forecasting natural gas demand include analytical, statistical, artificial intelligence, and hybrid approaches (manowska et al. 2021). analytical or physical methods heavily rely on variables influencing natural gas consumption, including weather-related parameters (temperature, humidity, sunshine, wind speed), economic factors (gross domestic or national product, gas prices), and demographic factors (general population, household composition, birth rate). these methods leverage mathematical equations to model interactions between input parameters and natural gas demand (delcroix et al. 2021). however, due to the inherent non-linear nature of natural gas demand as a time series problem, analytical modelling becomes increasingly challenging (rahmoune et al. 2021). this complexity has driven the development of new research techniques, such as statistical methods and artificial intelligence methods, as well as hybrid approaches, to address the evolving demands of forecasting in the energy sector. artificial neural networks (anns) are widely used for natural gas demand forecasting, alongside other ai techniques like support vector machines, adaptive neurofuzzy inference systems (anfis), long short-term memory (lstm), and meta-heuristic algorithms such as genetic algorithms and particle swarm optimization improved oil and gas recovery 3 algorithms (panapakidis and dagoumas 2017). anns are preferred due to their superior accuracy, especially in handling nonlinear datasets without predefined hypotheses. understanding ann architecture, including the combination and activation functions, is essential for effective utilization. various ann algorithms, such as multilayer perceptron (mlp), radial basis function neural network (rbf), and general regression neural network (grnn), are commonly used for energy demand forecasting (aruta et al. 2022). dynamic anns, including recurrent neural networks like nar, narx, and lrn, are also effective in estimating nonlinear input-output correlations in time sequence data (hassan et al. 2021). in this study, we employ a non-linear autoregressive with exogenous input (narx) neural network model for natural gas demand forecasting. this model utilizes a multivariate approach incorporating input variables such as population, gdp per capita, average natural gas price, and gas reserves, with data specific to nigeria. materials and method materials. the implementation of the narx ann modelling was conducted using matlab (r2022b). matlab has various toolboxes specifically designed for neural network modelling, which covers areas such as neural net fitting, clustering, pattern recognition, and time series models. neural net time series toolbox (in matlab) was deployed to address this nonlinear time series problem. methods. the method employed in this study involves modelling and simulation to achieve the desired objectives. specifically, the narx model principle, its implementation strategy, and simulation processes are described in detail. the overall methods can be succinctly summarized through the block diagram provided in figure 1. figure 1—methodology flowchart. the process begins with an explanation of the narx model and its fundamental equation, followed by data preparation steps like sourcing, cleansing, and normalization to refine the dataset. then, modelling involves training, validation, and testing, with sensitivity analyses determining the optimal model structure for forecasting based on input variables. ann narx model. the narx neural network, which stands for non-linear autoregressive exogenous with external input, is a dynamic tool for time series modelling. it distinguishes itself by incorporating external inputs, enabling it to analyse relationships among current and past values of a time series and external data. with its high memory capacity, it effectively captures time-varying patterns in datasets (alsumaiei 2020). eq. (1) provides the mathematical representation of the narx model, predicting the output f(t) based on input parameters x(t) and past values of the series y(t) and x(t). f(t) = f[x(t − 1), … x(t − d), y(t − 1) … . , y(t − d)],....................................................................................(1) the narx model operates on the principle that the current value of y(t) is influenced by past values of both y(t) and x(t) (necesito et al. 2022). in this model, inputs are linked to network weights, and adjustments to hidden neurons occur iteratively for different time delays. network configuration is chosen to minimize mean square error (mse). the hidden layer includes weight matrices connecting to other layers, each associated with specific narx model description data preparation modelling sensitivity analyses forecasting improved oil and gas recovery 4 inputs and biases based on weight function rules. the net input, formed by combining the outputs of these weight functions with the bias using the net input function rule, drives the network. the narx network is trained using matlab's neural net time series toolbox, employing the hyperbolic tangent sigmoid function for activation in both hidden and output layers. performance is assessed using metrics like mse and r2. successful training is indicated by minimal mse and a high r2 value, ensuring the model's effectiveness for forecasting. data sourcing and preparation. the dataset utilized in this study includes key inputs such as nigeria ’s population, gdp per capita, natural gas price, and reserves, with the target output being natural gas consumption demand. covering the period from 1975 to 2023, the data were obtained from multiple credible sources: population figures from the national population commission (npc), gdp per capita data from the national bureau of statistics (nbs), natural gas prices from the henry hub natural gas spot price statistics, natural gas reserves from the nigerian upstream petroleum regulatory commission (nuprc), and natural gas demand metrics from the nigeria gas company (ngc). this comprehensive dataset serves as the foundation for modeling and forecasting natural gas demand in nigeria. before training, thorough data cleaning and normalization were conducted to rectify errors and eliminate noisy data points. the specific dataset used for simulation is detailed in table 1. the simulation dataset comprises forty-nine data points for both the input and target output datasets. table 1—simulation data. year population, billion gdp per capita m$/person ng reserves tcm ng price, $/mmbtu ng demand, bcm 1975 0.0710 0.442 1.2546 0.43 0.4000 1976 0.0727 0.562 1.24611 0.58 0.6300 1977 0.0746 0.541 1.224 0.79 0.5000 1978 0.0765 0.532 1.203 0.91 0.3800 1979 0.0786 0.668 1.183 1.18 1.3800 1980 0.0807 0.88 1.16114 1.59 1.0702 1981 0.0828 2.188 1.14698 1.98 2.1524 1982 0.0848 1.845 1.38501 2.47 1.4160 1983 0.0868 1.224 1.37 2.59 2.2996 1984 0.0888 0.903 1.355 2.66 2.7471 1985 0.0908 0.882 1.34 2.51 3.0586 1986 0.0929 0.639 2.4 1.94 3.2852 1987 0.0952 0.598 2.407 1.66 3.7015 1988 0.0974 0.55 2.476 1.68 3.7706 1989 0.0998 0.474 2.832 1.7 4.7007 1990 0.1022 0.568 2.84 1.7 3.7100 1991 0.1046 0.503 3.4 1.49 4.7579 1992 0.1071 0.477 3.7162 1.77 4.9007 1993 0.1096 0.27 3.683 2.12 5.0507 1994 0.1121 0.321 3.45 1.92 4.5506 1995 0.1147 0.407 3.474 1.72 5.1906 1996 0.1173 0.46 3.475 2.73 5.4608 improved oil and gas recovery 5 1997 0.1201 0.479 3.483 2.48 5.8508 1998 0.1229 0.468 3.512 2.09 5.9008 1999 0.1257 0.496 3.512 2.27 6.2109 2000 0.1287 0.565 4.106 4.31 6.7310 2001 0.1317 0.587 4.6327 3.96 6.2109 2002 0.1348 0.734 4.9973 3.36 6.3609 2003 0.1380 0.787 5.055 5.49 8.5112 2004 0.1413 0.993 5.2289 5.89 9.3213 2005 0.1447 1.25 5.1518 8.92 10.3615 2006 0.1483 1.652 5.207 6.72 10.9215 2007 0.1519 1.876 5.292 6.98 10.6015 2008 0.1557 2.228 5.292 8.86 12.2767 2009 0.1597 1.884 5.292 3.95 9.8457 2010 0.1637 2.28 5.1775701 4.39 5.0307 2011 0.1679 2.505 5.1755877 4 5.4008 2012 0.1722 2.728 5.1183801 2.75 14.3070 2013 0.1766 2.977 5.1070518 3.72 15.6932 2014 0.1819 3.201 5.3239875 4.37 18.3704 2015 0.1871 2.68 5.2842779 2.61 18.4446 2016 0.1924 2.145 5.4752043 2.49 18.1679 2017 0.1977 1.942 5.62687 2.96 12.7952 2018 0.2030 2.126 5.6749974 3.16 10.7556 2019 0.2033 2.334 5.626 2.57 12.7050 2020 0.2083 2.075 5.674 2.01 14.3610 2021 0.2134 2.066 5.76 3.85 15.1652 2022 0.2185 2.184 5.832 6.45 15.6425 2023 0.2262 0.211 5.91 2.57 15.9922 the narx modelling technique. the modelling and forecasting of average annual natural gas demand was conducted using the narx model. three distinct narx configurations, denoted as narx-1, narx-2, and narx-3, were analysed, with the numerical suffix indicating the number of time delays in each configuration. these time delays play a crucial role in measuring dataset autocorrelation, filtering nonlinear data, and aiding in prediction. moreover, sensitivity analyses were performed on the number of neurons, exploring configurations with 5, 10, 15, and 20 neurons, respectively. the performance of the narx models was systematically compared, and the most effective model, determined by considering both time delays and the number of neurons, was selected for forecasting. the narx network was trained using the levenberg-marquardt training algorithm, involving multiple iterations and investigations. the dataset was divided into 70% training, 15% validation, and 15% testing data. the network structure for the narx model, considering a time delay of 1 and 20 neurons, is depicted in figure 2(a), while the step-ahead predictions (forecasting) are illustrated in figure 2(b). figure 2(a) illustrates the structure of the training model, with x(t) representing the input data and y(t) indicating the target (actual data) at 1. the artificial neural network time series model engages in simulation by analyzing the input and target to create a model that generates the modeled target y(t) from the provided output data during training. implementation of the narx model involves introducing a time delay, which excludes a certain number of data points from the beginning of the dataset. specifically, a time delay of 1:1 means one data point was omitted from both the predicted output response (x(t)) improved oil and gas recovery 6 and the actual response (y(t)) after training. additionally, the step-ahead prediction of the narx model incorporates an additional future value, one step ahead, into the predicted output data, accounting for the forecasted value. (a) open-loop view for training (b)one-step ahead prediction view figure 2—ann narx neural network. model performance evaluation metrics. the model's performance was evaluated using several metrics, such as mean squared error (mse), coefficient of determination (r2), root-mean-square error (rmse), mean absolute error (mae), and mean absolute percentage error (mape). the formulas for these statistical parameters are as follows: r2 = ∑ (xa,i−xp,i) 2n i=1 ∑ (xp,i−xa,ave) 2n i=1 ,........................................................................................................................................(2) mse = 1 n ∑ (xp,i − xa,i) 2n i=1 ,...............................................................................................................................(3) rmse = √ 1 n ∑ (xp,i − xa,i) 2n i=1 ,.........................................................................................................................(4) mae = 1 n ∑ |(xa,i − xp,i)|n i=1 ,.............................................................................................................................(5) mape = 1 n ∑ |(xa,i−xp,i)|n i=1 1 n ∑ xa,i n i=1 ....................................................................................................................................(6) where n is the number of experimental runs, xp,i is the estimated values, xa,i is the experimental values, xa,ave is the average experimental values. results and discussions time series data trends. the trends in the time series data were evaluated by plotting both the input and target output variables against the year. figure 3 displays the trend of the time series data. in general, the analysis reveals a rising trend in natural gas demand over time, with notable declines in 2010, 2019, and 2020 due to global economic downturns such as the 2008 recession and the covid-19 pandemic which impacted various economies and led to reduced natural gas prices in 2009. this demand is paralleled by continuous growth in population and natural gas reserves. additionally, the gdp per capita of nigeria shows fluctuations over time, with distinct phases of growth and decline, ultimately stabilizing at a relatively constant level. improved oil and gas recovery 7 figure 3—trend of time series data. modelling sensitivity analysis. sensitivity analyses were conducted to examine time-delays and the number of neurons, aiming to evaluate the parametric sensitivity of the models and understand the relationship between input variables and the target output response. table 2 provides a summary of the results for the narx-1 model. the analysis of table 2 reveals that the optimal number of neurons for the narx-1 model configuration is twenty. this conclusion is drawn from the more favorable training, validation, and testing mean squared error (mse) and coefficient of determination (r2) values compared to other neuron sizes. specifically, in the narx-1 simulation with twenty neurons, it was observed that the training mse was lower than that for validation and testing. table 2—detailed analysis of narx-1 configuration to determine the optimal hidden neuron. hidden neurons training validation testing mse r2 mse r2 mse r2 5 0.01246 0.95645 0.00205 0.98430 0.05489 0.86708 10 0.03551 0.90439 0.02557 0.86814 0.39930 0.97414 15 0.00012 0.99602 0.01098 0.99600 0.06121 0.94387 20 0.00030 0.99879 0.00624 0.98866 0.00443 0.98624 from table 3, it is evident that the optimal configuration for narx-2, based on the training, validation, and testing mse and r2 values, indicates that the most suitable number of neurons is twenty. this selection is justified by its combination of the lowest mse and favorable r2 value. therefore, for narx-2, it is recommended to utilize twenty neurons to achieve a representative and accurate forecast. 0 0.05 0.1 0.15 0.2 0.25 1970 1980 1990 2000 2010 2020 2030 0 2 4 6 8 10 12 14 16 18 20 p o p u la ti o n , b il li o n p re d ic to rs year gdp per capita m$/person ng reserves tcm ng price, $/mmbtu ng demand, bcm population, billion improved oil and gas recovery 8 table 3—detailed analysis of narx-2 configuration to determine the optimal hidden neuron. hidden neurons training validation testing mse r2 mse r2 mse r2 5 0.01272 0.95707 0.00546 0.96256 0.03637 0.85711 10 0.00867 0.97535 0.01063 0.96176 0.08585 0.90522 15 0.03552 0.91218 0.01640 0.96999 0.06402 0.95897 20 0.00936 0.97063 0.01877 0.98297 0.06082 0.95263 table 4 indicates that the narx-3 model performs best with ten neurons, based on lower mse values and higher r2 values across training, validation, and testing datasets. however, a comprehensive examination of tables 2, 3, and 4 demonstrates that the narx-1 model consistently outperforms others in terms of mse and r2 values. this specific setup consistently achieves r2 values exceeding 0.99 and mse consistently below 0.01, indicating exceptional performance. consequently, the narx-1 model with twenty neurons is chosen as the optimal configuration for forecasting natural gas demand. table 4—detailed analysis of narx-3 configuration to determine the optimal hidden neuron. hidden neurons training validation testing mse r2 mse r2 mse r2 5 0.05716 0.86065 0.10037 0.68184 0.01806 0.98133 10 0.00245 0.99776 0.05905 0.76065 0.01373 0.97828 15 0.00032 0.99960 0.12961 0.73309 0.03558 0.85381 20 0.02158 0.97164 0.02063 0.83458 0.19178 0.61553 as shown in figure 4, the increase in hidden neurons led to different mean squared errors (mse) for the training, validation, and testing phases of the narx network. notably, the testing mse appeared significantly larger than that of the training and validation sets, potentially due to the smaller dataset volume allocated for testing. the consistently low testing mse values, closely aligned with the training mse, suggest accurate model performance by the narx network. specifically, the narx model with a 1-time delay exhibited the lowest mse values for both training and validation, highlighting its superior performance. improved oil and gas recovery 9 (a) narx-1 (b) narx-2 (c) narx-3 figure 4—determination of hidden neurons for narx model using different models. performance evaluation of narx models. this section evaluates the performance of three narx models: narx-1, narx-2, and narx-3. throughout the training process, the entire dataset experienced multiple passes referred to as epochs. an epoch serves as a parameter denoting the number of passes the lm algorithm makes over the complete training dataset. each epoch involves a series of iterative processes to assess the model's performance, continuing until optimal performance is attained. in figure 5(a), the dataset underwent 12 epochs, while for figures 5(b) and 5(c), the datasets underwent 8 and 7 epochs, respectively. 0 0.1 0.2 0.3 0.4 0.5 5 10 15 20 m s e hidden neurons training validation testing 0 0.02 0.04 0.06 0.08 0.1 5 10 15 20 m s e hidden neurons training validation testing (b) 0 0.02 0.04 0.06 0.08 0.1 5 10 15 20 m s e hidden neurons training validation testing improved oil and gas recovery 10 (a) narx-1 (b) narx-2 (c) narx-3 figure 5—determination of the best validation performance for various models. in figure 5, the validation performance of narx-1, narx-2, and narx-3 models is analyzed. the mean squared error (mse) decreases across training, validation, and testing datasets with increasing epochs for each model. notably, the optimal performance for narx-1 is observed at epoch 8 with an mse of 6.24 × 10-3, for narx-2 at epoch 2 with an mse of 1.134 ×10-2, and for narx-3 at epoch 3 with an mse of 3.36 × 10-2. the decreasing trend of mse curves indicates prevention of overfitting. the time series plots in figures 6(a) to (c) offer detailed insights into the narx models in terms of output and target parameters. in figure 6(a), it is evident that the narx algorithm effectively trains the dataset, with residual errors from the training, validation, and testing outputs and targets all falling below 10%. this indicates that the narx-1 model is well-suited for modelling the prediction of natural gas demand. similarly, the narx model with a time delay of two, as depicted in figure 6(b), demonstrates significant potential in predicting both targets and outputs. the training, validation, and testing of the dataset show minimal residual errors, confirming (b) improved oil and gas recovery 11 the suitability of narx-2 network configurations for time series modelling of natural gas demand. figure 6(c) further illustrates that the narx model with a 3-time delay configuration is also appropriate for predicting natural gas demand, supported by the minimal residual errors observed in the training, validation, and testing outputs and targets. (a) narx 1 (b)narx 2 (c) narx-3 figure 6—time series-based prediction of average annual natural gas demand for various models. pattern trend analysis of narx models. this section examines a regression analysis comparison between actual data and predicted target output responses for the three narx models: narx-1, narx-2, and narx-3. figure 7 illustrates the non-linear fitting of actual data and the predicted output responses of the narx-1 model. the figure demonstrates the capability of the levenberg-marquardt training model to fit the actual data to the predicted target output based on the input variables. improved oil and gas recovery 12 figure 7—comparison of the pattern of actual and predicted average natural gas demand for the narx-1 model. observing figure 7 reveals that the predicted response output from the narx-1 model closely mirrors the path of the actual data used for training, with minimal deviations. this observation suggests that the model effectively captures the general trend and patterns of the actual data and input variables. the close alignment between the trend lines indicates that the model has successfully predicted the target output values with a high degree of accuracy. therefore, figure 7 illustrates that the narx-1 model, trained by the levenberg-marquardt algorithm, has effectively modelled the nonlinear relationship between the variables (including population, gdp per capita, natural gas reserves, and the average annual natural gas price as inputs, and the annual average natural gas demand as the target output). figure 8 displays the trendline pattern of the narx-2 model, illustrating the relationship between the actual data and the predicted target output. trained using the levenberg-marquardt algorithm, the model closely aligns its predictions with the actual data, indicating successful pattern recognition and effective capture of the inputoutput relationship. figure 8—comparison of the pattern of actual and predicted average natural demand for the narx-2 model. 0 2 4 6 8 10 12 14 16 18 20 1975 1985 1995 2005 2015 2025 a v er ag e a n n u al n at u ra l g as d em an d , b cm year actual data narx-1 predicted 0 2 4 6 8 10 12 14 16 18 20 1970 1980 1990 2000 2010 2020 2030 a v er a g e a n n u a l n a tu ra l g a s d em a n d , b cm year actual data narx-2 predicted improved oil and gas recovery 13 figure 9 compares the pattern trendlines of the actual data with the predicted target output of the narx-3 model, demonstrating its accurate modelling. this highlights the robustness of the narx-3 model in effectively capturing the input-output relationship. figure 9—comparison of the pattern of actual and predicted average natural demand for the narx-3 model. table 5 indicates that the narx-1 model outperforms narx-2 and narx-3 across all metrics considered. notably, narx-1 demonstrates a lower mse (0.003396) and a higher r2 (0.988155) compared to the other models. additionally, narx-1 exhibits lower rmse, mae, and mape values. consequently, narx-1 is chosen for forecasting, while narx-3 performs the least. these findings contrast with those of (ayodele et al. 2021), who found better performance in narx models with higher time-delays. table 5—overall performance summary of the narx models. metric narx-1 narx-2 narx-3 mse 0.003396 0.011074 0.011862 rmse 0.058271 0.105233 0.108911 mae 0.025333 0.041191 0.049559 mape 0.079376 0.080255 0.145622 r2 0.988155 0.961953 0.961411 forecasting performance of narx model. the narx-1 model, identified as the best-performing among the narx models, was chosen for forecasting average annual natural gas demand. table 6 presents the forecasted values of future average annual natural gas demand based on the predictions made by the narx-1 model. table 6 displays the projected values of average annual natural gas demand over a 10-year period from 2024 to 2033. the forecasted natural gas demand ranges between twelve to eighteen billion cubic meters (bcm) for the specified decade. 0 2 4 6 8 10 12 14 16 18 20 1975 1985 1995 2005 2015 2025 a v er ag e a n n u al n at u ra l g as d em an d , b cm year actual data narx-3 predicted improved oil and gas recovery 14 table 6—forecasted average annual natural gas demand. year forecast, bcm 2024 12.58929 2025 14.76996 2026 16.95775 2027 14.0357 2028 16.17459 2029 15.83146 2030 16.14099 2031 16.56538 2032 15.34007 2033 17.71746 table 7 compares the performance of the narx model in this study with similar studies in the literature, specifically focusing on forecasting energy demand. the narx-ann model utilized in this study demonstrates robust predictability, outperforming many other models with an r2 value of 0.988. this underscores the accuracy of the average natural gas demand forecast, with minimized prediction errors. table 7—comparison of the performance of the narx model in this study and literature. modelling technique country forecasting target performanc e reference narx model nigeria average annual natural gas demand 0.98816 this study narx model malaysia long term final energy demand per capita 0.99 ayodele et al. 2021 narx model usa short-term and medium-term uncertainty for electrical load and wind speed 0.9964 jawad et al. 2018 narx model nigeria forecasting volatility of nigerian crude price 0.986 gulumbe et al. 2016 narx model algeria forecasting natural gas prices 0.8918 sahed et al. 2020 conclusions the study utilized the non-linear autoregressive with external input (narx) model to forecast the average annual natural gas demand in nigeria. the narx-1 configuration demonstrated superior accuracy with an r2 of 0.988, outperforming other configurations. long-term projections indicated a consistent upward trend in natural gas demand, aligning with expected economic and demographic growth factors. the findings highlight the effectiveness of the narx model in energy demand forecasting and its potential to inform strategic planning for nigeria's natural gas sector. overall, the 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based in port harcourt, nigeria, and a master’s student in the department of petroleum engineering at the federal university of technology, owerri. he has expertise in subsea engineering, reservoir management, project management, and process safety management. he holds a b.eng. in petroleum engineering from abubakar tafawa balewa university, bauchi, and has contributed research in enhanced oil recovery and hydraulic fracturing. his professional interests include subsea engineering, reservoir analysis, hydraulic fracturing, and the development of sustainable energy practices. christian emelu okalla, mspe, mnse, mcoren is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, natural gas, reservoir simulation. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1369 received may 9, 2025; revised june 10, 2025; accepted july 23, 2025. *corresponding author: babusahmin1966@yahoo.ca 1 drilling optimization through rig hydraulics using a mathematical model mohammad na’il shamsuddin and bashir busahmin*, universiti teknologi brunei, bandar seri begawan, brunei darussalam abstract hydraulics play a crucial role in the advancement and enhancement of drilling operations. the utilization of the burgoyne and young models for predicting the rate of penetration (rop) and for the refinement of hydraulic parameters underscores the critical importance of jet velocity, jet impact force (jif), and equivalent circulation density (ecd). it is of utmost importance to optimize flow rates, as they have a direct and significant impact on both the impact force and the equivalent circulating density of the jets. consequently, this paper aims to thoroughly examine the fundamental interrelations among various parameters, including ecd, weight on bit (wob), revolutions per minute (rpm), and flow rate, as well as to assess and evaluate how hydraulic optimization contributes to the improvement of drilling efficiency. the initial rate of penetration has experienced an increase of tenfold, with the smallest recorded increase being 1.65 times, indicating that rop has been effectively optimized as a hydraulic parameter. the findings of this study suggest a substantial enhancement in the rate of penetration due to hydraulic optimization, underscoring the significance of flow rate in achieving optimal drilling outcomes. this research highlights the necessity of a well-planned and executed hydraulic strategy to maximize drilling efficiency and minimize operational challenges. by understanding and controlling the interplay between hydraulic parameters and drilling performance, operators can achieve significant improvements in drilling speed and overall operational effectiveness. introduction the drilling operation represents a significant financial investment in the process of hydrocarbon extraction from beneath the surface. therefore, enhancing drilling efficiency by optimizing parameters such as weight on bit is crucial, as it affects the rate of penetration. however, it is important to note that increasing the weight on bit does not always correlate with improved penetration rates. in softer formations, additional weight can lead to higher torque, while in harder formations, it may adversely affect the bit life (al-mahasneh 2017). increasing weight on bit (wob) sometimes resulted in the reduction of rate of penetration because of the bit foundering effect and that means increasing wob breaks the rock cuttings and enhances rate of penetration, rate of penetration (rop) up to the founder point and wob causes an excess damage to the bit and lowers the rop (islam and hossain 2021). whereas hydraulic optimization mainly discussed the optimizing of pump pressure while maintaining high enough flow rate to carry the rock cuttings to the surface (mustafa et al. 2021; song et al. 2022). one way to optimize the rig hydraulic is to improve the bit design, which means optimizing the nozzle diameter while minimizing the frictional pressure drop to obtain an optimum jet impact force (jif) (ramsey 2019). in addition, it was suggested by different scholars (longwa milia 2008; gulraiz and gray 2020; yavari 2023) that the optimum pressure drop across a polycrystalline diamond compact (pdc) bit should be 46% of the pump pressure, therefore higher rop is achieved when the pressure drop is higher than 50% of the total pump pressure, and hydraulic horsepower is higher than 65% of the standpipe pressure, another property should be considered is mailto:dike.chukwuebuka@futo.edu.ng improved oil and gas recovery 2 the effect of thixotropy on the drilling hydraulics, where the changes in shear rate results in the fluctuations in the annular pressure losses. additionally, geo-mechanical properties of the formation play a significant role such as torque and drag of the drill string, drilling vibrations, hole cleaning, to achieve more accurate rop from the estimation models (li 2023). a comprehensive understanding of the performance and wear characteristics associated with several types of drilling bits is crucial for enhancing drilling efficiency and minimizing operational costs. pdc bits are subjected to both axial and torsional impacts during the drilling process (huang and li 2018). research indicated that as the duration of impact increases, the average torque tends to decrease, and higher impact speeds further enhance rock-breaking efficiency. additionally, roller cone bits are susceptible to damage and wear, especially at the shoulder of the rubber ring and the sealing face of the metal ring, primarily due to elevated shear stress encountered during drilling activities. consequently, the wear of roller cone bits has a direct effect on the overall efficiency of the drilling operation (darwesh et al. 2020.). the rate of penetration is influenced by multiple factors, including wob, rotary speed, depth, formation strength, and hydraulic conditions, leading to the development of various mathematical models aimed at predicting the rate of penetration (tanko 2020). among these, the burgoyne and young model stands out as one of the most comprehensive for forecasting the rate of penetration for roller cone bits (li et al. 2023; huang and li 2018). darwesh et al. (2020) have suggested normalization factor values of 11200, 9, 4, and 1000 for the true vertical depth (tvd), equivalent pore pressure, weight on bit per inch of bit diameter, and jet impact force, respectively. additionally, the concept of mechanical specific energy (mse), initially was introduced (tanko 2020) and has gained significant traction in enhancing drilling efficiency and has proven effective in real-time estimation of optimal wob while varying revolutions per minute (rpm) to penetrate specific formation intervals using positive displacement motors (pdm). this paper aims to enhance drilling performance by optimizing hydraulic parameters, including flow rate, jet impact force, and equivalent circulating density, through a mathematical modeling approach. methodology drilling data was extracted from wells drilled in south-west queensland australia. different wells were drilled with roller cone bit and pdc bit. key parameters are as follows: rop, drill string design, tvd, wob, rotary speed, bit record, flow rate (q), bit diameter (db) and mud weight (mw) are recorded during drilling operations. table 1 presents the drilling data extracted from wells drilled in south-west queensland australia. this paper analyzed the data to improve the drilling efficiency by optimizing the hydraulic system while considering the effect of drilling parameters on rop, including pore pressure gradient (pg), equivalent circulating density (ecd), bit wear, and jet impact force (fj). table 1—drilling data from south-west, queensland, australia. rop, ft/hr tvd, ft wob, klb rotary, rpm q, gpm db, in ρg, ppg ecd, ppg bit tooth wear. jif, lbf 71.8 718.5 12.9 115 358 10.625 9.1 9.1 0.25 205.83 166.7 4416.0 6.3 132 327 7.875 9.1 9.3 0.125 365.96 147.6 720.1 13.5 118 367 10.625 9.1 9.1 0.125 273.12 195.2 4586.6 9.5 130 389 7.875 9.0 9.2 0.25 512.19 350.4 2103.0 6.0 120 370 12.25 9.0 9.0 0.125 347.73 537.7 18986.0 6.6 134 397 8.50 9.0 9.2 0.125 355.65 206.7 2519.7 7.9 132 499 10.625 9.0 9.1 0.25 619.84 74.1 7637.7 5.7 84 368 7.875 9.0 9.2 1 337.11 improved oil and gas recovery 3 rop prediction. the burgoyne and young model were employed in this study to forecast and enhance the hydraulic parameters on rop. the coefficients aj and xj were determined through the application of multiple regression analysis. subsequently, the data was utilized to calculate the parameters xj. ln(𝑅𝑂𝑃) = 𝑎1 + 𝑎2𝑥2 + 𝑎3𝑥3 + 𝑎4𝑥4 + 𝑎5𝑥5 + 𝑎6𝑥6 + 𝑎7𝑥7 + 𝑎8𝑥8 ,........................................................(1) or x5 = ln ( cr 1000wob db −0.02δpb( db−1 db ) ( 1000wob db ) c ) 𝑓𝑜𝑟 𝑃𝐷𝐶 𝑏𝑖𝑡𝑠,............................................................................................(2) whereby tvd is the true vertical depth, ft; pg is the pore pressure gradient, ppg; and pc is equivalent circulating density, ppg; cr represents the dimensionless weight distribution between the 12¼″ drill bit and 13½″ underreamer. in the absence of the under-reamer, cr is equal to 1. initially, the cr was 0.942, but it was later decreased to 0.02 due to being excessively high (tanko 2020). δpb is a bit pressure drop, psi; db denotes the bit diameter; wob indicates the weight, klb; n represents the rotary speed. x6 = ln ( n 100 ) for roller cone bits,...................................................................................................................(3) or x6 = ln ( n 160 ) for pdc bits,...............................................................................................................................(4) then, parameters for bit wear and jet impact force are: x7 = −h,............................................................................................................................................................(5) x8 = ln ( fj 1000 ),...................................................................................................................................................(6) where n represents the rotational speed in revolutions per minute, and fj denotes the jet impact force in poundsforce. hydraulics and rop optimization. the hydraulic parameters in the burgoyne and young model, eqs. 7 and 8 include the equivalent circulating density (𝑝𝑐) and the jet impact force (𝐹𝑗), fj = ρqvn 1930 = ρq2 6016an ,...........................................................................................................................................(7) ρc = ρ + pa 0.052×tvd ,...........................................................................................................................................(8) the calculation of annular pressure, 𝑃𝑎, involves the utilization of the darcy-weisbach equation, considering the reynolds’ number and chen’s correlation friction factor for the flow within the annulus. it is crucial to ensure that the carrying capacity of the cutting surpasses the slip-velocity, while optimizing the flow rate. 𝑣𝑠𝑙𝑖𝑝 = 1.54 √ 𝑑𝑐(𝑝𝑐−𝑀𝑤) 𝑀𝑤 ,...................................................................................................................................(9) 𝑣𝑚𝑖𝑛 = 2.5 × 𝑣𝑠𝑙𝑖𝑝,..........................................................................................................................................(10) 𝑄𝑚𝑖𝑛 = 𝑣𝑚𝑖𝑛 2.448(𝑑2 2−𝑑1 2) ..........................................................................................................................................(11) the slip velocity (vslip), minimum annular velocity (vmin) and minimum flow rate (qmin) are determined based on eqs. 9 to 11, accordingly. it is essential for the flow rate in the annulus to exceed the minimum flow rate to effectively transport the cuttings to the surface. the rop is calculated using the burgoyne and young improved oil and gas recovery 4 model, and the flow rate is optimized through the qoptimum model. subsequently, the optimized total nozzle area (an, min) is established based on the jet impact force. finally, the flow rate is cross-checked with the minimum flow rate to ensure proper hole cleaning. results and discussion the data related to pearson's correlation analysis is presented in figure 1. by examining the correlation matrix, relationships among various drilling parameters were identified. the rop shows a significant correlation with tvd, rpm, wob, and bit wear (h). while the burgoyne and young model initially assumed these parameters to be independent (li et al. 2023), it is important to note that tvd, rpm, wob, bit diameter (db), mud weight (mw), pore pressure gradient (pg), and flow rate (q) are all considered independent variables. the jet impact force is influenced by flow rate, mud weight, and pressure drop. given the low to moderate correlation among the model parameters, it is reasonable to conclude that these parameters are independent of one another. figure 1—pearson correlation matrix heatmap for the drilling data. as shown in figure 2, the rop generally decreases with increasing depth due to the increasing formation strength. however, one data point deviates from this trend, likely due to other factors that have a greater influence on rop, as previously discussed furthermore, there is a clear relationship between rop and revolutions per minute, with higher rotational speeds leading to faster drilling rates as illustrated in figure 3 illustrate that rop initially increases with an increase in wob, peaking at approximately seven kilo pounds. however, beyond this point, rop decreases due to the founder effect. this effect occurs when the bit encounters deeper layers with reduced cutting efficiency, likely due to damage, as supported by reference (islam and hossain 2021). the flow rate follows a similar trend, rising with rop before declining. in terms of hydraulic parameters, both jet impact force and hydraulic horsepower contribute to increased rop. however, jet impact force begins to decline at around 450 pounds per foot, whereas hydraulic horsepower continues to rise alongside rop. improved oil and gas recovery 5 figure 2—(a) rate of penetration against true vertical depth; (b) rate of penetration against rotary speed. figure 3—(a) rate of penetration against weight on bit; (b) rate of penetration against flow rate; (c) rate of penetration against jet impact force; (d) rate of penetration against hydraulic horsepower. the calculations for optimal nozzle area, ecd, and jet impact force were performed using the equations outlined in the methodology section. the results are presented in table 2. additionally, minimum flow rates were analyzed to ensure that the mud flow rates are sufficient for transporting rock cuttings to the surface. table 2—optimized hydraulic parameters. optimum bit pressure drop optimum flow rate optimum nozzle area optimum ecd optimum jet impact force minimum flow rate 2400 1259 0.744 9.35 3223.82 189 2400 1214 0.717 9.35 3106.32 189 2400 1010 0.593 9.09 2569.92 264 2400 573 0.337 9.07 1458.40 191 improved oil and gas recovery 6 the anticipated penetration rate was calculated through multiple regression analysis, with the evaluation of the burgoyne and young model coefficients presented in table 3. the findings revealed that rpm and bit wear exerted the greatest influence on rop, followed by hydraulics and weight on bit. furthermore, the results indicated a weak formation strength based on the coefficient range of a1, while coefficients a6, a7, and a8 highlighted the importance of focusing on rotary speed, bit wear, and jet impact force. at higher depth, normal compaction, under-compaction, and differential pressure are worth optimizing. table 3—coefficient of burgoyne & young model. factors coefficients values formation strength a1 24.34 normal compaction a2 -0.0013 under-compaction a3 -0.0620 differential pressure a4 0.0085 weight on bit a5 0.7686 rotary speed a6 -9.67 bit tooth wear a7 3.91 jet impact force a8 1.53 the impact of flow rate on rop is illustrated in figure 4. as the flow rate rises, the parameters x4 and x8, representing the equivalent circulating density and jet impact force, are impacted. specifically, an increase in jet impact leads to a higher rop, whereas a rise in equivalent circulating density results in a lower rate of penetration. despite this, rop experiences an increase with flow rate due to the heightened jet impact force. however, it decreases because of the differential pressure between equivalent circulating density and the high pore pressure gradient. figure 4—rate of penetration versus flow rate. figure 5 depicts the correlation between the rop and the jet impact force. elevating the jet impact force results in an increase in the rop. nevertheless, boosting the jet impact force necessitates a rise in the flow rate, which could potentially lead to a decrease in the rop once it reaches the optimal level. therefore, it is crucial to optimize the jet impact force by reducing the total nozzle area to the maximum bit pressure drop. furthermore, the enhancement in the rop is attributed to the reduction in the total nozzle area and becomes more pronounced at higher jet impact forces. improved oil and gas recovery 7 figure 5—rate of penetration against jet impact force at different total nozzle areas (an). the rop refers to how quickly the drill bit advances through the formation, while ecd represents the effective mud density inside the wellbore, accounting for both the static mud weight and the dynamic effects of fluid circulation. therefore, figure 6 presents the relationship between rate of penetration and equivalent circulating density, where rop increases with ecd, is primarily due to optimized differential pressure, improved jet impact force, and more efficient cuttings removal. however, controlling ecd within optimal limits is crucial to maintaining drilling efficiency without causing wellbore stability issues. figure 6—rate of penetration against equivalent circulating density. table 4 demonstrates that the optimized jet impact force has a considerable influence on the rop. on average, there is an increase of ten times the original rop and a minimum of 1.65 times the original rop. however, the actual rop value could be lower than expected due to other factors that may affect the rop when increasing the jet impact force or the accuracy of the model. table 4—the actual rop and optimized rop. actual rop optimized rop percentage increased (%) 71.85 1236.04 1620% 147.64 1709.97 1058% 350.39 2301.25 557% 206.69 548.30 165% improved oil and gas recovery 8 conclusions the research has demonstrated the efficacy of hydraulic optimization in enhancing drilling efficiency by concentrating on the improvement of the rate of penetration through the optimization of jet impact force and equivalent circulating density. additionally, the study noted an increase in rate of penetration when applying the burgoyne and young model. the findings suggest that factors, including depth, weight on bit, revolutions per minute, flow rate, equivalent circulating density, and jet impact force, require optimization. the effect of flow rate on both equivalent circulating density and jet impact force is vital for boosting drilling efficiency. on average, rate of penetration experienced a tenfold increase compared to the baseline, with a minimum enhancement of 1.65 times the original rate of penetration. in summary, this paper highlights the critical role of flow rate in influencing rate of penetration, emphasizing the necessity for further investigation and optimization of flow rate management strategies to attain optimal drilling performance. nomenclature ann =artificial neural network ecd =equivalent circulating density ga =genetic algorithm gpm =gallon per minute hhp =hydraulic horsepower jif =jet impact force mlr =multiple linear regression mse =mechanical specific energy pdc =polycrystalline diamond compact rf =random forest rop =rate of penetration rpm =rotary per minute spp =standpipe pressure tvd =true vertical depth wob =weight on bit ab =bit area aj =model coefficients an =nozzle area an min =minimum nozzle area cd =dimensionless nozzle discharge coefficient cr =dimensionless weight split d1 =drill pipe outer diameter d2 =hole inner diameter db =bit diameter dc =cutting diameter de =equivalent diameter 𝜖 =relative roughness f =friction factor fj =jet impact force h =fractional bit tooth wear hhp =hydraulic horsepower m =flow rate exponent improved oil and gas recovery 9 mw =mud density n =rotary per minute 𝜌 =mud density pa =annulus pressure pb =bit pressure drop δ𝑃𝑏 =bit pressure drop 𝜌𝑐 =cutting density 𝜌𝑔 =pore pressure gradient plot =leak-off test pressure pp =pump pressure q =flow rate qmin =minimum flow rate qoptimum =optimum flow rate t =bit torque va =annular velocity vmin =minimum velocity vn =nozzle velocity vslip =slip velocity (𝑊𝑂𝐵/𝑑)𝑡 =threshold weight on bit per inch bit diameter xj =model parameters conflict of interest the authors declare that there is no conflict of interest. references al-mahasneh, m. a. 2017. optimization of weight on bit during drilling operation based on rate of penetration. int. j. oil, gas coal eng. 5(2): 13-27. bani mustafa, a., abbas, a. k., alsaba, m., et al. 2021. improving drilling performance through optimizing controllable drilling parameters. j. pet. explor. prod. technol. 11(3): 1223-1232. darwesh, a. k., rasmussen, t. m., and al-ansari, n. 2020. controllable drilling parameter optimization for roller cone and polycrystalline diamond bits. j. pet. explor. prod. technol. 10(4): 1657-1674. gulraiz, s. and gray, k. e. 2020. thixotropy effects on drilling hydraulics. j. nat. gas sci. eng. 84(1): 103653. huang, z. and li, g. 2018. optimization of cone bit bearing seal based on failure analysis. adv. mech. eng. 10(3):168179. islam, m. r. and hossain, m. e. 2021. drilling engineering. amsterdam, netherlands: elsevier. li, l. 2023.intelligent optimization for a full-sized pdc bit with composite percussive rock breaking drilling. j. intell. constr. 1(4): 9180021. li, l. l., liu, x., zhou, y., et al. 2023. intelligent optimization for a full-sized pdc bit with composite percussive rock breaking drilling. j. intell. constr. 1(4): 9180021. longwa milia, r. l. 2008. optimization of drilling hydraulics in vertical holes. phd dissertation, bandar seri iskandaruniversiti teknologi petronas. ramsey, m. s. 2019. practical wellbore hydraulics and hole cleaning. amsterdam, netherlands: elsevier. song, x., li, g., xu, z., et al. 2022. fundamentals of horizontal wellbore cleanout. amsterdam, netherlands: elsevier. tanko, a. 2020. rate of penetration optimization using burgoyne and young model (a case study of niger delta formation). int. j. petrochemical sci. eng. 5(2):1-12. yavari, h. 2023. an approach for optimization of controllable drilling parameters for motorized bottom hole assembly in a specific formation. results eng. 20(1): 101548. improved oil and gas recovery 10 bashir busahmin, spe, ei, is a senior assistant professor of energy engineering at universiti teknologi brunei (utb), where he has served on the faculty for over 11 years. his research interests focus on petroleum engineering, with particular emphasis on technical drilling engineering, formation wettability, and reservoir characterization. he holds an m.sc. in petroleum engineering from agh university of science and technology in krakow, poland, as well as dual ph.d. degrees in petroleum engineering from agh university and the university of calgary, alberta, canada. dr. busahmin is a member of the society of petroleum engineers (spe) and a registered engineering institution (ei) professional. mohammad na’il shamsuddin is a graduate in petroleum engineering from universiti teknologi brunei (utb), and a member of the society of petroleum engineers (spe). his academic background and training focus on upstream oil and gas operations, with particular interest in drilling optimization. he continues to engage in professional development and research activities in the petroleum engineering field. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1312 received september 12, 2024; revised october 12, 2024; accepted november 10, 2024. *corresponding author: christian.okalla@futo.edu.ng 1 comparative analysis of linear regression and artificial neural networks for permeability prediction charlie iyke anyadiegwu, christian emelu okalla*, anthony kerunwa, solomon chukwuebuka igbo, joshua abiodun abah, federal university of technology owerri abstract permeability prediction from well log data is a critical aspect of reservoir characterization, providing essential insights for effective reservoir management and hydrocarbon recovery. this study investigates the efficacy of two distinct modeling approaches—linear regression and artificial neural networks (ann)—in predicting permeability from well log data. the linear regression models explored include standard linear regression, interactions linear regression, robust linear regression, while the ann approach focuses on varying network structures to optimize performance. the interactions linear regression model demonstrated strong predictive capabilities, with root mean square error (rmse) values of 4.47 and an r-squared (r²) value of 0.98, indicating a robust fit between the predicted and actual permeability values. however, the ann model, particularly with a structure of 10 neurons in the hidden layer (n-10), outperformed the linear models, achieving an rmse of 29.90 and a remarkably high r² value of 0.9996. this underscores the ann’s superior ability to capture complex, nonlinear relationships within the data. the study provides a detailed analysis of model performance, highlighting the strengths and limitations of each approach. the ann model’s superior accuracy makes it particularly suited for complex reservoirs where non-linear interactions are prevalent, while the interactions linear regression model offers a simpler, more interpretable alternative for less complex scenarios. based on these findings, the study recommends the adoption of ann models for intricate reservoir characterization tasks, while linear regression models can be utilized for quicker, more straightforward predictions. furthermore, comparison of this model with other existing models were made and this study’s model outperformed. introduction the prediction of subsurface physical properties, such as permeability and porosity, is a fundamental challenge in reservoir characterization, influencing decisions related to exploration, drilling, and production in the oil and gas industry (nelson 1994; ezekwe 2010; edlmann et al. 1996; zhang 2013; zhang et al. 1996; johnson 1963; ahmed 2006; newman and martin 1977; dullien 1992; byrnes 1994). accurate permeability prediction from well log data can significantly enhance reservoir management by providing critical insights into fluid flow and reservoir performance. traditional methods for predicting these properties often rely on linear regression models, which, while straightforward and interpretable, may not fully capture the complex, non-linear relationships present in subsurface geological formations (leiphart and hart 2001). recent advancements in machine learning have introduced more sophisticated approaches, such as artificial neural networks (anns), which have shown promise in improving the accuracy of subsurface property predictions. the artificial neural network (ann) technique is one of the latest techniques available to the petroleum industry for porosity and permeability prediction (wills 2019; jakhar and kaur 2020; azim 2020 and mailto:annagderyaev@outlook.com improved oil and gas recovery 2 2021). anns are particularly effective in modeling non-linear relationships, making them a powerful tool for predicting properties like permeability in geologically complex reservoirs. the flexibility of anns allows them to learn intricate patterns in data that linear models might overlook, offering a more nuanced understanding of reservoir characteristics (leiphart and hart 2001). the choice between linear regression models and anns is not merely a technical decision but one that can significantly impact the accuracy and reliability of permeability predictions. leiphart and hart (2001) compared the performance of linear regression models and a probabilistic neural network (pnn) in predicting porosity from 3-d seismic attributes. they found that while the linear regression model provided a reasonable prediction with an r² of 0.74, the pnn offered a better correlation (r² of 0.82) and more geologically realistic porosity distribution, particularly in complex geological settings (leiphart and hart 2001). smith et al. (1999) introduced a neural network algorithm designed to predict porosity, permeability, and grain density. their approach utilized gamma ray, neutron porosity, and sonic travel time as input variables, and the predicted results were compared to actual core data, with errors assessed against specified tolerances. similarly, osborne (1992) employed a back propagation neural network to estimate permeability using porosity and reservoir flow units as inputs. however, the robustness of the model was questionable as it was developed using the same data for both training and testing, with only about 10% of the data used for these purposes. despite this limitation, osborne found that the neural network model's permeability predictions were superior to those obtained from a regression model. jian et al. (1995) conducted a case study comparing genetic and non-genetic approaches for predicting porosity and permeability. additionally, other research has employed various machine learning techniques to predict porosity and permeability at different depths (huang et al. 1996; huang and williamson 1997; helle et al. 2001; rwechungura et al. 2011; saputro et al. 2016; ahmadi and chen 2019). the growing interest in machine learning techniques, such as anns, reflects their potential to enhance reservoir characterization. these models can handle large datasets with multiple variables, identifying patterns and correlations that may not be apparent with traditional statistical methods. this capability is particularly useful in the oil and gas industry, where datasets are often extensive and complex, requiring advanced techniques for effective analysis and interpretation (leiphart 2001). despite the advantages of anns, their application in reservoir characterization is not without challenges. the "black box" nature of these models can make them less interpretable compared to linear regression models, posing a challenge for geologists and engineers who need to understand the rationale behind predictions. however, when applied correctly and validated against geological data, anns can provide significant improvements in prediction accuracy, as demonstrated in various case studies and research (leiphart and hart 2001). in this study, we aim to explore and compare the efficacy of linear regression and ann models in predicting permeability from well log data. by evaluating these two approaches in a real-world scenario, we seek to identify the strengths and limitations of each method, providing insights that can guide the selection of appropriate modeling techniques for reservoir characterization. the results of this comparison will contribute to the ongoing discourse on the application of machine learning in the geosciences, offering practical recommendations for enhancing prediction accuracy in complex reservoir environments. materials and method software suites. for this study, two primary software suites were employed: 1. matlab (version 2024): matlab was utilized for various tasks, including the development of linear regression models and artificial neural networks (anns). the neural network toolbox in matlab played a crucial role in training, validating, and testing the ann for permeability prediction. 2. microsoft office excel (version 2013): excel was used for data collation, computation of statistical performance indicators, and cross-plot generation for model validation. the data analysis toolpak within excel was specifically employed for plotting pearson’s correlation matrix, aiding in feature selection. improved oil and gas recovery 3 data collection and description. the dataset used in this study was obtained from open source (kaggle). the dataset consists of log data and core data, with a total of 8,739 data points. the available log data includes gamma ray (gr), bulk density (rhob), and deep induction resistivity (rild). corresponding core data for each log data point includes core permeability values. table 1 shows a summary of the data used in this study. table 2 shows the statistical analysis of the dataset used in this study. table 1—summary of well log data used. factor type sub-type minimum maximum mean std. dev. gamma ray numeric continuous 0.0058 404.29 76.95 33.86 bulk density numeric continuous 1.19 2.74 2.03 0.4157 deep induction resistivity numeric continuous 0.2104 11510.6 34.51 251.24 table 2—statistical analysis of the dataset employed in this study. s/n parameters units min max average std 1 gamma ray, 𝛾 api units 0.006 404.288 76.949 33.859 2 bulk density, 𝜌𝐷 g/cm3 1.191 2.742 2.034 0.416 3 deep induction, 𝐼𝐷 ohm-m 0.210 11510.642 34.512 251.238 4 permeability, k md 0.001 782.431 27.628 25.561 linear regression model. the first approach involved the development of linear regression models using matlab. the well log data, collected from literature, was used to train various forms of linear regression models, including linear, interactions linear, robust linear, and interactions linear models. each model's performance was evaluated to identify the best-fitting model. the general form of the linear regression model used in this study is given by: y= βo+ʃ𝑖=1 𝑘 βixi+ʃ𝑖=1 𝑘 βii𝑋𝑖𝑖 2+ʃ𝑖≠𝑗 𝑘 βijxij+ϵ,...........................................................................................................(1) where y is the dependent variable; xi are the independent variables; βo is the intercept; βi, βii, βij are the regression coefficients determined using least squares techniques. matlab automatically determined these regression coefficients during model training. the best-performing model, based on data fit, was selected and exported from matlab for further analysis. the selected linear regression model was then evaluated by applying it to the entire dataset. the model’s accuracy was assessed by comparing predicted permeability values against measured values using statistical performance indicators such as mean absolute error (mae), root mean square error (rmse), and the correlation coefficient (r2). artificial neural network (ann) model. before developing the ann, feature selection was performed to identify the most significant input parameters. the pearson’s correlation matrix was plotted using excel’s data analysis toolpak to assess the correlation between input parameters (gamma ray, bulk density, and deep induction) and the output parameter (permeability). a threshold correlation coefficient of 0.01 was defined. parameters with a correlation coefficient greater than 0.01 were considered significant. to ensure consistent scaling across all input and output parameters, normalization was performed using the following equation: 𝑋𝑛(0: 1) = x−xmin xmax−xmin ,......................................................................................................................................(2) improved oil and gas recovery 4 where xn (0:1) is the normalized value of the parameter; x is the actual value of the parameter; xmin and xmax are the minimum and maximum values of the parameter, respectively. the dataset was then used to construct six different ann structures, each with one hidden layer containing 5 to 10 neurons. the dataset was randomly divided into three sets: 70% for training, 15% for testing, and 15% for validation. training continued until the following conditions were met: 1. the mses of the training dataset were lower than that of the validation and testing datasets. 2. the mses of the validation and testing datasets were approximately equal. 3. the r2 increased in the order of testing, validation, and training datasets. after training, each ann structure was evaluated using the entire dataset, and the best-performing ann was selected based on mae, rmse, and r2. the selected ann structure was then transformed into a set of equations using the activation functions and the extracted weights and biases from the ann. the developed ann model was validated by applying the training, validation, testing, and entire datasets to predict permeability. cross-plots of measured versus predicted permeability were generated to evaluate the model’s accuracy. these plots included a unit slope line, +10% and -10% deviation lines, and the r2 value. the model was considered accurate if 1. most of the data points were on the unit slope line and within the +10% and -10% deviation lines. 2. the r2 value increased in the order of testing, validation, and training datasets. results and analysis linear regression model. linear regression is a fundamental statistical technique that models the relationship between a dependent variable and one or more independent variables. in this study, three different linear regression models were evaluated: standard linear regression, interactions linear regression, robust linear regression. table 3 presents a summary of the performance metrics for the three linear regression models. the performance of each model is assessed using various statistical indicators: root mean square error (rmse), mean square error (mse), coefficient of determination (r²), and mean absolute error (mae) for both the validation and testing datasets. table 3—performance summary of different linear regression models. dataset type validation dataset test dataset metrics rmse mse r2 mae rmse mse r2 mae linear regression 3.193 10.193 0.981 1.789 4.657 21.689 0.982 1.828 interactions linear regression 3.080 9.484 0.982 1.746 4.466 19.943 0.983 1.797 standard linear regression model, while straightforward, yielded satisfactory results with an rmse of 3.1926 and an r² value of 0.9805 on the validation dataset. however, when tested, the rmse increased to 4.6572, indicating some level of overfitting or a potential lack of generalization to new data. interactions linear regression model, by incorporating interaction terms between the input variables, improved the prediction accuracy, evidenced by a lower rmse (3.0797) and a higher r² value (0.9819) on the validation set. the improvement was consistent in the test set, with an rmse of 4.4658 and an r² of 0.9830, making it one of the best-performing linear models. overall, the interactions linear regression model emerged as the top performer among the linear models. the inclusion of interaction terms provided a more nuanced understanding of the relationships between the input variables, leading to improved predictions. this model's robustness was validated across both the validation and improved oil and gas recovery 5 test datasets, indicating its suitability for permeability prediction in this context. therefore, the interactions linear regression model was chosen for further analysis. permeability response. figures 1 and 2 illustrate the permeability response for the training data, validation data, and test data, respectively. these plots compare the actual permeability values against the values predicted by the model. they are essential for evaluating how well the model predicts the actual permeability. the strong alignment of data points along the unit slope line in these plots indicates a high degree of accuracy in the model’s predictions. figure 1 shows that the model captured the underlying patterns in the training data very well, with most data points lying close to the line of equality. this strong correlation demonstrates that the model has successfully learned the relationships in the training data. figure 2(a) reveals that the model generalizes well to unseen data. the proximity of the data points to the line of equality indicates that the model maintains its predictive power when applied to new data, reinforcing the model's robustness. figure 2(b) further validates the model's accuracy with the testing data. consistent performance of training, validation and testing datasets suggests that the model is not overfitting and has a strong ability to generalize. figure 1—permeability response plot. (a)training dataset (b) testing dataset figure 2—validation cross plots. the high r² values and low rmse, mse, and mae values across all datasets indicate that the trained model is accurate and generalizes well to unseen data. the linear regression model equation derived from the bestperforming model (interactions linear regression) provides a mathematical framework for permeability improved oil and gas recovery 6 prediction. the coefficients of the linear regression model used for permeability prediction are detailed in table 4, offering insight into the relative influence of each predictor variable and their interactions on permeability. table 4—coefficients of linear model. estimate squared error t-sat* p-value** intercept 109.0659 0.495134 220.2755761 0 x1 0.118014 0.006208 19.00926865 1.34e-78 x2 -40.8582 0.2262 -180.628774 0 x3 0.075784 0.001037 73.05783645 0 x1*x2 -0.06092 0.002848 -21.3910936 2.19e-98 x1*x3 0.000154 1.54e-05 9.998604339 2.22e-23 x2*x3 -0.01466 0.000853 -17.1769302 8.35e-65 *the t-stat is simply the estimate divided by the squared error. **the p-value is associated with the t-stat and shows if a given response variable is significant in the model. the linear regression model equation derived from these coefficients is expressed as, perm=109.0659+0.1180x1−40.8582x2+0.0758x3−0.0609x1x2+0.000154x1x3−0.0147x2x3,.....................(3) eq. 3 can be applied in practical scenarios for quick and reliable permeability estimation, making it a valuable tool for reservoir engineers. figure 3—cross plot of actual versus model predicted permeability. figure 3 shows that actual permeability versus model-predicted permeability reveals a strong correlation between the measured and predicted values, with most of the data points lying close to the unit slope line. it further confirms the model’s accuracy and its potential for practical application in predicting permeability. artificial neural network (ann) model. figure 4 presents the pearson’s correlation matrix for all parameters in the dataset, providing insight into the relationships between input parameters (gamma ray, bulk density, and deep induction) and the output parameter (permeability). r² = 0.9909 0 200 400 600 800 1000 0 100 200 300 400 500 600 700 800 900 m o d el p re d ic te d p er m ea b il it y , m d actual permeability, md improved oil and gas recovery 7 figure 4—pearson’s correlation matrix for all parameter in the dataset. bulk density exhibited a strong negative correlation with permeability, indicating that as bulk density increases, permeability tends to decrease. this is consistent with geological principles, where higher density formations often have lower porosity and permeability. deep induction showed a positive correlation with permeability, suggesting that higher values of deep induction are associated with higher permeability, likely due to the presence of more conductive, porous formations. gamma rays had a weak correlation with permeability, implying that its influence on permeability is less significant compared to the other variables. these correlations are essential for understanding the influence of each parameter on the output and guiding the feature selection process. ann structure and performance. six different ann structures were constructed and evaluated based on 8,739 data points. the statistical performance of each structure is summarized in table 5. table 5—statistical performance of ann structures. ann structure mae rmse r2 n-5 1.0818 80.9924 0.9931 n-6 0.8362 75.7039 0.9963 n-7 0.6145 65.2532 0.9980 n-8 0.7439 76.8524 0.9962 n-9 0.5985 71.9866 0.9979 n-10 0.1445 29.9016 0.9996 among the six ann structures, the n-10 structure achieved the best performance. it achieved the lowest rmse (29.9016) and the highest correlation coefficient (0.9996), indicating an exceptionally accurate model with minimal prediction error. this structure outperformed the linear models, highlighting the strength of anns in capturing complex, non-linear relationships in the data. improved oil and gas recovery 8 the architecture of the n-10 ann, depicted in figure 5, includes an optimized number of neurons and layers that enable the model to learn the intricate patterns in the well log data. the ability of the ann to model nonlinear relationships gives it an edge over linear regression models, particularly in complex reservoir environments. figure 5—structure of the best trained ann. ann model equation. the ann model developed in this study is represented by a series of equations (eq. 4 to 9) that describe the transformation of input variables through the network's layers to produce the final permeability prediction. kp = 1 2 ((𝑏2 + 𝐿𝑊2 ∙ tanh(𝑏1 + 𝐼𝑊1 ∙ xn(−1:+1) )) + 1) (kmax − kmin) + kmin,..................................................(4) where, xn(−1:+1) = 2 [ 𝑋𝑛(0:1)−xmin 𝑋𝑚𝑎𝑥−xmin ]-1,...............................................................................................................................(5) xn(0:1) = x−xmin xmax−xmin ,..........................................................................................................................................(6) x = [γ ρd id]t ,................................................................................................................................................(7) xmin = [γmin ρdmin idmin]t,...........................................................................................................................(8) xmax = [γmax ρdmax idmax]t,.........................................................................................................................(9) the weights and biases extracted for the output layer (lw2 and b2) and the hidden layer (iw1 and b1) used in the model are shown in tables 6 and 7, respectively. table 6—key parameters for the output layer used in eq. 4. extracted weight vector (lw2) bias (b2) 0.2514 -1.4538 -1.7993 1.2766 0.4177 2.6805 0.5586 1.3820 -1.4926 2.3865 -0.3288 improved oil and gas recovery 9 table 7—key parameters for the hidden layer used in eq. 4. extracted weight matrix (iw1) bias vector (b1) 0.7447 -0.9934 2.7596 -2.0319 0.2320 0.3227 0.7401 -0.8480 -0.1124 -0.2926 0.0548 0.4594 -0.5512 3.7046 -6.9747 -10.0962 -0.6787 2.3096 1.5510 -0.7071 0.6146 -3.1447 -0.3321 2.3459 -0.1447 -0.5907 1.1009 1.2524 0.5512 -3.9675 10.4580 13.5564 0.0538 0.2011 -0.7062 0.1829 -0.6129 3.5097 -2.2764 -5.0852 these equations encapsulate the weights, biases, and activation functions used in the model, providing a detailed mathematical framework for understanding the ann’s operation. the ann model equation (eq. 4) is more complex than the linear regression model equation (eq. 1), reflecting the higher complexity and flexibility of anns. this complexity allows the ann to achieve higher accuracy, especially in cases where the relationships between variables are not purely linear. model validation and performance analysis. the performance of the ann model is further validated through cross-plots of measured versus predicted permeability values for the training, validation, and testing datasets are presented in figures 6 through 8. the alignment of data points along the unit slope line in figure 6 indicates that the ann has effectively learned the patterns in the training data, resulting in highly accurate predictions. the strong correlations between predicted and actual values in figures 7 and 8 confirm that the model generalizes well to new data, maintaining high accuracy across different datasets, confirming the model's accuracy. figure 6—measured and predicted permeability cross-plots based on the training dataset (6117 data points). r² = 0.9999 0 200 400 600 800 1000 0 100 200 300 400 500 600 700 800 900 p re d ic te d p er m ea b il it y , m d measured permeability, md unit slope 10% -10% training dataset improved oil and gas recovery 10 figure 7—measured and predicted permeability cross-plots based on the validation dataset (1311 data points). figure 8—measured and predicted permeability cross-plots based on the testing dataset (1311 data points). figure 9—measured and predicted permeability cross-plots based on the entire dataset (8739 data points). r² = 0.9998 0 200 400 600 800 1000 0 200 400 600 800 1000 p re d ic te d p er m ea b il it y , m d measured permeability, md unit slope 10% -10% validation dataset r² = 0.9992 0 200 400 600 800 1000 0 200 400 600 800 1000 p re d ic te d p er m ea b il it y , m d measured permeability, md unit slope 10% -10% testing dataset r² = 0.9996 0 200 400 600 800 1000 0 100 200 300 400 500 600 700 800 900 p re d ic te d p er m ea b il it y , m d measured permeability, md unit slope 10% -10% entire dataset improved oil and gas recovery 11 the cross-plot based on the entire dataset (8,739 data points) in figure 9 further demonstrates the robustness of the ann model in predicting permeability across diverse datasets. the high density of data points along the unit slope line across such a large dataset is a evidence of the model's reliability and effectiveness in real-world applications. the comparison across the three studies highlights differences in modeling approaches, model types, and performance (table 8). leiphart and hart (2001) utilized a combination of linear regression and probabilistic neural network (pnn), with pnn achieving the best performance with an r² value of 0.82. this model demonstrated better geological realism in predicting porosity distribution, effectively capturing non-linear relationships between seismic attributes and porosity. in contrast, azim and aljehani (2022) employed an artificial neural network (ann) using the back-propagation learning algorithm implemented in fortran. their ann model achieved an r² value of 0.94 and was particularly robust in predicting rock permeability with minimal wireline log data. in this study, a more diverse set of models was explored, including standard linear regression, interactions linear regression, and ann with varying structures. the best-performing model was the ann with 10 neurons in the hidden layer (n-10), achieving an exceptional r² value of 0.9996. this model provided superior accuracy in predicting permeability and was highly effective in capturing complex, non-linear relationships in well log data, surpassing the predictive capabilities of the models from the other two studies. table 8—comparison of modeling approaches across studies. feature leiphart and hart (2001) azim and aljehani (2022) this study modeling approaches linear regression and probabilistic neural network (pnn). ann model based on the back propagation learning algorithm using the fortran language. linear regression and artificial neural network (ann). model types standard linear regression, probabilistic neural network (pnn). ann model uses a weight visualization curve technique. standard linear regression, interactions linear regression, and artificial neural network (ann) with varying structures. best performing model probabilistic neural network (pnn) with r² = 0.82. ann with r² = 0.94. ann with 10 neurons in the hidden layer (n-10) with r² = 0.9996. performance metrics linear regression: r² = 0.74. pnn: r² = 0.82. r² = 0.94. interactions linear regression: r² = 0.983. ann (n-10): r² = 0.9996 strengths of best model better geological realism in predicted porosity distribution; higher accuracy in capturing nonlinear relationships between seismic attributes and porosity. ann model is robust and has strong capability of predicting rock permeability using a minimum number of wireline log data. superior accuracy in predicting permeability; effective at capturing complex, non-linear relationships in well log data. conclusions in conclusion, this study demonstrates the effectiveness of both linear regression and artificial neural network models in predicting permeability from well log data. the interactions linear regression model and the n-10 ann structure were identified as the best-performing models in their respective approaches. while the ann model improved oil and gas recovery 12 demonstrated superior accuracy and robustness, the linear regression models, particularly the interactions model, offered valuable insights into the relationships between variables. the models developed in this study can be effectively applied in reservoir characterization, leading to improved decision-making in the oil and gas industry. recommendation based on the results and discussion of the modeling approaches for predicting permeability from well log data, the following recommendations are proposed: 1. adoption of artificial neural networks (ann) for complex reservoirs: the ann model, particularly the n-10 structure, demonstrated superior accuracy in predicting permeability, especially in complex reservoirs where non-linear relationships prevail. this model should be prioritized for reservoir characterization in such environments. 2. use of interactions linear regression for simpler reservoirs: the interactions linear regression model performed well, with relatively high accuracy and strong generalization. this model is more interpretable and computationally less intensive than ann models, making it suitable for reservoirs where relationships are expected to be more linear. 3. integration of both modeling approaches: each modeling approach offers unique strengths--ann for capturing complex, non-linear relationships, and linear regression for simplicity and interpretability. integrating both approaches could provide a more comprehensive understanding of reservoir behavior. a hybrid approach can be employed where both models are run in parallel. the linear regression model can be used for initial, quick assessments, while the ann model provides a more detailed analysis. this strategy would ensure that different aspects of reservoir 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neural networks for combinatorial optimization: a review of more than a decade of research. informs journal on computing 11(1):15-34. wills, e. 2019. ai vs. machine learning: the devil is in the details. machine design 91(1):56-60. zhang, l. 2013. aspects of rock permeability. front. struct. civ. eng. 7(1):102-116. zhang, y., lollback, p., rojahn, j., et al. 1996. a methodology for estimating permeability from well logs in a formation of complex lithology. paper presented at the spe asia pacific oil and gas conference, 28-31 october. spe-37025-ms. charlie iyke anyadiegwu is a senior lecturer in the department of petroleum engineering, federal university of technology owerri where he has worked for over 25 years. he holds both b.eng and m.eng in petroleum engineering and gas engineering respectively from the university of portharcourt, rivers state, nigeria, and ph.d. degree in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in oil and gas production and processing from fossil fuel and non-fossil fuel (biomass), health, safety and environment (hse), oil spillage detection, control and prevention. christian emelu okalla is a technologist and researcher at the department of petroleum engineering, federal university of technology owerri. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, natural gas, reservoir simulation. anthony kerunwa is a senior lecturer in the department of petroleum engineering, federal university of technology owerri. he holds both b.eng and m.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria, and ph.d degree in petroleum engineering from centre for oil field chemical research (ips). his research interests are in drilling engineering, production engineering, reservoir engineering, and petroleum economics. solomon chukwuebuka igbo is a recent graduate of the department of petroleum engineering, federal university of technology owerri. he holds a b.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, and reservoir. improved oil and gas recovery 14 joshua abiodun abah is a recent graduate of the department of petroleum engineering, federal university of technology owerri. he holds a b.eng in petroleum engineering from the federal university of technology owerri, imo state, nigeria. his research interests are in drilling, production, and reservoir. copyright © the author(s). this work is licensed under a creative commons attribution 4.0 international license. improved oil and gas recovery doi: 10.14800/iogr.1364 received january 28, 2025; revised july 29, 2025; accepted september 14, 2025. *corresponding author: ahmed.noori203@aut.ac.ir 1 optimal miscible co2 injection for enhanced oil recovery: a case study of the asmari formation in the abu ghirab oil field, southeastern iraq mohammed alhwayzee, maaly asad, kerbala university, kerbala, iraq; ahmed al-dujaili*, amirkabir university of technology, tehran, iran; nabeel nasrawi, kerbala university, kerbala, iraq abstract this study focuses on optimizing the implementation of miscible co2 injection to enhance production from the asmari formation in the abu ghirab field, southeastern iraq, using cmg™ simulation software. various scenarios were simulated to evaluate the effectiveness of miscible co2 injection and identify areas where it could be applied successfully. key factors such as porosity, permeability, and reservoir thickness were considered, as they significantly influence the success of miscible co2 flooding. the results were compared between primary production and enhanced oil recovery using miscible co2 injection. the original oil in place (ooip) is estimated at 89,331 mstb, indicating a reduction in reserves in the southern dome of the field. simulations of miscible co2 injection from 2024 to 2030 revealed that miscible co2 injection would not affect the field until the third quarter of 2026. therefore, miscible co2 flooding should begin in september 2026 to achieve optimal results. the study also observed an increase in the gas-oil ratio starting in the third quarter of 2027. however, a decline in oil production is expected from late 2028 to 2030, suggesting that an alternative enhanced oil recovery (eor) method should be considered for continued oil recovery beyond this period. introduction enhanced oil recovery (eor) refers to the process of extracting oil through the injection of a fluid that is not naturally present in the reservoir. it is used to prolong the productive life of oil fields that are depleted or no longer economically viable. eor techniques are typically employed after more conventional, less complex methods— such as pressure depletion and water flooding have been exhausted (shao and chen 2024). one of the most established eor methods is the injection of carbon dioxide (co2), which has been widely applied in the oil and gas industry for several years (davoodi et al. 2024). co2 injection is generally carried out after primary recovery has extracted 10% to 20% of the original oil in place, followed by secondary recovery that contributes an additional 10% to 20% (hoteit et al. 2019). co2 typically functions as a solvent when injected into the reservoir, enhancing the extraction of remaining oil (zhou et al. 2024). when injected under reservoir conditions, co2 mixes with the oil to become miscible, which helps reduce the oil's viscosity and facilitates smoother flow through the reservoir (wang et al. 2023). a typical co2 flooding process, demonstrating miscibility, is shown in figure 1 (feather and archer 2010). mailto:v.javanbakht@alumni.iut.ac.ir improved oil and gas recovery 2 figure 1—miscible co2 flooding (feather and archer 2010). a large share of the world's remaining oil is found in tight formations, commonly of carbonate origin, and these formations exhibit significant heterogeneity (radwan et al. 2021). the goals of enhanced oil recovery (eor) vary considerably depending on the types of hydrocarbons involved (figure 2) (thomas 2008). figure 2—targets for enhanced oil recovery according to the type of hydrocarbon (thomas 2008). gas is injected into the reservoir oil at or above the minimum miscibility pressure (mmp) to achieve complete mixing of the two (li and luo 2017). this process is referred to as miscible gas injection. if the gas injection occurs below the mmp, it is termed immiscible gas injection (figure 3) (tileuberdi et al. 2024). improved oil and gas recovery 3 figure 3—evolution of co2 injection miscibility in oil at both miscible and immiscible pressures (asgarpour 1994). while most co2 enhanced oil recovery (eor) projects operate under miscible conditions, immiscible conditions can also be utilized to extract oil from a reservoir (chukwudeme and hamouda 2009; steinsbø et al. 2014; cooney et al. 2018; seyyedi and sohrabi 2020; chen et al. 2023). however, not every reservoir is suitable for co2 injection (janna and le-hussain 2020). factors such as oil composition, depth, temperature, and other reservoir characteristics must be carefully evaluated when considering co2 injection (kumar et al. 2022; eyinla et al. 2023). precise determination of the minimum miscibility pressure (mmp) for co2 flooding can greatly enhance reservoir recovery (song et al. 2024). this is typically effective at depths greater than 2500 feet, with oils having an api gravity greater than 22 degrees and a viscosity less than 10 cp. additionally, the oil’s saturation should exceed 20% of the pore volume (abdullah and hasan 2021). the recovery factor for the miscible co2 injection was higher than for the immiscible, indicating that the miscible injection was more effective. however, reaching miscible conditions in heavy oil reservoirs proved challenging (zhang et al. 2010; abedini et al. 2015; kudapa and krishna 2023). simulated pvt experiments revealed that miscible co2 injection with rich gases yields higher oil recovery than the injection with lean gases (zarei and azdarpour 2017). this case study on co2 injection for enhanced oil recovery in an iraqi oil field highlights its potential to boost oil recovery and extend the field’s productive life by promoting miscibility with the oil, co2 injection enhances extraction efficiency, leading to higher production rates. additionally, this method supports global efforts to reduce carbon emissions by beneficially utilizing co2 instead of releasing it into the atmosphere. the case study also offers valuable insights into the feasibility, challenges, and benefits of co2 injection in similar oil fields globally, contributing to advancements in sustainable energy practices and resource management. geological setting the abu ghirab oil field is situated in the missan governorate in southeastern iraq, near the iranian border (asad et al. 2024). it spans approximately 30 km in length and 5 km in width, with coordinates ranging from 3575000360000 northing and 71,000-73,500 easting (asad and hamd-allah 2022). the field features two domes (northern and southern) separated by a saddle zone, as depicted in figure 4 (al-mamouri et al. 2022). the asmari formation is characterized by heterogeneity, and fracture distribution and requires water control in later stages of development (alsinbili et al. 2013; daraei et al. 2023), using cased hole perforation for vertical and directional wells. the reservoir primarily consists of carbonate rocks from the cretaceous and tertiary periods (haghighat et al. 2021). located within the transitional zone between the zagros mountains and the arabian plate in the improved oil and gas recovery 4 southern mesopotamian basin (sang et al. 2017), the field lies about 350 km southeast of baghdad and 175 km north of basra, as shown in figure 4. figure 4—abu ghirab oil field, southeastern iraq (al-mamouri et al. 2022). the asmari formation is part of tertiary deposits (oligocene-lower miocene) in southeastern iraq (al-saad 2010; fouad 2012; al-saad and al-shahwan 2019; al-baldawi 2020). the kirkuk group consists of three subzones: a) the upper kirkuk, which includes limestone, dolomite, and some sandstone (karim et al. 2020); b) the buzurgan member, comprising dolomite, sandstone, limestone, and upper shale in the upper section (albaldawi 2020). pre-geological studies of the abu ghraib structure reveal the influence of two distinct forces caused by folding movements (alwan et al. 2017). these forces created tension in the upper part of the structure and compression in the lower portions, resulting in tangential deformation and a longitudinal shape. deformation was most intense along the limbs, while the anticline axis experienced less deformation (al-baldawi 2020). figure 5 shows the stratigraphic column of the area (al-khafaji et al. 2019). improved oil and gas recovery 5 figure 5—stratigraphic column of abu ghirab (al-khafaji et al. 2019) data and methods this study offers a detailed analysis of enhanced oil recovery (eor) methods applied to the asmari formation in the abu ghirab field, concentrating on optimizing oil production through various injection techniques. figure 6 depicts the wells investigated in the asmari formation within the abu ghirab field. the research utilizes a comprehensive dataset obtained from core analyses of the 22 wells, which includes essential reservoir properties such as porosity, permeability, water saturation, and relative permeability for both oil and water phases. these properties are critical for understanding fluid flow dynamics within the reservoir and modeling recovery processes. figure 7 provides oil and water relative permeability for different units of asmari formation by core flooding.the core flooding experiments were conducted under reservoir conditions to accurately capture the flow behavior of oil and water. the relative permeability curves depicted in figure 7 illustrate the varying degrees of mobility for oil and water phases across different units, highlighting the impact of rock heterogeneity on fluid flow. these curves serve as a fundamental input for reservoir simulation models, enabling more precise predictions of oil recovery efficiency and optimization of production strategies. in addition to core data, the study incorporates production data, which encompasses historical oil and gas production rates, as well as pressure-volume-temperature (pvt) data (figure 8). pvt data is vital for characterizing fluid behavior under varying reservoir conditions. it provides insights into the physical properties of the reservoir fluids, such as oil and gas densities, bubble point pressure, and formation volume factors, all of which are crucial for accurately modeling the reservoir's response to enhanced recovery techniques. the integration of core, production, and pvt data serves as the foundation for evaluating the reservoir performance and informs the selection of the most effective eor strategies for the asmari formation. improved oil and gas recovery 6 figure 6—location of wells in the asmari formation within the abu ghirab field. the study utilizes cmg™ commercial software to simulate well performance under miscible co2 injection. the primary objective is to estimate the optimal volume of co2 to be injected and assess the history of oil production. a key focus is determining the ideal depth for co2 injection and understanding how various factors, such as injection parameters, affect production rates. additionally, the study examines the optimal injection conditions, especially in scenarios where water cut fluctuations are observed. facies logs obtained from wireline logging data were used to construct a facies model in petrel™ (figure 9), which helped to best understand the reservoir heterogeneity. a simplified blackoil model was developed using standard correlations, assuming a reservoir temperature of 150°f and a pressure range of up to 2600 psi. the model incorporates a bubble point pressure of 2600 psi, stock tank oil gravity of 40 api, and a gas density of 0.8, they were input into the simulation to ensure accurate modeling of fluid behavior under reservoir conditions. this integrated approach allows for a more precise evaluation of co2 injection strategies and their impact on enhanced oil recovery in the asmari formation. improved oil and gas recovery 7 figure 7—oil and water relative permeability for different units of asmari formation by core flooding. figure 8—a) pressure versus solution gas-oil ratio (rs) and oil formation volume factor (bo), b)relative permeability of gas versus gas saturation (sg), c)pressure versus viscosity of oil and gas, and d)pressure versus compressibility gas factor (zg). improved oil and gas recovery 8 figure 9—facies model for asmari formation in abo ghirab field (asad and hamd-allah 2022). the locations of the production wells were first marked on the map, and subsequently, the proposed injection well sites were also identified on the same map. to build the reservoir model, the lithofacies and petrophysical properties of the wells, including porosity, permeability, and water saturation, were entered based on their depth profiles. these properties were integrated into the model to represent the reservoir more accurately. the reservoir was subdivided into 29 distinct layers, each corresponding to a specific flow unit, as shown in figure 10. the uppermost section of the reservoir consists of 4 layers, while the remaining sections were divided into 5 layers each. this stratification allows for a more detailed representation of reservoir heterogeneity and flow behavior, providing a better foundation for simulating fluid dynamics and optimizing both production and injection strategies. figure 10—flow units for lithofacies data. improved oil and gas recovery 9 results and discussion original oil in place (ooip). the simulation was run to estimate the (ooip) according to the equation, 𝑂𝑂𝐼𝑃 = 7758 ×𝐴 ×𝐻 ×𝜑 × 𝑆𝑜𝑖 𝐵𝑜𝑖 ,.....................................................................................................................(1) where a is the reservoir area, acres; h is the average net reservoir thickness, ft; 𝜑 is the average porosity formation; 𝑆𝑜𝑖 is the initial oil saturation; and 𝐵𝑜𝑖 represents the oil formation volume factor at initial pressure, bbl/stb. the results indicate that the estimated original oil in place (ooip) for the southern dome of the abu ghirab field is 89,331 mstb. this represents a decrease in the reserve size for this specific portion of the field, highlighting a potential reduction in recoverable oil from this area. given the presence of numerous faults within the asmari formation, which can both separate the reservoir and affect fluid flow, further exploration and appraisal of this region—along with other parts of the field—could prove valuable. additional seismic surveys, well logging, and drilling activities may uncover untapped reserves or more accurate reservoir models, potentially increasing overall production from the asmari formation. addressing the complexities introduced by faulting could also improve the understanding of fluid distribution and enhance recovery techniques, ultimately supporting long-term production in the abu ghirab field. simulation for the miscible co2 injection. the simulation of miscible co2 injection from 2024 to 2030 shows no significant effect on the oil field between 2024 and the third quarter of 2026. during this time, cumulative oil production remains nearly identical, regardless of whether co2 injection is used. this indicates that co2 injection does not significantly change the field dynamics at this stage. therefore, the simulation suggests that co2 injection should begin in september 2026 to initiate the miscible co2 flooding process, which is expected to improve oil recovery in the future (figure 11). after the start of co2 injection in september 2026, oil production gradually increases. this increase continues steadily through 2029, with a more substantial rise in production anticipated in the latter part of that period. the gradual increase in production is attributed to co2 injection, which helps maintain or enhance reservoir pressure, enabling ongoing oil production through the primary recovery mechanism (i.e., natural reservoir pressure and gas drive). as long as the reservoir pressure remains sufficiently high, the primary recovery process can continue to support effective oil production, especially in the initial stages of co2 flooding. however, the effects of co2 injection become more pronounced after the onset of miscible flooding, as co2 aids in mobilizing additional oil that would not be recoverable through primary recovery alone. figure 11—cumulative oil production with and without co2 injection for the period from 2024 to 2030. improved oil and gas recovery 10 figure 12 illustrates the oil production rate and cumulative oil production, both with and without co2 injection, from 2024 to 2030. the data indicates that, from 2024 until the third quarter of 2026, co2 injections have had minimal impact on the field, as oil production remains largely unchanged whether co2 is injected or not. however, starting from the fourth quarter of 2026, there is a noticeable increase in production linked to co2 injection, with production rates gradually rising as the miscible co2 flooding takes effect. despite this increase, the oil production rate declined from the end of 2028 through 2030. this decrease may be due to the gradual depletion of reservoir pressure and the dwindling effectiveness of the co2 injection in sustaining high production levels. this trend should be carefully considered when planning future production strategies for the wells, particularly concerning the oil prices during that period. if oil prices are lower from 2028 to 2030, the economic feasibility of continuing co2 injection and production may be affected, necessitating operational and financial planning adjustments. figure 12—the oil production rate in addition to the cumulative oil production with and without co2 injection from 2024 to 2030. this study observed an increase in the gas-oil ratio starting in the third quarter of 2027. the rise in the gas-oil ratio is attributed to the injection of co2, which, while enhancing oil production initially, leads to a higher gas content in the produced fluids as the oil production rate begins to decline. this shift occurs because, over time, the miscible co2 injection primarily stimulates gas production rather than oil, particularly as the reservoir pressure stabilizes and the effectiveness of the miscible co2 injection diminishes. as a result, the injection process could become less efficient in maintaining oil production, potentially reducing the overall recovery factor. this shift may make the co2 injection less economically viable unless oil prices during that period are high enough to offset the rising costs of co2 injection and the associated operational expenses. for the process to remain profitable, oil prices must be sufficiently high to cover both the capital and operational costs of injecting co2 and generate a reasonable return for the investor (figure 13). improved oil and gas recovery 11 figure 13—gas oil ration with and without co2 injection for the period from 2024 to 2030. conclusions the cmg™ simulator was used to model various scenarios and assess the effectiveness of miscible co2 injections for enhanced oil recovery (eor) and its potential applications. several factors, such as porosity, permeability, and formation thickness, were considered in evaluating the impact of co2 floods. the simulation results were compared between primary production and co2-enhanced production, showing an increase in oil recovery with co2 injection. key findings of the study include: 1. the initial oil-in-place (ooip) was determined to be 89331 mstb, indicating a reduction in reserves in the southern dome of the field. 2. the simulation for co2 miscible injection between 2024 and 2030 revealed that co2 injection would have no significant impact on production through the third quarter of 2026. however, starting in the fourth quarter of 2026, a noticeable increase in production is expected because of co2 injection. 3. co2 injection should begin in september 2026 to initiate effective co2 flooding. 4. a rise in the gas-oil ratio (gor) was observed starting from the third quarter of 2027, which indicates the changing dynamics of production. 5. from late 2028 to 2030, a decline in oil production rates is expected. this decline should be considered when selecting additional eor methods to optimize the recovery of remaining oil. 6. further exploration of the southern area of the field and other adjacent areas is recommended to enhance production from the asmari formation in the abo ghirab field, as the formation contains numerous faults that could offer new opportunities for oil recovery. 7. the expected decline in production rates between late 2028 and 2030 should be carefully factored in production planning, particularly in relation to future oil prices. 8. in conclusion, while miscible co2 injection offers promising potential for enhancing oil recovery, careful attention must be paid to the timing of injection and the planning of subsequent eor methods to manage declining production rates. additional exploration and resource evaluation in the southern field area could further boost production in the long term. nomenclature  = porosity a = reservoir area, acres api = oil gravity improved oil and gas recovery 12 bo = oil formation volume factor, bbl/stb boi = oil formation volume factor at initial pressure, bbl/stb co2 = carbon dioxide eor = enhanced oil 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maximize eor performance for heavy oils. journal of canadian petroleum technology 49(5): 25-33. zhou, x., wu, y.s., chen, h., et al. 2024. review of carbon dioxide utilization and sequestration in depleted oil reservoirs. renewable and sustainable energy reviews 202: 114646. mohammed alhwayzee earned his initial degree in chemical engineering from the university of technology in baghdad, iraq, pursued his master’s degree at the same institution, and subsequently obtained his phd from the university of cardiff in cardiff, united kingdom. he currently serves as a professor within the petroleum engineering department at the university of kerbala. dr. alhwayzee's scholarly pursuits encompass the study of fluidized bed reactors, the gasification of biomass, desalination processes, biomass fuel, and hydrodynamic phenomena within fluidized beds. maaly asad obtained her first degree in chemical engineering from college of engineering of baghdad university in 2000 and her master’s and phd degrees from college of engineering of baghdad university in 2010 and 2022, respectively. she is a professor in petroleum engineering department of university of kerbala. dr. maaly asad's research interest is in production engineering, reservoir engineering, and well logging. ahmed al-dujaili obtained his bachelor’s and master’s degree from petroleum engineering department of baghdad university, iran, and phd degree from amirkabir university of technology, tehran, iran. he serves as a professor in petroleum engineering department of university of kerbala. dr. al-dujaili's research interests include petroleum exploration, reservoir engineering, drilling engineering, petroleum geology, and water resources. nabeel nasrawi is a lecturer in petroleum engineering department of university of kerbala, iraq. he specializes in chemical technology.