A sample paper for presentation at ANZIIS 2001 Copyright Β© 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 real- time 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, π‘„π‘œ = π΄πΎπ‘œ πœ‡π‘œ βˆ†π‘ƒ βˆ†πΏ .……………………………………………..….…………….……………………………(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. πΎπ‘Ÿπ‘œ = πΎπ‘œ/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, 𝑓𝑀 = 𝑄𝑀/(π‘„π‘œ + 𝑄𝑀)..………………..…………...………………………………………..……..……(3) Integrate Eq. 1 and 2 into Eq. 3, the expression can be obtained as, 𝑓𝑀 = 1 1+ πΎπ‘Ÿπ‘œ πΎπ‘Ÿπ‘€ πœ‡π‘€ πœ‡π‘œ ,……………………….………………………………………..………………..……….(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 𝑓𝑀 = πΎπ‘Ÿπ‘€ πœ‡π‘€π‘…π‘˜ πΎπ‘Ÿπ‘€ πœ‡π‘€π‘…π‘˜ + πΎπ‘Ÿπ‘œ πœ‡π‘œ .…………………….…………….….…………………………..…………………..….(5) Jone’s formula (Yong and Zhang 1996; Zhao et al. 1997; Yu 1992) about the water-oil relative permeability curves is given as, πΎπ‘Ÿπ‘€ = | π‘†π‘€βˆ’π‘†π‘€π‘– 1βˆ’π‘†π‘€π‘– | 2 , πΎπ‘Ÿπ‘œ = | 1βˆ’π‘†π‘€βˆ’π‘†π‘œπ‘Ÿ 1βˆ’π‘†π‘€π‘–βˆ’π‘†π‘œπ‘Ÿ | 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. π‘†π‘œ = 1 βˆ’ 𝑆𝑀 = 1 βˆ’ (1βˆ’π‘†π‘€π‘–)(1βˆ’π‘†π‘œπ‘Ÿ)+𝐿(1βˆ’π‘†π‘€π‘–βˆ’π‘†π‘œπ‘Ÿ)𝑆𝑀𝑖 𝐿(1βˆ’π‘†π‘€π‘–βˆ’π‘†π‘œπ‘Ÿ)+(1βˆ’π‘†π‘€π‘–) ,…….…...…………………………………………..(7) where, 𝐿 = √| 1 𝑓𝑀 βˆ’ 1| πœ‡π‘œ πœ‡π‘€π‘…π‘˜ 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, liquid- producing 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, οΏ½Μ…οΏ½ = βˆ‘ β„Žπ‘–Γ—π‘˜π‘– βˆ‘ β„Žπ‘– 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 οΏ½Μ…οΏ½/𝐾𝑖 follows negative linear relationship as, 𝑓𝑀𝑖 = π‘Ž βˆ’ 𝑏 οΏ½Μ…οΏ½ 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, 𝑆𝑀𝑖 = 31.98 [1.26 βˆ’ 𝑙𝑔 ( πœ™ π‘‰π‘ β„Ž βˆ’ 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. π‘†π‘œπ‘Ÿ 𝑆𝑀𝑖 = 3.158 βˆ’ 9.762𝑆𝑀𝑖 + 8.94𝑆𝑀𝑖 2 .………………………………………………………………….(12) π‘†π‘œπ‘Ÿ 𝑆𝑀𝑖 Swi Figure 1β€”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 𝑆𝑀𝑖 ≀ 𝑆𝑀 ≀ 1 βˆ’ π‘†π‘œπ‘Ÿ .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, π‘†π‘œπ‘Ÿ = 62.440 + 1.3212πœ™ βˆ’ 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, π‘†π‘œπ‘Ÿπ‘ = π‘†π‘œπ‘Ÿπ‘’ βˆ’π΄π‘„/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, ο‚Ÿ Using Eq. 13 to calculate the residual oil saturation of each oil layer when injection begins; ο‚Ÿ 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 1β€”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 (ΞΌm2) 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 2β€”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 3β€”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 4β€”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 βˆ†π‘ βˆ†πΏ = pressure gradient upon the seepage direction Qo = oil rate, m3 Qw = water quantity, m3 ΞΌo = oil viscosity ΞΌw = 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.