Microsoft Word - 26-3137_s_ETASR_V9_N6_pp5011-5015 Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 5011-5015 5011 www.etasr.com Chachar et al.: Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach Muhammad Hanif Chachar PPL Chair, Institute of Petroleum & Natural Gas Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan mhanifchachar@gmail.com Sarfraz Ahmed Jokhio PPL Chair, Institute of Petroleum & Natural Gas Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan sjokhio1@hotmail.com Abdul Haque Tunio Institute of Petroleum & Natural Gas Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan haque.tunio@faculty.muet.edu.pk Haris Ahmed Qureshi PPL Chair, Institute of Petroleum & Natural Gas Engineering Mehran University of Engineering and Technology Jamshoro, Pakistan harisqureshi12.hq@gmail.com Abstract—Inflow performance relationship (IPR) accuracy in the condensate reservoir is a long-standing problem in the oil industry. This paper presents a new approach to project the gas phase IPR in condensate reservoirs. IPR is estimated by Rawlins and Schellhardt equation whereas the gas pseudo-pressure function is solved by two methods and their IPRs are compared. Additionally, an average of both IPR’s is estimated and compared. At the reservoir pressure, the difference between both flow rates is negligible i.e. at 6750 psi, the flow rate difference is 0.55 MMSCF/D. As pressure declines the difference is increasing at one stage, it is observed approximately 15 MMSCF/D. Keywords-gas; condensate; condensate reservoir; Pseudopressure; Well productivity; Relative Permeability; Permeability; IPR I. INTRODUCTION The gas condensate reservoirs are difficult to predict due to its multiphase behavior. Petroleum industry is struggling to obtain the accurate Inflow Performance Relation (IPR) in condensate reservoirs for decades. There is not much research conducted in the case of calculating gas phase IPR in a condensate reservoir. It is possible to calculate IPR by using gas phase pseudo-pressure function without using the relative permeability data. Pseudo-pressure equation is solved using effective permeability data which can be obtained by pressure buildup test [1]. In the solution gas drive reservoir, two phase flow causes the curvature in IPR due to the reduction in the relative permeability of the oil phase with the depletion [2]. Two phase pseudo-steady state equation was solved [3] based on Weller’s approximation of constant gas oil ratio (GOR) and constant de-saturation [4]. In this study, the proposed approach is compared with the conventional method. To generate the IPR, the relative equation in [5] is preferred. In several case studies, it has been shown through production data and well test data that condensate blockage may reduce the production from two to four times. The major cause of production loss is condensate blockage near the wellbore [6]. To understand the condensate behavior, it is divided into three regions. Region-1 (near wellbore), where both phases are presented and mobile, Region-2 where both phases are present but only gas phase is mobile, and Region-3 (above dew point pressure) where only the gas phase is present and mobile [7]. Experimental work on the long core of sandstone formation outcome shows that the mobility is increased with capillary number near the wellbore region [8]. Authors in [9] verified the existence of the three regions by using a compositional simulator. The estimation of total well productivity in condensate reservoir is complicated. Condensate extent must be known to identify the blockage effect so that remedial action can be taken [10]. In [11], common problems associated with the condensate reservoirs were investigated and several proposed solutions were reviewed. This paper provides key improvements in the calculation of gas phase pseudo-pressure function using the integral effective permeability technique proposed in [12]. II. MODEL DESCRIPTION AND WORKING EQUATIONS A. Gas Pseudo-Pressure Function It completely depends on the pressure. To calculate real gas pseudopressure function linearly, Kirchhoff integral transformation is used as follows [13]: ���� = 2� � �� �� (1) where P: pressure, �: viscosity, and Z: compressibility factor. Authors in [7] modified and introduced the pseudopressure equation in form of three regions [7]. The total gas pseudopressure equation is: ���� = � � ��� ��� �� + ��� ��� � � �� �� (2) where ���: relative permeability of oil, ��: viscosity of oil, ��: oil formation volume factor, Rs: the solution gas-oil ratio, and Corresponding author: Muhammad Hanif Chachar Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 5011-5015 5012 www.etasr.com Chachar et al.: Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach g: gas. Authors in [12] modified the pseudopressure equation to calculate it with the single-phase effective permeability of either gas or oil by using well test data. They proposed the following equation, using gas PVT properties: ���� = !� ��.����� �� #$�%&#�#'� #$&#' ��� �� � �� ( (3) where Rp: producing gas-oil ratio and Ro: oil vapors in gas. Calculations of the classic and the proposed method are given in Table VI and VII respectively. B. Derivative of Gas Pseudo-Pressure Function Time dependent derivative of the pseudopressure function is required in order to obtain the integral of effective permeability. To calculate the derivative, it is necessary to obtain a pseudopressure equation. At first, the pseudopressure equation was calculated by ignoring the permeability data. Then, the derivative of pseudopressure equation is calculated. C. Integral of Effective Permeability The effective permeability data were calculated from the semi log straight line (SSL) from Shut-in versus time in Figure 1. The start of SSL shows the MTR (Middle Time Region) on PBU (Pressure Build-up) plot. The following equation is used to calculate the integral of effective permeability: � )�* + �� �� = � )�.�� + �� �� = 162.6 . /�,123' 4 5 % ∆7� �8 (5) where �* : gas effective permeability, 9 ,7*:�: flow rate of gas measured, h: bed thickness and ∆m(p)΄: change in pseudopressure derivative. Now, extrapolate the integral of effective permeability versus pressure to zero using curve fit software. The equation from curve is used to calculate its integral on the desired pressure (Figure 4). D. Effective Permeability Once the integral of effective permeability is calculated, we take its derivative using a two-point numerical derivative as a function of pressure: �* = )��2�+;& )��2�+< � ;& <� (6) This effective permeability is used to calculate the final pseudopressure function as shown in Table VII. E. Gas Flow Rate for IPR To establish gas phase IPR, the equation from [5] is used. Additionally, both gas pseudopressure equations are solved and their IPRs are plotted and compared. Figures 6 and 8 show the classic and the proposed IPR whereas Figure 9 shows the comparison of both IPRs with their average. 9 = = × ?)���� + @ A − )���� + CD A EF (7) where C: flow coefficient, n: deliverability exponent, ���� : gas pseudopressure function, �G : initial pressure and �CD : wellbore flowing pressure. III. STEP-BY-STEP PROCEDURE TO GENERATE IPR This method of calculating IPR is slightly different from the classic one. Its steps are: 1. Calculate gas properties (viscosity, density, compressibility) by conventional equations. 2. Convert well test data into gas pseudopressure function, ignoring permeability terms. 3. Calculate the derivative of the time log .H∆7� �HIJ�K� 5 of pseudopressure data. 4. Plot well test data pressure versus time on semi-log and find the straight-line. 5. Estimate the integral of effective permeability following the straight line from the previous step. 6. Plot the estimated integral of effective permeability versus pressure extrapolated to zero limits. To get good curve fit the equation’s both limits should be extrapolated to zero. 7. Calculate the integral of effective permeability values using the generated equation from the curve obtained in Step 6. 8. Calculate the effective permeability using a two-point numerical derivative as a function of pressure from the previous step. 9. Calculate the pseudopressure function again this time including the effective permeability data. 10. Finally, establish condensate well performance by using the equation from [5]. IV. CONCLUDING INTERPRETATION IPR is often used to predict the natural flow of the well so it should be properly selected. This study presents a new approach to estimate IPR in a gas condensate reservoir. Furthermore, it concludes with the following observations: • A method is proposed to calculate pseudopressure equation for plotting IPR in gas condensate reservoir. It does not require relative permeability data, as effective permeability can be easily calculated from its integral. • Effective permeability must be used before solving the pseudopressure integral. The comparison of IPR with the classic method shows that as pressure declines the flow rate difference in classic method and the proposed one increases. It can reduce the error by 1-15MMSCF/d. V. RECOMMENDATIONS IPR can obtain optimum flow of the well. It is highly recommended to use the proposed method to reduce errors in IPR calculations. The error percentage shows the reliability of this work. For additional research, three-phase reservoir should be considered, and optimum flow can be obtained by plotting TPR vs. IPR. A. Abbreviations and Acronyms PPF = Pseudopressure function GOR = Gas Oil Ratio SSL = Semi-log-straight-line R-1 = Region-1 Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 5011-5015 5013 www.etasr.com Chachar et al.: Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach R-2 = Region-2 R-3 = Region-3 Bg = Gas formation volume factor µg = Gas viscosity Keg = Gas effective-permeability Krg = Gas relative-permeability qg = Gas flow-rate qo = Oil flow-rate Rp = Producing gas-oil ratio Rso = Solution gas-oil ratio m(p) = Pseudo-pressure function m(p)’= Derivative of pseudo-pressure function ∆����= Change in pseudo-pressure function B. Figures and Tables TABLE I. RESERVOIR AND FLUID DATA [14] Symbol Value Unit Symbol Value Unit Pi 6750 Pisa qg 75.4 MSCF/D Pd 6750 Pisa qo 2.8 STB/D Rp/GOR 10417 SCF/STB h 216.5 ft T 814 °R Ф 0.062 Gas SG 0.94 rw 0.54 ft MW 27.17 API 50 [Assumed] ∆T 2.85 °F/100ft TABLE II. WELL TEST DATA [14] LMNO (hrs) P (psi) LMNO (hrs) P (psi) LMNO (hrs) P (psi) 0 1083.1 6 2759.4 50 6487.3 0.167 1174.5 8 3246.5 58 6507.6 0.333 1226.7 12 4210 68 6526.5 0.5 1303.6 16 5162 82 6556.9 1 1490.6 22 6161 97 6574.3 2 1751.6 28 6336.5 112 6587.3 3 2046 34 6406.1 141 6601.8 4 2279.4 42 6452.5 Pr 6750 TABLE III. GAS PVT PROPERTIES AT WELL TEST PRESSURE P psi Q RS bbl/SCF TS gm/cc μS cc VW SCF/STB VX STB/SCF 1083.1 0.9145 0.0034 0.0539 0.0080 297.945 1.4E-05 1174.5 0.9101 0.0031 0.0585 0.0082 327.131 1.55E-05 1226.7 0.9075 0.0030 0.0611 0.0083 343.959 1.63E-05 1303.6 0.9038 0.0028 0.0649 0.0085 368.948 1.75E-05 1490.6 0.8947 0.0024 0.0742 0.0090 430.644 2.04E-05 1751.6 0.8820 0.0020 0.0872 0.0097 518.739 2.41E-05 2046.0 0.8672 0.0017 0.1019 0.0105 620.549 2.82E-05 2279.4 0.8716 0.0015 0.1135 0.0113 702.899 3.14E-05 2759.4 0.8807 0.0013 0.1374 0.0130 876.247 3.81E-05 3246.5 0.8899 0.0011 0.1617 0.0151 1056.97 4.54E-05 4210 0.9157 0.0008 0.2097 0.0200 1426.45 6.22E-05 5162.0 0.9962 0.0007 0.2572 0.0273 1804.60 8.39E-05 6161.0 1.0806 0.0007 0.3069 0.0376 2213.14 0.000115 6336.5 1.0954 0.0007 0.3157 0.0397 2286.02 0.000121 6406.1 1.1013 0.0007 0.3192 0.0406 2315.01 0.000124 6452.5 1.1052 0.0007 0.3215 0.0413 2334.36 0.00012 6487.3 1.1082 0.0007 0.3232 0.0417 2348.89 0.00012 6507.6 1.1099 0.0007 0.3242 0.0420 2357.37 0.000128 6526.5 1.1115 0.0006 0.3252 0.0422 2365.27 0.000129 6556.9 1.1140 0.0006 0.3267 0.0427 2377.98 0.000130 6574.3 1.1155 0.0006 0.3275 0.0429 2385.26 0.000131 6587.3 1.1166 0.0006 0.3282 0.0431 2390.70 0.000131 6601.8 1.1178 0.0006 0.3289 0.0433 2396.77 0.000132 6750.0 1.1304 0.0006 0.3363 0.0454 2458.94 0.000138 TABLE IV. PPF, ITS DERIVATIVE AND INTEGRAL OF EFFECTIVE PERMEABILITY P psi ∆Y(Z) MMpsi 2 /cp ∆Y(Z)’ ∫ \]S 1083.1 19.87139 1174.5 23.33366 1226.7 25.40711 1303.6 28.58367 7.475785 1490.6 36.87831 11.75797 1751.6 49.68891 29.24621 2046 65.64563 38.57398 2279.4 79.14166 55.36694 2759.4 108.0837 75.90609 3246.5 138.2613 107.2502 4210 196.2917 139.7734 5162 246.5346 135.301 6161 287.666 93.06389 SSL 6336.5 293.6161 56.13135 0.001008854 6406.1 295.8697 15.22777 0.003718756 6452.5 297.3387 8.76812 0.006458438 6487.3 298.423 5.343989 0.010596647 6507.6 299.0485 4.866248 0.011636966 6526.5 299.6263 4.524248 0.012516635 6556.9 300.5464 3.375618 0.016775701 6574.3 301.0679 3.658003 0.015480678 6587.3 301.4551 2.58145 0.021936645 6601.8 301.8845 6750 306.1246 TABLE V. PVT PROPERTIES AT ASSUMED PRESSURE P psi Q RS bbl/SCF TS gm/cc μS cc VW SCF/STB VX STB/SCF 100 0.98995 0.04061 0.0049 0.0062 19.08302 1.4E-05 300 0.97359 0.01331 0.0149 0.0065 67.76515 3.4E-06 600 0.94906 0.00648 0.0298 0.0070 150.7455 4.83E-06 900 0.92348 0.00421 0.0448 0.0076 240.6389 1.09E-05 1200 0.90888 0.00310 0.0597 0.0083 335.3379 1.59E-05 1500 0.89428 0.00244 0.0747 0.0090 433.7788 2.05E-05 1800 0.87969 0.00200 0.0896 0.0098 535.3081 2.48E-05 2100 0.86826 0.00169 0.1046 0.0107 639.48 2.89E-05 2400 0.87393 0.00149 0.1195 0.0117 745.9688 3.31E-05 2700 0.87962 0.00133 0.1345 0.0128 854.5257 3.73E-05 3000 0.88530 0.00121 0.1494 0.0140 964.9535 4.16E-05 3300 0.89099 0.00110 0.1644 0.0153 1077.092 4.62E-05 3600 0.89668 0.00102 0.1793 0.0168 1190.809 5.11E-05 3900 0.88955 0.00093 0.1943 0.0184 1305.991 5.63E-05 4200 0.91490 0.00089 0.2092 0.0202 1422.542 6.2E-05 4500 0.94025 0.00085 0.2242 0.0222 1540.379 6.82E-05 4800 0.96561 0.00082 0.2391 0.0244 1659.429 7.49E-05 5100 0.99096 0.00079 0.2541 0.0268 1779.628 8.23E-05 5400 1.01632 0.00077 0.2690 0.0295 1900.917 9.05E-05 5700 1.04167 0.00075 0.2840 0.0324 2023.246 9.94E-05 6000 1.06702 0.00073 0.2989 0.0357 2146.567 0.000109 6300 1.09238 0.00071 0.3139 0.0393 2270.839 0.00012 6750 1.13041 0.00068 0.3363 0.0454 2458.946 0.000138 The curve in Figure 4 is obtained from the equation generated by the curve fit. The smooth curve is an indication of accuracy and it should be used to calculate the other required data. The curve in Figure 6 shows the trend of effective permeability of gas against pressure. As the pressure is increased, the effective permeability of the gas is also increased. The graph trend in Figure 9 shows that error is reduced by 1-15 MMSCF/d. The difference between average IPR and classic IPR is 0.5-7.5 MSCF/d. Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 5011-5015 5014 www.etasr.com Chachar et al.: Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach TABLE VI. FINAL PPF AND FLOW RATE - CLASSIC METHOD P psi Y(Z)S MMpsi 2 /cp ∫ \]S Y(Z)S (Final) MMSCF ^S MMSCF/D 100 0.196978075 6.50266E-05 1.28088E-05 94.05954 300 1.742696934 8.13784E-05 0.00014181 94.04973 600 6.778583051 0.000100002 0.00067787 94.009 900 14.82858679 0.000117101 0.001736445 93.92854 1200 25.52693376 0.000134243 0.003426806 93.80002 1500 38.4846738 0.000152154 0.005855598 93.61529 1800 53.3722675 0.000171361 0.009145922 93.36488 2100 69.85112141 0.000192357 0.013436386 93.03811 2400 87.42029189 0.000215685 0.018855232 92.62498 2700 105.6132162 0.000241992 0.025557541 92.11336 3000 124.1582217 0.000272102 0.03378372 91.48445 3300 142.8181289 0.000307105 0.043860203 90.71261 3600 161.3865833 0.000348495 0.056242486 89.76188 3900 179.8151745 0.000398395 0.071637542 88.57631 4200 197.7524845 0.000459941 0.090954501 87.08307 4500 214.7604013 0.000537981 0.11553694 85.17347 4800 230.77076 0.00064044 0.147794924 82.65125 5100 245.7339194 0.000781243 0.191977821 79.16496 5400 259.6153259 0.000987312 0.256321205 74.01772 5700 272.3926848 0.001318394 0.359120865 65.6006 6000 284.0536412 0.001939033 0.550789526 49.10788 6300 294.5938878 0.003527854 0.811762171 27.12217 6750 308.3105787 0.003211887 0.990258889 0 TABLE VII. PPF AND FLOW RATE - PROPOSED METHOD P (psi) _]S Y(Z)S �MMpsi2/cp) ^S (MMSCF/D) 100 0 3.9E+08 80.29606 300 8.17589E-08 1.41E+08 80.40645 600 6.2078E-08 4.88E+08 80.25238 900 5.69979E-08 9.64E+08 80.04083 1200 5.71385E-08 1.57E+09 79.76904 1500 5.97042E-08 2.33E+09 79.43118 1800 6.4023E-08 3.26E+09 79.01951 2100 6.99885E-08 4.36E+09 78.52535 2400 7.77579E-08 5.66E+09 77.94393 2700 8.76901E-08 7.17E+09 77.26862 3000 1.00368E-07 8.91E+09 76.48462 3300 1.16677E-07 1.09E+10 75.572 3600 1.37967E-07 1.33E+10 74.50349 3900 1.66333E-07 1.61E+10 73.23101 4200 2.05152E-07 1.94E+10 71.71536 4500 2.60132E-07 2.34E+10 69.90629 4800 3.41533E-07 2.82E+10 67.69041 5100 4.69341E-07 3.42E+10 64.87688 5400 6.86896E-07 4.22E+10 61.11419 5700 1.10361E-06 5.35E+10 55.66273 6000 2.0688E-06 7.17E+10 46.58986 6300 5.29607E-06 1.1E+11 25.98219 6750 7.0215E-07 1.45E+11 0 Fig. 1. Pseudopressure function and its derivative vs. time Fig. 2. Integral of gas effective permeability as a function of pressure Fig. 3. Integral of gas effective permeability as a function of pressure extrapolated to zero Fig. 4. Integral of effective permeability versus pressure at assumed pressure points Fig. 5. IPR via classic method Fig. 6. Gas effective permeability vs. pressure Engineering, Technology & Applied Science Research Vol. 9, No. 6, 2019, 5011-5015 5015 www.etasr.com Chachar et al.: Establishing IPR in Gas-Condensate Reservoir: An Alternative Approach TABLE VIII. PROPOSED AND CLASSIC METHOD COMPARISON P (psi) ^S (MMSCF/D) ^S (MMSCF/D) ^S (difference) (MMSCF/D) ^S(avg) (MMSCF/D) 100 94.05954 80.29606 13.76348 87.1778 300 94.04973 80.40645 13.64328 87.22809 600 94.009 80.25238 13.75662 87.13069 900 93.92854 80.04083 13.88771 86.98468 1200 93.80002 79.76904 14.03098 86.78453 1500 93.61529 79.43118 14.18411 86.52323 1800 93.36488 79.01951 14.34537 86.1922 2100 93.03811 78.52535 14.51276 85.78173 2400 92.62498 77.94393 14.68105 85.28445 2700 92.11336 77.26862 14.84475 84.69099 3000 91.48445 76.48462 14.99984 83.98453 3300 90.71261 75.572 15.14061 83.1423 3600 89.76188 74.50349 15.25839 82.13268 3900 88.57631 73.23101 15.3453 80.90366 4200 87.08307 71.71536 15.36771 79.39921 4500 85.17347 69.90629 15.26718 77.53988 4800 82.65125 67.69041 14.96084 75.17083 5100 79.16496 64.87688 14.28808 72.02092 5400 74.01772 61.11419 12.90353 67.56595 5700 65.6006 55.66273 9.937865 60.63167 6000 49.10788 46.58986 2.518028 47.84887 6300 27.12217 25.98219 1.139977 26.55218 6750 0 0 0 0 Fig. 7. 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