Applicability Exploration of Superposition Principle for Pressure Transient Analysis in Polymer-flooding System

doi:10.19596/j.cnki.1001-246x.8262

Abstract

Abstract:

A mathematical model for pressure transient analysis in polymer-flooding system was established, in which the shear thinning effect of non-Newtonian polymer solution is considered. The governing equations were discretized by finite volume method with a hybrid grid consisting of Cartesian meshes with radial refinement around well positions. The shut-in pressures from numerical solution were compared with those obtained with the superposition principle method. It shows that shut-in bottom-hole pressure computed with superposition principle method is much lower than the numerical result for polymer-flooding system, which indicating that the superposition principle cannot be used for pressure transient analysis in polymer-flooding system. Shut-in pressure data of an injection well in a polymer-flooding system was interpreted. It is found that the permeability obtained with superposition principle method is very small, which shows that the superposition principle method cannot be used to solve the nonlinear model for pressure transient analysis in polymer-flooding system. The numerical method is more suitable for polymer-flooding system. The conclusions are applicable to similar nonlinear problems in pressure transient analysis.

Key words: polymer-flooding, non-Newtonian fluid, superposition principle, numerical solution, shut-in pressure drawdown

CLC Number:

TE357

Jia ZHANG, Shiqing CHENG, Yang ZENG, Man ZHANG, Haiyang YU. Applicability Exploration of Superposition Principle for Pressure Transient Analysis in Polymer-flooding System[J]. Chinese Journal of Computational Physics, 2021, 38(3): 324-332.

Figures/Tables 10

Fig.1 Polymer solution viscosity at different polymer concentration and shear rate

Fig.2 Hybrid grid consisting of Cartesian meshes with radial refinement around well positions

Fig.3 Schematic of shut-in pressure drawdown testing of an injection well and superposition principle (a) injecting and shut-in procedure of a polymer injection well; (b) superposition principle and virtual production well

Fig.4 Polymer solution viscosity distributions at different (a) injection time and (b) flooding rate

Table 1 Basic parameters of the reservoir

基础参数	值
初始地层压力/MPa	20
注聚浓度/(g·L^-1)	0.5
井筒半径/m	0.1
井储系数/(m³·MPa^-1)	0.1
表皮系数	0.1
渗透率/μm²	0.1
孔隙度	0.3
岩石压缩系数/MPa^-1	0.001
初始含水饱和度	0.5
初始含油饱和度	0.5
原油黏度/(mPa·s)	0.9
原油压缩系数/MPa^-1	0.001
原油体积系数	0.9
水黏度/(mPa·s)	0.9
水压缩系数/MPa^-1	0.000 2
水体积系数	1

Fig.5 Relative permeability curves

Fig.6 Shut-in pressure curves of an injection well in numerical solution and superposition principle method

Fig.7 Shut-in pressure curves of an injection well in composite model and homogeneous model

Fig.8 Matching examples with (a) numerical method and (b) superposition principle method

Table 2 Interpretation results of pressure drawdown well testing

	井储系数/(m³·MPa^-1)	表皮系数	复合半径/m	内区渗透率/(10^-3μm²)	外区渗透率/(10^-3μm²)
数值解	0.34	-3.10	15.20	15.25	1.01
叠加原理	0.31	-1.50	15.06	5.12	0.71

References 26

1	KAZEMI H. Pressure transient analysis of naturally fractured reservoirs[J]. Journal of Petroleum Technology, 1968, 20 (9): 989- &.
2	FANG S D, CHENG L S, XIN Y N, et al. Linear element method for multi-angle fractured horizontal well in anisotropic reservoir[J]. Chinese Journal of Computational Physics, 2015, 32 (5): 595- 602.
3	SETH P, MANCHANDA R, ZHENG S, et al. Poroelastic pressure transient analysis: A new method for interpretation of pressure communication between wells during hydraulic fracturing[C]. SPE Hydraulic Fracturing Technology Conference and Exhibition, Society of Petroleum Engineers, 2019.
4	DING M C, WU M L, LI X, et al. Characteristics of transient pressure for multiple fractured horizontal wells in fractal fractured shale gas reservoirs[J]. Chinese Journal of Computational Physics, 2019, 36 (5): 559- 568.
5	JI A Z, WANG Y F, ZHANG G S. Transient pressure for a fractured well with asymmetric fracture[J]. Chinese Journal of Computational Physics, 2019, 36 (1): 47- 52.
6	AFAGWU C, ABUBAKAR I, KALAM S, et al. Pressure-transient analysis in shale gas reservoirs: A review[J]. Journal of Natural Gas Science and Engineering, 2020, 103319.
7	KONWAR L, ALOWAINATI E, NEMMAWI N, et al. Understanding Mauddud waterflood performance in a heterogeneous carbonate reservoir with surveillance data and ensemble of analytical tools[C]. Abu Dhabi International Petroleum Exhibition & Conference, Society of Petroleum Engineers, 2020.
8	XU Y D. An interpretation method with "well-cave-crack" model of dissolves reservoir considering gravity factors[J]. Chinese Journal of Computational Physics, 2020, 37 (2): 189- 197.
9	POOLLEN H K V, JARGON J R. Steady-state and unsteady-state flow of non-Newtonian fluids through porous media[J]. Society of Petroleum Engineers Journal, 1969, 9 (1): 80- 88. DOI
10	IKOKU C U. Transient flow of non-Newtonian power-law fluids in porous media[J]. Society of Petroleum Engineers Journal, 1979, 19 (3): 164- 174. DOI
11	ODEH A S, YANG H T. Flow of non-Newtonian power law fluids through porous media[J]. Society of Petroleum Engineers Journal, 1979, 19 (3): 155- 163. DOI
12	LUND O, IKOKU C U. Pressure transient behavior of non-Newtonian/Newtonian fluid composite reservoirs[J]. SPE Journal, 1981, 21 (2): 271- 280.
13	VONGVUTHIPORNCHAI S, RAGHAVAN R. Well test analysis of data dominated by storage and skin: Non-Newtonian power-law fluids[J]. SPE Formation Evaluation, 1987, 2 (4): 618- 628. DOI
14	MAHANI H, SOROP T, VAN DEN HOEK P, et al. Injection fall-off analysis of polymer flooding EOR[C]. SPE Reservoir Characterisation and Simulation Conference and Exhibition, Society of Petroleum Engineers, 2011.
15	刘明明. 基于分形理论的聚合物驱试井分析[D]. 东营: 中国石油大学(华东), 2015.
16	贾智淳. 全隐式化学驱油藏教值模拟研究[D]. 合肥: 中国科学技术大学, 2016.
17	KAMAL M, TIAN C, SULEEN S. Use of transient tests to monitor progress of flooding in IOR/EOR operations[C]. SPE Technical Conference and Exhibition, 2016.
18	朱常玉, 程时清, 唐恩高, 等. 聚驱后水驱的试井解释方法[J]. 油气井测试, 2017, 26 (3): 15- 18. DOI
19	OMOSEBI O A, AKABOGU A K. Application of the Galerkin's finite element method to the flow of power-law non-Newtonian fluids through porous media[C]. SPE Western Regional Meeting, 2017.
20	刘文涛, 张德富, 程宏杰, 等. 聚合物驱牛顿-非牛顿-牛顿三区复合试井模型[J]. 油气藏评价与开发, 2019, 9 (4): 26- 30.
21	METER D M, BIRD R B. Tube flow of non-Newtonian polymer solutions PART I: Laminar flow and rheological models[J]. Aiche Journal, 1964, 10 (6): 878- 881. DOI
22	GUO W, CHENG J, YAO Y, et al. Commercial pilot test of polymer flooding in Daqing oil field[C]. SPE/DOE Improved Oil Recovery Symposium, Society of Petroleum Engineers, 2000.
23	方道斌, 聂贵权. 水解聚丙烯酰胺盐水溶液表观黏度的数学模拟(III)——表观黏度与剪切速率的通用关系式[J]. 化工学报, 1997, 48 (1): 80- 84.
24	PEACEMAN D W. Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability[J]. Society of Petroleum Engineers Journal, 1983, 23 (3): 531- 543. DOI
25	LIE K A. An introduction to reservoir simulation using MATLAB/GNU Octave: User guide for the MATLAB reservoir simulation toolbox (MRST)[M]. Cambridge University Press, 2019.
26	LIE K A, KROGSTAD S, LIGAARDEN I S, et al. Open-source MATLAB implementation of consistent discretisations on complex grids[J]. Computational Geosciences, 2012, 16 (2): 297- 322. DOI

[1]	XIE Chiyu, ZHANG Jianying, WANG Moran. Lattice Boltzmann Modeling of Non-Newtonian Multiphase Fluid Displacement [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(2): 147-155.
[2]	LI Junjian, JIANG Hanqiao, LIU Tongjing. Tracer Transport in Intraformational Water Channeling Reservoir [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 27(1): 45-50.
[3]	HOU Yingmin, TONG Dengke, ZHANG Huaqing. Dynamic Characteristics of Nonsteady Flows with Phase Redistribution in Double Porous Media and Fractal Reservoir [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(6): 865-871.
[4]	XU Kan, LIU Minghou, LIU Dong, CHEN Yiliang. Simulation of Multiphase Flows in Microscale Hemodialysis [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 26(1): 49-56.
[5]	ZHANG Xiao-guang, YANG Bo-jun, YU Zhong-yuan. Discussion on the Choice of the Fourier Transformation Form in Numerical Solutions of Nonlinear Schrödinger Equation [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 20(3): 267-272.
[6]	HU Zhan, JIN Ming-xing, LIU Hang, ZHANG Lin-iin, DING Da-jun. Application of a Simple Calculation Method of Ion Optical System to Reflectron Time-of-flight Mass Spectrometer [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 20(1): 44-50.
[7]	TONG Deng-ke, CAI Lang-lang. DYNAMICAL CHARACTERISTICS OF DOUBLE POROSITY/DOUBLE PERMEABILITY MODEL INCLUDING THE EFFECT OF QUADRATIC GRADIENT TERM [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2002, 19(2): 177-182.
[8]	Li Guangzheng. NUMERICAL INVESTIGATION OF NATURAL CONVECTION FOR NON-NEWTONIAN FLUIDS OVER A VERTICAL FLAT PLATE [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1998, 15(1): 19-28.
[9]	Wang Baoguo, Wangdong, Wu Honge. NUMERICAL SIMULATION OF OLDROYD B FLUID FLOWS THROUGH ABRUPT CONTRACTIONS [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1997, 14(2): 171-178.
[10]	Feng Tinggui, Lai Dongxian. A SIMPLIFIED NUMERICAL METHOD fOR CALCULATING 3-D RADIATION FIELD OF CAVITY [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1996, 13(1): 50-56.
[11]	Long Yongxing. THE SOLUTION OF SINGULAR BOUNDARY VALUE PROBLEMS IN TEARING MODE [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1995, 12(4): 541-546.
[12]	Duan Qing sheng, Qin Cheng sen. NUMERICAL SOLUTION FOR CRITICAL PARAMETER OF THERMAL EXPLOSION [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 11(2): 219-224.
[13]	Zhang Yuwen, Chen Zhongqi, Wang Qijie, Wu Qingjin. NUMERICAL SOLUTION OF MELTING IN A RECTANGULAR ENCLOSURE WITH DISCRETE HEAT SOURCES [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1994, 11(1): 9-16.
[14]	Niu Zhongrong. INTERPOLATING MATRIX METHOD FOR MULTI-POINT BVPS AND ITS ERROR ANALYSIS [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1993, 10(3): 336-344.
[15]	Lü Tongxing, Wang Xiaohong. A NUMERICAL SOLUTION OF THE MATRIX EQUATION AXB-CXD=E [J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 1992, 9(4): 451-454.