Nonlinear flow numerical simulation of low-permeability reservoir

Abstract

A nonlinear flow reservoir mathematical model was established based on the flow characteristic of low-permeability reservoir. The well-grid equations were deduced and the dimensionless permeability coefficient was introduced to describe the permeability variation of nonlinear flow. The nonlinear flow numerical simulation program was compiled based on black-oil model. A quarter of five-spot well unit was simulated to study the effect of nonlinear flow on the exploitation of low-permeability reservoir. The comprehensive comparison and analysis of the simulation results of Darcy flow, quasi-linear flow and nonlinear flow were provided. The dimensionless permeability coefficient distribution was gained to describe the nonlinear flow degree. The result shows that compared with the results of Darcy flow, when considering nonlinear flow, the oil production is low, and production decline is rapid. The fluid flow in reservoir consumes more driving energy, which reduces the water flooding efficiency. Darcy flow model overstates the reservoir flow capability, and quasi-linear flow model overstates the reservoir flow resistance. The flow ability of the formation near the well and artificial fracture is strong while the flow ability of the formation far away from the main streamline is weak. The nonlinear flow area is much larger than that of quasi-linear flow during the fluid flow in low-permeability reservoir. The water propelling speed of nonlinear flow is greatly slower than that of Darcy flow in the vertical direction of artificial fracture, and the nonlinear flow should be taken into account in the well pattern arrangement of low-permeability reservoir.

Keywords

low-permeability reservoir / nonlinear flow / mathematical model / numerical simulation

References

[1] KingF. H.Principles and conditions of the movements of ground water [R], 1899WashingtonGovernment Printing Office59

[2] FandR. M., KimB. Y. K., LamA. C. C., PhanR. T.. Resistance to the flow of fluids through simple and complex porous media whose matrices are composed of randomly packed spheres [J]. Journal of Fluids Engineering, 1987, 109(3): 268-273

[3] LiuS.-j., MasliyahJ. H.. Single fluid flow in porous media [J]. Chemical Engineering Communications, 1996, 148(1): 653-732

[4] BasakP.. Non-Darcy flow and its implications to seepage problems [J]. Journal of the Irrigation and Drainage Division, 1977, 103(4): 459-473

[5] MillerR. J., LowP. F.. Threshold gradient for water flow in clay systems [J]. Soil Science Society of American Journal, 1963, 27(6): 605-609

[6] NeuzilC. E.. Ground water flow in low-permeability environments [J]. Water Resources Research, 1986, 22(8): 1163-1195

[7] YanQ.-l., HeQ.-x., WeiL.-g., QuZ., RenX.-juan.. A laboratory study on percolation characteristics of single phase flow in low-permeability reservoirs [J]. Journal of Xi’an Shiyou University, 1990, 5(2): 1-6

[8] LiD.-pin.The development of the low-permeability sandstone oil field [M], 1997BeijingPetroleum Industry Press114-152

[9] TAHERI A, SAJJADIAN V A. WAG performance in a low porosity and low-permeability reservoir, Sirri-A field, Iran [C]// SPE Asia Pacific Oil & Gas Conference and Exhibition. Adelaide, Australia: 2006, SPE 100212.

[10] YangX.-l., HuangFu.. Influence of strain softening and seepage on elastic and plastic solutions of circular opening in nonlinear rock masses [J]. Journal of Central South University of Technology, 2010, 17(3): 621-627

[11] LEI Qun, XIONG Wei, YUAN Jiang-ru, GAO Shu-sheng, WU Yu-shu. Behavior of flow through low-permeability reservoirs [C]// Europe/EAGE Conference and Exhibition. Rome, Italy: 2008, SPE 113144.

[12] LIU Shun, HAN Feng-rui, ZHANG Kai, TANG Ze-wei. Well test interpretation model on power-law non-linear percolation pattern in low-permeability reservoir [C]// International Oil and Gas Conference and Exhibition in China. Beijing, China: 2010, SPE 132271.

[13] BLASINGAME T A. The characteristics flow behavior of low-permeability reservoir systems [C]// SPE Unconventional Reservoirs Conference. Keystone, Colorado, USA: 2008, SPE 114168.

[14] ShiY., YangZ.-m., HuangY.-zhang.. Study on non-linear seepage flow model for low-permeability reservoir [J]. Acta Petrolei Sinica, 2009, 30(5): 731-734

[15] HuangY.-zhang.Seepage mechanism in low-permeability reservoir [M], 1993BeijingPetroleum Industry Press80-101

[16] XiongW., LeiQ., LiuX.-g., GaoS.-s., HuZ.-m., XueHui.. Pseudo threshold pressure gradient to flow for low permeability reservoirs [J]. Petroleum Exploration and Development, 2009, 36(2): 232-235

[17] JiB.-y., WangC.-y., LiL., HeY.-fu.. Calculation method for production rate of rectangular well pattern and fracturing integration production mode in low-permeability reservoir [J]. Acta Petrolei Sinica, 2009, 30(4): 578-572

[18] ChengS.-q., HanH.-bao.. Numerical simulation of two-dimensional two-phase slow flow [J]. Petroleum Exploration and Development, 1998, 25(1): 41-43

[19] HanH.-b., ChengS.-qing.. Physical simulation and numerical simulation of ultra-low permeability reservoir in consideration of starting pressure gradient [J]. Journal of University of Petroleum, 2004, 28(6): 49-53

[20] ZhaoG.-zhong.. Numerical simulation of 3D and three-phase flow with variable start-up pressure gradient [J]. Acta Petrolei Sinica, 2006, 27(1): 119-128

[21] YuanY.-r., HanY.-ji.. Numerical simulation and application of three-dimensional oil resources migration-accumulation of fluid dynamics in porous media [J]. Science in China Series G: Physics Mechanics and Astronomy, 2008, 51(8): 1144-1163

[22] YangZ.-m., YuR.-z., SuZ.-x., ZhangY.-f., CuiD.-yong.. Numerical simulation of the nonlinear flow in ultra-low permeability reservoirs [J]. Petroleum Exploration and Development, 2010, 37(1): 94-98

[23] LongTeng.Development of numerical simulation system for non-Darcy flow in low-permeability reservoir [D], 2005BeijingTsinghua University Department of Hydraulic and Hydropower Engineering