MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (10): 1184-1193.

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MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

DENG Ying-er^1,2, LIU Ci-qun³

1. State Key Laboratory of Oil-Gas Reservoir Geology and Development Engineering, Chengdu University of Technology, Chengdu 610059, P. R. China;
2. Department of Energy, Chengdu University of Technology, Chengdu 610059, P. R. China;
3. Institute of Porous Flow and Fluid Mechanics, Chinese Academy of Sciences, Langfang, Hebei 065007, P. R. China

Received:2002-06-14 Revised:2003-05-06 Online:2003-10-18 Published:2003-10-18
Supported by:
the National Natural Science Foundation of China (40202036); the China National 973 Project (2002CB211700)

Abstract

Abstract: A mathematical model of two-phase fluid nonlinear flow in the direction of normal of ellipse through low-permeability porous media was established according to a nonlinear flow law expressed in a continuous function with three parameters, a mass conservation law and a concept of turbulent ellipses. A solution to the model was obtained by using a finite difference method and an extrapolation method. Formulas of calculating development index not only before but also after water breaks through an oil well in the condition of two-phase fluid nonlinear flow in the media were derived. An example was discussed. Water saturation distribution was presented. The moving law of drainage front was found. Laws of change of pressure difference with time were recognized. Results show that there is much difference of water saturation distribution between nonlinear flow and linear flow; that drainage front by water moves faster, water breaks through sooner and the index gets worse because of the nonlinear flow; and that dimensionless pressure difference gets larger at the same dimensionless time and difficulty of oil development becomes bigger by the nonlinear flow. Thus, it is necessary that influence of nonlinear flow on development indexes of the oil fields be taken into account. The results provide water-flooding development of the oil fields with scientific basis.

2010 MSC Number:

TE312

DENG Ying-er;LIU Ci-qun. MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1184-1193.

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References

[1] GUO Shang-ping. Preface[J]. Journal of Chongqing University (Natural Science Edition) ,2000,23(Supp): 1-1. (in Chinese)
[2] LIU Ci-qun. Nonliner flow in media with double-porosity[J]. Chinese Science Bulletin, 1980,(17): 1081-1085. (in Chinese)
[3] CHEN Zhong-xiang, JIANG Li-shang. Exact solutions of equations for flow in double-porosity media[J]. Science in China, 1980,(2):152-165. (in Chinese)
[4] CHEN Zhong-xiang,LIU Ci-qun. Theory of fluid displacement in a medium with double-porosity[J]. Acta Mechanica Sinica, 1980,12(2): 109-119. (in Chinese)
[5] LIU Ci-qun, GUO Shang-ping. Progress in study on flow through multiple-porosity permeability media[J]. Progress in Mechanics, 1982,12(4): 360-364. (in Chinese)
[6] GUO Shang-ping, LIU Ci-qun, YAN Qing-lia, et al. Recent development of mechanics of fluids in porous media[J]. Progress in Mechanics, 1986,16 (4) :441-454. (in Chinese)
[7] KONG Xiang-yan. Advanced Mechanics of Fluids in Porous Media[M]. Hefei: Press of University of Science and Technology of China, 1999,325-326. (in Chinese)
[8] Gorunov A T. Development of Abnormal Oil Fields[M]. ZHANG Shu-bao Transl. Beijing:Petroleum Industry Press, 1987,27-28. (Chinese Version)
[9] Development bureau of China National Petroleum Corporation. Development Techniques of LowPermeability Oil Fields[M]. Beijing: Petroleum Industry Press, 1994,353-354. (in Chinese)
[10] RUAN Min, HE Qiu-xuan. Distinguish of critical point and parameters of non-Darcy flow through low-permeability media[J]. Journal of Xi ' an Petroleum Institute, 1999, 14 (3): 9-10. (in Chinese)
[11] DENG Ying-er, LIU Ci-qun. Numerical simulation of unsteady flow through porous media with moving boundary[A]. In: ZHANG Feng-gan Ed. Proceedings of the Third International Conference on Fluid Mechanics[C]. Beijing: Beijing Institute of Technology Press, 1998,759-765.
[12] DENG Ying-er, LIU Ci-qun. Mathematical model of nonlinear flow law in low-permeability reservoir and its application[J]. Acta Petrolei Sinica,2001,22(4) :72-77. (in Chinese)
[13] Marquart D W. An algorithm for least-squares estimation of nonlinear parameters[J]. J SIAM,1963,11(2) :431-441.
[14] LIU Ci-qun. Two-and three-dimensional flow of mono-phase and two-phase fluid[A]. In:ZHOU Lian-di, SHAO Wei-wen, LU Yu Eds. Proceedings of the Tenth Chinese Conference on Hydrodynamics[C]. Beijing:Ocean Press, 1996,439-445. (in Chinese)
[15] Muskat M. The Flow of Homogeneous Fluids Through Porous Media[M]. New York: McGrawHill, 1937,158-160.
[16] Collins R E. Flow of Fluid Through Porous Materials[M]. CHEN Zhong-xiang,WU Wang-yi Transl. Beijing: Petroleum Industry Press, 1984,158-159. (Chinese Version).

MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS

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