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.

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

邓英尔^1,2, 刘慈群³

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

收稿日期:2002-06-14 修回日期:2003-05-06 出版日期:2003-10-18 发布日期:2003-10-18
基金资助:
the National Natural Science Foundation of China (40202036); the China National 973 Project (2002CB211700)

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)

摘要/Abstract

摘要： 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.

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.

中图分类号:

TE312

邓英尔;刘慈群. MATHEMATICAL MODEL OF TWO-PHASE FLUID NONLINEAR FLOW IN LOW-PERMEABILITY POROUS MEDIA WITH APPLICATIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(10): 1184-1193.

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

参考文献

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

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

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