Mathematical Model of Two-Phase Fluid Nonlinear Flow in Low-Permeability Porous Media With Applications
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摘要: 基于三参数非线性渗流运动定律、质量守恒定律及椭圆渗流的概念,建立了低渗透介质中两相流体椭圆非线性渗流数学模型,运用有限差分法与外推法求得了其解,导出了两相流体椭圆非线性渗流条件下油井见水前后开发指标的计算公式,进行了实例分析。结果表明:非线性渗流对含水饱和度分布影响较大;非线性渗流使得水驱油推进速度比线性渗流的快,使油井见水时间提前,使得石油开发指标变差;非线性渗流使得同一时刻的压差比线性渗流的大,使石油开发难度加大。这为低渗油藏垂直裂缝井开发工程提供了科学依据。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 tur-bulent 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.
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Key words:
- low permeability /
- porous media /
- two-phase fluid /
- nonlinear flow /
- finite difference method /
- extrapolation method
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[1] 郭尚平.序.重庆大学学报[J],2000,23(增刊):1-1. [2] 刘慈群.双重介质非线性渗流[J].科学通报,1980,(17):1081-1085. [3] 陈钟祥,姜礼尚.双重孔隙介质渗流方程组的精确解[J].中国科学,1980,(2):152-165. [4] 陈钟祥,刘慈群.双重孔隙介质二相驱替理论[J].力学学报,1980,12(2):109-119. [5] 刘慈群,郭尚平.多重介质渗流研究进展[J].力学进展,1982,12(4):360-364. [6] 郭尚平,刘慈群,阎庆来,等.渗流力学的新发展[J].力学进展,1986,16(4):441-454. [7] 孔祥言.高等渗流力学[M].合肥:中国科技大学出版社,1999,325-326. [8] ГорьуновАТ.异常油田开发[M].张树宝译.北京:石油工业出版社.1987:27-28. [9] 中国石油天然气总公司开发生产局.低渗透油田开发技术[M].北京:石油工业出版社,1994,353-354. [10] 阮敏,何秋轩.低渗非达西渗流临界点及临界参数判别法[J].西安石油学院学报,1999,14(3):9-10. [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] 邓英尔,刘慈群.低渗油藏非线性渗流规律数学模型及其应用[J].石油学报,2001,22(4):72-77. [13] Marquart D W. An algorithm for least-squares estimation of nonlinear parameters[J]. J SIAM, 1963,11(2) :431-441. [14] 刘慈群.单相和两相流体多维渗流问题[A].见:周连第,邵维文,陆煜编.第十届全国水动力学学术会议论文集[C].北京:海洋出版社,1996,439-445. [15] Muskat M. The Flow of Homogeneous Fluids Through Porous Media [M]. New York: McGrawHill, 1937,158-160. [16] Collins R E.流体通过多孔材料的流动[M].陈钟祥,吴望一译.北京:石油工业出版社,1984,158-159. -
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