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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