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结合分形理论与渗流理论 ,对分形油藏非牛顿幂律流体低速非达西不稳定渗流的试井分析问题的数学模型进行了推导 .该分形油藏模型由内域为非牛顿幂律流体低速非达西渗流 ,外域为非牛顿幂律流体达西渗流的同心圆域组成 .在考虑井筒储存、表皮效应影响下 ,建立了该油藏的不稳定渗流有效井径组合数学模型 ,在 3种外边界条件下求出了两个区域内压力在Laplace空间的解析解 ,应用Stehfest数值反演方法求得井底的无因次压力 ,分析了井底压力动态特征和参数影响 .非牛顿幂律流体的幂律指数、分形参数均对典型曲线产生较大的影响 ,呈现出与牛顿流体和均质油藏明显不同的特征 .这对非均质油藏非牛顿流体的不稳定试井分析及研究其非线性渗流特征均十分重要
Combining the fractal theory and seepage theory, the mathematic model of well test analysis for non-Darcy non-Darcy unsteady seepage flow in fractal reservoirs is deduced.The fractal reservoir model consists of a non-Newtonian power-law fluid Non-Darcy seepage and the outdomain is composed of concentric domains of non-Newtonian power-law fluid Darcy seepage.Under the influence of wellbore storage and skin effect, the mathematical model of combined effective well diameter of unstable seepage in this reservoir is established, The analytic solution of pressure in Laplace space is obtained under the outer boundary conditions. The dimensionless back pressure is calculated by Stehfest numerical inversion method, and the dynamic characteristics of borehole pressure and the influence of parameters are analyzed. Non-Newton power law The power law index and the fractal parameters all have a great influence on the typical curves, showing obviously different characteristics from Newtonian fluids and homogeneous reservoirs.This paper analyzes the unstable well test of non-Newtonian fluids in heterogeneous reservoirs and It is very important to study the nonlinear flow characteristics