对不稳定渗流的数学模型进行了推导,建立了以变流率生产、考虑有效井径影响和3种不同外边界(无穷大、定压、封闭)条件下的分形球向流油气藏的数学模型,先后通过无量纲变换和Laplace变换,再利用变型Bessel函数性质和数学物理方程方法求得在3种不同外边界条件下的Laplace空间储层压力和井底压力的表达式,并分析了分形维数、分形指数和有效井径对储层压力和井底压力的影响.%The paper establishes and discusses the mathematical model of unstable seepage for a fractal oil-gas reservoir, and the model considers the spherical flow and the variable flow rate production and the skin effect and the three kinds of outer boundary conditions (infinite boundary, finite with constant pressure and closed boundary). Successively using the dimensionless transformation, the Laplace transformation, and then according to the properties of Bessel function and the model of Mathematical Physics Equation, the expressions of the reservoir pressures and the wellborn pressures in Laplace space are attained. Effects of the fractal dimension, fractal index and effective wellbore radius are shown in the expressions of the reservoir pressures and the wellborn pressures.
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