分形球向流油气藏有效井径模型及其解  

Effective Wellbore Radius Model of Fractal Sphere Seepage Flow for an Oil-gas Reservoir and Its Solution

作　　者：盛翠翠[1] 李顺初[1] 暴喜涛[1] 

机构地区：[1]西华大学应用数学研究所,四川成都610039

出　　处：《西华大学学报（自然科学版）》2011年第5期29-31,37,共4页Journal of Xihua University:Natural Science Edition

基　　金：国家科技重大专项项目(2008ZX50443-14);西华大学重点学科-应用数学(XZD0910-09-1);西华大学创新基金(YCJJ200916)

摘　　要：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.

关 键 词：分形油气藏 球向流 变流率 有效井径 LAPLACE变换 BESSEL函数 

分 类 号：TE353[石油与天然气工程—油气田开发工程]