分形球向流油气藏模型及其解  

Fractal Sphere Seepage Flow Oil-gas Reservoir Model and its Solution

作　　者：盛翠翠[1] 李顺初[1] 许东旭[1] 

机构地区：[1]西华大学应用数学研究所,四川成都610039

出　　处：《天然气与石油》2011年第6期55-58,3,共4页Natural Gas and Oil

基　　金：国家科技重大专项项目(2008ZX50443-14);西华大学应用数学重点学科资助项目(XZD0910-09-1);西华大学创新基金(YCJJ201118)

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和考虑表皮效应影响的分形球向流油气藏的数学模型,利用Laplace变换、变型Bessel函数性质和数学物理方程方法求得在三种不同外边界(无穷大、定压、封闭)条件下的Laplace空间储层压力和井底压力的表达式,分析了分形维数、分型指数和表皮效应对储层压力和井底压力的影响。对研究分形球向流油气藏的试井分析和研究其渗流规律具有重要意义。Established and discussed is the mathematical model for unstable seepage flow for fractal oil and gas reservoir with spherical flow and variable flow rate production and the skin effect.Obtained are the expressions of Laplace space reservoir pressure and bottom hole pressure in three kinds of outer boundary(infinite boundary,constant pressure and closed boundary) conditions by using Laplace transformation,properties of Bessel function and the model of Mathematical Physics Equation and analyzed are influences of fractal dimension,fractal index and skin effect on space reservoir pressure and bottom hole pressure,which are very important for studies on well test analysis of fractal oil and gas reservoir with spherical flow and its seepage flow rules.

关 键 词：分形油气藏 球向流 表皮效应 LAPLACE变换 

分 类 号：P618.13[天文地球—矿床学]