分形球向渗流模型及其相似结构解  

FRACTAL SPHERE SEEPAGE FLOW MODEL AND ITS SIMILAR STRUCTURE SOLUTION

作　　者：盛翠翠[1] 李顺初[1] 李伟[1,2] 王俊超 何亚锐[3] 

机构地区：[1]西华大学应用数学研究所 [2]西南石油大学油气藏地质与开发工程国家重点实验室 [3]西南油气田分公司采气工程研究院

出　　处：《钻采工艺》2011年第4期35-38,3,共4页Drilling & Production Technology

基　　金：国家科技重大专项项目(编号:2008ZX50443-14);西华大学重点学科-应用数学(编号:ZX00910-09-1);西华大学创新基金(编号:YCJJ200916)

摘　　要：针对分形球向流油藏,将有效井径引入到内边界条件中,避免了直接考虑表皮效应和真实井径模型带来的求解难的问题,建立了以井底定产量生产、考虑井筒储集、表皮效应、二次梯度项的影响和三种外边界(无穷大、定压、封闭)条件下的不稳定球向渗流模型;通过线性化处理和Laplace变换将该渗流模型转化成常微分方程定解问题,再利用Bessel函数性质,得到了线性化后模型的Laplace空间精确解;经分析、整理发现在三种不同外边界条件下该类油藏的精确解之间具有相似结构,并作了进一步的讨论。这项研究,不仅为石油工作者编制试井分析软件和提高计算效率带来简便,也为非均质球向流油藏的非线性渗流问题研究奠定了基础。Aiming at the spherical seepage flow reservoir,the effective well diameter was introduced into inner boundary condition in this paper,avoided the difficulty of solving the equation caused by directly considering the real well diameter with skin effect,and the unstable spherical seepage flow model was established which took into account the wellbore storage,skin effect and the quadratic gradient term,and three outer boundary conditions(infinite,constant pressure and closed).Then the model was transformed into ordinary differential equation problem by linearization and Laplace transform.Then using Bessel function properties,the exact solutions in Laplace space were got.After systematic analysis and arrangement,it was discovered that there were similar structures between exact solutions under three different outer boundary conditions,and the further study has been done.This study was not only of great convenience to petroleum workers for programming well test analysis software and improving computational efficiency,but also laid a foundation for studying the non-homogeneity spherical nonlinear seepage flow problems.

关 键 词：分形油藏 球向流 井筒储集 有效井径 二次梯度项 相似结构 核函数 

分 类 号：TE353[石油与天然气工程—油气田开发工程]