均质油藏非线性渗流模型解的相似构造法  

Similar Constructive Method of Solutions of Nonlinear Seepage Model for Homogeneous Reservoir

作　　者：暴喜涛[1] 李顺初[1] 肖绪霞[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》2012年第5期47-51,108,共5页Natural Gas and Oil

基　　金：国家科技重大专项(2008ZX50443-14);四川省教育厅重点项目(12ZA164);西华大学创新基金(YCJJ201229)

摘　　要：根据油气藏渗流理论,针对均质油藏非线性渗流问题,建立了考虑二次压力梯度项、井筒储集、有效井径和封闭、定压、无穷大三种外边界条件下的渗流模型,通过变量替换将其线性化,利用Laplace空间变换得到渗流模型在Laplace空间中相对应的零阶变型Bessel方程边值问题,验证了该类边值问题的解具有相似结构,提出求解该类边值问题的新方法——相似构造法,利用该方法求解出渗流模型在Laplace空间中的无因次储层压力和无因次井底压力。相似构造法是求解该类模型简捷有效的新方法,极大地提高了求解该类模型的效率,该方法提出的构造性步骤也为试井分析软件提供了算法流程,易被工程技术人员掌握并应用于实际工程领域。Based on reservoir seepage theory,in view of nonlinear seepage in homogeneous reservoir,established is a seepage model in secondary pressure gradient,bottom hole storage,effective radius and three types of external boundary conditions which include the closed boundary,constant pressure boundary and infinity boundary. The seepage model is linearized through variable substitution. Obtained is the boundary value problem of zero order modification Bessel equation by utilization of Laplace space transformation,which is corresponding to the seepage model in Laplace space. It is proved that solutions of this kind of boundary value problem have similar structures and proposed is a new method—similar constructive method. By this method,the seepage model’s dimensionless reservoir pressure and dimensionless bottom hole pressure in Laplace space are obtained consequently. The similar constructive method is a new method for solving this type of seepage model easily and feasibly

关 键 词：非线性渗流 二次压力梯度 井筒储集 有效井径 变型Bessel方程 相似构造法 相似核函数 

分 类 号：TE31[石油与天然气工程—油气田开发工程]