一类非线性渗流数学模拟  

MATHEMATICAL SIMULATION OF NONLINEAR FLOW THROUGH POROUS MEDIA

作　　者：邓英尔[1] 刘慈群[2] 王允诚[1] 

机构地区：[1]成都理工学院油气藏地质及开发工程国家重点实验室,四川成都610059 [2]中国科学院渗流流体力学研究所

出　　处：《西南石油学院学报》2001年第1期22-24,共3页Journal of Southwest Petroleum Institute

基　　金：:中国博士后科学基金! (第 2 7批 ) ;"油气藏地质及开发工程"国家重点实验室基金 !(PLC990 1) ;成都理工学院青年科学基金!(2 0

摘　　要：活动边界非线性渗流是现代渗流力学的前沿研究领域之一。在文中建立的低渗透介质非线性渗流数学模型为活动边界非线性模型 ,不能求出其严格解析解 ,因此分别运用平均质量守恒法、数值模拟法求得了其近似解析解、数值解 ,二者吻合得较好 ;并得出了低渗透介质非线性渗流活动边界的运动规律和压力分布特征。结果表明 :起始比降越大 ,则活动边界发展的速度越小 ,压力传播越慢。近似解工程意义明确、分析计算简洁 。A nonlinear flow with a moving boundary is one of up-to-date research fields of modern mechanics of fluids in porous media. A mathematical model of a nonlinear flow through low permeability media with a moving boundary is established, an exact analytical solution of the model can not be presented because of the moving boundary. Not only is a numerical solution derived by a finite difference method, but also an approximate analytical solution is given by using an integral method. It is shown that there is good agreement between them. The law of the moving boundary and characteristics of the pressure distribution are derived. Results show that the larger the starting pressure gradient is, the slower the boundary moves, and the slower the pressure transmits. Both approximate analytical solution and numerical simulation can provide engineering design with theoretical basis. The approximate analytical solution has explicit meaning and simplifies analyses and calculation in engineering. The finite difference method that uses variable steps will provide numerical simulation of the three-dimensional nonlinear flow that has a moving boundary with a good method.

关 键 词：油气田 非线性渗流 活动边界 数学模型 数值模拟 

分 类 号：TE312[石油与天然气工程—油气田开发工程]