Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow
Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow
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DOI：
10.1155/2013/219218
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发表时间：
2013-05
期刊：
影响因子：
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通讯作者：
C. Sheng;Jin-Zhou Zhao;Yong-Ming Li;Shunchu Li;H. Jia
中科院分区：
文献类型：
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作者：
C. Sheng;Jin-Zhou Zhao;Yong-Ming Li;Shunchu Li;H. Jia
基于二阶线性微分方程边值问题解的相似结构，分析了这种相似结构与其核函数、微分方程和边界条件的关系，提出了一种新的简单解--相似构造法，并总结了它的具体步骤。建立了三种外边界条件(无限、恒压和闭合)下的多孔介质模型，模型中考虑了分维、球面流动、集肤效应和储存等因素的影响。然后，我们使用SCMS来解决这个问题。SCMS是求解具有复杂边界条件的微分方程边值问题，特别是求解石油工程中的油藏模型的一种直观方法。
On the basis of similar structure of solution for a second-order linear differential equation's boundary value problem, and our analysis of the relationship between this similar structure and its kernel function, the differential equation, and the boundary conditions, we propose a new simple solution—similar constructive method of solution (SCMS)—and sum up its detailed steps. We set up a porous media model under three kinds of outer boundary conditions (infinite, constant pressure, and closed), in which the influences of fractal dimension, spherical flow, skin effect, and storage are taken into consideration. And then we use SCMS to solve it. The SCMS is a straightforward method for differential equation's boundary value problems with complex boundary conditions, especially for solving the reservoir models in petroleum engineering.