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Journal of Applied Mathematics
Volume 2013, Article ID 219218, 8 pages
Research Article

Similar Construction Method of Solution for Solving the Mathematical Model of Fractal Reservoir with Spherical Flow

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu 610500, China
2Institute of Applied Mathematics, Xihua University, Chengdu 610039, China

Received 28 February 2013; Accepted 8 May 2013

Academic Editor: Kazutake Komori

Copyright © 2013 Cui-Cui Sheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.