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Journal of Chemistry
Volume 2015, Article ID 596597, 8 pages
Research Article

A Mathematical Model for the Analysis of the Pressure Transient Response of Fluid Flow in Fractal Reservoir

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 12 August 2014; Accepted 14 October 2014

Academic Editor: Jianchao Cai

Copyright © 2015 Jin-Zhou Zhao 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.


This study uses similar construction method of solution (SCMS) to solve mathematical models of fluid spherical flow in a fractal reservoir which can avoid the complicated mathematical deduction. The models are presented in three kinds of outer boundary conditions (infinite, constant pressure, and closed). The influence of wellbore storage effect, skin factor, and variable flow rate production is also involved in the inner boundary conditions. The analytical solutions are constructed in the Laplace space and presented in a pattern with one continued fraction—the similar structure of solution. The pattern can bring convenience to well test analysis programming. The mathematical beauty of fractal is that the infinite complexity is formed with relatively simple equations. So the relation of reservoir parameters (wellbore storage effect, the skin factor, fractal dimension, and conductivity index), the formation pressure, and the wellbore pressure can be learnt easily. Type curves of the wellbore pressure and pressure derivative are plotted and analyzed in real domain using the Stehfest numerical invention algorithm. The SCMS and type curves can interpret intuitively transient pressure response of fractal spherical flow reservoir. The results obtained in this study have both theoretical and practical significance in evaluating fluid flow in such a fractal reservoir and embody the convenience of the SCMS.