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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 405640, 8 pages
Research Article

A Pressure Transient Model for Power-Law Fluids in Porous Media Embedded with a Tree-Shaped Fractal Network

1State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Xindu Road 8, Chengdu 610500, China
2Shell China Exploration & Production Co. Ltd., 8F Yanlord Landmark Office Building, No. 1, Section 2, Renmin South Road, Chengdu 610500, China

Received 4 November 2013; Accepted 14 January 2014; Published 24 February 2014

Academic Editor: Hai Yu

Copyright © 2014 Xiao-Hua Tan 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 work studies the pressure transient of power-law fluids in porous media embedded with a tree-shaped fractal network. A pressure transient model was created based on the fractal properties of tree-shaped capillaries, generalized Darcy’s law and constitutive equation for power-law fluids. The dimensionless pressure model was developed using the Laplace transform and Stehfest numerical inversion method. According to the model’s solution, the bi-logarithmic type curves of power-law fluids in porous media embedded with a tree-shaped fractal network are illustrated. The influences of different fractal factors and Power-law fluids parameters on pressure transient responses are discussed.