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Mathematical Problems in Engineering
Volume 2015, Article ID 275057, 12 pages
http://dx.doi.org/10.1155/2015/275057
Research Article

Numerical Investigations of the Effect of Nonlinear Quadratic Pressure Gradient Term on a Moving Boundary Problem of Radial Flow in Low-Permeable Reservoirs with Threshold Pressure Gradient

1School of Petroleum Engineering, China University of Petroleum (Huadong), Qingdao 266580, China
2Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

Received 11 May 2014; Revised 18 July 2014; Accepted 18 July 2014

Academic Editor: Jun Liu

Copyright © 2015 Wenchao Liu and Jun Yao. 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.

Abstract

The existence of a TPG can generate a relatively high pressure gradient in the process of fluid flow in porous media in low-permeable reservoirs, and neglecting the QPGTs in the governing equations, by assuming a small pressure gradient for such a problem, can cause a significant error in predicting the formation pressure. Based on these concerns, in consideration of the QPGT, a moving boundary model of radial flow in low-permeable reservoirs with the TPG for the case of a constant flow rate at the inner boundary is constructed. Due to strong nonlinearity of the mathematical model, a numerical method is presented: the system of partial differential equations for the moving boundary problem is first transformed equivalently into a closed system of partial differential equations with fixed boundary conditions by a spatial coordinate transformation method; and then a stable, fully implicit finite difference method is used to obtain its numerical solution. Numerical result analysis shows that the mathematical models of radial flow in low-permeable reservoirs with TPG must take the QPGT into account in their governing equations, which is more important than those of Darcy’s flow; the sensitive effects of the QPGT for the radial flow model do not change with an increase of the dimensionless TPG.