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. (26th March 2015)

• Record Type: Journal Article
• Authors: Liu, Wenchao; Yao, Jun
• Other Names: Liu Jun Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2015(2015)
• Publication Date: 2015-03-26
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2015/275057
• Languages: English
• ISSNs: 1024-123X

Abstract

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.