Abstract

Abundant experimental and theoretical analyses have demonstrated that the fluid flow in low-permeable reservoirs and the Bingham non-Newtonian fluid flow in heavy oil reservoirs do not obey the conventional Darcy’s law; there exists a threshold pressure gradient or the yield stress.That is, the fluid flow happens only if the formation pressure gradient exceeds the threshold pressure gradient, or the shear stress for the fluid is larger than the yield stress. This petrophysical phenomena is academically called modified Darcy’s law (Prada and Civan, 1999)

Due to the existence of threshold pressure gradient in modified Darcy’s law, the resulting mathematical model for this physics, in which well testing and reservoir numerical simulation technology for unconventional reservoirs involve, belongs to moving boundary problems. For these problems, approximate analytical solution and numerical solution methods are the main research methodologies. In this article, the mathematical model is established, numerical solution are provided.