Exact Solution of Pressure Transient Model for Fluid Flow in Fractal Reservoir Including a Quadratic Gradient Term

Abstract

The models of the nonlinear radial flow for the finite fractal reservoirs including a quadratic gradient term are presented. Generalized orthogonal transform is given by using the orthogonality of eigenfunction. We give the exact solution in real space for flow equation including quadratic gradient term for both constant-rate and constant-pressure production cases from in a finite system by using generalized orthogonal transform. Both closed and constant pressure outer boundary conditions are considered. Moreover, the difference between the nonlinear pressure solution and linear pressure solution is analyzed, and the difference may be reached about 10% in the long time. The effect of the quadratic gradient term in the large time well test may be considered.