Abstract: Traditional well-test models for flow are not consistent with the material balance equation. According to the assumption of slightly compressible fluid, the quadratic gradient term in the nonlinear partial differential equation is usually neglected. It is known that neglecting the quadratic gradient term results in errors for large time well-test. A method which is consistent with the material balance equation for fractured reservoir with double porosity/double permeability is proposed. All terms in the nonlinear partial differential equation are retained. Double porosity/double permeability models are given. The numerical solutions of double porosity/double permeability models are obtained by the Douglas-Jones predictor-corrector method at a constant rate and the constant-pressure production for an infinitely large system. It also deals with the change rule of pressure while fluid compressibility and double porosity parameters change. Plots of the typical pressure curves are given, and the results can be applied to the well-test analysis.

Key words: double-permeability models, nonlinear, numerical solution, typical curve plots, well test