A nonlinear dual-porosity model

Abstract

A nonlinear dual-porosity formulation incorporating a quadratic gradient term in the governing flow equation is presented. To avoid solving the simultaneous system of equations, decoupling of fluid pressures in the matrix from the fractures is furnished by assuming a quasi-steady-state flow in the matrix with the pressure difference between matrix and fractures as a primary unknown. The nonlinear fracture flow equation is linearized using the function transformation currently adopted in the nonlinear single-porosity formulation. Analytical solutions are obtained in a radial flow domain using the Hankel transform. Both solution accuracy and efficiency are achieved by using an optimized algorithm when solving the inherent Bessel functions. The study indicates that the intensity of the dual-porosity effect is strongly conditioned by the magnitude of the initial pressure difference between matrix and fracture phases. The model presented appears to be suitable for simulating naturally fractured reservoirs subjected to high injection or production rate, or to significant fracture compressibility.