Exact solution and its behavior characteristic of nonlinear dual-porosity model

Abstract

A nonlinear dual-porosity model considering a quadratic gradient term is presented. Assuming the pressure difference between matrix and fractures as a primary unknown, to avoid solving the simultaneous system of equations, decoupling of fluid pressures in the blocks from the fractures was furnished with a quasi-steady-state flow in the blocks. Analytical solutions were obtained in a radial flow domain using generalized Hankel transform. The real value cannot be gotten because the analytical solutions were infinite series. The real pressure value was obtained by numerical solving the eigenvalue problem. The change law of pressure was studied while the nonlinear parameters and dual-porosity parameters changed, and the plots of typical curves are given. All these result can be applied in well test analysis.