Similar Constructive Method of Solution for the Model of Nonlinear Spherical Seepage in Composite Reservoir

Abstract

The nonlinear spherical seepage flow model has been established for the composite reservoir model. The nonlinear spherical seepage flow model considers the well produce at a constant rate, and the quadratic gradient term under three outer boundary conditions (closed, constant pressure and infinite). Firstly, through variable substitutions, the seepage flow equation is linearized; then the model is transformed into the boundary value problem of an ordinary differential equation by employing the Laplace transform method. It has been confirmed that the Laplace space analytic solutions of such boundary value problems has a formula under different external boundaries, using the Similar Constructive Method(it is a simple and effective new idea for solving this class seepage flow model, complicated calculus calculation is avoided). The prospect of this new method is promising for understanding and studying the inherent laws of fluids flow.