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

Abstract

The well testing model of nonlinear spherical percolation problems for composite reservoir is established under three different outer boundary conditions: closed boundary,constast pressure boundary,infinity boundary. the mathematical model are linearized by using variable substitution method, and then its solutions are derived by Laplace transform. According to the theory of similar structure of solutions to the differential equations, we obtain the similar structure of the solutions .The theory of similar structure is beneficial to understand the inherent laws of solutions and analyze the influence of parameters to solutions.

A Study on Solving the Seepage Flow Model of Three-Area Composite Reservoir

“…A similar structure of the solution was discovered by analyzing the percolation characteristics of fractal composite reservoir under three kinds of outer boundary conditions. By analyzing the solution of the reservoir pressure and dimensionless reservoir pressure distribution in Laplace space, [7] and [8] discovered the similar structure of the solution of the composite reservoir under the three kinds of outer boundary conditions. Furthermore, they made the theoretical graph and analyzed the impact of the well-bore storage and skin factor on dimensionless reservoir pressure and dimensionless bottom-hole pressure by using the numerical inversion.…”