Mathematical Simulation of Instability Phenomena as a Compositional Model during Oil Recovery Process

Mathematical models of petroleum reservoirs have been utilized since the late 1800s. A mathematical model consists of a set of equations that describe the flow of fluids in a petroleum reservoir. In this paper the applicability and effectiveness of a novel iterative method as a semi-analytical method is shown for solution of partial differential equation that model porous medium. This nonlinear partial differential equation describing instability phenomenon of two immiscible fluids (water and oil) flow through homogeneous porous cylindrical medium with impervious bounding surfaces on three sides of an oil reservoir. This method applied to a porous medium equation arising in instability phenomena in double phase flow through porous media. Furthermore, this technique is utilized to find closed-form solutions for the problem under consideration with appropriate initial/boundary conditions.