Investigation of Stokes flow on multi particles for prediction of a non-homogeneous porous media permeability

To investigate the fluid flow through the porous media, it is necessary to understand the characteristics of the media, and the fluid. Porous media is an extremely complicated network of channels with obstructions. This paper introduces new conceptual approach to fluid flow in porous media. A particle bed with non-homogeneous porosity with a few Lyapunov arbitrary shape particles is considered. Reynolds number assumed less than unity. The creep flow on one sphere is modeled by Stokes equations. While, there is no any solution available for multi particle flow, in literature. Also, numerical solution of such a problem is very lengthy and tedious. So, converting the governing equations from domain to boundaries using Green's theorem is considered. Equations are solved by boundary element method. One and two layer potential and Fredholm's integral forms are introduced. To cover all particles with Lyapunov arbitrary shape. Therefore, it is possible to model the nonhomogeneous bed with non-uniform solid particles. Equations are solved for a sample bed up to 32 particles having different particle diameter and porosity. The results are presented in the form of Forshheimer equation. This method is described in order to determine required parameters in analysis of fluid flow in porous medium. (author)