PERMEABILITY PREDICTION OF POROUS MEDIA WITH VARIABLE POROSITY BY INVESTIGATION OF STOKES FLOW OVER MULTI-PARTICLES

Investigation of fluid flow through porous media necessitates a comprehensive recognition of medium characteristics. Porous media represent an extremely complicated network of channels with obstructions. This paper introduces a new conceptual approach for fluid flow in porous media. A variable porosity bed including a few Liapanov arbitrary shape particles has been considered. The Reynolds number is assumed to be less than 1. The creep flow on one sphere is modeled by the Stokes equation, while there is no solution available for multi-particle flow in the literature. Also, numerical solution of such a problem is very lengthy and tedious. Conversion of the governing equotions from domain to boundaries using Green's theorem is considered. The equation is solved by the boundary element method. One- and two-layer potentials and Fredholm's integral forms are introduced over all particles with Liapanov arbitrary shape. Therefore, it is possible to model the variable porosity bed with nonuniform solid particles. Equal:ions are solved for a sample bed with an air gap between the wall and edge of the particles and the results are presented in the form of the Darcy equation. In addition, this method is described to predict the permeability of variable porosity porous media. Also, comparison of the motion equation numerical solution based on this evaluated permeability with the experimental results is presented. The experimental results are achieved from the tests with special apparatus that has been designed by the authors.