Computation of the effective permeability of 2D doubly porous materials with elliptical shaped pores by using boundary element method

Abstract

In recent years, the prediction of the effective transport properties have received a great number of investigations. The present work is dedicated to determining the effective permeability of two-dimensional (2D) doubly porous materials made of an isotropic permeable solid matrix in which elliptical shaped pores of any size are embedded. At the interface between the fluid and the solid, the Beaver–Joseph–Saffman conditions are applied. To achieve this objective, the Boundary Element Method (BEM) is first elaborated in the simulation of velocity and pressure solution fields of two coupled Stokes and Darcy problems. Afterwards, with the help of this solution results, the effective permeablity of the doubly porous material under investigation can be determined. For the purpose of assessing the accuracy and convergence of the BEM solution, the results obtained for the velocity and pressure fields are compared with the ones provided by the finite element method (FEM). Finally, several numerical examples are carried out to analyze the fluid/solid interface influence, the effect of area fraction and geometrical properties of pores, such as the size and distribution of the pores within the matrix phase.