Macroscopic permeability of doubly porous materials with cylindrical and spherical macropores

Abstract

We derivate analytic expressions for the effective permeability of a doubly porous medium which contains cylindrical or spherical macropores. The homogenization procedure is based on the consideration of a unit cell with a prescribed macroscopic pressure gradient or macroscopic velocity on its boundary. Within the unit cell, we have to solve the coupled Darcy–Stokes equations with appropriate interface models. The effective permeability of the bi-porous solid is determined by considering the composite cylinder and sphere assemblages. The solutions with prescribed macroscopic pressure gradient and velocity are provided and the influence in the choice of the interface model on the effective permeability of the doubly porous solid is studied. Finally, the results are compared with existing expressions provided in the literature and the estimate for the case of a cylindrical macropore is compared with finite element solutions.