Saturated Porous Media

Abstract

In this chapter, two different homogenization problems and their solving strategies with FEM are presented, related to porous media saturated with a Newtonian fluid. The first problem is associated with microstructures where the porous cavities are disconnected (see Fig. 6.1a). In that situation, the fluid cannot flow but induces a pressure on the solid matrix which affects the mechanical response of the solid. The overall behavior is then called “poroelastic”. The second problem is related to the case where the solid contains connected porosities (see Fig. 6.1b), in which a fluid can flow and cross the solid. In this second case, the problem is then to determine the transport properties, or effective permeability of the medium, given the morphology of the porosity network. In this chapter, we present the FEM methodologies to solve these problems and do not go into further theoretical aspects, which can be found in excellent books on this topic, such as [1, 2]. In the presented developments, we restrict to linearized problem, i.e., we assume small strains, small displacements, small variations of porosity of fluid mass density (see [1], p. 113), and constant viscosity (Newtonian fluid).