Flow Through Rigid Porous Media

Abstract

The best way to analyze the flow through a porous medium is to divide it into two phenomena, depending on whether the porous matrix is compressible or incompressible. In both cases, the result is useful for the process industry. Rigid porous media form the basis for a simplified filtration theory and compressible porous media form part of thickening theory. In this chapter the fundamental equations for the flow through rigid porous media based on the Theory of Mixtures is developed. Consider the flow of a incompressible viscous fluid through a bed of small solid incompressible particles with no mass transfer between the solid and the fluid. Such a mixture of particles is called an incompressible porous medium and can be described with the equations for particulate systems presented in Chap. 3. It is convenient in this case to use porosity as a variable instead of the solid volume fraction. Local balances are laid down for mass and momentum and Darcy’s and Forchheimer’s equations are used as constitutive equations. For a mono-phase flow, permeability is defined and for the case of a two-phase flow, the concepts of relative permeability, saturation and capillary pressure are introduced.