Fluid Flow in Porous Media

This chapter contains a discussion of the models employed to describe the fluid flow and the convection processes in a porous medium saturated by a fluid. The basic quantities, defined through an elementary representative volume scheme, are introduced. Among them, we mention the porosity and the seepage velocity field. Starting with Darcy’s law, the different formulations of the local momentum balance equation are analysed. The expressions of the local mass balance equation and of the local energy balance equation are introduced. The controversial problem of the viscous dissipation modelling for porous media with a large permeability is also outlined. The possible lack of local thermal equilibrium between the solid phase and the fluid phase is discussed, by employing a two-temperature model of the local energy balance. Finally, the seepage flow of non-Newtonian fluids in porous media is briefly surveyed relative to specific models: power-law, Bingham, and Oldroyd-B.