Equations Governing Flow and Transport in Porous Media

Abstract

Derivation of equations governing flow, heat, and mass transfer in porous media is discussed. The starting point is Darcy’s law that can be gradually extended to higher flow rates and porosity, leading to the non-Darcy form of the momentum equation. Complex pore geometries and the appearance of interfaces of immiscible fluids can be treated in this framework. A second starting point is the system of equations valid for a homogeneous fluid medium. It can be generalized to a multiphase system such as a porous medium by introducing source terms and effective medium properties. In each approach, the model carries a large number of parameters that are sensitive to the pore structure, though to a lesser extent on the thermophysical properties of the constituent media. Success in modeling transport in porous media is linked to careful parameter estimation from experiments. This step is expected to become critical in multiscale porous media where the pore scales span several orders of magnitude. The one-equation model and two-equation model of convective heat transfer and transport phenomena with chemical reactions are subsequently discussed in the chapter.