Non-isothermal transport of multi-phase fluids in porous media. Constitutive equations

Abstract

We define a representative elementary volume of a porous medium in terms of lumped extensive variables, including properties of homogeneous phases, interfaces, and contact lines. Using the grand potential, we define the pressure of the REV in a medium in a new manner. From the entropy production expressed in these variables, we develop new constitutive equations for multi-component, multi-phase, macro-scale flow. The system is exposed to temperature, composition, and pressure gradients. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior, and predict thermal osmosis special for porous media. An experimental program is suggested to verify Onsager symmetry in the transport coefficients. The analysis is limited to non-deformable systems, which obey Euler homogeneity on the REV level.