AUTHOR=Kjelstrup Signe , Bedeaux Dick , Hansen Alex , Hafskjold Bjørn , Galteland Olav TITLE=Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations JOURNAL=Frontiers in Physics VOLUME=6 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00150 DOI=10.3389/fphy.2018.00150 ISSN=2296-424X 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 porous 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.