Abstract
We develop constitutive equations for multi-component, multi-phase, macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of the volume and surface averaged pressure and the saturation, and the respective driving forces from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of a thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.
Highlights
We have recently [1] derived a coarse-grained form of the entropy production, σ, of a representative elementary volume (REV) in a non-deformable porous medium with multi-phase, multi-component, non-isothermal fluids
We find the pressure of the REV by starting, as above, with the extensive property that holds the pressure as the variable
The pressure variation across the REV is given by Equation (19), we have an interpretation of the pressure difference external to the porous medium; d p = d (p − pc)
Summary
We have recently [1] derived a coarse-grained form of the entropy production, σ , of a representative elementary volume (REV) in a non-deformable porous medium with multi-phase, multi-component, non-isothermal fluids. We shall see that we can obtain the same form of the constitutive equations as for homogeneous systems, but that the driving forces are particular for the porous medium. To write out this particularity, is one aim of the present paper. We restrict ourselves to nondeformable media, and systems with a constant ratio of fluid surface area to volume (no film formation) For such systems we proceed to find expressions for the chemical potential and the pressure in the context of non-deformable porous media, cf sections 2.2, 2.3. They obtain new contributions compared to their normal form in homogeneous systems. An experimental program is suggested in the end to verify Onsager symmetry in the transport coefficients
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