Abstract
We derive the entropy production for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in pressure, temperature, and chemical potentials. Thermodynamic extensive variables on the macro-scale are obtained by integrating over a representative elementary volume (REV). Using Euler homogeneity of the first order, we obtain the Gibbs equation for the REV. From this we define the intensive variables, the temperature, pressure and chemical potentials and, using the balance equations, derive the entropy production for the REV. The entropy production defines sets of independent conjugate thermodynamic fluxes and forces in the standard way. The transport of two-phase flow of immiscible components is used to illustrate the equations.
Highlights
The aim of this article is to develop the basis for a macro-scale description of multi-phase flow in porous media in terms of non-equilibrium thermodynamics
While the entropy production in the porous medium so far has been written as a combination of contributions from each phase, interface and contact line, we shall write the property for a more limited set of macro-scale variables
By writing Equation (18) we find that the normal thermodynamic relations apply for the heterogeneous system at equilibrium, for the additive properties U, S, V, Mi, obtained from sums of the bulk, excess surface, and excess line-contributions
Summary
The aim of this article is to develop the basis for a macro-scale description of multi-phase flow in porous media in terms of non-equilibrium thermodynamics. While the entropy production in the porous medium so far has been written as a combination of contributions from each phase, interface and contact line, we shall write the property for a more limited set of macro-scale variables. In this sense, we deviate widely from the Thermodynamically Constrained Averaging Theory [5]. The reduction of variables is possible as long as the system is Euler homogeneous of the first kind
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