Non-isothermal transport of multi-phase fluids in porous media. The entropy production

TL;DR

This paper derives the entropy production for multi-phase fluid transport in porous media under non-isothermal conditions, linking thermodynamic variables to flow processes and illustrating with two-phase flow examples.

Contribution

It introduces a thermodynamic framework for analyzing entropy production in non-isothermal multi-phase porous media transport, integrating macro-scale variables and deriving conjugate fluxes and forces.

Findings

Derived entropy production expression for multi-phase flow.

Defined thermodynamic fluxes and forces in porous media.

Illustrated the theory with two-phase flow examples.

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.