Energy and Entropy Balance Laws for Porous Media Saturated by One or Two Non-Miscible Pore Fluids at Different Temperatures

The energy and entropy balance equations of porous media saturated by one or more non-miscible fluids have been investigated by many Authors leading to expressions which are based on different thermodynamic potentials and include various simplifying assumptions. Thus the various approaches often appear to be unrelated with respect to each other. In this work, two thermodynamic potentials recently proposed in the literature for porous media saturated by one or two non-miscible and compressible pore fluids are exploited for reconsidering different and perfectly equivalent expressions of the energy balance equations given in terms of internal energies, entropies and enthalpies, without simplifying assumptions. In particular, the entropy fluxes and the dissipation functions are presented for a simple case of irreversible response of the solid skeleton, involving neither irreversibility of the solid grain response, nor elastoplastic coupling nor frozen inelastic energy. Some comparisons with the formulations proposed in the literature are discussed.