Thermo-chemo-mechanical coupling in single-fluid flows through porous media

Abstract

We consider a simple system, which captures thermal, chemical and mechanical effects. In the beginning, we consider a system of a solid, fluid and an interface, each having species and thermodynamic properties, which allows for further extension. This approach presents a more general setting for the system's entropy inequality. The entropy production is associated with thermodynamic irreversibility that can be found in all fluid flow with heat and mass transfer processes. The approach we follow , with our slight variation was pioneered by Gray and Miller in their Thermodynamically Constrained Averaging Theory (TCAT) approach. This approach involves the averaging of Classical Irreversible Theory (CIT) from microscale to macroascale. From the inequality, together with further restrictions we simplify it to produce desired entropy fluxes using the Curie-Prigogine principle and the Onsager phenomenological coefficients. Due to the dependence of fluid flow on the thermal conditions and flow conductivity, we modify Darcy's law to capture these effects. Depending on the temperature conditions and the flow forms we develop closed forms which are non-isothermal, locally isothermal and isothermal using the Darcy's law modifications. We present thermo-chemo-mechanical closed forms in the form of single-phase flow with species and thermo-mechanical closed forms in the form of single-phase flow without species.