New article on thermodynamically consistent modelling of flow in porous media

A new article has been published in the International Journal of Heat and Mass Transfer, entitled Thermodynamically consistent modeling of gas flow and adsorption in porous media. This is a work who my colleague Magnus Aa. Gjennestad and me have been working on for several years.

In modeling of gas flow through porous media width adsorption, the thermodynamic properties of the adsorbed phase are usually approximated by those of the bulk liquid. Using non-isothermal, gaseous transport of moist air through a porous insulation material as example, we show in the article that this leads to violation of the second law of thermodynamics and a negative entropy production.

To resolve this violation, we use information about the adsorption and thermodynamic properties of bulk fluids to derive consistent thermodynamic properties of the adsorbed phase, such as the chemical potential, enthalpy and entropy. The resulting chemical potential of the adsorbed phase can be a starting point for rate-based models for adsorption based on non-equilibrium thermodynamics. Incorporating the consistent thermodynamic description into the energy, entropy and momentum balances restores agreement with the second law of thermodynamics.

We show that the temperature evolution in the porous medium from the consistent description differs from the standard formulation only if the adsorption depends explicitly on temperature. This highlights the importance of characterizing the temperature dependence of the adsorption with experiments or molecular simulations for accurate non-isothermal modeling of porous media. An important aspect of the article is that we highlight how the entropy production is an important tool with much potential for further use in modelling of flow in porous media. The figure below shows the two sides of the entropy balance in a warm-up case study in a porous medium using (a) the thermodynamically consistent framework and (b) the bulk liquid model for the adsorbed phase.