The role of non-equilibrium thermodynamics in compositional modeling

We show how to derive compositional models from balance models including source terms representing mass transfer between phases. Mass transfer rate is taken proportional to the deviation from thermodynamic equilibrium. In the balance models, the mass transfer is very fast and local thermodynamic equilibrium is quickly attained. The derivation is done by means of an asymptotic expansion where the small parameter is the time scale of mass transfer relative to the hydrodynamical time scale. The new theory is illustrated by an example of thermal flow of steam, nitrogen and water in a porous medium, which can be useful in for soil remediation.