A local thermal non-equilibrium model for two-phase flows with phase-change in porous media

The assumption of local thermal equilibrium for describing macroscopic heat transfer in a porous medium subjected to a liquid–vapor flow with phase change has been often investigated. Under certain circumstances, this assumption appears to be too restrictive and fails to be valid. In this paper, the method of volume averaging is used to derive a three-temperature macroscopic model considering local thermal non-equilibrium between the three phases. A closed form of the evaporation rate at the macroscopic level is obtained depending on the macroscopic temperatures and the effective properties. Six pore-scale closure problems are proposed, which allow to determine all the effective transport coefficients for representative unit cells. These closure problems are solved for simple unit cells and analytical results are presented in these cases. For these simplified unit cells, a comparison between averaged temperatures obtained from direct pore-scale simulations and averaged temperatures obtained from the three-equation model has been carried out for purely diffusive phase-change processes. A good agreement is obtained between the theory and the pore-scale calculations. This confirms the validity and the practical interest of the proposed approach.