Modeling of the reflooding of a particle bed: contribution to the estimation of macroscopic transport properties

This work deals with the macroscopic modeling of heat and mass transfer in a superheated porous medium subjected to a liquid-vapor flow with phase change. Considering local thermal non-equilibrium between the three phases, a quasi-steady three-temperature macroscopic model is derived using the volume averaging method. An attractive feature of the scaling-up theory lies in the derivation of a closed form of the evaporation rate at the macroscopic level depending on the large scale temperatures and the effective properties. The resulting macroscopic model may be seen as a generalization of existing three-temperature models obtained from a heuristic approach. The main differences are the existence of additional transport terms and a coupling between the macroscopic continua (phases and interface) that seems to be more complex. The major interest of the proposed approach is to provide closure problems that allow to determine the effective transport coefficients, such as the thermal dispersion tensors and the heat exchange coefficients, from a local scale description over a representative cell of the porous medium under consideration. These problems have been solved for simple unit cells to provide first estimates of the effective properties. For these unit cells and for purely diffusive processes with phase change, comparisons with numerical solutions of the local problem have shown the practical interest and the potentialities of the macroscopic model. For more complex unit cells, a direct numerical simulation of the two-phase flow at the local scale has been performed to provide the required velocity field and the interface topology. The direct numerical simulation tool which has been developed is based on a diffuse interface method. These methods are well suited to the local scale characteristic lengths of the porous medium and the developments carried out show that it is possible to extend them to take into account phase change in the framework of Cahn-Hilliard models. Results obtained on 2D unit cells emphasize a strong impact of the pore-scale phase repartition and indicate that correlations for the effective properties involving saturation and Peclet numbers can be relatively complex. (author)