Asymptotic Transport Models for Heat and Mass Transfer in Reactive Porous Media

We propose in this paper an approach for deriving in a rigorous way a family of models of mass and heat transfer in reactive porous media. At a microscopic level we propose a model coupling the Boltzmann equation in the gas phase, the heat equation on the solid phase, and appropriate interface conditions, including adsorption-desorption reactions. Several scalings are proposed, each one corresponding to a particular regime. Then an asymptotic expansion mixing homogenization and fluid limit leads to a system of coupled diffusion equations where the effective diffusion tensors are defined from the microscopic geometry of the material through auxiliary problems. Finally, we prove that the diffusion operator is elliptic, and we give algebraic and geometric conditions of degeneracy.