About the dependence of the effective diffusivity and dispersion coefficients on chemical reaction in homogeneous porous media

This work is devoted to analyze the dependence of effective mass transport coefficients with the type of chemical reaction in homogeneous porous media. To this end, we use the method of volume averaging to carry out the upscaling of the corresponding microscale balance equations. As a first approach we studied cases in which there is only one chemical species undergoing a first-order reaction either in the fluid that saturates the porous matrix or at the solid-fluid interface. In both cases the upscaling process leads to effective medium equations expressed in terms of average diffusion or dispersion coefficients and an effective reaction term. Our analysis shows that these effective coefficients depend, in general, upon the nature and magnitude of the microscopic reaction rate as well as of the essential geometrical structure of the solid matrix and the flow rate. This study also shows that if the reaction rate at the microscale is arbitrarily large, the capabilities of the upscaled models are hindered, which is in agreement with the breakdown of the physical sense of the microscale formulation.