On diffusion, dispersion and reaction in porous media

The upscaling process of mass transport with chemical reaction in porous media is carried out using the method of volume averaging under diffusive and dispersive conditions. We study cases in which the (first-order) reaction takes place in the fluid that saturates the porous medium or when the reaction occurs at the solid–fluid interface. The upscaling process leads to average transport equations, which are expressed in terms of effective medium coefficients for (diffusive or dispersive) mass transport and reaction that are computed by solving the associated closure problems. 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.