Upscaling Mass Transport with Homogeneous and Heterogeneous 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 phase that saturates the porous medium or when the reaction occurs at the solid-fluid interface. The upscaling effort 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 in representative unit cells. Our derivations show that mass transport effective coefficients depend, in general, of the nature and magnitude of the microscopic reaction rate coefficient as well as of the essential geometrical structure of the solid matrix and the flow rate. Furthermore, if the chemical reaction is homogeneous, the effective reaction rate coefficient is found to be simply the multiplication of its microscopic counterpart with the porosity; whereas, if the reaction is heterogeneous, the effective reaction coefficient is determined from a closure problem solution.