Upscaling Mass Transport with Homogeneous and Heterogeneous Reaction in Porous Media

摘要

The upscaling process of mass transport with chemical reaction in porous media isrncarried out using the method of volume averaging under diffusive and dispersivernconditions. We study cases in which the (first-order) reaction takes place in the fluidrnphase that saturates the porous medium or when the reaction occurs at the solid-fluidrninterface. The upscaling effort leads to average transport equations, which are expressedrnin terms of effective medium coefficients for (diffusive or dispersive) mass transportrnand reaction that are computed by solving the associated closure problems inrnrepresentative unit cells. Our derivations show that mass transport effective coefficientsrndepend, in general, of the nature and magnitude of the microscopic reaction raterncoefficient as well as of the essential geometrical structure of the solid matrix and thernflow rate. Furthermore, if the chemical reaction is homogeneous, the effective reactionrnrate coefficient is found to be simply the multiplication of its microscopic counterpartrnwith the porosity; whereas, if the reaction is heterogeneous, the effective reactionrncoefficient is determined from a closure problem solution.