On the Upscaling of Reaction-Transport Processes in Porous Media with Fast Kinetics

This report is organized as follows: Provide a brief review of the upscaling constraints of the type (2) for a typical diffusion-reaction system. In this an analogy with two-phase flow in porous media was drawn. Then, using the methodology of QW a problem at the unit cell for the computation of the effective mass transfer coefficient, in processes where local thermodynamic equilibrium applies was derived. This problem is found to be different than in QW, as it depends on the gradients of the macroscale variable, and can be cast in terms of an eigenvalue problem. Two simple, examples, one involving advection-dissolution and another involving drying in a pore network, was presented to illustrate the coupling between scales and to show the quantitative effect in case this coupling was neglected. Finally, similar ideas and an illustrative example was applied to reaction-diffusion systems with fast kinetics, where an equilibrium state is approached