On the upscaling of reaction-transport processes in porous media with fast or finite kinetics

Abstract We show that for reaction-transport processes with fast kinetics (in the limit of thermodynamic equilibrium), conventional volume averaging for determining effective kinetic parameters applies only when the macroscopic variable approaches its equilibrium value. Even under such conditions, computing the effective mass transfer coefficient requires solving an eigenvalue problem, which couples the local microstructure with the global. Two examples, one involving a simple advection–dissolution problem and another a drying problem in a pore network, illustrate the theoretical predictions. Similar considerations apply for the case of finite kinetics, when the macroscale concentration approaches an equilibrium value. In that case, the effective kinetic parameter is not equal to the local, as typically assumed, but it becomes a function of the local Thiele modulus.