Limits of Classical Homogenization Procedure for Coupled Diffusion-Heterogeneous Reaction Processes in Porous Media

Upscaling of coupled diffusion-heterogeneous reaction problem in porous media is developed for different orders of magnitude of the Damköhler number. At the pore-scale, the mass transfer of two dilute species is ruled by a diffusion mechanism characterized by different diffusion coefficients. The pore-scale model is completed by reversible linear reaction occurring at the solid–fluid interface. Classical homogenization technique is then used to upscale the pore-scale model under three different scenarios: slow, moderate and high reaction rates corresponding to three orders of magnitude of the Damköhler number. The results show that the macroscopic model obtained for a slow reaction rate predicts accurately the coupled diffusion-reaction process at the macroscale in the range of small Damköhler number. However, the classical homogenization procedure for moderate and high reaction rates fails to capture correctly the complex physics at short time when chemical equilibrium is not reached. In these cases, upscaled models impose strictly the chemical equilibrium at the first order due to the dominance of reaction over diffusion. Numerical simulations highlight the error of the macroscopic models compared to direct numerical simulations.