A spectral approach for homogenization of diffusion and heterogeneous reaction in porous media

Macroscopic models for diffusion and heterogeneous reversible reaction of two species in porous media are developed by using coupled homogenization technique and spectral approach. Three representative cases related to the order of magnitude of the macroscopic Damkohler number DaL, namely predominating reaction, diffusion-reaction of the same order and dominating diffusion, are considered. The concentrations are developed as time series in an eigen-functions basis associated with periodic spectral problems formulated in the unit-cell, thus forming a new microscopic problem to be homogenized. Such an approach represents a powerful tool to upscale diffusion-reaction microscopic problems, especially for high Damkohler number values where classical asymptotic development fails. It enables to capture the physics at very short times, when the characteristic time of re-action involved is much faster than the diffusion one. This work allows us to formulate the complex macroscopic laws describing the heterogeneous diffusion/reaction problem for two species in high Damkohler number regime. (c) 2021 Elsevier Inc. All rights reserved.