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

• Diffusion and multi-species heterogeneous reactions in porous media are studied. Spectral approach is used to obtain new pore-scale models be homogenized. Macroscopic laws derived by homogenization technique. For high Damköhler number , complex behavior at short time successfully captured. for diffusion reversible reaction of two species developed using coupled technique spectral . Three representative cases related the order magnitude macroscopic Da L namely predominating reaction, diffusion-reaction same dominating diffusion, considered. The concentrations as series an eigenfunctions basis associated with periodic problems formulated unit-cell, thus forming a microscopic problem Such represents powerful tool upscale problems, especially values where classical asymptotic development fails. It enables capture physics very times, when characteristic involved much faster than one. This work allows us formulate describing diffusion/reaction regime.