The effective diffusivities in porous media with and without nonlinear reactions

Abstract

The question of whether effective diffusivities in porous materials under reactive and nonreactive conditions are equal is addressed. Previous studies had considered the problem with first-order reactions. We study the issue with two nonlinear reactions—a second-order reaction and one governed by the Michaelis–Menten kinetics. Pore network and continuum models of porous media are utilized to estimate the effective diffusivities under reactive and nonreactive conditions. We show that the two effective diffusivities are significantly different. The difference is due to the heterogeneities of the porous material, and the fluctuations that they cause in the spatially varying local concentrations and diffusivities, and can be as large as a few orders of magnitude. Theoretical analysis of diffusion and reactions in porous media is also presented that supports the results of the simulations. In particular, it is shown that the results of pore network simulations cannot be fitted to the classical continuum equation of diffusion and reaction, and that a more complex continuum equation should be used for this purpose.