Modelling of Pollutant Diffusion in Unsaturated Double-Porosity Medium by a Multiscale Method

Diffusion mechanism study of mass transport has received much attention in geo-environment domain, especially in waste containment applications. Diffusion of a substance in a homogeneous porous medium is traditionally modeled by Fick’s law. However, natural geology environments are often heterogeneous and thus that requires advanced models enabling to capture diffusion behavior in such media. “Double-porosity” medium concept can be replaced a class of heterogeneous media in which there exists two macro- and micro-porosity domains with very contrasted hydraulic properties, fractured rocks or aggregated soils, for example. In this paper, the development of a macroscopic model for pollutant diffusion in unsaturated double-porosity medium is presented, applying a multiscale method. The resulting model consists of coupled two equations for the diffusion in the macro- and micro-porosity domains. The effective diffusion tensor representing for the double-porosity medium is also obtained. The developed model is verified by comparing with the reference solution of the fine scale model through a numerical example of hydrogeology problem.