Macroscopic modeling of the diffusive transport: Contribution of upscaling techniques

A modeling at the macroscopic scale for combined advective and diffusive flows in a porous material is presented in this paper as a result of a homogenization process. The domain of validity is characterized by means of two adimensional parameters which respectively allow to define the concepts of moderate advection and slow transient state. The homogenization method allows to estimate the diffusion and tortuosity tensors introduced in the macroscopic formulation of Fick's law. These estimates depend on the morphological parameters of the microstructure which represent the geometry of the domain occupied by the phase in which the diffusion process takes place. Two different homogenization techniques are compared. On the one hand from describing the solid grains as inclusions in the fluid phase inclusion-based estimates are derived. On the other hand periodic homogenization approach is applied to 3D geometries of the porous space.