Macroscopic modeling of the diffusive transport: Contribution of upscalingtechniques

A modeling at the macroscopic scale for combined advective and diffusive fl ows in a porous material is presented in this paper as a result of a homoge nization process. The domain of validity is characterized by means of two a dimensional parameters which respectively allow to define the concepts of m oderate advection and slow transient state. The homogenization method allows to estimate the diffusion and tortuosity t ensors introduced in the macroscopic formulation of Fick's law. These estim ates depend on the morphological parameters of the microstructure which rep resent the geometry of the domain occupied by the phase in which the diffus ion 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-base d estimates are derived. On the other hand periodic homogenization approach is applied to 3D geometries of the porous space.