Multiscale modeling of fluid permeability of a non-homogeneous porous media

We discuss various models describing single phase fluid flow in a porous media with non-uniform distribution of pore sizes. Treating such a media as a heterogeneous one we adopted various approximate schemes used in micromechanics of materials. For this aim, we introduced the fluid permeability contribution tensor that describes effect of a single inhomogeneity onto the overall properties. We also compare these derived micromechanical schemes with formulas used in geomechanics. We show that the different approaches lead to similar results. The main advantages of micromechanical schemes are, (1) they do not contain adjustable parameters; (2) they can be used to describe fluid permeability in materials with more than two phases.