Study of permeability by periodic and self-consistent homogenisation

This paper presents a study into permeability of porous media in which both homogenisation of periodic media (HPM) and self-consistent method (SCM) are used. By taking advantage of the physical principles identified with HPM, the application of SCM led to the determination of two permeability assessments. It is shown that these conjectured values correspond in fact to the exact bounds of permeability of various classes of porous media with a clear identification of their microstructures (grain and fluid size distribution). Applications are presented for granular media with spherical grains, and for fibrous media with parallel cylindrical fibres.