SIMILARITY OF SHARP-EDGED POROUS-MEDIA

The dynamic interaction between a rigid porous structure (porosity phi ) and its saturating fluid is studied. From the microscopic conservati on laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like Levy, A uriault and Burridge and Keller is used. The macroscopic equations are studied in the high-frequency limit. The high-frequency behaviour is characterized by the tortuosity parameter alpha(infinity) and by an ef fective pore radius LAMBDA, defined previously by Johnson et al. The l ow frequency behaviour is characterized by the ratio of the steady-sta te permeability k0 and the porosity phi. A similarity parameter M = 8a lpha(infinity)k0/phiLAMBDA2 (in the two-dimensional case M = 12alpha(i nfinity)k0/phiLAMBDA2) is defined, which is approximately equal to 1 f or configurations that have smooth microscopic geometries. For sharp-e dged pore geometries, however, M is no longer found equal to one. Nume rical computations are performed using a Schwartz-Christoffel transfor mation.