Similarity of sharp-edged porous media

The dynamic interaction between a rigid porous structure (porosity f) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by authors like Lévy, Auriault 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 a¿ and by an effective pore radius ¿, denned previously by Johnson et al. The low frequency behaviour is characterized by the ratio of the steady-state permeability K0 and the porosity f. A similarity parameter M = 8a¿K0/f¿2 (in the two-dimensional case M = 12a¿K0/f¿2) is defined, which is approximately equal to 1 for configurations that have smooth microscopic geometries. For sharp-edged pore geometries, however, M is no longer found equal to one. Numerical computations are performed using a Schwartz-Christoffel transformation.