Dynamic permeability: reformulation of theory and new experimental and numerical data

Abstract

The dynamic interaction between a rigid porous structure (porosity ϕ) 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 for example Lévy, Auriault and Burridge & Keller is used, from which we reformulate the theory by Johnson, Koplik & Dashen. The macroscopic equations then serve to describe the high-frequency behaviour of an oscillating fluid within a porous sample. This behaviour may be characterized by the length parameter Λ and by the tortuosity parameter α ∞ . It is shown that Λ and α ∞ , which describe an oscillatory flow behaviour, may be evaluated on the basis of steady potential flow theory. Numerical results are then presented for several pore geometries, and for these geometries, the steady-state permeability k 0 is computed numerically also. The parameter 8α ∞ k 0 /ϕΛ 2 , first introduced by Johnson et al. , is then evaluated and appears to be weakly dependent on pore geometry. This implies that for many porous media the dynamic interaction is described by an approximate scaling function. New experimental data, concerning oscillating flows through several porous media, are presented. Within limits of accuracy, these data are in agreement with the approximate scaling function.