The Frequency Dependence of Harmonic Fluid Flow Through Networks of Cracks and Pores

Abstract

—The "dynamic" permeability k(ω) of heterogeneous networks of cracks, tubes and spheres, was determined by numerically simulating the harmonic flow of an interstitial fluid for a wide range of frequencies. For comparison with previous works, this procedure was applied to the 100 network realizations used in Bernabe (1995). In most cases, the calculated frequency dependence of the real and imaginary parts of k(ω) was consistent with the JKD model (Johnson et al., 1987), showing a transition from "viscous", macroscopic flow at low frequencies to "inertial" flow at high frequencies. The viscous skin depth δ c at the transition was found to be proportional to the critical capillary radius r c from a capillary invasion (Katz and Thompson, 1986). A simple explanation is that these two length scales arise from the same percolation problem. On the other hand, δ c was not well correlated with the JKD parameter Λ. The conclusion is that Λ and δ c (or r c ) are two independent parameters, derived from two unrelated approaches (i.e., weighted averaging and percolation theory). Finally, an attempt was made to relax the initial assumptions of a rigid solid matrix and an incompressible fluid. It was observed that the effect of the fluid compressibility could occasionally be very large, especially when networks with large amounts of storage pore space were considered.