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 Bernabé (1995). In most cases, the calculated frequency dependence of the real and imaginary parts of k(ω) was consistent with the JKD model (Johnsonet 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.
 Publication:

Pure and Applied Geophysics
 Pub Date:
 1997
 DOI:
 10.1007/s000240050037
 Bibcode:
 1997PApGe.149..489B
 Keywords:

 Key words: Permeability;
 electrical conductivity;
 porous rocks.