Abstract :
The ‘‘dynamic’’ permeability k(v) 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(v) 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 dc at the transition was found to be proportional to the critical capillary radius
rc 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, dc was not well correlated with the
JKD parameter L. The conclusion is that L and dc (or rc ) 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.
