Effective Dynamic Permeability for Seismic Waves in Inhomogeneous, Porous Media Using White's Patchy Saturation Model

Abstract

We obtain an effective dynamic permeability model for a porous acoustic medium having mesoscopic heterogeneities of spherical inclusions by applying the non-self consistent theory to the scattered wavefield from a single spherical inclusion. At low frequency, our dynamic permeability tends to the real value of the effective static permeability, which depends on the host medium for small inclusion concentrations. This result is compared with the effective hydraulic permeability by replacing the permeability of the components with their dynamic values as determined from the JKD model For frequencies lower than the resonance frequency, these simple dynamic permeability models are very similar to those determined from the scattering model of this paper. However, the model which uses the arithmetic mean of the constituent phase permeabilities is not valid for inclusions having higher permeability than the host phase, and the model which uses the harmonic mean of the constituent phases is not valid for inclusions having lower permeability than that of the host material. In both cases, the effective dynamic permeability calculated from the static model of random spherical inclusions is in good agreement with our scattering model.