Dynamic Permeability in Porous Media

We calculate from first principles the frequency-dependent permeability $\kappa \left(\omega \right)$ in porous media for a variety of microstructures. It is found that when $\kappa \left(\omega \right)$ is scaled by its static value ${\kappa }_0$ and the frequency by a characteristic ${\omega }_c$ particular to the sample, the resulting function exhibits excellent universal behavior independent of microstructure. We advance arguments that delineate the physical reason for the scaling behavior as well as the condition for its validity. Our predictions are supported by observed correlations in sedimentary rocks and experimental $\kappa \left(\omega \right)$ measurements.