Cellular-automata calculation of frequency-dependent permeability of porous media

Abstract

We use a cellular-automata (CA) method to determine the frequency-dependent permeability k(ω) of a channel and a disordered porous medium. The CA results for the channel flow agree completely with the analytical solution of the problem. For flow in a porous medium, we calculate k(ω) over a wide range of the frequencies ω and for several values of the porosity. Our CA results for disordered porous media support the relation k(ω)/k0=f(ω/ωc), where k0 is the static permeability of the medium, ωc is a characteristic frequency, and f(x) is a universal function, proposed previously, based on experimental data. © 1993 The American Physical Society.