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Inhomogeneous fluid-saturated porous materials are often probed with diffusion waves to estimate their effective hydraulic conductivity and diffusivity. Analysis of diffusion wave fields in randomly inhomogeneous poroelastic structures provides new insight into how fluctuations of the compressible constituents affect the effective diffusivity. Based on the method of statistical smoothing an effective wave number of the coherent diffusion wave field is computed. From this wave number both an effective hydraulic conductivity and diffusivity are identified. These transport properties are frequency dependent. The correspondence between this conductivity and that estimated from unsteady flow through porous media based on Darcy’s law is elucidated.

Effective hydraulic conductivity and diffusivity of randomly heterogeneous porous solids with compressible constituents