Homogenization of acoustic waves in strongly heterogeneous porous structures

• Fluid saturated periodic structures treated by two-scale homogenization.
• Scaling permeability ansatz applied in the dual porosity.
• Homogenized model of pressure waves in rigid skeleton was derived.
• New homogenized frequency-dependent dynamic compressibility involved.
• Dispersion formula obtained, illustrated on layered periodic structures.

We consider acoustic waves in fluid-saturated periodic media with dual porosity. At the mesoscopic level, the fluid motion is governed by the Darcy flow model extended by inertia terms and by the mass conservation equation. In this study, assuming the porous skeleton is rigid, the aim is to distinguish the effects of the strong heterogeneity in the permeability coefficients. Using the asymptotic homogenization method we derive macroscopic equations and obtain the dispersion relationship for harmonic waves. The double porosity gives rise to an extra homogenized coefficient of dynamic compressibility which is not obtained in the upscaled single porosity model. Both the single and double porosity models are compared using an example illustrating wave propagation in layered media.