A study of the propagation of waves in porous media with an interconnected network of pores and micropores of very different characteristic sizes, saturated by a compressible Newtonian fluid, is proposed. With this aim, the homogenization technique for periodic separated scales media, is applied to realistic double porosity materials with motionless skeleton. From preliminary explicit estimations of wavelengths in the two fluid networks, it is shown that the macroscopic descriptions depend on the contrast of static permeability between pores and micropores and on frequency. The local equations are solved in the cases of low and high contrasts of permeability, and two main macroscopic behaviors are obtained. In the low contrast situation, the macroscopic flow is given by a kind of generalized Darcy's law involving both pores and microscopes, and their respective characteristic frequencies. Regarding compressibility effects, both pore networks act in parallel. The high permeability contrast reveals that the macroscopic flow law is governed by the pores. The microporous part of the material is submitted to pressure diffusion effects, bringing dissipation, and modifying the dynamic bulk modulus of the material. The two situations of coupling are illustrated for simple geometry of double porosity materials, including perforated-and slits-microporous materials.
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