Comparison of two modeling approaches for highly heterogeneous porous media

The purpose of this paper is to study the acoustic behavior of highly heterogeneous, low density porous structures having a complex pore size distribution using two distinct theoretical approaches. The first approach requires the direct numerical integration of the Biot viscosity correction function. The main requirement here is a knowledge of the probability density function of the pore size, which can be achieved by an optical pore-counting technique. The fact that the observed pore size distribution in these materials could be distinctively split into two parts suggested the use of the second approach based upon the double-porosity theory by Olny and Boutin [J. Acoust. Soc. Am. 114(1), 73-89 (2003)]. The latter approach assumes a low permeability contrast between the two porous scales so that the acoustic properties could be estimated using the semi-phenomenological models of Johnson and Lafarge for the viscous and thermal dynamic permeabilities. Numerical results predicted by the two models are then compared with impedance tube experimental data showing good accuracy of the selected prediction methods.