Propagation of longitudinal elastic waves in a fluid-saturated porous medium with spherical inclusions

The Frenkel-Biot theory is used to study the propagation of a longitudinal harmonic wave of the first kind in an isotropic porous matrix with inclusions contrasting in elastic properties and hydrodynamic permeability. The generation of elastic waves of the second kind at the boundaries of inclusions is taken into account. The effective wave number of the longitudinal wave is calculated using the equations of multiple scattering theory. The characteristic size of inhomogeneities is assumed to be much greater than the size of pores. The parameters of the model used for calculations correspond to sandstone with centimeter-scale inhomogeneities. The presence of such inhomogeneities is typical of sedimentary rocks. Calculations show that, in the frequency range of acoustic logging, the effective attenuation factor of the longitudinal wave may noticeably exceed the attenuation factors of longitudinal waves of the first kind in both matrix and inclusions. From the results obtained, it follows that, when studying the propagation of elastic waves in fluid-saturated porous media, it is necessary to take into account the hydrodynamic effects associated with the filtration overflows that arise at the boundaries of inhomogeneities.