Effective elastic properties of porous rocks with fluid-filled vugs

The problem of determination of the effective elastic properties , particularly, the velocity and attenuation of the compressional wave propagating in porous rocks containing fluid-filled vugs is considered. Usually the correct interpretation of double- or triple-porosity formations using sonic logs is a complex problem, even nowadays with the use of the most advanced inversion algorithms and the contribution of other petrophysical tools. In this work, the proposed model considers spherical inclusions filled with viscous or ideal fluids aimed to represent geological vugs. This approach also considers the cases of “open” and “closed” interfaces at the boundary between the porous rock and the vug. To describe the propagation of elastic waves in porous rocks, the well-known Biot's theory is implemented. The calculations were fulfilled for the incidence of plane compressional harmonic waves. As the first step of performed calculations the so-called one-particle problem is solved. Then, the first order (single-scattering) approximation is applied to calculate the effective wave number of elastic waves propagating in a poroelastic rock containing sets of randomly distributed vugs. The results reported here show that the hydrodynamic effects associated with the fluid filtration at the boundaries between the vugs and the porous rock at the scale of the incident compressional wave, lead to significant frequency dispersion of the effective elastic wave velocity and its correspondent Q-factor. These hydrodynamic effects on the elastic properties are clearly appreciated at the sonic log frequency range. From the findings of this paper, it can be sustained that the elastic response of the fluid viscosity in the vugs is not so significant. This implies that it is possible to use the simple model of an ideal fluid in the vugs. • The effective elastic parameters of porous rocks containing fluid-filled vugs are obtained. • To describe the propagation of elastic waves in porous rocks, the Biot theory is used. • We have considered two models: an ideal fluid and a viscous fluid in the vugs. • The single-scattering approximation is applied to calculate the effective wave number. • The influence of hydrodynamic effects on parameters of the effective wave is significant.