Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy

Abstract

There is relative motion and inertial coupling between solids and fluids during seismic and acoustic propagation in rocks with fluids. This inertial coupling is anisotropic because of the microvelocity anisotropy of the fluid relative to solid in an anisotropic medium. The Biot mechanism and the squirt-flow mechanism are the two most important mechanisms of solid/fluid interaction in rocks. We extend the Biot/squirt (BISQ) theory to include the solid/fluid coupling anisotropy and develop a general poroelastic wave equation including both mechanisms simultaneously. The new model estimates velocity/frequency dispersion and attenuation of waves propagating in the 2D PTL ( periodic thin layers )+ EDA (extensive dilatancy anisotropy) medium with fluids. The attenuation and dispersion of the two quasi-P-waves and the quasi-SV-wave, which are related to the solid/fluid coupling density and the permeability tensors, are anisotropic. The anisotropy are simultaneously affected by the anisotropies of the solid skeleton, the permeability, and the solid/fluid coupling effect of the formation. Numerical modeling suggests that variations of attenuation of both the fast quasi-P-wave and the quasi-SV-wave strongly depend on the permeability anisotropy. In the low-frequency range, the maximum attenuation is in the direction of the maximum permeability for the fast quasi-P-wave and in the direction of the minimum permeability for the quasi-SV-wave. The attenuation behaviors of the two waves in the high-frequency range, however, are opposite to those in the low-frequency range. This paper also presents numerically how the attenuation and velocity dispersion of both the fast quasi-P-wave and the quasi-SV-wave are influenced by the anisotropic solid/fluid coupling density. The model results demonstrate when the wave propagation is perpendicular to the direction of maximum solid/fluid coupling density, the wave motion exhibits maximum attenuation ( Q −1) and maximum velocity dispersion for the fast quasi-P-wave, and minimum attenuation ( Q −1) and minimum velocity dispersion for the quasi-SV-wave. These phenomena may be applied in extracting anisotropic permeability and further determining the preferential directions of fluid flow in a reservoir containing fluid-filled cracks from attenuation and dispersion data derived from sonic logs and crosswell seismics.