Wave motion in a viscous fluid-filled fracture

Abstract

The wave motion in a viscous fluid between two semi-infinite isotropic elastic solids is considered. The wave solutions in both the fluid and the elastic half-spaces are investigated; and the complex dispersion equation of Stoneley-wave motion in the fluid is obtained. This equation relates the viscosity of the fluid, the S-wave, and the P-wave velocities in the formation, and the fracture thickness to the dispersion velocity and the attenuation coefficient of Stoneley-wave in the viscous fluid-filled fracture. The effect of the fracture width on both the dispersion velocity and the attenuation coefficient of Stoneley-wave is investigated. The results of the numerical simulation study show that the fluid viscosity has a slight effect on the velocity dispersion of Stoneley-wave, especially, in the case of hard formation (sandstone). In the case of soft formation, this effect increases especially for small fracture width (less than one millimeter). On the other hand, it dramatically changes the attenuation coefficient versus frequency curves in both shape and amplitude. Also, the results show the existence of a critical frequency corresponding to a maximum attenuation. The results obtained from this study can be used in hydraulic fracturing. Namely in the detection of fracture as well as in the estimation of the fracture width.