Effects of borehole stress concentration on elastic wave velocities in sandstones

The stress redistribution that occurs in the vicinity of a borehole may lead to damage or failure of the rock. If the vertical stress is a principal stress, the principal stresses at the wall of a vertical well are the hoop, radial, and vertical stresses. The hoop stress varies with position around the wellbore and takes its maximum compressive value at the azimuth of the far-field minimum horizontal stress. This may lead to compressive failure at this azimuth if the compressive strength of the rock is exceeded. Recent developments in sonic logging allow the variation in elastic wave velocities with radius and azimuth around a borehole to be characterized. Since elastic wave velocities in sandstones are sensitive to changes in stress, owing to the presence of stress-sensitive grain boundaries within the rock, this allows the changes in stress to be monitored. An expansion of the elastic compliance of the grain boundaries to first order in stress shows that a radially polarized, vertically propagating shear wave is more sensitive to radial stress than to hoop stress. Close to the wellbore, however, large changes in stress occur, and any nonlinearity in the variation in compliance of the grain boundaries as a function of stress becomes important. This nonlinearity increases the sensitivity to the wellbore pressure, and can cause significant reductions in the velocity of compressional and shear waves in the vicinity of the wellbore.