Permeability estimation from velocity anisotropy in fractured rock

Abstract

Cracks in a rock mass subjected to a uniaxial stress will be preferentially closed depending on the angle between the fracture normal vectors and the direction of the applied stress. If the prestress fracture orientation distribution is isotropic, the effective elastic properties of such a material after application of the stress are then transversely isotropic due to the overall alignment of the cracks still open. Velocity measurements in multiple directions are used to invert for the probability density function describing orientations of crack normals in such a rock. This is accomplished by expanding the crack orientation distribution function into generalized spherical harmonics. The coefficients in this expansion are functions of the crack density and the crack aspect ratio distribution. The information on fracture distribution obtained from the velocity inversion allows an estimation of the anisotropic permeability of the fractured rock system. Permeability estimates are based on the number of cracks open of each aspect ratio, and the contribution of a given crack is weighted by the cosine of the angle between the crack and the direction of the applied pressure gradient. This approach yields a prediction of permeability as a function of the angle from the uniaxial stress axis. The inversion for crack orientation is applied to ultrasonic velocity measurements on Barre granite, and permeability predictions for this sample are presented. The inversion results are good and reproduce velocity measurements well, and the permeability predictions show some of the expected trends. Initial comparisons of the predictions with available permeability data, however, show deviations, suggesting that further information on partial crack closure and connectivity of cracks should be included into the permeability model.