Estimation of In-situ Stresses From Ultrasonic Measurements

Abstract

Summary The results of an effort to develop a technique for estimating in-situ stresses by measurement of stress-induced velocity anisotropy around a borehole are presented. Relevant parameters required to make the estimate were identified and measured in the laboratory on a 35.6-cm [14.0 in.] cube of Nugget sandstone with a 10.2-cm 14.0-in.]-diameter hole under biaxial loading. Two pairs each of radially and tangentially polarized transducers were placed inside the hole with displacement directions either parallel or perpendicular to the principal stress directions. With this parallel or perpendicular to the principal stress directions. With this configuration, relative travel times were measured by both a pulsed phase-locked loop (p2L2) technique and a cross correlation of digitize phase-locked loop (p2L2) technique and a cross correlation of digitize waveforms. The biaxial velocity data were used to back-calculate the applied stress. The standard deviation of the differences between the calculated and applied stresses is 0.62 MPa [90 psi] for a stress level up to 8.63 MPa 11,252 psi]. Introduction In the stimulation of gas reservoirs by hydraulic fracturing, it is desirable to predict the direction and extension (containment) of the fractures. To do so, knowledge of in-situ stresses is required. A variety, of techniques have been developed to estimate stresses in rock. At depths beyond a few hundred meters, the only viable technique is microhydraulic fracturing. This, however. is an expensive and time-consuming method. The goal of this research is to develop an alternative but complementary stress-measuring technique to support the stimulation of gas reservoirs. It has been known for some time that the velocity of propagation of ultrasonic waves is stress-dependent. The propagation of ultrasonic waves is stress-dependent. The velocity of a compressional wave is strongly affected by stress if the stress direction is parallel to the propagation direction. The velocity of shear waves is strongly affected by stress if the direction of applied stress is parallel to the polarization direction. In particular, the shear wave generally will be resolved into two components with orthogonal polarization vectors and different velocities if the material is stressed. This phenomenon is called acoustic double refraction or acoustic birefringence. Conversely, it may be possible to infer stresses from the stress-induced velocity anisotropy in a rock mass. Peng et al. reported a scheme to infer in-situ stresses from stress-induced compressional wave velocity anisotropy around a borehole. The approach we have used measures shear-wave velocity anisotropy in a rock mass and differentiates stress-induced velocity anisotropy from velocity anisotropy caused by texture or structures. Assumptions for the velocity-measurement technique are that the borehole is a straight, vertical, circular hole parallel to the vertical stress; the vertical stress can be estimated from overburden; and the medium along the acoustic path is homogeneous. The term "homogeneous" refers to a condition of acoustic homogeneity in the x- y, plane. In other words, it is transversely homogeneous but not necessarily isotropic. The velocity-measurement technique cannot measure the six components of the stress tensor, but it does provide a way to estimate the orientation and magnitude of the principal horizontal stresses.