In situ calibrated velocity-to-stress transforms using shear sonic radial profiles for time-lapse production analysis

Abstract

Borehole acoustic waves are affected by near- and far-field stresses within rocks that exhibit stress sensitivity, typically in medium- to high-porosity formations. Nonlinear, or third-order, elastic constants are obtained from the inversion of borehole sonic shear radial profiles with an elastic wellbore stress model. The stress-to-velocity relationship determined from these profiles in the elastic region surrounding the wellbore is used for calibration to compare with empirical laboratory data traditionally used in time-lapse seismic-feasibility studies to assess simulated production. This analysis enables rock physicists to use the wellbore as a laboratory and to examine the stress dependence of the acoustic velocities from in situ field data in their zone of interest. Laboratory experiments on core samples can yield both empirical and mathematical rock-physics models to describe the relationship between stress and velocity to link rock properties to in situ measurements of acoustic data (seismic and sonic). In an example from offshore Malaysia, full-waveform borehole sonic data are processed to produce shear radial profiles in a deepwater environment. The compressional velocities are mainly sensitive to stress in the polarization-propagation direction, and shear velocities are mainly sensitive to stresses in propagation and polarization directions, as expected from nonlinear elasticity. The three compressional and shear velocities vary greatly with vertical stress depending on the stress path because they depend on the three principal stress magnitudes. In contrast, a classical empirical model that depends on porosity, clay content, and effective stress cannot capture differences caused by stress path because it relies on only one stress. Results show that stress sensitivities are significantly stronger with borehole radial profiles than the empirical model for all considered stress paths (K = −0.5, 0, 0.5, and 1).