Estimation of Thomsen’s Epsilon and Delta in a single core using ultrasonic phase and group velocity measurements

This report shows results from a method we develop to estimate the stress-dependent V [subscript P0], Epsilon and Delta, using a single core placed inside a triaxial frame. First, we measure phase and group velocities using ultrasonic transducers while the rock undergoes confining and deviatoric stress. Phase velocities are obtained using conventional ultrasonic end-caps in the triaxial frame while group velocities are obtained by adding small-size transducers around the core sample. The small-size transducers work both as receivers and transmitters, generating a waveform dataset with tomographic coverage. Then, we apply a Bayesian inversion method to calculate V [subscript P0], Epsilon and Delta using the group velocity measurements. We combine inversion results with phase measurements to estimate the stress-dependent velocity anisotropy. The developed method accurately captures anisotropy in a single horizontal core under conditions of stress. We test the method by applying isotropic and deviatoric stress paths on two samples: a Berea sandstone with negligible initial anisotropy and a Mancos shale with a high degree anisotropy. Results show that the elastic response from velocity and strains is linked to pre-existing anisotropy within the rock. Inverted anisotropy parameters are consistent with previous work where anisotropy parameters were obtained using the conventional method that requires three cores. This work has been published in the 60th Annual Symposium of the SPWLA with the title Estimation of Thomsen’s Epsilon and Delta in a Single Core Using Ultrasonic Phase and Group Velocity Measurements