In a vertically transverse isotropic (VTI) medium, accurate prediction of the vertical and horizontal Young's moduli (E) and Poisson's ratios (ν) is crucial to predicting minimum horizontal stress (σhmin) and hence selecting drilling mud, cement weights, and perforation locations. Fully characterizing geomechanical properties of VTI shale requires five independent stiffness coefficients: C33, C44, C66, C11, and C13. In a vertical well, C33 and C44 are directly calculated from the velocity of the vertically propagating P- and S- waves, while C66 is estimated from the Stoneley wave velocity. To obtain C11 and C13, an empirical model must be employed. This study integrates laboratory mechanical and sonic measurements to evaluate the ANNIE and modified-ANNIE models and extend the dynamic-to-static conversion equation.
Laboratory static and dynamic geomechanical methods were applied to multiple core materials extracted at different depths from a target shale play. The dynamic elastic moduli were measured using a laboratory sonic scanner; velocities were measured in different directions to obtain C33, C44, C11, C66, and C13. The dynamic data were then applied in the ANNIE and modified-ANNIE models for estimating the dynamic elastic moduli, including dynamic Young's modulus and Poisson's ratio. The static elastic moduli were measured using axial compression experiments; horizontal and vertical core plugs were tested to account for anisotropy.
Static and dynamic results illustrated horizontal Young's moduli were predominantly higher than vertical Young's moduli, which suggested a horizontal layered structure. Vertical Poisson's ratios can be greater or smaller than horizontal Poisson's ratios, which is consistent with the prediction of the modified-ANNIE model. Conversely, the ANNIE model always predicts ν(vert) ≥ ν(horz). Static and dynamic data illustrated the anisotropic σhmin was predominantly higher than the isotropic σhmin. This implied that using an isotropic model to predict laminated shale will underestimate σhmin. It was noticed that the static Young's modulus increased with decreasing porosity for the target interval. The elastic moduli measured from the dynamic method were consistently higher than those measured from the static method. The dynamic and static data were used to fit the widely-used dynamic-to-static conversion equations—the Canady and Morales equations. The Canady equation was extended to the "very hard" (greater than 70 GPa Young's modulus) regime, while the Morales equation was extended to the regime of porosity < 10%. Finally, σhmin predicted by different models was compared with the measurements, showing that modified-ANNIE improved the prediction by solving the stress underestimation issue of the ANNIE and isotropic models.