Characterization of Anisotropic Elastic Moduli and Stress for Unconventional Reservoirs Using Laboratory Static and Dynamic Geomechanical Data
Authors: Hamza Farrukh , Chen Cheng , Gu Ming , Quirein John , Martysevich Vladimir , Matzar Luis 
Published: February 2018

Summary
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 the geomechanical properties of VTI shale requires five independent stiffness coefficients. In a vertical well, two of them are directly calculated from the velocity of the vertically propagating compressional waves (P-waves) and shear waves (S-waves), whereas a third is estimated from the Stoneley-wave velocity. To obtain the last two stiffness coefficients, an empirical model must be used. This study integrates laboratory mechanical and sonic measurements to evaluate the ANNIE and modified-ANNIE models and extend the dynamic-to-static conversion equations. The ANNIE model is a three-parameter empirical model proposed by Schoenberg et al. (1996) to interpret anisotropic stiffness coefficients.
Laboratory static and dynamic geomechanical experiments were applied to multiple core plugs extracted at different depths from a target shale play. Using a laboratory ultrasonic scanner, velocities were measured in different directions to obtain the five stiffness coefficients. To compare the performance of the two empirical models, three stiffness coefficients were then applied along with the ANNIE or modified-ANNIE models for estimating the dynamic Young's modulus and Poisson's ratio. The static elastic moduli were measured using triaxial compression experiments; horizontal and vertical core plugs were tested to account for anisotropy.
Static and dynamic results illustrated that 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 (vertical) ≥ν (horizontal). Static and dynamic data illustrated that the anisotropic σhmin (minimum horizontal stress) was predominantly higher than the isotropic σhmin. This implied that using an isotropic model to predict laminated shale will underestimate σhmin. 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 (2011) and Morales and Marcinew (1993) equations. The Canady (2011) equation was extended to the “very hard” (greater than 70-GPa or 10.2-Mpsi Young's modulus) regime, whereas the Morales and Marcinew (1993) equation was extended to the regime of porosity less than 10%. Mpsi = 1,000 psi. Finally, the results of σhmin predicted by the isotropic and two anisotropic models (ANNIE and modified-ANNIE) were compared with the values of σhmin calculated using full ultrasonic data measured in the laboratory, showing that modified-ANNIE improved the prediction by solving the stress-underestimation issue of the ANNIE and isotropic models.