Geomechanical Workflow and Sensitivity Study for Calibrating and Predicting Elastic Moduli and Minimum Horizontal Stress from Well Logs in an Anisotropic Formation Available to Purchase

Shale and other formations exhibit vertical transverse isotropic (VTI) anisotropy in the sense that rock properties are different in the vertical and horizontal directions; thus, the horizontal acoustic velocity is different from that of vertical velocity. Elastic moduli, the vertical and horizontal Young’s modulus and Poisson’s ratio, are parameters required to estimate formation stress in VTI anisotropic formations. The elastic moduli can be described in terms of five stiffness coefficients. Two of which (C33 and C₄₄) are obtained from density combined with vertical compressional and shear logs, respectively. A third elastic stiffness (C₆₆), is estimated using the full-waveform sonic measurements of Stoneley and Flexural mode data, along with input log data. The other two stiffness coefficients (C₁₁ and C₁₃) must be estimated by construction and calibration of a model. Calibration and construction of such a model ideally occurs by means of laboratory static and dynamic measurements of the velocities and elastic moduli; and, failing that, trends drawn from published laboratory and field data can be used. The main challenge is to construct and calibrate a model for estimating stiffness coefficients and elastic moduli. Additionally, using the predicted and calibrated static elastic moduli, along with total vertical stress, pore pressure, the Biot Coefficient, and the principle elastic strains, calibrate from fracture injection test data the formation minimum and maximum horizontal stresses.

An empirical model is constructed and calibrated to estimate C₁₁ and C₁₃ from C₃₃, C₄₄, and C₆₆, thus filling in the five required parameters to compute the dynamic elastic stiffnesses. The model is constructed such that, if the vertical and horizontal shear velocities are equal, there is no formation anisotropy. Finally, based on core data, a dynamic-to-static elastic moduli correction is defined and used to compute the final static elastic moduli. It is assumed, for simplicity, that the total vertical stress, pore pressure, and Biot Coefficient are correct, and the principle elastic strains are solved for from fracture injection test data. With all these parameters and the model defined, it is possible to estimate the maximum and minimum formation stress and, thus, describe the faulting regime (Normal, Strikeslip, or Reverse).

Robustness and sensitivity of the calibrated stiffness coefficient and elastic moduli model is demonstrated using laboratory data. Results are also presented and discussed for an unconventional shale example. Here, the model correctly distinguishes between an isotropic formation and the shale above and below. A two-layer model is derived for each shale; a highly anisotropic layer with high total organic carbon and a weakly anisotropic model wherein there is minimal or no organic carbon. This model is consistent with the core data and demonstrates the necessity of adequate sampling.