In-Situ Stress Models for an Anisotropic Rock Formation Using Well Log Sonic Data - A Comparison of Different Approximations

Abstract

The evaluation and estimation of in-situ stress regimes are vital in many subsurface engineering processes such as borehole stability in deep well drilling, hydraulic fracturing design, water injection for pressure maintenance, geothermal recovery, and geological carbon sequestration. For complex lithology and highly laminated rock formations such as an organic-rich shale gas reservoir or a clay-rich overburden caprock, the anisotropic mechanical rock properties can be described as transversely isotropic with a vertical symmetry axis - the so-called vertical transverse isotropic (VTI) models. The use of the poro-elasticity concept is one of the most common approaches in the determination of in-situ stresses. It assumes a porous rock medium and uses elastic parameters, vertical stress, and pore pressure for horizontal stress determination. The application is relatively trivial for isotropic rocks as the elastic parameters can be estimated/obtained from compressional and shear velocity waves available from well logs. However, for anisotropic rocks with transverse isotropy, the approach becomes more complicated. Only three of the five unknown independent stiffness coefficients can be calculated from well logs, requiring advanced sonic logging tools in vertical wells to provide compression, shear and Stoneley waves. The remaining two coefficients involve various assumptions and empirical correlations for their approximations, with no clear consensus or indication as to which is more valid or more accurate than the other. In this paper, we examine 3 different well-known models and assumptions to derive the VTI minimum in-situ stress for a deep anisotropic rock formation. Specifically, we examine a class of established models and a more recently developed lab-based regression/empirical model. The strengths and weaknesses of each approach are discussed, and a straightforward workflow is proposed. This workflow integrates all possible constraints on the critical stiffness coefficients based on data quality and availability and includes a pragmatic approach to calibrating the log-derived in-situ stress profile with field injection data. Here, we adopt a simplified calibration approach and compare its merit to the traditional scheme.