Quantifying static and dynamic stiffness anisotropy and nonlinearity in finely laminated shales: Experimental measurement and modeling

Abstract

Sedimentary rocks contain layers and a wide range of microstructures that may produce mechanical complexities including dynamic and quasistatic stiffness anisotropy and nonlinearity. However, most applications in geophysics and geomechanics disregard these mechanical complexities, which can lead to significant error and uncertainty in rock properties and may increase the risk associated with cost-intensive drilling and completions operations in shales. We have conducted simultaneous triaxial stress tests and ultrasonic wave propagation monitoring to measure and model stiffness anisotropy and nonlinearity of Mancos Shale plugs with varying bedding orientations. Results highlight the need for different sets of nonlinear coefficients to describe different stress loading paths, in which isotropic loading exhibits larger increases in stiffness for a given change in mean stress (and strain) than deviatoric loading. The vertical transverse isotropic (VTI) nonlinear model helps to account for the appreciable anisotropy and nonlinearity of Mancos samples, in which the dynamic Young’s moduli [Formula: see text] are more than 25% higher than [Formula: see text] and [Formula: see text] increases by approximately 35% during deviatoric stress loading. Measured static moduli are typically less than 50% of their dynamic equivalent and exhibit separate anisotropic and nonlinear relationships. Therefore, we have developed anisotropic stress-dependent dynamic-static transforms to estimate the static moduli from the nonlinear VTI model. Although heterogeneity and discontinuities cause samples to deviate from VTI symmetry, our modified dynamic-static transforms provide an excellent fit to the experimentally measured Young’s moduli and Poisson’s ratios. Post-test X-ray micro-CT imaging evidences the impact of sample layering and heterogeneity on rock failure and failure geometry. Bedding planes can act as preferential failure planes, whereas layering-induced mechanical stratigraphy can cause fractures to reorient due to changes in lithology. Our combined experimental, modeling, and imaging results provide insight into the complex deformational and failure behavior of shales. The analysis and results also highlight the need to consider the elastic and plastic deformations in shales.