The stress dependence anisotropic elastic properties of shale

Abstract

The stress dependence anisotropic elastic properties of shale is experimentally evident. It is well explained by the homogenization theory for a medium containing imperfect contact areas (ICA) of which the elastic properties are functions of the effective confining stress. For practical purpose, a minimum number of parameters related to the ICA is considered and calibrated on experimental data. It is observed that the trends of the five transversely isotropic elastic stiffnesses versus the effective confining stress can be well captured by four microscopic parameters: (1) a parameter that characterizes the orientation distribution of the contacts; (2) a ratio between the normal and in-plane compliances of the contacts; (3) the magnitude of the contact compliance at the stress-free condition; and (4) a curvature parameter that defines the dimensionless evolution of the contact compliance versus the effective confining stress. More importantly, these parameters can be fixed for different groups of materials: e.g. wet shale, dry shale, kerogen-rich shale, etc. therefore, a strong predictive capacity of the proposed method is approved. It is then used to predict the effective stiffnesses of shale at a high stress range using the measured data at a low stress range. It can also be used to explain the difference between the elastic properties of in-situ shale and shale samples at a stress-free or a modified stress condition in laboratory. Taking into account the stress dependence contact effect can also offers a capacity to analyze the relationship between its dynamic and static elastic properties.