Stress Dependency of Shale Elastic Properties: Measurements, Modelling and Prediction

Abstract

Stress dependency of the TI elastic tensor of shales is important for seismic interpretation, fluid identification, 4D monitoring, etc. Using Sayers-Kachanov formalism, we develop a new model for transversely isotropic (TI) media which predicts stress dependency of all five elastic coefficients. The four fitting parameters (namely, tangential compliance, the ratio of normal to tangential compliance of a single crack, characteristic pressure and crack orientation anisotropy parameter) are calculated for stress dependencies of elastic properties of about 20 shales obtained from our laboratory measurements and also from a literature survey. The ratio of normal to tangential compliance of a single crack is equal to 0.1-0.2 for the majority of the shales and shown to be close to unity just for a few shales. Thus, it appears that the socalled scalar crack approximation (that implies that shear and normal compliances are equal) is not generally applicable to shales and the full form of Sayers- Kachanov formulae is used for further analysis. The four fitting parameters show moderate correlations with the depth from which the shale was extracted. With increasing depth, the tangential compliance broadly decreases exponentially and the ratio of normal to tangential compliance generally increases linearly. The crack orientation anisotropy parameter exponentially increases with the depth for most of the shales indicating that cracks may be more aligned in the bedding plane. The characteristic pressure shows no simple correlation with depth. The suggested model allows prediction of the stress dependency of all five elastic coefficients if only three of them are known. This can be useful, for instance, for the reconstruction of all five elastic coefficients of shale from log data.