An efficient rock-physics workflow for modeling and inversion in anisotropic organic-shales

Abstract

In this work we present a workflow for modeling and inversion of physical parameters using ultrasonic wave velocities measured on dry and saturated samples of Bakken, Bazhenov shales and Niobrara marls. The forward problem is based on the well known theory of Ciz and Shapiro (2007) combined with the anisotropic generalization of two empirical elastic models for the rock matrix: the critical porosity model Nur et al. (1998) and Krief et al. model (1990). Moreover, taking into account the high variability of the physical properties of kerogen and clay minerals, and their influence on the mechanical properties of these rocks, the procedure also involves the numerical inversion of such properties, using an efficient numerical routine. The results found for the effective elastic properties and density of clay minerals and kerogen are reasonable taking into account those published in the reference literature. In all cases the quality of fit between real and synthetic data is analysed by means of an adequate error measure. The stability of the predicted elastic coefficients is verified using strain energy restrictions. The calibrated models are also used to quantify the influence of the effective porosity on the computations and for a fluid substitution problem. Finally, we found that even for weak anisotropy the generalized Krief's model requires at least three empirical parameters. We conclude that our novel anisotropic critical porosity model is a simpler and more efficient choice for rock-physics applications.