Statistical representative elementary area of shale inferred by micromechanics

Abstract

This paper provides new estimates for the Representative Elementary Area (REA) sizes of the following two shales that are actively being studied in the framework of deep disposal of radioactive waste: Callovo-Oxfordian (COx) claystone from the Meuse/Haute-Marne underground research laboratory (Eastern France) and Toarcian argillite from the experimental station of Tournemire (Southern France). The REA sizes, named LREA, were obtained from two mineral maps following the classic “counting box” (CB) method and a statistical approach that introduces the concept of a “statistical” REA. Following this approach, a “statistical” REA is related not only to the microstructure and the properties of each of the components but, above all, to a given precision in the estimation of the effective property depending on the number of realizations that one is ready to generate. The probabilistic concept of realization is here, from a practical viewpoint, a subdomain of a mineral map in which the apparent morphological or mechanical properties have to be calculated. In this study, the apparent elastic moduli of the subdomain have been estimated using two micromechanical models. The first micromechanical model consisted of an inclusion-based model for which spherical nonclay grain is embedded in a clay matrix in which the values of its transverse isotropic stiffness tensor have been taken from literature. The second micromechanical model was an isotropic inclusion-based model for which a spherical nonclay grain is embedded in a clay matrix; the elastic moduli values have been inverted by a Monte-Carlo approach from the engineering moduli of both shales under study. Our calculations have shown the following results: (i) the statistical morphological LREA considering the surface clay fraction are of the same order of magnitude as those measured in other shales and those obtained by the simple CB method, with relative error values between 5 and 10%, (ii) the mechanical LREA values associated with the bulk modulus and shear modulus are significantly greater than that of the morphological LREA, and (iii) the mechanical LREA estimates of the shear modulus are greater than that of the bulk modulus. Moreover, our study highlights that these qualitative results do not depend on the chosen micromechanical models and, thus, would be independent of the underlying anisotropic nature of shale.