Representative elementary area of shale at the mesoscopic scale

Abstract

The Representative Elementary Area (REA) of two shales (Callovo-Oxfordian claystone and Tournemire argillite) that are actively studied in the framework of the deep disposal of radioactive waste have been estimated from two mineral maps by classical methods (i.e., the box-counting and statistical approaches) and by different microstructural descriptors (i.e., the two-point probability function, lineal path function, percolation length, and variogram). The classical box-counting method provides estimates of the REA size of the clay fraction in the range from 129 μm to 441 μm, consistent with estimates obtained from the literature on other shales. However, these estimates show an extreme sensitivity to the chosen ε threshold or error and a wide scatter, thereby bringing the statistical homogeneity of both maps into question. Although the two-point probability function and lineal path function infer lower bounds of the REA size, these microstructural descriptors are relevant to demonstrate the microstructural anisotropy of both shales due to the alignment of nonclay grains parallel to bedding at the study scale. The results from the two-point probability function and variogram undoubtedly confirm that the Tournemire mineral map is not statistically homogeneous with regard to its mineral composition. This aspect it makes difficult to interpret the results and even questions the REA size determination of this particular map. Finally, our set of results allow us to recommend the use of the two-point probability function and variogram to preliminarily validate the statistical homogeneity of maps under study before calculating the REA size using conventional methods, e.g. the box-counting and statistical approaches.