Beyond Porosity: The Fractality of Grain Size Distributions and Rock Property Prediction

Abstract The objective of this work is to help enable image-based predictions of mechanical properties while contributing to the general understanding of the microstructural drivers for stiffness and strength in natural aggregates such as sedimentary rocks. Initial results on an investigation into the relationship between internal structure and elastic stiffness are presented. Stiffness values are computed using commercial simulation software on 3D X-ray CT images of Boise sandstone, Fontainebleau sandstone, as well as on synthetic media comprising a spherical grain pack and a homogeneous material containing spherical inclusions. In order to isolate the structural component, a monomineralic composition is assumed with identical solid elastic properties throughout. Image volumes exhibiting the same porosity, but different computed stiffness values are extracted for further study. The volumes are analyzed with a morphological image processing tool that measures local thickness, and which is used as a proxy for material size distribution within the rock skeleton. The resulting distributions are compared within the framework of grading curves as is routinely done in other engineering domains. The results indicate possible fractal characteristic for the size distributions, with the fractal dimension visually ranking with stiffness for a fixed porosity. Further work is warranted to confirm these results via improved image processing.