Application of percolation theory to microtomography of rocks

Abstract Percolation Theory has made significant breakthroughs in the understanding of physical processes through identification of an infinite connected cluster. It allows the definition of critical material parameters such as percolation threshold, critical exponents, crossover length and fractal dimension and has evolved from a purely mathematical approach to an applied field of study. In geosciences, the most popular application of percolation theory is the analysis of fluid flow in porous media. The capability to image the 3D structure of such porous networks through Computed Tomography (CT) opens new avenues for the concise application of percolation theory. Here we summarize digital rock techniques developed to derive rock properties and the critical percolation parameter from CT-scans and compare the results to the mathematical ideal structures and laboratory experiments. We demonstrate that a near ideal synthetic rock, which has been designed to reproduce a homogenous sample for geophysical experiments, portrays significantly different percolation properties to their mathematical counterparts. Furthermore, we present a variety of rock specimens with different microstructures and report stronger departures to the mathematical ideal structures. The generation of derivative models of the digital rock and their percolation analysis allows the identification of the percolation threshold, crossover length and critical exponent of correlation length. The technique is demonstrated in application for upscaling permeability, elastic moduli and yield stress. Three independent techniques for the identification of a Representative Volume Element (RVE) are presented: stochastic analysis, thermodynamic averaging and crossover length. A worked example for a dynamic environment is presented in a transect across a deformation zone, where several RVE subsamples are analyzed in terms of their percolation properties. A clear trend from a 2-D dominated to a 3-D network in the deformation center allowed unprecedented insights into the microphysical dynamic processes that established the percolation network. Examples for the newly emerging trend of time-lapse imaging (so-called 4-D tomography) are also discussed. The provided techniques and concepts thus open a new era in digital rock physics.