Multiple Cubes Growth Algorithms for Simple Representative Elementary Volume Determination on 3D Binary Images

Abstract

Porosity analysis is fundamental for understanding various material properties and transport phenomena in scientific and engineering disciplines. This study delves into the challenging task of determining the representative elementary volume (REV) in porous media, crucial for accurate analyses. Two novel algorithms, Center-Corner Cubes Growing (3CG) and Random Cubes Growing (RCG), were proposed and tested on synthetic body-centered cubic (BCC) sphere packing and natural porous structures of Berea sandstone and Indiana limestone, obtained using µCT. First algorithm (3CG) operates by analyzing porosity within cubes growing from each of the eight corners and a central region of a 3D binarized stack. In contrast, the Random Cube Growing (RCG) algorithm randomly selects seed points within the 3D stack and grows cubic regions around them. Both algorithms systematically compute porosity for various cube sizes, determining the average porosity and standard deviation for each extent. These visual analytics tools contribute to identifying the specific size ranges where porosity curves converge and stabilize, indicating potential REV within the material. While 3CG simplifies the approach by focusing on a limited number of curves, RCG provides a broader view, capturing diverse porosity patterns. The absence of consistent local minima in certain cases indicates high porosity heterogeneity and the impossibility of achieving REV in certain sample sizes.