Understanding Heterogeneous and Anisotropic Porous Media Based on Geometric Properties Derived From Three-Dimensional Images

Natural porous media are generally heterogeneous and anisotropic. The structure of porous media plays a vital role and is often the source of their heterogeneity and anisotropy. In physical processes such as fluid flow in porous media, a small number of dominant features, here referred to as wide channels, are responsible for the majority of the flow. The thickness and orientation of these channels often determine the permeability characteristics of the media. Typically, identifying such dominant features requires extensive and costly simulations. Here, we propose a prompt approach based on geometric properties derived from three-dimensional (3D) images. The size or radius of the dominant features is obtained via distance maps, and their orientations are determined using Principal Component Analysis. Subsequently, we visualize these dominant features with color and color brightness according to their orientation and size, together with their location and distribution in 3D space. The combined visualization of anisotropy (orientation) and heterogeneity (size) in a single plot provides a straightforward way to enhance our understanding of pore structure characteristics. Besides, we propose a refined stereographic projection method to statistically illustrate both heterogeneity and anisotropy. Based on these insights, we further present a potential approach to reduce model size in numerical simulations, significantly reducing computational costs while preserving essential characteristics.