Understanding heterogeneous and anisotropic porous media based on geometric properties derived from three-dimensional images

Natural porous media is generally heterogeneous and anisotropic. The structure of porous media plays a vital role and is often the source of the heterogeneity and anisotropy. In physical processes such as fluid flow in porous media, a small number of major 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. Typically, the identification of such major features is conducted through time-consuming and expensive simulations. Here we propose a prompt approach based on geometric properties derived from three-dimensional (3D) images. The size or radius of the major features is obtained via distance maps, and their orientations are determined by Principal Component Analysis. Subsequently, we visualize these features with color and color brightness according to their orientation and size, together with their location and distribution in 3D space. The simultaneous visualization of anisotropy (orientation) and heterogeneity (size) in one 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 new way to compress the model size in numerical simulation, therefore significantly reducing the computational cost, while retaining its essential characteristics.