Resolution-Dependent Multifractal Characteristics of Flow in Digital Rock Twin Simulated Using the Lattice Boltzmann Method

Abstract

Digital rock twins are widely used to obtain hydraulic properties of porous media by simulating pore-scale fluid flow. Multifractal characteristics of pore geometry and flow velocity distribution have been discovered with two-dimensional (2D) images and three-dimensional (3D) models, whereas the dependency of results on the resolution is not well known. We investigated resolution-dependent multifractal properties of 3D twin models for a sandstone sample with originally 3 μm resolution images. 3D pore-scale water flow was simulated with the lattice Boltzmann method (LBM). As indicated by multifractal analyses, the generalized dimension spectra, the Hölder exponent spectra, and singularity spectra of the flow velocity are similar to that of the pore geometry but different in ranges and sensitivities to the change in the model resolution. Nonlinear dependencies of 2D/3D porosity, holistic/slice permeability, equivalent pore radius squared, and multifractal parameters on the resolution were discussed.