Three-Dimensional Lattice Boltzmann Simulations of Single-Phase Permeability in Random Fractal Porous Media with Rough Pore–Solid Interface

Lacunarity as a quantitative measure of mixing—a micro-CT analysis-based case study on granular materials

In practically every industry, mixing is a fundamental process, yet its 3D analysis is scarce in the literature. High-resolution computed tomography (micro-CT) is the perfect X-ray imaging tool to investigate the mixing of granular materials. Other than qualitative analysis, 3D micro-CT images provide an opportunity for quantitative analysis, which is of utmost importance, in terms of efficiency (time and budget) and environmental impact of the mixing process. In this work, lacunarity is proposed as a measure of mixing. By the lacunarity calculation on the repeated micro-CT measurements, a temporal description of the mixing can be given in three dimensions. As opposed to traditional mixing indices, the lacunarity curve provides additional information regarding the spatial distribution of the grains. Discrete element method simulations were also performed and showed similar results to the experiments.

Characterization of Two-Phase Flow from Pore-Scale Imaging Using Fractal Geometry under Water-Wet and Mixed-Wet Conditions

High resolution micro-computed tomography images for multiphase flow provide us an effective tool to understand the mechanism of fluid flow in porous media, which is not only fundamental to the understanding of macroscopic measurements but also for providing benchmark datasets to validate pore-scale modeling. In this study, we start from two datasets of pore scale imaging of two-phase flow obtained experimentally under in situ imaging conditions at different water fractional flows under water-wet and mixed-wet conditions. Then, fractal dimension, lacunarity and succolarity are used to quantify the complexity, clustering and flow capacity of water and oil phases. The results show that with the wettability of rock surface altered from water-wet to mixed-wet, the fractal dimension for the water phase increases while for the oil phase, it decreases obviously at low water saturation. Lacunarity largely depends on the degree of wettability alteration. The more uniform wetting surfaces are distributed, the more homogeneous the fluid configuration is, which indicates smaller values for lacunarity. Moreover, succolarity is shown to well characterize the wettability effect on flow capacity. The succolarity of the oil phase in the water-wet case is larger than that in the mixed-wet case while for the water phase, the succolarity value in the water-wet is small compared with that in the mixed-wet, which show a similar trend with relative permeability curves for water-wet and mixed-wet. Our study provides a perspective into the influence that phase geometry has on relative permeability under controlled wettability and the resulting phase fractal changes under different saturations that occur during multiphase flow, which allows a means to understand phase geometric changes that occur during fluid flow.

Comparative Study of Lattice Boltzmann Models for Complex Fractal Geometry

A standard model, one of the lattice Boltzmann models for incompressible flow, is broadly applied in mesoscopic fluid with obvious compressible error. To eliminate the compressible effect and the limits in 2D problems, three different models (He-Luo model, Guo’s model, and Zhang’s model) have been proposed and tested by some benchmark questions. However, the numerical accuracy of models adopted in complex geometry and the effect of structural complexity are rarely studied. In this paper, a 2D dimensionless steady flow model is proposed and constructed by fractal geometry with different structural complexity. Poiseuille flow is first simulated to verify the code and shows good agreements with the theoretical solution, supporting further the comparative study on four models to investigate the effect of structural complexity and grid resolution, with reference results obtained by the finite element method (FEM). The work confirms the latter proposed models and effectively reduces compressible error in contrast to the standard model; however, the compressible effect still cannot be ignored in Zhang’s model. The results show that structural error has an approximately negative exponential relationship with grid resolution but an approximately linear relationship with structural complexity. The comparison also demonstrates that the He-Luo model and Guo’s model have a good performance in accuracy and stability, but the convergence rate is lower, while Zhang’s model has an advantage in the convergence rate but the computational stability is poor. The study is significant as it provides guidance and suggestions for adopting LBM to simulate incompressible flow in a complex structure.

Pore Structure of Grain-Size Fractal Granular Material

Numerous studies have proven that natural particle-packed granular materials, such as soil and rock, are consistent with the grain-size fractal rule. The majority of existing studies have regarded these materials as ideal fractal structures, while few have viewed them as particle-packed materials to study the pore structure. In this study, theoretical analysis, the discrete element method, and digital image processing were used to explore the general rules of the pore structures of grain-size fractal granular materials. The relationship between the porosity and grain-size fractal dimension was determined based on bi-dispersed packing and the geometric packing theory. The pore structure of the grain-size fractal granular material was proven to differ from the ideal fractal structure, such as the Menger sponge. The empirical relationships among the box-counting dimension, lacunarity, succolarity, grain-size fractal dimension, and porosity were provided. A new segmentation method for the pore structure was proposed. Moreover, a general function of the pore size distribution was developed based on the segmentation results, which was verified by the soil-water characteristic curves from the experimental database.