A Study of Geometrical Effects on Permeability Estimation in Three-dimensional Fractures Using the Lattice Boltzmann Method

Abstract

This study investigates the effect of geometry on permeability estimation in three-dimensional fractures using the Lattice Boltzmann Method. Fractures have irregular and complex shapes, which can significantly impact their permeability. Anisotropy of permeability is important as it indicates the influence of changes in fracture orientation on the flow and transport properties of fluids. To examine the relationship between permeability and fracture geometry, we generated three-dimensional fracture geometries using fractal Brownian motion with a Hurst exponent to describe the roughness on the fracture surface. The fractures in this study have varying mean aperture, ranging from narrow to wide, with surface roughness that can be either uniform or non-uniform. The Lattice Boltzmann Method was performed to calculate permeability and investigate the relationship between permeability and geometric parameters of fractures, such as mean aperture and surface roughness. Our results were in good agreement with previous studies on two-dimensional fractures. We found a clear relationship between permeability and mean aperture. Both in uniform and non-uniform geometry have the same trend as the mean aperture increased, permeability generally increased, while rougher surface roughness permeability generally decreased but in non-uniform geometry the data on the graph appears more random and irregular. We extended our investigation to real fractures by digital rock portal data. The analysis revealed that the geometry of the real fractures closely resembled non-uniform geometry, and the permeability exhibited anisotropic behaviour. In addition, the anisotropy of permeability and computation time were also investigated; and it was found that both can be influenced by the three-dimensional fracture geometry.