THE STUDY OF GEOMETRICAL EFFECT ON PERMEABILITY ESTIMATION IN THREE-DIMENSIONAL FRACTURE USING THE LATTICE BOLTZMANN METHOD Fatimah Az-Zahra, Irwan Ary Dharmawan*
Faculty of Mathematics and Natural Science, Universitas Padjadjaran
Jalan Raya Bandung Sumedang KM.21, Sumedang 45363, Indonesia
Abstract
In this study, we aimed to investigate the effect of geometry on permeability estimation in three-dimensional fractures using the Lattice Boltzmann Method. Fractures are known to have irregular and complex shapes, and the geometry of a fracture can significantly impact its permeability. To examine the relationship between permeability and fracture geometry, we generated three-dimensional geometries of fractures using fractal Brownian motion with a Hurst exponent to describe the roughness of the fracture surface. The fractures in our study had a mean aperture that ranged from narrow to wide and had a surface roughness that ranged from smooth to rough. The Lattice Boltzmann Method is employed to numerically calculate permeability and investigate the relationship between permeability and fracture parameters such as mean aperture and surface roughness. The results obtained in this study showed good agreement with two-dimensional case study. We found that there is a clear relationship between permeability and both mean aperture and surface roughness in three-dimensional fractures. As mean aperture increased, permeability generally increased as well. Similarly, as surface roughness increased, permeability generally decreased.
Keywords: Fractures, Lattice Boltzmann Method, Mean Aperture, Permeability, Surface Roughness
