Influence of the fractures roughness of rock on fluid flow by the lattice Boltzmann method

Abstract

Objective The morphological structure of the fractures in the rock mass is complex, and the fissures rough characteristics of the rock have a great influence on the permeability of the fractures. The current traditional numerical simulation software is mainly based on the macroscopic evaluation of equivalent continuous media, which cannot simulate the mesoscopic fluid flow characteristics within the tiny structure of the fracture. Although there exist models for assessing the permeability of rough fractures considering fracture roughness characteristics, it lacks physical meaning and has limitations in taking standard deviation of the profile height of rough fractures as the quantitative representation of rough characteristics. Methods Firstly, the W-M (Weierstrass-Mandelbrot) function was applied to construct a numerical model of a two-dimensional rough single fracture with different fractal dimensions. Secondly, the simulation of fluid flow at the mesoscopic scale was realized by programming based on the lattice Boltzmann method theory and analysed by combining the cubic law formulation with the value of standard deviation of the fracture profile height as a quantitative characterization of roughness. Results The results show that the cubic law formula using standard deviation value of the fracture profile height as a quantitative characterization of the roughness feature is inadequate. It is feasible to use the fractal dimension as a local modified cubic law formulation for the quantization of rough features. Conclusion The study of rock fracture fluid flow has important engineering practical significance for groundwater pollution control and groundwater resource assessment.

Keywords

• lattice boltzmann method
• two-dimensional rough single crack
• fractal dimension
• cubic law