An investigation of nonlinear flow behaviour along rough-walled fractures considering the effects of fractal dimensions and contact areas

Abstract

This study focuses on the investigation of the nonlinear flow behaviour along rough-walled fractures with contact areas in the framework of the lattice Boltzmann method. The numerical results indicate that the fracture surface roughness controls both the advective aperture and the eddy aperture in the analysis of pressure, velocity, and vorticity fields. The eddy volume fraction increases from 28% to 40% with the increase in the fractal dimension from D=2.0 to D=2.4. The parametric analysis based on Forchheimer’s equation further demonstrates that the enhancement in the vorticity field contributes to the strengthened nonlinear flow behaviour. The two competing roles of fractal dimension and contact area greatly impact the non-Darcy flow patterns. The fractal dimension is the main factor affecting flow nonlinearity at a low contact ratio, while the contact area dominates the nonlinear flow behaviour at a high contact ratio. The increase in the contact ratio strengthens the boundary effect, and thus greatly increases the volume of the eddy region and enhances the nonlinearity of the flow field. These observations provide a promising pathway to analyse the flow behaviour along the fracture based on vorticity analysis, and enlighten the understanding of the competing mechanism between fractal dimensions and contact areas for the influence of nonlinear flow behaviours.