Understanding how surface roughness influences nonlinear fluid flow in rock fractures is essential for a wide range of engineering and geophysical applications, including groundwater migration, oil and gas extraction, and the long-term stability of subsurface energy storage. In this study, we employ the lattice Boltzmann method to investigate the nonlinear flow characteristics in fractures containing different roughness element geometries, including rectangular, semicircular, and triangular forms. Numerical simulations are conducted across Reynolds numbers from 50 to 200 and relative roughness ratios (b/H) from 0.2 to 0.6, capturing the transition from Darcy to non-Darcy regimes. The results show that the geometry and height of roughness elements exert a profound influence on local flow behavior, including velocity distributions, pressure gradients, and vortex formation. Rectangular elements cause the strongest flow obstruction and energy loss, while triangular elements lead to smoother streamlines and reduced drag. Semicircular elements exhibit an intermediate response, balancing viscous and inertial effects. Based on the simulation data, an empirically fitted drag coefficient model is proposed that explicitly incorporates both the Reynolds number and relative roughness height. In addition, a shape-dependent Forchheimer seepage model is formulated to describe nonlinear flow behavior beyond Darcy's law quantitatively. Compared with traditional empirical models, the proposed correlations explicitly account for geometric effects, providing a physically grounded framework for predicting hydraulic performance in rough-walled fractures. The findings contribute to the theoretical foundation for modeling fluid transport in fractured media and offer a potential reference for multi-scale simulations involving complex rough fracture networks.
Ma et al. (2026) studied this question.