Predictive model for solute transport in a rough rock fracture based on fractal theory

To investigate the effect of fracture surface roughness on solute transport in a rough fracture and the effect on the hydrodynamic dispersion coefficient D_L and transport velocity V_t, roughness and hydraulic aperture of various fractures under constant head were calculated using fractal theory. The study discussed the influence of roughness on solute transport in rough fractures, as well as the seepage flow and solute velocity with different fractal dimensions. Breakthrough curves were generated by integrating the Navier-Stokes equation and the advection-diffusion equation (ADE). The breakthrough curves from direct simulation were coupled using the classical ADE approach. Subsequently, D_L and V_t were determined. The study explored the control exerted by D_L and V_t on solutes and their correlation with roughness. A prediction model based on fractal theory for solute transport in rough fractures was established and compared with direct simulation and geometric feature-based models. Results indicate that fractal dimension D and amplitude parameter K_v effectively characterize surface roughness, with a strong correlation between D_L, V_t, and fractal parameter DK_v. The established model demonstrates high applicability and accuracy in simulating solute transport in rough fractures.