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 <i>D</i>_L and transport velocity <i>V</i>_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, <i>D</i>_L and <i>V</i>_t were determined. The study explored the control exerted by <i>D</i>_L and <i>V</i>_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 <i>D</i> and amplitude parameter <i>K</i>_v effectively characterize surface roughness, with a strong correlation between <i>D</i>_L, <i>V</i>_t, and fractal parameter <i>DK</i>_v. The established model demonstrates high applicability and accuracy in simulating solute transport in rough fractures.