Effect of Pore-Wall Roughness and Péclet Number on Conservative Solute Transport in Saturated Porous Media

While modeling solute transport has been an active subject of research in the past few decades, the influence of pore-wall roughness on contaminant migration has not yet been addressed. We therefore conduct particle tracking simulations in three porous domains that have different pore-wall roughness characteristics. Specifically, we consider five surface fractal dimensions d_s = 1.0, 1.1, 1.2, 1.4, and 1.6, and four different Péclet numbers Pe = 10, 10², 10³, and 10⁵. Overall, arrival time distributions are simulated for 60 scenarios (3 domains (Formula presented.) 5 surface fractal dimensions (Formula presented.) 4 Péclet numbers) some of which show heavy-tailed patterns indicating non-Fickian transport. To interpret the simulations and quantify the transport behavior, we analyze the resulting arrival time distributions by the continuous time random walk (CTRW) approach. Results show that, on average, as the surface fractal dimension increases from 1.0 to 1.6, the CTRW model parameters (Formula presented.), an exponent showing the degree of anomalous transport, v, the average solute velocity, and t₂, the cut-off time to Fickian transport, remain nearly constant. However, the dispersion coefficient, D, increases and the characteristic transition time, t₁, decreases. We found t₁ and D are more sensitive to pore-wall roughness compared to the other CTRW parameters. We also found that as the Péclet number increases from 10 to 10⁵, on average, v and D increase, t₁ and (Formula presented.) decrease, and t₂ remains nearly constant. The simulations demonstrate that the exponent (Formula presented.) and the dispersion coefficient are correlated to the average solute velocity.