A general transport model for advection-diffusion process through fractures featuring self-affine properties and mismatched phenomena

Quantitative description of the advection-diffusion behavior in a single fracture is of fundamental importance for the accurate evaluation of the solute transport behavior and properties, and even for the analysis of the complex hydrodynamic problems. However, the surface roughness and mismatch featured in natural fractures significantly affect the solute advection-diffusion process, with the effect from latter not been fully verified. In this work, the effects of surface roughness and mismatch on advection-diffusion process were reexamined, four control factors (i.e., local roughness factor (f(r)), hydraulic tortuosity (tau), surface tortuosity (tau(s)), and surface mismatch factor (f(m))) were identified by analytical derivation, and a new modified Taylor-Aris equation was accordingly established. To further reveal the influence mechanism of surface roughness and mismatch on advection-diffusion behavior, a series of Lattice Boltzmann simulations of the advection-diffusion process were conducted. Results indicate that, surface roughness and mismatch affect the advection-induced dispersion behavior both in the form of decreasing the average fluid velocity, with an inverse S-shaped decreasing relationship presented between the latter and the average fluid velocity. Moreover, the influence of surface mismatch on advection-diffusion is independent of surface roughness, and the advection-induced dispersion is inversely proportional to f(r) tau(2) tau(6)f(m)(4.5). Numerical comparison demonstrated the performance of our modified model, and its generalization was approved by theoretical analysis.