Non-equilibrium solute transport in a fractured rock matrix system under a radial flow pattern

An improved understanding of complex solute transport processes in a single fracture is the foundation for advancing fracture network research. This study addresses a radial reactive transport problem in a fractured rock matrix system, with an emphasis on the role of non-equilibrium sorption. A new model that integrates a two-site nonequilibrium sorption framework was developed in a single fracture under a radial flow condition. Semianalytical models were derived utilizing Laplace transform techniques. These solutions offer insights into the spatio-temporal concentration, back diffusion and diffusive mass flux issues. When benchmarked against prior solutions, the approach presented here demonstrates superior accuracy and robustness. Several significant results were obtained. First, nonequilibrium sorption leads to a more pronounced peak in the breakthrough curves (BTCs) and diminishes the tailing of BTCs in the system. Second, a higher degradation rate for nonequilibrium sorption reduces the concentration of BTCs in the later stage but has minimal impact in the early stage. Third, after clean water injection, the back diffusion from the rock matrices into the fracture was observed, predominantly near the wellbore, accounting for the tailing behavior. Meanwhile, the diffusive mass flux exhibits a sharp rise and then declines in the early stages. Finally, an increased proportion of equilibrium sorption in the fracture leads to a decrease in the diffusive mass flux, whereas it displays the inverse trend in the rock matrix. In general, these findings underscore the essential role of nonequilibrium sorption considerations for the accurate representation of solute transport processes in fractured rock matrix systems.