Analytical model for reactive solute transport in a channel-matrix system

Objective The accurate quantitative characterization of fractured media and the theoretical research on solute transport in fractured media have become the key to the prevention and control of groundwater contamination in fractured aquifers. Currently, fractured aquifers are generalized to horizontal fractures, ignoring the geometric characteristics of the open parts of fractures, called channels, and the impacts of matrix diffusion on solute transport. Methods A model for solute transport in a single channel-matrix system was established, obtaining the semi-analytical solutions using Laplace transform and numerical inverse transforms. The COMSOL Multiphysics software was employed to construct a numerical model for verification. Furthermore, the impacts of parameters like hydrodynamic dispersion coefficient and retardation factor on the solute transport pattern were quantitatively analyzed, and the spatio-temporal patterns of solute transport were revealed by calculating the solute diffusion flux and storage. Results and conclusions The results indicate that a higher hydrodynamic dispersion coefficient of the channel was associated with a higher early solute concentration and a lower peak concentration in the breakthrough curves. Moreover, the solute concentration in the fracture decreased with an increase in the retardation factor. The peak diffusion flux decreased with an increase in the dispersion coefficient in the fracture. By analyzing the breakthrough curves at different positions and the spatial distribution curves of diffusion flux, this study posits that back diffusion is the main cause of the significant tailing of the breakthrough curves. Under the boundary condition of pulsed injection, the total amount of solute stored in the fracture—the primary storage space—rapidly increased and then gradually decreased, while that in the matrix increased. Overall, the calculation and analysis of the theoretical model necessitate emphasizing the impacts of the solute storage capacity of the matrix and back diffusion on the solute transport patterns in the channel-matrix system.