Spatial moment analysis of solute transport with Langmuir sorption in a fracture–skin–matrix coupled system

Sorption is one of the key processes that plays a major role in the transport of contaminants in fractured porous media. Extensive studies have been conducted on sorption isotherms in fracture matrix coupled system but studies pertaining to sorption in fractured porous media with fracture–skin are very limited. In this study, a numerical model is developed for analysing the influence of sorption intensities on velocity, macro dispersion coefficient and dispersivity using the method of spatial moments. Implicit finite difference numerical technique has been used to solve the coupled non-linear governing equations. A varying grid is adopted at the fracture and skin interface to capture the mass transfer at the interface. Results suggest that the role of non-linear sorption is dominant in comparison with that of advection and dispersion in deciding the final relative concentration within the fracture. The role of sorption partition coefficients is not always enhancing the mixing phenomena which lead to dilution of solutes. Furthermore, the role of sorption partition coefficients is extremely sensitive in the sense that the resultant magnitude of effective dispersivity may either get enhanced or mitigated depending on the magnitude of sorption partition coefficients.