Confronting heterogeneous sorption and hydrodynamic dispersion on solute transport in a fracture-skin-matrix system using spatial moment analysis.

Understanding the intricacies of inter-dependency of fluid flow and solute transfer at the scale of a single fracture is limited by various simplifying assumptions employed for computational purposes. In the present study, the fracture-rock matrix interface is assumed to be consisting of a skin layer with sufficient mass transfer properties where non-linear adsorption is considered to be the limiting reaction among the various interfaces. A numerical model has been developed using implicit finite difference method with varying grids at the fracture-skin interface to capture the mass transfer during solute transport in the presence of non-linear Sips adsorption. The model was used to identify the critically influencing parameters on the temporal profiles of fluid velocity, macro-dispersion coefficient and dispersivity using the method of spatial moments. The results indicate that the presence of the skin has enhanced the mixing phenomenon as well as the sorptive mass transfer rates. Summary of the sensitivity analysis provides the critical factors to be considered while employing such comprehensive models for elucidating details at a small scale. The presence of fracture-skin evades the sensitive role played by (a) the fracture adsorption coefficient (with a reduced rate constant for adsorption and an increased rate constant for desorption) at early times, while resulting in an enhanced mixing characteristics at later times, and (b) maximum sorption capacity of fracture as a function of solute velocity; and in turn, it provides an improved control over the transportation of solutes through the fracture.