Sorbing and Non-Sorbing Solute Migration in Rough Fractures with a Multi-Species LGA Model: Dispersion Dependence on Retardation and Roughness

A multi-species Lattice-Gas cellular automaton model was applied to the study of the migration of sorbing and non-sorbing tracers in 2D smooth fractures and in a series of increasing roughness fractures. A tenfold increase of the dispersion of the non-sorbing tracer was calculated in the highest roughness case compared to the smooth fracture. Up to a threefold increase of the dispersion of the sorbing tracers was calculated compared to the non-sorbing tracer. These enhanced dispersions were found to be of a Fickian form and were interpreted in terms of the classical Taylor–Aris dispersion. The effects of roughness and retardation over the increase of dispersion were identified and quantified through a semi-empirical relation. These effects were found additive and independent.