Validation of classical density-dependent solute transport theory for stable, high-concentration-gradient brine displacements in coarse and medium sands

A series of careful laboratory soil column experiments was carried out for the purpose of providing data for testing recently presented theories of miscible density-dependent flow and transport. In particular, modifications to the standard theory involve extensions to both Darcyʹs (for flow) and Fickʹs laws (for diffusive/dispersive solute flux). Both coarse- and medium-grained sands were used in the experiments. All experiments concerned upward (i.e., stable) displacement of fresh water within the soil by a brine solution, under either constant head or constant volume flux conditions. The experimental data were analysed using accurate numerical solutions of the standard governing flow and transport model, as well as models with modified Darcyʹs and Fickʹs laws. Model parameters were determined by a step-wise fitting procedure based on the least-squares criterion. The results show clearly that, for large density contrasts, an extended Darcyʹs law was not necessary. On the other hand, an extension to Fickʹs Law was needed to model the experimental data accurately.