Predicting Solute Flux through a Clay Membrane Barrier

Measured solute flux breakthrough curves (FBCs) from column tests performed on a semipermeable clay membrane subjected to KCl solutions are compared with predicted FBCs using independently measured flow and transport properties. The predicted FBCs are based on three scenarios: (1) Advective–dispersive transport that neglects membrane behavior; (2) advective–dispersive transport that accounts for the concentration dependency of the effective salt-diffusion coefficient (Ds*) resulting from membrane behavior, referred to as partially coupled transport; and (3) fully coupled transport that includes both the explicit coupling terms (e.g., hyperfiltration, chemico-osmosis) associated with clay membrane behavior and the concentration dependency of Ds*. The FBCs predicted by fully coupled transport agree best with the measured FBCs. However, for the diffusion-controlled conditions of the column tests, the steady-state solute fluxes predicted by partially coupled transport are only 23–69% higher than the measured steady-state fluxes. The results imply that the advective–dispersive transport theory can be used to provide reasonably accurate, albeit somewhat conservative, estimates of steady-state solute flux through clays that behave as semipermeable membranes, provided diffusion is a significant, if not dominant, solute transport process and the concentration dependency of Ds* are taken into account.