An evaluation of Sherwood-Gilland models for NAPL dissolution and their relationship to soil properties

Predicting the longevity of non-aqueous phase liquid (NAPL) source zones has proven to be a difficult modeling problem that has yet to be resolved. Research efforts towards understanding NAPL depletion have focused on developing empirical models that relate lumped mass transfer rates to velocities and organic saturations. These empirical models are often unable to predict NAPL dissolution for systems different from those used to calibrate them, indicating that system-specific factors important for dissolution are not considered. This introduces the need for a calibration step before these models can be reliably used to predict NAPL dissolution for systems of arbitrary characteristics. In this paper, five published Sherwood-Gilland models are evaluated using experimental observations from the dissolution of two laboratory-scale complex three-dimensional NAPL source zones. It is shown that the relative behavior of the five models depends on the system and source zone characteristics. Through a theoretical analysis, comparing Sherwood-Gilland type models to a process-based, thermodynamic dissolution model, it is shown that the coefficients of the Sherwood-Gilland models can be related to measurable soil properties. The derived dissolution model with soil-dependent coefficients predicts concentrations identical to those predicted by the thermodynamic dissolution model for cases with negligible hysteresis. This correspondence breaks down when hysteresis has a significant impact on interfacial areas. In such cases, the derived dissolution model will slightly underestimate dissolved concentrations at later times, but is more likely to capture system-specific dissolution rates than Sherwood-Gilland models.