Time-Fractional Advection-Dispersion Equation (tFADE) to Quantify Aqueous Phase Contaminant Elution from a Trichloroethene (TCE) NAPL Source Zone in Sand Columns

Pore-scale heterogeneity, NAPL distribution, and sorption/desorption processes can significantly affect aqueous phase elution and mass flux in porous media systems. The application of a scale-independent fractional derivative model (tFADE) was used to simulate elution curves for a series of columns (5 cm, 7 cm, 15 cm, 25 cm, and 80 cm) homogeneously packed with 20/30-mesh sand and distributed with uniform saturations (7-24%) of NAPL phase trichloroethene (TCE). An additional set of columns (7 cm and 25 cm) were packed with a heterogeneous distribution of quartz sand upon which TCE was emplaced by imbibing the immiscible liquid, under stable displacement conditions, to simulate a spill-type process. The tFADE model was able to better represent experimental elution behavior for systems that exhibited extensive long-term concentration tailing requiring much less parameters compared to typical multi-rate mass transfer models (MRMT). However, the tFADE model was not able to effectively simulate the entire elution curve for such systems with short concentration tailing periods since it assumes a power-law distribution for the dissolution rate for TCE. Such limitations may be solved using the tempered fractional derivative model, which can capture the single-rate mass transfer process and therefore the short elution concentration tailing behavior. Numerical solution for the tempered fractional-derivative model in bounded domains however remains a challenge and therefore requires further study. However, the tFADE model shows excellent promise for understanding impacts on concentration elution behavior for systems in which physical heterogeneity, non-uniform NAPL distribution, and pronounced sorption-desorption effects dominate or are present.