Assessment of scaling and information requirements of the classical advection dispersion equation and a temporal-nonlocal advection dispersion equation at the MADE site, An
The MacroDispersion Experiment (MADE) Site in Columbus, MS, is a research site where tracer tests have been performed to further understand transport processes in heterogeneous material. Tracer tests have exhibited anomalous plume behavior, including early arrival times and heavy, power-law late-time tails that the classical Advection-Dispersion Equation (ADE) is unable to match. The heavy tailing is due to mass transfer into low velocity zones where dissolved solute becomes relatively immobile for certain periods of time. Transport modeling insufficiencies have led to two additional areas of research: collecting more hydraulic conductivity ($K$) data to better define subsurface heterogeneities and modifying the ADE to account for anomalous transport. This study seeks to further both research areas through the investigation of a single-well injection withdrawal test (SWIW) at the MADE Site with a skewed breakthrough curve (BTC). High resolution hydraulic conductivity and facies data were collected in the area of the SWIW test. This data was used to statistically generate a high resolution $K$ domain of the aquifer material and was spatially upscaled (averaged) to examine transport model capabilities while destroying $K$ information. Two models were compared at a range of $K$ domain resolutions, the ADE and a temporal-nonlocal advection dispersion equation (t-fADE). The t-fADE model was used as an alternative to the classical ADE because it is able to simulate the power-law tailing observed in the SWIW BTC. Water table fluctuations throughout the SWIW test were also included by solving Richard's equation. When the $K$ domain was defined at a high-resolution the ADE was able to match the heavy, power-law, late-time tailing. By explicitly defining small-scale heterogeneities, the ADE can simulate solute trapping in low $K$ zones where solute becomes immobile for a period of time. As $K$ information was destroyed, the ADE model's accuracy decreased and simulating the SWIW test with the t-fADE model became more advantageous. Both transport model simulations exhibited their largest decline in performance at the scaling point where facies boundaries were averaged out, indicating the importance of mass transfer between facies rather than within facies boundaries. The vadose zone proved to be a significant contributor of solute trapping. To explore the predictive capabilities of both transport models at such a highly heterogeneous site, many equally probable realizations at the finest $K$ resolution were created. The variability between realizations as well as simulated BTCs were analyzed to assess if the best-fit parameter values, which represent hydraulic properties of the subsurface, are characteristic of the aquifer or of the particular $K$ field realization. While both transport models were able to fit the measured data with enough $K$ information, the predictive capabilities were poor. Additional $K$ field realizations could not repeatedly simulate the same BTC. Aquifer heterogeneity was too complex for a predictive transport model to be obtained.
groundwater modeling, contaminant transport
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Colorado School of Mines. Arthur Lakes Library