Comparison of the Classical Advection Dispersion Equation and a Temporally Nonlocal Version of the Advection Dispersion Equation to Model Solute Transport in Highly Heterogeneous Media at the Macrodispersion Experiment (MADE) Site.

Abstract:

The Macrodispersion Experiment (MADE) site in Columbus, Mississippi is an ongoing research field site used to study current macrodispersion transport theories in highly heterogeneous media. Researchers have observed anomalous plume behavior at the MADE site that produces asymmetric breakthrough curves (BTCs). These BTCs are defined by early-time peaks and late-time heavy tails that the classical advection dispersion equation (ADE) is unable to reproduce. The early-time peaks are likely due to small-scale preferential flow paths, whereas the late-time heavy tailings are likely due to the slow release of solute from low permeability or immobile zones. Two courses of action have been proposed in order to overcome the insufficiencies of the ADE to predict solute transport at the MADE site: employing the use of alternative nonlocal models and obtaining more detailed representation of small-scale heterogeneities. The following study examines these two methodologies and their influences on one another. We compared a temporal nonlocal model, the time fractional advection dispersion equation (t-fADE) to the classical ADE. The t-fADE model was chosen as the most suitable nonlocal model for this study because it is better able to capture the late-time mass decay observed in MADE BTCs. To compare the models associated with the two aforementioned methodologies, we will simulate the BTC from the single-well injection-withdraw (SWIW) test conducted by Liu et al. (2010) in the Intensively Cored Area (ICA) under variably saturated flow conditions. Hydraulic conductivity (K) data provided by Dogan et al. (2011) was used to generate a detailed K field. This fine K field was progressively coarsened until the coarsest domain was essentially a homogeneous K field. Model error will be quantified at each coarseness level to analyze trends at varying degrees of velocity information and to see if certain data thresholds contribute to significant model improvement. The robustness of both models to predict solute transport in highly heterogeneous aquifers will be assessed by generating a second equally probable K field at the finest scale and comparing the variability in optimized parameter sets.