Collaborative Research: A Comparison of Local and Nonlocal Transport Theories

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This project will evaluate several emerging theoretical treatments of the dispersion of a conservative solute, with respect to their data needs and ability to represent dispersion. We will apply classical local, and non-local, methods at perhaps the best-studied and most representative heterogeneous site in North America - the MADE site in Columbus, Mississippi. We will evaluate the traditional advection-dispersion equation (ADE), which is thought to require tens of millions of nodes with local velocity values, and several non-local methods, including the time-non-local multiple-rate mass transfer (MRMT) and continuous time random walk (CTRW) methods, and/or the space-fractional advection-dispersion equation (fADE). Each of the non-local methods show great promise in reducing the amount of information needed to make accurate predictions of anomalously rapid and/or recalcitrant pollution migration. However, given the same site, we must ask the questions: How much data, of what types, are needed to obtain a given level of accuracy for each method? Are some methods capturing the resulting behavior of the process and, thus are inherently superior? Can simple guidelines for model use and data collection be generated? The proposed work would give the first systematic evaluation of the accuracy and data needs of the most recent and widely used theories of conservative solute transport. The final product would be a unifying model that includes the salient features of current time- and space-non-local governing equations, and places information about the geologic complexity in either the local velocities or in non-local terms in the governing equation. Furthermore, we will provide a guide to the tradeoff of information from the local scale (and discretization thereof) to the non-local terms. We will apply the analysis to synthetic aquifers of many types, in addition to the extensively studied MADE site.