Predicting the tails of breakthrough curves in regional-scale alluvial systems.

The late tail of the breakthrough curve (BTC) of a conservative tracer in a regional-scale alluvial system is explored using Monte Carlo simulations. The ensemble numerical BTC, for an instantaneous point source injected into the mobile domain, has a heavy late tail transforming from power law to exponential due to a maximum thickness of clayey material. Haggerty et al.'s (2000) multiple-rate mass transfer (MRMT) method is used to predict the numerical late-time BTCs for solutes in the mobile phase. We use a simple analysis of the thicknesses of fine-grained units noted in boring logs to construct the memory function that describes the slow decline of concentrations at very late time. The good fit between the predictions and the numerical results indicates that the late-time BTC can be approximated by a summation of a small number of exponential functions, and its shape depends primarily on the thicknesses and the associated volume fractions of immobile water in "blocks" of fine-grained material. The prediction of the late-time BTC using the MRMT method relies on an estimate of the average advective residence time, t(ad). The predictions are not sensitive to estimation errors in t(ad), which can be approximated by L/v , where v is the arithmetic mean ground water velocity and L is the transport distance. This is the first example of deriving an analytical MRMT model from measured hydrofacies properties to predict the late-time BTC. The parsimonious model directly and quantitatively relates the observable subsurface heterogeneity to nonlocal transport parameters.