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On the late-time behavior of tracer test breakthrough curves

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  • We investigated the late-time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate-limited mass transfer( e.g., in dual-porosity or multiporosity systems) and found that the late-time concentration c is given by the simple expression C = tₐ𝒹{C₀g-- [m₀(∂g/∂t)]}, for t >> tₐ𝒹 and tα >> tₐ𝒹, where tad is the advection time, C₀ is the initial concentration in the medium, m₀ is the zeroth moment of the injection pulse, and tα is the mean residence time in the immobile domain (i.e., the characteristic mass transfer time). The function g is proportional to the residence time distribution in the immobile domain; we tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression, we examine the behavior of late-time concentration for a number of mass transfer models. One key result is that if rate-limited mass transfer causes the BTC to behave as a power law at late time (i.e.,c ~ t⁻ᵏ), then the underlying density function of rate coefficients must also be a power law with the form αᵏ⁻³ as α → 0. This is true for both density functions of first order and diffusion rate coefficients. BTCs with k < 3 persisting to the end of the experiment indicate a mean residence time longer than the experiment, and possibly an infinite residence time, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. We apply our analysis to breakthrough curves from single-well injection-withdrawal tests at the Waste Isolation Pilot Plant, New Mexico.
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  • Haggerty, R., S. A. McKenna, and L. C. Meigs (2000), On the late-time behavior of tracer test breakthrough curves, Water Resources Research, 36(12), 3467–3479, doi:10.1029/2000WR900214.
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  • 36
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  • 12
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  • The published article can be found at AGU - American Geophysical Union.
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  • This work was funded by Sandia National Laboratories and by the Swedish Nuclear Fuel and Waste Management Co. (SKB). Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy under contract DE-AC04-94AL85000.
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