Haggerty, Roy; Harvey, Charles F.; Von Schwerin, Claudius F.; Meigs, Lucy C.
Estimates of mass transfer timescales from 316 solute transport experiments reported in 35 publications are compared to the pore-water velocities and residence times, as well as the experimental durations. New tracer experiments were also conducted in columns of different lengths so that the velocity and the advective residence time could be varied independently. In both the experiments reported in the literature and the new experiments, the estimated mass transfer timescale (inverse of the mass-transfer rate coefficient) is better correlated to residence time and the experimental duration than to velocity. Of the measures considered, the experimental duration multiplied by 1 + β (where β is the capacity coefficient, defined as the ratio of masses in the immobile and mobile domains at equilibrium) best predicted the estimated mass transfer timescale. This relation is consistent with other work showing that aquifer and soil material commonly produce multiple timescales of mass transfer.
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. 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 ≫ t ad, 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.
This report provides (1) an overview of all tracer testing conducted in the Culebra Dolomite Member of the Rustler Formation at the Waste Isolation Pilot Plant (WPP) site, (2) a detailed description of the important information about the 1995-96 tracer tests and the current interpretations of the data, and (3) a summary of the knowledge gained to date through tracer testing in the Culebra. Tracer tests have been used to identify transport processes occurring within the Culebra and quantify relevant parameters for use in performance assessment of the WIPP. The data, especially those from the tests performed in 1995-96, provide valuable insight into transport processes within the Culebra. Interpretations of the tracer tests in combination with geologic information, hydraulic-test information, and laboratory studies have resulted in a greatly improved conceptual model of transport processes within the Culebra. At locations where the transmissivity of the Culebra is low (< 4 x 10{sup -6} m{sup 2}/s), we conceptualize the Culebra as a single-porosity medium in which advection occurs largely through the primary porosity of the dolomite matrix. At locations where the transmissivity of the Culebra is high (> 4 x 10{sup -6} m{sup 2}/s), we conceptualize the Culebra as a heterogeneous, layered, fractured medium in which advection occurs largely through fractures and solutes diffuse between fractures and matrix at multiple rates. The variations in diffusion rate can be attributed to both variations in fracture spacing (or the spacing of advective pathways) and matrix heterogeneity. Flow and transport appear to be concentrated in the lower Culebra. At all locations, diffusion is the dominant transport process in the portions of the matrix that tracer does not access by flow.