Abstract. 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{COg --[mo(Og/Ot)]}, for t >> tad and t• >> tad , where tad is the advection time, Co is the initial concentration in the medium, m 0 is the zeroth moment of the injection pulse, and t• 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-t:), then the underlying density function of rate coefficients must also be a power law with the form ak-3 as a -• 0. This is true for both density functions of firstorder 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.

Groundwater transport models that accurately describe spreading of nonreactive solutes in an aquifer can poorly predict concentrations of reactive solutes. The dispersive term in the advection-dispersion equation can overpredict pore-scale mixing, and thereby overpredict homogeneous chemical reaction. We quantified this experimentally by imaging instantaneous colorimetric reactions between solutions of aqueous CuSO4 and EDTA4- within a 30-cm long translucent chamber packed with cryolite sand that closely matched the optical index of refraction of water. A charge-coupled device camera was used to quantify concentrations of blue CuEDTA2- within the chamber as it was produced by mixing of the two reactants at different flow rates. We compared these experimental results with a new analytic solution for instantaneous bimolecular reaction coupled with advection and dispersion of the product and reactants. For all flow rates, the concentrations of CuEDTA2- recorded in the experiments were about 20% less than predicted by the analytic solution, thereby demonstrating that models assuming complete mixing at the pore scale can overpredict reaction during transport.

Abstract. We investigated multiple-rate diffusion as a possible explanation for observed behavior in a suite of single-well injection-withdrawal (SWIW) tests conducted in a fractured dolomite. We first investigated the ability of a conventional double-porosity model and a multirate diffusion model to explain the data. This revealed that the multirate diffusion hypothesis/model is consistent with available data and is capable of matching all of the recovery curves. Second, we studied the sensitivity of the SWIW recovery curves to the distribution of diffusion rate coefficients and other parameters. We concluded that the SWIW test is very sensitive to the distribution of rate coefficients but is relatively insensitive to other flow and transport parameters such as advective porosity and dispersivity. Third, we examined the significance of the constant double-log late time slopes (-2.1 to -2.8), which are present in several data sets. The observed late time slopes are significantly different than would be predicted by either conventional doubleporosity or single-porosity models and are believed to be a distinctive feature of multirate diffusion. Fourth, we found that the estimated distributions of diffusion rate coefficients are very broad, with the distributions spanning a range of up to 3.6 orders of magnitude. Fifth, when both heterogeneity and solute drift are present, late time behavior similar to multirate mass transfer can occur. Although it is clear that multirate diffusion occurs in the Culebra, the number of orders of magnitude of variability may be overestimated because of the combined effects of drift and heterogeneity.

[1] 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 + b (where b 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.

Solute transport displaying mass transfer behavior (i.e., tailing) occurs in many aquifers and soils. Spatial patterns of hydraulic conductivity may play a role because of both advection and diffusion through isolated low conductivity areas. We demonstrated such processes in laboratory experiments designed to visualize solute transport through a thin chamber (40 cm x 20 cm x 0.64 cm thick) packed with glass beads and containing circular emplacements of smaller glass beads with lower conductivity. The experiments used three different contrasts of conductivity between the large-bead matrix and the emplacements, targeting three different regimes of solute transport: low contrast, targeting macrodispersion; intermediate contrast, targeting advection-dominated mass transfer between the high-conductivity regions and the emplacements; and high contrast, targeting diffusion-dominated mass transfer. Use of a strong light source, a high-resolution CCD camera, and a colorimetric dye produced images with a spatial resolution of about 400 microm and a concentration range of approximately 2 orders of magnitude. These images confirm the existence of the three different regimes, and we observed tailing driven by both advection and diffusion. Outflow concentration measured by spectrophotometer achieved 3 orders of magnitude in concentration range and showed good agreement with known models in the case of dispersion and diffusive mass transfer, with estimated parameters close to a priori predictions. Existing models for diffusive mass transfer did notfitthe breakthrough curves from the intermediate-contrast chamber, but a model of slow advection through cylinders did. Thus, both breakthrough curves and chamber images confirm that different contrasts in small-scale K lead to different regimes of solute transport and thus require different models of upscaled solute transport.

Abstract. Convergent flow tracer tests conducted in the Culebra dolomite (Rustler Formation, New Mexico) are analyzed with both single-and multiple-rate, double-porosity models. Parameter estimation is used to determine the mean and standard deviation of a lognormal distribution of diffusion rate coefficients as well as the advective porosity and longitudinal dispersivity. At two different test sites both multirate and single-rate models are capable of accurately modeling the observed data. The single-well injection-withdrawal test provides more precise estimates of the mass transfer parameters than the convergent flow tracer tests. Estimation of the multirate distribution parameters is consistent across locations for the two types of tests. Limits of resolution are calculated for the multirate distribution, and these limits explain the precision with which the standard deviation of the multirate distribution can be estimated. These limits also explain the necessary increase in the advective porosity for the single-rate model at one location and not the other. Implications of the multirate mass transfer model at time and length scales greater than those of the tracer tests include the instantaneous equilibrium of a significant fraction of the matrix and the possibility of a fraction of the diffusive porosity not reaching an equilibrium solute concentration at long times.

Abstract.A series of tracer tests has been conducted in a 7-m-thick fractured dolomite at two sites in southeastern New Mexico. The tests were designed to evaluate transport processes, especially matrix diffusion, in fractured, permeable media. Both single-well injection-withdrawal (SWIW) and multiwell convergent flow (MWCF) tests were conducted. Seventeen different organic tracers (the fluorobenzoic and chlorobenzoic acids) and iodide were used as conservative tracers for the tests. The MWCF tests included repeated tracer injections while pumping the central well at different rates, injection of tracers with different aqueous diffusion coefficients, and injection of tracers into both the full and partial formation thickness. This paper describes the tracer test sites and aquifer characteristics, the experimental methods, and the tracer data produced. The tracer test results provide a high-quality data set for a critical evaluation of the conceptual model for transport. Both the SWIW and MWCF tracer test data showed gradual mass recovery and breakthrough (or recovery) curve tailing consistent with matrix diffusion. However, the SWIW recovery curves did not display the -1.5 log-log slope expected from a conventional double-porosity medium with a single rate of diffusion. The breakthrough curves from MWCF tests conducted at two different pumping rates showed similar peak heights, which is also not what was expected with a conventional double-porosity model. However, the peak heights were different for two tracers with different aqueous diffusion coefficients that were injected simultaneously in one test, consistent with the effects of matrix diffusion. The complexity of the tracer test results suggests that a simple doubleporosity conceptual model for transport in the Culebra with a single rate of diffusion is overly simplistic.

Abstract:Laboratory experiments were performed to investigate the effects of spatial variation in porosity on matrix-diffusion processes. Four centimeter-scale slabs of Culebra dolomite taken from the Waste 'Isolation Pilot Plant site were used in the tests. Experiments involved the simple diffusion of iodine into a single edge of each rock slab while X ray absorption imaging was used to measure the resulting two-dimensional solute concentration field as a function of time. X ray imaging was also used to quantify the two-dimensional porosity field of each rock slab. Image analysis provided a unique opportunity to both visualize and quantify the effects of the spatially variable porosity on matrixdiffusion. Four key results were obtained. First, significant variation in rates of diffusion were realized over the relatively small length (centimeter) and time scales (months) investigated. Second, clear evidence of diffusion preferentially following zones of relatively higher porosity was noted. Third, rate of diffusion was found to vary as tracer diffused into the rock slabs encountering changing porosity conditions. Fourth, strong correlation between porosity and the calculated diffusion coefficients was found. In fact, the nature of the correlation can be related to the geometry, position, and orientation of the heterogeneous porosity features populating each rock slab.