Lucy C. Meigs

On the late‐time behavior of tracer test breakthrough curves

The authors investigated the late-time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate-limited mass transfer (e.g., in dual or multi-porosity systems) and found that the late-time concentration, c, is given by the simple expression: c = t{sub ad} (c{sub 0}g {minus} m{sub 0}{partial_derivative}g/{partial_derivative}t), for t >> t{sub ad} and t{sub a} >> t{sub ad} where t{sub ad} is the advection time, c{sub 0} is the initial concentration in the medium, m{sub 0} is the 0th moment of the injection pulse; and t{sub a} 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, the authors tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression they examine the behavior of late-time concentration for a number of mass transfer models. One key results is that if rate-limited mass transfer causes the BTC to behave as a power-law at late-time (i.e., c {approximately} t{sup {minus}k}), then the underlying density function of rate coefficients must also be a power-law with the form a{sup k{minus}}, as a {r_arrow}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 infinite, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. They apply their analysis to breakthrough curves from Single-Well Injection-Withdrawal tests at the Waste Isolation Pilot Plant, New Mexico.

Tracer tests in a fractured dolomite: 2. Analysis of mass transfer in single‐well injection‐withdrawal tests

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 double-porosity 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.

Tracer tests in a fractured dolomite: 3. Double‐porosity, multiple‐rate mass transfer processes in convergent flow tracer tests

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-sswithdrawal 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.

Tracer tests in a fractured dolomite: 1. Experimental design and observed tracer recoveries

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 (he 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 double- porosity conceptual model for transport in the Culebra with a single rate of diffusion is overly simplistic.

Interpretations of Tracer Tests Performed in the Culebra Dolomite at the Waste Isolation Pilot Plant Site

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 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.

Three‐dimensional groundwater flow near narrow surface water bodies

A series of natural gradient tracer tests was conducted to delineate groundwater flow patterns near a drainage ditch in glacial outwash of central Wisconsin. Water level and precipitation data were collected to document factors that could contribute to temporal variations in the flow field. Year-to-year variations in recharge generated shifts in flow paths between replicate tracer experiments. The field data provided the basis for numerical modeling designed to elucidate the sensitivity of flow paths to variations in recharge. A three-dimensional aspect of flow paths identified in this study is a “wrap-around” pattern, in which groundwater passes under a surface water body prior to turning in the downstream direction and continuing to migrate as subsurface flow. This feature was suggested by the path of a tracer injected deep in the aquifer and was simulated at all recharge rates employed in the modeling. The three-dimensional nature of the flow field and temporal variability of flow paths can have important implications for design of monitoring networks near narrow surface water bodies.