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SPECIAL SECTION: SAVANNAH RIVER SITE

Tracer Migration in a Radially Divergent Flow Field: Longitudinal Dispersivity and Anionic Tracer Retardation

Savannah River Ecology Lab., Univ. of Georgia, Drawer E, Aiken, SC 29802
^* Corresponding author (seaman{at}srel.edu).

All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.

Received 4 August 2006.

	ABSTRACT

TOP ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions REFERENCES

 
Hydrodynamic dispersion, the combined effects of chemical diffusion and differences in solute path length and flow velocity, is an important factor controlling contaminant migration in the subsurface environment. However, few comprehensive three-dimensional datasets exist for critically evaluating the impact of travel distance and site heterogeneity on solute dispersion, and the conservative nature of several commonly used groundwater tracers is still in question. Therefore, we conducted a series of field-scale experiments using tritiated water (³H¹HO), bromide (Br^–), and two fluorobenzoates (2,4 Di-FBA, 2,6 Di-FBA) as tracers in the water-table aquifer on the USDOE's Savannah River Site (SRS), located on the upper Atlantic Coastal Plain. For each experiment, tracer-free groundwater was injected for approximately 24 h (56.7 L min^–1) to establish a steady-state forced radial gradient before the introduction of a tracer pulse. After the tracer pulse, which lasted from 256 to 560 min, the forced gradient was maintained throughout the experiment using nonlabeled groundwater. Tracer migration was monitored using six multilevel monitoring wells, radially spaced at approximate distances of 2.0, 3.0, and 4.5 m from the central injection well. Each sampling well was further divided into three discrete sampling depths that were pumped continuously (0.1 L min^–1) throughout the course of the experiments. Longitudinal dispersivity (_L) and travel times for ³H¹HO breakthrough were estimated by fitting the field data to analytical approximations of the advection–dispersion equation (ADE) for uniform and radial flow conditions. Dispersivity varied greatly between wells located at similar transport distances and even between zones within a given well, which we attributed to variability in the hydraulic conductivity at the study site. The radial flow equation generally described tritium breakthrough better than the uniform flow solution, as indicated by the coefficient of determination, r², yielding lower _L while accounting for breakthrough tailing inherent to radial flow conditions. Complex multiple-peak breakthrough patterns were observed within certain sampling zones, indicative of multiple major flow paths and the superposition of resulting breakthrough curves. A strong correlation was found between _L and arrival times observed from one experiment to the next, indicative of the general reproducibility of the tracer results. Temporal moment analysis was used to evaluate tracer migration rate as an indicator of variations in hydraulic conductivity and flow velocity, as well as mass recovery and retardation for the ionic solutes compared with tritiated water. Retardation factors for Br^– ranged from 0.99 to 1.67 with no clear trend with respect to transport distance; however, Br^– mass recovery decreased with distance, suggesting that the retardation values are biased in terms of early arrival because of limited detection and an insufficient monitoring duration. Anion retardation was attributed to sorption by iron oxides. Similar results were observed for the FBA tracers. The assumption of conservative behavior for the anionic tracers would generally result in higher _L values and lower estimated flow velocities.

Abbreviations: ADE, advection–dispersion equation • FBA, fluorobenzoate • ITS, injection test site • IW, injection well • SRS, Savannah River Site.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions REFERENCES

 
Hydrologic tracer experiments are generally conducted to address one of the following objectives: (i) to estimate the degree of hydraulic interconnection between various locations, (ii) to estimate physical transport parameters used in describing solute migration (e.g., hydraulic conductivity, transport volume, dispersivity, or pore velocity), (iii) to determine a solute–matrix interaction parameter, or (iv) to calibrate and validate a flow or transport model (Maloszewski and Zuber, 1992). Implicit in many of these objectives is the "conservative" or nonsorbing behavior of the compound being used as the nonreactive tracer. The one-dimensional transport for a nonsorbing solute is governed by the following mass balance equation:

[1]

where C is the solute concentration in solution, D is the hydrodynamic dispersion coefficient (L² T^–1), t is time (T), v is the mean pore velocity (L T^–1), and x is distance (L). Additional terms can be added to the equation to account for multiple flow domains, solute partitioning and decay, and other related processes.

A nonsorbing tracer is transported advectively in the flow stream and spreads by hydrodynamic dispersion, a combination of molecular diffusion and mechanical dispersion resulting from differences in pore water velocity and flow path. The hydrodynamic dispersion coefficient, D, is

[2]

where _L is the longitudinal dispersivity (L), v is the seepage velocity (L T^–1), and D^* is the molecular diffusion coefficient (Valocchi, 1986; Welty and Gelhar, 1994). If one assumes that molecular diffusion is insignificant compared to the flow velocity, that is, D^* << _Lv, the mass balance equation becomes

[3]

As evident from Eq. [3], _L, generally considered a scale-dependent function of the geologic heterogeneity encountered during solute transport, is a key factor in describing the physical aspects of contaminant migration in the subsurface environment. Estimating _L is one of the primary goals of most groundwater tracer experiments (Domenico and Robbins, 1984; Gelhar et al., 1992; Welty and Gelhar, 1994). Longitudinal dispersivity values are thought to increase initially with transport scale before approaching a constant asymptotic value (Gelhar et al., 1992; Pang and Hunt, 2001; Pickens and Grisak, 1981), with dispersivity values reported in the literature varying more than two to three orders of magnitude at a given transport scale (Gelhar et al., 1992). However, most commonly used solute transport models assume a constant _L and require a unique dispersion coefficient for each sampling location (Pang and Hunt, 2001; Ptak and Teutsch, 1994). Dispersivity values derived from laboratory-scale tracer experiments tend to be much lower than field-scale–derived values for materials of similar texture and hydraulic conductivity. This has been attributed in part to the greater heterogeneity and residence time encountered at the field scale (Pickens and Grisak, 1981). Furthermore, previous studies have suggested that _L values determined under forced-gradient conditions may actually underestimate solute dispersion under natural gradient flow (Freyberg, 1986; Garabedian et al., 1991; MacKay et al., 1994; Thorbjarnarson and Mackay, 1994a, 1994b). Even the sampling method can strongly influence estimated _L values derived from field-scale tracer experiments (Gelhar et al., 1992; Pickens and Grisak, 1981; Taylor and Howard, 1987).

The axisymmetric gradient induced by groundwater sampling, or injection and capture wells in a pump-and-treat reclamation system, results in a nonuniform flow field; that is, flow rate changes as a function of distance and, potentially, direction from the well. In contrast to a uniform flow field in which movement of the tracer center of mass is linear with time, movement of the center of tracer mass in a radial flow field is proportional to t (Neuweiler et al., 2001). Despite this difference, field-scale tracer experiments are often misinterpreted based on the assumption of a uniform flow field, requiring higher _L values to account for the greater degree of tailing inherent in nonuniform flow systems (Chao et al., 2000; Gelhar and Collins, 1971; Gelhar et al., 1992; Indelman and Dagan, 1999; Welty and Gelhar, 1994).

In addition to dispersive processes, extensive tailing observed under any flow condition can result from both physical and chemical disequilibrium that may be conveniently, although incorrectly, described by the dispersion coefficient (Pickens et al., 1981; Seaman et al., 1995). In relatively simple one-dimensional column studies, similar elution patterns can be derived from different combinations of chemical retardation processes and physical transport phenomena (Schweich and Sardin, 1981). Even at a fundamental level, the mathematical equations used to describe physical and chemical nonequilibrium are identical, and thus distinguishing such processes from the breakthrough curve of a reactive solute requires the presence of a conservative tracer as well (van Genuchten and Wierenga, 1986). The potential for such behavior makes the initial assumption of nonreactive transport much more critical in explaining field data. For example, a broad, tailing elution curve may be indicative of a wide distribution of flow velocities, path lengths, and diffusive transfer across these transport regions or the result of a nonlinear sorption or pore exclusion processes occurring under the influence of a fairly limited flow velocity distribution.

The seepage velocity in a radially diverging flow field established by a fully penetrating injection well in a homogeneous confined aquifer is

[4]

where r is the radial distance (L) from the recharge well and

[5]

where Q_w is the volumetric injection rate (L³ T^–1), is the formation porosity (L³ L^–3), and b is the aquifer thickness (L) (Chen, 1987; Valocchi, 1986; Welty and Gelhar, 1994). Under radial flow conditions hydrodynamic dispersion becomes

[6]

where |v| is the magnitude of the seepage velocity. Considering only _L in a radial system and again assuming that molecular diffusion is insignificant, that is, D^* << _Lv, the advection–dispersion equation (ADE) can be written as follows:

[7]

with r representing radial distance (L) as described above.

Welty and Gelhar (1994) provided a number of approximate analytical solutions for describing tracer breakthrough under several commonly encountered nonuniform flow conditions (i.e., converging and diverging radial flow fields, and two-well tracer tests) for two common inlet boundary conditions, a step input tracer test and an instantaneous Dirac pulse, representing end-member contrasts in the way tracer experiments are generally conducted. In most experiments the initial step change in tracer concentration is maintained for some practical duration that may be considerably less than required to observe full breakthrough (i.e., C/C₀ = 1) within even closely spaced monitoring wells at the field scale. Therefore, the analytical solution for an arbitrary pulse duration can be solved through superposition using the appropriate step input approximation (Welty and Gelhar, 1994), assuming tracer displacement can be viewed as two distinct step inputs: (i) the initial tracer solution followed by (ii) the breakthrough of nonlabeled water, separated by a known time interval equivalent to the pulse duration. For a step input in which the inlet tracer concentration is held constant, the dimensionless form for uniform one-dimensional flow is (Model 1)

[8]

where R_dis is the distance from the injection point to sampling point (L), and is the dimensionless time, that is, the experiment time, t (T), divided by the average travel time required for a tracer to reach the monitoring well, t_m (Gelhar and Collins, 1971). This approximate solution has been commonly used in displacement experiments and generally provides a close approximation to more involved analytical solutions when the Peclet number is high and advection dominates transport (van Genuchten and Wierenga, 1986). Under radial flow conditions assuming _L has reached an asymptotic constant value, the approximate step breakthrough is (Model 2)

[9]

where is the same as above and R_dis is the radial distance of the sampling well from the center of the injection well (Welty and Gelhar, 1994).

In a step experiment the tracer is injected at a continuous fixed concentration (C₀) until the concentration at the monitoring well is the same as in the injection well (C = C₀). At the field scale this can be impractical because of the large volume of the labeled tracer solution required to obtain complete breakthrough at even relatively close transport scales. In most cases the tracer solution is applied or injected for some arbitrary duration and then switched back to the nonlabeled water to push the tracer solution out into the formation in what is called a pulse. For a tracer pulse of known duration,

[10]

tracer breakthrough under uniform flow conditions can be described as follows, assuming Fickian flow:

[11]

where pd is the duration of the initial tracer pulse (min). The same approach can be used for the radial solution.

The analytical solutions described above assume the solutes of interest are behaving in a conservative, nonsorbing manner. Anionic solutes such as chloride (Cl^–), bromide (Br^–), iodide (I^–), and fluorinated benzoic acid derivatives, which are anionic under typical groundwater pH conditions, have been widely used as nonreactive tracers for evaluating the physical processes associated with subsurface migration (Boggs et al., 1992; Boggs and Adams, 1992; Bowman, 1984; Bowman and Gibbens, 1992; Garabedian et al., 1991; Hoehn and Roberts, 1982; MacKay et al., 1994; Molz et al., 1988; Palmer and Nadon, 1986; Pickens and Grisak, 1981; Pickens et al., 1981; Reimus et al., 2003a). In some instances multiple "conservative" tracers with differing chemical diffusion properties have been used in an attempt to distinguish between the influence of matrix diffusion and hydrodynamic dispersion on solute transport (Hu and Brusseau, 1995; Jardine et al., 1999; Reimus et al., 2003a, 2003b).

The assumption of conservative behavior for anionic tracers is generally based on the predominance of clay minerals that impart a net negative charge or cation exchange capacity to the soil or aquifer matrix and, therefore, repel dissolved anions. This repulsion, commonly called anion exclusion, can actually result under some conditions in the early arrival of anionic tracers when compared with tritium (Hoehn and Roberts, 1982; Melamed et al., 1994). Although the assumption of conservative tracer behavior may be valid in many instances, significant retardation of anionic solutes has been observed in field and laboratory studies conducted with soils and unconsolidated sediments containing appreciable quantities of iron and aluminum oxides (Boggs and Adams, 1992; Chan et al., 1980a, 1980b; Ishiguro et al., 1992; Katou et al., 1996; McCarthy et al., 2000; McMahon and Thomas, 1974; Seaman, 1998; Seaman et al., 1995, 1996). The retardation of reactive tracers is further complicated by the fact that sorption behavior may differ under forced-gradient conditions, even when the mechanism of retention is largely electrostatic and reversible (MacKay et al., 1994; Pickens et al., 1981). Anion retention can also vary dramatically within materials of similar hydraulic conductivity as a consequence of rather minor variations in reactive mineralogy within a given aquifer (Seaman et al., 1995). In addition, the difficulty in performing accurate tracer mass balances in field-scale experiments can make it extremely difficult to recognize tracer retardation under the complex heterogeneous systems encountered at the field scale (Boggs and Adams, 1992; Novakowski, 1992), and significant nonequilibrium effects may occur in the vicinity of the injection well (Valocchi, 1986). Deviations from nonideal behavior resulting from chemical processes such as tracer sorption may be interpreted as having a physical significance. At the field scale solute tracers often display complex breakthrough patterns and extensive tailing that can be misinterpreted as having a physical significance in the absence of an a priori understanding of the solute sorption behavior (Boggs and Adams, 1992; McCarthy et al., 2000; Pickens et al., 1981; Seaman, 1998; Seaman et al., 1995, 1996).

Objectives
Our objectives were to evaluate longitudinal dispersivity in a nonuniform, radially divergent flow field as a function of travel distance, and to compare the transport behavior of several commonly used anionic tracers with that of a conservative tracer, tritiated water (³H¹HO), within the highly weathered, coarse-textured sediments of the upper Atlantic Coastal Plain underlying the USDOE's SRS.

	Materials and Methods

TOP ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions REFERENCES

 
Injection Test Site
The injection test site (ITS) was constructed on the SRS, near Aiken, SC. In the vicinity of the ITS, the shallow Aquifer Unit IIB is divided into two zones, IIB₁ (Barnwell–McBean) and IIB₂ (water-table aquifer). Aquifer IIB₂, the focus of this study, is unconfined and consists predominantly of sands and clayey sand with interbeds of clay, sandy clay, and gravel (Strom and Kaback, 1992; WSRC, 1992, 1997). The ITS consisted of a 15-cm i.d. central injection well, designated IW (total depth 19.1 m), screened over a 4.56-m interval starting at 13.5 m from the surface (Fig. 1). Well Obs-1, a previously existing well located within the study site and screened within the first confined aquifer underlying the water-table aquifer, the Barnwell–McBean aquifer (IIB₁), was used to monitor water depth to confirm the integrity of the confining layer. The injection and monitoring wells were constructed of flush-threaded PVC casing and slotted PVC screen. Composite drilling logs for aquifer zone IIB₂ revealed that the transmissive region of the water-table aquifer consists primarily of sand without any major confining or retarding layers (WSRC, 1992). A pump test conducted in the vicinity of the site before well installation for the current study reported a hydraulic conductivity for the water-table aquifer that was estimated at 10.7 to 12.2 m d^–1 (35–40 ft d^–1), indicative of a slightly silty sand to clean sand medium. Groundwater flow is generally south toward Fourmile Branch Creek located several hundred meters away (WSRC, 1997).

View larger version (13K): [in this window] [in a new window]   FIG. 1. (A) Relative location of injection well (IW) and monitoring wells (S1–S6) at the injection test site (ITS), and (B) location of monitoring zones in relation to the natural water-table depth and forced radial gradient established before tracer injection for Exp. A.

Multilevel Groundwater Sampling
The screened interval for each monitoring well was further divided into three discrete sampling zones or depths with screened sampling intervals approximately 0.15 m in depth centered at 14.7, 16.6, and 18.6 m below the soil surface (Fig. 1B), with the deepest zone designated as Zone 1, using a modified Waterloo multilevel groundwater sampler (Solinst Canada, Ltd., Georgetown, ON) equipped with inflatable packers to isolate multiple sampling zones within the screened interval of the outer well casing (Seaman et al., 2007).

Injection Experiments
Each experiment consisted of injecting tracer-free groundwater from a nearby well screened within the Crouch Branch Aquifer Unit (Table 1), through the injection well, IW, for approximately 24 h at a fixed rate of 56.7 L min^–1 (15 gallons per minute) to establish a steady forced radial gradient. Tracer pulse injectate volumes for the three experiments ranged from approximately 15 000 to 32 000 L, with tritium levels approximately 2000 pCi mL^–1 (Table 2). The tracer solution pulse for Exp. A consisted of approximately 15 000 L of tritiated water. For Exp. B the tracer solution pulse was composed of 0.003 M Br made from reagent grade CaBr₂ and KBr diluted in a tritium-containing solution similar to Exp. A. For Exp. C, the tracer solution contained tritium, as well as 0.007 M KBr, 2,4 Di-FBA, and 2,6 Di-FBA. At the onset of an experiment, the nonlabeled injection water was replaced by the tracer solution, which was injected at the same rate (56.7 L min^–1) for a specified duration ranging from 256 to 560 min. After injection of the tracer solution was complete, injection continued using the nonlabeled water for approximately 1 wk to force the labeled solution out past the monitoring wells. Each sampling zone within the six monitoring wells was pumped continuously at a rate of approximately 0.1 L min^–1 throughout the course of the tracer experiment, resulting in the capture of approximately 3% of the injected tracer solution. Periodically (4–6 h), water depths were recorded within the IW, each of the six dedicated sampling wells, and two additional monitoring wells in the vicinity of the test site to observe hydraulic mounding as an indicator of formation damage (i.e., reduced hydraulic conductivity), a common problem affecting pump-and-treat systems. Before the onset of each experiment, the depth to the water table at the ITS was approximately 11.7 m (Fig. 1B). Water-table depths within each well immediately following the injection of the tracer pulse in Exp. A are provided in Fig. 1B. For all experiments no hydraulic response to injection was observed in Well Obs-1, confirming the integrity of the confining layer in limiting injection to the water-table aquifer.

Bromide and FBA Analysis
Simultaneous anion tracer analyses were performed using a Dionex chromatography system equipped with a UV/Vis spectroscopic detector. The tracers were separated using a strong-anion exchange column (Omnipac Pax-100; Dionex Corp., Sunnyvale, CA) at a flow rate of 0.001 L min^–1 with a degassed eluent solution containing 20% acetonitrile (v/v), 5% of a mixture containing 1 M NaCl and 0.004 M NaOH, and 75% HPLC water (Dionex Document No. 034216). Chromatographic analysis was performed at a wavelength of 200 nm to allow for simultaneous detection of Br^– and the benzoate tracers. Detection limits for the anionic tracers were approximately an order of magnitude higher (1–3%) than for tritium. Due to analytical constraints, FBA analysis for Exp. C was limited to samples collected from monitoring Wells S4, S5, and S6.

Tracer Data Analysis
Bowman and Gibbens (1992) reported aqueous diffusion coefficients (D^*) for FBA tracers that ranged from 7.2 to 7.6 x 10^–10 m² s^–1, compared with 18 to 20 x 10^–10 m² s^–1 for common inorganic anionic tracers, such as Br^– and Cl^–, and 2.6 x 10^–10 m² s^–1 for tritiated water, ³H¹HO (Bowman and Gibbens, 1992; Brusseau, 1993; Szecsody and Streile, 1992). Based on initial travel time estimates, _Lv was several orders of magnitude greater than D^*, validating the initial assumption that D^* << _Lv for Eq. [3]. The two approximate analytical solutions for uniform and radially diverging flow fields described above (Eq. [9–10]) were used to evaluate _L based on tritium breakthrough behavior. Estimates of _L and for tritium breakthrough within each zone of a given sampling well were obtained using the Levenberg-Marquardt method in MATLAB (Version 7.1.0246 [R14] Service Pack 3; The Mathworks, Inc., Natick, MA) to minimize the sum of squared residuals between the observed data and the analytical approximations, assuming the appropriate boundary conditions. For starting values, the average tracer arrival time estimate was based on the maximum tracer peak arrival time for each sampling zone, and an initial _L value of 0.1 m. Confidence intervals for the fitted parameters were calculated as standard error of the fitted parameters times the critical value from the t distribution.

For comparison purposes, the goodness-of-fit for each model was based on the coefficient of determination, r² (Motulsky and Christopoulos, 2003). Model convergence occurred when the difference in the residual sum of squares between iterations was <10^–8. Essentially the same fitting parameter values (_L and ) were obtained when the analytical transport solutions (i.e., Models 1 and 2) were analyzed using the SAS Nlin procedure (SAS Institute, Inc., Cary, NC 27513-2414). In addition, the fitting parameter values derived from the uniform flow model were validated using the CXTFIT Inverse data parameter estimation routine within STANMOD, version 2.2 (imnek et al., 1999; Toride et al., 1999).

Temporal Moment Analysis
Tritium recovery at the monitoring wells was estimated by comparing the area of the tritium breakthrough curve to that of the initial tracer pulse of a defined duration, assuming ideal radial flow in a confined aquifer with a fully penetrating injection well screened zone. Temporal moment analysis was used to compare tritium breakthrough behavior relative to that of the anionic tracers, Br, 2,4 Di-FBA, and 2,6 DiFBA, because it does not require the same assumptions necessary to fit the data to a specific transport model. The nth temporal moment for tracer breakthrough is

[12]

where C is the tracer concentration, r is the transport distance (m), or distance to the well, and t is time (min), as presented above. The mean arrival time for the tracer is then (Appelo and Postma, 2005)

[13]

The average arrival time for each tracer was calculated using the interpolation–extrapolation function in Origin 7.0 (OriginLab Corporation, Northampton, MA) to account for unequal sampling time intervals. In some instances the breakthrough curve for a specific tracer was not complete when monitoring was terminated, underestimating calculated arrival times. The mean travel time for each solute at a given monitoring location was calculated as the mean arrival time for the entire experiment, that is, the first temporal moment of the breakthrough curve, minus the mean pulse duration, or in other words, one-half the initial pulse duration (Divine et al., 2003; MacKay et al., 1994). To determine relative mass recovery for solutes other than tritium, the integral areas for the breakthrough curves at a given monitoring location were divided by the integral area derived for the conservative tracer, tritium. The retardation factor for a given solute was defined as the average velocity of water (v_w), that is, tritiated water, divided by the average velocity of the contaminant (v_c) or solute of interest:

[14]

In the current study, the retardation factor estimated by Eq. [14] was used as a means of comparing the arrival time of various solutes as an indicator of tracer sorption rather than fitting the data to a specific ADE model because many of the assumptions inherent in such an approach, such as sorption equilibrium, linear sorption behavior, and so on, may not be valid (Seaman, 1998; Seaman et al., 1995, 1996).

	Results and Discussion

TOP ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions REFERENCES

 
Eight extended tracer experiments were conducted at the ITS; however, the current discussion is limited to tritium, Br^–, and FBA behavior observed for the three tracer experiments summarized in Table 2 because they represent the most comprehensive datasets generated for solute breakthrough. All tracer data are presented in terms of dimensionless concentration, C/C₀. Tracer monitoring at the ITS resulted in detailed breakthrough histories for six monitoring wells, each with three discrete sampling intervals, potentially generating 18 detailed tracer breakthrough histories for each experiment. Multidepth sampling was viewed as crucial for evaluating _L, as vertical mixing may be overestimated when a sampling well is screened over a large depth-span of the aquifer, especially when the tracer has not been injected over the full aquifer depth (Gelhar et al., 1992; Pickens and Grisak, 1981; Pickens et al., 1981).

It is clear from the breakthrough data (Fig. 2–7) that the flow patterns were quite complex, indicating considerable three-dimensional variability in the hydraulic conductivity of the water-table aquifer at the study site. Figure 2 provides an example of tritium breakthrough behavior observed for Exp. A at the various sampling locations. For comparison, the wells have been arbitrarily grouped in columns according to their relative location with respect to the injection well and the natural flow gradient, with Wells S1 through S3 located downgradient and Wells S4 through S6 located upgradient of the IW (Fig. 1A). Data for wells located similar radial distances from IW are presented side-by-side in Fig. 2. Note, however, that a strong radial gradient, as indicated by water-table depth gauges within each monitoring well casing (Fig. 1B), was maintained throughout each tracer experiment.

View larger version (27K): [in this window] [in a new window]   FIG. 2. Observed tritium breakthrough curves from Exp. A for each sampling zone within the six radially spaced monitoring wells (S1–S6). For some monitoring wells sampling continued beyond the duration presented in the figure.

View larger version (24K): [in this window] [in a new window]   FIG. 3. Observed tritium breakthrough data from Exp. A for Well S1, Zone 3; simulated breakthroughs (solid lines) and model-derived parameters based on (A) Model 1 and (B) Model 2.

View larger version (32K): [in this window] [in a new window]   FIG. 4. Observed tritium breakthrough data (squares) for Well S6, Zone 3 for all experiments with simulated breakthroughs (solid lines) and model-derived physical transport parameters based on Model 1 (left column) and Model 2 (right column).

View larger version (26K): [in this window] [in a new window]   FIG. 5. Tritium breakthrough data and radial model fits for Well S4, Zone 3.

View larger version (24K): [in this window] [in a new window]   FIG. 6. Bromide breakthrough history for Exp. B. For some monitoring wells sampling continued beyond the duration presented in the figure.

View larger version (28K): [in this window] [in a new window]   FIG. 7. Tritium, Br, and FBA breakthrough curves for Exp. C. For some monitoring wells sampling continued beyond the duration presented in the figure.

Significant tailing was evident in many of the tritium breakthrough patterns that in some instances apparently continued after sampling for a given well had been terminated (Fig. 2). An example of tritium breakthrough data and calibrated model simulations for Well S1, Zone 1 of Exp. A can be seen in Fig. 3. Model 1, based on one-dimensional uniform flow, overpredicted initial tracer arrival, underpredicted the maximum tracer breakthrough concentration, overpredicted initial leach-out, and underpredicted the long-term tailing (Fig. 3A). Model 2 (Fig. 3B), based on radial flow with a constant dispersivity, better predicted initial tracer breakthrough and leach-out tailing.

As indicated by the coefficient of determination, r², the radial equation (Model 2) describes the data better than the uniform flow (Model 1) equation while yielding lower longitudinal dispersivities, _L. In most instances the radial equation more precisely reproduces the tailing observed in many tritium datasets, but there are still instances for which tritium displays significant tailing that is not captured by the radial breakthrough equation. Such extensive tailing may suggest the need for a multiple-region model to account for the large range in flow velocities encountered at the study site that resulted in physical nonequilibrium or mixing of stratigraphic layers of differing hydraulic conductivities indicative of transverse spreading. Even when using a radial solution to describe radially divergent tracer breakthrough, Hoehn and Roberts (1982) combined two distinct breakthrough curves representing two independent transmissive layers to generate a composite breakthrough pattern that accounted for the extensive tailing that could not be explained with a single _L and flow velocity combination. A similar rationale, stratification within the aquifer that yields different flow domains or fractured materials with multiple distinct flow pathways, has been used to account for the high degree of variability in observed tracer arrival times and dispersivity estimates for multiple distinct sampling zones within a single well, and complex multiple-peak tracer breakthrough behavior observed for a specific sampling zone (MacKay et al., 1994; Molz et al., 1988; Reimus et al., 2003a, 2003b). However, specific geophysical evidence of distinct flow domains is required to fully validate such an explanation.

Mass recovery estimates, optimized model parameters, and the associated 95% confidence intervals for tritium breakthrough for the three tracer experiments, including the coefficients of determination, r², are presented in Tables 3, 4, and 5, which correspond to Exp. A, B, and C, respectively. Instrument failure precluded the sampling of any zones within Well S1 for Exp. C (Table 5). The radial flow model (Model 2) typically provided the best description of breakthrough data, as indicated by the r², with lower _L values than observed for the uniform case. Calibrated _L values for the radial flow model ranged from 0.11 to 0.64 m, 0.18 to 1.2 m, and 0.14 to 2.8 m for Exp. A, B and C, respectively. The extremely high _L values (>1 m) are generally derived from relatively poor model fits to the breakthrough data and should be viewed with skepticism. Compared with the uniform flow solution (Model 1), the radial flow solution (Model 2) fit the data better for 34 of the 44 tritium breakthrough curves observed in the three tracer experiments, approximately 77%. However, the 95% confidence intervals for the estimated parameters (travel time and _L) often overlap for the two models.

Regardless of which model best describes the data for a given sampling zone, estimated travel times and _L values for different zones within the same well differed in some cases by a factor of three or more (e.g., Well S5, Exp. A; Table 3). Although there appears to be a trend in terms of decreasing travel times with decreasing depth for a given sampling well (in most instances the shortest arrival time was observed in Zone 3), there is no strong correlation between _L and arrival time. More important, there appears to be no clear relationship between _L and migration distance, contrary to our current understanding of dispersion. To some degree, such discrepancies may reflect non-Fickian solute transport behavior adjacent to the injection well that cannot be described by the ADE. However, if the breakthrough patterns are scaled with respect to the maximum breakthrough concentration for a given monitoring zone (maximum breakthrough C = 1) and then analyzed in a similar manner to that described above using Welty and Gelhar's (1994) analytical solution for a radially diverging instantaneous Dirac pulse, _L does increase with migration distance. To simplify analysis, investigators may be tempted choose the Dirac solution or related-type curves in cases where the tracer arrival time is much longer than the pulse duration. However, if the breakthrough concentration data for each monitoring location are scaled to 1, the resulting _L values are largely a function of peak width that in the present example does generally increase with increasing transport scale. This illustrates the importance of applying the appropriate inlet conditions when analyzing tracer data.

Previous studies have reported similar variability in _L values that can differ by an order of magnitude for various depths within a give monitoring well (Palmer and Nadon, 1986; Pickens and Grisak, 1981; Pickens et al., 1981; Thorbjarnarson and Mackay, 1994a). In a forced-gradient experiment similar to the current study, Palmer and Nadon (1986) found that _L values differed by greater than an order of magnitude, from 0.02 to 0.26 m, for a multilevel monitoring well located 6.5 m from the injection well. Their reported values, however, are generally lower than observed in the current study. Furthermore, high flow velocities within the aquifer, as indicated by shorter tracer arrival times, increased with increasing aquifer depth. Palmer and Nadon (1986) attributed this to stratified differences in hydraulic conductivity within the aquifer that were confirmed to some degree by resistivity logs in the vicinity of the sampling well. Unfortunately, such geophysical data is not available for the current study site.

Palmer and Nadon (1986) also noted that _L was directly correlated with increasing transport time, which they attributed to greater transverse diffusion at the lower flow velocities increased the apparent _L, and structural characteristics of the aquifer that affect both dispersivity and hydraulic conductivity. In another radial flow study, _L values differed by a factor of three for various depths within a specific well and showed no clear trend with distance for wells at 0.36, 0.66, and 2.06 m from the injection well (Pickens et al., 1981). In a related two-well tracer test where samples were collected at depths reflecting the natural stratigraphy, Pickens and Grisak (1981) found no clear relationship between _L and transport distance, asserting that the constant or asymptotic _L value may have been reached at the first sampling point, 0.36 m from the injection well.

Well S6, Zone 3 tritium data for all three experiments are presented in Fig. 4, including the model calibrations provided side-by-side for the uniform flow (Model 1) and radial flow (Model 2) solutions. Despite differences in the duration of the tracer pulse for each experiment, the same complex multiple-peak breakthrough is evident in each dataset. Similar multiple-peak behavior was also observed in all three experiments for Well S6, Zone 2. MacKay et al. (1994) attributed multiple-peak breakthrough for a conservative tracer to differences in transmisivity for various strata contributing to tracer migration. In the current study, the uniform breakthrough equation, Model 1, better describes the more Gaussian breakthrough pattern resulting from the multiple-peak arrival as indicated by the r² values, although the confidence intervals overlap for both travel time and _L values (Tables 3–5).

Poor model fits and rare problems with solution convergence were observed in some instances, as demonstrated in Table 5 and Fig. 5 for Well S4, yielding estimated travel times that are inconsistent with the results from previous experiments and that differ greatly from the tritium travel time based on temporal moments analysis in Table 6. As noted above, such datasets also displayed poor tritium mass recovery. Although the injection durations were quite similar for Exp. A and C, the lower peak tritium breakthrough and extensive tailing observed for Well S4, Zone 3 indicate that there may be some changes in the transmissive properties of the aquifer close to the injection well resulting from the prolonged injection experiments.

Results from the temporal moment analysis of tritium breakthrough behavior for Exp. A, B, and C are provided in Table 6. For some wells, the mean arrival time for the three sampling zones are quite similar (e.g., Well S4), while the arrival times for the three zones in other wells can differ by a factor greater than two (e.g., Well S5). In addition, arrival times for the same depth zones varied greatly between wells at similar radial distances from the IW, such as Zone 1 of Wells S1 and S4, located 1.82 and 2.04 m from the IW, respectively. With a few exceptions, the temporal moment estimates for tritium mean travel time are generally higher than values derived for the uniform flow model because they better account for tailing that was underpredicted for many of the curve fits (Table 6). If the datasets from each experiment are grouped according to zone, that is, sampling depth, travel time generally increases with increasing travel distance, with the exception of wells that are placed at very similar radial distances. Relatively high correlations (r² 0.978) were observed between the mean travel times for tritium calculated for any two injection experiments, indicating that previous breakthrough results are highly predictive of arrival time in subsequent tests despite differences in the duration of tracer injection pulses (range: 267–560 min). This suggests that the variability observed in tracer arrival within different sampling zones of the same well reflects inherent differences in flow velocity or travel path, and not transient conditions unique to each injection experiment.

For Exp. B, the first in which solute tracers other than tritium were introduced, initial Br^– breakthrough was somewhat delayed, with a lower peak concentration and more extensive tailing compared with the conservative tracer, tritium (Fig. 6). Table 7 provides bromide retardation factors and mass recovery estimates based on temporal moment analysis and integration of the Br^– and tritium breakthrough curves. Bromide retardation factors ranged from a conservative 0.99 to 1.67, with values differing quite dramatically for sampling depths within a given monitoring well. Bromide mass recoveries ranged from 39 to 111%. Without the presence of a truly conservative tracer, determining mass recoveries for radial divergent tracer studies is complicated by the potential uncertainties in flow field geometry (Novakowski, 1992). Although no clear trend in Br^– retardation was observed in Exp. B with increasing transport scale, mass recoveries clearly decreased with migration distance. This suggests that the temporal moment results for Br^– are biased to some degree in terms of shorter arrival times due to data truncation because monitoring was stopped prematurely before breakthrough was complete, and the higher detection limits for the anionic tracer compared with tritium. In an extensive series of laboratory column studies using SRS aquifer materials from the same formation, Seaman et al. (1995, 1996), Seaman (1998), and others (Korom, 2000) observed significant anionic tracer retardation that increased with transport scale and decreasing inlet concentration, indicative of a nonlinear sorption behavior.

Sorption of anionic tracers was observed in previous laboratory studies, primarily at low concentration. These studies indicated that sorption was relatively weak and reversible. Further, the lab results exhibited a degree of mechanistic complexity (e.g., nonlinear sorption, multicomponent competition, pH dependence, hysteresis) that is not represented by available analytical solutions of chemical transport, even for geologically homogeneous materials. As a result, we selected an advection–dispersion model (without sorption) for initial interpretation of the field data. In this case any sorption effects will be reflected in the velocity and dispersivity terms and the magnitude of differences in the coefficients between the anionic tracers and aqueous tritium species will provide insight into the potential significance of sorption.

Assuming the anionic tracers are behaving in a conservative manner, both ADE models were reasonably successful in describing the Br^– breakthrough data for Exp. B (Table 9), as well as the breakthrough data for Br^– and the two FBAs in Exp. C (Fig. 7), often yielding r² values similar to or better than those observed for tritium. However, anion sorption behavior is reflected in the resulting dispersivity term and tracer arrival time, that is, flow velocity. In most instances greater tailing was observed for the anionic tracer data due to sorption, increasing the likelihood of truncation error associated with an insufficient experimental duration or analytical detection limitations that preclude accurate monitoring of tracer tailing. However, the ability of a model to describe the observed tracer behavior does not necessarily validate the underlying mechanisms that are supposedly described by the model.

As expected, the Br^– travel time estimates based on the two models were longer than the travel time estimates for tritium. The _L values were generally larger as well, as Pickens et al. (1981) observed for the radial transport of a reactive tracer, ⁸⁵Sr. The higher effective dispersivity reflects not only the true physical dispersivity observed for tritium but also the effects on chemical nonequilibrium with respect to sorption and nonlinear sorption behavior.

	Conclusions

TOP ABSTRACT INTRODUCTION Materials and Methods Results and Discussion Conclusions REFERENCES

 
As illustrated in the present study, discerning nonconservative tracer behavior at the field scale is often difficult due to the high degree of physical heterogeneity one encounters and the inability to thoroughly monitor displacement of the tracer plume, which limits the accuracy of mass recovery estimates and spatial moments analysis. Analytical detection limitations and logistical concerns further hamper field-scale monitoring efforts. Despite such heterogeneity, high tritium recoveries (>90%) confirm the general radial nature of the induced flow gradient. The ability to replicate the complex breakthrough patterns observed in successive tracer experiments further suggests that such transport behavior reflects the inherent physical properties of the aquifer, and not transient conditions unique to each injection experiment. As indicated by r² values for the calibrated parameters, the radial analytical solution for solute transport was generally better than the one-dimensional uniform flow solution at describing tracer breakthrough and leach-out tailing with a lower _L. However, the 95% confidence intervals for the estimated parameters (travel time and _L) often overlap for the two calibrated models. Longitudinal dispersivity values and mean arrival times differed greatly for monitoring wells placed at similar radial distances, and between sampling zones within a given well, with no clear trend in _L observed with travel distance.

Temporal moment analysis confirmed the retardation of anionic tracers (Br^–, 2,4 Di-FBA, 2,6 Di-FBA) that are generally considered to travel in a conservative manner, despite analytical limitations and tracer data truncation due to extensive tailing that biased retardation estimates compared with tritium. Based on the results and observations, we are developing a numerical model that accounts for nonlinear and conditional sorption to improve the mechanistic description of the differences in tracer behavior. Despite tracer retardation and incomplete mass recovery, both ADE models reasonably described the anion data without specifically accounting for anion sorption reactions or apparent multiple flow domains, indicating that chemical interactions with the geologic matrix may be interpreted in terms of a physical transport process, such as flow velocity, path length, pore connectivity, multiple flow domains, or dispersivity.

	ACKNOWLEDGMENTS

 
The authors thank Troy Rea, Jennifer McIntosh, Angel Kelsey-Wall, and Jane Logan for their assistance in the field and with tracer analyses, Richard H. Williams for assistance with statistical analysis of the model results, Dr. L. Janecek for her assistance in creating the figures, and Dr. C. Strojan for his helpful comments on a draft version of the manuscript. Financial assistance was provided through Financial Assistance Award number DE-FC09-96SR18546 from the USDOE to the University of Georgia Research Foundation.

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