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Published online 17 May 2007
Published in Vadose Zone J 6:344-353 (2007)
DOI: 10.2136/vzj2006.0042
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
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SPECIAL SECTION: SAVANNAH RIVER SITE

Modeling Long-Term Plutonium Transport in the Savannah River Site Vadose Zone

Deniz I. Demirkanlia, Fred J. Molza,*, Daniel I. Kaplan, Robert A. Fjelda and Steven M. Serkiz

a Dep. of Environmental Engineering and Science, Clemson University, L.G. Rich Environmental Research Laboratory, 342 Computer Court, Anderson, SC 29625
b Savannah River National Laboratory, Aiken, SC 29808
* Corresponding author (fredi{at}clemson.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 16 March 2006.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
 Conclusions
 REFERENCES
 
Improved understanding of flow and radionuclide transport in vadose zone sediments is fundamental to future planning involving radioactive materials. To that end, long-term experiments were conducted at the Savannah River Site (SRS), where a series of lysimeters containing sources of different Pu oxidation states were placed in the shallow subsurface and exposed to the environment for 2 to 11 yr. After the experiments, Pu activity concentrations were measured along vertical cores from the lysimeters. Plutonium distributions were anomalous in nature—transport from oxidized Pu sources was less than expected, and a small fraction of Pu from reduced sources moved more. Studies conducted with these lysimeter sediments indicated that surface-mediated, oxidation–reduction (redox) reactions may be responsible for the anomalies. This hypothesis is tested by performing transient Pu transport simulations that include retardation and first-order redox reactions on mineral surfaces within a steady-state flow field. These simulations affirm the consistency of the surface-mediated, redox hypothesis with observed Pu activity profiles below the source. Such profiles are captured well by a steady-state, net downward flow model. The redox model explains how Pu(V/VI) sources release activity that moves downward more slowly than expected, and how Pu(III/IV) sources result in a small fraction of activity that moves downward farther than expected. The calibrated parameter values were robust and well defined throughout all simulations. Approximate retardation factors for Pu(V/VI) were 15, and for Pu(III/IV) were 10,000. For these values, ko averaged 2.4 x 10–7 h–1; kr averaged 7.1 x 10–4 h–1 (standard deviations are 1.6 x 10–7 h–1 and 1.6 x 10–4 h–1 respectively).

Abbreviations: INL, Idaho National Lab • Puo, oxidized class of Pu • Pur, reduced class of Pu • SRS, Savannah River Site.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
 Conclusions
 REFERENCES
 
The production of radioactive materials for defense, medical, and energy purposes has resulted in large amounts of waste and releases of radioactive constituents to the environment. High-level radioactive waste repositories, such as Yucca Mountain, or waste repositories for low level radioactive wastes may be located in the vadose zone. Accidental release or leaching above or below ground may result in radioactive contamination in this zone. Thus, an improved understanding of flow and radionuclide transport in vadose zone sediments is fundamental to future planning involving waste disposal and environmental remediation of radioactive materials.

Plutonium is often a nuclide of concern in disposal and remediation scenarios because of its high toxicity and very long half-life. Once released into the environment, the movement of Pu is strongly related to its oxidation state. In aqueous solutions, Pu can exist in oxidation states III, IV, V, and VI, with two or three such oxidation state combinations commonly present at equilibrium (Choppin, 2003). The reduced states of Pu (III, IV) are more stable in acidic media, while oxidized species (V, VI) become more stable at higher pH values (Choppin et al., 1997; Silva and Nitsche, 1995). In porous media, it is generally observed that the Pu (III) and (IV) oxidation states are much less mobile, while the V and VI oxidation states are more mobile (Choppin, 2003).

Even though the primary redox state of Pu in the subsurface is commonly thought to be in the oxidation state of Pu(IV) (Keeney-Kennicutt and Morse 1985; Sanchez et al., 1985), and the migration is expected to be very restricted because of its high affinity for the solid phase, examples of greater than expected subsurface Pu transport have been reported. Some sites in the USA where significant plutonium transport has been observed are the Mortandad Canyon at the Los Alamos National Laboratory, the 100K-Area at the U.S. Department of Energy's Hanford Site, the Nevada Test Site, and the Savannah River Site (Penrose et al., 1990; Marty et al., 1997; Dai et al., 2002, 2005; Kersting et al., 1999). Several mechanisms have been proposed to explain enhanced migration, including acidic soil water, colloidal transport, oxidation state transformations due to microorganisms, and soil-surface mediated oxidation of reduced, less mobile forms of Pu.

It has been known for some time that reactive mineral surfaces, such as Fe and Mn oxides, can oxidize or reduce Pu in environmental and laboratory systems. Powell et al. (2004, 2005) studied Pu(V) reduction following adsorption by synthetic magnetite, hematite, and goethite, and they were able to develop overall reaction rates from experimental data. They also observed no reduction of Pu(V) when there was no adsorption on either goethite or hematite, further suggesting that this reduction is a surface-mediated process. Several other studies also reported Pu oxidation state transformations by interactions with solid surfaces of Fe and Mn oxides (Morgenstern and Choppin, 2002; Keeney-Kennicutt and Morse, 1985; Sanchez et al., 1985; Penrose et al., 1987). Fjeld et al. (2001) observed a high-mobility fraction of Pu in column studies conducted with sediments from the Snake River Plain at the Idaho National Laboratory (INL). In a separate column study conducted with soils from the SRS, two distinct physicochemical forms of Pu were also observed, each with a different mobility (Fjeld et al., 2003). Their results indicated that a small high-mobility fraction of Pu can cause enhanced transport behavior, and predicting Pu behavior in soil might be more complicated and problematic than the traditional, single-species transport model in which species are subject only to linear reversible adsorption. Thus, Fjeld et al. (2003) developed a conceptual model for the subsurface transport of Pu involving surface-mediated reduction of Pu(V/VI) to Pu(III/IV) and equilibrium partitioning of Pu(V/VI) and Pu(III/IV) between aqueous and sorbed phases. Overall, the model was able to capture salient features of the data better than a single-species adsorption approach.

Long-term field experiments are often beneficial in understanding the chemistry-dependent Pu transport in complex natural systems. With this in mind, a series of field experiments were initiated at the SRS in the early 1980s. A group of lysimeters containing sources of known oxidation states of Pu were placed in the shallow subsurface. From 1981 until 1991 all lysimeters were left open to the environment except one, which was capped in 1983 and stored until it was analyzed. Aqueous leachate samples from these lysimeters were collected and analyzed for gross alpha and beta activity during the field period. At the end of this period, a cover was put over these lysimeters in the field for an additional 5 yr. Then these lysimeters were cored through the center and the cores were stored in a cooler for another 6 yr. Plutonium activities in the cores were measured as a function of depth from the ground surface at the end of the storage period.

The climatic environment to which the lysimeters were exposed was very transient, with numerous periods of rainfall alternating with evapotranspiration drying of the sediments and seasonal changes. The question arises, can we apply a steady, net flow model to this system, since such a model is computationally much simpler and requires much less information than a fully transient model? Thus, the primary objective of this paper is to describe the development of our transient reactive transport model, including surface-mediated redox chemistry based on a steady-state soil water flow, and compare simulated and measured profiles as a means to estimate parameter values and assess model utility. A secondary objective is to discuss the strength, weaknesses, and insights of the steady flow approach.


   Lysimeter Experiments
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
 Conclusions
 REFERENCES
 
As illustrated in Fig. 1, lysimeters were constructed using 52-L polyethylene carboys with the bottoms removed. The carboys were filled with remolded natural soil from the Burial Ground at the SRS. During the filling process, a small disc of filter paper spiked with Pu solutions of selected oxidation states and known total activity was placed near each lysimeter center, and the entire apparatus was buried with the top left open to the natural climate. The lysimeter bottoms were connected to a reservoir so that any leachate exiting the containers could be collected and studied. Kaplan et al. (2004b, 2006) provided physical and chemical details concerning preparation of the lysimeter experiments, including obtaining the cores and subsequent measurements of Pu activity. Table 1 lists experiment durations, oxidation state of the Pu source solutions, and total activity released into the domain for the four experiments that were modeled. The two different durations shown in the table are the "field experiment duration," the time the lysimeters were in the field and open to the environmental conditions, and the "capped/storage duration," the time after the lysimeters were capped until the cores were analyzed.


Figure 1
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  		FIG. 1. Experimental setting of the small field lysimeters used in plutonium migration studies at the Savannah River Site. The Pu source (spiked filter paper) was initially placed 21.6 cm below the surface.

 

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  		TABLE 1. Data sets available from the lysimeter experiments.{dagger}

 
During the first 4 yr of the experiments, rainfall data were collected at the lysimeter site, along with leachate volumes. For the entire duration of the experiments, rainfall data were collected at the nearby Area-200F weather station. The leachate data allowed us to calculate the average net downward water flow rates during the first 4 yr of the experiments and then extrapolate these data to leachate generation periods where only rainfall data were available. (Leachate Pu activity exiting the Pu-containing lysimeters did not exceed natural activity leaving a set of control lysimeters.)

Shown in Fig. 2 and 3 are experimental data (symbols) that are sorbed activity concentrations normalized by the total sorbed concentration, So, at the source location. Also shown are simulations of Pu(IV) and Pu(VI) activity distributions based on single species transport subject only to linear reversible adsorption (retardation). Average net downward advective velocities were obtained from the leachate volume data collected from the lysimeters and ranged from 0.016 to 0.028 cm h–1. As expected, there was a marked difference in mobility depending on whether the source was reduced Pu(IV) or oxidized Pu(VI), with apparent retardation factors in the range of 3,000 to 15,000 for Pu(IV) and 25 to 100 for Pu(VI). The pH of the SRS soil is about 6, so these values fall into the range measured experimentally and reported by Fjeld et al. (2003) for Pu(IV), but the values for Pu(VI) are high compared with experimental measurements of retardation factors of around 20. The shapes of the curves are also anomalous, with activity resulting from the Pu(IV) source having a leading edge at low concentrations and that from the Pu(VI) source not fitting the simulated curves well even at the higher activity levels.


Figure 2
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  		FIG. 2. Measured activity distribution due to a Pu(IV)(NO3)4 source versus results of simulations with a single species transport model with adsorption only.

 

Figure 3
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  		FIG. 3. Measured activity distribution due to a Pu(VI)O2(NO3)2 versus results of simulations with a single species transport model with adsorption only.

 
It is surprising that the amount of mass moving upward in Fig. 2 is comparable to the amount moving downward, and at present we don't have a good explanation for this observation. As mentioned previously, however, the actual system is highly dynamic, with large downward water fluxes during periods of rainfall and smaller but longer lasting upward fluxes during periods of evapotranspirative drying. Also, the moisture content of the soil system is not constant due to these dynamic flow conditions. Thus, it is evident that a more dynamic analysis will ultimately be needed. In the remainder of this communication, however, we will concentrate on the net downward migration below the source. In particular, the influence of the initial oxidation state of Pu on the downward migration in these vadose zone lysimeters will be examined.

The most striking feature of the Pu profile in Fig. 2 for the Pu(IV)(NO3)4 lysimeter is the overall movement of Pu much deeper into the profile than expected based on experimental sorption phenomena alone, while the penetration shown in Fig. 3 for the Pu(VI)O2(NO3)2 lysimeter is less than expected. For the Pu(IV) experiment shown in Fig. 2, penetration is expected to be about 3 or 4 cm for a retardation factor of 10,000. However, actual penetration was observed approximately 10 cm beyond the expected penetration, albeit at low concentrations. This observation is consistent with earlier findings by Fjeld et al. (2001, 2003), who were able to distinguish a very small, high-mobility fraction of Pu and attributed this form to differences in redox state. Microscopic examination by synchrotron X-ray fluorescence spectroscopy of portions of the core samples did not provide any evidence for colloid transport (Kaplan et al., 2004a). Another proposed cause for enhanced Pu migration was low soil pH values; however, the SRS soil has a relatively high pH of about 6 (Kaplan et al., 2004b).

Given the range of retardation factors associated with the reduced (III/IV) and oxidized (V/VI) states of Pu, the observed anomalous migration behavior of Pu in the lysimeter experiments may be attributed to the development of two distinct classes of Pu species based on redox state, with each state exhibiting a different mobility. The overall objective of the following quantitative analysis is to determine if this hypothesis is consistent with the measured details of the lysimeter activity distributions below the sources.


   Reactive Transport Model Development
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
Numerical Modeling
 Results and Discussion
 Conclusions
 REFERENCES
 
Based on the findings above, we developed a conceptual model including equilibrium, reversible partitioning between aqueous and solid phases; kinetic oxidation–reduction reactions in the sorbed phase; steady-state, unsaturated net downward advection; and one-dimensional hydrodynamic dispersion along the vertical axis. The advection due to the net downward flow is cancelled for the storage period because of no flow during that time, and the dispersion takes the form of molecular diffusion adjusted for the storage temperature. Because of the similar relatively low mobility of the reduced pair "Pu(III/IV)" compared with the higher mobility of the oxidized pair "Pu(V/VI)," we only consider two possible Pu classes, an oxidized class (Puo) (i.e., [Pu(V)] + [Pu(VI)]) and a reduced class (Pur) (i.e., [Pu(III)] + [Pu(IV)]). For each class of Pu, the equations state that the change of activity stored with respect to time in both the liquid and solid phases in a small control volume is equal to the net outflow rate due to advection, plus the net outflow rate due to dispersion, plus sources of activity, minus sinks of activity. The resulting equations in microcuries per cubic centimeter per hour may be written as

Formula 1[1]
and

Formula 2[2]

In Eq. [1] and [2], C is the activity concentration in terms of activity per volume for Puo and Pur as indicated by subscripts, t is time, z is depth below the core top, {theta} is the average volumetric water content (which in the assumed steady downward flow system plays a role similar to the porosity), Rr is the retardation factor for Pur and Ro is the retardation factor for Puo, v is the net downward advective velocity, and D is the hydrodynamic dispersion coefficient that includes molecular diffusion and mechanical dispersion. It is the source and sink terms that will be used to represent redox reactions in the adsorbed phase.

It is assumed that on the surfaces, Pur can be oxidized to Puo, and Puo can be reduced to Pur. First-order reaction rates based on Pu concentration were selected for both oxidation and reduction reactions. At any particular time, the activity on the surfaces are the sum of {rho}KdrCPur and {rho}KdoCPuo, respectively, where Kdr and Kdo are distribution coefficients and {rho} is soil bulk density. If ko is the oxidation rate constant and kr is the reduction rate constant, then the oxidation and reduction rates in microcuries per cubic centimeter per hour are given by

Formula 3[3]
and

Formula 4[4]
When these expressions are substituted into Eq. [1] and [2], the result is

Formula 5[5]
and

Formula 6[6]
To begin simulations based on Eq. [5] and [6], initial values are needed for the model parameters Ro, Rr, v, D, ko, and kr.

Retardation factors, which are largely defined by the lysimeter data, are quantified as described above. Net downward Darcy velocity for each data set is calculated from the measured leachate volumes averaged over the 4-yr collection period. For the experiments in which the experiment duration exceeded 4 yr, the average Darcy velocity per year was assumed to be maintained. Correlating the measured Darcy velocities with the annual rainfall and using rainfall data to project future average Darcy velocities did not have a significant effect on simulations.

To change Darcy velocities to seepage velocities, average water content, {theta}, is needed. This average is estimated by using unsaturated hydraulic conductivity (K) measurements and particle size distribution measurements that were determined by using three soils collected at the SRS near the lysimeter study location. A particle size distribution analysis was performed by using a standard sieve analysis refined by the hydrometer method. The results showed very good agreement with an independent measurement done by Kaplan et al. (2004b). The unsaturated hydraulic conductivity measurements were made using an unsaturated flow apparatus (UFA Ventures Inc., Richland, WA) based on open-flow centrifugation (Nimmo and Mello, 1991; Conca and Wright, 1992). Soil bulk density was estimated to be 1.55 g cm–3 based on the particle size distribution (Dragun, 1998). The average particle size distribution of the soil was approximately 70% sand, 7.8% silt, and 22.2% clay. This information was used as input to Rosetta, a program developed by Schaap et al. (2001) to estimate the van Genuchten soil hydraulic parameters. The resulting function agrees well with the first three centrifuge-measured unsaturated hydraulic conductivity values as shown in Fig. 4. Estimated van Genuchten functions—saturation (Se), hydraulic conductivity (K), and volumetric water content ({theta})—as functions of pressure head ({Psi}) are given by

Formula 7[7]
and

Formula 8[8]


Figure 4
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  		FIG. 4. Measured and estimated unsaturated hydraulic conductivity as a function of water content.

 
Obtaining the K({psi}) and {theta}({psi}) functions enables one to estimate a water content value consistent with the measured net downward flow, assumed to be due to gravity. In such a situation, the hydraulic gradient is one, and K is flux per unit gradient. The measured Darcy velocities range between 4.01 x 10–3 and 6.98 x 10–3 cm h–1 (Table 2). The corresponding water contents for these fluxes, treated as K values in Fig. 4, fall between 0.243 and 0.264. As a result, the average steady-state volumetric water content consistent with the net downward flow is selected as 0.25 for the simulations. Thus, seepage velocities are calculated for each data set by dividing the Darcy velocities with the average steady-state volumetric water content.


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  		TABLE 2. Estimated Darcy and seepage velocities for a water content of 0.25.

 
Hydrodynamic dispersion coefficients are defined by Eq. [9]. An average molecular diffusion coefficient (Dd) estimated using the Nernst equation is 3.16 x 10–6 cm2 s–1 at 0°C, and 6.82 x 10–6 cm2 s–1 at 25Co. Based on high levels of sand content of the sediment determined by mean particle size data, tortuosity ({omega}) is estimated as 0.4, knowing that clean uniform sand would yield a tortuosity value of about 0.7 (Fetter, 1998). Dispersivity ({alpha}L) is estimated based on a combination of column experiments reported in McGinnis (2000) and curves relating dimensionless dispersion coefficients to Peclet number presented in Fetter (1998). The direct measurements from columns 8 cm in length resulted in an average dispersivity of 0.33 cm. Fetter's (1998) dimensionless curves with a mean particle diameter (D50) of 0.029 cm resulted in a dispersivity of 0.3 cm. This results in an overall mean value of about 0.3 cm. At a mean net downward seepage velocity of 0.02 cm h–1 (5.6 x 10–6 cm s–1) and a mean annual temperature of 10 Co, the resulting dispersion coefficient is about 0.013 cm2 h–1 (3.7 x 10–6 cm2 s–1), essentially the same as molecular Pu diffusion in free water. During the storage period for each experiment, the seepage velocity was set to zero, which reduces the transport process to effective molecular diffusion. Since the overall results were dominated by advective transport during the field portion of the lysimeter experiments, simulations were not sensitive to {omega}, Dd, or {alpha}L.

Formula 9[9]

Surface-mediated oxidation and reduction reactions on different mineral surfaces have been reported in the literature as stated previously. Based on those findings, the oxidation–reduction reactions in the model are assumed to occur in the sorbed phase only due to the surface reaction of Pu with the sediments. The rate constants ko and kr are fitted to the data resulting from the lysimeter experiments.

The total activity released into the domain is calculated for each data set by using the initial, known activity on the filter disks and the measured activities recovered on the filter disks after the experiments. The difference yields the total activity released into the domain, and it is assumed that all activity is released during the field portion of the experiments, when there is an assumed constant net downward flow through the domain. Furthermore, no Pu was assumed to leach out of the lysimeter, consistent with monthly and quarterly monitoring data of the lysimeter leachate. Two release scenarios shown in Fig. 5 were studied, a constant rate release and an exponentially decreasing rate of release. Over the duration of the experiments, both release rates were adjusted so that the same amount of activity was released. No significant differences were observed in the resulting simulated activity distributions, so in all following simulations, the activity is released at a constant rate from the node where the filter disk was located at the time when the data were collected (Fig. 6).


Figure 5
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  		FIG. 5. Constant and exponential release rate functions for the Pu(IV)(C2O4)2 data set with a total released activity of 455 µCi.

 

Figure 6
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  		FIG. 6. One-dimensional finite difference approximation of the domain.

 

   Numerical Modeling
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
Results and Discussion
 Conclusions
 REFERENCES
 
Transport in the cored portions of the lysimeters, which were analyzed at the end of the experiments for the sorbed Pu distribution profiles, is simulated using Equations (5) and (6). Implicit finite difference approximations to the coupled governing equations are solved simultaneously using Picard iteration for the coupling and the Gauss Siedel iterative method to solve the difference equations (Evans et al., 2000). The upper boundary condition in the model is defined as zero activity concentration for both Pur and Puo. To define the lower boundary condition at z = z1, we make use of the fact that the advective water flux (qw) is constant, so the Pu flux out of the system (either oxidized or reduced forms) is given by:

Formula 10[10]

The boundary condition is then defined by qPu(-{Delta}z/2) = qPu(+{Delta}z/2). In finite-difference form, this condition allows the Pu to simply disperse and drain out with the water flux at the bottom boundary, as illustrated in more detail in Fig. 6. At the end of each simulation, the total activity remaining in the domain is calculated for mass balance purposes. (Only simulations using unrealistically small retardation factors resulted in drainage.) A summary of all parameter values used in the model is given in Table 3.


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  		TABLE 3. Summary of all parameter values used in the model.

 

   Results and Discussion
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
Conclusions
 REFERENCES
 
Pu(VI)O2(NO3)2 Simulation Results
During this 118-wk experiment, a total of 244 µCi of activity was released to the domain from the Pu(VI) source at a constant rate of 0.011588 µCi cm–3 h–1. A range of retardation factors for Pu(VI) (treated as Puo in the model) was applied, and the results are presented in Fig. 7 as three different simulations sets, with the retardation factor for Pu(IV) held constant at 10,000. For all three of the sets, Simulation 1 showed the single species transport front with retardation only. Since no oxidation or reduction was allowed during these initial simulations, the oxidation state of the Pu species transported was the same oxidation state as that of the Pu source. As discussed (Fig. 2), single-species retarded transport is not able to capture the overall Pu distribution characteristics. As shown in Fig. 7 for Puo, Simulation 1 always indicates the maximum migration possible for the particular retardation factor, since the Pu stayed in the more mobile form throughout the simulation. The addition of surface-mediated redox reactions always decreases the overall migration for a Puo source. A Puo retardation factor of 50 is clearly too large because the front did not migrate sufficiently far. When the retardation factor decreased to 25, the total distance of the migration was captured, but the bulk movement of the Pu was slightly overestimated. Therefore, the Puo retardation factor was chosen as 15 for the last set of simulations, and the results, as shown in Fig. 7c, were able to match the data reasonably well. This leads us to infer that the more mobile Puo was retarded by being reduced to a less mobile form. Even though the actual retardation of Puo during the experiments was not known exactly, on the basis of the simulations one can infer that the retardation factor was about 15, and this was the value used in the remaining simulations reported herein.


Figure 7
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  		FIG. 7. Comparison of activity distribution measurements with modeling results for the Pu(VI)O2(NO3)2 data set for different oxidation (ko) and reduction (kr) rate constants, and retardation factors, Ro and Rr. (a) Ro = 50, Rr = 10,000; (b) Ro = 25, Rr = 10,000; (c) Ro = 15, Rr = 10,000. (So = 7.86 µCi g–1 for the best fit curve in Fig. 7c.)

 
Figure 7c also shows the effect of including surface-mediated redox reactions on the migration of Pu. When a high reduction rate (kr) relative to the oxidation rate (ko) is applied to the system, the migration was excessively retarded, as seen in Simulation 2. The simulations did not show any significant change due to the oxidation rate constant, as shown by Simulations 2, 3, and 4. Since oxidation is a very slow process, this result is attributed to the relatively short duration of this particular experiment, which was about 2 yr. The response of the system to the reduction rate constant can be seen through Simulations 3, 5, 6, and 7, with 7 giving the best fit to the experimental data, based on a coefficient of determination (R2) value of 0.98.

A set of simulations was performed with the Puo retardation factor kept at 15, and the oxidation and the reduction rate constants chosen from Simulation 7 of Fig. 7c. The Pur retardation factor was then varied from 5000 through 15,000. As can be seen in Fig. 8, the Pur retardation factor had little effect on the simulations. The important factors in simulating Pu(VI) transport in the SRS lysimeter were the Puo retardation, and how fast Puo reduced to Pur. Due to its low mobility and the relatively short duration of the experiment, once Puo became reduced it essentially remained in place in the Pur form. A summary of the best fit oxidation and reduction rate constants for different Puo retardation factors is presented in Table 4.


Figure 8
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  		FIG. 8. Comparison of simulated and measured activity distributions for the Pu(VI)O2(NO3)2 source as a function of the reduced retardation factor Rr. Clearly, Rr has little effect on these profiles.

 

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  		TABLE 4. Best fit values of oxidation and reduction rate constants for Pu(VI) data set simulations as a function of Ro.

 
Pu(IV)(NO3)4, Pu(IV)(C2O4)2, and Pu(III)Cl3 Simulation Results
As stated earlier, Pu(III) and Pu(IV) are the less mobile forms of Pu and show similar transport characteristics (Duff et al., 1999) and are therefore both modeled as Pur. (This is also consistent with the observation that the data presented in Fig. 9 are quite similar for both reduced states). The Pu(III) and Pu(IV) activity distributions showed significant differences compared with the Pu(VI) distributions. During the 11-yr Pu(III) and Pu(IV) experiments, the bulk of the Pu migration was retained in the first few centimeters below the filter. (The corresponding distance for the 2-yr Pu(VI) experiment was about 15 cm). Previously, the Pur retardation factor was determined to be between 5000 and 15,000 as a result of the single species retarded transport analysis. For the simulations presented in Fig. 9, the Pur retardation factor was 10,000, and the Puo retardation factor was 15.


Figure 9
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  		FIG. 9. Comparison of simulated and measured activity distributions for each of the Pur sources. (a) Pu(IV)(NO3)4 – Ro = 15, Rr = 10,000; (b) Pu(IV)(C2O4)2 – Ro = 15, Rr = 10,000; (c) Pu(III)Cl3 – Ro = 15, Rr = 10,000. (So = 6.05 x 101 µCi g–1, So = 5.42 x 101 µCi g–1, and So = 5.74 x 101 µCi g–1 for the best fit curves in Fig. 9a, 9b, and 9c, respectively.)

 
Figure 9 shows results of the model simulations for different oxidation and reduction rate constants, compared with the measured data for each data set. When oxidation and reduction were eliminated by setting the values of the rate constants to zero, as shown in Simulation 1 for each data set, the model behaved as a single species transport with only Pur in the domain and retarded by the Pur retardation factor. Without any oxidation and reduction occurring, the Pu stayed in the less mobile form throughout the simulation, and the leading edges were highly underestimated. This also shows that modeling Pu transport in the environment assuming that it stays in the reduced form may not be a good approximation.

The oxidation rate constant in the Pur data sets had a very significant effect on the Pu activity distributions due to the longer durations of the experiments. As seen in Simulations 2, 3, 4, 5, and 6 in Fig. 9a, the value of this rate constant (ko) determines the fraction of Pu that moves farthest into the domain. Even though the bulk of the Pur activity distributions are consistent with single species retarded transport, the oxidation process produces the small, high-mobility fraction that is observed in all the Pur data sets. Figures 9b and 9c show similar behavior for the other Pur data sets.

If we assume there is only oxidation in the system with no reduction, as seen in Simulations 2 and 3 in the graphs for each data set in Fig. 9, a poor fit to the data results. Simulations 6, 7, and 8 in Fig. 9b show that the reduction rate constant (kr) determines how fast the high-mobility fraction moves; in other words, it determines the amount of retardation that fraction undergoes, since it converts more mobile forms of Pu (Puo) to less mobile forms (Pur) following contact with mineral surfaces. After adsorption of Puo, as the reduction rate increases, the amount of Puo converted to Pur in a given time also increases. So, in simulation 6 with a higher reduction rate, the high-mobility fraction was retarded more, whereas in simulation 8 with a lower reduction rate, the high-mobility fraction moved more quickly in the domain, in some cases exiting the lower model boundary, which was not observed in the field experiments. Similar behavior is shown in Fig. 9a and 9c. Thus, both oxidation and reduction are needed in the Pur simulations to match the data. The oxidation and reduction rate constants in Simulation 6 in Fig. 9a, 9b, and 9c for each data set gave the best fit to the data based on R2 values of 0.96, 0.99, and 0.89, respectively. Also, a summary of the best fit oxidation and reduction rate constants is presented for different Pur and Puo retardation factors in Table 5.


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  		TABLE 5. Resulting best fit values of oxidation and reduction rate constants for Pu(IV) and Pu(III) data set simulations.

 
Figure 10 shows simulated activity distributions for a reduced Pu source just before the storage period (time = 11 yr). Comparison of Fig. 9a and this figure illustrates the effect of the storage period, where only molecular diffusion takes place. It is evident that the distributions undergo only minor changes while the cores are stored at low temperatures.


Figure 10
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  		FIG. 10. Simulation results for a Pu(IV)(NO3)4 source with retardation factor values of Ro = 15 and Rr = 10,000 just before coring and refrigerated storage (time = 11 yr).

 

   Conclusions
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
 Conclusions
REFERENCES
 
On the basis of the results of our simulations, we conclude that the surface-mediated, oxidation–reduction hypothesis is consistent with the observed downward Pu activity profiles in the lysimeter experiments at the SRS. The implication of these possible redox reactions is that Pu(V/VI) sources release activity that moves downward more slowly than expected based on adsorptive retardation alone, and Pu(III/IV) sources result in a small fraction of activity that moves downward more rapidly than expected. These two phenomena in combination with varying adsorptive effects produced simulated activity profiles that agreed rather well with the anomalous activity profiles observed in the experiments. In principle, other mechanisms that can be represented with first-order rate equations could produce equally good fits, so this study does not prove the surface-mediated, oxidation–reduction hypothesis conclusively. However, it would appear that alternative processes would have to take place on the matrix surfaces, simply because the Pu ions are so strongly sorbed. At any given time, only a small percentage of activity is found in the aqueous phase. One alternative explanation for unexpected Pu migration is colloidal transport. However, this mechanism would only enhance the migration, not retard it, as observed below the Pu(V/VI) source.

The calibrated parameter values were robust and relatively well defined throughout all four sets of simulations. The Pu(V/VI) retardation factors were about 15, and Pu(III/IV) retardation factors were about 10,000. For these values, ko averaged 2.4 x 10–7 h–1 with a standard deviation of 1.6 x 10–7 h–1, and kr averaged 7.1 x 10–4 h–1 with a standard deviation of 1.6 x 10–4 h–1. These rate constant values are about two orders of magnitude lower than the laboratory measured values by Kaplan et al. (2004b), as expected due to the enhanced conditions in a laboratory setting. However, our model's prediction of four to five orders of magnitude faster reduction rates compared with oxidation rates is also observed in the laboratory-measured data by the same study. The results of sensitivity analyses around these values may be found in Tables 4 and 5. By far, the most important variable affecting transport, as one would expect, is the oxidation state [Pu(III/IV) or Pu(V/VI)] of the source material.

Returning again to the question of why a steady-state, net downward flow model might be expected to reproduce the activity profiles below the source in experiments exposed to highly transient boundary conditions (natural climate), we note that most of the material transported is dominated by the strong adsorption of Pu(III/IV), which has a retardation factor on the order of 104. This means that a given ion spends roughly 99.99% of its time in the adsorbed state. For a Pu(V/VI) ion with a retardation factor of 15, about 93% of its time is spent on surfaces. However, with a first order reduction rate constant of 7.1 x x10–4 h–1, Pu(V/VI) changes essentially irreversibly to Pu(III/IV) with a reaction half-life of 60 d. So collectively, one can visualize the ions as spending most of their time on the surfaces, hopping off briefly to sample the velocity of the liquid phase and undergo diffusion, and returning to the surfaces. This process would happen repeatedly, but with very brief stays in the liquid phase. Under such conditions, one would expect the advective transport to reflect the long-term average movement of the pore fluid, which is in the net downward direction. However, as mentioned previously, this conceptualization does not explain significant Pu migration above the source, as observed in the experiments.

One can speculate that a reason for the upward migration is that the surface-mediated oxidation reactions are a function of available oxygen in the pores and enhanced toward the drier surface, which would cause formation of more mobile Pu forms above the source. Thus, to further test the surface-mediated redox hypothesis, future research should be devoted to developing fully transient simulations of the Pu release and transport process, a much more complicated and data intensive effort than the steady flow analysis presented herein. To accomplish this, transient rainfall must be applied in a realistic manner, and water extraction by plant roots (transpiration) must be applied also, since natural vegetation, mainly weed grass, was allowed to grow in the lysimeters. Thus, one might also have to consider Pu transport in plant roots. It will be interesting to see if calibration of the redox rate constants for transient conditions will result in significantly different or similar values.


   ACKNOWLEDGMENTS
 
This research was supported in part by Task Prder SC0194, subcontract C001572-O assigned to Clemson University by the Savannah River National Laboratory, USDA.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 Lysimeter Experiments
 Reactive Transport Model...
 Numerical Modeling
 Results and Discussion
 Conclusions
 REFERENCES
 




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