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Colloid-Facilitated Plutonium Transport in Fractured Tuffaceous Rock Andrew Wolfsberg,† Zhenxue Dai,*,†,‡,§ Lin Zhu,†,∥ Paul Reimus,† Ting Xiao,†,⊥ and Doug Ware† †

Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States College of Construction Engineering, Jilin University, Changchun 130026, China § Key Laboratory of Groundwater Resources and Environment, Ministry of Education Jilin University, Changchun 130026, China ∥ College of Resources Environments and Tourism, Capital Normal University, Beijing 100048, China ⊥ Energy and Geoscience Institute, University of Utah, Salt Lake City, Utah 84108, United States ‡

S Supporting Information *

ABSTRACT: Colloids have the potential to enhance the mobility of strongly sorbing radionuclide contaminants in groundwater at underground nuclear test sites. This study presents an experimental and numerical investigation of colloid-facilitated plutonium transport in fractured porous media to identify plutonium reactive transport processes. The transport parameters for dispersion, diffusion, sorption, and filtration are estimated with inverse modeling by minimizing the least-squares objective function of multicomponent concentration data from multiple transport experiments with the shuffled complex evolution metropolis algorithm. Capitalizing on an unplanned experimental artifact that led to colloid formation, we adopt a stepwise strategy to first interpret the data from each experiment separately and then to incorporate multiple experiments simultaneously to identify a suite of plutonium−colloid transport processes. Nonequilibrium or kinetic attachment and detachment of plutonium−colloid in fractures were clearly demonstrated and captured in the inverted modeling parameters along with estimates of the source plutonium fraction that formed plutonium−colloids. The results from this study provide valuable insights for understanding the transport mechanisms and environmental impacts of plutonium in groundwater aquifers.

1. INTRODUCTION A large number of underground nuclear tests at the Nevada National Security Site (NNSS; formerly the Nevada Test Site) were conducted in volcanic tuffs (Figure 1). Predictions of reactive and nonreactive radionuclide transport through the test site are needed to assess the current and future impacts on groundwater quality of historic subsurface nuclear testing. Radionuclide transport in these tuffs may be associated with both matrix and fracture flow, although migration of reactive radionuclides over significant distances is likely to be dominated by fracture transport because of very low groundwater velocities and abundant surface area for sorption in the porous matrix.1−4 The NNSS is divided into several corrective action units (CAUs) for assessment of subsurface nuclear testing impacts on groundwater quality (Figure 1). In the Yucca Flat/Climax Mine CAU, 747 nuclear detonations were conducted, comprising about 38% of the total unclassified tritium (3H) inventory at the NNSS, decay corrected to 2012.5 Yucca Flat is of interest because a regional carbonate aquifer underlies local volcanic and alluvial material, where most of the subsurface tests were conducted.6 Thus, understanding potential transport mechanisms through the volcanic tuffs in this CAU is important for the overall risk assessment of potential radionuclide migration to the regional carbonate aquifer. The history of nuclear testing © XXXX American Chemical Society

in Yucca Flat and other areas of the NNSS is described by the U.S. DOE.7 In Yucca Flat, the volcanic tuffs are generally grouped into the tuff confining unit (TCU) or welded tuff aquifers (WTAs). The TCU is prominent throughout the central part of the CAU7 and is where, or below where, most of the Yucca Flat tests were conducted. Ware et al.8 conducted experiments on radionuclide transport in fractured rock with Yucca Flat TCU samples, with the goal of understanding radionuclide transport processes and deriving site-specific transport parameter distributions for use in conceptual and numerical radionuclide migration models. The results of those experiments are used here in conjunction with inverse modeling to estimate transport parameters for solute and colloid-facilitated plutonium migration in TCU fractures. Inverse modeling is used to determine unknown flow and transport parameters by fitting model outputs to measurements. A general framework and description of coupled groundwater flow and solute transport inverse modeling are given by Parker and Valocchi9 and Sun.10 For such problems, Received: Revised: Accepted: Published: A

February 21, 2017 April 3, 2017 April 18, 2017 April 18, 2017 DOI: 10.1021/acs.est.7b00968 Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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Figure 1. Location of the Nevada National Security Site and the corrective action units (CAUs) within dashed lines.

posterior distribution. This method has been successfully applied to many case studies with various complexities.27−29 In this study, we identify appropriate transport processes and parameters, such as matrix diffusion for 3H, Peclet numbers, plutonium−colloid formation fractions, and kinetic vs equilibrium filtration of plutonium−colloid, to better understand the characteristics of radionuclide transport in the fractured rock. Inverse modeling of the transport experiments8 is conducted in conjunction with the SCEM method. We quantify the uncertainty of the estimated parameters of nonreactive radionuclide and colloid-facilitated solute transport in the fractured tuffaceous rock.

gradient-based optimization techniques such as Gauss−Newton−Levenberg−Marquardt (GNLM)11−16,18,17,19−21 method can converge fast and save large computational resources. However, these techniques suffer from many difficulties, especially in cases involving multiple local optima in the parameter space with both small and large domains of attraction (a subregion of the parameter space surrounding a local minimum), discontinuous first derivatives, and curving multidimensional ridges.22 Parameters derived from local minimal solutions with gradient-based inversion may lead to inadequate model predictions, especially for long-term (more than 1000 years) prediction of radionuclide transport in groundwater.23 More recently, optimization algorithms based on stochastic theory have been developed and applied to hydrologic model inversion.24,25 Among these algorithms, the shuffled complex evolution metropolis (SCEM) method is a general-purpose optimization algorithm that uses adaptive Markov chain Monte Carlo (MCMC) sampling to provide an efficient search of the parameter space.22 The method uses a predefined number of different Markov chains to independently explore the search space. These chains communicate with each other through an external population of points, which are used to continuously update the size and shape of the proposed distribution in each chain. The MCMC evolution is repeated until the R-statistic of Gelman and Rubin26 indicates convergence to a stationary

2. MATERIALS AND METHODS Fracture Transport Experiments and Tuffaceous Rock Samples. Ware et al.8 conducted fracture transport experiments considering seven radionuclide tracers (3H, 14C, 90Sr, 137 Cs, 233U, 237Np, and 239Pu) and numerous geologic samples from both the tuff confining unit (TCU) and the lower carbonate aquifer (LCA) in Yucca Flat. One unplanned result of these experiments is that a fraction of the injected plutonium (239Pu) was sorbed onto colloids in the solution and column inlet (because the laboratory was forced to stand-down for more than 3 weeks) and migrated with colloids in the fracture.8 The solution is synthetic groundwater prepared mainly to match the reported water chemistry of the Yucca Flat groundwater, with a pH of 7.7, in which mineral colloids are B

DOI: 10.1021/acs.est.7b00968 Environ. Sci. Technol. XXXX, XXX, XXX−XXX

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Environmental Science & Technology formed from precipitation of amorphous silica and calcite (or other calcium−carbonate phases such as aragonite). Detailed mineral colloid analysis of the Yucca Flat groundwater is presented in the Supporting Information, which indicates that the mineral colloids have a mean size of 120 nm and a mean concentration of 7.31 × 107 particles/mL or 1.8 × 10−8 mol/L (including immobile colloids). The 239Pu, with a concentration of 1.1 × 10−7 mol/L, was in the Pu(V) oxidation state at the start of each experiment. Due to the forced laboratory standdown, a portion ( 1. These two criteria indicate that the filtration process is close to equilibrium. The kinetic models provide much better fitting to the observation data, and their objective functions are about 2 times less than those of equilibrium models. Therefore, we conclude that the Pu-Col filtration process in the low-flow rate experiment is still in the kinetic state (but close to equilibrium). Therefore, all subsequent computations in this analysis use ratelimited filtration models for plutonium−colloid transport. In these preliminary simulations, we modeled individual breakthrough curves separately and derived different parameter values (τ and Pe) for the same experiment, based on interpretation of different solutes. τ varies from 5.73 to 7.32 h for the experiment with a flow rate of 2.0 mL/h and from 13.22 to 19 h for the experiment with a flow rate of 0.5 mL/h. The estimated Peclet number Pe varies from 1.0 to 7.17, since we set the lower bound for this parameter as 1.0 (which means the dispersivity is generally less than the model length or column length53). Likewise, the rate constant estimates vary substantially between the low-flow and high-flow experiments. The estimated fractions of Pu sorption onto colloids are 0.08− 0.15. Step 2: Parameter Estimates from Multiple Solute Breakthrough Curves. Extending the individual curve-fitting simulations, breakthrough curves for tritium and Pu-Col from the same experiment (same flow rate) are now fitted simultaneously. The results of the inversions for parameters τ, Pe, Dm, and Pu-Col fraction Fm are presented in Table 2. The comparison of estimated Pu-Col filtration rates for high and low flow rates indicates that the rate constants may be flowrate-dependent. The lower the flow rate, the larger the fluid residence time, corresponding to a smaller rate constant of detachment (kr). By comparing the estimated values of residence time (τ) from two experiments, we find they are not proportional by a factor of 4, since they were estimated separately. Therefore, in the next section, we combine the data from the two experiments to estimate the parameters that should be flow rate invariant.

Pu-Col

1.0 × 10−30 0.004 0.093 23.48 0.15

Step 3: Parameter Estimates from Multiple Experiments. In this step, the breakthrough curves for tritium and Pu-Col for both high and low flow rate experiments are coupled together and simulated simultaneously. In the simultaneous inversion, we constrain τ, ratios between high and low flow rate experiments to be equal to the inverse of the flow rate ratios, and Pe to be the same value for the four data sets. Then, parameters for all four data sets are estimated simultaneously. We assume that the rate constants kr and kf for Pu-Col filtration are flow-rate-dependent and tritium matrix diffusion to be flowrate-invariant in the inversions (Table 3 and Figure 4). Our Table 3. Estimated Parameters and 95% Confidence Intervals by Inverse Modeling of Four Breakthrough Curves Simultaneously (High and Low Flow Rates) parameters

estimated value

confidence interval (95%)

τ (h, high flow) τ (h, low flow) Pe Dm (cm2/s) kr (g/cm3·h, low flow) kf (h−1, low flow) kr (g/cm3·h, high flow) kf (h−1, high flow) Fm

6.56 26.24 2.08 4.78 × 10−6 0.002 0.039 0.004 0.113 0.145

(6.14, 6.75) (24.57, 27.01) (1.95, 2.25) (4.66 × 10−6, 5.85 × 10−6) (0.0015, 0.005) (0.025, 0.073) (0.002, 0.006) (0.090, 0.158) (0.11, 0.18)

estimations of the fractions of the injected plutonium sorbed onto colloids for these specific experimental conditions are 0.13 and 0.16. Since the fractions for high- and low-flow experiments should be very similar, we use the average (0.145) as the final estimated fraction. Thus, the remaining fraction of the total Pu, 0.855, would sorb irreversibly onto matrix minerals. The corresponding Pu-Col retardation factors are 20.5 and 29.25 for the low-flow and high-flow experiments, respectively. These retardation factors are consistent with the published mean values of colloid filtration into fractured tuffaceous rock.36 These values in this study are significantly lower than those estimated by Zavarin et al.,38 who assumed that all injected Pu sorbs irreversibly on (or forms) mobile colloids, which leads to much larger colloid retardation factors because only a fraction of the initial Pu mass in these specific experiments elutes. Although this current study does not seek to address if, how, or how much Pu-Col forms in NNSS groundwater, the implication of the approach described in this paper is that if Pu-Col forms, further migration of small quantities of Pu may be predicted, but at much smaller concentrations, for field-scale models with these parameters than if much higher equilibrium retardation factors are used. To predict if, how much, and how far Pu-Col migrates, the parameters would need to be utilized F

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Figure 4. Fitting four breakthrough curves simultaneously, using the same tracer diffusion coefficients for high-flow (a) and low-flow (b) experiments.

in a field-scale transport model with appropriate scaling,54−57 source terms, groundwater velocities, and rock properties, including fracture properties. A detailed uncertainty analysis of the estimated parameters is included in the Supporting Information.

analyses. Note that the fraction of source Pu forming mobile Pu-Col in this experiment has no bearing on the actual source function near an underground nuclear detonation, where a large portion of the total Pu source is trapped in a solid form known as melt glass.5,34,58

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4. DISCUSSION AND IMPLICATION For the multiple experimental data sets, the stepwise inversion method is implemented to identify the filtration processes and to estimate transport parameters for tritium and plutonium colloids. The stepwise strategy provides optimum solutions for complex inverse problems involving many flow, transport, and reaction parameters that have too many degrees of freedom and may not be identified with a single inverse run. One cannot necessarily foresee what parameter values will result from the joint estimation of flow, transport, and reaction parameters. Therefore, until sufficient insight is gained into the properties of the estimated parameters from individual breakthrough curve fittings, we follow the scientific principle of analyzing complex problems by using models of increasing complexity. This stepwise inversion of radionuclide transport through the fractured tuffaceous rock has provided optimum estimates of transport and sorption parameters: the mean fluid residence time in fractures, Peclet number, matrix diffusion coefficient, retardation factor, attachment and detachment rate constants, and, importantly, estimates of the Pu source fraction that forms Pu-Col. The nonequilibrium transport behavior of Pu-Col and its interactions with immobile fracture surfaces were demonstrated by the stepwise inversion and the chemical reaction criteria. The kinetic model fits the breakthrough curves much better than the equilibrium model, and the objective function values are about 2 times less than those obtained from the equilibrium model. The analysis of the two chemical criteria (the half-time of the reaction and Damköhler number) also confirms that, in these fracture transport experiments, the filtration of Pu-Col onto fracture surfaces is kinetically controlled. Note also that if kinetics was not significant, the optimal forward and reverse rates would have converged to very large values that approximate equilibrium conditions. The transport parameters estimated in this paper are differentiated from those estimates in a previous study of the same data where all source Pu is assumed to form Pu-Col.38 Here, the fraction of source Pu that forms Pu-Col is estimated simultaneously with the transport parameters, leading to (a) less Pu-Col available for transport approximately 14.5% of Pu source for this experimentand (b) kinetic filtration parameters for Pu-Col that compare with lower retardation factors than those estimated in previous

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.est.7b00968. Colloid concentrations in the experimental solution, uncertainty analysis of the inverse models, a table summarizing the colloid particle size distributions and the fractions to Pu concentrations in the groundwater of the Yucca Flat wells, a graph of the evolution of the Gelman and Rubin scale-reduction factors for the selected parameters with the SCEM algorithm, and a figure showing the marginal posterior probability distributions of the selected parameters (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Z.D. e-mail: [email protected], [email protected]; telephone: 505665-6387. ORCID

Zhenxue Dai: 0000-0002-0805-7621 Notes

The authors declare no competing financial interest. The experimental measurements (including the normalized time-series concentrations of tritium and plutonium) are available upon request (e-mail: [email protected], [email protected], and [email protected]).

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ACKNOWLEDGMENTS The reported research was supported by Los Alamos National Laboratory’s Directed Research and Development Project (number 20070441ER). We are extremely grateful to Kay Birdsell, Mei Ding, Irene Farnham, and Joe Johnston for their reviews, corrections, and constructive comments on this paper.

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DOI: 10.1021/acs.est.7b00968 Environ. Sci. Technol. XXXX, XXX, XXX−XXX