Uranium(VI) diffusion in low-permeability subsurface

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adsorption and molecular diffusion processes [2, 3,6]. The adsorption .... spheric CO2 pressure (pCO2 = 10−3.5). The pH in the ..... was 1.1×105,. 7.3×105, 3.0×10−2 M in the reservoir solution at pH 4, 7, .... 2− = UO2(CO3)2. 2−. 16.61. 1.
Radiochim. Acta 98, 719–726 (2010) / DOI 10.1524/ract.2010.1773 © by Oldenbourg Wissenschaftsverlag, München

Uranium(VI) diffusion in low-permeability subsurface materials By C. Liu∗, L. Zhong and J. M. Zachara Pacific Northwest National Laboratory, Richland, WA 99354, USA (Received October 19, 2009; accepted in revised form March 10, 2010)

Uranium / Diffusion / Species-based diffusion / Retardation / Surface complexation Summary. Uranium(VI) diffusion was investigated in a finegrained saprolite sediment that was collected from U.S. Department of Energy (DOE) Oak Ridge site, TN, where uranium contamination in groundwater is a major environmental concern. U(VI) diffusion was studied in a diffusion cell with one cell end in contact with a large, air-equilibrated electrolyte reservoir. The pH, carbonate and U(VI) concentrations in the reservoir solution were varied to investigate the effect of solution chemical composition and uranyl speciation on U(VI) diffusion. The rates of U(VI) diffusion were evaluated by monitoring the U(VI) concentration in the reservoir solution as a function of time; and by measuring the total concentration of U(VI) extracted from the sediment as a function of time and distance in the diffusion cells. The estimated apparent rate of U(VI) diffusion varied significantly with pH, with the slowest rate observed at pH 7 as a result of strong adsorptive retardation. The estimated retardation factor was generally consistent with a surface complexation model. Numerical simulations indicated that a species-based diffusion model that incorporated both aqueous and surface complexation reactions was required to describe U(VI) diffusion in the low permeability material under variable geochemical conditions. Our results implied that low permeability materials will play an important role in storing U(VI) and attenuating U(VI) plume migration at circumneutral pH conditions, and will serve as a long-term source for releasing U(VI) back to the nearby aquifer during and after aquifer decontamination.

1. Introduction Contaminant diffusion into and out of low permeability materials is an important process that attenuates groundwater plume migration and resupplies contaminants into the nearby groundwater during and after aquifer remediation. Understanding uranium(VI) diffusion in low permeability materials is important for assessing the environmental risks in radionuclide waste disposal [1–3], describing radionuclide reactive transport in subsurface sediments [4–7]; and evaluating remediation approaches [8, 9]. Uranium diffusion in low permeability materials is commonly controlled by adsorption and molecular diffusion processes [2, 3, 6]. The adsorption process increases the capacity of low permeability materials for storing contaminants and attenuating plume *Author for correspondence (E-mail: [email protected]).

migration during aquifer contamination. On the other hand, the sorption-retarded diffusion may slow the rate of contaminant removal during aquifer remediation [10]. Uranium(VI) diffusion in low permeability materials is typically described using a sorption-retarded diffusion model [2, 3, 6]. In such models, U(VI) adsorption and diffusion are described with respect to total dissolved U(VI) concentration as a sole diffusing chemical. The effect of U(VI) aqueous speciation reactions and other major chemicals on U(VI) adsorption and diffusion is lumped into linear or nonlinear sorption isotherms and apparent diffusion coefficient. These diffusion models implicitly assume that all uranyl species diffuse with the same diffusion coefficient by ignoring the diffusion coefficient difference between individual species that may lead to ion charge separation [11]. This type of modeling approaches significantly simplify the mathematical complexity in describing the diffusion process of charged species, such as uranyl species, which may have species-specific diffusion coefficients as a result from the effects of species valence, molecular size, and hydration properties [12]. The applicability of such diffusion models is, however, unclear under variable geochemical conditions that may affect U(VI) aqueous and surface speciation. A rigorous species-based uranyl diffusion model has also been established [4] that explicitly considers the variability of uranyl species diffusion coefficients, species mass and charge coupling, and speciation reactions. The applicability of such a species-based diffusion model has not been evaluated against experimental data because of the limited availability of diffusion coefficients for aqueous species and ion pairs. In this study, a series of diffusion experiments were performed to investigate the uranyl diffusion properties in low permeability materials under variable geochemical conditions. A saprolite material that was collected from the US Department of Energy (DOE) Oak Ridge background site was used as an example to investigate U(VI) diffusion in low permeability materials. The long-term matrix diffusion in the saprolite material is a major concern at the Oak Ridge site that may affect the contaminant reactive transport and remediation at the site [5, 8, 13]. Diffusion experiments were performed in diffusion cells with one cell end in contact with a large solution reservoir. Three solutions containing variable pH and carbonate concentrations that affect U(VI) aqueous and surface complexation reactions were used in the solution reservoir to investigate the diffusion rates of U(VI) into or out of the sediment. The experimental results

720

were used to estimate the retarded diffusion rates as a function of geochemical conditions, and to evaluate the apparent and species-based diffusion models in describing U(VI) diffusion in the low permeability material. Uranyl diffusion coefficients that were recently calculated using molecular dynamics were used in the species-based diffusion model.

2. Materials and methods 2.1 Materials The sediment was obtained from the US DOE Office of Biological and Environmental Research ERSP (Environmental Remediation Science Program) Integrative Field Research Challenge (IFRC) site in West Bear Creek Valley on the Oak Ridge Site in eastern Tennessee. The sediment was uncontaminated background one, but a nearby U(VI) plume exists in the same sediment type. The sediment was composited from several distinct strata of a shale saprolite. The shale saprolite is highly structured, forming a fracture and matrix system. Advection in the fracture and diffusion in the matrix has been proposed as a major mechanism controlling solute transport at the site [13, 14]. The subsurface material was air-dried and passed through a 2-mm sieve before use. The mineralogical properties of the sediment have been reported elsewhere [15, 16].

2.2 Sorption-retarded diffusion experiments Diffusion experiments were performed in a diffusion cell system (Fig. 1), which consists of: 1) cylindrical diffusion cells of 7.0 cm long and 2.54 cm in inner diameter and 2) a large volume solution reservoir (5 L). The uncontaminated sediment was wet-packed in lofts into the diffusion cells. Each loft of the sediment was consolidated by tapping the diffusion cell with a rubber hammer. The reservoir solution (0.05 M NaNO3 ) with a desired pH for a specific diffusion experiment was used in wet-packing and saturating the sediment in the diffusion cells. The solution in the reservoir was prepared by bubbling wet-air in 0.05 M NaNO3 electrolyte with a desired pH to equilibrate with air CO2 . Variable amount of aqueous HCO3 was provided into the reservoir solution to expedite the equilibration with atmospheric CO2 partial pressure. The amount of the added HCO3 was calculated from equilibrium speciation calculation at a desired pH in equilibrium with atmospheric CO2 pressure ( pCO2 = 10−3.5 ). The pH in the reservoir solution was fixed at 4.0, 7.0, or 9.5. After bubbling with wet-air for 7 d, the reservoir solution was spiked with U(VI) with a final U(VI) concentration of 3 µmol/L. For the

C. Liu, L. Zhong, and J. M. Zachara

case at pH 7.0, the reservoir solution was spiked with U(VI) again at days 220 and 350 to compensate for the U(VI) loss in the solution as it diffused into and adsorbed in the sediment in the diffusion cells. The pH was monitored continuously with a pH probe that was installed in the solution reservoir (Fig. 1). The solution pH was adjusted with acid or base if it deviated over 0.2 pH unit from a desired pH. The U(VI) concentration in the reservoir solution was monitored by periodic sampling and analyzed using kinetic phosphoric analyzer (KPA). At a select time, one diffusion cell was removed from the solution reservoir, freezed at 4 ◦ C to minimize porewater movements, and sectioned along the column length direction. The length of the sectioned samples ranged from 0.3 to 0.6 cm with a denser sampling toward the interface between the bulk solution and sediment. Total 12 samples were extracted from each diffusion cell. The sectioned sediment samples were weighted into centrifugal tubes for acid extraction (1 M HNO3 ) to determine total U(VI) (aqueous and sorbed) concentration. After 30 h of acid extraction, the tubes were centrifuged and supernatants were measured for U(VI) by the KPA.

2.3 Desorption and diffusion The desorption and diffusion experiment was performed to evaluate the reversibility of sorption-retarded diffusion process and evaluate species-based diffusion model under a transient, but well-controlled condition of chemical composition. The sediment was first loaded with U(VI) in a batch system containing 0.05 M NaNO3 with a solid solution ratio of 100 g/L at pH 7. Before the batch experiment, the sediment was washed with 0.05 M NaNO3 for 3 times to replace ion exchangeable cations with Na in the sediment. This washing process was to minimize the potential effect of ion exchange reactions on uranyl speciation and diffusive mass transfer [17]. The washed sediment was equilibrated with 0.05 M NaNO3 solution at pH 7 containing 30 µmol/L U(VI) for 24 h, which was sufficient long to reach equilibrium U(VI) adsorption [16]. After equilibration, the aqueous solution in the suspension was collected by centrifugation and analyzed to determine U(VI) concentration. The sorbed U(VI) (92 µmol/kg) in the sediment was determined from the difference between the added U(VI) and aqueous U(VI) concentrations at the equilibrium. The U(VI)-loaded sediment was collected by centrifugation and packed into two diffusion cells according to the procedures described in the sorption-retarded diffusion experiments. The diffusion cells were then immersed into a solution reservoir (5 L) of 0.05 M NaNO3 at pH 9.5 to desorb

Fig. 1. Schematic diagram showing the experimental apparatus for measuring U(VI) diffusion in the sediment.

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Uranium(VI) diffusion in low-permeability subsurface materials

U(VI) from the sediment. As described before, the reservoir solution was added with HCO3 and equilibrated with atmospheric CO2 for 7 d by bubbling wet-air before the diffusion cells were inserted into the solution. The pH in the reservoir solution was continuously monitored and adjusted if necessary to maintain pH 9.5 ± 0.2. The reservoir solution was periodically sampled to determine aqueous U(VI) concentration as U(VI) desorbed and diffused out of the sediment. At selected times, the diffusion cells were removed from the solution reservoir, freezed at 4 ◦ C, and sacrificially sectioned, and the sectioned sediment samples were acidextracted as described before to determine total residual U(VI) in the sediment as a function of distance.

2.4 Modeling Two kinds of sorption-retarded diffusion modeling approaches were used in describing the experimental results. One approach treated total dissolved U(VI) concentration as a sole chemical in aqueous phase that was linked with adsorbed phase through sorption isotherm. This is a common approach currently used in describing U(VI) diffusion data [2, 3, 6]. This kind of diffusion models is termed as the apparent diffusion model hereafter because theoretically, the diffusive flux of total U(VI) is the summation of the diffusive fluxes of individual uranyl species. Another approach used here is the species-based diffusion model, which considers the diffusion of individual uranyl species, species mass and charge coupling, and aqueous and surface U(VI) complexation reactions. This model is considered to be more mechanistic than the apparent diffusion model, and is termed as the species-based diffusion model hereafter. 2.4.1 Apparent diffusion model For the diffusion system shown in Fig. 1, the apparent diffusion model may be described by the following mathematical equations:   ∂2C K d ρb ∂C (1) = De 2 1+ θ ∂t ∂x  dCb ∂C  (2) = MθADe  Vb dt ∂x x=0  ∂C  =0 (3) C|x=0 = Cb ; ∂x x=L where C and Cb are the total aqueous U(VI) concentration (µmol/L) in the sediment and in the reservoir solution, respectively, θ is the sediment porosity in the diffusion cell, De is the effective U(VI) diffusion coefficient, K d is the effective partitioning coefficient between aqueous and solid phases in the sediment, A is the cross section area of diffusion cell that is in contact with reservoir solution, Vb is the volume of reservoir solution (5 L), L is the length of the diffusion cell, and M is the number of diffusion cells in the system.

diffusive fluxes of individual uranyl species. Because uranyl speciation is affected by other ions, such as proton and carbonate that form complexes with U(VI), U(VI) species diffusion has to couple with the diffusion of all other related species. The species-based diffusion may be described by the following equations [4]: s ∂ci  ∂ = ∂t ∂x k=1

N

 Dik

 ∂ck + ri ∂x

(4)

where ci is the aqueous concentration of species i in the diffusion cell, ri is the production rate of species i from aqueous and surface reactions, Ns is the number of species in the system including aqueous and surface species, Dik is the species-coupled diffusion coefficient: ⎞ ⎛ ⎜ Z i Z k Di Dk ci ⎟ ⎟ Dik = τ ⎜ ⎠ ⎝ Di δik −  N Z k2 ck Dk

(5)

k=1

where Di and Z i are the self-diffusion coefficient and valence for species i, τ is the tortuosity factor, and δik is the Kronecker symbol. The species-based diffusion equation (Eq. (4)) and diffusion coefficient (Eq. (5)) result from the charge-coupling of diffusing species to maintain local charge neutrality [4]. Note that for the convenience in the following treatment, Eq. (4) includes surface species, which is normalized to aqueous volume and has a zero selfdiffusion coefficient. Solving Eq. (4) for individual species requires the production rates for each species as a result of aqueous and surface speciation reactions. This creates a significant challenge in experimentally determining the rates of species transformation as a function of aqueous species concentrations. Because such speciation reactions are typically fast and consequently treated as equilibrium reactions, a chemical component approach may be more convenient in describing species-based diffusion. The component approach separates chemical species into two sets: i) components and ii) product species that result from the reactions of components. The selection of chemical components from species depends on the mathematical convenience. Once chemical components are selected, their total concentrations can be described by: Tj =

Ns 

aji ci ,

j = 1, 2, . . ., Nc

(6)

i=1

where aji is the stoichiometric coefficient of the j th chemical component in the i th chemical species, and Nc is the total number of chemical components in the system. The reaction rate for the total concentration of component j (Rj ) can be described by: Rj =

Ns 

aji ri ,

j = 1, 2, . . ., Nc .

(7)

i=1

2.4.2 Species-based diffusion model The species-based diffusion model assumes that the diffusive flux of total U(VI) results from the combination of the

In this study, all aqueous and surface complexation reactions were considered to be equilibrium reactions. Consequently, the overall reaction rate (Rj ) for each chemical component

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C. Liu, L. Zhong, and J. M. Zachara

becomes zero. The concentration of the product species (ci ) can be expressed in terms of component concentrations: Nc

ν γj C j ij ci = K i

(8)

j=1

where C j is the free concentration of component j, and K i is the equilibrium constant for species i, γj is the activity coefficient for species j, and vij is the stoichiometric coefficient for the chemical reaction relating species i to chemical component j. Multiplying Eq. (4) by aji and summing over i from 1 to Ns yields the following vector-matrix equation after some algebraic calculations:   ∂ ∂T −1 ∂T = G·F · +R (9) ∂t ∂x ∂x where T is the vector of total concentrations for chemical components, and the elements in matrix G and F have the following expression: gjl =

Ns 

aji

i=1

f jl =

Ns  i=1

Ns  k=1

aji

Dik

∂ck , ∂Cl

∂ci ∂Cl

(10) (11)

The derivative ∂ci /∂Cl in Eqs. (10) and (11) can be evaluated from Eq. (8). The correspondent mass balance equation for the reservoir solution can be expressed as:   ∂Tb −1 ∂T  . (12) = MθAG · F · Vb ∂t ∂x x=0 The boundary conditions for Eq. (9) become:  ∂T  = 0. T|x=0 = Tb ; ∂x x=L

(13)

As described before, the reaction rate vector R in Eq. (9) is zero because only equilibrium reactions were considered in this study. Once Eq. (9) and 12 are solved for total chemical components in diffusion cells and reservoir solution, the free concentration of chemical components, and product species can be computed by equilibrium speciation reactions using mass action equations (Eq. (8)). Equations (9) and (12) were solved with a finite difference scheme through sequential iteration at each time step. Matrix G and F were updated during iteration because their elements dependent on species concentrations. A relative error of 10−6 was specified as a global convergence criterion.

3. Results and discussions 3.1 Sorption-retarded diffusion The rates of U(VI) diffusion in the fine-grained sediment varied significantly with pH and carbonate in equilibration with pH and atmospheric CO2 pressure (Figs. 2 and 3). The U(VI) diffusion was relatively fast at pH 9.5 and 4, but was significantly slow at pH 7. After about 2 years of diffusion in the case of pH 7, U(VI) only migrated less than 0.5 cm

Fig. 2. Measured and calculated diffusion profiles of total U(VI) concentration in the sediment in contact with an air-equilibrated reservoir solution at pH 9.5 (a), pH 4 (b), and pH 7 (c).

into the sediment (Fig. 2). The rate of U(VI) mass loss in the reservoir solution was, however, much faster at pH 7 than at pH 9.5 and 4 (Fig. 3), indicating that U(VI) diffused into the sediment, but was significantly retarded at pH 7 by U(VI) adsorption to the sediment. In the cases of pH 9.5 and 4, the negligible changes of U(VI) concentrations in the reservoir solutions and relatively faster diffusion of U(VI) in the sediment indicated that U(VI) diffusion was less retarded under these conditions. The much lower retardation at pH 9.5 and 4 than at pH 7 was expected in the sediment because U(VI) adsorption was low due to the proton competition at pH 4 for the adsorption sites and the competition from aqueous uranyl carbonate species at pH 9.5 [18]. Equilibrium calculation showed that carbonate concentration in equilibrium with air CO2 pressure was 1.1 × 10−5 , 7.3 × 10−5 , 3.0 × 10−2 M in the reservoir solution at pH 4, 7, and 9.5, respectively. The experimental results were modeled using the apparent diffusion model (Eqs. (1) and (3)) to evaluate the applicability of the modeling approach to describe U(VI) diffusion under variable geochemical conditions. In the cases of pH 9.5 and 4, the model was used to fit the total U(VI) concentrations in the sediment by adjusting the apparent diffusion coefficient and K d value, and the U(VI) concentration in the reservoir solution was calculated by the model. In the

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Uranium(VI) diffusion in low-permeability subsurface materials

6

pH 4 and 9.5

5

Data, pH 9.5 Data, pH 4.0 Model, pH 9.5 Model, pH 4.0

4

log (Kd, L/kg)

U(VI), µmol/L

6

3 2 1

4 2 0

Calculated from sorption model Estimated from diffusion data

-2

0 0

50

3

100 150 200 250 300 350

4

U(VI), µmol/L

Time (days) 16 14 12 10 8 6 4 2 0

Model

U(VI) spike

400

600

800

Time (days)

case of pH 7.0, the measured U(VI) concentration in the solution reservoir was used to fit the diffusion model because the U(VI) was below detection in the most locations in the sediment. Because the measured data were total U(VI) concentration, the aqueous U(VI) concentration calculated by the model (Eqs. (1) and (3)) was converted to the total U(VI) concentration by the following equation: Ctot = (θ + ρb K d )Caq

(14)

where Caq and Ctot are the aqueous and total U(VI) concentrations, respectively. Try-and-error approach was used in this study to determine the model parameters by visually

Table 1. Apparent diffusion coefficient and K d values for total dissolved U(VI). Sorption/diffusion 4.0 218 5.8 8.6 × 10−8

7.0 376 4.0 4.1 × 10−7

2.5 × 104 2.5 × 10−7

9.5 67 0.45 5.8 × 10−8

430 0.24 8.2 × 10−7

Desorption/diffusion pH Sampling time (day) a K d (L/kg) De (cm2 /s)

8

9

10

examining the match between the calculated and measured data. Model fitting and simulation showed that the fitted diffusion coefficient and K d value varied with experimental condition (Table 1). The fitted K d , as expected, changed significantly with pH, with a highest K d value at pH 7. The estimated K d values were generally consistent with those calculated from a surface complexation model that was quantified previously for the same sediment (Fig. 4) [16]. The surface complexation model, which involves both aqueous speciation and surface complexation reactions, was provided in Table 2. In the pH 4 and 9.5 cases, the slight higher K d values estimated from the earlier diffusion profiles in the sediment were attributed to the pH buffering by the sediment. The pH in the sediment and its surrounding groundwater was near neutral to mildly acidic at the field site [19]. Although the sediment was wet-packed using the same solution in the reservoir, the initial pH in the diffusion cell may have been buffered by reactions such as ion exchange and surface protonation/deprotonation in the sediment. The pH increase or decrease toward the neutral pH region would increase the U(VI) adsorption (Fig. 4). With increasing time, however, the pH and chemical composition (e.g., carbonate) in the diffusion cell would approach to those in the solution reservoir. Consequently, the fitted K d value decreased with time. The fitted effective diffusion coefficients in the cases of pH 4 and 9.5 were also smaller from the earlier diffusion

Fig. 3. Measured and calculated total U(VI) concentration as a function of time in the reservoir solution corresponding to the diffusion profiles in Fig. 2.

pH Sampling time (day) a K d (L/kg) De (cm2 /s)

7

Fig. 4. Calculated and estimated K d values for U(VI) adsorption to the sediment in the diffusion cells. The aqueous and surface reactions in Table 2 were used in calculating K d values.

Data

200

6

pH

pH 7.0

0

5

9.5 28 0.2 5.7 × 10−7

240 0.4 9.1 × 10−7

a: The sampling time denotes the time when diffusion cell was removed from the reservoir solution.

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Table 2. U(VI) speciation reactions used in modeling. Reaction

log K (I = 0)

Source

−5.25 −12.15 −20.25 −32.40 −2.70 −5.62 −11.90 −15.55 −32.20 −21.90 9.94 16.61 21.84 −0.86 −1.72 −5.67 −17.88 −21.11

1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2

UO2 2+ + H2 O = UO2 + H+ UO2 2+ + 2H2 O = UO2 (OH)2 (aq) + 2H+ UO2 2+ + 3H2 O = UO2 (OH)3 − + 3H+ UO2 2+ + 4H2 O = UO2 (OH)4 2− + 4H+ 2UO2 2+ + H2 O = (UO2 )2 OH3+ + H+ 2UO2 2+ + 2H2 O = (UO2 )2 (OH)2 2+ + 2H+ 3UO2 2+ + 4H2 O = (UO2 )3 (OH)4 2+ + 4H+ 3UO2 2+ + 5H2 O = (UO2 )3 (OH)5 + + 5H+ 3UO2 2+ + 7H2 O = (UO2 )3 (OH)7 − + 7H+ 4UO2 2+ + 7H2 O = (UO2 )4 (OH)7 + + 7H+ UO2 2+ + CO3 2− = UO2 CO3 (aq) UO2 2+ + 2CO3 2− = UO2 (CO3 )2 2− UO2 2+ + 3CO3 2− = UO2 (CO3 )3 4− 2UO2 2+ + CO3 2− + 3H2 O = (UO2 )2 CO3 (OH)3 − + 3H+ 2>S1OH + UO2 2+ = (>S1O)2 UO2 + 2H+ 2>S2OH + UO2 2+ = (>S2O)2 UO2 + 2H+ 2>S1OH + UO2 2+ + H2 CO3 = (>S1O)2 UO2 CO3 2− + 4H+ 2>S2OH + UO2 2+ + H2 CO3 = (>S2O)2 UO2 CO3 2− + 4H+

1. Ref. [20], 2. Ref. [16]. Two site model was used in describing U(VI) surface complexation reaction [16]. >S1OH and >S2OH denote site one and two with their site concentrations of 1.45 × 10−6 and 1.23 × 10−4 mol/g, respectively.

profiles. This was attributed to the apparent nature of the diffusion model, which only considered total U(VI) diffusion and ignored diffusion of protons, hydroxyl, carbonate, and other species. For example, during the diffusion of proton, hydroxyl, or carbonate, the K d value would continuously decreases. However, such temporal K d change may have been lumped into the effective diffusion coefficient. Other factors such as the interaction between solution chemistry (e.g., proton) and the sediment that may affect sediment properties such as porosity, constrictivity, and tortuosity may have also affected the effective diffusion coefficient.

3.2 U(VI) desorption and diffusion The experimental and modeling results of the sorptionretarded U(VI) diffusion indicated that the parameters in the apparent diffusion model varied with geochemical conditions, indicating that the apparent diffusion model with a fixed set of diffusion parameters was not able to describe U(VI) diffusion under transient geochemical conditions. The species-based diffusion model was not tried, however, because the geochemical processes controlling the initial chemical condition in the sediment, such as initial pH and exchangeable cations, were not well understood. The role of the initial chemical conditions have recently been demonstrated in controlling U(VI) aqueous speciation and U(VI) diffusive mass transfer [17]. To further evaluate the applicability of the diffusion models, the U(VI) desorption and diffusion experiment was performed under well controlled, but transient geochemical condition. The sediment was first washed and loaded with U(VI) in 0.05 M NaNO3 solution at pH 7 to minimize the ion exchange or other reactions that may affect U(VI) aqueous and surface complexation reactions during U(VI) diffusion. The equilibrated sediment was then subject to U(VI) desorption and diffusion to the reservoir solution at pH 9.5 ± 0.2. The known initial

and boundary geochemical conditions for the diffusion cell allowed evaluating both the apparent and species-based diffusion models. The apparent diffusion model was first applied to fit the desorption and diffusion data in Fig. 5. The fitted parameters were different for the diffusion profiles measured at different times (Table 1) for the similar reasons as described for the sorption-diffusion cases, further indicating that the apparent diffusion model with a fixed set of diffusion parameters was not able to describe U(VI) diffusion under transient geochemical conditions. The species-based diffusion model (Eq. (4) or (9)) was also applied to describe the desorption and diffusion data in Fig. 5. The model requires using self-diffusion coefficients for all species in the diffusion system. Obtaining such diffusion coefficients is a significant challenge for the application of such diffusion models because often the self-diffusion coefficients for some or most important species are not available in literature or difficult to independently measure. For the uranyl diffusion problem described here, some important uranyl species diffusion coefficients have recently been calculated using molecular dynamics simulation [12]. The diffusion coefficients for all the species used in this study were provided in Table 3. Among all the species involved in the U(VI) diffusion model (Table 3), seven species UO2 2+ , CO3 2− , Na+ , NO3 − , H+ , >S1OH, and >S2OH were selected as the chemical components and the rest species as the product species that can be calculated from the mass action equations (Eq. (8)) for the species reactions in Table 2. The Davies equation was used in calculating the activity coefficients in Eq. (8). The tortuosity factor (τ) (Eq. (5)) was the only parameter to be determined for the species-based model. In the modeling, the measured U(VI) concentration in the reservoir solution was used to determine the tortuosity factor (τ = 0.2). The total U(VI) concentration profiles in the diffusion cells were used to validate the model.

725

Reservoir U(VI), µmol/L

Uranium(VI) diffusion in low-permeability subsurface materials

1.2

U(VI) in bulk solution Data Model,

1.0 0.8 0.6 0.4 0.2 0.0 0 2.5

50

100

150

200

250

Time (days) U(VI) in soil data, 28 days data, 240 days Model, 28 days Model, 70 days Model, 240 days

2.0

Utot/U0 (%)

Table 3. Diffusion coefficient (D) and valence (Z) of modeled species.

1.5 1.0 0.5 0.0 0

1

2

3

4

5

6

7

Distance from interface (cm) Fig. 5. (a) Measured and calculated U(VI) concentration as a function of time in the reservoir solution during U(VI) desorption and diffusion out of the sediment; and (b) Measured and calculated diffusion profiles of total U(VI) concentration in the sediment during U(VI) desorption and diffusion out of the sediment. The measured total U(VI) concentration in the sediment was normalized to the initial total U(VI) concentration.

The species-based diffusion model provided a well description for the U(VI) concentration in the reservoir solution as a function of time, and in the diffusion cells as a function of time and distance (Fig. 5) with the same set of diffusion coefficients and equilibrium constants for U(VI) aqueous and surface complexation reactions. The simulation showed the transient changes of dissolved U(VI), total dissolved carbonate, and pH as a function of space and time in the sediment (Fig. 6). Both experimental and modeling results showed an interesting peak of total U(VI) concentration that was higher than the initial value in the diffusion profiles at earlier times in the sediment (Fig. 5). This peak resulted from the coupled effect of carbonate, proton, and U(VI) diffusion. Initially, U(VI) was dominantly in adsorbed phase in equilibrium with initial solution conditions (pH 7) in the sediment. The diffusion of carbonate and hydroxyl from the high pH and carbonate reservoir solution into the sediment led to the local desorption of U(VI) from the sediment and generated dissolved U(VI) concentration profiles (Fig. 6a) that had a concentration gradient toward both exterior and interior in the diffusion cell at earlier times. The diffusion of dissolved U(VI) toward interior as driven by its concentration gradient led to the increase of the total U(VI) concentration that was above the initial value in the interior region near the peak of the dissolved U(VI) concentration

Species

D (cm2 /s)

Z

Source

H+ OH− UO2 2+ Na+ NO3 − HCO3 − CO3 2− H2 CO3 (aq) UO2 CO3 (aq) UO2 (CO3 )2 2− UO2 (CO3 )3 4− UO2 (OH)2 (aq) UO2 (OH)3 − UO2 (OH)4 2− (UO2 )2 OH3+ (UO2 )2 (OH)2 2+ (UO2 )3 (OH)4 2+ (UO2 )3 (OH)5 + (UO2 )3 (OH)7 − (UO2 )4 (OH)7 + (UO2 )2 CO3 (OH)3 − >S1OH >S2OH (>S1O)2 UO2 (>S2O)2 UO2 (>S1O)2 UO2 CO3 2− (>S2O)2 UO2 CO3 2−

9.31 × 10−5 5.27 × 10−5 4.26 × 10−6 1.33 × 10−5 1.90 × 10−5 1.19 × 10−5 9.23 × 10−6 1.19 × 10−5 4.9 × 10−6 3.9 × 10−6 2.9 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 4.26 × 10−6 2.7 × 10−6 0.0 0.0 0.0 0.0 0.0 0.0

1 −1 2 1 −1 −1 −2 0 0 −2 −4 0 −1 −2 3 2 2 1 −1 1 −1 0 0 0 0 −2 −2

1 1 1 1 1 1 1 1 2 2 2 3 3 3 3 3 3 3 3 3 2 4 4 4 4 4 4

1. Ref. [21]; 2. Ref. [12]; 3. Assume to be the same as for UO2 2+ ; and 4. Ref. [16].

profile. Such coupled behavior of U(VI) diffusion with other chemicals, which cannot be simulated by the apparent diffusion model, has a strong implication in slowing the rate of U(VI) release from the low permeability sediment.

3.3 Implication This study showed that the apparent rate of U(VI) diffusion significantly varied with pH and carbonate concentration. The slow, but strong sorptive diffusion of U(VI) at the neutral pH condition implied that given a long contact time, the low permeability materials can play an important role for storing U(VI). The storage capacity and time scale for sorption saturation will, however, depend on pore water chemical composition in the low permeability materials and in the flowing groundwater in contact with the materials. Once contaminated, the low permeability materials can release U(VI) back into the groundwater as a long-term source for U(VI) contamination. The rate of U(VI) release will also depend on geochemical condition. It will therefore require careful evaluation of sorption-retarded diffusion as a function of geochemical conditions in order to accurately assess the effects of low permeability materials in both storing U(VI) and as a long-term contaminant source. This study showed that a species-based modeling approach is required to describe U(VI) diffusion under variable geochemical conditions. Only under conditions when variation of local geochemical condition is negligible, the apparent diffusion model may be used. Even under the constant geochemical condition, the estimated diffusion parameters from the apparent diffusion model would still be conditioned

726

Fig. 6. Calculated dissolved U(VI) (a), dissolved inorganic carbon (b), and pH (c) in the diffusion cell. The corresponding calculated total U(VI) concentrations in the diffusion cell and in reservoir solution were provided in Fig. 5.

on specific experimental conditions that dictate uranyl aqueous and surface complexation reactions. The application of such apparent diffusion coefficient and diffusion model to other geochemical condition will therefore require careful consideration on the effect of geochemical conditions on the effective U(VI) diffusion coefficient. Acknowledgment. This research was supported by US Department of Energy (DOE), Biological and Environmental Research (BER) Division through Subsurface Biogeochemical Research Program (SBR) Science Focus Area (SFA) Research Program at Pacific Northwest National laboratory (PNNL). A portion of the research was performed at Environmental Molecular Science Laboratory (EMSL), a national scientific user facility sponsored by DOE-BER and located at PNNL. PNNL is operated for DOE by Battelle under contract DE-AC0676RLO 1830.

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