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Sep 15, 2009 - Department of Energy Hanford site, WA. “Inward-flux” diffusion studies were conducted in which [U(VI)] in both aqueous and solid ph...
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Environ. Sci. Technol. 2009, 43, 7706–7711

Study of Sorption-Retarded U(VI) Diffusion in Hanford Silt/Clay Material J I N G B A I , * ,† C H O N G X U A N L I U , ‡ A N D WILLIAM P. BALL† Department of Geography and Environmental Engineering, Johns Hopkins University, 3400 N. Charles Street, Baltimore, Maryland 21218, and Environmental Dynamics and Simulations, Pacific Northwest National Laboratory, Richland, Washington 99352

Received May 1, 2009. Revised manuscript received August 5, 2009. Accepted August 25, 2009.

A diffusion cell method was applied to measure the effective pore diffusion coefficient (Dp) for U(VI) under strictly controlled chemical conditions in a silt/clay sediment from the U.S. Department of Energy Hanford site, WA. “Inward-flux” diffusion studies were conducted in which [U(VI)] in both aqueous and solid phases was measured as a function of distance in the diffusion cell under conditions of constant concentration at the cell boundaries. A sequential extraction method was developed to measure sorbed contaminant U(VI) in the solid phase containing extractable background U(VI). The effect of sorption kinetics on U(VI) interparticle diffusion was evaluated by comparing sorption-retarded diffusion models with sorption described either as equilibrium or intraparticle diffusion-limited processes. Both experimental and modeling results indicated that (1) a single pore diffusion coefficient can simulate the diffusion of total aqueous U(VI), and (2) the local equilibrium assumption (LEA) is appropriate for modeling sorption-retarded diffusion under the given experimental conditions. Dp of 1.6-1.7 × 10-6 cm2/s was estimated in aqueous solution at pH 8.0 and saturated with respect to calcite, as relevant to some subsurface regions of the Hanford site.

Introduction Migration of hexavalent uranium (U(VI)) in subsurface sediments is a concern at sites of uranium contamination or storage. While short-term and large-scale U(VI) migration can be dominated by advection along preferential flow pathways, smaller scale and/or longer-term transport in the subsurface is often affected by diffusion in slow advection or water-stagnant zones. Diffusion can dominate transport in intragranular regions of sediments and regions of low permeability, such as rock matrices or strata of fine-grained sediment. For example, the importance of intragranular U(VI) diffusion in sediments from the DOE site at Hanford, WA, has been demonstrated in the context of U(VI) mineral precipitates, which can slowly dissolve and subsequently diffuse to mobile groundwater (1-3). The importance of interparticle diffusion has also been recognized in the context of radionuclide waste disposal at Yucca Mountain, NV, and elsewhere (4-6). * Corresponding author phone: (443)858-6618; fax: (410)516-8996; e-mail: [email protected]. † Johns Hopkins University. ‡ Pacific Northwest National Laboratory. 7706

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Diffusion in porous media is commonly measured using diffusion cells (7-9). Most U(VI) diffusion studies apply a through-diffusion type of cell (5, 6, 10), in which U(VI) diffuses from a source solution chamber, through the sediment, and into a collecting solution. A disadvantage of this approach, however, is the difficulty in controlling both boundary conditions (8). Diffusion-cell experiments can also be designed to measure transient “inward-flux” diffusion, where U(VI) diffuses from a source chamber to the sediment from one or both ends of the cell, and transient concentration profiles are measured. For example, Tokunaga et al. (11) applied an in-diffusion cell to measure the profiles of total U(VI) in sediment using an X-ray microprobe and micro XANES. Unfortunately, however, this approach requires expensive and specialized instruments that are not commonly available, such that simpler methods are needed. For any diffusion experiment, it is useful to define an effective pore diffusion coefficient as Dp ) D0δ/τF (12), where τF is the tortuosity factor and D0 is the molecular diffusivity of the diffusing species. δ is the constrictivity. δ accounts for steric hindrance and can be approximated as unity when the size of the diffusing molecule/ion is small compared with the pore size (13). When considering the diffusion of “total dissolved U(VI),” the measured D0 is conditioned on the distribution of U(VI) species and is therefore dependent on the chemical conditions of solution, such as pH and carbonate content (14-16). In this regard, a few U(VI) diffusion studies have been conducted under strictly controlled and consistent chemical conditions (5, 6), whereas others have not (10, 11, 17). Because D0 values obtained from these past studies are variable and dependent on the specific experimental conditions of the work, their applicability to other experimental conditions is still unclear. U(VI) transport is strongly affected by sorption/desorption to/from the solid phase due to surface complexation or ion exchange mechanisms of sorption (18-21). In modeling U(VI) transport through porous media, it is common to assume that sorbed U(VI) is at equilibrium with aqueous U(VI) (11, 22), and that the equilibrium can be independently described through batch sorption experiments. Sorption and (especially) desorption of U(VI) with sediment materials from many sites including Hanford, however, have been found to be rate-limited by processes such as intraparticle diffusion or possibly the kinetics of surface complexation and desorption (23-25). If the time to attain equilibrium at the particle scale is comparable with or longer than the time scale of U(VI) migration in pore water, then the local equilibrium assumption (LEA) cannot be applied. The validity of the LEA remains to be tested in the specific context of U(VI) diffusion (1, 26, 27). In this study, a short-term, inwardflux diffusion cell method was applied for studying U(VI) diffusion in a silt/clay composite taken from the U.S. Department of Energy (USDOE) Hanford site (16, 28), under well-controlled and well-defined chemical conditions. U(VI) profiles in the pore water and the solid phase were obtained by an extraction method designed in this work. Numerical models were used to interpret results, evaluate the LEA and estimate Dp for U(VI) in the sediment.

Materials and Methods Subsurface Solids, Stock Solutions, and Aqueous U(VI) Measurement. The Hanford Silt Composite (HSC) was a composite of sand-, silt-, and clay-sized materials collected from a background borehole (RCRA borehole no. 299-W2248 (28),) beneath the DOE Hanford site at selected depth intervals between 42 and 44 m below ground surface. The 10.1021/es901306c CCC: $40.75

 2009 American Chemical Society

Published on Web 09/15/2009

silt/clay-sized portion (900 ng/g. (See Supporting Information (SI).) While most of this background U(VI) exists in mineral phases that are not readily dissolved in aqueous solution, a portion exists in sorbed or other readily dissolvable forms that can participate in sorption/desorption equilibrium (29). This amount is hereafter referred to as “labile” background U(VI). The labile background U(VI) was estimated to be 100 h). Sample (0.1 mL) of the batch mixture was taken at 1, 3, 6, 9, 22, 29, 46, 70, 122, 188, 257, 409, 669 h, centrifuged at 10 000rcf at T ) 22.5 °C for 20 min (Centrifuge 5417R, Eppendorf), and the supernatant was analyzed for [U(VI)] by KPA-11. Desorption kinetic study was conducted by replacing centrifuged sorption-sample supernatant at 884 h with 50 mL U(VI)-free stock solution, and was analyzed for solution [U(VI)] similarly at 1.5, 4.0, 10, 26, 73, 97, 176, 279, 514, and 984 h. [U(VI)] was found stable for sufficient time at 984 h of desorption. U(VI) sorption isotherm was determined in 5 mL suspension containing 0.5 g solid and U(VI) concentration ranging from 1.0 × 10-7 to 1.0 × 10-5 mol/L (n ) 4). After 15 days of equilibration that was enough to reach sorption equilibrium based on kinetic results, the suspension was centrifuged and the supernatant measured for [U(VI)]. U(VI)-free stock solution was then added to the solids for the desorption of sorbed U(VI). The solution was analyzed for [U(VI)] after 21 days of desorption, when [U(VI)] was stable based on kinetic desorption results.

Sequential Extraction. To independently determine the amount of U(VI) sorbed to the HSC S-C solids in the diffusion cell, an extraction method was developed that would measure only the labile U(VI), that is, the fraction that can participate in sorption and desorption. (See SI for discussion of differences between labile and nonlabile background U(VI).) The method used takes advantage of the fact that U(VI) sorbs less at higher pH, with very low sorption at pH ∼ 10.0 (16). A 3-day batch sorption experiment with initial U(VI) concentrations of 1.0 × 10-7 to 2.5 × 10-5 mol/L (n ) 3) was first performed. These samples were centrifuged and then subjected to a sequential extraction using Na2CO3-NaHCO3 buffered solutions of increasing pH as follows: pH 8.0 extraction; pH 9.45 extraction (two times); pH 9.85 extractions. Each extraction lasted 6 days, which was a time empirically determined to be sufficient for these 3-day samples; however, (and as further discussed subsequently), 2-4 weeks of extraction have been found necessary when sorption times exceed 30 days. Nonetheless our kinetic uptake experiments revealed that 85% of total U(VI) uptake was achieved within 3 days and equilibrium reached within 15 days (SI). For these reasons, we believe that the 6 days of extraction gave good estimates of sorbed phase concentration in these 3-day batch systems. All extraction solutions were saturated with respect to calcite and atmospheric CO2 prior to use. The pH 9.45 and 9.85 solutions had I ) 0.045 and 0.1 M, respectively, with no additional electrolytes added. Control experiments (n ) 3) were performed without added U(VI) to measure background U(VI) that was extracted in each step. Diffusion Cell Experiments. The sediment was divided into 16 portions using a 16-way spinning riffler (Gilson Company, Inc.) and these portions were packed in lofts into the Cell Chamber (SI Figure S1), which was an acrylic cylinder 4.0 cm long and 2.54 cm in inner diameter. Each portion was pressed into the chamber using a flat-ended acrylic rod of slightly smaller diameter than the cell. After pressing, each loft was consolidated by tapping the rod with a rubber hammer. All lofts were consolidated in identical manner in order to maximize homogeneity and reproducibility. Saturation and Pre-Equilibration of Sediment Materials. After packing, the sediment in the diffusion cell was prewashed with the U(VI)-free pH 8.0 ((0.1) stock solution in a manner intended to simulate the pre-equilibrations of batch samples. The cell chamber was connected to two dispersion chambers at each end, separated by 0.4 µm membrane filters and stainless steel screen supports. The dispersion chambers were filled with 1 mm-diameter nonreactive borosilicate glass beads to uniformly distribute and collect flow from 1/8 in. tubing at the inlet and outlet (SI Figure S1). Before the first pre-equilibration wash, pure CO2 gas was flushed into the cell to replace air. U(VI)-free stock solution was then pumped through the column to dissolve the CO2 and fully saturate the pore spaces. The solution used to remove CO2 was discarded before the pre-equilibration washes, during which fresh U(VI)-free stock solution was recirculated through the cell column until pH stabilized. Similar to the batch systems, four such pre-equilibrations were applied, using a mass ratio of pre-equilibration solution: cell solids of ∼100 g/L. Pore volumes of fluid circulated through the cell during the four pre-equilibrations were 275, 155, 199, and 354. After preequilibration, the water-saturated cell chamber was disconnected from the flow-distribution chambers and weighed for estimation of porosity ( ) 0.45) and bulk density (mass of solids per volume of cell, Fb ) 1.48 g/cm3). Diffusion Phase. For the diffusion phase, each Dispersion Chamber was replaced by an end-cap with a 2.54 cm-diameter hole in the center to allow the full internal diameter of the cell to be in close proximity with external solution (separated only by the membrane). The Cell Chamber was then horizontally submerged in a polypropylene tank filled with 4.5 L of 2.43 µM VOL. 43, NO. 20, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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U(VI) stock solution, such that U(VI) could diffuse into the sediment from both ends. Tank volume was sufficiently large that the external U(VI) concentration change was less than 3% over the course of the experiment. The tank solution was gently stirred with a magnetic stir bar. Schematic illustration of the diffusion phase is shown by SI Figure S2. Cell Sectioning and Extraction of U(VI). After 918.5 h (38.3 days), the diffusion phase was terminated and the cell sediment extruded, using the same acrylic rod previously used for packing. As the HSC S-C exited the cell, it was sectioned into fourteen 2-3 mm-thick slices. Each slice was measured for thickness at three or four locations around the perimeter for an averaged thickness. Each slice was divided into three parts. One part (∼1 g) was centrifuged at 25 000 rcf (T ) 22.5 °C) for 10 min (centrifuge 5417R, Eppendorf), after which a small quantity (∼10 µL) of pore water was removed, diluted 100 times and analyzed for [U(VI)]. The effective detection limit of pore water [U(VI)] was therefore 100 × 0.1 µg/L(KPA detection limit) ) 10 µg/L. The other two parts were placed into 5 mL centrifuge vials, each weighed and used as duplicate samples for solid-phase extraction. The same extraction approach was used as for batch sorption samples, except that the extraction time for each extraction step was increased from 6 days (batch system) to 2-4 weeks, by which time [U(VI)] in the extraction solution had stabilized. This was out of consideration of the fact that U(VI) in diffusion cells had equilibrated with solids for longer time than the in the batch systems. The total U(VI) extracted from solids and pore water was measured, and the separately measured pore water U(VI) was subtracted to calculate the solid phase [U(VI)]. Control Experiments. Control experiments (n ) 3) for the diffusion cell were performed in batch systems to quantify the background U(VI) removed during sequential extraction. Four pre-equilibration washes were conducted at the same overall SSR (∼100 g/L). These control samples were then equilibrated with U(VI)-free stock solution for the same duration as the diffusion-cell experiment (918.5 h). They were then extracted using the same sequential extraction procedure. Modeling of U(VI) Batch Kinetics. Rates of U(VI) sorption-desorption are often assumed to be limited by intraparticle diffusion of U(VI) species to sorption sites in intragranular regions of solid particles and solid surface coatings (24, 27, 30, 31). Modeling efforts for U(VI) or other radioactive contaminants have been attempted, including assumptions of Fickian-diffusion in intraparticle regions or rock matrix fractures (1, 26). Recently, empirical models have been employed that incorporate multiple kinetic rates to address the concepts of microscopic heterogeneity in mineralogy, geometry, chemistry, and morphology of the intraparticle/intra-aggregate zones in the porous media (24, 27, 30). Such approaches have had success in simulating of U(VI) transport in advective columns (24, 30) or in continuous stirred-tank reactors (27). In this study, a multirate, firstorder sorption kinetics model was applied that assumed the first-order rate coefficient, kLA (L/kg-hr) to follow a log-normal distribution, whereas sorption equilibrium parameters were assumed uniform. This multirate model was used to approximate diffusive processes on mineral surfaces and within intragranular regions

( )

ms dCb )dt VL

N

∑fk

batch i)1

i LA,i(Cb

- Cp,i)

(1)

fi and kLA,i are the mass fraction and rate coefficient at site i, respectively. The distribution is evenly discretized into N ()100 in numerical code) intervals (i.e., fi ) 1/N) corresponding to N site types so that kLA,i is the averaged value in the ith interval of a discretized (natural) log-normal distribution with a log-normal mean µ (log(L/kg-hr)) and a 7708

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log-normal standard deviation σ (log(L/kg-hr)); Cb is [U(VI)] in batch solution (µg/L), Cp,i (µg/L) is [U(VI)] in the intraparticle pore solution for site of type i. The quantity (ms/ VL)batch is the solid:liquid ratio in the batch kinetics systems (∼100 g/L). The right-hand side term represents the total mass transfer from the batch bulk solution to the solid particles. Ignoring the very small U(VI) mass associated with intraparticle pore water at site i, we have dSi ) kLA,i(Cb - Cp,i) dt

(2)

Si is the [U(VI)] in the solid phase associated with site i (µg/ kg). We assumed that sorption equilibrium was maintained at sorption sites, and Si and Cp,i could be related by a single Freundlich sorption isotherm at all sites: n Si ) KFCp,i

(3)

KF ((µg/kg)/(µg/L)n) is the Freundlich capacity parameter; and n [-] is the Freundlich heterogeneity parameter. The model was numerically solved using a backward-in-time finite difference method. The kinetic rate distribution parameters were fitted by minimizing the sum of squared percentage errors (SSPE) between model calculations and experimental results. Modeling of U(VI) Diffusion. In modeling U(VI) concentrations within the cell sediment, we assumed that transport occurred only by aqueous phase diffusion in the interparticle pores, but with simultaneous accumulation of sorbed-phase U(VI) through sorption to HSC S-C solids. Using a single Dp for total interparticle U(VI) diffusion, this leads to the following equation (7): εm

∂C ∂S ∂2C + Fb ) εmDp 2 ∂t ∂t ∂x

(4)

C is the [U(VI)] in pore water (µg/L), S is [U(VI)] in the solid phase (µg/kg), m is the intergranular (mobile water) porosity, Fb is the previously defined bulk density (kg/L or g/cm3), and Dp is the effective pore diffusion coefficient (cm2/h). t is the diffusion time (hr) and x is the distance into the cell from the membrane surface (cm). Two modeling approaches were used to describe sorption (S) in eq 4: one based on the LEA and the other based on sorption kinetics as defined by eqs 2 and 3, using the same batch sorption Freundlich isotherm. For the LEA-based model, we assumed that U(VI) sorption within the cell was at local equilibrium and governed by the isotherm, using KF and n values previously determined from the batch sorption experiments. Thus:

(

1+

)

Fb ∂C ∂2C nKFC n-1 ) Dp 2 εm ∂t ∂x

(5)

For the kinetics-based model, eq 4 was rewritten as Fb ∂C ∂2C ) Dp 2 ∂t ε ∂x m

N

∑fk

i LA,i(C

- Cp,i)

(6)

i)1

Equation 6, coupled with eqs 2 and 3 formed the sorption kinetics-based diffusion model, with Si (in eq 2) and Cp,i related by the batch sorption isotherm for each site i, and one single distribution of kLA assumed for all locations within the diffusion cell. Both models were solved numerically using a backwardin-time centered-in-space finite difference method that incorporated the known constant-concentration boundary conditions, Cx)0 ) Cx)L ) C0, with L being the length of the cell chamber, and the known initial conditions with a background

FIGURE 1. U(VI) sorption-desorption kinetics results on HSC S-C. Experiments were conducted at solid:solution ratio ) 95 g/L, I ) 0.02 M (NaNO3), pH ) 8.0 ( 0.1, PCO2 ) 10-3.5atm, 22.5 °C. Initial [U(VI)] at the onset of sorption was 0.25 (squares), 0.92 (triangles), and 2.38 (circles) µmol/L. Solid line: kinetic model fit to data for (a) sorption (b) desorption kinetics. The log means and standard deviations of the log-normal distributions of rate parameters were µ ) 0.7, σ ) 2.3 for sorption and µ ) -2.7, σ ) 6.3 for desorption. Duplicate samples were used in reaction. Error bars show the range of the duplicate results.

FIGURE 2. U(VI) 15-day batch sorption (triangles) and 21-day batch desorption (circles) isotherm data on HSC S-C. Experiments were conducted at solid:solution ratio (SSR) ) 94-100 g/L, I ) 0.02 M (NaNO3), pH 8.0 ( 0.1, PCO2 ) 10-3.5atm, 22.5 °C. Initial [U(VI)] varied between 0.1 and 10.0 × 10-6 mol/L. Results with SSR values of approximately 95 g/L, 185 g/L and 363 g/L are also plotted (squares) for comparison. Exact SSR of each sample was gravimetrically determined. Straight line: Freundlich isotherm fit to sorption data; Dashed line: Freundlich isotherm fit to desorption data.

pore water [U(VI)] C092%, as previously discussed (32)). Such incomplete extraction could contribute to the observations of lower Ceq than C (and higher Seq than S). Overall, these results showed a good consistency of C with Ceq (and S with Seq), indicating that aqueous and solid phase U(VI) were reasonably close to the local sorption equilibrium expected on the basis of batch sorption data.

Results and Discussion Batch Sorption/Desorption Kinetics. The kinetic experiments revealed a fast initial rate followed by a much slower process toward equilibrium for both U(VI) sorption and desorption (Figure 1). For sorption, [U(VI)] appeared to reach a stable level after ∼400 h (∼16.7 days). Taking the final (884 h) [U(VI)] as the sorption equilibrium concentration (Ce) and using the initial [U(VI)] (C0), the fractional approach to equilibrium was defined as feq,ads ) (C-C0)/(Ce-C0). Calculations found feq, ads >85% within 72 h, feq, ads >95% within 260 h, and feq, ads ≈ 1 within 400 h. The values of feq,ads as a function of time were found to be consistent for all three initial [U(VI)], suggesting no discernible dependence of sorption kinetics on [U(VI)]. Desorption approached equilibrium more slowly than sorption, with [U(VI)] stabilizing after ∼510 h (∼21 days). Using the desorption final (984 h) [U(VI)] for Ce and calculating feq,des in similar manner as for sorption, we found feq,des >85% within 144 h, again showing no significant dependence on [U(VI)]. The calculated values of feq are listed in SI Table S2. The kinetic data of U(VI) sorption and desorption can be well described by the multirate, first-order kinetic model. The average modeling error was 4.7% for sorption and 3.2% for desorption in simultaneously fitting the three curves with different initial U(VI) concentrations in Figure 1. The best-fit log-normal distribution parameters for kLA are µ ) 0.7, σ ) 2.3 for sorption, and µ ) -2.7, σ ) 6.3 for desorption. Reasons for lower rate parameters of desorption are not known, but there are several possible causes. In particular, the applicability of the multirate model to diffusion under conditions of nonlinear sorption have not yet been proven, and it is also possible that mechanisms other than diffusion are at play, possibly including chemical kinetics that are slower during desorption. Batch Sorption/Desorption Isotherm. Figure 2 shows the sediment-solution distributions of U(VI) at 22.5 °C (isotherms) from the 15-day sorption and 21-day desorption

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FIGURE 3. Experimental and modeling results of U(VI) in the pore water and the solid phase of the diffusion cell after 918.5 h (38.3 days) of diffusion. Solid line: simulation using LEA-based diffusion model with Dp ) 1.6 × 10-6cm2/s; Dashed line: simulation using batch sorption isotherm (KF )28.16(µg/kg)/(µg/L)n, n ) 0.81) and kinetics-based sorption-diffusion model with the following fitted parameters: Dp ) 1.7 × 10-6cm2/s, µ ) -0.5, σ ) 2.5; Dash-dot line: sensitivity study for sorption kinetics-based model with Dp ) 1.7 × 10-6cm2/s, µ ) 1.0, σ ) 2.5; Dotted line: sensitivity study for sorption kinetics-based model, with Dp ) 1.7 × 10-6cm2/s, µ )-2.0, σ )2.5. Shown are (a) [U(VI)] in pore water; (b) [U(VI)] in solid phase. Modeling results using both the LEA-based model and the kinetics-based model are shown in Figure 3. The LEAmodeling results were derived by fitting the model to C and Ceq, assigning equal weights to both, keeping KF and n from the batch tests, and adjusting Dp. The optimal fitted value of Dp was 1.6 × 10-6 cm2/s. For the kinetics-based model, both C and S data were used in model fitting with equal weights applied to each. Parameter Dp and rate parameters for U(VI) kinetic sorption (µ and σ) were simultaneously fitted with fitted values of Dp ) 1.7 × 10-6 cm2/s, µ ) -0.5, and σ ) 2.5. The 10th, 50th, and 90th percentiles for the kLA distribution based on the rate parameters were 2.0 × 10-2, 6.1 × 10-1, and 1.5 × 10+1 (mL/g-hr), respectively. The calculated diffusion profiles from both models agreed well with the experimental data. In addition, the “goodness of fit” for the two models was essentially the same, consistent with our conclusion that the LEA is a valid modeling approach for this case. (See SI for more details.) Sensitivity analysis was conducted by altering the rate parameters µ and σ from their optimal values (base case) and revealed an extremely minor effect of µ (Figures 3a and 3b) and σ (data not shown). These results further confirmed that a kinetic model offers little to no improvement, relative to the LEA, for modeling this diffusion cell system. The insensitivity of diffusion cell data to the kinetic sorption rate parameters indicated that a slight experimental uncertainty could cause a significant difference in the estimated rate parameters. A further study is therefore needed to resolve this inconsistency of the rate parameters from batch and diffusion cell systems. The estimated Dp is an effective value for all U(VI) species present in solution under the given experimental conditions 7710

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of pH 8.0 ( 0.1, I ) 0.02 mol/L, and with the solution at equilibrium with normal air and calcite solids. Under these conditions, dominant U(VI) species are Ca2UO2(CO3)30 (68.3%), CaUO2(CO3)32- (30.8%), UO2(CO3)22- (0.5%) and UO2(CO3)34- (0.4%). (See SI for details.) In other experiments conducted on similar HSC S-C diffusion cells, we employed tritiated water as a tracer and observed tortuosity factors (τF) of 2.45-2.88 for these cells (32), assuming that HTO was not reactive with the solid matrix. Using this range of τF estimates as approximations for our current work, we obtain an “apparent” D0 value in the range of 3.9-4.9 × 10-6 cm2/s for the migration of total U(VI) under the conditions of our experiments, using estimated Dp of 1.6-1.7 × 10-6 cm2/s. This range is close to estimates that have been made for unhydrated forms of the dominant species. In particular, we estimate a D0 value of 4.7 × 10-6 cm2/s at 25 °C for Ca2UO2(CO3)30 using the Stokes-Einstein equation and an estimated molecular size of 5.24 Å the species in its unhydrated form (see SI). For a point of comparison, we have also estimated D0 values of 4.3 × 10-6 cm2/s and 4.5 × 10-6 cm2/s at 25 °C for Ca2UO2(CO3)30 and CaUO2(CO3)32-, respectively, using the equation suggested by Worch (33), which uses the formula weight of the species and assumes negligible hydration. (See SI for details.) It is noteworthy that hydration will increase the size and weight of the complexed U(VI) species and reduce the values of D0. In addition, we note that the D0 estimates are simple empirical and crude approximations without consideration of specific solutesolvent interactions, such as dipole-dipole interactions or hydrogen bonding as is possible with Ca2UO2(CO3)30. For all these reasons, the estimated value should be regarded only as an “order-of-magnitude” check on the measured results, with the latter taken as the more accurate measure. In the latter regard, however, we must note that the estimated D0 is conditioned on τF. If a substantial fraction of the HTO interacts with the solid phase, such as through exchange with H2O molecules in the clay interlayer regions (30), the τF would be overestimated, as would the value D0. In summary, we have performed an inward-flux diffusion cell experiment for quantifying the diffusion coefficient of U(VI) under strictly controlled chemical conditions, and we have developed cell sectioning, extraction and measurement approaches that are valuable tools. The multirate kinetic modeling approach was proven effective for the batch sorption/desorption kinetics and may apply to a wide variety of pollutants that are retarded by similar mechanisms of sorption (i.e., by surface complexation at intraparticle sites). Moreover, the results suggest that diffusion-based transport can be well approximated using independent data under certain circumstances, that is, so long as local sorption equilibrium applies and independent measures or estimates can be made for D0 of the dominant species, τF of the porous medium, and the sorption characteristics of the system. On the other hand, other work in our laboratory has shown that nonequilibrium can be manifest for diffusion cells of these same materials with different external boundary conditions (32), emphasizing the importance of using independent tests of aqueous and solid phases to verify the LEA assumption. More generally, it should be clear that the characteristics of sorption kinetics and its impact on U(VI) diffusion will be dependent on the physical and geochemical properties of the sediment media. Therefore, independent experimental tests of sorption-desorption rate are necessary in order to test LEA validity for each given situation to be modeled. In cases where such equilibrium cannot be assumed, more complex modeling is required to incorporate the possible effects of particle-scale rate limitations, such as possible diffusion to intragranular or intra-aggregate regions where apparent diffusivities are lower due to altered pore-scale

geophysical/chemical conditions relative to the interparticle spaces (27, 32).

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Acknowledgments The research described in this manuscript was supported in large part by the Environmental Remediation Science Program of the office of Science, U.S. Department of Energy under contract DE-FG07-02ER63498.

Supporting Information Available Experimental details on the following topics: (1) Estimating total and labile background uranium in the HSC materials; (2) Iterative calculation of the sorption isotherm and labile background U(VI) from batch sorption data (Table S1); (3) Schematic illustrations of diffusion cell construction and operation (Figure S1, Schematic illustration of the diffusion cell as assembled for pre-equilibration of solids; Figure S2, Schematic illustration of the “inward-flux” diffusion system.); (4) Extent of equilibrium in sorption/desorption batch kinetics experiments (Table S2); (5) Removal efficiency for sorbed-phase U(VI) extraction by the sequential extraction procedure (Table S3); (6) U(VI) speciation (Table S4). Concentrations of major cations in the 95 g/L batch sorption system; Table S5, Major species and complexation constants for U(VI); (7) Estimation of D0 for U(VI) species; (8) Experimental data for the diffusion cell (Table S6); (9) Goodness of fit in modeling of batch rate data and diffusion cell results. This material is available free of charge via the Internet at http://pubs.acs.org.

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Literature Cited (1) Liu, C.; Zachara, J. M.; Qafoku, O.; McKinley, J. P.; Heald, S. M.; Wang, Z. Dissolution of uranyl microprecipitates from subsurface sediments at Hanford Site, USA. Geochim. Cosmochim. Acta 2004, 68, 4519–4537. (2) Liu, C.; Zachara, J. M.; Yantasee, W.; Majors, P. D. Microscopic reactive diffusion of uranium in the contaminated sediments at Hanford, United States. Water Resour. Res. 2006, 42, W12420. (3) McKinley, J. P.; Zachara, J. M.; Liu, C.; Heald, S. C.; Prenitzer, B. I.; Kempshall, B. W. Microscale controls on the fate of contaminant uranium in the vadose zone, Hanford Site, Washington. Geochim. Cosmochim. Acta 2006, 70, 1873–1887. (4) Arnold, B. W.; Kuzio, S. P.; Robinson, B. A. Radionuclide transport simulation and uncertainty analyses with the saturated-zone site-scale model at Yucca Mountain, Nevada. J. Contam. Hydrol. 2003, 63, 401–419. (5) Yamaguchi, T.; Nakayama, S. Diffusivity of U, Pu and Am carbonate complexes in a granite from Inada, Ibaraki, Japan studied by through diffusion. J. Contam. Hydrol. 1998, 35, 55– 65. (6) Yamaguchi, T.; Sakamoto, Y.; Nakayama, S.; Vandergraaf, T. T. Effective diffusivity of the uranyl ion in a granite from Inada, Ibaraki, Japan. J. Contam. Hydrol. 1997, 26, 109–117. (7) Cussler, E. L. Diffusion Mass Transfer in Fluid Systems; 2nd ed.; Cambridge University Press: New York, 1997. (8) Shackelford, C. D. Laboratory diffusion testing for waste disposal-A review. J. Contam. Hydrol. 1991, 7, 177–217. (9) Shackelford, C. D.; Daniel, D. E. Diffusion in saturated soil. I: background. ASCE J. Geotechnol. Eng. 1991, 117, 467–484. (10) Muurinen, A. Diffusion of uranium in compacted sodium bentonite. Eng. Geo. 1990, 28, 359–367. (11) Tokunaga, T. K.; Wan, J. M.; Pena, J.; Sutton, S. R.; Newville, M. Hexavalent uranium diffusion into soils from concentrated acidic and alkaline solutions. Environ. Sci. Technol. 2004, 38, 3056–3062. (12) Ball, W. P.; Goltz, M. N.; Roberts, P. V. Modeling the transport of solutes influenced by multiporcess nonequilibrium. Water Resour. Res. 1991, 27, 653–656. (13) Grathwohl, P. Diffusion in Natural Porous Media: Contaminant Transport, Sorption/Desorption and Dissolution Kinetics; Kluwer Academic Publishers: Norwell, MA, 1998. (14) Chisholm-Brause, C. J.; Berg, J. M.; Marzner, R. A.; Morris, D. E. Uranium(VI) sorption complexes on montmorrillonite as a

(24)

(25)

(26)

(27)

(28)

(29)

(30) (31)

(32) (33)

function of solution chemistry. J. Colloid Interface Sci. 2001, 233, 38–49. Davis, J. A.; Payne, T. E.; Waite, T. D. Simulating the pH and pCO2 dependence of uranium(VI) adsorption by a weathered schist with surface complexation models. In Geochemistry of Soil Radionuclides; Soil Science Society of America Special Publication: Madison, WI, 2002; 59, pp 61-86. Dong, W. M.; Ball, W. P.; Liu, C.; Wang, Z. M.; Stone, A. T.; Bai, J.; Zachara, J. M. Influence of calcite and dissolved calcium on uranium(VI) sorption to a Hanford subsurface sediment. Environ. Sci. Technol. 2005, 39, 7949–7955. Millard, A. R.; Hedges, R. E. M. A diffusion-adsorption model of uranium uptake by archaeological bone. Geochim. Cosmochim. Acta 1996, 60, 2139–2152. Arai, Y.; McBeath, M.; Bargar, J. R.; Joye, J.; Davis, J. A. Uranyl adsorption and surface speciation at the imogolite-water interface: Self-consistent spectroscopic and surface complexation models. Geochim. Cosmochim. Acta 2006, 70, 2492–2509. Barnett, M. O.; Jardine, P. M.; Brooks, S. C. U(VI) adsorption to heterogeneous subsurface media: Application of a surface complexation model. Environ. Sci. Technol. 2002, 36, 937–942. Davis, J. A.; Coston, J. A.; Kent, D. B.; Fuller, C. C. Application of the surface complexation concept to complex minerals assemblages. Environ. Sci. Technol. 1998, 32, 2820–2828. Davis, J. A.; Meece, D. E.; Kohler, M.; Curtis, G. P. Approaches to surface complexation modeling of uranium(VI) adsorption on aquifer sediments. Geochim. Cosmochim. Acta 2004, 68, 3621– 3641. Kohler, M.; Curtis, G. P.; Kent, D. B.; Davis, J. A. Experimental investigation and modeling of uranium(VI) transport under variable chemical conditions. Environ. Sci. Technol. 1996, 32, 3539–3551. Bond, D. L.; Davis, J. A.; Zachara, J. M. Uranium(VI) release from contaminated vadose zone sediments: Estimation of potential contributions from dissolution and desorption. In Adsorption of Metals by Geomedia II: Variables, Mechanisms, and Model Applications; Barnett, M. O., Kent, D. B., Eds.; Elsevier: Amsterdam., 2008; pp 375-416. Qafoku, N. P.; Zachara, J. M.; Liu, C.; Gassman, P. L.; Qafoku, O. S.; Smith, S. C. Kinetic desorption and sorption of U(VI) during reactive transport in a contaminated Hanford sediment. Environ. Sci. Technol. 2005, 39, 3157–3165. Sims, R.; Lawless, T. A.; Alexander, J. L.; Bennett, D. G.; Read, D. Uranium migration through intact sandstone: effect of pollutatnt concentration and the reversibility of uptake. J. Contam. Hydrol. 1996, 21, 215–288. Liu, C.; Zachara, J. M.; Smith, S. C.; McKinley, J. P.; Ainsworth, C. C. Desorption kinetics of radiocesium from subsurface sediments at Hanford Site, USA. Geochim. Cosmochim. Acta 2003, 67, 2893–2912. Liu, C.; Shi, S.; Zachara, J. M. Kinetics of uranium(VI) desorption from contaminated sediments: Effects of geochemical conditions and model evaluation. Environ. Sci. Technol. 2009, Submitted. Serne, R.; Bjornstad, B. N.; Schaef, H. T.; Williams, B. A.; Lanigan, D. C.; Horton, D. G.; Clayton, R. E.; LeGore, V. L.; O’Hara, M. J.; Brown, C. F.; et al. Characterization of Vadose Zone Sediment: Uncontaminated RCRA Borehole Core Samples and Composite Samples, PNNL-13757-1; Pacific Northwest National Laboratory: Richland, WA, 2002. Kohler, M.; Curtis, G. P.; Meece, D. E.; Davis, J. A. Methods for estimating adsorbed uranium(VI) and distribution coefficients of contaminated sediments. Environ. Sci. Technol. 2004, 38, 240–247. Liu, C.; Zachara, J. M.; Qafoku, N. P.; Wang, Z. M. Scaledependent desorption of uranium from contaminated subsurface sediments. Water Resour. Res. 2008, 44, W08413. Zachara, J. M.; Davis, J. A.; Liu, C.; McKinley, J. P.; Qafoku, N. P.; Wellman, D. M.; Yabusaki, S. B. Uranium Geochemistry in Vadose Zone and Aquifer Sediments from the 300 Area Uranium Plume, PNNL-15121; Pacific Northwest National Laboratory: Richland, WA, 2005. Bai, J.; Liu, C.; Ball, W. P. Unpublished data (manuscript in preparation: Experimental and modeling study of U(IV) diffusion by in-diffusion cells: Kinetic aspects), 2009. Worch, E. Eine neue Gleichung zur Berechnung von Diffusionkoeffizienten geloster Stoffe. Vom Wasser 1993, 81, 289–297.

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