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Jun 11, 2013 - Sherwood number and the Thiele modulus to provide insight into the limiting mechanism. The value of the Sherwood number suggests that t...
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Characterization of Uranium Uptake Kinetics from Seawater in Batch and Flow-Through Experiments Jungseung Kim, Yatsandra Oyola, Costas Tsouris,* Cole R. Hexel, Richard T. Mayes, Christopher J. Janke, and Sheng Dai Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge, Tennessee 37831-6181, United States ABSTRACT: A laboratory study of uranium uptake from seawater has been conducted using batch and flow-through recycling experiments. Uranium adsorption from seawater, using amidoxime-based polymeric adsorbents, has been described by transport and kinetic models under the assumption of transport-limited or reaction-limited process for batch adsorption experiments. Mathematical models based on liquid film mass transfer, diffusion, or reaction kinetics have been evaluated in terms of the Sherwood number and the Thiele modulus to provide insight into the limiting mechanism. The value of the Sherwood number suggests that the external mass-transfer resistance is much smaller than the intraparticle diffusion resistance. The Thiele modulus was estimated on the basis of the rate constants from independent batch tests analyzed by a reaction kinetic model, and its value suggests that the uranium binding is the rate-limiting step compared to diffusion. The uranium uptake in batch experiments reached 4 mg U/g adsorbent over a period of nine weeks, which is much higher than the uranium uptake by a leading previously developed adsorbent tested at conditions similar to those in this study. The maximum uranium uptake in the flow-through recycling experiments was approximately 3.3 mg U/g adsorbent over a period of six weeks. complex [UO2(CO3)3]4‑ is the rate-limiting step in uranium complexation by amidoxime functional groups from seawater.5 On the other hand, the influence of the transport of the uranyl complex on the uptake rate was investigated by using an intraparticle diffusion model.5 It was also reported that intraparticle diffusion may be the rate-limiting step for uranium adsorption by amidoxime-based polymeric adsorbents prepared by suspension polymerization.18,19 Likewise, it was pointed out that intraparticle diffusion can determine the overall rate of uranium adsorption from seawater by amidoxime-grafted polymeric adsorbents.11,12 The influence of uranium species transport on the overall uptake process is supported by the observation that the adsorption rate increased with enhanced porosity and hydrophilicity of the polymeric adsorbents.19 Adsorption rates of uranium from real seawater were reported for different reactor configurations, such as batch20 and packedbed.11,12,16 The liquid film mass-transfer model described the uranium adsorption behavior from seawater, indicating that the film resistance can be the rate-limiting step in the overall process.20 On the other hand, uranium adsorption was reported as a rate-limited process by both the complexation reaction between the amidoxime and uranyl species and diffusion through hollow amidoxime-grafted polymer in a packed bed.11 Previous reports suggested that tailored amidoxime-grafted polymeric adsorbents should be characterized under different regimes in order to predict and improve the adsorption performance under real conditions. In this study, the rate of uranium adsorption from natural seawater (postsand bed filtration) by an effective amidoxime-grafted

1. INTRODUCTION Amidoxime is known as a versatile functional ligand that undergoes complexation with various metal ions.1−3 Amidoximegrafted polymeric adsorbents, which are generally prepared by radiation-induced grafting polymerization (RIGP),4−6 have been the dominant materials for uranium recovery from spiked solution and seawater due to their high affinity and capacity for uranium in comparison with other inorganic or biological adsorbents.1,7 The synthesis scheme through the RIGP process has been investigated for ligand conversion from acrylonitrile to amidoxime on different polymeric supports, and currently, there is continuing effort to improve the uranium-adsorption performance of these materials.5 Amidoxime-based adsorbents have been tested for uranium adsorption from seawater in laboratory-scale3−5,8,9 and field experiments.7,10−12 Several laboratory-scale studies have focused on synthetic routes with various characterization techniques to prepare improved amidoxime-based adsorbents.4,5,13−15 The mechanical strength of adsorbents based on any type of commercially available polymeric matrix is greater for RIGPprocessed materials than those grafted by other approaches, which is an advantage of the RIGP route.16 It has been suggested that functional groups grafted through the RIGP process can have better accessibility to bind uranium species in seawater by positioning the functional ligands mostly onto the polymeric backbone, in contrast with other polymerization methods,3,17 through which functional ligands may be positioned deep inside the microporous polymeric network. The adsorption kinetics of uranium from seawater has been investigated mainly on the basis of a reaction-limited assumption. For instance, pseudo-first-order and pseudo-second-order reaction kinetic models, which are single-species reaction models, have been frequently used to describe the uranium adsorption behavior by amidoxime polymeric adsorbents.5 Das and co-workers also suggested that the decomplexation step of the uranyl tricarbonate © 2013 American Chemical Society

Received: Revised: Accepted: Published: 9433

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10-mL samples were collected periodically, using a pipet, for a test duration of 6 to 9 weeks. Collected seawater samples were acidified with Optima nitric acid for analysis. The adsorbent fibers were recovered after the experiment and treated with concentrated acid solution (high-purity HCl + HNO3 at a ratio of 3:1) for uranium elution and subsequent analysis. 2.2.1.2. Spiked Solution Tests. Uranium-spiked solutions consisted of uranyl nitrate (2.52 × 10−5 M), sodium bicarbonate (2.29 × 10−3 M), and sodium chloride (0.43 M). The concentrations of sodium and bicarbonate were selected to be similar with those of seawater.22 The amidoxime adsorbent (15−17 mg) was introduced into the solution (500 mL) for uranium adsorption experiments. Samples of solution were taken periodically for chemical analysis using ICP-OES, equilibrium was reached within 24 h. 2.2.2. Adsorption in Flow-Through Recycling Reactors. A PTFE diaphragm pump of 0.8 L/min maximum flow rate (Cole-Parmer, IL, U.S.A.) was used to pump seawater from a 110-gallon tank into a series of adsorption beds. After passing through the series of the adsorbent beds, the seawater was recycled back into the feed tank. Each bed was prepared by loading 10 mg of the adsorbent in 47-mm diameter PFA (perfluoroalkoxy) in-line filter holders (Cole-Parmer, IL, U.S.A.). The flow rate and temperature of seawater were monitored for the duration of the experiment. 2.2.3. Sample Analysis. Inductively coupled plasma mass spectroscopy (ICP-MS, Thermo Scientific X-Series II) was used for quantitative analysis. Sample aspiration was performed at 100 μL/min with a Teflon SP nebulizer coupled to an Elemental Scientific Inc. PC3 and Fast combination spray chamber. Matrix effects were corrected by adding internal standards containing Bi, In, Sc, Tb, Y offline before sample introduction. The average of six replicate measurements per sample was used to quantify uranium-238 against a 6-point calibration curve. Prior to sample analysis, semiquantitative full mass range survey scans were collected. Wash out for the instrument was monitored between samples. Standards NASS-5 (seawater), CASS-6 (seawater), SLEW-5 (estuarine), and SLRS-5 (riverine), supplied by the National Research Council of Canada, were used for seawater quality-control experiments. High-purity nitric acid (2%, Optima, Fisher Scientific) was used to dilute samples after adding a five-element internal standard cocktail (High Purity Standards ICP-MS-IS-2, Perkin-Elmer, consisting of 100 ppb Bi, In, Sc, Tb, Y in 2% nitric acid). 2.3. Adsorption Data Analysis. 2.3.1. Adsorption Kinetics in Batch Reactors and Flow-Through Recycling Reactors. The uranium uptake rate was investigated for transport-limited and reaction-limited adsorption, respectively. It was assumed that uranium uptake by the adsorbent occurs in four steps: (i) interparticle diffusion of uranium species through the adsorbent fibers, (ii) external-film (interphase) mass transfer, (iii) intraparticle diffusion of uranium species through adsorbent fibers, and (iv) binding reaction of uranyl ions with amidoxime ligands. In the following analysis, when a particular model is employed to describe one of the above steps, the hypothesis is that the corresponding mechanism is the uranium uptake ratelimiting step. For batch experiments, it was assumed that interparticle diffusion is not the rate-limiting mechanism because the fibers were fluidized in seawater. The uptake rate based on the transport-limited case was investigated by using two mathematical models. First, considering the dilute concentration (3−4 ppb) of uranium in seawater, the importance of liquid film mass transfer on the overall uranium

polymeric adsorbent, prepared through the RIGP route, has been investigated for the dynamic and equilibrium macroscopic adsorption performance in batch and flow-through recycling experiments. Specifically, porous polyethylene fibers have been used to graft the adsorbent ligands, with the goal to have a reaction-limited rate process using real seawater. Batch experiments have been performed employing mass-transfer and reaction kinetics models to characterize the adsorption behavior in order to determine the conditions under which a kinetic-limited process can be achieved. In the case that transport is the rate-limiting process, there is opportunity for improving the performance of the adsorbent by optimization of process parameters or modification of such properties as porosity and pore size. Thus, it is important to know the ratelimiting mechanism of the overall adsorption process.

2. MATERIALS AND METHODS 2.1. Materials. Seawater used in adsorption experiments came from two sources: (i) coastal gulfstream seawater from a location 210 m deep, 75 miles east of Savannah, GA, collected in 5-gallon tanks and (ii) near-surface seawater from Charleston, SC, collected in 110-gallon tanks. The tanks were rinsed first with fresh water and then with seawater prior to filling. Seawater from Charleston had a lower pH at 7.7 than the deep water (pH 8.2), probably due to dilution by land water of lower pH. The salinities of the Charleston (34.5 g/L) and Savannah seawater (35.5 g/L) were measured by a CTD (conductivity, temperature, and depth) instrument using Niskin bottles. For spiked solution experiments, uranyl nitrate hexahydrate was supplied by B&A Quality (ACS reagent grade). Sodium chloride and sodium bicarbonate were purchased from SigmaAldrich (St. Louis, MO, U.S.A.). Amidoxime-based polymeric adsorbent grafted by the RIGP method was prepared.22 The general scheme of the RIGP method is summarized in a review article.1 There are three major steps in the adsorbent preparation approach: irradiation, grafting, and conditioning. Polyethylene fibers were irradiated under electron beam to produce radicals; the fibers were then grafted with a mixture of acrylonitrile and methacrylic acid. Subsequently, the fibers were contacted with hydroxylamine to obtain amidoxime ligands. A potassium hydroxide (KOH) solution was used to condition the adsorbent prior to seawater contact.21 Porous polyethylene fibers of a relatively high surface area were used as the supporting polymer matrix for the grafting of functional ligands.22 The average density was 0.941 g cm−3, respectively. The average thickness of wet amidoxime-based polymeric fibers was about 153 μm, measured using optical microscopy. Japan Atomic Energy Agency (JAEA) provided their previously reported amidoxime-based adsorbent from nonwoven polyethylene sheets for comparison.10 The difference between the ORNL materials (adsorbents 1−3) and the JAEA adsorbent is the form of polyethylene material used for the grafting of the functional groups. ORNL fibers have relatively higher surface area (adsorbents 1−3) when compared to the nonwoven polyethylene sheets that were used in the synthesis of the JAEA adsorbent. 2.2. Experimental Setup. 2.2.1. Adsorption in Batch Reactors. 2.2.1.1. Seawater Test. The 5-gallon plastic tanks of coastal gulfstream seawater were used for batch adsorption experiments. The adsorbent (5 mg) was added into the 5-gallon tanks, with the adsorbent fibers freely suspended in the seawater. An initial seawater sample of 10 mL was collected prior to the addition of the adsorbent. The containers were shaken constantly at 100 rpm at room temperature (∼23 °C). 9434

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uptake process was evaluated. The liquid film mass transfer can be derived from the mass balance between bulk liquid phase and surface liquid phase using the following mass balance formula. −V ·

dC = A ·kL·(C[t ] − Ce) dt

C[t ] = (C0 − Ce) ·e[(−

A·kL )·t ] V

resistance and intraparticle diffusion resistance are of the same order.20,25 With the assumption of a reaction-limited process, the experimental data are analyzed by a reaction kinetic model. Azizian presented a theoretical kinetic model that can be employed to estimate the rate constants for uranium adsorption on amidoximegrafted polymeric adsorbents:26

(1)

+ Ce

(2)

ka A + L ←⎯⎯⎯⎯⎯→AL kd

Here, V is the volume of seawater in the reactor and A is the surface area of the adsorbent; kL is the liquid film mass transfer coefficient and t is time; C, C0, and Ce are the concentrations of uranium in bulk solution at any time, initially (∼3.3 ppb), and at equilibrium, respectively. Here A, kL, and Ce are assumed to be constants and independent of time. From the mass balance between the uranium lost from the bulk solution, V·(C0 − C[t]), and the amount adsorbed, M·q[t], the following equations can be written: M ·q[t ] = V ·(C0 − C[t ])

q[t ] =

Here A and L denote the adsorbate and functional ligand on adsorbent, respectively. AL is the complex of adsorbate and the ligand grafted on the adsorbent surface. ka and kd are the rate constants for adsorption and desorption, respectively. The amidoxime ligand showed affinity to other metal ions beside uranyl in seawater such as sodium, vanadium, copper, manganese, and others, which can lead to ion exchange in a mixture of ions.1 Therefore, a general kinetic model that includes both adsorption and desorption was considered. The initial amount of uranium adsorbed is assumed zero in all cases. The following equations apply for the rate of reaction:

(3)

A·kL V ·(C0 − Ce) ·[1 − e[(− V )·t ]] M

(4)

where M is the mass of the adsorbent and q[t] is the amount of uranium adsorbed per unit mass of the adsorbent. Another case of a transport-limited process is due to intraparticle diffusion, which describes the mass transfer of uranyl inside the amidoximated porous fiber, expressed by the following equation:23,24

1 ⎡ ⎤⎫ ⎢ 2 1 + 4α · D ⎥⎪ · t ⎥⎬ erfc⎢ α·r ⎢⎣ ⎥⎦⎪ ⎭

(

2

)

)

(8)

C = C0 − βθ

(9)

m·q C − Ce = 0 V θe

(10)

dθ = ka(C0 − βθ )(1 − θ ) − kdθ dt

(11)

a = kaβ

(12)

⎛ 1⎞ b = − ⎜β + C 0 + ⎟k a ⎝ K⎠

(13)

f = kaC0

(14)

(5)

K=

This relationship is the result of the diffusion equation derived for the case of diffusion from a stirred solution of limited volume into a cylinder. The parameter α is defined as the ratio between solution volume and cylinder volume. The apparent diffusivity and the radius of cylindrical adsorbent are expressed as D and r, respectively. In this analysis, amidoxime-grafted polymeric adsorbent fibers of a high aspect ratio were considered having a cylindrical shape. The contribution of the intraparticle diffusion resistance can be evaluated by batch adsorption tests at good mixing conditions, which can minimize the effect of the liquid film mass-transfer resistance. The relative importance between liquid film mass transfer and intraparticle diffusion can be evaluated by using the dimensionless Sherwood (Sh) number: k ·L Sh = L D

dθ = va − vd = kaC(1 − θ ) − kdθ dt

β=

⎧ ⎡ ⎤ 1 ⎢ 4 1 + 4 α ·D ⎥ q[t ] 1+α ⎪ = ·⎨1 − exp⎢ ·t ⎥· 1 qe α 2· r 2 1 + 4α ⎪ ⎢⎣ ⎥⎦ ⎩

(

(7)

ka kd

(15)

⎛ dθ 1⎞ = kaβθ 2 − ⎜β + C0 + ⎟kaθ + kaC0 ⎝ dt K⎠ = aθ 2 + bθ + f λ=

b2 − 4af

(16) (17)

γ=b−λ

(18)

ξ=b+λ

(19)

θ=

q ξγ(e λt − 1) = qm 2a(ξ − γ e λt )

(20)

θ is the coverage of adsorbate on the adsorbent, defined here as the amount of uranium adsorbed at a specific time divided by the maximum amount at equilibrium concentration (qm) of uranium adsorbed. va and vd are the adsorption and desorption rates, respectively. C0 is the initial concentration of uranium and K is the equilibrium constant for the adsorption and desorption processes. q and qe are the amounts of adsorbed uranium at a specified time

(6)

Here, the characteristic length L is taken equal to the diameter of the adsorbent fibers. Liquid film mass transfer is considered as the rate-limiting step if Sh is less than 1. On the other hand, if Sh is larger than 200, intraparticle diffusion is the rate-limiting step. If Sh is between 1 and 200, the liquid film mass transfer 9435

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active sites of the adsorbent.27,28 In this study, the first step, which is referred to as interparticle diffusion, is assumed to occur rapidly, since the adsorbent is fluidized in seawater, so it is not considered the slowest step in batch experiments and is negligible in the overall uptake process.27,28 In some cases, however, the adsorbent forms aggregates in a confined space, and as a result interparticle diffusion may become slow. This case is not considered in this work, where the importance of liquid film mass transfer,20 intraparticle diffusion, and chemical reaction11 is evaluated. In the case that the reaction is the ratelimiting step, the uptake rate is governed by interactions between the grafted functional ligand and uranium species. Results from uranium adsorption from seawater in 5-gallon batch reactors are presented in Figure 2. The uranium concentration in seawater vs time decreased quickly initially and then approached a plateau. Adsorbent 1 showed the highest uranium uptake compared to adsorbents 2 and 3 for the duration of the experiment. Higher uranium uptake from adsorbent 1 was observed as compared to the uranium uptake by the supplied JAEA adsorbent, tested under similar conditions for 30 days. The uranium uptake by adsorbent 1, after 30 days in seawater, was higher than the reported amount of uranium adsorbed by the JAEA adsorbent (3.2 mg U/g adsorbent) after a period of 180 days.29 3.1. Modeling Considerations. 3.1.1. Liquid Film MassTransfer Model. If uranium adsorption from seawater in a batch reactor is controlled by liquid film mass transfer, eqs 2 and 4 can be used to describe the rate of decay in uranium concentration and the amount of uranium adsorbed vs time. According to Figure 3, the equations simulated the uranium adsorption behavior well with correlation coefficient values approaching 1. The regression results are summarized in Table 1. The liquid film mass transfer coefficient (kL) can be estimated from the matching of theoretical and experimental data. It has been reported that amidoxime-grafted polyethylene fibers are swollen in aqueous solutions.30−37 Swelling is most likely to be caused by the penetration of water molecules due to the hydrophilicity of the amidoxime functional groups inside the porous polymeric structure resulting in surface area and porosity modifications of the fibers.18,19,38 An average diameter of the wet fibers of 153 ± 15 μm, which was obtained from optical microscopy (Nikon Microphot-SA) measurements, was used as the length scale in eq 6 for the estimation of the Sherwood number.

and at equilibrium, respectively. According to the theoretical analysis, the rate constants of the kinetic model combine the results of the complex reactions occurring during adsorption and desorption.26 In this study, the rate constant of the adsorption process was used to estimate the Thiele Modulus for uranium uptake from seawater to determine the relative importance of intraparticle diffusion and binding reaction. Experimental data were employed for the estimation of the rate constants in eq 7. A nonlinear least-squares regression method was used to determine the parameters ka and kd in the above model equations. The maximum uranium adsorption capacity was obtained from the experiment. Modeling results using the best values of ka and kd are compared with experimental data in Figure 6.

3. RESULTS AND DISCUSSION As shown in Figure 1, the adsorbent consists of fibers of approximately 153 ± 15 μm diameter. The adsorption process

Figure 1. Wet adsorbent fibers (left) and mechanisms involved in the adsorption process (right): 1 - interparticle diffusion; 2 - external (film) mass transfer; 3 - intraparticle diffusion; 4 - complexation reaction. Images were obtained using an optical microscope (Nikon Microphot-SA).

is shown to occur in four steps: (i) transport of adsorbate from bulk liquid phase to the exterior film of the adsorbent (interparticle diffusion); (ii) transport of adsorbate from the film to the surface of adsorbent (liquid film mass transfer); (iii) transport of adsorbate in the interior of adsorbent fibers (intraparticle diffusion); and (iv) reaction of adsorbate with the

Figure 2. Experimental results for adsorption of uranium from seawater in 5-gallon batch reactors: (1) Adsorbent 1. (2) Adsorbent 2. (3) Adsorbent 3. (4) JAEA adsorbent. Mixing rate: 100 rpm. 9436

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Figure 3. Comparison of experimental data with the liquid film mass transfer model. Adsorbent 1. Adsorbent 2. Adsorbent 3. (The model parameters are summarized in Table 1.)

Table 1. Regression Results for Batch Adsorption Data Using a Liquid Film Mass-Transfer Model eq 3

eq 5

(C0 − Ce) (A·kL/V) Ce no. [ppb] [1/day] [ppb] (1) (2) (3)

1.17 1.15 0.89

0.06 0.04 0.06

r2

2.28 0.9996 2.44 0.9998 2.75 0.9994

(V/M)·(C0 − Ce) (A·kL/V) [mg-U/g ads] [1/day] 4.13 4.04 3.43

0.07 0.05 0.06

r2 0.9967 0.9977 0.9881

3.1.2. Intraparticle Diffusion Model. Intraparticle diffusion may be the rate-limiting step in uranium uptake by the adsorbent. For instance, Nilchi and co-workers observed that a highly porous amidoxime structure allowed a fast rate of uptake of metal ions.17 In that study, the porous amidoxime-based polymeric adsorbents were synthesized through polymerization of a mixture of acrylonitrile, divinylbenzene, and methylacrylate. The adsorbents had a pore volume of 0.96 cm3/g adsorbent, a surface area of 45.1 m2/g adsorbent, and an average pore size of 43.8 nm. Hirotsu and co-workers suggested that uranium adsorption is governed by diffusion, depending on the hydrophilicity of amidoxime-bearing polymer.38 Zhang and co-workers also assumed that intraparticle diffusion is the rate-limiting step for uranium adsorption from seawater.39 In this study, the contribution of the intraparticle diffusion was investigated by using eq 5. Although the equation proposed was used with moderate values of alpha, the diffusion equation can represent well the experimental data of the amount of uranium adsorbed vs time. Figure 4 presents a comparison of experimental data with the best agreement from nonlinear regression with the intraparticle diffusion model, eq 5, for cylindrical-shaped adsorbents. It is assumed that no salt precipitation occurs inside and on the surface of the fibers. Although adsorbents of a spherical shape were frequently used in mathematical modeling,27,40,41 cylindrical adsorbent fibers were employed in this study because they can be deployed easier in seawater in a real process. In eq 5, the diffusivity can be related to the diameter of the adsorbent. Diffusion occurs in the radial direction of the adsorbent fibers due to their high aspect ratio. With the assumption of diffusionlimited process for uranium uptake from seawater, the estimated diffusion coefficient using eq 5 was 3.79 × 10−11 m2/day which is orders of magnitude smaller than the reported values (3−10 × 10−6 m2/day)5,42 from experiments involving uranium spiked solutions. This discrepancy came from the fact that in other studies,5,42 the dominant uranium species was UO22+, which readily reacts and diffuses through the amidoxime-functionalized membrane used to estimate the diffusion coefficient, while the dominant species in seawater at equilibrium is the uranium

Figure 4. Comparison of experimental data with the intraparticle diffusion model. Adsorbent 1. Adsorbent 2. Adsorbent 3. (The model parameters are summarized in Table 2.)

Table 2. Regression Results for Batch Adsorption Data Using an Intraparticle Diffusion Model eq 5 no.

(4(1 + 1/4α)2 ·D/α2 ·R2 [1/day])

r2

1 2 3

0.035 ± 0.001 0.036 ± 0.001 0.043 ± 0.001

0.9939 0.9979 0.9872

tricarbonate anion, which is a stable complex. It should be noted that in reference 5, the reported values were self-diffusion coefficients measured by radiotracer techniques. The discrepancy is mainly due to the differences of the two systems. The adsorbate analyzed in this work is adsorbed with different cations present in seawater, thus this system is far from the one used in reference 5, which was saturated by uranyl cations only. 3.1.3. Sherwood Number. The determination of Sh through eq 6 depends on the physical properties of the adsorbent, including the surface area and diameter. The surface area relevant to the external mass-transfer coefficient is the external surface area per unit mass of the fibers, which is 0.03 m2/g for a 153-μm fiber diameter. The corresponding value of the Sherwood number is over 10,000 suggesting that, between liquid film mass-transfer resistance and intraparticle diffusion resistance, the intraparticle diffusion resistance is much bigger. This result is consistent with experimental data shown in Figure 5, where a comparison of uranium uptake is presented using the 9437

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that uranium uptake in spiked solutions is a reaction-limited process. Optimization results shown in Figure 6 led to the estimation of the rate constants for adsorption and desorption as 1.33 (L/mg)/day and 0.06 1/day, respectively. 3.1.5. Thiele Modulus. The relative importance between transport and reaction kinetics can be determined by the calculation of Thiele modulus (ϕn) for a reaction order n:44 ϕn = L T ·

(n + 1) ·kn·C n − 1 2D

(25)

In this study, LT is equal to half the radius of a cylinder.44 Intraparticle diffusion is considered to be negligible when the Thiele modulus is smaller than 0.4. For a Thiele modulus larger than 4, a strong diffusion limitation occurs.44 Adsorbent 1, which showed the most promising performance, was used for the calculation of the Thiele modulus. For kn, the estimated value of the adsorption rate constant (ka) was employed in the calculation. The diffusion coefficient obtained from batch seawater experiments was used, and a value of 0.63 was calculated for the Thiele modulus. This value indicates that the overall adsorption process is near the limit where the process is reaction limited. It should be pointed out, however, that the diffusion coefficient was estimated under the assumption of a transport-limited process; therefore, the value of the diffusion coefficient obtained is the lowest possible. For greater diffusivity values, the Thiele modulus becomes even smaller than 0.63, which means that the uptake process is controlled by the reaction. Since adsorption processes by polymerbased adsorbents are usually diffusion limited,3,17 further research is needed to independently obtain the diffusion coefficient of uranyl complexes and verify our calculations. 3.2. Increasing the Rate of Uranium Uptake. It is desired to increase the rate of uranium uptake, as well as the amount of adsorbed uranium at equilibrium. One way of increasing the uptake rate is by making sure that the uranium adsorption process is limited by the reaction kinetics. Another way is by increasing the uranium capacity of the adsorbent. The behavior of uranium adsorption from seawater as a function of increased capacity was simulated using batch experimental data with adsorbent 1. Specifically, after optimizing the model parameters to describe the experimental data, we assumed that the adsorbent capacity was doubled or quadrupled, and calculated the corresponding uranium uptake rate. Results shown in Figure 7 indicate that higher adsorption capacity leads to faster adsorption rates. Therefore, by increasing the adsorbent capacity, one increases also the mass of uranium recovered per unit mass of adsorbent over a fixed

Figure 5. Comparison of experimental results of amount of uranium adsorbed vs time calculated from the uranium concentration decrease in 5-gallon batch reactors using adsorbent 1 at different mixing rates.

adsorbent1 at different mixing rates. The amounts of uranium adsorbed are similar for 100 and 200 rotations per minute of the shaker, indicating that both interparticle diffusion and external mass transfer resistances are negligible under these experimental conditions. Flow-through experiments are needed to investigate further the effect of mixing, in terms of linear velocity, on the amount of uranium uptake vs time. 3.1.4. Reaction Kinetic Model. An independent batch experiment with a spiked solution of uranium was performed to estimate the adsorption rate constant using the Azizian kinetic model.26 A recent study investigated how amidoxime binds the uranyl cation.43 Different binding motifs including monodentate binding involving either the oxygen or nitrogen atom of the oxime group, bidentate chelation involving the oxime oxygen atom and the amide nitrogen atom, and η2 binding involving the N−O bond showed the most stable forms. However, more work is needed to determine a reaction pathway in a detailed manner that better represents the uranium uptake process. Until the reaction pathway is fully understood, the general approach presented by eqs 7−20 can be employed to estimate the overall reaction rate constant. Experimental data from the spiked uranium solutions of 2.52 × 10−5 M uranyl nitrate concentration were used to estimate the model parameters. Because of the relatively high uranium concentration (∼6 ppm) in these experiments, as compared to the uranium concentration (∼3.3 ppb) in seawater, it was assumed

Figure 6. Rate of amount of uranium adsorbed (left) and surface coverage change (right) for uranium uptake in spiked solution. The initial concentrations were 2.52 × 10−5 M uranyl nitrate, 2.29 × 10−3 M sodium bicarbonate, and 0.43 M sodium chloride. 9438

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observed in flow-through recycling experiments as compared with the uranium uptake in batch experiments.

4. SUMMARY AND CONCLUSIONS In efforts to accelerate the uranium uptake from seawater by amidoxime-based polymeric adsorbents, transport-limited and reaction-limited adsorption cases were evaluated to provide a better understanding of the limiting mechanism. Uranium adsorption was investigated in batch and flow-through recycling systems. Different mathematical models were evaluated for the adsorption process to determine the limiting step in the uptake process. The dimensionless Sherwood number revealed that, for batch experiments with seawater, the external mass-transfer resistance is negligible compared to the intraparticle diffusion resistance. The Thiele modulus was adopted to identify the relative importance of intraparticle diffusion and complexation reactions. Results suggested that reaction kinetics is more likely to be the rate-limiting step for the overall uranium-uptake process from seawater in batch experiments. The uranium uptake in batch experiments was higher than the uranium uptake by the supplied JAEA adsorbent over a period of 6 weeks. A lower uranium uptake was observed in flow-through recycling experiments, for the same period of time, which is attributed to increased interparticle diffusion resistance.

Figure 7. Simulated adsorption behavior using batch experimental data for adsorbent 1.

period of time. Thus, future work should focus on synthesizing adsorbents of higher uranium capacity, under the competitive environment of seawater. 3.3. Laboratory Flow-Through Recycling Experiments. Flow-through recycling experiments were also performed to investigate the uranium adsorption behavior in a flow-through recycling system. Adsorbent 1, which showed the best performance in batch experiments, was employed for flow-through recycling experiments, and the temperature and flow rate were monitored during the experiments. Experimental data of uranium uptake from seawater obtained from three separate experiments performed at different temperature and flow rate conditions are presented in Figure 8. The uranium uptake after 6 weeks reached

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected].: 865-241-3246. Fax: 865-241-4829. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was conducted at the Oak Ridge National Laboratory and supported by the U.S. DOE Office of Nuclear Energy, under Contract DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed by UT-Battelle, LLC. The JAEA adsorbent was kindly donated for testing by the Japan Atomic Energy Agency. We are also thankful to Mr. Colden Battey, NOAA/NOS/NCCOS Seawater Systems Manager, for providing seawater from the Hollings Marine Laboratory, Charleston, SC.

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REFERENCES

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Figure 8. Schematic diagram (top) and experimental data (bottom) of uranium adsorption behavior obtained from flow-through adsorption beds with adsorbent 1. Temperature: 16.4 ± 2.2 °C (Experiment 1); 23 ± 2 °C (Experiments 2 and 3). Flow rates: 288.3 ± 13.5 mL/min (Experiment 1); 273 ± 23 mL/min (Experiment 2); and 231 ± 11 mL/min (Experiment 3).

3.3 mg U/g adsorbent, which is lower than the maximum uranium uptake observed in batch experiments. This behavior is attributed to mass transfer limitations arising by interparticle diffusion through the immobilized fibrous adsorbent in a confined space. The result is that a lower uranium uptake was 9439

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