Experiments and Modeling of Uranium Uptake by Amidoxime-Based

Nov 19, 2015 - Adsorption models are also developed to describe the experimental data of uranium extraction from seawater. Results show that the ... C...
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Experiments and Modeling of Uranium Uptake by Amidoxime-Based Adsorbent in the Presence of Other Ions in Simulated Seawater A. P. Ladshaw,‡ S. Das,† W.-P. Liao,† S. Yiacoumi,‡ C. J. Janke,† R. T. Mayes,† S. Dai,† and C. Tsouris*,‡,† ‡

Georgia Institute of Technology, Atlanta, Georgia 30332-0355, United States Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6181, United States

†

ABSTRACT: Seawater contains uranium at an average concentration of 3.3 ppb, as well as a variety of other ions at either overwhelmingly higher or similar concentrations, which complicate the recovery of uranium. This report describes an investigation of the effects of various factors such as uranium speciation and presence of salts including sodium, calcium, magnesium, and bicarbonate, as well as trace elements such as vanadium on uranium adsorption kinetics in laboratory experiments. Adsorption models are also developed to describe the experimental data of uranium extraction from seawater. Results show that the presence of calcium and magnesium significantly slows down the uranium adsorption kinetics. Vanadium can replace uranium from amidoxime-based adsorbent in the presence of sodium in the solution. Results also show that bicarbonate in the solution strongly competes with amidoxime for binding uranium, and thus slows down the uranium adsorption kinetics. Developed on the basis of the experimental findings, the model is capable of describing the effects of pH, ionic strength, temperature, and concentration of various species. The results of this work are useful in the understanding of the important factors that control the adsorbent capacity and kinetics of uranium uptake by amidoxime-based adsorbents.

1. INTRODUCTION During the last few decades, poly(acrylamidoxime) (PAO) has been found to be chemically suitable for uranium recovery from seawater. PAO based adsorbents have been tested for uranium uptake from seawater in laboratory-scale1−5 as well as in natural sea.6−11 Amidoxime ligand is known to undergo complexation with various metal ions besides uranium.1,12,13 Seawater is a vast source of uranium at a relatively low concentration of 3.3 ppb.14 The presence of other ions15 (Table 1) at overwhelmingly

respectively in seawater, may act adversely by significantly decreasing the uranium adsorption capacity. A recent study by Endrizzi et al.20 reports that the ternary Ca−UO2−CO3 and Mg−UO2−CO3 species dominate the aqueous chemistry of uranium and the species, Ca2UO2(CO3)3(aq) accounts for nearly 60% of uranium. Leggett et al.21 claimed that calcium and magnesium are expected to occupy a significant fraction of the active sites of amidoxime-based adsorbents due to their overwhelmingly higher concentrations relative to uranium in seawater. Among the other metal ions present in seawater, vanadium not only reduces the uranium adsorption capacity, but it also binds so strongly that eluting this metal may irreversibly damage the adsorbent.22,23 The focus of the present work is on the investigation of effects of such parameters as uranium speciation and presence of high-concentration salts and trace elements on the uranium adsorption kinetics in batch reactors using simulated seawater environment and modeling based on the conditions of the laboratory-scale experiments.

Table 1. Concentration of Selected Elements in Seawater trace element

concentration (ppm)

element

concentration (ppm)

U V Mo Rb Li Sr

0.0033 0.0019 0.01 0.12 0.17 8.1

Na Mg Ca Cl SO4 HCO3

10752 1295 416 19345 2701 145

2. MODELING METHODS The system that we intend to model can be reasonably simplified based on the conditions of the laboratory-scale experiments. However, as we look further ahead to modeling a real uranium recovery from seawater system, we realize that the problem is extraordinarily complex. Seawater has specific solution characteristics such as pH (7.5−8.5),24 temperature (12−40 °C),25,26 complex ion speciation,18,27 and high salt

higher or similar concentrations complicates the recovery of uranium from seawater. Understanding the speciation of uranium in the seawater environment is of great importance in the development of strategies for uranium extraction from seawater. Extraction of uranium from seawater is further complicated by uranium speciation which is mainly affected by uranyl hydrolysis products and carbonate complexes including UO 2 (CO 3 ) 3 4 − , UO 2 (OH) 3 − , UO 2 (CO 3 ) 2 2 − , UO 2 + , UO2(OH)+, and UO2(OH)2 although the tricarbonate species [UO2(CO3)34−] is the most dominant form by higher abundance (∼84.9%).9,16−19 On the other hand, the presence of alkali and alkaline earth metals, especially calcium and magnesium which are present at 411 and 1290 ppm © XXXX American Chemical Society

Special Issue: Uranium in Seawater Received: September 15, 2015 Revised: November 2, 2015 Accepted: November 19, 2015

A

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research concentration (0.6−0.7 M)18,28,29 among others. The overall problem involves multispecies complexation, precipitation, phase changes, adsorption reactions, and mass transfer mechanisms and may even include biological processes. Therefore, a model to handle these complexities must be carefully designed and implemented in a piece-by-piece, or object-oriented fashion. To accomplish this task, we first divided the problem into its constituent parts and represent each part as a C++ object. For instance, since our problem will clearly involve chemical speciation reactions and several mass balances, we have devised and developed different objects to handle the tasks associated with each different chemical subproblem. Each object will have an independent residual equation that must be resolved with each other objects’ residual equations. Then, the culmination of all those objects and equations will be used to form the overall residual function that will be fed into a nonlinear solver routine, which will find the solution to all variables simultaneously. The underlying solver routine was based on the JacobianFree Newton Krylov (JFNK) method,30 because it is tremendously efficient compared to traditional Newton methods that require use of the full Jacobian matrix. Linear subproblems for the nonlinear iterations are then solved using either GMRES31 or GMRESR32 depending on the problem size and whether or not a linear preconditioner was supplied to the routine. Our implementation of the JFNK method also includes a simple backtracking line search subroutine33 to ensure smooth convergence of the nonlinear system. For the laboratory-scale model, we decided to represent the adsorption of uranium by amidoxime-functionalized fibers as standard metal−ligand complexation reactions34 coupled with speciation reactions between all involved species in solution with mass balances between the major species’ groups (i.e., uranium, carbonate, nitrate, etc.). To account for ionic strength, we used the Davies activity model,35 which is used to account for nonidealities in solutions with ionic strengths up to 0.5 M. The time evolution of adsorption uses a simple unsteady version of the metal−ligand complexation reactions between uranyl and carbonate ions and the amidoxime ligands (eqs 1 and 2). Those reaction equations would then formulate the rate expressions for adsorption of the uranium (eqs 3 and 4). Although this formulation of the problem idealizes the actual kinetics of adsorption, it will allow us to implicitly include the effects of carbonate concentration and pH into the overall adsorption model. UO22 + + A(OH)2 ⇔ UO2 AO2 + 2H+

involving uranium, nitrate, and carbonate. Note that reactions involving sodium (Na+) and/or chlorine (Cl−) are not shown here. This is because those complexes will typically dissociate completely and are generally only important for ionic strength and electroneutrality calculations. (5)

UO22 + + 3H 2O ⇔ UO2 (OH)−3 + 3H+

(6)

2UO22 + + 2H 2O ⇔ (UO2 )2 (OH)22 + + 2H+

(7)

3UO22 + + 5H 2O ⇔ (UO2 )3 (OH)+5 + 5H+

(8)

UO22 + + NO−3 ⇔ UO2 NO+3

(9)

UO22 + + 2NO−3 ⇔ UO2 (NO3)2

(10)

UO22 + + CO32 − ⇔ UO2 CO3

(11)

UO22 + + 2CO32 − ⇔ UO2 (CO3)22 −

(12)

UO22 + + 3CO32 − ⇔ UO2 (CO3)34 −

(13)

HNO3 ⇔ H+ + NO−3

(14)

H 2CO3 ⇔ H+ + HCO−3

(15)

HCO−3 ⇔ H+ + CO32 −

(16)

UT = [UO22 +] + [UO2 OH+] + [UO2 (OH)−3 ] + 2[(UO2 )2 (OH)22 + ] + 3[(UO2 )3 (OH)+5 ] + [UO2 NO+3 ] + [UO2 (NO3)2 ] + [UO2 CO3] + [UO2 (CO3)22 − ] + [UO2 (CO3)34 − ] + [UO2 AO2 ] + [UO2 CO3AO22 − ]

(17)

NT = [NO−3 ] + [HNO3] + [UO2 NO+3 ] + 2[UO2 (NO3)2 ] (18)

CT = [CO32 −] + [HCO−3 ] + [H 2CO3] + [UO2 CO3] + 2[UO2 (CO3)22 − ] + 3[UO2 (CO3)34 − ] + [UO2 CO3AO22 − ]

(1)

(19)

A T = [A(OH)2 ] + [UO2 AO2 ] + [UO2 CO3AO22 − ]

UO22 + + CO32 − + A(OH)2 ⇔ UO2 CO3AO22 − + 2H+ (2)

(20)

Each of these reactions and mass balances will contribute residual functions for the solver routine to work on. That routine solves the speciation/complexation reactions at each discrete time step for the transient problem. To step the simulation through time, we used a standard implicit discretization technique for greater numerical stability. While the routine is intended to run unsteady problems and seek out the system pH using the electroneutrality condition, it can also be run as a steady state simulation and/or hold the system pH constant to a specified value. Additionally, since the major speciation reactions are equilibrium reactions, the model is also implicitly temperature dependent since the stability/dissociation constants are related to temperature through the van’t Hoff relationship.

d{UO2 AO2 } = k f,1{UO22 +}{A(OH)2 } − k r,1{UO2 AO2 }{H+}2 dt (3) d{UO2 CO3AO22 − } = k f,2{UO22 +}{CO32 −}{A(OH)2 } dt − k r,2{UO2 CO3AO22 − }{H+}2

UO22 + + H 2O ⇔ UO2 OH+ + H+

(4)

To finish the construction of this speciation and complexation model, we must add in the equilibrium reactions between all the ions in solution and provide mass balances for all the major species. Equations 5−20 below outline the most important reactions and mass balances for an aqueous system B

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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3. EXPERIMENTAL METHODS 3.1. Adsorbent Preparation. Adsorbent fibers were prepared by radiation-induced graft polymerization (RIGP) at the NEO Beam Electron Beam Cross-linking Facility (Middlefield, OH), as described by Das et al.36 Prior to irradiation, the polylactic acid (PLA) that was coextruded with the polyethylene trunk fibers was removed by submerging the fibers in excess tetrahydrofuran (THF) at 60 °C overnight. The preweighed dry fiber samples were irradiated with the electron beam for 16 passes to a dose of approximately 200 ± 10 kGy using 4.4−4.8 MeV electrons and 1 mA current from an RDI Dynamitron electron beam machine. After irradiation, the fibers were immersed in a 300 mL flask containing previously degassed grafting solutions consisting of acrylonitrile (AN) and itaconic acid (ITA) in dimethyl sulfoxide and were then placed in an oven at 64 °C for 18 h for grafting. After grafting, the fibers were washed with N′, N′ dimethylformamide DMF to remove unreacted monomers and homo polymers, followed by rinsing with methanol and dried at 50 °C under vacuum. The nitriles in the grafted fiber (AF1) samples were converted to amidoxime (AO) by reaction with 10 wt % hydroxylamine hydrochloride in 50/50 (w/w) water/methanol at 80 °C for 72 h. The samples were then washed under vacuum filtration with deionized water followed by a methanol rinse and allowed to dry at 50 °C under vacuum. The amidoximated AF1 fibers were treated with 0.44 M KOH solution at 70 °C for 1 h. The KOHtreated samples were immediately filtered and washed with DI water until the pH was neutral, and then used for the uranium adsorption study. 3.2. Batch Reactor Experiments with Deionized Water. 3.2.1. Speciation Effect. AF1 adsorbents (∼8 mg), conditioned with 0.44 M of KOH at 60 °C for 1 h, were added into three 5 gal plastic containers with deionized water, where adsorbent fibers were freely suspended. Deionized water in container 1 was spiked only with 10 ppm uranium in the form of nitrate. Sodium bicarbonate (140 ppm) was added along with 10 ppm uranium, in the form of nitrate, in container 2. Sodium chloride (0.43 M) was added in container 3 in addition to uranium nitrate and sodium bicarbonate at similar concentrations as in containers 1 and 2. The concentrations of sodium bicarbonate and sodium chloride were maintained as those in seawater. After adsorbent fibers were brought in contact with the solution, the experiments continued for a period of 57 days. During this period, samples of the solution were periodically taken to determine the uranium concentration vs time. 3.2.2. Effect of Presence of Other Cations. 3.2.2.1. Replacement of Uranium by Vanadium. Vanadium in the form of sodium orthovanadate (Na3VO4) was added in the 5 gal plastic containers, after completion of the experiments mentioned in section 3.2.1. The objective was to investigate possible replacement of uranium adsorbed by the AF1 adsorbent by vanadium. These experiments lasted for another 43 days. 3.2.2.2. Competitive Adsorption of Uranium and Vanadium. AF1 adsorbents (∼15 mg), conditioned with 0.44 M of KOH at 70 °C for 1 h, were added into 1 L plastic bottles with deionized water, with constant shaking. In one set of experiments, the adsorption of uranium was studied in deionized water having 75 ppm uranium in the presence and absence of NaCl and NaHCO3. In another set of experiments, the adsorption of uranium was studied in deionized water having 75 ppm uranium and 45.5 ppm vanadium in the

presence and absence of NaCl and NaHCO3. These studies were carried out for a total period of 311 h. 3.2.2.3. Effect of Calcium and Magnesium. A study of the effect of calcium and magnesium on uranium adsorption was conducted using 1 L plastic bottles containing deionized water and 15 mg AF1 adsorbent fibers conditioned with KOH at 70 °C for 3 h. The AF1 fiber samples were equilibrated for 360 h under constant shaking at room temperature with deionized water solution which was spiked with 75 ppm uranium, 45.5 ppm vanadium, 140 ppm sodium bicarbonate, or 0.43 M sodium chloride, with or without adding calcium (411 ppm) and magnesium (1290 ppm). 3.2.3. Effect of Bicarbonate Concentration. The study of the effect of bicarbonate concentration was carried out in 1 L bottles containing deionized water spiked with 0.43 M sodium chloride, 75 ppm uranium nitrate, and different concentrations of sodium bicarbonate (i.e., 0, 35, 70, and 140 ppm). AF1 adsorbent fibers (∼8 mg), conditioned with 0.44 M of KOH at 70 °C for 1 h, were added into 1 L plastic bottles, which underwent constant shaking at room temperature over a period of 28 days. In all of the batch reactor experiments, an initial sample of one milliliter was collected prior to addition of adsorbent. The containers were shaken constantly at 100 rpm at room temperature. This agitation speed was proven sufficient for fluidized fibers to adsorb uranium in the reaction-limited regime, in the presence of bicarbonate ions.7 One-milliliter aliquot samples were collected periodically over the whole period. The quantitative analysis of the aliquots was carried out using inductively coupled plasma mass spectroscopy (ICP-MS, Thermo Scientific X-Series II). 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. An internal standard solution containing Bi, In, Sc, Tb, and Y (High Purity Standards ICP-MS-IS-2, PerkinElmer) was added to eliminate the matrix effect. High-purity nitric acid (2%, Optima, Fisher Scientific) was used as the sample diluent and carrier phase and for wash out of the instrument, which was monitored between samples. The average of six replicate measurements per sample was used to quantify uranium-238 against a 6-point calibration curve. The standards, NASS-5 (seawater) and CASS-6 (seawater) supplied by the National Research Council of Canada, were used for seawater qualitycontrol experiments.

4. RESULTS AND DISCUSSION 4.1. Effect of Uranium Speciation. Uranium speciation has a strong effect on the adsorption kinetics. The results of 5 gal batch reactor experiments on the effect of different uranium speciation on adsorption by AF1 adsorbent fibers are demonstrated in Figure 1. The uranium uptake kinetics from solution spiked only with uranyl nitrate is very fast. On the other hand the kinetics is slowed down after addition of sodium bicarbonate and sodium chloride, indicating that (i) salinity plays an important role on adsorption kinetics and (ii) bicarbonate strongly competes with amidoxime for uranium binding. 4.2. Effect of the Presence of Other Cations. Comparisons of uranium uptake by AF1 adsorbent fibers from the solutions in the presence or absence of vanadium, along with or without salt and bicarbonate, are shown in Figure 2, where the normalized uranium concentration, i.e., the ratio of uranium concentration at any time over the initial uranium C

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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sodium chloride, or any other major salt, may have a dramatic impact on the activities of other species and, in general, will lower their activities. This is also demonstrated in Figure 1 in which a reduction in uranium adsorption, simply by adding salt to the solution, can be seen. An investigation of the effect of the charge balancing ions, i.e., calcium and magnesium, on uranium adsorption was carried out in deionized water in the presence of vanadium, sodium chloride, and sodium bicarbonate. The concentrations of uranium and vanadium were 75 and 45.5 ppb (at the same ratio as in seawater, i.e., 3.3 ppb uranium to 1.9 ppb vanadium). The concentrations of other ions were adjusted exactly to those in seawater. The results of this study are summarized in Figure 4. The uranium adsorption kinetics was significantly slowed down in the presence of calcium and magnesium as compared to vanadium. The uranium adsorption equilibrium in the presence or absence of vanadium was reached in approximately 5 days, but on the other hand, it took approximately 10 days for the adsorption to reach equilibrium in the presence of calcium and magnesium. Thus, it can be hypothesized that calcium and magnesium occupied a significant fraction of sites in the amidoxime-based adsorbent due to their overwhelmingly higher concentrations relative to uranium. 4.3. Effect of Bicarbonate Concentration. An investigation for the effect of bicarbonate on uranium adsorption was also conducted by keeping the uranium concentration constant (75 ppb) and varying the bicarbonate concentration in the solution (from 0 to 140 ppm of HCO3− by adding NaHCO3). The results of this study are illustrated in Figure 5. As can be seen in the figure, increasing the bicarbonate concentration in the solution gradually slowed the uranium adsorption kinetics down. This observation suggests that bicarbonate effectively competes with amidoxime ligand on the AF1 adsorbent for uranium complexation in seawater conditions.38 4.4. Model Calibration. To model the lab scale experiments, we need to have all the necessary chemical parameters that describe the system. These parameters include equilibrium constants for the speciation reactions from eqs 5−16, as well as the rate constants for the metal−ligand complexation reactions from eqs 3 and 4. For the basic speciation reactions (eqs 5−16), the equilibrium parameters can be found recorded in various literature sources.35,37 However, the thermodynamic and kinetic parameters for amidoxime complexation are not known. Therefore, those parameters are calibrated for based on the experimental data. For parameter calibration, we used three of the 5 gal batch experimental data sets to find the optimum equilibrium and kinetic parameters for eqs 1−4. These experiments all used about 10 ppb of uranium with 8 mg of amidoxime fibers (Figure 1b). The experiment which did not involve carbonate in the system (blue diamonds: Figure 1b) will be used to find the parameters for eqs 1 and 3, while the experiments with 140 ppm of sodium bicarbonate, both with (red squares: Figure 1b) and without 0.43 M of NaCl (green triangles: Figure 1b), will be used to find the parameters for eqs 2 and 4. Ideally, all experiments should be describable from the same set of equilibrium and kinetic parameters. Calibration of the equilibrium constant for eq 1 is fairly straightforward. This parameter is varied until we see an agreement between the model’s steady-state solution and the projected adsorption equilibrium of 23.5 mg-U/g-adsorbent. However, to calibrate the kinetics of the model requires a more detailed analysis of the data. We know that the reaction kinetics

Figure 1. Kinetics of uranium uptake by AF1 adsorbent from different solutions having different uranium species: (a) concentration measurements of solution samples; (b) uranium uptake by the adsorbent vs time calculated through a mass balance. The initial concentration of uranium in all solutions was 10 ppb.

concentration, is plotted vs time. The results indicate that the uranium adsorption kinetics is not significantly affected by the presence of vanadium, but does so in the presence of salt and bicarbonate. However, as it is reported that polyamidoxime has a strong affinity for vanadium,22,23 we decided to add vanadium to a completed 5 gal batch reactor experiment, as described in section 3.2.2.1, to see whether vanadium can replace uranium from the AF1 adsorbent. In the beginning, 2 ppb vanadium (Na3VO4) was added after the completion of the experiment mentioned in section 3.2.1, and the concentration of uranium in the solution was monitored for 20 days. It was realized that uranium was still adsorbed by the fibers with a slower rate, and 2 ppb vanadium was not enough to desorb uranium from the fibers (Figure 3). Therefore, the concentration of vanadium added was increased to 75 ppm after 20 days. It is interesting to see that uranium continued to be adsorbed from the solution in the reactors containing uranyl nitrate alone and uranyl nitrate with sodium bicarbonate. In the reactor that contained sodium chloride, on the other hand, adsorbed uranium appeared to desorb, and its concentration increased in the solution. Although vanadium speciation is not known, these data suggest that sodium ions play a role in binding of vanadium with amidoxime and replacing uranium on the adsorbent. Sodium ions may not be involved directly in the reactions between vanadium, uranium, and amidoxime; however, the concentration of sodium ions in solution contributes significantly to the ionic strength of the solution. Therefore, the presence of D

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Figure 2. Effect of the presence of vanadium, along with or without salt and bicarbonate, on uranium adsorption kinetics. The uranium concentration at any time over the initial uranium concentration is plotted vs time.

Figure 3. Continuation of the experiment described in section 3.2.1 with addition of vanadium at concentration of 2 ppb for first 20 days and 75 ppb for last 23 days. Figure 5. Kinetics of uranium uptake by AF1 adsorbent from deionized water in the presence of different concentrations of bicarbonate. The uranium concentrations were kept constant as 75 ppb.

of uranyl with amidoxime, in the absence of carbonate, is very fast,2 but the data show a sharp uptake after 1 day, which is then followed by a slow, gradual increase in adsorption capacity over time (blue diamonds: Figure 1b). This indicates that the initial adsorption on the outer surface of the adsorbent fiber is likely reaction controlled, but the long-term adsorption of uranyl into the fiber is diffusion controlled. To model this data more accurately, we devised a 2-part model in which the adsorption from experiment start to end of day 1 consisted of only the reaction expression from eq 3. Then, after that initial loading, it is assumed that intraparticle diffusion dominates the kinetic uptake of uranyl ions. The diffusion portion of the model was done using a cylindrical diffusion equation where the concentration on the outer edge

Figure 4. Kinetics of uranium uptake by AF1 adsorbent from deionized water in the presence of vanadium and/or calcium and magnesium. E

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research of the cylinder is assumed constant (eq 21).39 In this model, a is the radius of a single fiber, D is the diffusion coefficient of uranyl through the polyethylene, q(t) and qe are average fiber adsorption and equilibrium adsorption respectively, and αn are roots of the zero order Bessel function, Jo(aαn) = 0. The results of the calibrated reaction kinetic model and combined reaction/diffusion model are shown in Figure 6, and

Figure 7. Comparison between the complexation reaction models for adsorption and the data collected in 5 gal batch reactors (Figure 1b) with and without salt present. The total carbonate and uranium concentrations were 140 ppm and 10 ppb, respectively.

between the models’ optimum values with and without salt present are likely caused by errors introduced by the activity model. In both cases, the systems have the same uranium, carbonate, and amidoxime concentrations, but the introduction of NaCl into the system has a significantly raised the ionic strength. Therefore, the only difference mathematically between the two models would be the activity coefficients determined through the Davies activity model. Since the Davies model is a semiempirical activity model that only calculates the average activity of each charged species in solution, it is possible that this is the primary cause of error in the model for this set of simulations. 4.5. Model Validation. After calibrating the model with the experimental data from the 5 gal experiments, we can use the optimal parameters to try to predict the behavior of the system at different conditions, i.e., different uranium and carbonate concentrations, as a validation step for our model. For this validation, we modeled attempted to predict the data observed in the 1 L system containing 0.43 M of NaCl, 75 ppb of uranium, 8 mg of amidoxime fibers, and various concentrations of carbonate (Figure 5). These predictions were based solely on our kinetic model described in eqs 1−20 and the parameters from Table 2. Figure 8 shows the comparisons between the experimental data and the model predictions based on the calibrations with the 5 gal experiments. The model performed reasonably well to predict the aqueous uranium removal at a carbonate concentration of 35 and 70 ppm. Additionally, we can also see that the model qualitatively responded correctly to the stimuli: (i) faster overall kinetics, compared to the 5 gal experiments, when uranium levels were increased and (ii) a reduction in the removal rates as the carbonate concentration increases. However, the model predictions at 140 and 0 ppm showed kinetics that were too slow and too fast, respectively, resulting in a relatively poor overall prediction of the system at all conditions. There are two possible explanations for the errors observed between our model and the data in Figure 8: (i) as the carbonate concentration decreases, the controlling uptake mechanism switches from reaction controlled to diffusion controlled, as demonstrated in Figure 6, or (ii) the simple rate equations derived for the complexation reactions with

Figure 6. Comparison between experimental data [from Figure 1b, with UO2(NO3)2] and the reaction-based and reaction/diffusion models. Results indicate that in the absence of carbonate, long-term uranyl uptake is primarily intraparticle-diffusion controlled.

Table 2. Summary of Model Parameters equation/model eqs 1 and 3 eqs 2 and 4: no salt eqs 2 and 4: 0.43 M NaCl eqs 2 and 4: averaged equation/model eq 21

log(K) −1.35 3.45 3.45 3.45 D μm2/h 1.05

kf (L/mol)m/h 4.50 × 106 5.75 × 1015 8.90 × 1015 7.30 × 1015 a μm 76.5

parameters used for this model are detailed in Table 2. These results clearly suggest that when carbonate is not present, reaction kinetics is extremely fast and the overall uptake of uranium becomes primarily controlled by long-term intraparticle diffusion. Additionally, we see that by combining both reactions and diffusion into the model, we can significantly improve the model’s description of the experimental data. Five gallon experiments with bicarbonate (Figure 1b) were used to calibrate the model parameters associated with the uranyl, carbonate, and amidoxime complexation reactions of eqs 2 and 4. While the optimum equilibrium parameters from each data set were found to be the same, the optimum kinetic parameters did vary slightly with salt content. To create a single set of parameters for all data sets used, a weighted average of the kinetic parameters optimized for the experiments both with and with out salt was created. All of the model parameters are summarized in Table 2. q(t ) =1− qe

∞

∑ n=1

4 exp( −Dαnt ) (aαn)2

(21)

Figure 7 shows the comparison between the complexation reaction models’ with the experimental data both with and without added salt. The solid lines show the optimized model, while the dashed lines show the averaged model. Discrepancies F

DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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From these results, we have a clear path forward for improvement of the model, but we also are able to show the strengths of this model as well. By representing the system with its full suite of species and thermodynamic speciation constants, the model is capable of implicitly including the effects of pH, ionic strength, temperature, and concentration of each species. This capacity was demonstrated through the model’s kinetic results when the system parameters were altered from Figures 6 to 7 to 8. When uranium concentration increased from 10 ppb (Figures 6 and 7) to 75 ppb (Figure 8), the uptake kinetics became much faster, as indicated by the time scales on the figures. Additionally, when the carbonate concentration was reduced (Figure 8), the model responded accordingly and showed an increase in the rate of uranium adsorption. Therefore, the model does respond qualitatively correctly to external stimuli and only needs to include new objects to represent mass transfer effects and reaction mechanisms to fully describe our system.

Figure 8. Comparison between model predictions and experimental data at various carbonate concentrations. The model predicts the 35 and 70 ppm bicarbonate experimental data fairly well, but overestimates the kinetics at 0 ppm and underestimates the kinetics at 140 ppm.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. amidoxime are too much of a simplification of the actual adsorption reaction kinetics. We know from our analysis of the data in Figure 6 that the diffusion process becomes dominant when no carbonate is present. Therefore, intraparticle diffusion may still be important even at low carbonate concentrations, which will contribute to the errors observed in the model results at 0 ppm of carbonate. Other errors are most likely introduced by our model only considering an overall, unsteady complexation reaction (eqs 3 and 4) instead of a reaction mechanism. A better model would probably be to represent the adsorption process based on an actual adsorption mechanism coupled with intraparticle diffusion. Such a model is a topic for future work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was sponsored by the US department of Energy, Office of Nuclear Energy. Notice: This manuscript has been authored by UT-Battelle, LLC, under Contract No. DE-AC0500OR22725 with the U.S. Department of Energy. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. The Department of Energy will provide public access to these results of federally sponsored research in accordance with the DOE Public Access Plan (http://energy. gov/downloads/doe-public-access-plan).

5. CONCLUSIONS Investigations on different parameters affecting the kinetics of uranium adsorption from seawater were successfully demonstrated experimentally and theoretically. The speciation study revealed that bicarbonate strongly competes with amidoxime sites for uranium binding and, thus, slowed down the uranium adsorption kinetics. The uranium uptake kinetics was initially much faster in the absence of bicarbonate, and gradually decreased with increasing bicarbonate concentration in the solution. The presence of calcium and magnesium in the solution is more severe in slowing down the uranium uptake kinetics, as compared to the presence of vanadium. However, vanadium was able to replace adsorbed uranium in the presence of sodium salt in the solution. Although our simple kinetic model worked well to describe the uranium uptake kinetics in the 5 gal experiments, it was less adequate of accurately modeling systems in the absence of carbonate, where diffusion became important. Therefore, we must include intraparticle mass transfer effects into the overall model. Additionally, we have shown that this simplified kinetic model did not perform well to quantitatively predict all of the 1 L experiments. This may be partially attributed to the lack of diffusion mass transfer in the model, but may also be attributable to the oversimplification we made in the representation of the reaction kinetics from the complexation reactions in eqs 3 and 4, instead of using a reaction mechanism for the kinetics.

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SYMBOLS kf,r = forward/reverse reaction rates for unsteady reactions UT = total uranium concentration in system CT = total carbonate concentration in system NT = total nitrate concentration in system AT = total amidoxime concentration in system q(t) = average uranyl adsorption on the fibers qe = equilibrium adsorption capacity for uranyl a = single fiber radius D = intraparticle diffusivity for uranyl in polyethylene αn = roots of the zero order Bessel function, Jo(aαn) = 0 m = exponent for the units of the reaction rate constants REFERENCES

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DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

Article

Industrial & Engineering Chemistry Research

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DOI: 10.1021/acs.iecr.5b03456 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX