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Computer-assisted design and experimental validation of multielectrode electrorefiner for spent nuclear fuel treatment using a tertiary model
Nuclear Engineering and Design 257 (2013) 12–20
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Computer-assisted design and experimental validation of multielectrode electrorefiner for spent nuclear fuel treatment using a tertiary model Seung Hyun Kim a,1 , Sung Bin Park b,2 , Sung Jai Lee b,3 , Jeong Guk Kim b,4 , Han Soo Lee b,5 , Jong Hyeon Lee a,c,∗ a
Graduate School of Green Energy Technology, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea Korea Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea c Department of NanoMaterials Engineering, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea b
h i g h l i g h t s
We simulate laboratory scale electrorefiner for spent nuclear fuel. 19 kg/24 h of uranium is theoretically attainable with 100 mA/cm2 for 24 h. Polarization behaviors of the electrorefiner well agree with simulation results. Anodic overpotential is found to be larger than that of cathode.
a r t i c l e
i n f o
Article history: Received 6 September 2012 Received in revised form 16 January 2013 Accepted 19 January 2013
a b s t r a c t It is important to understand electrochemical phenomena in order to design an electrorefiner system suitable for pyroprocessing, particularly one equipped with complicated electrodes. Computer simulation of the electrochemical cells is an effective tool for the visualization of processing parameters such as the potential distribution, current density, and concentration profile. The electrochemical parameters considered in this study are the exchange current density distribution and electrode arrangement. The application of a numerical model to design an electrorefiner for spent metallic nuclear fuel is discussed with respect to throughput, impurity contamination, and operating mode. A commercial finite element method package was used. In addition, calculations of the tertiary current density and an experimental validation of these results are presented. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The Korea Atomic Energy Research Institute (KAERI) has been developing pyroprocessing methods since 1997. By 2006, concept development, bench-scale testing, and laboratory-scale key unit process demonstrations had been conducted (Song et al., 2010; Lee et al., 2011). Electrorefining is one of the key steps in efficient pyrochemical recycling of metalized spent nuclear fuel; efficiency
∗ Corresponding author at: Graduate School of Green Energy Technology, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea. Tel.: +82 42 821 6596; fax: +82 42 822 5850. E-mail addresses: [email protected] (S.H. Kim), [email protected] (S.B. Park), [email protected] (S.J. Lee), [email protected] (J.G. Kim), [email protected] (H.S. Lee), [email protected] (J.H. Lee). 1 Tel.: +82 42 821 7632; fax: +82 42 822 5850. 2 Tel.: +82 42 868 2523; fax: +82 42 822 2080. 3 Tel.: +82 42 868 8650; fax: +82 42 822 2080. 4 Tel.: +82 42 868 8650; fax: +82 42 822 2080. 5 Tel.: +82 42 868 2395; fax: +82 42 822 1236. 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.01.009
is important because of the large volumes of uranium that must be treated. However, throughput enhancement is not an easy task, especially when sufficient separation efficiency in a hightemperature molten salt environment is necessary. To increase the throughput, 24 graphite cathodes were installed in the current laboratory-scale electrorefiner (with a recovery rate of 20 kg of heavy metal per day), as shown in Fig. 1 (Lee et al., 2009). The anode was designed for up to 50 kg of heavy metal to be loaded into anode baskets to decrease the anode overpotential. On the basis of the experimental results, a new electrorefiner is being designed at KAERI, and the recovery of 50 kg of heavy metal per day is expected to be demonstrated in 2012. Considering the design requirements of a high-throughput electrorefiner and the need for easy loading of fuel into the anode, a new, efficient cathode configuration should be investigated. Computer simulation of electrochemical cells is an effective tool for the optimization of the electrorefining process. Several researchers have reported numerical methods for simulating the electrorefining process of spent nuclear fuel. Bae analyses revealed the three-dimensional analysis of deposition rate, in couple with
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Fig. 1. Schematic view of high-throughput electrorefiner and geometries for numerical analysis. (a) Mesh for CV and LSV calculation, (b) laboratory-scale electrorefiner, and (c) geometry for numerical analysis.
the one-dimensional electrochemical analysis model, REFIN in PEACER as the lead–bismuth cooled fast reactor fuel cycle (Bae et al., 2010). Also Choi investigated the three-dimensional simulation of multispecies and multi-reaction electrorefining by using the fluid-dynamics code (Choi et al., 2010, 2011). Kim analyzed concentration and current distribution by coupling the Butler–Volmer equation with subroutine which was enabled by using CFX and REFIN codes. Electro-fluid analysis on molten salt in an electrorefiner was carried out and discussed with respect to the recovery of pure uranium when thermochemical data are used (Kim et al., 2009, 2010). Nawada numerically simulated the electrotransport behavior of uranium and plutonium in a molten salt with an improved thermochemical model (Nawada and Bhat, 1998). Shibuta predicted uranium dendrite growth on the cathode by using a novel phase-field model, in which the electrodeposition of uranium and zirconium in the molten salt occurred (Shibuta et al., 2011). Also Hoover estimated changes in current density of anode and cathode and the polarization characteristics in relation to various operating conditions in the electrorefining process by using ORIGEN code and utilized it for estimation of Mark-IV electrorefiner operation (Hoover et al., 2009). Before the construction of the current laboratory-scale electrorefiner, the fundamental electric field and metal ion movement were examined using the primary current density model (Lee et al., 2008; Oh et al., 2009). However, a more reliable and practical model is necessary to predict the electrodeposition and separation behaviors of the system, which are needed for complicated electrode configurations. The growth characteristics of uranium deposits are also a cause for concern in high-throughput electrorefiners, which have a compact electrode arrangement within a cell, because electrical short circuit can occur if deposits are not removed at an appropriate time. In this paper, numerical analysis of a high-throughput electrorefiner was performed by using a commercial finite element method code, namely, COMSOL multiphysics software (COMSOL, 2012). A tertiary current density model was applied to evaluate the performance of the laboratory-scale electrorefining cell, in particular the throughput and separation behavior, and to predict the amount of deposition on multiple cathodes at different distances from the anode. Also, to predict short circuit time by dendritic growth of uranium on the cathode surface, a moving mesh was used with the bulk density of uranium dendrite. This approach should be useful to design a compact electrorefiner which is operated in a limited area such as a hot cell. The calculated polarization behavior and the uranium deposit growth were validated using experimental data obtained from uranium electrorefining.
2. Theory of laboratory-scale electrorefiner modeling 2.1. Fundamental theory The concentration change in an electrorefiner is the sum of the changes due to diffusion, convection, and migration, and is given by the so-called tertiary model as
∂C ∂t
=
∂C ∂t
+ diffusion
∂C ∂t
+ convection
∂C ∂t
(1) migration
The concentration gradient normal to the electrode surface is significantly larger than that in the lateral direction. Thus, the concentration gradient normal to the electrode surface controls the direction and speed of mass transfer near the electrode surface (Brett and Brett, 1993; Britz, 2005). In this calculation, chemical reactions of the electrolyte in the solution were not considered. In addition, convection terms were ignored because there was no vigorous agitation during the actual electrorefining experiments. The local current density is expressed by a modified Butler–Volmer equation with concentration-dependent terms, as shown in Eq. (2) (Bard and Faulkner, 2001; Pickett, 1979). The set of equations solved by the COMSOL Electrodeposition modules was the Butler–Volmer equations in their conservation form. This means that for a lower surface concentration (Cs ≤ Cbulk ) at the electrode surface, a higher overpotential () is necessary to achieve the same current density.
iloc = i0
COS CObulk
˛F
CRS
RT
CRbulk
exp −
−
exp
(1 − ˛)F RT
(2)
In Eq. (2), F is Faraday’s constant, R is the gas constant, is the overpotential, and ˛ is the charge transfer coefficient. The superscripts s and bulk refer to locations at the electrode surface and in the bulk electrolyte, respectively. The subscripts O and R indicate the oxidized and reduced species, respectively, and i0 is the exchange current density. The potential–current responses such as CV, LSV and I–V curve were simulated as shown in Eq. (2). To consider multiple components in CV, three elements, namely, zirconium, hafnium and uranium were considered in this calculation; the boundary conditions and material parameters are listed in Tables 1–3. The currents induced by each element were calculated at the cathode electrode, and the obtained currents were then summed to calculate the total current as follows: itotal =
n k=1
k iloc
(3)
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Table 1 Boundary condition and parameters. Anodic transfer coefficient Cathodic transfer coefficient Diffusion coefficient, Do (Martinet and Calligary, 1973) Initial concentration of A Initial concentration of B Scan rate Reduction potential (V vs. Ag(|)/Ag(0)) (Martinet and Calligary, 1973)
Table 3 Parameters for comparison with actual polarization curves. 0.5 0.5 U(III)7e−10 at 450 ◦ C, U(III)1.03e−9 m2 /s at 500 ◦ C 1 mol/m3 0 mol/m3 0.1, 0.4, 0.8 V/s Zr (−1.11 V), Hf (−1.24 V), U (−1.86 V)
where itotal is the final current induced by each element, and k is the component number. 2.2. Geometry and mesh for simulation of laboratory-scale electrorefiner The tertiary model should describe the fundamental electrochemical behaviors when the correct model equations are used. The model was validated using a single-electrode geometry, which is generally used for cyclic voltammetry (CV) before the model is applied to a high-throughput electrorefiner. This numerical analysis was based on a 2D model to minimize the calculation resources required because of the symmetrical geometry of the 2D model. To achieve linear sweep voltammetry (LSV) and CV in the electrolyte, the potential variations were defined as a function of time on the surface of the electrode as follows. To calculate the amount of uranium deposited at the cathode electrode, the local current density was integrated over the cathode surface area and then multiplied by the electrochemical equivalent of uranium (2.96 gA−1 h−1 ). The electrode and electrolyte were meshed with tetragonal boundary layer elements. Fig. 1(a) shows the 2D meshed geometry of the computational domain used for the CV and LSV simulations. Fig. 1(b) and (c) shows a photograph of the high-throughput electrorefiner and its simplified geometry, respectively. Two cathodes and the part of the anode surface facing the cathodes were considered because the cathodes are uniformly arranged around the electrorefiner. 3. Results and discussion The deposition behavior of uranium at the cathode electrode was studied to determine the optimum operating mode. Subsequently, the macroscopic deposition behavior of uranium and the electrochemical responses were studied to estimate the total throughput and proper scraping time of the electrochemical system in the laboratory-scale electrorefiner. 3.1. Verification of model using cyclic voltammetry and linear sweep voltammetry As described above, a series of simulations of the fundamental electrochemical response of the electrorefiner was conducted. Table 1. lists the boundary conditions used in these simulations. Time-dependent analysis of the electrochemical system was performed using the COMSOL Electrodeposition module code. To
Anodic transfer coefficient Cathodic transfer coefficient Diffusion coefficient, Do (Martinet and Calligary, 1973) Initial concentration Exchange current density Ion mobility Applied current Operating temperature
0.5 0.5 6.8e−10 m2 /s (450 ◦ C), 1.03e−9 m2 /s (500 ◦ C), 1.36e−9 m2 /s (550 ◦ C) 500 mol/m3 15 mA/cm2 4.036e−11 S mol/kg 50, 100, 150 A 450 ◦ C, 500 ◦ C, 550 ◦ C
develop a comprehensive modeling approach, CV results were first obtained assuming that three elements having different properties, such as diffusion coefficient, and reduction potential are dissolved in a molten salt. The elements considered in this study were zirconium(III), hafnium(IV), uranium(III). Fig. 2 shows the calculation results of the CV simulation in terms of the (a) reduction potential (E0 ), (b) diffusion coefficient, and (c) scan rate. These results clearly show that the response is similar to that of an actual electrode cell. As the voltage decreased from 2 V to −2.5 V over time at the different reduction potentials from zirconium(III), hafnium(IV), uranium(III), the reduction current appeared when the oxidant was reduced at the equilibrium potential and began to decrease after it reached the peak current (ip ), as shown in Fig. 2(a). When a reverse potential was applied, the reduced substance began to oxidize at the electrode surface, which generated an anodic current. It was confirmed that this anodic current decreased again after it reached its maximum value. Fig. 2(b) shows the calculated CV according to the difference diffusion coefficient from uranium (Martinet and Calligary, 1973). The magnitude of the electric current during CV measurement is due to mostly diffusional concentration changes as defined by Eq. (1). Therefore, a higher diffusion coefficient induces a higher peak current, as shown in Fig. 2(b). As the potential sweep rate increased at the reduction potential of uranium (–1.8 V), the peak current height increased, as shown in Fig. 2(c), which is also an indicator of the reliability of the model. The changes in the concentrations of the oxidant and reductant during the CV simulation at the surface of the working electrode are depicted in Fig. 2(d). This graph was designed to show whether the oxidation–reduction reaction is implemented properly on the electrode surface depending on the concentration; it shows that when working electrode was applied with change of voltage from 2 V to −2 V for 20 s, the initial uranium ions (1 mol) were reduced to uranium metal with the concentration decreasing as time passed; however, when the potential was forced in the opposite direction, the uranium metal proceeded to uranium ion and the concentration increased. The results confirmed that the Butler–Volmer equation coupled with the diffusion calculation could realistically simulate CV with various processing parameters, namely, the equilibrium potential, diffusion coefficient, and potential sweep rate. Fig. 3 present the LSV curves calculated with the conditions in Table 2 where various reduction potentials were considered for uranium (−1.86 V), thorium (−1.77 V) and cerium (−2.45 V) (Martinet and Calligary, 1973; Cassayre et al., 2007; lizuka, 1998).
Table 2 Variables for multiple components in linear sweep voltammetry.
Reactions Reduction potential (V vs. Ag(|)/Ag(0)) (Martinet and Calligary, 1973) Reactant concentration Product concentration Diffusion coefficient, Do (Cassayre et al., 2007; Martinet and Calligary, 1973; lizuka, 1998) Temperature (◦ C)
Uranium(III)
Thorium(IV)
Cerium(III)
U3+ + 3e− = U −1.86 V 1 mol/m3 0 mol/m3 1.03e−9 m2 /s 500 ◦ C
Th4+ + 4e− = Th −1.77 V 1 mol/m3 0 mol/m3 3.70e−9 m2 /s 500 ◦ C
Ce3+ + 3e− = Ce −2.45 V 1 mol/m3 0 mol/m3 1.53e−9 m2 /s 500 ◦ C
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Fig. 2. Results of cyclic voltammetry simulated on a cathode electrode for various (a) reduction potentials, (b) diffusion coefficients, (c) scanning rates, and (d) concentrations.
Clearly, the reduction potentials were represented correctly with multiple peaks as shown in Fig. 3(a). Even in cases where the reduction potentials of two reactions were similar, uranium (−1.86 V) and thorium (−1.77 V), the ip (peak current) value represented the reduction potential as seen in Fig. 3(a). The cases of uranium (−1.86 V) and cerium (−2.4 V) also showed the reduction potential under the multicomponent conditions as seen in Fig. 3(b).
3.2. Laboratory-scale electrorefiner analysis On the basis of the electrochemical model, a series of computer simulations of the laboratory-scale electrorefiner were conducted. Fig. 4 shows the quantity of deposited uranium under current densities of 1 mA/cm2 , 10 mA/cm2 , 50 mA/cm2 , and 100 mA/cm2 for 24 h. The total deposition quantity increased as the applied current density increased. A maximum of 19 kg of uranium was
Fig. 3. Calculated linear sweep voltammetry results of multicomponent system having different reduction potentials for uranium (−1.86 V) vs. thorium (−1.77 V) and uranium (−1.86 V) vs. cerium (−2.45 V).
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Fig. 4. Deposition quantity of uranium under various current densities for 24 h. A current density of 100 mA/cm2 yields 19 kg of uranium in 24 h of operation.
deposited when a current of 100 mA/cm2 was applied in 24 h. Thus, the calculated throughput of the laboratory-scale electrorefiner is 0.75 kgU/h. The maximum potential of the anode at 100 mA/cm2 is below the cutoff voltage, −0.5 V, to prevent noble metal dissolution. This calculation result indicates that the computer simulation predicted the maximum throughput of uranium acquired during operation under optimum conditions. Throughput is an important factor for estimating the efficiency of electrorefining of spent fuel, because a compact design is desirable in hot cell operation. Hence, this method can be the first step in obtaining a design basis for a larger-scale electrorefiner. Fig. 5 shows the arrangement of the two cathodes used to describe the thickness of the uranium deposited by each portion of the internal and external cathodes and to interpret the simulation results. In this calculation, a uranium density of 2 g/cm3 was used to consider the dendritic structure of uranium deposits produced in molten salt (Totemeier et al., 1997). The angle is defined as the radial location of the cathode; a higher angle indicates a position closer to the anode. The deposition is thicker in the area where a higher current density is applied. The deviation increases to 83%, 372%, and 1233% for applied currents of 10 mA/cm2 , 50 mA/cm2 ,
Fig. 5. Uranium deposit layer thickness distribution between inner and outer cathodes under total applied current of (a) 1 mA/cm2 , (b) 10 mA/cm2 , (c) 50 mA/cm2 , and (d) 100 mA/cm2 for 24 h.
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Fig. 6. Deposit thickness at six cathode positions for uranium densities of 0.5, 1, 2, or 3 g/cm3 with current applied for 5 h. (a) 1 mA/cm2 , (b) 10 mA/cm2 , (c) 50 mA/cm2 , and (d) 100 mA/cm2 .
and 100 mA/cm2 , respectively, as shown in Fig. 5(b)–(d). For the inner cathode, the thickness deviations are 21%, 27%, 37%, and 43% for 1 mA/cm2 , 10 mA/cm2 , 50 mA/cm2 , and 100 mA/cm2 , respectively. These results indicate that higher current density tends to produce preferential growth of uranium deposits, especially for the outer cathode. The uranium deposit thickness varies according to the radial location of the cathode, and the deviation increases as the applied current increases. For an applied current of 1 mA/cm2 , the deviation in the thickness of the uranium deposited at the outer cathode ranges from 0.125 mm to 0.215 mm, which is a difference of 72%, as shown in Fig. 5(a). The deposition was thickest at 180◦ from the outer cathode at each current density owing to the creation of higher current density distributions because of proximity to the anode. To obtain continuous electrorefining without the deposited uranium contacting the anode, it is necessary to perform scraping to remove the uranium deposit at appropriate times. Fig. 6 shows the deposit thickness at the outer cathode (position No. 6 in the figure) for various uranium bulk densities after 5 h of applied current. At lower uranium densities, the
electrodeposition rate and thickness increased depending on the applied current. The density of the uranium deposited during electrorefining is reportedly very important for minimizing handling operation (Westphal and Mariani, 2000). When a current density of 1 mA/cm2 was applied for 5 h, the maximum thickness was 0.17 mm, and it decreased as the uranium deposit density increased, as shown in Fig. 6(a). The maximum thickness increased as the current density increased; the values were 1.7 mm and 13.5 mm, as shown in Fig. 6(b) and (c), respectively. At an applied current density of 100 mA/cm2 and a uranium density of 0.5 g/cm3 , 31 mm was deposited on the anode surface after 5 h. It is very hard to quantify the uranium density as a function of the processing parameters. However, a higher current density was found to generate finer uranium deposits; thus, the dendritic growth rate is expected to accelerate at higher current densities. This calculation result is particularly noteworthy for practical high-throughput electrorefining, in which multiple cathodes are in close contact with the anode, because electrical shorts would occur without proper scraping of the uranium deposit.
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Fig. 7. Variation in anode–cathode distance according to the applied current with uranium deposit density. (a) 0.5 g/cm3 , (b) 1 g/cm3 , (c) 2 g/cm3 , and (d) 3 g/cm3 .
Fig. 7 shows a graph representing the variations of the anode–cathode distance according to the uranium density difference with 0.5, 1, 2, and 3 g/cm3 . The density of electrodeposited uranium becomes low as the applied current is low. Hence, various densities of uranium deposit were taken into consideration in this calculation.
iloc ds = Itotal
(4)
∂˝
M = Itotal Weq,U
(2.96 g/A h)
M/Pdeposit,U tsi = l/t
(5) (6)
The electrodeposited volume of uranium can be calculated by using the series of equations from Eq. (4) to Eq. (6). The local current density (iloc ) is integrated with cathode surface areas to calculate the total current (Itotal ) as shown in Eq. (4). Thus, the calculated Itotal is multiplied by the electrochemical equivalent of uranium (Weq,U , 2.96 g/A h) as shown in Eq. (5). The thickness change rate (l/t) of uranium deposit can be calculated with the predefined density of uranium (Pdeposit ,U ) and the initial electrode surface area (si ) according to Eq. (6). Fig. 7 shows the calculation results of distance change between anode and cathode by growth of uranium deposit. The deposit thickness can be modeled by evaluating the local changes in thickness and, moving mesh, with respect to time. Because the initial gap between the anode and the cathode is 20 mm, the scraping time is estimated by measuring the time required for this value to reach 0 mm. In the case of 0.5 g/cm3 of uranium density, electrical
short circuit was found at 3 h with 100 mA/cm2 of applied current density as shown in Fig. 7(a). The short circuit time increases with decreasing current density. When the uranium density increased to 1 g/cm3 (see Fig. 7(b)), the electric short circuit time increased to 5.8 h, which means scraping operation should be done before this time to prevent electric shortage. In the case of a uranium density of 2 g/cm3 , Fig. 7(c), no scraping is needed until after 24 h of deposition time at applied current densities of 1 mA/cm2 , 10 mA/cm2 , or 50 mA/cm2 because the gap distance is 19.8, 17.5, and 2.5 mm, respectively. When the applied current is 100 mA/cm2 , it is necessary to perform scraping before about 11.3 h to ensure continuous operation and avoid contact between the external cathode and the anode. The scraping time is further increased with increasing density of uranium deposit as shown in Fig. 7(d). Hence, the appropriate scraping time and the distance between the electrodes can be obtained through this kind of calculation. Fig. 8 shows the results of experimental validation of the uranium deposit thicknesses. Dendritic uranium was deposited on the cathode surfaces as shown in Fig. 8(a). In this experiment, a 150 mA current was applied to each cathode. The deposit thickness on the outer cathode appeared to be much higher than that on the inner cathode. This result agrees well with the calculation results shown in Figs. 5 and 6. To quantitatively compare the uranium deposit thicknesses at various surface locations, six points were chosen, as shown in Fig. 8(b). The results confirm those in Fig. 6, and the lowest growth rate was found at point 1. The measured deposit thickness on the actual cathodes exhibited large deviations
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Fig. 8. (a) Experimental validation of electrodeposition of uranium in 150 mA applied conditions. (b) Calculated uranium deposit thicknesses at various cathode locations under 150 mA applied current and 2 g/cm3 uranium density conditions.
Fig. 9. Polarization curves for laboratory-scale electrorefiner. Comparison of (a) experimental data with numerical data at (b) 450 ◦ C, (c) 500 ◦ C, and (d) 550 ◦ C.
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because of the random growth characteristics of uranium dendrites, but the tendency agrees well with the calculated deposit thickness shown in Fig. 8(b). Fig. 9 compares the experimental polarization curves with the calculated data. The material properties used for the calculation are shown in Table 3 (Martinet and Calligary, 1973). The cathodic current reached 150 A at cathode potentials of −1.5, −1.55, and −1.58 V at molten salt temperatures of 550 ◦ C, 500 ◦ C, and 450 ◦ C, respectively. As shown in Fig. 9(a), the anodic potential changed dramatically with the temperature, whereas the cathodic potential difference was only 0.03 V. The anodic potentials at 150 A of applied current were 0.25 V, −0.3 V, and −0.4 V at molten salt temperatures of 450 ◦ C, 500 ◦ C, and 550 ◦ C; this is attributed to an increase in the diffusion coefficient, as shown in Table 3. In addition, the larger surface area of the cathode is believed to contribute to the stable cathode potential. Hence, the resistance increase in the anode (low slope of the anodic curves) is believed to be responsible for the limited anodic dissolution rate owing to its relatively small surface area compared to the cathode. The calculated data generally agree with the experimentally obtained polarization curves at 450 ◦ C, 500 ◦ C, and 550 ◦ C, as shown in Fig. 9(b)–(d), respectively. These experimental and numerical data imply that the anodic overpotential is significant for the current laboratory-scale electrorefiner at a molten salt temperature of 450 ◦ C. The high anodic overpotential could cause noble metal impurity dissolution, which would decrease the uranium’s purity. Hence, an improved design with a larger anode surface area is necessary to increase the applied current. Using our calculations based on the tertiary model, the operational behavior of a laboratory-scale electrorefiner composed of multiple electrodes was successfully simulated. Hence, this result could be used not only for operation of the laboratory-scale electrorefiner but also for further development of a commercial-scale electrorefiner. 4. Conclusion In this paper, the electrodeposition behavior of uranium was successfully simulated using the COMSOL Electrodeposition modules, which are part of a commercial program for multiphysics. The simulation results indicate that 19 kg of uranium is theoretically attainable under an applied current density of 100 mA/cm2 after 24 h of operation using the current laboratory-scale electrorefiner at KAERI. The polarization behavior of this electrorefiner was compared to numerical data, and the anodic overpotential was found to be larger than that of the cathode owing to the anode’s relatively small surface area. The above results demonstrate that electrochemical transport strongly depends on the applied current in the electrolyte. A higher electric current is needed to deposit more mass of the metal at the cathode per hour. In addition, we believe that information on the electrorefiner characteristics will also be very helpful in determining the optimum operating conditions, and this model will provide crucial data for the design and manufacture of a commercial electrorefiner.
Acknowledgment This work was conducted under a national nuclear long-term research and development program supported by the Korea Ministry of Science and Technology. References Bae, J.D., Nam, H.O., Yi, K.W., Park, B.G., Hwang, I.S., 2010. Numerical assessment of pyrochemical process performance for PEACER system. Nucl. Eng. Des. 240, 1679–1687. Bard, A.J., Faulkner, L.R., 2001. Electrochemical Methods: Fundamentals and Applications. Wiley, New York. Brett, C.M.A., Brett, A.M.O., 1993. Electrochemistry: Principles, Methods, and Applications. Oxford University Press, New York. Britz, D., 2005. Digital Simulation in Electrochemistry. Springer, New York. Cassayre, L., Serp, J., Soucek, P., Malmbeck, R., Rebizant, J., Glatz, J.-P., 2007. Electrochemistry of thorium in LiCl–KCl eutectic melts. Electrochim. Acta 52, 7432–7437. Choi, S.Y., Park, J.Y., Kim, K.R., Jung, H.S., Hwang, I.S., Park, B.G., Yi, K.W., Lee, H.S., Ahn, D.H., Paek, S.W., 2010. Three-dimensional multispecies current density simulation of molten-salt electrorefining. J. Alloys Compd. 503, 177–185. Choi, S.Y., Park, J.Y., Hoover, R.O., Phongikaroon, S., Simpson, M.F., Kim, K.R., Hwang, I.S., 2011. Uncertainty studies of real anode surface area in computational analysis for molten salt electrorefining. J. Nucl. Mater. 416, 318–326. COMSOL, 2012. COMSOL4.3 Electrodeposition Module User’s Guide. COMSOL, Inc. Hoover, R., Phongikaroon, S., Li, S., Simpson, M., Yoo, T.-S., 2009. A computational model of the Mark-IV electrorefiner: phase I-fuel basket/salt interface. J. Eng. Gas Turbines Power 131, 054503. Kim, K.R., Bae, J.D., Ahn, D.H., Paek, S., Kwon, S.W., Shim, J.B., Kim, S.H., 2009. Modeling and analysis of a molten-salt electrolytic process for nuclear waste treatment. J. Radioanal. Nucl. Chem. 280, 401–404. Kim, K.R., Choi, S.Y., Ahn, D.H., Paek, S., Lee, H.S., Hwang, I.S., 2010. Electro-fluid analysis of a molten-salt electrorefiner with rotating cruciform anode baskets. J. Radioanal. Nucl. Chem. 286, 801–806. Lee, J.H., Kang, Y.H., Hwang, S.C., Lee, H.S., Kim, E.H., Park, S.W., 2008. Assessment of a high-throughput electrorefining concept for a spent metallic nuclear fuel—I: computational fluid dynamics analysis. Nucl. Technol. 165, 107–116. Lee, J.H., Oh, K.H., Kang, Y.H., Hwang, S.C., Lee, H.S., Shim, J.B., Kim, E.H., Park, S.W., 2009. Assessment of a high-throughput electrorefining concept for a spent metallic nuclear fuel—II: electrohydrodynamic analysis and validation. Nucl. Technol. 165, 370–379. Lee, H.S., Park, G.I., Kang, K.H., Hur, J.M., Kim, J.G., Ahn, D.H., Cho, Y.Z., Kim, E.H., 2011. Pyroprocessing technology development at KAERI. Nucl. Eng. Technol. 43, 317–328. lizuka, M., 1998. Diffusion coefficients of cerium and gadolinium in molten LiCl–KCl. J. Electrochem. Soc. 145, 84–88. Martinet, L., Calligary, F., 1973. Actinides in molten salt. At. Energy Rev. 11, 23– 55. Nawada, H.P., Bhat, N.P., 1998. Thermochemical modeling of electrotransport of uranium and plutonium in an electrorefiner. Nucl. Eng. Des. 179, 75–99. Oh, K.H., Kang, Y.H., Hwang, S.C., Lee, H.S., Shim, J.B., Kim, E.H., Park, S.W., 2009. Assessment of a high-throughput electrorefining concept for a spent nuclear fuel—II: electrohydrodynamic analysis and validation. Nucl. Technol. 165, 370–379. Pickett, D.J., 1979. Electrochemical Reactor Design, 2nd ed. American Elsevier, New York. Shibuta, Y., Unoura, S., Sato, T., Shibata, H., Suzuki, T., 2011. A phase-field simulation of uranium dendrite growth on the cathode in the electrorefining process. J. Nucl. Mater. 414, 114–119. Song, K.C., Lee, H.S., Hur, J.M., Kim, J.G., Ahn, D.H., Cho, Y.Z., 2010. Status of pyroprocessing technology development in Korea. Nucl. Eng. Technol. 42, 131– 144. Totemeier, C., Mariani, R.D., 1997. Morphologies of uranium and uranium-zirconium electrodeposits. J. Nucl. Mater. 250, 131–146. Westphal, B.R., Mariani, R.D., 2000. Uranium processing during the treatment of sodium-bonded spent nuclear fuel. JOM 52 (9), 21–25.
Contents lists available at SciVerse ScienceDirect
Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
Computer-assisted design and experimental validation of multielectrode electrorefiner for spent nuclear fuel treatment using a tertiary model Seung Hyun Kim a,1 , Sung Bin Park b,2 , Sung Jai Lee b,3 , Jeong Guk Kim b,4 , Han Soo Lee b,5 , Jong Hyeon Lee a,c,∗ a
Graduate School of Green Energy Technology, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea Korea Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea c Department of NanoMaterials Engineering, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea b
h i g h l i g h t s
We simulate laboratory scale electrorefiner for spent nuclear fuel. 19 kg/24 h of uranium is theoretically attainable with 100 mA/cm2 for 24 h. Polarization behaviors of the electrorefiner well agree with simulation results. Anodic overpotential is found to be larger than that of cathode.
a r t i c l e
i n f o
Article history: Received 6 September 2012 Received in revised form 16 January 2013 Accepted 19 January 2013
a b s t r a c t It is important to understand electrochemical phenomena in order to design an electrorefiner system suitable for pyroprocessing, particularly one equipped with complicated electrodes. Computer simulation of the electrochemical cells is an effective tool for the visualization of processing parameters such as the potential distribution, current density, and concentration profile. The electrochemical parameters considered in this study are the exchange current density distribution and electrode arrangement. The application of a numerical model to design an electrorefiner for spent metallic nuclear fuel is discussed with respect to throughput, impurity contamination, and operating mode. A commercial finite element method package was used. In addition, calculations of the tertiary current density and an experimental validation of these results are presented. © 2013 Elsevier B.V. All rights reserved.
1. Introduction The Korea Atomic Energy Research Institute (KAERI) has been developing pyroprocessing methods since 1997. By 2006, concept development, bench-scale testing, and laboratory-scale key unit process demonstrations had been conducted (Song et al., 2010; Lee et al., 2011). Electrorefining is one of the key steps in efficient pyrochemical recycling of metalized spent nuclear fuel; efficiency
∗ Corresponding author at: Graduate School of Green Energy Technology, Chungnam National University, 79 Daehak-ro, Yuseong-gu, Daejeon 305-764, Republic of Korea. Tel.: +82 42 821 6596; fax: +82 42 822 5850. E-mail addresses: [email protected] (S.H. Kim), [email protected] (S.B. Park), [email protected] (S.J. Lee), [email protected] (J.G. Kim), [email protected] (H.S. Lee), [email protected] (J.H. Lee). 1 Tel.: +82 42 821 7632; fax: +82 42 822 5850. 2 Tel.: +82 42 868 2523; fax: +82 42 822 2080. 3 Tel.: +82 42 868 8650; fax: +82 42 822 2080. 4 Tel.: +82 42 868 8650; fax: +82 42 822 2080. 5 Tel.: +82 42 868 2395; fax: +82 42 822 1236. 0029-5493/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.nucengdes.2013.01.009
is important because of the large volumes of uranium that must be treated. However, throughput enhancement is not an easy task, especially when sufficient separation efficiency in a hightemperature molten salt environment is necessary. To increase the throughput, 24 graphite cathodes were installed in the current laboratory-scale electrorefiner (with a recovery rate of 20 kg of heavy metal per day), as shown in Fig. 1 (Lee et al., 2009). The anode was designed for up to 50 kg of heavy metal to be loaded into anode baskets to decrease the anode overpotential. On the basis of the experimental results, a new electrorefiner is being designed at KAERI, and the recovery of 50 kg of heavy metal per day is expected to be demonstrated in 2012. Considering the design requirements of a high-throughput electrorefiner and the need for easy loading of fuel into the anode, a new, efficient cathode configuration should be investigated. Computer simulation of electrochemical cells is an effective tool for the optimization of the electrorefining process. Several researchers have reported numerical methods for simulating the electrorefining process of spent nuclear fuel. Bae analyses revealed the three-dimensional analysis of deposition rate, in couple with
S.H. Kim et al. / Nuclear Engineering and Design 257 (2013) 12–20
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Fig. 1. Schematic view of high-throughput electrorefiner and geometries for numerical analysis. (a) Mesh for CV and LSV calculation, (b) laboratory-scale electrorefiner, and (c) geometry for numerical analysis.
the one-dimensional electrochemical analysis model, REFIN in PEACER as the lead–bismuth cooled fast reactor fuel cycle (Bae et al., 2010). Also Choi investigated the three-dimensional simulation of multispecies and multi-reaction electrorefining by using the fluid-dynamics code (Choi et al., 2010, 2011). Kim analyzed concentration and current distribution by coupling the Butler–Volmer equation with subroutine which was enabled by using CFX and REFIN codes. Electro-fluid analysis on molten salt in an electrorefiner was carried out and discussed with respect to the recovery of pure uranium when thermochemical data are used (Kim et al., 2009, 2010). Nawada numerically simulated the electrotransport behavior of uranium and plutonium in a molten salt with an improved thermochemical model (Nawada and Bhat, 1998). Shibuta predicted uranium dendrite growth on the cathode by using a novel phase-field model, in which the electrodeposition of uranium and zirconium in the molten salt occurred (Shibuta et al., 2011). Also Hoover estimated changes in current density of anode and cathode and the polarization characteristics in relation to various operating conditions in the electrorefining process by using ORIGEN code and utilized it for estimation of Mark-IV electrorefiner operation (Hoover et al., 2009). Before the construction of the current laboratory-scale electrorefiner, the fundamental electric field and metal ion movement were examined using the primary current density model (Lee et al., 2008; Oh et al., 2009). However, a more reliable and practical model is necessary to predict the electrodeposition and separation behaviors of the system, which are needed for complicated electrode configurations. The growth characteristics of uranium deposits are also a cause for concern in high-throughput electrorefiners, which have a compact electrode arrangement within a cell, because electrical short circuit can occur if deposits are not removed at an appropriate time. In this paper, numerical analysis of a high-throughput electrorefiner was performed by using a commercial finite element method code, namely, COMSOL multiphysics software (COMSOL, 2012). A tertiary current density model was applied to evaluate the performance of the laboratory-scale electrorefining cell, in particular the throughput and separation behavior, and to predict the amount of deposition on multiple cathodes at different distances from the anode. Also, to predict short circuit time by dendritic growth of uranium on the cathode surface, a moving mesh was used with the bulk density of uranium dendrite. This approach should be useful to design a compact electrorefiner which is operated in a limited area such as a hot cell. The calculated polarization behavior and the uranium deposit growth were validated using experimental data obtained from uranium electrorefining.
2. Theory of laboratory-scale electrorefiner modeling 2.1. Fundamental theory The concentration change in an electrorefiner is the sum of the changes due to diffusion, convection, and migration, and is given by the so-called tertiary model as
∂C ∂t
=
∂C ∂t
+ diffusion
∂C ∂t
+ convection
∂C ∂t
(1) migration
The concentration gradient normal to the electrode surface is significantly larger than that in the lateral direction. Thus, the concentration gradient normal to the electrode surface controls the direction and speed of mass transfer near the electrode surface (Brett and Brett, 1993; Britz, 2005). In this calculation, chemical reactions of the electrolyte in the solution were not considered. In addition, convection terms were ignored because there was no vigorous agitation during the actual electrorefining experiments. The local current density is expressed by a modified Butler–Volmer equation with concentration-dependent terms, as shown in Eq. (2) (Bard and Faulkner, 2001; Pickett, 1979). The set of equations solved by the COMSOL Electrodeposition modules was the Butler–Volmer equations in their conservation form. This means that for a lower surface concentration (Cs ≤ Cbulk ) at the electrode surface, a higher overpotential () is necessary to achieve the same current density.
iloc = i0
COS CObulk
˛F
CRS
RT
CRbulk
exp −
−
exp
(1 − ˛)F RT
(2)
In Eq. (2), F is Faraday’s constant, R is the gas constant, is the overpotential, and ˛ is the charge transfer coefficient. The superscripts s and bulk refer to locations at the electrode surface and in the bulk electrolyte, respectively. The subscripts O and R indicate the oxidized and reduced species, respectively, and i0 is the exchange current density. The potential–current responses such as CV, LSV and I–V curve were simulated as shown in Eq. (2). To consider multiple components in CV, three elements, namely, zirconium, hafnium and uranium were considered in this calculation; the boundary conditions and material parameters are listed in Tables 1–3. The currents induced by each element were calculated at the cathode electrode, and the obtained currents were then summed to calculate the total current as follows: itotal =
n k=1
k iloc
(3)
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Table 1 Boundary condition and parameters. Anodic transfer coefficient Cathodic transfer coefficient Diffusion coefficient, Do (Martinet and Calligary, 1973) Initial concentration of A Initial concentration of B Scan rate Reduction potential (V vs. Ag(|)/Ag(0)) (Martinet and Calligary, 1973)
Table 3 Parameters for comparison with actual polarization curves. 0.5 0.5 U(III)7e−10 at 450 ◦ C, U(III)1.03e−9 m2 /s at 500 ◦ C 1 mol/m3 0 mol/m3 0.1, 0.4, 0.8 V/s Zr (−1.11 V), Hf (−1.24 V), U (−1.86 V)
where itotal is the final current induced by each element, and k is the component number. 2.2. Geometry and mesh for simulation of laboratory-scale electrorefiner The tertiary model should describe the fundamental electrochemical behaviors when the correct model equations are used. The model was validated using a single-electrode geometry, which is generally used for cyclic voltammetry (CV) before the model is applied to a high-throughput electrorefiner. This numerical analysis was based on a 2D model to minimize the calculation resources required because of the symmetrical geometry of the 2D model. To achieve linear sweep voltammetry (LSV) and CV in the electrolyte, the potential variations were defined as a function of time on the surface of the electrode as follows. To calculate the amount of uranium deposited at the cathode electrode, the local current density was integrated over the cathode surface area and then multiplied by the electrochemical equivalent of uranium (2.96 gA−1 h−1 ). The electrode and electrolyte were meshed with tetragonal boundary layer elements. Fig. 1(a) shows the 2D meshed geometry of the computational domain used for the CV and LSV simulations. Fig. 1(b) and (c) shows a photograph of the high-throughput electrorefiner and its simplified geometry, respectively. Two cathodes and the part of the anode surface facing the cathodes were considered because the cathodes are uniformly arranged around the electrorefiner. 3. Results and discussion The deposition behavior of uranium at the cathode electrode was studied to determine the optimum operating mode. Subsequently, the macroscopic deposition behavior of uranium and the electrochemical responses were studied to estimate the total throughput and proper scraping time of the electrochemical system in the laboratory-scale electrorefiner. 3.1. Verification of model using cyclic voltammetry and linear sweep voltammetry As described above, a series of simulations of the fundamental electrochemical response of the electrorefiner was conducted. Table 1. lists the boundary conditions used in these simulations. Time-dependent analysis of the electrochemical system was performed using the COMSOL Electrodeposition module code. To
Anodic transfer coefficient Cathodic transfer coefficient Diffusion coefficient, Do (Martinet and Calligary, 1973) Initial concentration Exchange current density Ion mobility Applied current Operating temperature
0.5 0.5 6.8e−10 m2 /s (450 ◦ C), 1.03e−9 m2 /s (500 ◦ C), 1.36e−9 m2 /s (550 ◦ C) 500 mol/m3 15 mA/cm2 4.036e−11 S mol/kg 50, 100, 150 A 450 ◦ C, 500 ◦ C, 550 ◦ C
develop a comprehensive modeling approach, CV results were first obtained assuming that three elements having different properties, such as diffusion coefficient, and reduction potential are dissolved in a molten salt. The elements considered in this study were zirconium(III), hafnium(IV), uranium(III). Fig. 2 shows the calculation results of the CV simulation in terms of the (a) reduction potential (E0 ), (b) diffusion coefficient, and (c) scan rate. These results clearly show that the response is similar to that of an actual electrode cell. As the voltage decreased from 2 V to −2.5 V over time at the different reduction potentials from zirconium(III), hafnium(IV), uranium(III), the reduction current appeared when the oxidant was reduced at the equilibrium potential and began to decrease after it reached the peak current (ip ), as shown in Fig. 2(a). When a reverse potential was applied, the reduced substance began to oxidize at the electrode surface, which generated an anodic current. It was confirmed that this anodic current decreased again after it reached its maximum value. Fig. 2(b) shows the calculated CV according to the difference diffusion coefficient from uranium (Martinet and Calligary, 1973). The magnitude of the electric current during CV measurement is due to mostly diffusional concentration changes as defined by Eq. (1). Therefore, a higher diffusion coefficient induces a higher peak current, as shown in Fig. 2(b). As the potential sweep rate increased at the reduction potential of uranium (–1.8 V), the peak current height increased, as shown in Fig. 2(c), which is also an indicator of the reliability of the model. The changes in the concentrations of the oxidant and reductant during the CV simulation at the surface of the working electrode are depicted in Fig. 2(d). This graph was designed to show whether the oxidation–reduction reaction is implemented properly on the electrode surface depending on the concentration; it shows that when working electrode was applied with change of voltage from 2 V to −2 V for 20 s, the initial uranium ions (1 mol) were reduced to uranium metal with the concentration decreasing as time passed; however, when the potential was forced in the opposite direction, the uranium metal proceeded to uranium ion and the concentration increased. The results confirmed that the Butler–Volmer equation coupled with the diffusion calculation could realistically simulate CV with various processing parameters, namely, the equilibrium potential, diffusion coefficient, and potential sweep rate. Fig. 3 present the LSV curves calculated with the conditions in Table 2 where various reduction potentials were considered for uranium (−1.86 V), thorium (−1.77 V) and cerium (−2.45 V) (Martinet and Calligary, 1973; Cassayre et al., 2007; lizuka, 1998).
Table 2 Variables for multiple components in linear sweep voltammetry.
Reactions Reduction potential (V vs. Ag(|)/Ag(0)) (Martinet and Calligary, 1973) Reactant concentration Product concentration Diffusion coefficient, Do (Cassayre et al., 2007; Martinet and Calligary, 1973; lizuka, 1998) Temperature (◦ C)
Uranium(III)
Thorium(IV)
Cerium(III)
U3+ + 3e− = U −1.86 V 1 mol/m3 0 mol/m3 1.03e−9 m2 /s 500 ◦ C
Th4+ + 4e− = Th −1.77 V 1 mol/m3 0 mol/m3 3.70e−9 m2 /s 500 ◦ C
Ce3+ + 3e− = Ce −2.45 V 1 mol/m3 0 mol/m3 1.53e−9 m2 /s 500 ◦ C
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Fig. 2. Results of cyclic voltammetry simulated on a cathode electrode for various (a) reduction potentials, (b) diffusion coefficients, (c) scanning rates, and (d) concentrations.
Clearly, the reduction potentials were represented correctly with multiple peaks as shown in Fig. 3(a). Even in cases where the reduction potentials of two reactions were similar, uranium (−1.86 V) and thorium (−1.77 V), the ip (peak current) value represented the reduction potential as seen in Fig. 3(a). The cases of uranium (−1.86 V) and cerium (−2.4 V) also showed the reduction potential under the multicomponent conditions as seen in Fig. 3(b).
3.2. Laboratory-scale electrorefiner analysis On the basis of the electrochemical model, a series of computer simulations of the laboratory-scale electrorefiner were conducted. Fig. 4 shows the quantity of deposited uranium under current densities of 1 mA/cm2 , 10 mA/cm2 , 50 mA/cm2 , and 100 mA/cm2 for 24 h. The total deposition quantity increased as the applied current density increased. A maximum of 19 kg of uranium was
Fig. 3. Calculated linear sweep voltammetry results of multicomponent system having different reduction potentials for uranium (−1.86 V) vs. thorium (−1.77 V) and uranium (−1.86 V) vs. cerium (−2.45 V).
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Fig. 4. Deposition quantity of uranium under various current densities for 24 h. A current density of 100 mA/cm2 yields 19 kg of uranium in 24 h of operation.
deposited when a current of 100 mA/cm2 was applied in 24 h. Thus, the calculated throughput of the laboratory-scale electrorefiner is 0.75 kgU/h. The maximum potential of the anode at 100 mA/cm2 is below the cutoff voltage, −0.5 V, to prevent noble metal dissolution. This calculation result indicates that the computer simulation predicted the maximum throughput of uranium acquired during operation under optimum conditions. Throughput is an important factor for estimating the efficiency of electrorefining of spent fuel, because a compact design is desirable in hot cell operation. Hence, this method can be the first step in obtaining a design basis for a larger-scale electrorefiner. Fig. 5 shows the arrangement of the two cathodes used to describe the thickness of the uranium deposited by each portion of the internal and external cathodes and to interpret the simulation results. In this calculation, a uranium density of 2 g/cm3 was used to consider the dendritic structure of uranium deposits produced in molten salt (Totemeier et al., 1997). The angle is defined as the radial location of the cathode; a higher angle indicates a position closer to the anode. The deposition is thicker in the area where a higher current density is applied. The deviation increases to 83%, 372%, and 1233% for applied currents of 10 mA/cm2 , 50 mA/cm2 ,
Fig. 5. Uranium deposit layer thickness distribution between inner and outer cathodes under total applied current of (a) 1 mA/cm2 , (b) 10 mA/cm2 , (c) 50 mA/cm2 , and (d) 100 mA/cm2 for 24 h.
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Fig. 6. Deposit thickness at six cathode positions for uranium densities of 0.5, 1, 2, or 3 g/cm3 with current applied for 5 h. (a) 1 mA/cm2 , (b) 10 mA/cm2 , (c) 50 mA/cm2 , and (d) 100 mA/cm2 .
and 100 mA/cm2 , respectively, as shown in Fig. 5(b)–(d). For the inner cathode, the thickness deviations are 21%, 27%, 37%, and 43% for 1 mA/cm2 , 10 mA/cm2 , 50 mA/cm2 , and 100 mA/cm2 , respectively. These results indicate that higher current density tends to produce preferential growth of uranium deposits, especially for the outer cathode. The uranium deposit thickness varies according to the radial location of the cathode, and the deviation increases as the applied current increases. For an applied current of 1 mA/cm2 , the deviation in the thickness of the uranium deposited at the outer cathode ranges from 0.125 mm to 0.215 mm, which is a difference of 72%, as shown in Fig. 5(a). The deposition was thickest at 180◦ from the outer cathode at each current density owing to the creation of higher current density distributions because of proximity to the anode. To obtain continuous electrorefining without the deposited uranium contacting the anode, it is necessary to perform scraping to remove the uranium deposit at appropriate times. Fig. 6 shows the deposit thickness at the outer cathode (position No. 6 in the figure) for various uranium bulk densities after 5 h of applied current. At lower uranium densities, the
electrodeposition rate and thickness increased depending on the applied current. The density of the uranium deposited during electrorefining is reportedly very important for minimizing handling operation (Westphal and Mariani, 2000). When a current density of 1 mA/cm2 was applied for 5 h, the maximum thickness was 0.17 mm, and it decreased as the uranium deposit density increased, as shown in Fig. 6(a). The maximum thickness increased as the current density increased; the values were 1.7 mm and 13.5 mm, as shown in Fig. 6(b) and (c), respectively. At an applied current density of 100 mA/cm2 and a uranium density of 0.5 g/cm3 , 31 mm was deposited on the anode surface after 5 h. It is very hard to quantify the uranium density as a function of the processing parameters. However, a higher current density was found to generate finer uranium deposits; thus, the dendritic growth rate is expected to accelerate at higher current densities. This calculation result is particularly noteworthy for practical high-throughput electrorefining, in which multiple cathodes are in close contact with the anode, because electrical shorts would occur without proper scraping of the uranium deposit.
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Fig. 7. Variation in anode–cathode distance according to the applied current with uranium deposit density. (a) 0.5 g/cm3 , (b) 1 g/cm3 , (c) 2 g/cm3 , and (d) 3 g/cm3 .
Fig. 7 shows a graph representing the variations of the anode–cathode distance according to the uranium density difference with 0.5, 1, 2, and 3 g/cm3 . The density of electrodeposited uranium becomes low as the applied current is low. Hence, various densities of uranium deposit were taken into consideration in this calculation.
iloc ds = Itotal
(4)
∂˝
M = Itotal Weq,U
(2.96 g/A h)
M/Pdeposit,U tsi = l/t
(5) (6)
The electrodeposited volume of uranium can be calculated by using the series of equations from Eq. (4) to Eq. (6). The local current density (iloc ) is integrated with cathode surface areas to calculate the total current (Itotal ) as shown in Eq. (4). Thus, the calculated Itotal is multiplied by the electrochemical equivalent of uranium (Weq,U , 2.96 g/A h) as shown in Eq. (5). The thickness change rate (l/t) of uranium deposit can be calculated with the predefined density of uranium (Pdeposit ,U ) and the initial electrode surface area (si ) according to Eq. (6). Fig. 7 shows the calculation results of distance change between anode and cathode by growth of uranium deposit. The deposit thickness can be modeled by evaluating the local changes in thickness and, moving mesh, with respect to time. Because the initial gap between the anode and the cathode is 20 mm, the scraping time is estimated by measuring the time required for this value to reach 0 mm. In the case of 0.5 g/cm3 of uranium density, electrical
short circuit was found at 3 h with 100 mA/cm2 of applied current density as shown in Fig. 7(a). The short circuit time increases with decreasing current density. When the uranium density increased to 1 g/cm3 (see Fig. 7(b)), the electric short circuit time increased to 5.8 h, which means scraping operation should be done before this time to prevent electric shortage. In the case of a uranium density of 2 g/cm3 , Fig. 7(c), no scraping is needed until after 24 h of deposition time at applied current densities of 1 mA/cm2 , 10 mA/cm2 , or 50 mA/cm2 because the gap distance is 19.8, 17.5, and 2.5 mm, respectively. When the applied current is 100 mA/cm2 , it is necessary to perform scraping before about 11.3 h to ensure continuous operation and avoid contact between the external cathode and the anode. The scraping time is further increased with increasing density of uranium deposit as shown in Fig. 7(d). Hence, the appropriate scraping time and the distance between the electrodes can be obtained through this kind of calculation. Fig. 8 shows the results of experimental validation of the uranium deposit thicknesses. Dendritic uranium was deposited on the cathode surfaces as shown in Fig. 8(a). In this experiment, a 150 mA current was applied to each cathode. The deposit thickness on the outer cathode appeared to be much higher than that on the inner cathode. This result agrees well with the calculation results shown in Figs. 5 and 6. To quantitatively compare the uranium deposit thicknesses at various surface locations, six points were chosen, as shown in Fig. 8(b). The results confirm those in Fig. 6, and the lowest growth rate was found at point 1. The measured deposit thickness on the actual cathodes exhibited large deviations
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Fig. 8. (a) Experimental validation of electrodeposition of uranium in 150 mA applied conditions. (b) Calculated uranium deposit thicknesses at various cathode locations under 150 mA applied current and 2 g/cm3 uranium density conditions.
Fig. 9. Polarization curves for laboratory-scale electrorefiner. Comparison of (a) experimental data with numerical data at (b) 450 ◦ C, (c) 500 ◦ C, and (d) 550 ◦ C.
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because of the random growth characteristics of uranium dendrites, but the tendency agrees well with the calculated deposit thickness shown in Fig. 8(b). Fig. 9 compares the experimental polarization curves with the calculated data. The material properties used for the calculation are shown in Table 3 (Martinet and Calligary, 1973). The cathodic current reached 150 A at cathode potentials of −1.5, −1.55, and −1.58 V at molten salt temperatures of 550 ◦ C, 500 ◦ C, and 450 ◦ C, respectively. As shown in Fig. 9(a), the anodic potential changed dramatically with the temperature, whereas the cathodic potential difference was only 0.03 V. The anodic potentials at 150 A of applied current were 0.25 V, −0.3 V, and −0.4 V at molten salt temperatures of 450 ◦ C, 500 ◦ C, and 550 ◦ C; this is attributed to an increase in the diffusion coefficient, as shown in Table 3. In addition, the larger surface area of the cathode is believed to contribute to the stable cathode potential. Hence, the resistance increase in the anode (low slope of the anodic curves) is believed to be responsible for the limited anodic dissolution rate owing to its relatively small surface area compared to the cathode. The calculated data generally agree with the experimentally obtained polarization curves at 450 ◦ C, 500 ◦ C, and 550 ◦ C, as shown in Fig. 9(b)–(d), respectively. These experimental and numerical data imply that the anodic overpotential is significant for the current laboratory-scale electrorefiner at a molten salt temperature of 450 ◦ C. The high anodic overpotential could cause noble metal impurity dissolution, which would decrease the uranium’s purity. Hence, an improved design with a larger anode surface area is necessary to increase the applied current. Using our calculations based on the tertiary model, the operational behavior of a laboratory-scale electrorefiner composed of multiple electrodes was successfully simulated. Hence, this result could be used not only for operation of the laboratory-scale electrorefiner but also for further development of a commercial-scale electrorefiner. 4. Conclusion In this paper, the electrodeposition behavior of uranium was successfully simulated using the COMSOL Electrodeposition modules, which are part of a commercial program for multiphysics. The simulation results indicate that 19 kg of uranium is theoretically attainable under an applied current density of 100 mA/cm2 after 24 h of operation using the current laboratory-scale electrorefiner at KAERI. The polarization behavior of this electrorefiner was compared to numerical data, and the anodic overpotential was found to be larger than that of the cathode owing to the anode’s relatively small surface area. The above results demonstrate that electrochemical transport strongly depends on the applied current in the electrolyte. A higher electric current is needed to deposit more mass of the metal at the cathode per hour. In addition, we believe that information on the electrorefiner characteristics will also be very helpful in determining the optimum operating conditions, and this model will provide crucial data for the design and manufacture of a commercial electrorefiner.
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