Multi physics modeling of a molten-salt electrolytic process for nuclear waste treatment

Transcription

1 IOP Conference Series: Materials Science and Engineering Multi physics modeling of a molten-salt electrolytic process for nuclear waste treatment To cite this article: K R Kim et al 010 IOP Conf. Ser.: Mater. Sci. Eng View the article online for updates and enhancements. Related content - Electro-deposition behavior of minor actinides with liquid cadmium cathodes H Kofuji, M Fukushima, S Kitawaki et al. - Galvanically coupled gold/soi microstructures in hydrofluoric acid electrolytes C R Becker, D C Miller and C R Stoldt - Electrodeposition experiments in microgravity conditions K Nishikawa, Y Fukunaka, E Chassaing et al. Recent citations - First-principles prediction of universal relation between exchange current density and adsorption energy of rare-earth elements in a molten salt Choah Kwon et al - Scientific and Engineering Literature Mini Review of Molten Salt Oxidation for Radioactive Waste Treatment and Organic Compound Gasification as well as Spent Salt Treatment Petr Kovaík et al This content was downloaded from IP address on 30/10/018 at 1:46

2 Multi physics modeling of a molten-salt electrolytic process for nuclear waste treatment K R Kim 1, S Y Choi, J G Kim 1, S Paek 1, D H Ahn 1, S W Kwon 1, J B Shim 1, S H Kim 1, H S Lee 1, B G Park 3, K W Yi and I S Hwang 1 Korea Atomic Energy Research Institute, 1045 Daedeok-daero, Yuseong-gu, Daejeon, Korea Seoul National Univ., San 56-1, Sillim-dong, Gwanak-gu, Seoul, Korea 3 Soonchunhyang Univ., Sinchang-myeon, Asan-si, Chungcheongnam-do, Korea krkim1@kaeri.re.kr Abstract. Multi physics electrochemical modeling in a framework of Computational Fluid Dynamics (CFD) code was proposed and dealt with in detail to simulate the electro-transport behaviour that appears in a molten-salt electrolytic system. The modeling approach in this study is focused on the mass transport and current arising due to the concentration and the surface overpotential based on a cell configuration and electrolyte turbulence. This comprehensive modelling approach was applied and compared to electroplating model in a prepared rotating cylinder Hull (RCH) cell system. 1. Introduction A nuclear fuel cycle based on pyroprocessing technology offers substantial improvements in waste management, proliferation resistance and economic potential compared to conventional processing technologies used overseas countries [1]. The most effective way to accelerate the development of these technologies is to formulate physical models of the underlying electrochemical and transport processes. In addition, an integrated multi physics simulation offers an efficient approach to designing, testing, and implementing these processes [,3]. In the field of pyrochemical electrometallurgy, an electrorefining step is one of the important techniques that allow for recovery of uranium to an extreme degree. The throughput is determined by the cell configuration, operating conditions (mixing, applied current and cell voltage), and the chemical state of the electrolytic cell. The ion current in the bulk electrolyte requires knowledge of the electrode surface phenomena which needs an electro-fluid analysis of a mixing and mass transport. The electrode kinetics requires empirical and analytical knowledge of the exchange current density, and the parameters for a deposition and dissolution of the ions [4,5]. In a uranium electrorefining system, the deposition model on a rotating cathode is almost similar to a metal electroplating system. The rotating cylinder Hull (RCH) cell has been used as an experimental tool for the investigations of single metal, alloy and composite deposition [6]. This design enables a wide range of electrochemical features to be achieved in a single experiment and is useful to benchmark a proposed model. Copper electroplating has recently become the standard technique for metalizing interconnects in high-end electrodeposition studies. c 010 Ltd 1

3 In this study, an implementation of the electro-fluid analysis within a CFD framework is carried out to simulate the electrorefining process. In an electrorefiner geometry, the comprehensive approach and algorithm for representing the more realistic electro-fluid features are described. In addition, benchmark simulation for the proposed modelling technique with the copper electroplating system in a prepared RCH cell is conducted to know the validity of this approach and model capabilities.. Mathematical model.1. Computational fluid dynamics (CFD) model The CFD model can be set up within the ANSYS CFX-11.0 framework [7]. The electrolyte fluid flow of the electrolytic process is assumed to be well represented by the incompressible Navier-Stokes equation with the continuity equation. A scalar transport equation is used to describe the transport of the reactive ion from the bulk to the electrode surface. The transport equation for the ionic concentration (C) with external mass source (S C ) term is given by: C ρ + ρ ( uc) = ρ ( D C) + t C S C where u is the velocity, Dc is the diffusion coefficient and ρ is the density. The choice of spatial coordinate and the boundary conditions depend on the electrode geometry... Electrochemical reaction kinetics The polarization equation is necessary to express the dependence of the local rate of the electrochemical reaction on the various concentrations and on the potential drop at the interface. It is common to use the Butler-Volmer equation [8] of electrode kinetics of the form for metal/ion systems. Local current density (i) distribution on the electrode surface is modeled by the following equation: S S C O αf CR (1 α) F i = i0 exp η exp η bulk bulk CO RT CR RT () where F is the Faraday s constant, R is the gas constant, η is the overpotential, superscripts s and bulk are the locations at the electrode surface and bulk electrolyte, subscripts O and R are the oxidized and reduced species, and i 0 is the exchange current density: bulk 1 ( ) α bulk C ( ) α O C 0 i0 = nk F R (3) where α and k 0 are kinetic parameters, n is the charge number. This equation is a modified-type Butler Volmer equation that includes terms of concentration overpotential as commonly used [9]..3. Electric field in a bulk electrolyte For electrolyte salt in the interior of an electrolytic cell, there are no free electrical charges. The ohmic potential drop across the concentration boundary layer is negligibly small compared to the ohmic potential drop across the bulk of the electrolyte. Therefore, the potential drop across the electrolyte is governed by the Laplace equation: Φ = 0 (4) where, Φ represents the local electrical potential. And the current density distribution is obtained by solving the following equation (k= electrical conductivity): (1)

4 i = k Φ Assuming that we impose a specific voltage drop (E Cell ) across the electrodes, the overall voltage balance may be written as: ECell = φ where E Cell is the difference between the applied cell voltage and the thermodynamic equilibrium cell voltage. Φ ohm is the ohmic voltage drop, η a and η c are the voltage drops due to activation polarization (i.e., kinetic effects) and concentration polarization (due to concentration gradients between the electrode surface and the bulk electrolyte), respectively. Thus to determine the current density and concentration distributions along the electrode, the convective diffusion equation and the Laplace equation must be solved simultaneously along with electrochemical kinetics using suitable geometry-dependent boundary conditions..4. Boundary conditions A scalar transport equation is solved for the concentration of the ionic species, with source/sink (S C ) at the appropriate anode and cathode boundary based on Faraday s law. The electric boundary conditions include the specification of a current flux equivalent to an applied current through the electrodes. The boundary conditions for the ionic species for the source/sink at the wall of electrodes are calculated as follows: ohm S C = ± On the anode side, a positive flux is applied, while a negative flux of a same size is applied on the cathode. At the wall of an electrolyte fluid field, no slip boundary (friction) conditions are enforced upon at all solid walls, whilst a free slip (no friction) boundary condition is applied at the top free surface..5. Computational algorithms The calculation is implemented through the user Fortran link in the CFX-11.0 solver as seen in figure 1. A user Fortran source is compiled and linked into a platform of specific shared library. The shared library is dynamically loaded at runtime. The local overpotential at the electrode surface is calculated from the electric fields obtained from the latest solution fields for the locations on which the subroutine is currently operating. Then a linear solver of the CFX-11.0 runs for a coefficient loop until its solution satisfies the convergence criteria of the equation residuals. + η a i nf + η c (5) (6) (7) 3

5 Figure 1. Calculation procedures of the user Fortran link in a CFX-11.0 framework. 3. Experiment for model benchmarking The design of RCH cell has been available and provided an important experimental tool for electrodeposition studies. Such geometries have been used for the measurement of non-uniform current distribution, mass transport and throwing power of plating baths at controlled turbulent flow condition. In this study, a RCH typed cell was prepared and set up to find out a local potential and current density distribution on the working electrode at various rotating conditions as shown in figure. The detailed geometry, configurations and experimental conditions of the RCH cell are described by Low et al. [6]. In order to measure the local potentials at the 8 positions along the working electrode, the connected tubing tips of Ag/AgCl reference electrodes are installed with a gap of 1 mm just around the rotating electrode at a regular interval. Each detecting channel is connected to a 16-bit A/D converter (Model ED161, edaq Pty Ltd). The operational current is controlled by the galvanostat (WPG100, Wonatech. Co.) Figure 3 shows 6 o segment with meshed D planar area for the computational domain. Figure. The RCH cell typed experimental system [6]. The working electrode is a rotating cylindrical electrode (316 stainless steel, m diameter, 0.08 m length); the counter electrode is a concentric Figure 3. The 6 o segment with meshed D planar area is the computational domain used in the numerical simulation. 4

6 cylindrical electrode (Pt/Ti, 0.1 cm thickness, 0.05 m inside diameter, 0.05 m height). 4. Results and discussion 4.1. Simulation of uranium electrorefining cell According to the above-mentioned approach, a simple electrorefiner was modelled as shown in figure 4. The electrolytic vessel consists of an anode basket of a cruciform arrangement and a steel cathode submerged in a molten LiCl-KCl eutectic containing approximately 8 wt% of U. Table 1 is the properties of the LiCl-KCl eutectic used in this study. The molten salt electrolyte is mixed during the electrorefining process by the rotating cathode (5 rpm clockwise) and anode basket assemblies (50 rpm clockwise). The operational conditions, physical properties and kinetic parameters for the electrorefining analysis are summarized in table. Table 1. Data of the molten eutectic salt (LiCl-KCl) used as an electrorefiner electrolyte [10] Data Values Molten salt composition (Li/K mole ratio) 59/41 Molar mass (kg mol -1 ) Density (kg m -3 ) 1551 Dynamic viscosity (N s m - ) Table. Parameters and thermodynamic data used in the calculation at 773K [10] Parameters and thermodynamic data Values Volume of molten salt electrolyte (m 3 ) 0.6 Surface area of anode basket (m ) 0.75 Surface area of solid cathode (m ) Applied current (A) 50 Operating temperature (K) 773 Initial weight fraction of U in electrolyte ( ) 0.08 Standard potential (V vs. AgCl/Ag) of U 3+ /U 0 in LiCl-KCl Electrochemical kinetic parameters Faraday constant, F(C mol -1 ) Rate constant, k 0 (m s -1 ) Transfer coefficient, α( ) 0.5 The concentration profiles of ionic reacting species of uranium are shown between the both electrodes in figure 5. As expected, uranium ion depletion near the cathode surface and generation from the anode are depicted under this convective turbulent condition. It is shown that the concentration distribution of uranium in the bulk electrolyte region is almost uniform. In an electrorefining cell, all of the potentials in the electrolyte solution must fall between the potentials imposed on the anode and cathode. This principle is used in making the estimates and 5

7 adjustments of the electrode potential reflected with an overpotential at a given current density. Figure 6 shows the potential distribution along the symmetry plane between the electrodes and corresponding value of a local overpotential distribution at the electrode. Ohmic overpotential is the loss associated with resistance to electron transport in the electrolyte region. For a given applied current, magnitude of this overpotential is dependent on the path of the electron. The diffusion overpotentials are related to the concentration gradient near the electrodes. It is found that the concentration gradient at the electrode surface is proportional to the applied current over a wide current range up to around the limiting current density. Figure 7 depicts the local current density distribution along the electrode surface in case of coupled computation with the concentration gradient. The effects of electrolyte concentration are taken into account. It is found that a higher local potential is arisen from a lower ionic concentration at the electrode surface. In order to maintain the given current density, a higher overpotential is necessary for the compensation of the ionic reactant depletion. The proposed approach is a technique accounts for all possible configuration and operational alternatives of the molten salt electrochemical system. Figure 4. Schematic of a molten salt electrorefiner for a computational model. Figure 5. Concentration profiles of ionic uranium species between both electrodes. Figure 6. Potential distribution between both electrodes and local overpotential distribution on the electrodes. Figure 7. Current density distribution coupling uranium concentration gradient between both electrodes. 4.. Simulation of RCH cell and tests By using the same approach used in an electrorefining simulation, an attempt was made to model the electroplating system of the RCH cell. This experimental tool has been a proven technology to obtain the electrochemical features for a wide range of hydrodynamic and operational conditions. All the dimensions and parameters used for the numerical simulation are same as ones used in Ref. [6]. The test system is copper electrodeposition from an acid sulfate electrolyte containing 50mM 6

8 CuSO 4 and 0.5M Na SO 4 at ph and 0 o C. In this model, the Tafel approximation was used for the electrochemical kinetics instead of the Butler-Volmer equation [9]. Figure 8 shows the simulated primary potential pattern throughout the electrolyte region. The primary current distribution assumes both the charge transfer and mass transport conditions are negligible. In this case, the main aspect that determines the current distribution is the ohmic resistance within the RCH cell. The electrochemical reaction on the working electrode is considered reversible, and the primary distribution is dependent solely on the geometry of the electrolyte field. The simulated potential pattern coupling with concentration is shown in figure 9. This pattern can be obtained when the electrochemical reaction is dependent on the charge transfer and concentration gradient. In preliminary experiments, we have measured the local potentials near the electrode surface for eight different positions. Figure 10 shows the typical time courses of electrical potential differences between the pairs of reference electrodes at different rotating rates. It is seen that the local potential increases (in negative) roughly along the upper direction of the working electrode. At a higher rotating speed, more uniform potential distributions are shown. Since higher turbulent leads to increased surface reactant concentration, the potential distribution at the working electrode becomes slightly uniform. Figure 8. Primary potential distribution. Figure 9. Potential distribution coupled with charge transfer and concentration. The morphology of the copper deposit on the working electrode is partly dendritic powder near the bottom under given current density condition of 600 A m - as seen in figure 11. Because the deposition rate depends directly on the local current density, a future study is planned for a benchmark simulation taking into account of the reactant concentration effects and the validation against experimental data gathered. The proposed CFD approach could offer a new possibility for the multi physics computational model of uranium electrorefining in the molten salt electrolyte which required special care in handling due to the high temperature and radioactivity. This model can predict all aspects of the electrodeposition process and reduce the experimental works for finding an optimized design or operational condition. 7

9 Potential (V vs. Ag/AgCl) Potential (V vs. Ag/AgCl) Time (sec.) (a) 00 rpm Time (sec.) (b) 400 rpm Potential (V vs. Ag/AgCl) Potential (V vs. Ag/AgCl) Time (sec.) Time (sec.) (c) 600 rpm (d) 800 rpm Figure 10. Time courses of electric potential distributions (0.5M CuSO 4, 600 A m - ). Figure 11. Copper deposit on the working electrode (0.5M CuSO 4, 600 A m - ). 5. Conclusions A computational electro-fluid dynamics model of a uranium electrorefiner was proposed on a CFD framework. This model provides valuable information about the transport phenomena inside the electrolytic cell such as concentration, potential and overpotential distribution. A unique feature of this model is the implementation of the potential-to-current algorithm that allows for a more realistic spatial variation of the electrochemical kinetics. In order to benchmark the proposed modeling approach, a RCH type cell has been built. In an experimental approach, it was found to be possible for the model verification. Primary and secondary current distributions along the rotating electrode have been calculated and a future work will address the experimental verification against the electrodeposition data. Acknowledgments This work was supported by Nuclear Research & Development Program of the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MEST). 8

10 References [1] IAEA 008 Spent Fuel Reprocessing Options IAEA-TECDOC-1587 August 008 Vienna Austria p 139 [] Li S X, Sofu T, Johnson T A and Laug D V 000 Journal of New Materials for Electrochemical System 3 59 [3] Ahluwalia R K, Hua T Q and Geyer H K 000 Nuclear Technology [4] Kim K R et al 009 Journal of Radioanalytical and Nuclear Chemistry [5] Bae J D, Yi K W, Park B G, Hwang I S and Lee H Y 005 Development of an Electrochemical-Hydrodynamic Model for Electrorefining Process: Proceedings of Global 005 (Tsukuba, Japan, 9-13 October 005) [6] Low C T J, Roberts E P L and Walsh F C 007 Electrochimica Acta [7] ANSYS CFX-11.0 Solver 008 (Cannonsburg: USA/ANSYS: [8] Pickett D J 1979 Electrochemical Reactor Design (New York: American Elsevier) p 48 [9] Bard A J and Faulkner L R 001 Electrochemical Methods, Fundamentals and Applications (New York: John Wiley & Son) p 87 [10] KANG Y H et al 1999 Pyrometallurgical Data Book (Korea Atomic Energy Research Institute Report KAERI/TS-110/99) 9