Industrial Aluminium Production: The Hall-Heroult Process Modelling Paris cedex, France

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1 ECS Transactions, 19 (26) 1-1 (29) / The Electrochemical Society Industrial Aluminium Production: The Hall-Heroult Process Modelling Ph. Mandin 1, R. Wüthrich 2 & H. Roustan 3 1 LECIME UMR 7575 CNRS-ENSCP-Paris6, ENSCP, 11 rue Pierre et Marie Curie, Paris cedex, France 2 Department of Mechanical & Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8 Canada 3 Alcan Centre de Recherche de Voreppe -725 rue Aristide Bergès - BP Voreppe Cedex, France Aluminium is produced according with the Hall-Heroult process. During this complex electrolyte two-phase electrolysis, it is difficult to model the current distribution and to optimize the process. The flow is the result of the magneto-hydrodynamic phenomena induced by the strong imposed currents and of the bubbles evolving. The reactivity and species concentration distribution are difficult to model. Bubbles are motion sources for the electrolysis cell flow, hydrodynamic properties are strongly coupled with species transport and electrical performances. Bubbles presence modifies these global and local properties. The goal of this proposition is to present the electrochemical engineering modelling of the Hall-Heroult two-phase electrolysis properties in the inter electrode interval. The numerical simulations are performed from both the chemistry and two-phase hydrodynamic point of views. 1. Introduction Aluminium is produced according with the Hall-Heroult process. At the cathode, Al x F y species are reduced and lead to liquid aluminium. At the consumable carbon anode, Al x O z F y species are oxidized to lead to carbon dioxide bubbles evolving and not O 2 bubbles because of the carbon anode consumption. During this complex electrolyte twophase electrolysis, it is difficult to model the current distribution and to optimize the process. The flow is the result of the magneto-hydrodynamic phenomena induced by the strong imposed currents and of the bubbles evolving. The reactivity and species concentration distribution are difficult to model: the molten salt chemistry is few developped compared with the aqueous chemistry. The mass, heat and charge transport are also stongly difficult to model, because of the created bubbles which imply transfer properties disturbance. Bubbles are motion sources for the electrolysis cell flow, hydrodynamic properties are strongly coupled with species transport and electrical performances. Bubbles presence modifies these global and local properties: the electrolysis cell and the current density distribution are modified. The goal of this proposition is to present the electrochemical engineering modelling of the Hall-Heroult two-phase electrolysis properties in the inter electrode interval. The numerical simulations are performed from both the chemistry and two-phase hydrodynamic point of views. Chemical calculations are first performed to describe dissolved gas species and bubble nucleation and growth. In a second step, a simple Euler-Lagrange two-phase model is presented to calculate hydrodynamic properties in Downloaded on to IP address. Redistribution subject to ECS terms 1 of use (see ecsdl.org/site/terms_use)

2 ECS Transactions, 19 (26) 1-1 (29) the cell. Calculations have been peformed with the finite volume software Fluent with additional user defined functions for the electrochemical engineering calculation. The bubble formation rate is simply modelled with the local current density, the Faraday law and the Bruggeman phenomenological law. Figure 1. Hall-Heroult process for aluminium production Aluminium production is performed in power plants with a process current between 1 to 3 kamperes. This current is flowing through numerous electrolysis reactors according with industrial set-up presented in figure 1. Important works have been performed concerning the Hall-Heroult process for aluminium production. Works are early invested in the magnetohydrodynamic properties, and more recently in the twophase hydrodynamic properties near the anode (1-12). Each electrolysis reactor is rectangular with a set of 8 to 1 graphite carbon cubic shape anodes which are about 1 meter dimension. These anodes are put in the hot (96 C), cryolithe (Na, F and Al melting bath defined with CR= NaF / AlF 3 ) bath of the electrolysis reactor according with configuration shown in figure Electrolysis process chemical modelling The first difficulty is due to the extreme bath condition in temperature and fluorine composition. Then, the usual input data for continuous modelling are in this case not available. The goal of the modelling is to build information, mostly at the anode surface, bubbles and two-phase character birth place. The bubble evolving rate is related to the over saturation in dissolved oxygen at anode and then it is necessary to be abble to build chemical information here from the preparation bath process. There are two accepted chemical modelling ways. The historical one is based on the atomic element Al, F, Na and O mass balance. Nevertheless, the representative transport and reaction properties are difficult to define. The second, and chosen here, one is a 7 species (+Al (l) ) and 1 reactions one. Among the reactions, 3 electrochemical ones are Downloaded on to IP address. Redistribution subject to ECS terms 2 of use (see ecsdl.org/site/terms_use)

3 ECS Transactions, 19 (26) 1-1 (29) considered at cathode, 2 electrochemical ones at anode, and 5 homogeneous reactions (2 dissolutions, 3 complex species equilibrium). The invested current allows the aluminium production at the reactor bottom according with the following electrochemical cathode reactions: - AlF 4 + 3e = Al (l) + 4F - (R1) AlF 5 + 3e - = Al (l) + 5F - (R2) AlF 6 + 3e - = Al (l) + 6F - (R3) At the graphite carbone anodes the following electrochemical reactions occur: Al 2 O 2 F 4 + 4F - + C = 4e CO 2 + 2AlF 4 (R4) 2Al 2 OF 6 + 4F - + C = 4e CO 2 + 4AlF 4 (R5) As it can be seen there are CO2 gas bubbles evolving at these consumed anodes, according with the geometrical configuration shown in figure 2. The electro active species Al 2 O 2 F 4 and 2Al 2 OF 6 are obtained with Al 2 O 3 dissolution according with following reactions: Al 2 O AlF 6 = 3Al 2 OF 6 + 6F - (R6) 2Al 2 O AlF 6 = 3 Al 2 O 2 F 4 (R7) The 5 electro active species AlF - 4, AlF 5, AlF 6, Al 2 O 2 F 4 and 2Al 2 OF 6 obey the following equilibriums: AlF 6 = AlF 5 + F - (K 1 = 3.3) (R8) AlF 5 = - AlF 4 + F - (K 2 =.5) (R9) 2Al 2 OF 6 + 2F - = Al 2 O 2 F 4 + 2AlF 5 (K 3 = 15) (R1) Anode? Figure 2. Magneto-hydrodynamic and two-phase coupled flows scheme. Figure 2 shows the consequences of the bubbles production at horizontal ceiling anode and the interaction between the two phase flow created at anode and general magnetohydrodynamics in the bath. The resulting flow is of course difficult and then it is modelled according with the measured limiting current density which are about 1 4 A m -2 whereas the average applied current density is around.8 x 1 4 A m -2. In these condition, the equivalent (same limiting current density) rotating disk electrode induced flow is obtained at about ω=1 rad s -1 (1 rpm). Downloaded on to IP address. Redistribution subject to ECS terms 3 of use (see ecsdl.org/site/terms_use)

4 ECS Transactions, 19 (26) 1-1 (29) 3. Chemical modelling calculation The flow is supposed to be equivalent to a RDE flow with ω=1 rad s -1. Then the species concentration boundary layer thicknesses around the associated electrodes are given by the Levich law: δ k = 1.6 D k 1/3. υ 1/6. ω -1/2 [1] The kinetic viscosity of the cryolithe bath is υ= 2 x 1-6 m².s -1. The diffusion coefficients D k for each considered species are reported in table 1. They have been calculated under the assumption that oxygen species have a 1-9 m².s -1 diffusion coefficient value. Molecular scale considerations lead to species diffusion coefficient ratio estimation. Previous works performed at the molecular scale (13), with DFT-based calculations, have focused their attention upon the structures of oxyfluoroaluminates in molten cryolitealumina mixtures. These investigations have allowed the evaluation of the ionic species radius: r k =2.8 Angström for k=alof x, r k =1.8 Angström for k=alf x, r k =.7 Angström for k=f -. According with the Stokes-Einstein equation D k =k B.T/(6.π.µ.r k ), k B =1.38 x 1-23 m 2 kg s -2 K -1 is the Boltzman constant, the species diffusion coefficient ratio is equal to the species radius ratio and leads to results presented in table I. TABLE I. Seven species diffusion coefficients and bulk concentration Species F - - AlF 4 AlF 5 AlF 6 Al 2 OF 6 Al 2 O 2 F 4 O 2 D k (m².s -1 ) Ck, bulk (mol m -3 ) 4 x x x x x x x x x x 1 3 Table I also gives the species bulk concentration for CR=2.2. This calculation is obtained under the assumption of equilibrium for reactions (R8), (R9) and (R1) with the associated thermodynamic constant values (14). The solving of the 6 unknowns, 6 equations (3 atomic species mass balance and 3 equilibrium contsnt to satisfy) non linear algebraic constant has been performed using generalised Newtonian Jacobian algorithm. Resulst have been validated using the Mapple software. According with the species boundary layer thicknesses, the calculation domain can be now defined and discretized. The figure 3 shows the discretization with three blocks of the inter electrode calculation domain (About 4 cm long). The larger diffusion coefficient D k is used to define the reference thickness δ (m) according with Levich law. Boundary layer A Boundary layer C Figure 3. Inter electrode calculation domain discretization: finite volume methode with 3 blocks. Downloaded on to IP address. Redistribution subject to ECS terms 4 of use (see ecsdl.org/site/terms_use)

5 ECS Transactions, 19 (26) 1-1 (29) The species concentration profiles are these obtained from the associated mass balance resoltuion according with the finite volume method for discretization and with the Thomas algorithm for matrix inversion. For a given electrical condition (current density at anode and potential value at cathode), it is then demonstrated that direct calculation is possible. Concentration C k (mol m -3 ) AlF 5 F - AlF 4-2 Al 2 OF 6 Al 2 O 2 F 4 2 AlF 6 O 2 Position x (m) Figure 4. 7 species modelling concentration profiles at the anode vicinity. Concentration C k (mol m -3 ) AlF 5 F - AlF 4-2 Al 2 OF 6 Al 2 O 2 F 4 2 AlF 6 O 2 Position x (m) Figure 5. 7 species modelling concentration profiles at the cathode vicinity. The figures 4, 5, 6 and 7 show the species profiles concentration at the electrodes vicinity and their evolution with the local current density value. With this modelling, new interfacial information has been built. From the known bath preparation condition and electrical imposed current, it is possible to evaluate the local chemical properties at the electrode material-electrolyte bath interface. The O 2 and F - concentration are particularly important for respectively the oxidizer and acidity potential at the electrode material interface. The regular consumption, erosion and flow accelerated corrosion are strongly related with these, for instance, impossible to measure information. The modelling strategy is then the only adapted strategy to optimize interface condition. For all the realistic local current density values possible for a given current density distribution, according with a given total current value, the oxygen concentration at Downloaded on to IP address. Redistribution subject to ECS terms 5 of use (see ecsdl.org/site/terms_use)

6 ECS Transactions, 19 (26) 1-1 (29) interface is larger than the cryolite O 2 or CO 2 saturation concentration. Because, over saturation concentration values are reached at the electrode interface, bubbles are then nucleating and growing, leading to a very difficult two-phase electrochemically induced flow, which one modelling is now presented. Concentration C k (mol m -3 ) F - Increasing current Position x (m) Figure 6. evolution of F - concentration profiles at the anode vicinity with the applied local current density value Concentration C k (mol m -3 ) Increasing current AlF 4 - Position x (m) Figure 7. evolution of AlF 4 - concentration profiles at the anode vicinity with applied local current density value 4. Two-phase flow modelling A primary current distribution model at anode has been first developped (6). One conclusion of this first work is that the primary current distribution is unable, alone, to describe correctly the local and global electrolysis reactor performances. This is the reason why the chemical process properties have been investigated first to increase the modelling efficiency. It has then been decided to upgrade this first modelling with a ternary current distribution modelling. The necessary species concentration calculation has been presented in the previous chapter. The present chapter is dedicated to the twophase hydrodynamic modelling and calculation algorithm. The schematic mathematical configuration is presented in figure 8. Experiments are in progress to explore classical experimental factors such as the electrodes material composition, the electrolyte bath condition, the geometrical parameters, the hydrodynamic flow and even, the natural convection with the gravity factor. This last factor is explored using parabolic flights experiments (8-1) and also drop tower experiments (11-12). Downloaded on to IP address. Redistribution subject to ECS terms 6 of use (see ecsdl.org/site/terms_use)

7 ECS Transactions, 19 (26) 1-1 (29) I imp U Figure 8. Vertical gas-evolving electrode experimental set-up The figure 9 shows the simplified calculation algorithm for current distribution at working electrode (hydrogen production). The local current density is calculated according with the electro active species convective and diffusive transport presented in the first part. The classical Fluent CFD software is used to solve the Navier-Stokes equations under laminar hypothesis with finite volume methods. Electrolyte Hydrodynamics Velocity field V Void fraction ε Electrical Current density Current density distribution Navier-Stokes relations Newton law for discrete Bruggeman relation : κ = κ (1-ε) 3/2 [2] Charge balance : div j = [3] Bubble mass flow rate q Faraday relation : q = M j n / (n F ) [4] Figure 9. Calculation flow-sheet for the coupling effect in the electrochemical cell due to the presence of bubble release. Then, for a given injected gas mass flow rate with constant spherical shape and diameter, mono disperse bubbles, each particles trajectory is calculated according with local conditions. The bubble friction is associated to a liquid electrolyte local motion source Downloaded on to IP address. Redistribution subject to ECS terms 7 of use (see ecsdl.org/site/terms_use)

8 .6 ECS Transactions, 19 (26) 1-1 (29) term which ensures the strong coupling between continuous liquid phase and discrete bubbles phase. According with the bubble residence time, an average void fraction ε (-) is calculated and then the local electrical conductivity κ (S m -1 ) which value is smaller than the pure liquid one value κ because of the insulating character of the gas, according with the Bruggeman law [2]. Then the local current density j (A m -2 ) balance equation [3] can be calculated and yields to smaller current density value where the bubbles concentration is large at the electrodes top. According with the Faraday law [4], the smaller the current density j, the smaller local gas mass flow rate q (kg s -1 m -2 ). Calculations are in progress. The Navier-Stokes calculation leads to a proposition of hydrodynamic profile which must be validated with PIV experiments (figure 1). These experiments are in progress. Y (m) position(2) Vy position X(m) Figure 1. PIV measurements experimental set-up (top) and exemple of hydrodynamic field properties (bottom). 5. Conclusion Downloaded on to IP address. Redistribution subject to ECS terms 8 of use (see ecsdl.org/site/terms_use)

9 ECS Transactions, 19 (26) 1-1 (29) The aluminium production process is a two-phase electrolysis which implies numerous chemical, electro chemical and transport phenomena. It is then difficult to model. The bath conditions are extreme with 96 C for a fluorine bath. Then modelling is particularly needed to build information particularly at electrodes. At cathode the aluminium quality depends on the chemistry at vicinity. At anode, the capacive discharge effect, called anode effect, is responsible for important efficiency and quality losses and also for pollutants such as CFx production. Actually the anode material is reacting with bath during electrolysis and leads to carbon dioxide production which must be avoided in the future years. Acknowledgments Authors would like to thank the French National Research Agency, materials and processes research program Amelhyflam and the French National Center of Spatial Studies for their technical help and their financial support. References References 1. C.W. Tobias. The influence of attached bubbles on Potential Drop and Current Distribution at Gas-Evolving Electrodes. J. Electrochemical Society, vol 134, 2 (1959). 2. H. Vogt, J. Thonstad. The Voltage Alumina Reduction Cells Prior To The Anode Effect. J. of Applied Electrochemistry, 32, (22). 3. F. Hine, M. Murakami. Bubble Effects On The Solution Ir Drop In A Vertical Electrolyzer Under Free And Forced-Convection. J. Electrochem. Society, Vol 127, (198). 4. L. Kiss, S. Ponscak. Effect Of Bubble Growth Mechanism On The Spectrum Of Voltage Fluctuations In The Reduction Cell. TMS Light Metals, (22). 5. H. Vogt, R.J. Balzer. The bubble coverage of gas-evolving electrodes in stagnant electrolytes. Electrochimica Acta. 25, Volume 5, Issue 1, (25). 6. Ph. Mandin, J. Hamburger, S. Bessou, G. Picard. Calculation of the current density distribution at vertical gas-evolving electrodes. Electrochimica Acta, Volume 51, Issue 6, (25). 7. J.A. Drake, C.J. Radke and J. Newman. Transient linear stability of a Simonsprocess gas liquid electrochemical flow reactor using numerical simulations. Chemical Engineering Science, Volume 56, Issue 2, (21). 8. Ph. Mandin, J.M. Cense, B. Georges, V. Favre, Th. Pauporte, Y. Fukunaka, D. Lincot. Prediction of the electrodeposition process behavior with the gravity or acceleration value at continuous and discrete scale. Electrochimica Acta, 53, (27). 9. Ph. Mandin, A. Ait Aaissa, H. Roustan, J. Hamburger, G. Picard. Two-phase electrolysis process: from the bubble to the electrochemical cell properties. Chemical Engineering and Processing: Process intensification, 47, (28). 1. Ph. Mandin, H. Matsushima, Y. Fukunaka, R. Wuthrich, E. Herrera Calderon, D. Lincot. One to two-phase electrolysis processes behavior under spatial conditions. Journal of the Japanese Society of Microgravity Applications, vol 25, 3 (28). Downloaded on to IP address. Redistribution subject to ECS terms 9 of use (see ecsdl.org/site/terms_use)

10 ECS Transactions, 19 (26) 1-1 (29) 11. H. Matsushima, T. Nishida Y. Konishi, Y. Fukunaka, Y. Ito, K. Kuribayashi. Water electrolysis under microgravity: Part I. Experimental technique. Electrochimica Acta, Volume 48, Issue 28, (23). 12. H. Matsushima, Y. Fukunaka and K. Kuribayashi. Water electrolysis under microgravity: Part II. Description of gas bubble evolution phenomena. Electrochimica Acta, Volume 51, Issue 2, (26). 13. G. Picard, F. Bouyer, M. Leroy, Y. Bertaud, S. Bouvet. Structures of Oxyfluoroaluminates in molten cryolite-alumina mixtures investigated by DFTbased calculations. J. of Molecular Structures (Theochem), 368, 67-8 (1996). 14. E. Robert, J.E. Olsen, V. Danek, E. Tixhon, T. Ostvold, B. Gilbert. Structure and thermodynamics of alkali fluoride-aluminium fluoride-alumina melts. Vapor Pressure, Solubility and Raman spectroscopic studies. Journal of Physical Chemistry B, Vol. 11, No. 46, (1997). Downloaded on to IP address. Redistribution subject to ECS 1 terms of use (see ecsdl.org/site/terms_use)