EFFECT OF ANODIC GAS RELEASE ON

EFFECT OF ANODIC GAS RELEASE ON CURRENT EFFICIENCY IN HALL-HÉROULT CELLS

Torstein Haarberg, Asbjørn Solheim , and Stein Tore Johansen SINTEF Materials Technology, N-7034 Trondheim, Norway Per Arinn Solli Hydro Aluminium Metal Products, N-5870 Øvre Årdal, Norway

Abstract The convection in Hall-Héroult cells caused by anodic gas evolution is computed for different cell geometries. The fluid flow data are applied to compute local mass transfer coefficients, in order to estimate the current efficiency as a function of the internal cell geometry defined by the sideledge thickness at the metal-bath interface. The results indicate that there is a non-linear relationship between current efficiency and the width of the side channel. When increasing the channel width, there is initially a sharp drop in current efficiency, while the current efficiency seems to be less affected if the channel is wide. The model results show good agreement with measured data from industrial cells. Introduction The formation and release of anodic gas bubbles in the HallHéroult cell have dramatic effects on the process. In later years flow and mass transport phenomena due to gas bubble release have been studied by several authors, both by physical models in the laboratory and by computer simulations [ 1-9], as well as by measurements in industrial cells [ 1,4,10]. Gas induced convection in the electrolyte is of particular interest concerning alumina dissolution [ 1,2], side ledge formation [ 3,4]and current efficiency (CE) loss [ 4-6]. In the present work, the relation between gas induced flow and current efficiency is further investigated. The dependence of current efficiency on cathodic current density is also analyzed. It is generally accepted that mass transfer at the metal-bath interface is the rate determining step concerning current efficiency loss in industrial cells. Electronic conduction [ 11] may enhance the mass transfer through the interface and thus contribute to current efficiency loss. In the literature, current efficiency is extensively measured in the laboratory [ 12-14], and the effects of temperature and bath composition on

current efficiency are well established [ 14,15]. However, temperature and bath chemistry can only partly explain current efficiency in industrial cells, and this is due to several complicating factors: • The complexity of the industrial Hall-Héroult process makes it very difficult to isolate effects of different variables on current efficiency. CE is related to other process aspects in complicated ways [ 16-18]. • Lack of short term measurement methods; there are still no methods available for accurate instantaneous determination of current efficiency in industrial cells. • When comparing different cell types it is important to keep in mind that the current efficiency is dependent on cell geometry (metal surface area) and convection, which determine mass transfer at the metal-bath interface [ 4]. Apparently, a better understanding of current efficiency in industrial cells can be achieved in a combined approach where cell geometry, electrolyte flow and mass transport processes are considered, as well as the traditional bath chemistry based analysis. Theory. Description of Model The current efficiency [ %]may be defined by

CE / 100 = 1 − Iloss / I ,

(1)

where Iloss is the electric current associated with parasitic (non-aluminium producing) side reactions, and I is the total cell current. By assuming that all current loss is localized to the metal-bath interface, the current efficiency for the total cell is given by the relation

∫i dA CE / 100 = 1 − loss I

(2)

where iloss is the total cathodic current density for all side reactions and A is the area of the metal-bath interface. Eqn. (2) shows that the problem mathematically reduces to finding the iloss variation along the metal-bath interface. By localizing all current loss to the metal-bath interface, it is implicitly assumed that the extent of the side reactions is governed by diffusion of reaction products across the boundary layer close to the interface. The rate of the side reactions then depends on convection, which is a local entity. In principle, iloss varies with the cathodic current density and the bath composition and temperature, as well as the flow conditions. The variation of iloss with temperature and bath composition is known from laboratory measurements [ 14]and will not be dealt with in further detail here.

where i is the anodic current density (8000 Am-2), R is the universal gas constant (8.314 Jmol-1K-1), T is the absolute temperature (1233 K), P is the pressure (101325 Pa), and F is Faraday’s constant (96487 Jmol-1equiv.-1), giving a value of q equal to 0.002 m3s-1m-2. In the calculation of the drag forces between electrolyte and bubbles, a modified drag coefficient (Cd) was applied, [ 19]

Cd =

0.622 Eo

(4)

1 + 0.235 Eo

where Eo is the dimensionless Eötvös number,

Eo =

( ρ bath − ρ gas ) g d 2p σ

≈

g d p2 σ / ρ bath

(5)

Fluid flow computations In the present work, a customized version of the commercial CFD-code FLUENT 4.4 was utilized to compute the gas induced electrolyte flow and mass transfer coefficients. Steady-state, time-averaged two-dimensional computations were performed, leaving out possible important transient effects on current loss, e.g., bubble induced oscillations of the metal-bath interface. Figure 1 shows the model geometry used in the computations.

1.0 m

0.061 m

0.1 m

o

Bath

Figure 1: Model geometry used in flow computations. In the model, gas bubbles were formed at 40 points along the underside of the anode, and a two degree inclination of the anode as shown in Figure 1 allowed the bubbles to move upwards. The rate of gas evolution, q, is given by [ 7]

iRT 4 FP

[ m3s-1m-2]

∆p g( ρ metal − ρ bath )

[ m]

(6)

where ρmetal = 2300 kgm-3 and the pressure difference ∆p was obtained from the fluid flow calculation. A new fluid flow calculation was performed using a deformed bath-metal interface obtained from Eqn. (6), and the procedure was repeated until convergence.

Metal

q=

The gas induced bath flow creates pressure variations along the bath-metal interface, which lead to a deformation of the interface. The steady state shape of the deformed interface was computed from the pressure distribution and its effect on the flow was accounted for by an iterative procedure. Initially, a calculation was performed for a flat bath-metal interface. The relative height difference (∆h) was then calculated using the relation

∆h =

0.2 m

r=

Anode 2

L

Here, ρbath is the bath density (2100 kgm-3), g is the acceleration of gravity (9.82 ms-2), dp is the equivalent bubble diameter (0.04 m), and σ is the surface tension of the bath (approx. 0.13 Nm-1 [ 20]).

(3)

Calculation of mass transfer coefficients There are two main classes of theories concerning mass and heat transfer across fluid-fluid interfaces. One possibility is to treat the interface as a solid wall (Boundary layer theories) where the convection decreases and falls to zero when the surface is approached. The other possibility is to allow convection to reach the interface, so that "new" interface may be formed at some places and "old" interface disappers at other places (Surface renewal theories). Both classes of

theories are discussed extensively in common text books [ 21,22]. Generally, surface renewal leads to considerably higher mass transfer coefficients. In the present work, the solid wall assumption was used. This choice is supported by the relatively high metal-bath interfacial tension (0.55 Nm-1 [ 20]) and also by the dimension of the typical eddies in the system, which are relatively small (≈ 0.05 m). In this situation, the ratio between the turbulent energy and the energy of the surface (σ⋅A) is small, so that surface renewal will not take place to any appreciable extent [ 23]. To calculate the mass transfer coefficient (k) the following relationship was applied, [ 24]

k = 0.075 ⋅Sc − 2 / 3 ⋅

τw ρ

[ ms-1]

(7)

where τw is the shear stress [ Pa]obtained from the fluid flow calculations and Sc is the dimensionless Schmidt number defined by Sc = ν /D where ν is the kinematic viscosity (approx. 1.3 ⋅10-6 m2s-1), and D is the diffusion coefficient.

coefficients for all species. There is one complication, however, which needs to be discussed. As mentioned above, dissolved sodium plays a major role in the CE loss, and dissolved sodium originates from the reaction

NaF +

1 3

Al =

1 3

AlF3 + Na

(10)

which must be considered to be at equilibrium at the interface. Hence, the sodium concentration at the interface is − 1/ 3

proportional to the activity product a NaF ⋅a AlF . AlF3 must 3

be brought to the interface by diffusion, since Na+ is the only current carrier, as illustrated in Figure 2. The concentrations of AlF3 and NaF at the interface are functions of the current density and the effective mass transfer coefficient for AlF3, in such a way that the concentration of sodium at the interface increases with increasing current density and decreasing mass transfer coefficient.

A lF 3 D iffusion

+

3 Na M igration

3 NaF D iffusion

Relation between mass transfer coefficients and current efficiency It is well known that aluminium reacts with cryolite melts through formation of reduced entities soluble in the electrolyte. The current density associated with these parasitic side reactions can be calculated according to

iloss = ∑ ni F ki (ci * − ci ∞ )

B a th

C a thode reaction

M e tal

3 e

Al

(8) Figure 2: Schematic representation of the main cathode reaction.

where n is the number of electrons and c are concentrations of reaction products, "*" representing the metal-bath interface and " ∞ " representing the bulk of the bath. The reaction products are dissolved sodium and reduced aluminium complexes; the latter can probably be regarded as intermediate products in the main aluminium-producing reaction. Dissolved sodium is probably the most important species concerning current loss, since it appears to have a very high diffusion coefficient which can be related to electronic conductivity [ 11]. In general, little is known concerning the concentrations and diffusion coefficients of the reaction products, however. Assuming that the concentrations in the bulk are zero, Eqn. (8) must therefore be represented by the simplified equation

i loss = F K

(9)

To simplify the calculations, however, the factor K in Eqn. (9) was assumed to be independent of the current density, i.e., the variation in the sodium concentration at the interface was not accounted for. By introducing this simplification, the cathodic current distribution needs not to be known when computing the current loss. It follows from Eqs. (7) - (9) and the simplification discussed above that the total current loss at a given temperature and bath composition can be calculated according to

Iloss ∝

∫ τ dA

(11)

Modelling Results Current efficiency as a function of current density

where the factor K comprises the products of concentration at the interface, number of electrons, and mass transfer

The simplest possible model is to assume no variation of iloss with respect to current density. This assumption will apply if

the sodium concentration at the interface is independent of the current density, but only in situations with no variations of shear forces (turbulence) at the cathode. The current efficiency in this case is given by (from Eqn. 2):

CE / 100 = 1 − b / ic( av )

(12)

τ dA CE /100 = 1 − β ⋅∫ Itot

(13)

where the proportionality factor β can be adjusted to give a certain current efficiency at given conditions. Flow computations

where b is a constant at given temperature and bath composition, and ic(av) is the average cathodic current density (ic(av) = I/Ametal). As shown in Figure 3, there is good agreement between experimental CE data obtained in a laboratory cell [ 14,26]and Eqn. (12).

The computed flow velocities at 200 mm channel width for the cases of flat and deformed interface are shown in Figure 4 and Figure 5, respectively.

100 Current efficiency / %

The gas induced flow was computed for five different widths of the side channel, in the range 100 mm to 500 mm (the channel width is marked L in Figure 1). Two different types of computations were performed; with and without a deformed interface.

80 60 40 20 0 0

0.5

1.0

1.5 -2

Current density / Acm

Figure 3: Current efficiency versus cathodic current density. o: Solli et al. [ 14], •: Skybakmoen and Sterten [ 26], ___:Eqn. 2 (12) with b = 0.035 A/cm .

Figure 4: Computed flow velocities below and outside the anode. Channel width 200 mm, flat bath-metal interface, umax = 1.0 ms-1.

The calculated current efficiency is slightly too high at high current densities, however. This is probably due to neglect of increasing sodium concentration at the metal-bath interface with increasing current density. Another factor not accounted for when comparing model and experimental data, is increased turbulence in the laboratory cell at increasing current densities due to enhanced gas induced flow. Anyhow, it was decided that the simplified approach, Eqn. (11), was accurate enough for the main purpose of the present work. Eqn. (12) may contribute to explain current efficiency differences between industrial cells, e.g., the difference between the performance of Søderberg cells and prebaked cells can partly be explained by different cathodic current densities. However, Eqn. (12) is restricted to situations with constant mass transfer coefficients, which cannot be assumed for an industrial cell. It follows from the discussion above that even though the local current efficiency may show considerable variation, the average (or integrated) current efficiency can still be calculated according to

Figure 5: Computed flow velocities below and outside the anode, channel width 200 mm, deformed bath-metal interface, umax =0.58 ms-1.

As seen from the figures, the computed flow velocities decreased when the interface was allowed to deform. Computed shapes of the metal-bath interface at different side channel widths are shown in Figure 6. The maximum predicted deformation increased with increasing channel width up to 300 mm, while for wider channels, the interface was less deformed. It appears that the predicted deformation of the bath-metal interface due to gas induced flow was considerable in all cases. A possible reduction of the deformation due to the bath-metal interfacial tension was not considered, however. Interfacial deformations caused by electromagnetic forces were also neglected.

quadratic (the bath height was also 200 mm). That case represented the lowest resistance to fluid flow and, consequently, the highest flow velocities. By increasing the channel width above 200 mm the current efficiency increased, in spite of increasing metal-bath interfacial area. However, when deformation of the interface was taken into account, this picture changed, and the current efficiency showed the expected decrease with increasing channel width.

1.5

4 k . 10 / m s -1

1.2

Deformation / mm

40

0 400 mm

-40 100 mm

100

0.3

0

200 mm

200

0.6

0

300 mm

0.4

0.8

1.2

Distance / m

-80 0

0.9

300

400

Figure 7: Computed mass transfer coefficients for AlF3 at the bath-metal interface. 200 mm channel width, ____: deformed interface, -----: flat interface.

Distance from anode / mm

Figure 6: Time - averaged deformation of the bath-metal interface due to gas induced flow for different channel widths.

Evaluation of mass transfer coefficients and current efficiency In calculating the mass transfer coeffient for AlF3, the value D = 1 ⋅ 10-8 m2s-1 was used [ 25]. The estimated local mass transfer coefficients at the bath-metal interface are presented in Figure 7 for 200 mm channel width (the local current loss will be proportional to the mass transfer coefficients). As can be observed, the mass transfer coefficients were higher for the flat interface, as compared to the deformed interface. This was due to the higher flow velocities for the flat interface (see Figures 4 and 5). In both cases, the calculated mass transfer coefficients were higher outside the anode projection, due to the gas induced flow. Figure 8 shows the current efficiency as a function of the side channel width, calculated according to Eqn. (13). The constant β was chosen to give 95 % CE for 100 mm channel width (deformed interface). For the flat interface case, the computed current efficiency has a minimum at 200 mm. This was probably due to a special geometric effect on the fluid flow; at this particular channel width the channel was

Figure 8: Predicted current efficiency versus channel width. •: deformed bath-metal interface, ∆: flat interface, o : model with constant mass transfer coefficient, Eqn. (12).

The deformed interface simulation, which represents a physically more realistic situation than the flat interface simulation, gave a more plausible variation of CE with the channel width. As can be observed in Figure 8, there was an initial reduction in the predicted current efficiency of 1.7 % per 10 cm increase in channel width, whereas for channel widths larger than 300 mm, the CE was less affected by additional increase in channel width. A possible interpretation of this result with respect to mass transfer is that increasing interfacial area is compensated by decreased turbulent energy when the channel is sufficiently wide. The simplified model, Eqn. (12), in which a constant mass transfer coefficient was assumed, is also shown in Figure 8. This model gave a linear decrease in current efficiency of about 0.3 % per 10 cm increase in channel width (i.e. this is the effect of increased area for mass transfer). This model appears to underestimate the influence of the channel width, as compared with the results from the more elaborate calculations using fluid flow determined mass transfer coefficients. Test of model against industrial cell measurements There are only a few references in the literature concerning the relationship between current efficiency and cell geometry. Bearne et al. [ 4] reported results from a one year full scale trial with 12 cells having reduced spacing between anode and sidewall from 450 mm to 250 mm. Solli [ 27] performed a statistical analysis of current efficiency variations on 6 test cells over a two year period, based on monthly measurements of the current efficiency (using the radio-tracer method) as well as the side ledge thickness at the metal-bath interface. In Table I, the available measurements from industrial cells are compared with the model results for the deformed metal-bath interface.

Table I Current efficiency dependence of side channel width, comparison between measurements in industrial cells and model results for deformed interface. ∆CE is the difference in current efficiency between narrow channel and wide channel. Reference Bearne et al. [ 4] Solli [ 27]

Channel widths [ mm] 200, 350 *) 180, 280

∆CE [ %] Model Measured 1.9 1.8 1.7 2.0

*) Assumed 50 mm sideledge thickness for narrow channel and 100 mm thickness for wide channel (not reported by Bearne et al.

It appears from the data in Table I that the predicted relationship between current efficiency and channel width, based on the deformed interface simulations, is in good agreement with available measurements performed in industrial cells. It is also evident that a model assuming

constant mass transfer coefficients cannot be applied successfully to predict current efficiency variations in industrial cells. Conclusion The gas induced bath flow in the Hall-Héroult cell is shown to have a significant influence on the current efficiency. In order to predict reliable current efficiencies, it is important to take into account the flow induced deformation of the metal-bath interface. The model results agree well with measured current efficiencies in industrial cells, which strongly indicates that the side channel width defined by cell geometry and sideledge thickness at the metal-bath interface, is an important parameter in understanding and improving the current efficiency in industrial cells. Acknowledgements Peter Johansson is thanked for performing many of the flow calculations. Financial support from the Research Council of Norway and from the Norwegian aluminium industry is gratefully acknowledged. References 1. O. Kobbeltvedt, “Dissolution kinetics for alumina in cryolite melts. Distribution of alumina in the electrolyte of industrial aluminium cells” (Dr.Ing. thesis, Norwegian University of Science and Technology, Trondheim, 1997). 2. D.C Chesonis and A.F. LaCamera, “The influence of gasdriven circulation on alumina distribution and interface motion in a Hall-Heroult cell”, Light Metals, 1990, 211220. 3. K.J. Fraser, M.P. Taylor, and A.M. Jenkin, “Electrolyte heat and mass transport processes in Hall Heroult electrolysis cells”, Light Metals, 1990, 221-226. 4. G. Bearne, A. Jenkin, L. Knapp, and I. Saeed, “ The impact of cell geometry on cell performance”, Light Metals, 1995, 375-380. 5. A.I. Begunov and B.S. Gromov, “Fluid dynamic effects of gas circulation in aluminium cells”, Light Metals, 1994, 295-304. 6. A. Dernedde and E.L. Cambridge, “Gas induced circulation in an aluminium reduction cell”, Light Metals, 1975, 111-122. 7. A. Solheim, S.T. Johansen, S. Rolseth, and J. Thonstad, “Gas driven flows in Hall-Heroult cells”, Light Metals, 1989, 245-252.

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