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Eierrrwkimio ACT. Vol. 25, pp. 131-137.Rrgamon Press Ltd 980. Printed in Great Britain.

CURRENT EFFICIENCY AND BACK REACTIONIN ALUMINIUM ELECTROLYSIS

B. LILLHIUEN and S. A. YTTERDAIILNorsk Hydra as Research Centre 3900 Porsgrunn Norway

and

R. HUGLEN and K. A. PAU~RFNNorsk Hydra a.s, Karm#y Fabrikker 4265 Havik Norway

Abstract - The rate of back reaction in aluminium electrolysis is discussed in terms of mass transfer theory.The rate of dissolution of aluminium seems to be the most important step in this reaction.

By using the physical.data which are available in the literature current efficiency variations have beencalculated as a function of the most important parameters n the electrolytic ells. These calculated variationsagree reasonably well with experimentally determined variations.

1. INTRODUCTION

Current efficiency is one of the most important para-meters that are being used to characterize the workingcondition of an aluminium electrolysis cell. The cur-rent efficiency provides information which is relevantboth to the energy consumption and to the metaloutput of the cell. Accordingly, a large number ofexperimental investigations has been made[l-31 inorder to define cell working conditions that secure ahigh current efficiency.

The present work is an effort to approach thecurrent efficiency problem both from a theoretical andfrom an experimental point of view. Similar theoreticalefforts have recently been made by Rob1 et al[14].

2. THEORETICAL PART

2.1 Back reaction ratesIt seems to be widely accepted[4,6] that the current

efficiency loss in aluminium electrolysis cells is mainlydue to the back reaction between metal and anodegas:

Al + ;C02- fAl,O, + +ZO. 1)

Other explanations have been suggested[5], whichmay have some significance, but we will in thefollowing assume reaction (1 to be solely responsiblefor current elI?ciency losses. We will in addition makethe following assumptions :

a) Reaction (1) occurs between dissolved reactants.b) The simple film theory is vahd, and we disregard

the transportation of the heat of reaction andthe reaction products.

(c) The chemical reaction between dissolved metaland dissolved carbon dioxide is instantaneous:and the rate of reaction (1) is considered to becontrolled by the mass transfer rates ofdissolvedreactants through stagnant films.

Experiments have indicated the chemical reaction tobe much faster than the mass transfer processesinvolved[4].

Up to this time, most authors have concluded thatthe back reaction occurs between dissolved aluminiumand gaseous carbon dioxide[b]. We believe, however,that the following calculations lend support to a

reaction model that involves dissolved carbon dioxideas well as dissolved aluminium.

If the assumptions we have made above are valid, wemay, according to Aarebrot et al[7,8] write for thedissolution rates of aluminium and carbon dioxide:

kc,, . Go,h, . (3, >

CXl - CA,) (2)

wherer = dissolution rate

A = interfacial area against electrolytek = mass transfer coefficient

C = concentration of dissolved species in the bulkelectrolyte

C* = thermodynamic solubility.Note the implication From assumption (c) that fromC,, > 0 follows that Go, = 0 and uice uerso C z 0makes C,, = 0.

Combining (2) and (3), and introducing the sto-chiometric requirements of (1) lead to the followingexpression :

x Cl + k) $jCct,- Gil

[I + ( J(@m, - C l = ;. (4)The interfacia1 area between metal and electrolyte isobviously smaller than the area gas/electrolyte. Theratio A JA will depend upon bubble size, metaldispersion, side crust profile and metal pad height etc.As a first guess, based on observations in plant cellsand ofgas-bubble behaviour in a hydraulic model cell,we estimate this ratio to 0.1. By using (23) in the workof Aarebrot 8) we estimate the ratio k /k -o l to 1.0.

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132 B. LILLEBUEN, S. A. YTTERDAHL, . HUGLEN AND K. A. PAULSEN

Both of these estimates contain of course consider-able uncertainty, and further refinement should beencouraged. In this respect a precise determination ofthe diffusivity coefficient of dissolved CO2 would hevery useful. We have adopted a value for Dco, =iOmE m2 -s-[9] and for D*t = 3 .10-s .mz *s-[lo].

We proceed by assuming a finite amount of dissol-ved aluminium to be present in the bulk electrolyte,and write

C*, = f. CXI (5)

where f is the fraction present (relative to thermody-namic solubility).

By inserting (5) into (4), remembering that CA, > 0implies Ccoz = 0, and setting[6]

Cx, = lOed mol .IXII-~ (uncertain)

Go,, = 2. 10m6 mol .crnm3

we find:

f= 0.113

which means that the bulk electrolyte contains approx1.13 . lo- mol cm- of dissolved aluminium at steadystate. The frequently discussed question of which stepin the back reaction that is rate determining, cannot ofcourse be definitely answered by means of suchcalculations. We would like to suggest, however, on thebasis of these calculations, one probable concentrationpattern for the interelectrode gap of an aluminium cell,as shown in Fig+ 1. The model developed by Rob1 eral[14] is based on a similar concentration pattern.

The dissolution rate of carbon dioxide equals that of

aluminium in spite of the smaller solubility for carbondioxide. This is possible because the dissolution rate ofthe gas will be increased due to the finite amount ofdissolved aluminium in the bulk electrolyte, andbecause of the large interfacial area for the gas.

Since a very small increase in the bulk concentrationof dissolved aluminium is sufficient to bring about asubstantial increase in the carbon dioxide dissolutionrate (3), we will assume, from the calculations above,that the physical dissolution of metal from the cathode

Dissolved AL

ANODEo Dissolved CO,

c-o

c concentration

CATHODE

Fig. 1. Concentration profiles (schematic) for dissolvedahuninium nd dissolved carbon dioxide in the electrolyte of

an aluminium electrolytic cell.

is (still disregarding the possibility of metal disper-sions) the rate determining step in the back reaction.The rate of the back reaction is then:

r = rA, = I . k*, . aI11 9)z 0.887/l,, . k,, cx,. (61

Following Aarebrot[7,8], the mass transfer coef-ficients can be calculated from

Ns,, = O.O~~N;,=IV:;~~ (71

where

Sh _ ht.21---D*,

(10)

For the physical properties we assume the followingvalues[6, lo]

density of electrolyte p = 2050 kg/m3viscosity of electrolyte p = 3.10-3Pa*sdiffusivity of dissolved metal DM = 3 . lbzB m/sinterelectrode gap i tm)interfacial velocity V, (m/s)(velocity of metal relative toelectrolyte)

The finat expression for the mass transfer coefficientbecomes

k,, = 1.540. 10-a. Yf.63 .I-0.17111)

and for the back reactionr = 1.366 . 10m4 AAl - VO,, . l-o.17 . CX,. (12)

Current efficiency is defined by

(13)

where r. is the amount of metal produced with 100%current efficiency. Inserting r from (12) into (13) yieldsfinally

lo- . A,~ - V:.E3 .l-o.17 .CX, 1W-0

(14)Equation (14) is useful for predicting how the currentefficiency will vary with parameters like metai area,in&-electrode distance, metal solubility, and inter-facial velocity.

2.2 Variation of current efficiency with interelectrodedistance

Assuming q = 90/, or I = 0.06 m gives by (14) thecorrelation shown in Fig. 2.

Figures 3-5 gives the expected variations, as calcu-lated from (14). We have somewhat arbitrarily as-sumed q = 90% for V, = 0.10 m s- , AL = 1.5 mjmanode area and Cx, = 0.05 wt%, respectively, since

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Current efficiency and back reaction in rtluminium electrolysis

90

2 3 4 5 6 7 8I/cm

Fig. 2. Current efficiency, q. calculated as a function of interelectrode distance (I).

i -I I I I I I

F

90 -

60 I I I I I I _0.02 0.04 0.06 0.0 8 0.10 0.12

c&&J t %

Fig. 3. Current efficiency, 1. calculated as a function of Al-solubility, (CX,), in the electrolyte.

Eh 25/21

801 I t I1.0 1.5 2.0A,, /cmz/c~

Fig. 4. Current &ciency, 0, calculated as a function of metal area per unit anode area (A,,).-_

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134 B. LILLEBIJ EN, S. A. YITERDAHL, R. HUGLEN AND K. A. PAULWN

Fig. 5. Current fficiency, Q, alculated as a function of the metal interfacial elocity relative o the electrolyte(VJJ

precise data are lacking. From the correlation betweencurrent efficiency and metal solubility (Fig. 3), togetherwith experimental data for metal solubility as afunction of temperature[ll] and oxide content in theelectrolyte[6], we have calculated the variation of thecurrent efficiency with temperature and with the oxidecontent in the electrolyte. Metal solubility data in theliterature are conflicting, but the calculated cor-rel tions are compared with experimental ones in thediscussion of the experimental data given later.

3. EXPERIMENTAL

Current efficiency was determined on Siiderbergtype cells by measuring the CO/COI ratio in the anodegas, and assuming the well-known Pearson-Waddington formula to be valid :

q = 100-5oc COCO+ CO, > (15)The anode gas analysis was made by gas chromatog-raphy. The sum of %CO and %C02 was aIways closeto 100A, except during anode effects.

The gas was sampled by means of 121 n. dia irontubes that followed the anode mass down into the melt.The gas was filtered before sampling, and for theBoudouard-reaction to have small significance wefound it necessary to maintain a steady gas-flow of atleast 200 N ml/min. The tube was periodically blownwith pressurized air to remove dust in the system.

In general the anode gas analysis gave currentefficiencies that were 2-3% lower than the actualvalues, as judged from the metal production. This isprobably due to the effect of the Boudouard-reactionon the gas composition[GJ However, as long as thegas-flow remains steady, we believe this to be a ratherconstant error with littie influence on the correlations

under study. Attempts to calculate corrections to thegas analysis for the temperature dependence of theBoudouard-reaction rates were not very successful dueto conflicting rate data. The effect of such correctionson the correlation between current efficiency and

temperature was in any case modest, and we have notincluded these corrections here.

4. RESULFS AND DI SCLJSSION

Results from current efficiency measurements areplotted in Fig. 6 and 7. Operations on the cell, like crustbreaking, tapping of metal etc have been indicated onthe figures, The occurrence ofanode effects is seen to bethe dominant factor for the dynamics of the cell.

The variations in the oxide content of theelectrolyte

as well as in the electrolyte temperature are shown inthe same figures. Electrolyte samples for analysis weretaken under the anode, and care was exercised to avoidphysical oxide in the samples.

Results from regression analysis of the experimentaldata from two direrent runs are shown in the tablebelow (cf Figs 8-9).

Some important parameters like bath acidity andthe interelectrode distance were not measured duringthese experiments. This may partly explain the differ-ence in the result from run no. 1 as compared to thosefrom run no. 2. Also, as seen from Figs 6 and 7 theobservations in run no. 2 have been made during aperiod with frequent anode effects, and this may havedisturbed the gas compositions, since some primaryCO may be formed during anode effects[6]. Further-more, the data from run no. 2 are much more scattered,and the regression model are only able to explainabout 31.6% of the variations, while it explained 58.5%in the data from run no. 1. Theconfidence intervals forthe regression coefficients are likewise much larger forthe data from run no. 2.

Equation (14) can obviously be used to calculatehow q should vary with for instance temperature, if weknow the relation between Al-solubility (CX,) andtemperature, and assume all the other parameters of(14) to remain constant. The same calculations may be

carried out for q =f(C,,,,,). This is shown, in com-parison with experimental data, in Tables 2 and 3.Solubility data have been selected from[6,11,12].

It should be noted that BC:,/BT in Table 2 has beenmeasured in melts saturated with A1,03, and the

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Current efticiency and back reaction in aluminium electrolysis 135

Fig. 6. Current efficiency, 1. oxide content, C*,,ol. and temperature, T, variations with time during run no. I.AE indicates anode effects, CB crust breaking and TP tapping of metal.

12 16 20 24 04 08 12 16 Time

Fig 7. Current efficiency, n. oxide content, CA,,03, and temperature, T, variations with time during run no. 2.AE indicates anode effects, CB crust breaking and TP tapping of metat.

Table 1. Regression analysis on current efficiency data from two different runs

Regression model

Calculated coefficientsand 90% confidence intervals

Run no. I Run no. 2

q=A+B*(T-T) A: 84.7*0.3 A : 83.6 + 0.3B : -0.183+O.B6 B: --0.279+0.1S: 30.6% S: 28.5%

tl = A + C . (CAIN, - CM,,,) A : 84.7 +0.3 A : 83.6 +0.4C: 0.565kO.2 c: 0.05-t_o.33S: 27.7% s: 0.1%

q = A+i 3- T-T)+C~ C, , ,o , - ~*, , J A 84.7 + 0.25 A : 83.6 i 0.3B: -o.1i33+o.o5 8: -0.304~0.1c: 0.467+0.16 C : 0.275 + 0.29S: 58.5% S: 31.6%

T ad CA,~O>re the arithmetic mean values, being 9753C and 3.133 wt/_ in run no. I ; and977.2C and 3.197 wt? in run no. 2. S is % variation in q which is explained by the regressionmodel. Interaction terms bctwecn T and CAIzoa were not found significant.

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136 B. LILLEBUEN. S. A. YTFERDAH L, R. H UGLEN AND K. A. PAULSEN

90

M RUN1A--. 3 RUN2 a

0

. 560 970 980 990T/W

Fig. 8. Current efficiency, q, plotted US melt temperatu re. 9 is average d over 1C ranges.

8

75

s n

M RUN 1

A---A RUN 2

I 11 2 3 4

Fig. 9. Current efficiency, q, plotted 0.7 oxide content, C *Izoj. q is average d over 0.5 wt AI,O, ranges.

Table 2. Measured and cakulated current efficiency correlations with electrolytetemperature

Data usedin (14) Calculations by (14)

Measuredcorrel tions

3.10-4[11]5.5.10-4[12]

_

-0.06-0.11

-(0.087-o.138)~13]-0.139[1]- (0.183-0.304)(present results)

Table 3. Measu red and calculated current efficiency correlations with oxide content inthe electrolyte

_~Data used Measured

in (14) Calculations by (14) correlations

-- Y.sL wt /wt )acAl,o,-4.10-6] 0.8 1.0[13]

0.05-0.567(present results)

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Current efficiency and back reaction in aluminium electrolysis 137

increase of C:, with increasing temperature is pro-bably larger in melts with lower Al ,-content[6].With this in mind, the calculated correlations seem tobe of the same orders of magnitude as the measuredones, which should encourage a further pursuit of thisapproach to current efficiency. Such studies shouldinclude precise measurements of metal- and gas-

solubilities, and the corresponding diffusivities. Inaddition the possibility of getting metai disper-sionsC7, S] should be further investigated and also thesize and behaviour of the carbon dioxide bubbles. Therelative velocity metal-electrolyte at the interface isalso highly important.

REFERENCES

1. B. Berge er ai, in Light Met 1975. Vol. 1, p. 37 (1975).2. H. J. Kent, J. Merals 22, 30 (1970).

3.4.5.6.

7.

8.9.

10.

Il.12.13.

14.

A. Czeke, Aluminium 52. 315 19761.J. GerIach and J. Webe;, Me . 28, 218 (1974).D. R. Morris, Can. Met. Quclrr. 14, 169 (1975).K. Grjotheim et al, Aluminium Ehcrrolysis. Aluminium-Verlag, Diisseldorf (1977).E. Aarebrot et al, in Light Mrtuls 1977. Vol. 1, p. 491(1977).E. Aarebrot et al, Metoll. 32, 41 (1978).D. Bratland, Thesis, p. 49, Institute of Inorganic Chem-istry, NTH, Trondheim (1966).E. Dewing and K. Yoshida, Can. Mer. Quart. 15, 299(1976).k. Ydshida and E. Dewing, Met. Trans. 3, 1817 1972).J. Thonstad, Can. J. Cliem. 43, 3429 (1965).R. T. Poole et al, in Light Metals 1977. Vol. 1, p. 163(1977).R. F. Rob1 er al,in Li ght A decals 1977. Vol. 1,~. 185 (1977).