Journal of Applied Electrochemistry

, Volume 37, Issue 3, pp 303–310 | Cite as

Mathematical model to evaluate the ohmic resistance caused by the presence of a large number of bubbles in Hall-Héroult cells

Article
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Abstract

Bubbles play an important role in the productivity of an electrolysis cell. They induce flow in the cell and increase the overvoltage, which is still two times greater than the thermodynamic voltage. Their contribution to the total electrical resistance of the electrolyte must be known for several reasons such as the energy efficiency and control. A computationally efficient mathematical model has been proposed that computes the total resistance of the electrolyte by using the concept of parallel-connected current tubes. The resistance of the individual current tubes has been determined earlier by the solution of the Laplace equation around the bubbles by the finite element method. Both electrical resistance models take into account the morphology (position, size and shape of each bubble) of the bubble layer. The current-tube model has been compared to the solutions obtained by a finite element method (FEM) for several real and hypothetical situations, using a large number of bubbles. The agreement between the results obtained by the proposed model and the FEM is very good. The difference between the two approaches is around 5% for a covering factor of 50%.

Keywords

alumina reduction cell gas bubbles interelectrode resistance mathematical model 

List of symbols

A0

unperturbed area (m2)

Aa

anode area (m2)

At

total projected area (m2)

AP

total perturbed area (m2)

b

bubble resistance factor

h

thickness of the bubble layer (m)

c

relative size of the perturbed zone

dB

bubble diameter (m)

d

diameter (m)

LACD

anode–cathode distance (m)

N(j)

number of bubbles at time step j

R

electrical resistance (Ω)

VB

bubble volume (m3)

Greek symbols

κ

electrical conductivity (Ω−1m−1)

ɛ

volume fraction of gas or void fraction

Θ

covering factor

Subscripts

0

bubble free-electrolyte

n

index of a bubble

T

electrolyte with the presence of the bubbles

Superscript

*

electrical current tube

j

time step

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Notes

Acknowledgements

The first author gratefully acknowledges the support of the Fonds québécois de recherches sur la nature et les technologies (FQRNT) and that of the Conseil de Recherches en Sciences Naturelles et en Génie du Canada (CRSNG) in the form of post-graduate scholarships.

References

  1. 1.
    K. Grjotheim and H. Kvande (eds), Introduction to Aluminium Electrolysis, 2nd edn., (Aluminium-Verlag, 1993)Google Scholar
  2. 2.
    Haupin W.E. (1971) . J. Metals 23:46Google Scholar
  3. 3.
    Vogt H. (1983) . J. Appl. Electrochem. 13:87CrossRefGoogle Scholar
  4. 4.
    Solheim A., Thonstad J. (1986). In: Miller R.B., Peterson W.S. (eds), Light Metals. TMS, Warrendale, PA, pp. 397–403Google Scholar
  5. 5.
    Zoric J., Solheim A. (2000) . J. Appl. Electrochem. 30:787CrossRefGoogle Scholar
  6. 6.
    Thonstad J., Kleinschrodt H.D., Vogt H. (2004) . In Tabereaux A.T. (ed.), Light Metals. TMS, Warrendale, PA, pp. 427–432Google Scholar
  7. 7.
    Dorward R.C. (1983) . J. Appl. Electrochem. 13:569CrossRefGoogle Scholar
  8. 8.
    Hyde T.M., Welch B.J. (1997). In Huglen R. (ed.), Light Metals. TMS, Warrendale, PA, pp. 333–340Google Scholar
  9. 9.
    R.J. Aaberg, V. Ranum, K. Williamson and B.J. Welch, in R. Huglen (ed.), Light Metals, (TMS, Warrendale, PA, 1997), pp. 341–346Google Scholar
  10. 10.
    Quian K., Chen J.J.J., Matheou N.J. (1997) . J. Appl. Electrochem. 27:434CrossRefGoogle Scholar
  11. 11.
    Quian K., Chen D., Chen J.J.J. (1998) . J. Appl. Electrochem. 28:1141CrossRefGoogle Scholar
  12. 12.
    Kasherman D., Skyllas-Kazacos M. (1991). J. Appl. Electrochem. 21:716CrossRefGoogle Scholar
  13. 13.
    Bruggeman D.A.G. (1935). Ann. Phys. 24:636Google Scholar
  14. 14.
    Kiss L.I., Poncsák S. (2002). In Schneider W. (ed.), Light Metals. TMS, Warrendale PA, pp. 217–223Google Scholar
  15. 15.
    Kiss L.I., Poncsák S., Antille J. (2005). In Kvande H. (ed.), Light Metal. TMS, Warrendale, PA, pp. 559–564Google Scholar
  16. 16.
    Poncsák S., Kiss L.I., Toulouse D., Perron A.L., Perron S. (2006) . In Galloway T.J. (ed.), Light Metals. TMS, Warrendale, PA, pp. 557–562Google Scholar
  17. 17.
    Purdie J.M., Bilek M., Taylor M.P., Zhang W.D., Welch B.J., Chen J.J.J. (1993). In Das S.K. (ed.), Light Metal. TMS, Warrendale, PA, pp. 355–360Google Scholar
  18. 18.
    Haarberg T., Solheim A., Johansen S.T., Solli P.A. (1998). In Welch B.J. (ed.), Light Metal. TMS, Warrendale, PA, pp. 475–481Google Scholar
  19. 19.
    Bech K., Johansen S., Solheim A., Haarberg T. (2001). In Anjier J.L. (ed.), Light Metals. TMS, Warrendale, PA, pp. 463–468Google Scholar
  20. 20.
    C. Kleinstreuer, ‘Two-Phase Flow Theory and Applications’, (Taylor and Francis Books Inc., 2004)Google Scholar
  21. 21.
    A.L. Perron, Rôle de la couche gazeuse dans les phénomènes de transport se produisant à l’intérieur d’une cuve Hall-Héroult, Ph.D Thesis, (Université du Québec à Chicoutimi, Canada, 2006)Google Scholar
  22. 22.
    A.L. Perron, L.I. Kiss and S. Poncsák, J. Appl. Electrochem. (in Press)Google Scholar
  23. 23.
    Fortin S., Gerhardt M., Gesing A.J. (1984). In McGeer J.P. (ed.), Light Metals. TMS, Warrendale, PA, pp. 721–741Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Département des sciences appliquéesUniversité du Québec à ChicoutimiQuébecCanada

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