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Hydrodynamic modelling of the liquid-solid behaviour of the circulating particulate bed electrode

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Abstract

Experimental and modelling investigations of the hydrodynamics of the internal flow structure in the circulating particulate bed electrode (CPBE) are reported. The CPBE, a hybrid between an expanded packed bed and an entrained/fluidized bed, is particularly well suited for many electrochemical applications such as metal recovery and pollution treatments for metal containing effluents. This study deals with the fundamental hydrodynamics and particle dynamics of the CPBE. A mathematical model of the CPBE has been developed which successfully describes the motion of the particles and the fluid in the bed. It is shown that many of the flow characteristics of the circulating bed can be predicted using fundamental data. The validity of the proposed model was demonstrated by comparing predictions to experimental observations of several bed characteristics under various operating conditions.

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Abbreviations

A :

cross-sectional area of the cell (m2)

d p :

mean particle diameter (m)

C D :

experimentally determined constant calculated by Haider and Levenspiel [26]

C :

proportional constant in Equation 15

CR :

circulation rate of solids (m3 s−1)

D :

hydraulic diameter of the vessel (m)

g :

gravitational constant (kg m s−2)

G :

flow rate (kg s−1)

H D :

height of the particles inside the descending layer (m)

H R :

height of the particles inside the rising layer (m)

L :

length (m)

n :

Richardson and Zaki index (−)

ΔP :

pressure drop (N m−2)

Q :

inlet liquid flow rate (m3 s−1)

R :

reaction force between the descending layer and the cell wall (kg m-¨)

T :

total bed thickness (m)

t D :

descending layer thickness

t R :

rising layer thickness tan θ coefficient of friction (−)

U l :

superficial liquid velocity (m s−1)

U i :

a function of terminal velocity (equation 3) (m s−1)

U t :

particle terminal velocity (m s−1)

V :

interstitial velocity or actual velocity (m s−1)

V 1 :

slip velocity in the rising layer (m s−1)

V 2 :

slip velocity in the descending layer (m s−1)

W :

width of the bed (m)

ε:

bed voidage (the fraction of the total volume which is made up of the free space between the particles and is filled with fluid) (−)

εI :

packed bed voidage before bed expansion (−)

θ:

tilt angle (radians or degrees)

ϱs :

solid density (kg m−3)

ϱf :

fluid density (kg m−3)

µfPf:

solution viscosity (kg m s−1)

θs :

particle sphericity (−) Subscripts

D:

descending layer

L(f):

liquid (fluid) component

R:

rising layer

S:

solid component

L:

liquid component

T:

total depth of the bed

P:

particles

t:

terminal

References

  1. K. B. Mathur and N. Epstein, ‘Spouted Beds’, Academic Press, New York (1974).

    Google Scholar 

  2. F. Goodridge, C. J. King and A. R. Wright, Electrochim. Acta 22 (1977) 1087.

    Google Scholar 

  3. J. R. Backhurst, J. M. Coulson, F. Goodridge and R. E. Plimley, J. Electrochem. Soc. 116 (1969) 1600.

    Google Scholar 

  4. F. Coeuret, J. Appl. Electrochem. 10 (1980) 687.

    Google Scholar 

  5. H. D. Steppke and R. Kammel, Erzmetall. Bd., ‘Electrolysis with Fluidized Bed Electrodes’, 26 H11 (1973) 533.

  6. G. S. James, B. I. Dewar and W. R. Moergeli, US Patent 3981787 (1976).

  7. G. S. James, B. I. Dewar and W. R. Moergeli, US Patent 3945892 (1976).

  8. A. F. R. Newton, US Patent 4065375 (1977).

  9. J. A. E. Wilkinson, R. S. H. Leslie, D. M. Glindon, K. P. Haines and K. Baker, US Patent 4035278 (1977).

  10. R. Kammel and H. W. Lieber, Galvanotechnik 69 (1978) 687.

    Google Scholar 

  11. F. Goodridge, Electrochim. Acta 22 (1977) 929.

    Google Scholar 

  12. F. Goodridge and C. J. Vance, Electrochim. Acta 22 (1977) 1073.

    Google Scholar 

  13. K. Scott, J. Appl. Electrochem. 18 (1988) 504.

    Google Scholar 

  14. K. Nakamura and C. E. Capes, Can. J. Chem. Eng. 51 (1973) 39.

    Google Scholar 

  15. S. Morooka, K. Kawazuishi and Y. Yayo, Powder Tech. 26 (1980) 75.

    Google Scholar 

  16. S. Morooka and K. Leschonski, J. Chem. Eng. 36 (1987) 59.

    Google Scholar 

  17. F. Berruti and N. Kalogerakis, Can. J. Chem. Eng. 67 (1989) 1010.

    Google Scholar 

  18. M. J. Rhodes, Power Technol. 60 (1990) 27.

    Google Scholar 

  19. H. Arastoopour and D. Gidapow, Ind. Eng. Chem. Fund. 18 (1979) 123.

    Google Scholar 

  20. Y. Li and M. Kwauk, in ‘Fluidization’ (edited by J. R. Grace and J. M. Matsen), Plenum Press, New York (1980), p. 537.

  21. B. Dinrong, J. Yong and Y. Zhiqing, in ‘Fluidization’ (edited by M. Kwauk and D. Kunii), Science Press, Beijing, China (1988), p. 155.

  22. M. Horio, K. Morishita, O. Tachibana and N. Murata, in ‘Circulating Fluidized Bed Technology II’, (edited by P. Basu and J. F. Large), Pergamon Press, Toronto (1988), p. 147.

  23. H. Ishii, T. Nakajima and M. Horio, Jap. J. Chem. Eng. 22(5) (1989) 484.

    Google Scholar 

  24. M. Horio and Y. Takei, in Proceedings of the 3rd International Conference on Circulating Fluidized Beds, 15 Oct., Nagoya, Japan (1990).

  25. H. Zhang, Y. Xie, Y. Chen and M. Hasatani, inProceedings of the 3rd Conference on Circulating Fluidized Beds, 15 Oct., Nagoya, Japan (1990).

  26. D. Kunii and O. Kevenspiel, ‘Fluidization Engineering’, 2nd edn, J. Wiley & Sons, New York (1991).

    Google Scholar 

  27. W. K. Lewis, E. R. Gilliland and W. C. Bauer, Ind. Eng. Chem. 41 (1949) 1104.

    Google Scholar 

  28. A. Richardson and W. N. Zaki, Trans. Inst. Chem. Eng. 32 (1954).

  29. G. B. Wallis, ‘One Dimensional Two Phase Flow’, McGrawHill, New York (1967).

    Google Scholar 

  30. V. D. Stankovic, G. Lazarevic and A. A. Wragg, J. Appl. Electrochem. 25 (1995) 864.

    Google Scholar 

  31. S. Ergun, Chem. Eng. Progr. 48 (1952) 89.

    Google Scholar 

  32. N. Epstein, Ind. Eng. Chem. Process. 7 (1968) 158.

    Google Scholar 

  33. J. M. Matsen, Ind. Eng. Chem. 7 (1969) 159.

    Google Scholar 

  34. B. M. Dweik, MSc thesis, Case Western Reserve University, May (1995).

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Authors and Affiliations

  1. Ernest B. Yeager Center for Electrochemical Sciences, Chemical Engineering Department, Case Western Reserve University, 44106, Cleveland, OH, USA

    B. M. Dweik, C. C. Liu & R. F. Savinell

Authors
  1. B. M. Dweik
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  2. C. C. Liu
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  3. R. F. Savinell
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Dweik, B.M., Liu, C.C. & Savinell, R.F. Hydrodynamic modelling of the liquid-solid behaviour of the circulating particulate bed electrode. J Appl Electrochem 26, 1093–1102 (1996). https://doi.org/10.1007/BF00243733

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