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Particle suspension in (air-agitated) pachuca tanks

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Abstract

Particle suspension is an important parameter in the design of an energy-efficient Pachuca tank. Unfortunately, very little attention has been focused on the suspension behavior of air-agitated Pachucas. In the present investigation, therefore, extensive experiments have been carried out in three laboratory-scale Pachuca tanks to examine the effect of design and operating parameters, as well as scale-up, on particle suspension. A mathematical model that combines the Bernoulli’s equation and the theory of transport of particles in the horizontal flow of a liquid has been developed to predict the critical gas velocity for particle suspension in Pachuca tanks. Some important results, crucial to the design and scale-up of Pachuca tanks, have emerged. Full-center-column (FCC) Pachuca tanks with a draft tube-to-tank diameter ratio (D d/Dt) on the order of 0.1 are found to be energetically more efficient in suspending particles than free-air-lift (FAL) and stub-column (SC) Pachuca tanks. It is also observed that taller tanks require lower air flow rates for particle suspension than shallower tanks. Finally, it is explained why industrial Pachuca tanks operate at lower air velocities than laboratory-scale tanks.

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Abbreviations

A :

cross-sectional area (m2)

D :

diameter (m)

f :

friction factor averaged over a rough flat surface (—)

H :

height (m)

K :

empirical factor defined by Eq. [17] (—)

K fd :

frictional energy loss coefficient in the draft tube (—)

K ru :

energy loss coefficient due to flow reversal and sudden expansion at the top of the tank (—)

K rl :

energy loss coefficient due to flow reversal and sudden contraction at the bottom of the tank (—)

K s :

sand equivalent roughness (m)

n 1 through n 4 :

constants defined by Eq. [16] (—)

Re p :

particle Reynolds number (ρ lU∞dp/μl)

U c :

critical superficial air velocity for particle suspension (m s−1)

U ∞ :

terminal velocity of a particle in a stagnant liquid (m s−1)

U gd :

superficial air velocity in the draft tube (m s−1)

U ld :

superficial liquid velocity in the draft tube (m s−1)

U la :

superficial liquid velocity in the annulus (m s−1)

U lf :

mean liquid velocity over a flat plate (m s−1)

U l,c :

critical mean liquid velocity at the cone (m s−1)

u*:

friction velocity (m s−1)

V ld :

absolute liquid velocity in the draft tube (m s−1)

v*:

root-mean-square of vertical velocity component of turbulent eddies

FAL:

free-air-lift Pachuca tank

FCC:

full-center-column Pachuca tank

SC:

stub-column Pachuca tank

α :

turbulence damping coefficient, defined by Eq. [3]

φ :

gas holdup

ɛ :

volume fraction of solid

ρ :

density (kg m−3)

μ :

viscosity (kg m−1 s−1)

τ 2 :

wall shear stress (kg m−1 s−1)

a :

annulus

b :

bottom

c :

cone

d :

draft tube

g :

gas

l :

liquid

t :

tank

w :

wall

References

  1. A.G.W. Lamont: Can. J. Chem. Eng., 1958, Aug. pp. 153–60.

  2. C.J. Hallett: Ph.D. Thesis, Imperial College of London, London, 1981.

    Google Scholar 

  3. G.G. Roy and R. Shekhar: Trans. Inst. Min. Metall., Sec. C, 1996, vol. 105, pp. C9-C15.

    CAS  Google Scholar 

  4. G.G. Roy and R. Shekhar: Trans. Inst. Min. Metall., Sec. C, 1996, vol. 105, pp. C16-C21.

    CAS  Google Scholar 

  5. P. Harriot: AIChE J., 1962, vol. 8, pp. 93–102.

    Article  Google Scholar 

  6. C.J. Hallett, A.J. Monhemius, and D.G.C. Robertson: Extraction Metallurgy ’81, Symp. Institute of Mining and Metallurgy, London, Sept. 21–23, 1981, Institute of Mining and Metallurgy, pp. 308–19.

    Google Scholar 

  7. K. Koide, K. Horibe, H. Kawabata, and S. Ito: J. Chem. Eng. Jpn., 1984, vol. 17 (4), pp. 368–74.

    CAS  Google Scholar 

  8. N.K. Roy, D.K. Guha, and M.N. Rao: Chem. Eng. Sci., 1964, vol. 19, pp. 215–25.

    Article  CAS  Google Scholar 

  9. K. Imafuku, T.Y. Wang, K. Koide, and H. Kuboto: J. Chem. Eng. Jpn., 1968, vol. 1, pp. 153–58.

    CAS  Google Scholar 

  10. Y. Kato: J. Chem. Eng. Jpn., 1972, vol. 5, pp. 112–17.

    CAS  Google Scholar 

  11. H. Kojima and K. Asano: J. Chem. Eng. Jpn., 1982, vol. 15, pp. 321–25.

    CAS  Google Scholar 

  12. B. Furchner and A. Mersmann: Chem. Eng. Technol., 1983, vol. 55, p. 972.

    CAS  Google Scholar 

  13. K. Koide, T. Yasuda, S. Iwamoto, and E. Fukuda: J. Chem. Eng. Jpn., 1983, vol. 16 (1), pp. 7–12.

    CAS  Google Scholar 

  14. D.N. Smith, J.A. Reuther, Y.T. Shah, and M.N. Badjugar: AIChE, 1986, vol. 32, pp. 426–36.

    Article  CAS  Google Scholar 

  15. M. Abraham, A.S. Khare, S.B. Sawant, and J.B. Joshi: Ind. Eng. Chem. Res., 1992, vol. 31, pp. 1136–47.

    Article  CAS  Google Scholar 

  16. K. Koide, S. Iwamoto, Y. Takasaka, S. Matsuura, E. Takahashi, and M. Kimura: J. Chem. Eng. Jpn., 1984, vol. 17 (6), pp. 611–18.

    CAS  Google Scholar 

  17. R. Shekhar and J.W. Evans: Metall. Trans. B, 1989, vol. 20B, pp. 781–91.

    CAS  Google Scholar 

  18. R. Shekhar and J.W. Evans: Metall. Trans. B, 1990, vol. 21B, pp. 191–203.

    CAS  Google Scholar 

  19. G.G. Roy: Ph.D. Thesis, Indian Institute of Technology, Kanpur, 1996.

    Google Scholar 

  20. K. Koide, M. Terasawa, and T. Hiroshi: J. Chem. Eng. Jpn., 1986, vol. 19 (4), pp. 341–44.

    CAS  Google Scholar 

  21. J. Heck and U. Onken: Chem. Eng. Sci., 1987, vol. 42, pp. 1211–12.

    Article  CAS  Google Scholar 

  22. W. Parzonka, J.M. Kenchington, and M.E. Charles: Can. J. Chem. Eng., 1981, vol. 59, pp. 2916–21.

    Article  Google Scholar 

  23. W.L. McCabe, J.C. Smith, and P. Harriott: Unit Operations in Chemical Engineering, 4th ed., McGraw-Hill, Book Co., Inc., New York, NY, 1985, pp. 156–57.

    Google Scholar 

  24. J.T. Davies: Chem. Eng. Sci., 1987, vol. 42 (7), pp. 1667–70.

    Article  CAS  Google Scholar 

  25. N.P. Cheremisinoff: Encyclopedia of Fluid Mechanics, vol. 4, Gulf Publishing Co., Houston, TX, 1986, pp. 390–94.

    Google Scholar 

  26. A.J. Raudkivi: Loose Boundary Hydraulics, 3rd ed., Pergamon Press, Elmsford, NY, 1990.

    Google Scholar 

  27. J.O. Hinze: Turbulence, McGraw-Hill Book Co., Inc., New York, NY, 1975, pp. 640–45.

    Google Scholar 

  28. Y.T. Shah, B.G. Kelkar, and S.P. Godbole: AIChE J., 1982, vol. 28 (3), pp. 353–79.

    Article  CAS  Google Scholar 

  29. K. Ueyama and T. Miyauchi: AIChE J., 1979, vol. 25, pp. 258–66.

    Article  Google Scholar 

  30. H. Hikita, S. Asai, K. Tanigawa, K. Segawa, and M. Kitao: Chem. Eng. J., 1980, vol. 20, pp. 59–67.

    Article  CAS  Google Scholar 

  31. D.H. Ying, E.N. Givens, and R.F. Weimer: Ind. Eng. Chem. Process Des. Dev., 1980, vol. 19, pp. 635–39.

    Article  CAS  Google Scholar 

  32. N.W. Cook and E.D. Water: AEC Research and Development Report No. HW-39432, Henford Atomic Products Operation, Richland, WA, Dec. 1, 1955.

    Google Scholar 

  33. J. Szekely and N.J. Themelis: Rate Phenomena in Process Metallurgy, 1st ed., Wiley-Interscience, New York, NY, 1971, p. 649.

    Google Scholar 

  34. P. Bradshaw: Momentum Transfer in Boundary Layers, Hemisphere Publishing Corporation, Washington, DC, 1977, p. 189.

    Google Scholar 

  35. S.N. Shah and D.L. Lord: AIChE J., 1991, vol. 37 (6), pp. 863–70.

    Article  CAS  Google Scholar 

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Author notes

  1. G. G. Roy (Graduate Student, Visiting Lecturer)

    Present address: Department of Metallurgical Engineering, Indian Institute of Technology, 721 302, Kharagpur, India

Authors and Affiliations

  1. the Department of Materials and Metallurgical Engineering, Indian Institute of Technology, 208 016, Kanpur, India

    R. Shekhar (Associate Professor) & S. P. Mehrotra (Professor)

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  2. R. Shekhar
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  3. S. P. Mehrotra
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Roy, G.G., Shekhar, R. & Mehrotra, S.P. Particle suspension in (air-agitated) pachuca tanks. Metall Mater Trans B 29, 339–349 (1998). https://doi.org/10.1007/s11663-998-0111-1

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  • DOI: https://doi.org/10.1007/s11663-998-0111-1

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