Rate Processes in Multiparticle Metallurgical Systems

  • J. A. Herbst


In the preceding chapter, the kinetic behavior of individual particles isolated in an infinite fluid medium has been discussed. The various steps or combinations of steps which can control the rate of heterogeneous reactions were identified and appropriate types of mathematical models to describe individual particle behavior were reviewed. In the present chapter, consideration is extended to the behavior of multiparticle systems. By definition, a multiparticle system consists of an assembly of particles that make up the disperse phase plus the environment surrounding the particles that makes up the continuous phase in a processing vessel. Virtually all particulate assemblages encountered in extractive metallurgical practice are polydisperse in nature, i.e., the particles being processed have a broad distribution of properties such as size, mineralogical composition, etc., which contribute to the overall behavior of the system. In addition, in practical systems the particles often interact with one another and/or with the fluid environment. If one wishes to accurately design a reactor, optimize an existing operation, or specify an effective automatic control strategy for an extractive metallurgical process, it is necessary to be able to describe, in quantitative terms, the influence of material property distributions and particle-particle or particle-fluid interactions on the overall reaction behavior of the system.


Volume Flow Rate Extractive Metallurgy Population Balance Copper Extraction Multiparticle System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    H. M. Hulburt and S. Katz, Chem. Eng. Sci. 19, 555 (1964).CrossRefGoogle Scholar
  2. 2.
    A. D. Randolph, Can. J. Chem. Eng. 42, 280 (1964).CrossRefGoogle Scholar
  3. 3.
    P. Yu, A kinetic study of the leaching of chalcopyrite at elevated temperatures and pressures, Ph.D. Dissertation, University of Utah, 1972.Google Scholar
  4. 4.
    C. Orr and J. M. Dallavalle, Fine Particle Measurement, Macmillan, New York (1959).Google Scholar
  5. 5.
    R. D. Cadle, Particle Size, Reinhold Publishing, Stamford, Conn. (1965).Google Scholar
  6. 6.
    R. Irani and C. Callis, Particle Size: Measurement, Interpretation and Application, Wiley, New York (1963).Google Scholar
  7. 7.
    T. Allen, Particle Size Measurement, Chapman and Hall, London (1968).Google Scholar
  8. 8.
    G. Herdan, Small Particle Statistics, Academic Press, New York (1960).Google Scholar
  9. 9.
    E. Parzen, Modern Probability Theory and Its Applications, Wiley, New York (1963).Google Scholar
  10. 10.
    M. Fisz, Probability Theory and Mathematical Statistics, Wiley, New York (1960).Google Scholar
  11. 11.
    H. D. Lewis and A. Goldman, Theoretical small particle statistics, Los Alamos Scientific Laboratory Report (1967).Google Scholar
  12. 12.
    D. M. Himmelblau, Process Analysis by Statistical Methods, Wiley, New York (1969).Google Scholar
  13. 13.
    A. D. Randolph and M. Larson, Theory of Particulate Processes, Academic Press, New York (1971).Google Scholar
  14. 14.
    R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, Wiley, New York (1960).Google Scholar
  15. 15.
    V. G. Jenson and G. V. Jeffereys, Mathematical Methods in Chemical Engineering, Academic Press, New York (1963).Google Scholar
  16. 16.
    D. C. Tim and M. A. Larson, AIChE J. 14, 452 (1968).CrossRefGoogle Scholar
  17. 17.
    L. G. Austin, Powder Technol. 5, 1 (1972–72).CrossRefGoogle Scholar
  18. 18.
    T. Meloy and A. Gaudin, Trans. AIME 223, 43 (1962).Google Scholar
  19. 19.
    A. Filippov, Theory Probab. Its AppL (USSR) 6, No. 3 (1961).Google Scholar
  20. 20.
    L. G. Austin and P. T. Luckie, Trans. AIME 252, 82 (1972).Google Scholar
  21. 21.
    J. A. Herbst and T. Mika, Proceedings IX International Mineral Processing Congress, Prague (1970).Google Scholar
  22. 22.
    V. K. Gupta and P. C. Kapur, Fourth European Symposium on Comminution, H. Rumpf and K. Schonen, eds., Dechema-Monographien, Verlag Chemie (1976), p. 447.Google Scholar
  23. 23.
    K. Rajamani and J. A. Herbst, Computer evaluation of errors involved in the use of size discretized grinding models, manuscript in preparation.Google Scholar
  24. 24.
    K. J. Reid, Chem. Eng. Sci. 20, 953 (1965).CrossRefGoogle Scholar
  25. 25.
    J. A. Herbst et al., Fourth European Symposium on Comminution, H. Rumpf and K. Schonert, eds., Dechema-Monographien, Verlag Chemie (1972), p. 475.Google Scholar
  26. 26.
    J. A. Herbst and D. W. Fuerstenau, Trans. AIME 241, 538 (1968).Google Scholar
  27. 27.
    S. K. Freidlander and C. S. Wang, J. Colloid Interface Sci. 22 (2), 126 (1966).CrossRefGoogle Scholar
  28. 28.
    K. V. S. Sastry, The agglomeration of particulate materials by green peptization, Ph.D. Thesis, University of California (1970).Google Scholar
  29. 29.
    J. Valentas and N. Amundsen, Ind. Eng. Chem. Fundam. 4, 533 (1966).CrossRefGoogle Scholar
  30. 30.
    R. K. Bjpai and D. Ramkrishna, Chem. Eng. Sci. 31, 913 (1976).CrossRefGoogle Scholar
  31. 31.
    D. E. Brown and K. Pitt, Chem. Eng. Sci. 27, 577 (1972).CrossRefGoogle Scholar
  32. 32.
    L. W. Beckstead et al, Trans. TMS-AIME, 2 611 (1976).Google Scholar
  33. 33.
    D. M. Himmelblau, Process Analysis of Simulation, Wiley, New York (1968).Google Scholar
  34. 34.
    J. A. Herbst and K. V. S. Sastry, unpublished results (1977).Google Scholar
  35. 35.
    J. A. Herbst, K. Rajamani, and D. Kinneberg, ESTIMILL, University of Utah, Dept. of Metallurgy (1977).Google Scholar
  36. 36.
    M. Siddique, A kinetic approach to ball mill scale-up, M.S. Thesis, University of Utah (1977).Google Scholar
  37. 37.
    J. A. Herbst et al., Trans. IMM 80, C193 (1971).Google Scholar
  38. 38.
    R. P. Gardner and K. Verghese, Powder Technol. 11, 87 (1975).CrossRefGoogle Scholar
  39. 39.
    J. A. Herbst, An approach to the modeling of continuous leaching systems, Annual AIME Meeting, New York (1975).Google Scholar
  40. 40.
    R. W. Bartlett, Met. Trans. 2, 2999 (1971).CrossRefGoogle Scholar
  41. 41.
    P. Harriot, AIChE J. 8, 93 (1962).CrossRefGoogle Scholar
  42. 42.
    S. Pohlman, The dissolution kinetics of chrysocolla using a weight loss technique, Ph.D. Thesis, University of Utah (1974).Google Scholar
  43. 43.
    D. M. Himmelblau and D. A. Paviani, Operations Res. 17, 872 (1969).CrossRefGoogle Scholar
  44. 44.
    L. Lapidus, Numerical Methods for Chemical Engineers, Wiley, New York (1962)/Google Scholar
  45. 45.
    D. Ramkrishna, Chem. Eng. Sci. 28, 1423 (1973).CrossRefGoogle Scholar
  46. 46.
    D. Ramkrishna, Chem. Eng. Sci. 29, 1711 (1974).CrossRefGoogle Scholar
  47. 47.
    H. Imai and T. Miyauchi, J. Chem. Eng. Japan 1 (1), 77 (1968).CrossRefGoogle Scholar
  48. 48.
    R. P. King, S. African IMM 341 (1973).Google Scholar
  49. 49.
    P. C. Kapur and D. W. Fuerstenau, Ind. Eng. Chem. Process Design Develop. 8 (1) (1969).Google Scholar
  50. 50.
    D. Kunii and O. Levenspiel, Fluidization Engineering, Wiley, New York (1971).Google Scholar

Copyright information

© Plenum Press, New York 1979

Authors and Affiliations

  • J. A. Herbst
    • 1
  1. 1.Department of Metallurgy and Metallurgical EngineeringUniversity of UtahSalt Lake CityUSA

Personalised recommendations