Problems Inherent in Using the Population Balance Model for Wet Grinding in Ball Mills

  • T. P. Meloy
  • M. C. Williams
  • P. C. Kapur


A stuffing matrix S is the PBM solution to any Inverse Problem for wet grinding with straight line product curves observed for some types of wet ball mills. This PBM solution assumes all particles are broken out of their own size class. In other words, if one starts the mill, no matter when it is stopped, every particle in every class is a new particle. This corresponds to no known physical situation. Dry grinding feed matrices can all be inverted, because the product size distributions all curve to the right in the larger sizes showing that not all the larger particles are broken in a finite length of time. For parallel straight line feed and product size distributions, the use of a simple function for the product distribution is proposed but not described.


Inverse Problem Straight Line Plot Population Balance Model Specific Power Input Breakage Function 
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. Agar, G., and Charles, R., 1962, “Size Distribution Shift in Grinding”, AIME Trans.. 223, pp. 390–395.Google Scholar
  2. Arbiter, N., and Bhrany, U., 1960, “Product Size, Power and Capacity in Tumbling Mills”, AIME Trans., 217, pp. 245–252.Google Scholar
  3. Austin, L.G., “A Review Introduction to the Mathematical Descriptions of Grinding”, Powder Technology, 5, pp. 1–17 (1971).CrossRefGoogle Scholar
  4. Broadbent, S.R. and Calcott, T.B., “Coal Breakage Processes II: A Matrix Representation of Breakage”, J.INST. Fuel, 29, pp. 258–265 (1960).Google Scholar
  5. Fuerstenau, D.W., Sullivan, D.A., 1961, Size Distribution and Energy Conservation in Grinding Mills,“ AIME Trans., 220, pp. 397–402.Google Scholar
  6. Fuerstenau, D.W., K.S. Venkataraman, and M.C. Williams, “Simulation of Mill Dynamics of Grinding Mixtures Using PBMs.” in Control’84, AIME, New York, 1984.Google Scholar
  7. Herbst, J.A. and Mika, T.S., “Mathematical Simulation of Tumbling Mill Grinding: An Improved Method”, Rudy, 18, pp. 75–80 (1970).Google Scholar
  8. Herbst, J.A., Gandy, G.A. and Mika, T.S., “On the Development and Use of Lumped Parameter Models for Continuous Open-and Closed-Circuit Grinding Systems,” Inst.Min.Metall.Trans, 80, C. 193–198 (1971).Google Scholar
  9. Klimpel, R.R. and Austin, L.G., “Determination of Selection-for-Breakage Functions in the Batch Grinding Equations by Nonlinear Optimization,” Ind.Eng.Chem.Fund., 9, pp. 230–237 (1970).CrossRefGoogle Scholar
  10. Malghan, S.G. and Fuerstenau, D.W., “The Scale-up of Ball Mills Using Population Balance Models and Specific Power Input,” in Zerkleinern.DECHEMA-Monogr., 79(II), No. 1586, pp. 613–30 (1976).Google Scholar
  11. Meloy, T.P. and Gaudin, A.M., “Model and Comminution Distribution Equation for Repeated Fracture”, Trans. AIME, 223, pp. 243–50 (1962).Google Scholar
  12. Meloy, T.P., “Analysis and Optimization of Mineral Processing and Coal Cleaning Circuits–Circuit Analysis”, IJMP, 10, pp. 61–80 (1983).Google Scholar
  13. Mika, T.S., Population Balance Models of a Continuous Grinding Mill as a Distributed Process, Diss., Univ. Calif., Berkeley. Ca., 424 pp. (1970).Google Scholar
  14. Reid, K.J., “A Solution to the Batch Grinding Equation,” Chem.Eng.Sci., 20, pp. 953–963 (1965).CrossRefGoogle Scholar
  15. Williams, M.C. and Meloy, T.P., “Dynamic Model of Flotation Cell Banks–Circuit Analysis”. IJMP. 10, pp. 141–160 (1983).Google Scholar

Copyright information

© Elsevier Science Publishing Co., Inc. 1990

Authors and Affiliations

  • T. P. Meloy
    • 1
  • M. C. Williams
    • 1
  • P. C. Kapur
    • 2
  1. 1.Particle Analysis CenterWVUMgtn.USA
  2. 2.IIT KanpurIndia

Personalised recommendations