Energy and population balances in comminution process modelling based on the informational entropy

Powder Technology

Volumn 167, Issue 1, 2006, Pages 33-44

  Otwinowski, Henryk ^a  

^a CZESTOCHOWA UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Breakage functions; Comminution modelling; Energy balance; Informational entropy; Particle size distribution; Population balance

Indexed keywords

COMPUTER SIMULATION; ENTROPY; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; PROCESS ENGINEERING; RANDOM PROCESSES; SAND;

BREAKAGE FUNCTIONS; COMMINUTION MODELING; ENERGY BALANCE; INFORMATIONAL ENTROPY; POPULATION BALANCE;

COMMINUTION;

COMMINUTION; COMPUTER SIMULATION; ENTROPY; MATHEMATICAL MODELS; PARTICLE SIZE ANALYSIS; PROCESS ENGINEERING; RANDOM PROCESSES; SAND;

ARTICLE; CHEMICAL MODEL; ENERGY BALANCE; ENTROPY; GLACIAL MASS BALANCE; LABORATORY; MATHEMATICAL ANALYSIS; METHODOLOGY; PARTICLE SIZE; STOCHASTIC MODEL; THEORY;

EID: 33747036657     PISSN: 00325910     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.powtec.2006.05.011     Document Type: Article

References (90)

1. P.R. Rittinger, Lehrbuch der Aufbereitungskunde, Verlag, Ernst und Korn, Berlin, 1867.
2. Kick F. Dinglers Polytechnisches Journal 247 (1883) 1
3. Kick F. Dinglers Polytechnisches Journal 250 (1883) 141
4. Kick F. Das Gesetz der proportionalen Widerstände und seine Anwendung (1885), A. Felix, Leipzig
5. Bond F.C. The third theory of comminution. AIME Transactions 193 (1952) 484-494
6. Bond F.C. Confirmation of the third theory. AIME Transactions 217 (1960) 139-153
7. Bond F.C. Crushing and Grinding Calculations (1962), Allis-Chalmers Publications, Milwaukee, Wisconsin
8. Charles R.J. High velocity impact in comminution. Mining Engineering 10 (1956)
9. Charles R.J., and Bruyn P.L. Energy transfer by impact. Mining Engineering 1 (1956)
10. Charles R.J. Energy-size reduction relationships in comminution. Mining Engineering 9 (1957) 80-88
11. Djingheuzian L.E. A study of present day grinding. The Canadian Mining and Metallurgical Bulletin 42 (1949)
12. Djingheuzian L.E. Developments of the science of grinding. The Canadian Mining and Metallurgical Bulletin 45 (1953)
13. Djingheuzian L.E. The influence of temperature on efficiency of grinding. The Canadian Mining and Metallurgical Bulletin 47 (1954)
14. Guillot R. Le problème du broyage et son èvolution (1960), Edit Gauthier, Villars
15. Mielczarek E. Free Comminution of Brittle Solid Substances vol. 25 (1982), Czestochowa University of Technology Press (in Polish)
16. Mielczarek E. Particle size distribution of free comminution product. Archives of Mining Sciences 29 (1984) 29-56 (in Polish)
17. Epstein B. The material description of certain breakage mechanisms leading to the logarithmic-normal distribution. Journal of the Franklin Institute 244 12 (1947) 471-477
18. Sedlatschek K., and Bass L. Contribution to the theory of milling processes. Powder Metallurgy Bulletin 6 (1953) 148-153
19. Broadbent S.R., and Callcott T.G. A matrix analysis of processes involving particle assemblies. Philosophical Transactions of the Royal Society of London. A 249 (1956) 99-123
20. Rumpf H. Teorie der Zerkleinerung, Fortschritte der Verfahrenstechnik Bd.4 (1958/59) (1961), Verlag Chemie GmbH, Weinheim 535-548
21. Rumpf H. Die Einzelkornzerkleinerung als Grundlage einer technischen Zerkleinerungswissenschaft. Chemical Engineering Technology 37 (1965) 187
22. Gardner R.P., and Austin L.G. A chemical engineering treatment of batch grinding. 1st Proc. European Symposium on Size Reduction (1962), Verlag Chemie, Düsseldorf 217-248
23. Gardner R.P., and Austin L.G. Journal of the Institute of Fuel London 35 (1962) 174
24. Gaudin A.M., and Meloy T.P. Model and comminution distribution equation for single fracture. Transactions of the Society of Mining Engineers of AIME 223 (1962) 1
25. McGrady E.D., and Ziff R.M. Shattering transition in fragmentation. Physical Review Letters 58 (1987) 892-895
26. Liou J.-J., Srienc F., and Fredrikson A.G. Solutions of population balance models based on successive generations approach. Chemical Engineering Science 52 (1997) 1529-1540
27. Hill P.J., and Ng K.M. New discretization procedure for the breakage equation approach. AIChE Journal 42 (1995) 1600-1611
28. Kumar S., and Ramkrishna D. On the solution of population balance equations by discretizations. Chemical Engineering Science 51 (1996) 1311-1332
29. Vanni M. Discretization procedure for the breakage equation. AIChE Journal 45 (1999) 916-919
30. Campbell G.M., and Webb C. On predicting roller milling performance I: The breakage equation. Powder Technology 115 (2001) 234-242
31. Campbell G.M., and Webb C. On predicting roller milling performance II: The breakage function. Powder Technology 115 (2001) 243-255
32. Attarakih M.M., Bart H.-J., and Faqir N.M. Numerical solution of the spatially distributed population balance equation describing the hydrodynamics of interacting liquid-liquid dispersions. Chemical Engineering Science 59 (2004) 2567-2592
33. Liu Y., and Tadé M.O. New wavelet-based adaptive method for the breakage equation. Powder Technology 139 (2004) 61-68
34. Wang T., Wang J., and Jin J. An efficient numerical algorithm for a novel theoretical breakup kernel function of bubble/droplet in a turbulent flow. Chemical Engineering Science 59 (2004) 2593-2595
35. Bove S., Solberg T., and Hjertager B.H. A novel algorithm for solving population balance equations: the parallel parent and daughter classes. Derivation, analysis and testing. Chemical Engineering Science 60 (2005) 1449-1464
36. Kostoglou M., and Karabelas A.J. Toward a unified framework for the derivation of breakage functions based on the statistical theory of turbulence. Chemical Engineering Science 60 (2005) 6584-6595
37. Attarakih M.M., Bart H.-J., and Faqir N.M. Numerical solution of the bivariate population balance equation for the interacting hydrodynamics and mass transfer in liquid-liquid extraction columns. Chemical Engineering Science 61 (2006) 113-123
38. Bilgili E., Yepes J., and Scarlett B. Formulation of a non-linear framework for population balance modeling of batch grinding: Beyond first-order kinetics. Chemical Engineering Science 61 (2006) 33-44
39. Sommer M., Stenger F., Peukert W., and Wagner N.J. Agglomeration and breakage of nanoparticles in stirred media mills - a comparison of different methods and models. Chemical Engineering Science 61 (2006) 135-148
40. Kostoglou M., and Karabelas A.J. An assessment of low-order methods for solving the breakage equation. Powder Technology 127 (2002) 116-127
41. Kostoglou M., and Karabelas A.J. Optimal low order methods of moments for solving the fragmentation equation. Powder Technology 143-144 (2004) 280-290
42. Nopens I., Beheydt D., and Vanrolleghem P.A. Comparison and pitfalls of different discretised solution methods for population balance models: a simulation study. Computers and Chemical Engineering 29 (2005) 367-377
43. Heim A., and Pietrzykowski M. Grinding in a ball mill. Powder Handling and Processing 5 4 (1993) 363
44. Heim A., and Olejnik T. Simulation of milling in ball mills. Proc. 2nd Israel Conference for Conveying and Handling of Particulate Solids, Israel (1997)
45. Mielczarek E., and Urbaniak D. Particle size distribution of product of jet milling of monodispersed quartz sand. Archives of Mining Sciences 44 (1999) 351-364 (in Polish)
46. Pastucha L., Mielczarek E., Otwinowski H., and Urbaniak D. Particle size distribution function of monodispersion fed material's free comminution product. Proc. 4th International Conference on Measurement and Control of Granular Materials MCGM '97 (1997), Shenyang, China
47. Lee K., and Matsoukas T. Simultaneous coagulation and break-up using constant-N Monte Carlo. Powder Technology 110 (2000) 82-89
48. Mishra B.K. Monte Carlo simulation of particle breakage process during grinding. Powder Technology 110 (2000) 246-252
49. Zhao H., Zheng C., and Xu M. Multi-Monte Carlo approach for general dynamic equation considering simultaneous particle coagulation and breakage. Powder Technology 154 (2005) 164-178
50. Zhukov V.P., Mizonov V.E., Filitchev P.V., and Bernotat S. The modeling of grinding processes by means of the principle of maximum entropy. Powder Technology 95 (1998) 248-253
51. Kostoglou M., and Karabelas A.J. On the self-similar solution of fragmentation equation: Numerical evaluation with implications for the inverse problem. Journal of Colloid and Interface Science 284 (2005) 571-581
52. Frances C. On modelling of submicronic wet milling processes in bead mills. Powder Technology 143-144 (2004) 253-263
53. Bilgili E., and Scarlett B. Population balance modelling of non-linear effects in milling processes. Powder Technology 153 (2005) 59-71
54. Fang C., and Campbell G.M. On predicting roller milling performance IV: Effect of roll disposition on the particle size distribution from first break milling of wheat. Journal of Cereal Science 37 (2003) 21-29
55. Fang C., and Campbell G.M. On predicting roller milling performance V: Effect of moisture content on the particle size distribution from first break milling of wheat. Journal of Cereal Science 37 (2003) 31-41
56. Austin L.G., and Bhatia V.K. Experimental methods for grinding studies in laboratory mills. Powder Technology 5 (1971/72) 261-266
57. Gardner R.P., and Sukanjnajtee K. A combined tracer calculation-back method for determining particulate breakage functions in ball milling, Part I. Powder Technology 6 (1972) 65-74
58. Tavares L.M., and King R.P. Single particle fracture under impact loading. International Journal of Mineral Processing 54 (1998) 1-28
59. D.E. Lebedev, 2001. Energy distribution in comminution process and its influence on predicting of particle size distribution, PhD Thesis, Ivanovo (in Russian).
60. Liu J., and Schönert K. Modelling of interparticle breakage. International Journal of Mineral Processing 44-45 (1996) 101-115
61. Williams M.C., Meloy T.P., and Tarsham M. Assessment of numerical solution approaches to the inverse problem for grinding systems: dynamic population balance model problems. Powder Technology 78 (1994) 257-262
62. Berthiaux H., Varinot C., and Dodds J. Approximate calculation of breakage parameters from batch grinding tests. Chemical Engineering Science 51 19 (1996) 4509-4516
63. Das P.K. Use of cumulative size distribution to back-calculate the breakage parameters in batch grinding. Computers and Chemical Engineering 25 (2001) 1235-1239
64. C.E. Shannon, 1948. A mathematical theory of communication - part I and II, Bell System Technical Journal, 27, 379-423, 623-656.
65. Jaynes E.T. Information theory and statistical mechanics. Physical Review 106 (1957) 620-630
66. Jaynes E.T. Information theory and statistical mechanics II. Physical Review 108 (1957) 171-190
67. Jaynes E.T. Statistical Physics (1963), W.K.Ford, Benjamin, New York
68. Otwinowski H. Informational Entropy in the Modelling of Comminution Process (2003), University of Mining and Metallurgy Press, Cracow No 124 (in Polish)
69. Bodziony J. Personal Information (2003)
70. Forray M.J. Variational Calculus in Science and Engineering (1968), McGraw-Hill Book Company, New York
71. Nowak R. Statistics for Physicists (2002), WN PWN, Warsaw (in Polish)
72. Brandt S. Data Analysis (2002), WN PWN, Warsaw (in Polish)
73. Ouchiyama N., Rough S.L., and Bridgwater J. A population balance approach to describing bulk attrition. Chemical Engineering Science 60 (2005) 1429-1440
74. Berthiaux H., and Dodds J. Modelling fine grinding in a fluidized bed opposed jet mill. Powder Technology 106 (1999) 78-87
75. Müller F., Polke R., and Schäfer M. Model-based evaluation of grinding experiments. Powder Technology 105 (1999) 243-249
76. Shinohara K., Golman B., Uchiyama T., and Otani M. Fine-grinding characteristics of hard materials by attrition mill. Powder Technology 103 (1999) 292-296
77. Nikolov S. A performance model for impact crushers. Minerals Engineering 15 (2002) 715-721
78. Kotake N., Daibo K., Yamamoto T., and Kanda Y. Experimental investigation on a grinding rate constant of solid materials by a ball mill - effect of ball diameter and feed size. Powder Technology 143-144 (2004) 196-203
79. Vogel L., and Peukert W. Determination of material properties relevant to grinding by practicable labscale milling tests. International Journal of Mineral Processing 74S (2004) S329-S338
80. Petukhov Y., and Kalman H. Empirical breakage ratio of particles due to impact. Powder Technology 143-144 (2004) 160-169
81. Austin L.G., and Luckie P.T. Methods for determination of breakage distribution parameters. Powder Technology 5 (1971/72) 215-222
82. Yekeler M., Ozkan A., and Austin L.G. Kinetics of fine wet grinding in a laboratory ball mill. Powder Technology 114 (2001) 224-228
83. Deniz V. The effect of mill speed on kinetic breakage parameters of clinker and limestone. Cement and Concrete Research 34 (2004) 1365-1371
84. Nair P.B.R. Breakage parameters and the operating variables of a circular fluid energy mill. Powder Technology 106 (1999) 45-61
85. Gommeren H.J.C., Heitzmann D.A., Moolenaar J.A.C., and Scarlett B. Modelling and control of a jet mill plant. Powder Technology 108 (2000) 147-154
86. Wang Y., and Forssberg E. Product size distribution in stirred media mills. Minerals Engineering 13 (2000) 459-465
87. Austin L.G. A preliminary simulation model for fine grinding in high speed hammer mills. Powder Technology 143-144 (2004) 240-252
88. Kis P.B., Mihálykó C., and Lakatos B.G. Discrete model for analysis and design of grinding mill-classifier systems. Chemical Engineering and Processing 45 (2006) 340-349
89. Bertrand D., Guibert D., Melcion J.-P., and Duc G. Evaluation of the transition matrix for comminuting pea seeds in an impact mill using a linear neural network. Powder Technology 105 (1999) 119-124
90. Tatarkiewicz K. Variational Calculus, Part I and II, WNT, Warsaw (1969, 1970) (in Polish)