SIZE-BY-SIZE ANALYSIS OF BREAKAGE PARAMETERS OF CEMENT CLINKER FEED AND PRODUCT SAMPLES OF AN INDUSTRIAL ROLLER PRESS

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SIZE-BY-SIZE ANALYSIS OF BREAKAGE PARAMETERS OF CEMENT CLINKER FEED AND PRODUCT SAMPLES OF AN INDUSTRIAL ROLLER

PRESS

A THESIS SUBMITTED TO

THE GRADUATE SCHOOL OF NATURAL AND APPLIED SCIENCES OF

MIDDLE EAST TECHNICAL UNIVERSITY

BY

MAHMUT CAMALAN

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR

THE DEGREE OF MASTER OF SCIENCE IN

MINING ENGINEERING

AUGUST 2012

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Approval of the thesis:

SIZE-BY-SIZE ANALYSIS OF BREAKAGE PARAMETERS OF CEMENT CLINKER FEED AND PRODUCT SAMPLES OF AN INDUSTRIAL

ROLLER PRESS

submitted by MAHMUT CAMALAN in partial fulfillment of the requirements for the degree of Master of Science in Mining Engineering Department, Middle East Technical University by,

Prof. Dr. Canan ÖZGEN _____________________

Dean, Graduate School of Natural and Applied Sciences

Prof. Dr. Ali İhsan Arol _____________________

Head of Department, Mining Engineering Prof. Dr. Çetin Hoşten

Supervisor, Mining Engineering Dept., METU _____________________

Examining Committee Members:

Prof. Dr. Ali İhsan Arol _____________________

Mining Engineering Dept., METU

Prof. Dr. Çetin Hoşten _____________________

Mining Engineering Dept., METU

Prof. Dr. Yavuz Topkaya _____________________

Metallurgical and Materials Engineering Dept., METU

Asst. Prof. Dr. Sinan Turhan Erdoğan _____________________

Civil Engineering Dept., METU

Dr. Tuğcan Tuzcu _____________________

Dama Engineering

Date: 15.08.2012 Date: 15.08.2012

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I hereby declare that all information in this document has been obtained and presented in accordance with academic rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and referenced all material and results that are not original to this work.

Name, Last Name:

Signature:

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iv ABSTRACT

SIZE-BY-SIZE ANALYSIS OF BREAKAGE PARAMETERS OF CEMENT CLINKER FEED AND PRODUCT SAMPLES OF AN INDUSTRIAL ROLLER

PRESS

Camalan, Mahmut

M.Sc., Department of Mining Engineering Supervisor: Prof. Dr. Çetin Hoşten

August 2012, 189 pages

The main objective in this study is to compare breakage parameters of narrow size fractions of cement clinker taken from the product end and feed end of industrial-scale high pressure grinding rolls (HPGR) in order to assess whether the breakage parameters of clinker broken in HPGR are improved or not. For this purpose, drop weight tests were applied to six narrow size fractions above 3.35 mm, and batch grinding tests were applied to three narrow size fractions below 3.35 mm.

It was found that the breakage probabilities of coarse sizes and breakage rates in fine sizes were higher in the HPGR product. This indicated that clinker broken by HPGR contained weaker particles due to cracks and damage imparted. However, no significant weakening was observed for the -19.0+12.7 mm HPGR product.

Although HPGR product was found to be weaker than HPGR feed, fragment size distribution of HPGR product did not seem to be finer than that of the HPGR feed at a given loading condition in either the drop weight test or batch grinding test. Also, drop weight tests on HPGR product and HPGR feed showed that the breakage distribution functions of coarse sizes depended on particle size and impact energy (J).

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Batch grinding tests showed that the specific breakage rates of HPGR product and HPGR feed were non-linear which could be represented with a fast initial breakage rate and a subsequent slow breakage rate. The fast breakage rates of each size fraction of HPGR product were higher than HPGR feed due to cracks induced in clinker by HPGR. However, subsequent slow breakage rates of HPGR product were close to those of HPGR feed due to elimination of cracks and disappearance of weaker particles. Besides, the variation in breakage rates of HPGR product and HPGR feed with ball size and particle size also showed an abnormal breakage zone where ball sizes were insufficient to effectively fracture the coarse particles.

Breakage distribution functions of fine sizes of HPGR product and HPGR feed were non-normalizable and depended on particle size to be ground. However, batch grinding of -2.36+1.7 mm and -1.7+1.18 mm HPGR feed yielded the same breakage pattern.

Keywords: Clinker, HPGR, Ball Mill, Drop Weight Test, Breakage Parameters

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vi ÖZ

YÜKSEK BASINÇLI MERDANELİ PRESTEN ALINAN GİRİŞ VE ÜRÜN NUMUNELERİNİN KIRMA PARAMETRELERİNİN KARŞILAŞTIRILMASI

Camalan, Mahmut

Y. Lisans, Maden Mühendisliği Bölümü Tez Yöneticisi: Prof. Dr. Çetin Hoşten

Ağustos 2012, 189 sayfa

Bu çalışmada yüksek basınçlı merdaneli preste (HPGR) kırılan klinkerin kırılma parameterlerinin değişip değişmediğini belirlemek amacıyla; endüstriyel ölçekli, yüksek basınçlı merdaneli presin girişinden (HPGR besleme) ve çıkışından (HPGR ürün) alınan klinkerin dar tane aralıklarındaki kırılma parametreleri karşılaştırılmıştır. Bu amaçla, 3.35 mm’nin üzerinde 6 adet dar tane aralığına, ağırlık düşürme yöntemi uygulanmış; 3.35 mm’nin altındaki 3 adet dar tane aralığı ise laboratuvar ölçekli bilyalı değirmen ile test edilmiştir. Bu testler sonucunda, iri tanelerdeki kırılma olasılığı ile ince tanelerdeki özgül kırılma hızlarının HPGR ürününde daha fazla olduğu bulunmuştur. Bu durum, HPGR’de kırılan klinkerin içindeki çatlaklar ve hasarlar nedeniyle zayıfladığını göstermektedir. Ancak, -19.0+12.7 mm HPGR ürüründe belirgin bir zayıflama görülememiştir. HPGR ürünü, HPGR beslemesine nazaran daha zayıf olduğu halde; aynı yükleme koşullarında yapılmış ağırlık düşürme yöntemi ya da değirmen testlerinde, kırılan parça boyutunun HPGR ürününde daha ince çıktığını gösteren bir yönelim bulunamamıştır. Ayrıca, ağırlık düşürme yöntemi, iri boyutların kırılım dağılım fonksiyonlarının tane boyu ve kırılım enerjisine (J) bağlı olduğunu göstermektedir.

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Bilyalı değirmen testleri, HPGR ürünü ve HPGR beslemesinin kırılma hızlarının doğrusal olmadığını göstermektedir. Bu aşamada özgül kırılma hızı, öncül hızlı kırılma sonra da yavaş kırılma olarak ifade edilebilmektedir. Belli bir tane boyundaki HPGR ürününün öncül özgül kırılma hızı, HPGR tarafından klinkerde oluşturulan çatlaklar yüzünden, HPGR beslemesine göre daha yüksektir. Ancak, sonrasındaki yavaş kırılmalarda HPGR ürünü, HPGR beslemesine yakın kırılma hızları vermekte, bu ise çatlakların ve zayıf parçaların ortadan kaybolduğunu göstermektedir. Bunun yanı sıra, HPGR ürünü ve HPGR beslemesindeki özgül kırılım hızlarının bilya ve parçacık tane boyuna göre değişimi, bilya boyutunun iri taneleri kırmakta yetersiz kaldığı anormal kırılım davranışını işaret etmektedir.

HPGR ürünü ve HPGR beslemesindeki ince tanelerin kırılım dağılım fonksiyonları

normalize olmamakta ve tane boyuna bağlı değişim göstermektedir. Ancak, -2.36+1.7 mm ve -1.7+1.18 mm HPGR beslemesi aynı kırılım şekli vermektedir.

Anahtar Kelimeler: Klinker, HPGR, Bilyalı Değirmen, Ağırlık Düşürme Testi, Kırılma Parametreleri

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To My Family and My Late Father

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ACKNOWLEDGEMENTS

I would like to express my gratitude to my supervisor, Prof. Dr. Çetin Hoşten, for guiding me throughout the experimental procedure and thesis preparation with his deep knowledge and inspirational criticism.

I would also like to thank the members of the examining committee for their kind suggestions and contributions to the content and format of my thesis.

I would like to thank METU Central Laboratory for the experimental support given to this study.

I would like to thank my colleague Cemil Acar for kindly supporting and guiding me throughout the experimental work. Also, I would like to thank my colleagues Mahmut Çavur, Mustafa Çırak, Mustafa Erkayaoğlu, Selin Yoncacı, Ömer Erdem and Mustafa Kemal Emil for their moral support and guidance throughout the thesis writing.

I would like to thank Tahsin Işıksal, Aytekin Aslan, Hakan Uysal and İsmail Kaya for their help in the experimental work.

I would like to thank my friends Fatih Açıkgöz, Sarper Çubuk, Habip Demir, Metehan Demir, Erbil Postallı and Mehmet Ali Recai Önal for their friendship and moral support throughout the thesis preparation.

Finally, I would like to give my deepest love to my family who has supported and loved me at every moment of my life.

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TABLE OF CONTENTS

ABSTRACT... iv

ÖZ... ... vi

ACKNOWLEDGEMENTS ... ix

TABLE OF CONTENTS... x

LIST OF TABLES ... xii

LIST OF FIGURES ... xxi

LIST OF SYMBOLS ... xxix

CHAPTERS 1. INTRODUCTION ... 1

1.1 General ... 1

1.2 Objective and Scope of the Thesis ... 2

2. BACKGROUND ... 4

2.1 Comminution Methods ... 4

2.1.1 High Pressure Grinding Rolls ... 5

2.1.2 Ball Mill ... 6

2.2 Comminution Models ... 8

2.2.1 Breakage Parameters of the Kinetic Model ... 9

2.2.2 Single Particle Breakage Tests ... 14

2.2.2.1 Drop Weight Testing ... 15

2.3 Portland Cement Clinker ... 18

2.3.1 Cement Clinker Grinding ... 19

2.4 Utilization of HPGR Prior To Ball Mill ... 21

3. EXPERIMENTAL MATERIAL AND METHODS ... 23

3.1 Material ... 23

3.2 Methods ... 24

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4. RESULTS AND DISCUSSION... 36

4.1 Evaluation of Single Particle Breakage Tests ... 36

4.2 Evaluation of Batch Grinding Tests ... 54

4.2.1 Product Size Distributions ... 54

4.2.2 Specific Rates of Breakage ... 59

4.2.3 Primary Breakage Distribution Functions ... 67

5. CONCLUSIONS ... 76

REFERENCES ... 79

APPENDICES A. SIZE DISTRIBUTIONS OF HPGR PRODUCT AND HPGR FEED ... 82

B. DROP WEIGHT TEST DATA ... 84

C. BLANK SIEVE ANALYSIS OF MONOSIZE MATERIAL USED IN BATCH GRINDING OF HPGR PRODUCT AND HPGR FEED ... 151

D. BATCH GRINDING TEST DATA ... 161

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LIST OF TABLES

TABLES

Table 2.1. Breakage distribution functions in a matrix form ... 12 Table 3.1. Experimental conditions for drop weight testing of -4.7+3.35 mm of HPGR product ... 25 Table 3.2. Experimental conditions for drop weight testing of -4.7+3.35 mm of HPGR feed ... 25 Table 3.3. Experimental conditions for drop weight testing of -6.35+4.7 mm of HPGR product ... 26 Table 3.4. Experimental conditions for drop weight testing of -6.35+4.7 mm of HPGR feed ... 26 Table 3.5. Experimental conditions for drop weight testing of -9.53+6.35 mm of HPGR product ... 27 Table 3.6. Experimental conditions for drop weight testing of -9.53+6.35 mm of HPGR feed ... 27 Table 3.7. Experimental conditions for drop weight testing of -12.7+9.53 mm of HPGR product ... 28 Table 3.8. Experimental conditions for drop weight testing of -12.7+9.53 mm of HPGR feed ... 29 Table 3.9. Experimental conditions for drop weight testing of -19.0+12.7 mm of HPGR product ... 30 Table 3.10. Experimental conditions for drop weight testing of -19.0+12.7 mm of HPGR feed ... 30 Table 3.11. Experimental conditions for drop weight testing of -25.4+19.0 mm of HPGR product ... 31 Table 3.12. Experimental conditions for drop weight testing of -25.4+19.0 mm of HPGR feed ... 31

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Table 3.13. Experimental conditions for batch ball mill grinding of HPGR product and HPGR feed (d_B = 19.05 mm)... 33 Table 3.14. Experimental conditions for batch ball mill grinding of HPGR product and HPGR feed (dB = 25.4 mm)... 34 Table 3.15. Experimental conditions for batch ball mill grinding of HPGR product and HPGR feed (dB = 31.75 mm)... 35 Table 4.1. Fast (S1) and slow (S2) breakage rates of the size fractions of HPGR product and HPGR feed (Raw data at Appendix C and Appendix D) ... 60 Table A.1. Size distribution of HPGR product ... 82 Table A.2. Size distribution of HPGR feed ... 83 Table B.1. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR product (specific impact energy=0.54 kWh/t) ... 84 Table B.2. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR product (specific impact energy=1.09 kWh/t) ... 85 Table B.3. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR product (specific impact energy=2.18 kWh/t) ... 86 Table B.4. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR product (specific impact energy=3.32 kWh/t) ... 87 Table B.5. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR feed (specific impact energy=0.54 kWh/t) ... 88 Table B.6. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR feed (specific impact energy=1.09 kWh/t) ... 89 Table B.7. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR feed (specific impact energy=2.18 kWh/t) ... 90 Table B.8. Product size distribution after impact breakage of -4.7+3.35 mm of HPGR feed (specific impact energy=3.32 kWh/t) ... 91 Table B.9. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR product (specific impact energy=0.23 kWh/t) ... 92 Table B.10. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR product (specific impact energy=0.45 kWh/t) ... 93

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Table B.11. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR product (specific impact energy=0.88 kWh/t) ... 94 Table B.12. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR product (specific impact energy=1.74 kWh/t) ... 95 Table B.13. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR feed (specific impact energy=0.23 kwh/t) ... 96 Table B.14. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR feed (specific impact energy=0.45 kWh/t) ... 97 Table B.15. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR feed (specific impact energy=0.88 kWh/t) ... 98 Table B.16. Product size distribution after impact breakage of -6.35+4.7 mm of HPGR feed (specific impact energy=1.74 kWh/t) ... 99 Table B.17. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=0.10 kWh/t) ... 100 Table B.18. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=0.22 kWh/t) ... 101 Table B.19. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=0.55 kWh/t) ... 102 Table B.20. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=0.92 kWh/t) ... 103 Table B.21. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=2.21 kWh/t) ... 104 Table B.22. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR product (specific impact energy=4.35 kWh/t) ... 105 Table B.23. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=0.10 kWh/t) ... 106 Table B.24. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=0.22 kWh/t) ... 107 Table B.25. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=0.55 kWh/t) ... 108

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Table B.26. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=0.92 kWh/t) ... 109 Table B.27. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=2.21 kWh/t) ... 110 Table B.28. Product size distribution after impact breakage of -9.53+6.35 mm of HPGR feed (specific impact energy=4.35 kWh/t) ... 111 Table B.29. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=0.03 kWh/t) ... 112 Table B.30. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=0.11 kWh/t) ... 113 Table B.31. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=0.22 kWh/t) ... 114 Table B.32. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=0.44 kWh/t) ... 115 Table B.33. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=0.88 kWh/t) ... 116 Table B.34. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=1.32 kWh/t) ... 117 Table B.35. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR product (specific impact energy=1.7 kWh/t) ... 118 Table B.36. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=0.03 kWh/t) ... 119 Table B.37. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=0.11 kWh/t) ... 120 Table B.38. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=0.22 kWh/t) ... 121 Table B.39. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=0.44 kWh/t) ... 122 Table B.40. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=0.88 kWh/t) ... 123

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Table B.41. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=1.32 kWh/t) ... 124 Table B.42. Product size distribution after impact breakage of -12.7+9.53 mm of HPGR feed (specific impact energy=1.70 kWh/t) ... 125 Table B.43. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR product (specific impact energy=0.03 kWh/t) ... 126 Table B.44. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR product (specific impact energy=0.11 kWh/t) ... 127 Table B.45. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR product (specific impact energy=0.22 kWh/t) ... 128 Table B.46. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR product (specific impact energy=0.44 kWh/t) ... 129 Table B.47. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR product (specific impact energy=0.88 kWh/t) ... 130 Table B.48. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR feed (specific impact energy=0.03 kWh/t) ... 131 Table B.49. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR feed (specific impact energy=0.11 kWh/t) ... 132 Table B.50. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR feed (specific impact energy=0.22 kWh/t) ... 133 Table B.51. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR feed (specific impact energy=0.44 kWh/t) ... 134 Table B.52. Product size distribution after impact breakage of -19.0+12.7 mm of HPGR feed (specific impact energy=0.88 kWh/t) ... 135 Table B.53. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.01 kWh/t) ... 136 Table B.54. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.05 kWh/t) ... 137 Table B.55. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.11 kWh/t) ... 138

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Table B.56. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.22 kWh/t) ... 139 Table B.57. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.59 kWh/t) ... 140 Table B.58. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR product (specific impact energy=0.88 kWh/t) ... 141 Table B.59. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.01 kWh/t) ... 142 Table B.60. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.05 kWh/t) ... 143 Table B.61. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.11 kWh/t) ... 144 Table B.62. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.22 kWh/t) ... 145 Table B.63. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.59 kWh/t) ... 146 Table B.64. Product size distribution after impact breakage of -25.4+19.0 mm of HPGR feed (specific impact energy=0.88 kWh/t) ... 147 Table B.65. t10 and d₅₀ of HPGR product ... 148 Table B.66. t10 and d50 of HPGR feed ... 149 Table C.1. Size distribution of -3.35+2.36 mm HPGR product used for ball milling (dB =19.05 mm, ɸBALL=0.35) ... 151 Table C.2. Size distribution of -3.35+2.36 mm HPGR product used for ball milling (dB =25.4 mm, ɸBALL=0.35) ... 152 Table C.3. Size distribution of -3.35+2.36 mm HPGR product used for ball milling (dB =31.75 mm, ɸBALL=0.35) ... 152 Table C.4. Size distribution of -3.35+2.36 mm HPGR feed used for ball milling (dB=19.05 mm, ɸBALL=0.35) ... 153 Table C.5. Size distribution of -3.35+2.36 mm HPGR feed used for ball milling (dB=25.4 mm, ɸBALL=0.35) ... 153

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Table C.6. Size distribution of -3.35+2.36 mm HPGR feed used for ball milling (d_B=31.75 mm, ɸ_BALL=0.35) ... 154 Table C.7. Size distribution of -2.36+1.7 mm HPGR product used for ball milling (dB =19.05 mm, ɸBALL=0.35) ... 154 Table C.8. Size distribution of -2.36+1.7 mm HPGR product used for ball milling (dB =25.4 mm, ɸBALL=0.35) ... 155 Table C.9. Size distribution of -2.36+1.7 mm HPGR product used for ball milling (dB=31.75 mm, ɸBALL=0.35) ... 155 Table C.10. Size distribution of -2.36+1.7 mm HPGR feed used for ball milling (dB=19.05 mm, ɸBALL=0.35) ... 156 Table C.11. Size distribution of -2.36+1.7 mm HPGR feed used for ball milling (d_B=25.4 mm, ɸ_BALL=0.35) ... 156 Table C.12. Size distribution of -2.36+1.7 mm HPGR feed used for ball milling (d_B=31.75 mm, ɸ_BALL=0.35) ... 157 Table C.13. Size distribution of –1.7+1.18 mm HPGR product used for ball milling (d_B=19.05 mm, ɸ_BALL=0.35) ... 157 Table C.14. Size distribution of –1.7+1.18 mm HPGR product used for ball milling (d_B=25.4 mm, ɸ_BALL=0.35) ... 158 Table C.15. Size distribution of –1.7+1.18 mm HPGR product used for ball milling (dB=31.75 mm, ɸBALL=0.35) ... 158 Table C.16. Size distribution of –1.7+1.18 mm HPGR feed used for ball milling (dB=19.05 mm, ɸBALL=0.35) ... 159 Table C.17. Size distribution of –1.7+1.18 mm HPGR feed used for ball milling (dB=25.4 mm, ɸBALL=0.35) ... 159 Table C.18. Size distribution of –1.7+1.18 mm HPGR feed used for ball milling (dB=31.75 mm, ɸBALL=0.35) ... 160 Table D.1. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR product (dB =19.05 mm, ɸBALL=0.35)... 161 Table D.2. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR product (dB =25.4 mm, ɸBALL=0.35)... 163

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Table D.3. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR product (d_B =31.75 mm, ɸ_BALL=0.35)... 165 Table D.4. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR feed (dB =19.05 mm, ɸBALL=0.35) ... 167 Table D.5. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR feed (dB =25.4 mm, ɸBALL=0.35) ... 168 Table D.6. Product size distribution after batch grinding of -3.35+2.36 mm of HPGR feed (dB =31.75 mm, ɸBALL=0.35) ... 170 Table D.7. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR product (dB =19.05 mm, ɸBALL=0.35) ... 171 Table D.8. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR product (d_B =25.4 mm, ɸ_BALL=0.35) ... 173 Table D.9. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR product (d_B =31.75 mm, ɸ_BALL=0.35) ... 174 Table D.10. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR feed (d_B =19.05 mm, ɸ_BALL=0.35) ... 176 Table D.11. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR feed (d_B =25.4 mm, ɸ_BALL=0.35) ... 177 Table D.12. Product size distribution after batch grinding of -2.36+1.7 mm of HPGR feed (dB =31.75 mm, ɸBALL=0.35) ... 179 Table D.13. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR product (dB =19.05 mm, ɸBALL=0.35)... 181 Table D.14. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR product (dB =25.4 mm, ɸBALL=0.35)... 182 Table D.15. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR product (dB =31.75 mm, ɸBALL=0.35)... 184 Table D.16. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR feed (dB =19.05 mm, ɸBALL=0.35) ... 185 Table D.17. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR feed (dB =25.4 mm, ɸBALL=0.35) ... 187

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Table D.18. Product size distribution after batch grinding of -1.7+1.18 mm of HPGR feed (d_B =31.75 mm, ɸ_BALL=0.35) ... 188

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LIST OF FIGURES

FIGURES

Figure 2.1. Operating principle of HPGR (De, 1995) ... 6

Figure 2.2. Non-linear deviations observed in breakage rates (Bilgili et al., 2006) 11 Figure 2.3. Graphical procedure for estimating parameters of  and Ф1 in functional form of Bi1 ... 14

Figure 2.4. Schematics of a drop weight tester ... 16

Figure 2.5. One-parameter family curves ... 17

Figure 2.6. Conceptual flowsheet of cement production ... 19

Figure 2.7. The modes of operation for cement grinding circuits (Patzelt, 1992) ... 20

Figure 3.1. Particle size distributions of HPGR product and HPGR feed (Raw data at Table A.1 and Table A.2 in Appendix A) ... 23

Figure 4.1. Mass-Basis Breakage Probabilities of -4.7+3.35 mm HPGR product and HPGR feed (Raw data at Table B.1 through Table B.8 in Appendix B) ... 37

Figure 4.5. Mass-Basis Breakage Probabilities of -19+12.7 mm HPGR product and HPGR feed (Raw data at Table B.43 through Table B.52 in Appendix B) ... 39

Figure 4.6. Mass-Basis Breakage Probabilities of -25.4+19 mm HPGR product and HPGR feed (Raw data at Table B.53 through Table B.64 in Appendix B) ... 40

Figure 4.7. Cumulative breakage distribution functions after impact breakage of -4.7+3.35 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.1 through Table B.8 in Appendix B) ... 41

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Figure 4.8. Cumulative breakage distribution functions after impact breakage of -6.35+4.7 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.9 through Table B.16 in Appendix B) ... 42 Figure 4.9. Cumulative breakage distribution functions after impact breakage of -9.53+6.35 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.17 through Table B.28 in Appendix B) ... 42 Figure 4.10. Cumulative breakage distribution functions after impact breakage of -12.7+9.53 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.29 through Table B.42 in Appendix B) ... 43 Figure 4.11. Cumulative breakage distribution functions after impact breakage of -19.0+12.7 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.43 through Table B.52 in Appendix B) ... 43 Figure 4.12. Cumulative breakage distribution functions after impact breakage of -25.4+19.0 mm of HPGR product and HPGR feed at various energy levels (Raw data at Table B.53 through Table B.64 in Appendix B) ... 44 Figure 4.13. Non-self similar product size distributions after drop weight tests of -4.7+3.35 mm HPGR product with varying specific impact energy levels (Raw data at Table B.1 through Table B.4, and at Table B.65 in Appendix B) ... 45 Figure 4.14. Non-self similar product size distributions after drop weight tests of -4.7+3.35 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.5 through Table B.8, and at Table B.66 in Appendix B)... 46 Figure 4.15. Non-self similar product size distributions after drop weight tests of -6.35+4.7 mm HPGR product with varying specific impact energy levels (Raw data at Table B.9 through Table B.12, and at Table B.65 in Appendix B) ... 46 Figure 4.16. Non-self similar product size distributions after drop weight tests of -6.35+4.7 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.13 through Table B.16, and at Table B.66 in Appendix B) ... 47 Figure 4.17. Non-self similar product size distributions after drop weight tests of -9.53+6.35 mm HPGR product with varying specific impact energy levels (Raw data at Table B.17 through Table B.22, and at Table B.65 in Appendix B) ... 47

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Figure 4.18. Non-self similar product size distributions after drop weight tests of -9.53+6.35 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.23 through Table B.28, and at Table B.66 in Appendix B) ... 48 Figure 4.19. Non-self similar product size distributions after drop weight tests of -12.7+9.53 mm HPGR product with varying specific impact energy levels (Raw data at Table B.29 through Table B.35, and at Table B.65 in Appendix B) ... 48 Figure 4.20. Non-self similar product size distributions after drop weight tests of -12.7+9.53 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.36 through Table B.42, and at Table B.66 in Appendix B) ... 49 Figure 4.21. Non-self similar product size distributions after drop weight tests of -19.0+12.7 mm HPGR product with varying specific impact energy levels (Raw data at Table B.43 through Table B.47, and at Table B.65 in Appendix B) ... 49 Figure 4.22. Non-self similar product size distributions after drop weight tests of -19.0+12.7 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.48 through Table B.52, and at Table B.66 in Appendix B) ... 50 Figure 4.23. Non-self similar product size distributions after drop weight tests of -25.4+19.0 mm HPGR product with varying specific impact energy levels (Raw data at Table B.53 through Table B.58, and at Table B.65 in Appendix B) ... 50 Figure 4.24. Non-self similar product size distributions after drop weight tests of -25.4+19.0 mm HPGR feed with varying specific impact energy levels (Raw data at Table B.59 through Table B.64, and at Table B.66 in Appendix B) ... 51 Figure 4.25. Non-normalizable breakage distribution functions of -4.7+3.35 mm, -6.35+4.7 mm, -9.53+6.35 mm, and -12.7+9.53 mm HPGR product (Raw data at Table B.1, Table B.9, Table B.17 and Table B.29 in Appendix B) ... 52 Figure 4.26. Non-normalizable breakage distribution functions of -4.7+3.35 mm, -6.35+4.7 mm, -9.53+6.35 mm, and -12.7+9.53 mm HPGR feed (Raw data at Table B.5, Table B.13, Table B.23 and Table B.36 in Appendix B) ... 52 Figure 4.27. Non-normalizable breakage distribution functions of -12.7+9.53 mm, -19+12.7 mm, -25.4+19.0 mm HPGR product (Raw data at Table B.30, Table B.43 and Table B.53 in Appendix B) ... 53

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Figure 4.28. Non-normalizable breakage distribution functions of -12.7+9.53 mm, -19+12.7 mm, -25.4+19.0 mm HPGR feed (Raw data at Table B.37, Table B.48 and Table B.59 in Appendix B) ... 53 Figure 4.29. Product size distributions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; d_B = 19.05 mm, ɸ_Ball = 0.35, 633 g of material (Raw data at Table D.13 and Table D.16 in Appendix D) ... 55 Figure 4.30. Product size distributions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; dB = 25.4 mm, ɸBall = 0.35, 633 g of material (Raw data at Table D.14 and Table D.17 in Appendix D) ... 55 Figure 4.31. Product size distributions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; dB = 31.75 mm, ɸBall = 0.35, 633 g of material (Raw data at Table D.15 and Table D.18 in Appendix D) ... 56 Figure 4.32. Product size distributions after batch grinding of -2.36+1.7 mm of HPGR product and HPGR feed; d_B = 19.05 mm, ɸ_Ball = 0.35, 633 g of material (Raw data at from Table D.7 and Table D.10 in Appendix D) ... 56 Figure 4.33. Product size distributions after batch grinding of -2.36+1.7 mm of HPGR product and HPGR feed; d_B = 25.4 mm, ɸ_Ball = 0.35, 633 g of material (Raw data at Table D.8 and Table D.11 in Appendix D) ... 57 Figure 4.34. Product size distributions after batch grinding of -2.36+1.7 mm of HPGR product and HPGR feed; dB = 31.75 mm, ɸBall = 0.35, 633 g of material (Raw data at Table D.9 and Table D.12 in Appendix D) ... 57 Figure 4.35. Product size distributions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; dB = 19.05 mm, ɸBall = 0.35, 720 g of material (Raw data at Table D.1 and Table D.4 in Appendix D) ... 58 Figure 4.36. Product size distributions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; dB = 25.4 mm, ɸBall = 0.35, 720 g of material (Raw data at Table D.2 and Table D.5 in Appendix D) ... 58 Figure 4.37. Product size distributions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; dB = 31.75 mm, ɸBall = 0.35, 720 g of material (Raw data at Table D.3 and Table D.6 in Appendix D) ... 59

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Figure 4.38. Breakage rate plots after batch grinding of -1.7+1.18 mm of HPGR

product and HPGR feed; d_B = 19.05 mm, ɸ_Ball =0.35, 633 g of material (Raw data at Table C.13, Table C.16 in Appendix C, and Table D.13, Table D.16 in

Appendix D) ... 61 Figure 4.39. Breakage rate plots after batch grinding of -1.7+1.18 mm of HPGR

product and HPGR feed; dB = 25.4 mm, ɸBall =0.35, 633 g of material (Raw data at Table C.14, Table C.17 in Appendix C, and Table D.14, Table D.17 in

Appendix D) ... 64

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Figure 4.45. Breakage rate plots after batch grinding of -3.35+2.36 mm of HPGR

Appendix D) ... 65 Figure 4.47. Variation of S1 and S2 with particle size in batch grinding of HPGR product and HPGR feed (dB = 19.05 mm) ... 66 Figure 4.48. Variation of S1 and S2 with particle size in batch grinding of HPGR product and HPGR feed (d_B = 25.4 mm) ... 66 Figure 4.49. Variation of S1 and S2 with particle size in batch grinding of HPGR product and HPGR feed (d_B = 31.75 mm) ... 67

Figure 4.50. Primary breakage distribution functions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; d_B = 19.05 mm, ɸ_Ball = 0.35, 633

g of material (Raw data at Table C.13, Table C.16 in Appendix C, and Table D.13, Table D.16 in Appendix D) ... 68

Figure 4.51. Primary breakage distribution functions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; dB = 25.4 mm, ɸBall = 0.35, 633 g

of material (Raw data at Table C.14, Table C.17 in Appendix C, and Table D.14, Table D.17 in Appendix D) ... 68

Figure 4.52. Primary breakage distribution functions after batch grinding of -1.7+1.18 mm of HPGR product and HPGR feed; dB =31.75 mm, ɸBall =0.35, 633 g

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Figure 4.54. Primary breakage distribution functions after batch grinding of -2.36+1.7 mm of HPGR product and HPGR feed; d_B =25.4 mm, ɸ_Ball =0.35, 633 g

Figure 4.56. Primary breakage distribution functions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; dB=19.05 mm, ɸBall=0.35, 720 g

Figure 4.57. Primary breakage distribution functions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; d_B =25.4 mm, ɸ_Ball =0.35, 720 g

Figure 4.58. Primary breakage distribution functions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; d_B =31.75 mm, ɸ_Ball =0.35, 720

g of material (Raw data at Table C.3, Table C.6 in Appendix C, and Table D.3, Table D.6 in Appendix D) ... 72 Figure 4.59. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR product; dB = 19.05 mm, ɸBall = 0.35 (Raw data at Table C.1, Table C.7, Table C.13 in Appendix C, and Table D.1, Table D.7, Table D.13 in Appendix D) ... 73 Figure 4.60. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR product; dB = 25.4 mm, ɸBall = 0.35 (Raw data at Table C.2, Table C.8, Table C.14 in Appendix C, and Table D.2, Table D.8 and Table D.14 in Appendix D) ... 73

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Figure 4.61. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR product; d_B= 31.75 mm, ɸBall = 0.35 (Raw data at Table C.3, Table C.9, Table C.15 in Appendix C, and Table D.3, Table D.9, Table D.15 in Appendix D) ... 74 Figure 4.62. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR feed; dB = 19.05 mm, ɸBall = 0.35 (Raw data at Table C.4, Table C.10, Table C.16 in Appendix C, and Table D.4, Table D.10, Table D.16 in Appendix D) ... 74 Figure 4.63. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR feed; dB = 25.4 mm, ɸBall = 0.35 (Raw data at Table C.5, Table C.11, Table C.17 in Appendix C, and Table D.5, Table D.11, Table D.17 in Appendix D) ... 75 Figure 4.64. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR feed; d_B = 31.75 mm, ɸ_Ball = 0.35 (Raw data at Table C.6, Table C.12, Table C.18 in Appendix C, and Table D.6, Table D.12, Table D.18 in Appendix D) ... 75

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LIST OF SYMBOLS

Vmill Empty volume inside the mill (dm³)

ɸB Fraction of ball bed in the empty mill volume εball Porosity of the ball bed expressed as fraction Mball Mass of ball bed inside mill (kg)

ρball Density of ball (kg/dm³)

dB Ball size (mm)

fc Fraction of particle bed in the empty mill volume εpowder Porosity of the particle bed expressed as fraction

ɸ_M Fraction of particle bed in the empty volume of ball bed ρpowder Density of particle (kg/dm³)

M_powder Mass of particle bed ground in ball mill (kg) D Internal diameter of the mill (m)

d Largest ball diameter used in the mill (m) N_c Critical speed of the mill (rpm)

ɸc Ratio of operating speed to critical speed of the mill S_i Breakage rate of size interval “i” in ball milling (min^-1) bij Individual breakage distribution function

B_ij Cumulative breakage distribution function

S1 Fast Breakage Rate of top size class “1” in ball milling (min^-1) S2 Slow Breakage Rate of top size class “1” in ball milling (min^-1) wi(t) Fraction or percentage of material of size “i” inside mill at time “t”

Pi(t) Cumulative fraction of the ground material passing below the upper sieve size of the size interval “i” at time “t”

xi Upper sieve size of the size interval “i”

Eis Specific impact energy in drop weight testing (kWh/t) M Mass of drop head (kg)

h0 Drop height (cm)

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xxx

h_f Height between bottom of the drop weight and surface of the anvil after impact (cm)

̅ Average mass of a particle in a given set of particles (g)

tn Percentage of material passing 1/n^th of the original feed size after drop weight testing

d₅₀ Median product size (µm)

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1 CHAPTER 1

INTRODUCTION

1.1 General

Comminution is an essential, but an energy-inefficient part of mineral processing, providing fine material for downstream beneficiation process. As an example, energy consumption in comminution is estimated to be 29.3 % of the total mining energy in USA. This is approximately equal to 1.14 % of the energy used in industrial sector of USA, being more or less the same at other countries (Tromans, 2008). Moreover, the energy consumption in the comminution process will increase as finer grinding is adopted due to subsequent downstream processes of low-grade ores.

Size reduction processes also play a crucial role in cement production. These processes mainly involve grinding raw feed that yields cement clinker at high- temperature and grinding cement clinker which is the major constituent of cement.

Considering that about 40 % of the total energy expended in the cement-making process goes into clinker grinding, there exists a need for lower energy usage in cement clinker grinding in order to reduce high production costs and environmental problems (Jankovic et al., 2004).

Increasing energy expenditure in size reduction processes pushes toward the development of new energy-efficient comminution equipment. A recently- developed machine to serve this purpose is the high pressure grinding rolls (HPGR)

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which is commonly adopted to cement grinding circuits; gold, diamond and iron ore crushing circuits. HPGR consists of a pair of rotating rolls through which a bed of particles are nipped and ground with high external pressure exerted on the particle bed. It is found that high interparticle stresses induced around the particles are responsible for breakage, and this breakage mode makes HPGR more energy- efficient than a ball mill at low reduction ratios (Fuerstenau et al., 1990; Fuerstenau and Vazquez-Favela, 1997). It is also believed that HPGR is not only energy- efficient at low reduction ratios, but it also induces cracks throughout the particle due to high interparticle stresses acted on the particle bed, which facilitates breakage in downstream size reduction processes (De, 1995; Fuerstenau et al., 1999; Patzelt et al., 1995; Tavares, 2005).

1.2 Objective and Scope of the Thesis

In this study, breakage parameters of narrow size clinker samples taken from the product end of an industrial-scale HPGR (HPGR product) were compared with the feed end of HPGR (HPGR feed) in order to assess the extent to which breakage parameters of the product end of HPGR is improved with respect to fresh feed clinker. For this purpose, single particle breakage tests were performed to compare breakage parameters of narrowly sized HPGR product and HPGR feed above 3.35 mm, while batch grinding tests were performed to compare fine sizes of HPGR product and HPGR feed below 3.35 mm. Single particle breakage tests were performed over six size fractions of clinker by means of drop-weight test. Each size fraction was tested at four to six specific impact energies. The product size distributions, experimental breakage probabilities and energy-dependent impact breakage distribution functions of each narrow size fraction of HPGR product and HPGR feed were compared at the same specific impact energy.

The batch ball mill experiments were performed with three size fractions of HPGR product and HPGR feed using three different ball sizes. For each size fraction and ball size combination tested, an equal mass of balls and material were put in the ball

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3

mill, assuming that specific grinding energy applied to HPGR product and HPGR feed would be the same. The resultant product size distributions, specific breakage rate and primary breakage distribution functions of HPGR product and HPGR feed were compared at each size fraction and ball size combination.

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4 CHAPTER 2

BACKGROUND

2.1 Comminution Methods

Comminution methods can be broadly classified as single-particle comminution, loose-bed comminution and particle-bed comminution (Fuerstenau and Vazquez- Favela, 1997). Single-particle breakage can be achieved either by breaking particles individually in a testing machine or by breaking it in a rigidly mounted roll mill individually so that particles don’t interact with each other. The mode of loading in single particle breakage could be impact, shear or slow compression. Loose-bed comminution is achieved in grinding vessels where the energy is transferred to a loose bed of particles by grinding media. The common example for loose-bed comminution is the ball mill where the energy is transferred to particles by tumbling steel balls. This transfer mode makes loose-bed comminution the most inefficient size reduction method, since there exist non-productive collision events between ball and ball, ball and liner, particle and particle. Moreover, frictional losses could occur during tumbling motion of grinding media and particle bed. Particle-bed comminution is achieved by externally stressing a bed of particles. This external stress induces high interparticle stresses within the bed, which is responsible for the breakage of the particles. The inefficiency in particle-bed comminution arises from frictional losses due to the interaction between particles, and compaction or briquetting of fines produced (Fuerstenau et al., 2004).

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5 2.1.1 High Pressure Grinding Rolls

A recently developed equipment for particle-bed comminution is the High Pressure Grinding Rolls (HPGR) which was invented in 1979. It was first developed by KHD^® and Polysius^® in Germany (Fuerstenau et al., 1993; Gutsche et al., 1993;

Schönert, 1988). At the beginning, it was utilized on industrial scale for the grinding of clinker and raw material in cement production. Since then, HPGR has been adopted into various size reduction processes including gold ore crushing prior to heap leaching; diamond ore crushing; iron ore pre-pelletizing, etc.

Breakage in HPGR is accomplished by passing the material through two counter- rotating rolls. One of the rolls rotates on a fixed axis while the other moves linearly with external pressure applied to the movable roll. The material is fed into the gap between the rolls through a feed hopper. As the material is nipped into the gap, it is compacted by external pressure. This external pressure on the particle bed induces high interparticle stresses on each particle, which causes breakage. It is estimated that these stresses are 40 to 60 times the external pressure applied (Schönert, 1988).

The operating principle of the HPGR is illustrated in Figure 2.1. As shown in Figure 2.1, three zones form during breakage in HPGR. The first zone is the acceleration zone where particles are nipped through the gap into the breakage zone. In this zone, densification of the particle bed occurs. Then, the bed is compacted and comminuted in the compression zone due to interparticle stresses acted on each particle. Lastly, the material bed expands and leaves the gap at the dilation zone (De, 1995).

The breakage behavior inside HPGR and the resultant product size distribution depend upon operating and material variables such as:

- External grinding pressure applied to the rolls - Roll diameter, roll speed, surface pattern of rolls

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6 - Operating gap distance between rolls

- Particle size distribution, chemical composition and moisture content of the feed

Figure 2.1. Operating principle of HPGR (De, 1995)

2.1.2 Ball Mill

The most commonly used size reduction equipment in mineral processing and cement production is the ball mill. It is a cylindrical vessel containing steel balls and the material to be ground. It can be operated in either dry or wet condition.

Grinding is performed by rotating the mill such that the material is comminuted by the motion of loose grinding medium. When the mill is rotated at low rotational speeds, the balls move frequently in an inclined path where the balls are emerging, rolling down, and getting back to the surface, referred to as cascading state. At high rotational speeds, more balls are ejected from the ball bed, known as cataracting state. In the former case, the material bed is expanded between ball bed, and breakage is achieved by a series of collisions between balls. In the latter case, ejected balls fall onto ball bed, nipping and stressing the particles in between.

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The complete explanation of grinding behavior in a ball mill is complex. It depends on material properties, mill environment, and operating variables such as:

- Physical and chemical characteristics of the feed such as particle size distribution, chemical composition of feed, etc.

- Ball diameter and ball density

- Mill diameter, mill length and lifter design

- The fraction of feed material filling the mill volume (powder loading) - The fraction of balls filling the mill volume (ball loading)

- Rotational speed of the mill - Dry or wet grinding condition - Mass transport and hold-up - Pulp density for wet grinding

It is necessary to define some test variables in order to describe the ball mill grinding conditions. In a ball mill, ball loading, ɸ_B, is defined as the fraction of the volume of ball bed in the mill volume, including porosity inside the ball bed. It is formulated as

ɸB = (M_b ρ_b) V_m 1 (1-ε_b) (1)

where M_ball is the mass of balls (kg), ρ_ball is the density of balls (kg/dm³), V_mill is the empty volume inside the mill and ε_ball is the porosity of the ball bed, expressed as fraction. ε_ball values for mono-size ball bed is generally taken as 0.4. Similarly, powder loading, f_c, is defined as the fraction of the volume of feed material in the mill volume, including porosity inside powder bed. It is defined as

f_c= (M_p ρ_p) V_mill (1 (1-ε_p) (2)

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where M_powder is the mass of powder to be ground (kg), ρ_powder is the density of powder (kg/dm³), V_mill is the empty volume inside the mill (dm³) and εpowder is the porosity of the powder bed, expressed as fraction. Knowing the true density of the powder, εpowder can be estimated easily. ɸB and fc can be related with each other by defining the fraction of powder volume in the empty volume between balls, ɸ_M, by;

ɸM=f_c (ε_ball ) (3)

The number of balls and the weight of the feed material added to the batch mill can be computed easily after selecting ɸM and ɸB.

Critical speed, Nc, is also another variable affecting the mill performance. It is defined as the rotational speed of the mill above which balls start to centrifuge around the mill case (Austin et al., 1984). Thus, the tumbling motion of the balls does not occur above critical speed, i.e., no breakage occurs. The critical speed depends on mill diameter and ball diameter. It is expressed as;

N (rpm) =42.2 √D-d (4)

where D is the internal mill diameter and d is the maximum ball diameter in meters.

Rotational mill speed is determined as a fraction of critical speed, ɸc.

2.2 Comminution Models

It is necessary to adopt accurate mathematical models into comminution systems so as to describe the milling operations fully. The models constructed should determine optimal conditions and circuit designs to use as little energy as possible while providing better product specifications suitable for downstream processes. In developing comminution models, the main purpose is to develop a relationship between feed and product size distribution. A popular method used for this purpose

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is population balance modeling (PBM). It basically explains the breakage of any monosize interval based on the average of individual breakage events in a mill.

Then, for a number of repetitive steps of breakage or a time of breakage, accumulation or depletion of each size interval can be estimated which eventually leads to estimation of overall product size distribution. There are mainly two approaches for PBM of size reduction. The first one is the matrix model where each breakage event is assigned to a stage, and shown in a matrix form. Details of the matrix model can be found in the literature (Lynch, 1977). The kinetic model, on the other hand, accepts breakage as a continuous process, and implements time- dependent process characteristics into the model. The difference between kinetic model and matrix model is that time is explicitly defined in the former while it is implicitly defined in the latter. For both models, two parameters should be determined. First, the fraction for each size interval that is to be broken should be found. This fraction is called the selection function in the matrix model or specific breakage rate in the kinetic model. The broken fraction then yields a progeny size distribution, which is called the breakage function in the matrix model and breakage distribution function in the kinetic model.

2.2.1 Breakage Parameters of the Kinetic Model

The specific rate of breakage, Si, is defined as the mass fraction of material in size

“i” broken per unit time. For a monosize interval of size “i”, it was found that rate of disappearance of size “i” follows first-order law for most of the materials tested (Austin et al., 1984):

dw_i(t) d(t) =-S_i w_i(t) (5)

where wi(t) is the mass fraction retained inside the mill at time t. Solving Equation 5 for time t will yield:

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w_i(t)=w_i(0) e p (-S_i t) (6)

where w_i(0) is the mass fraction retained inside the mill before grinding. S_ivalue can be estimated by fitting experimental w_i(t)-t pairs to Equation 6. Also, S_i could be determined graphically by transforming Equation 6 to:

log w_i(t) w_i(0) = – S_i t 2.3 (7)

Then, plotting log[w_i(t)/w_i(0)] versus time gives the slope of (-S_i/2.3).

Although breakage rates are considered to be first-order, non-linearity in breakage rates might also be observed (Austin and Bagga, 1981; Austin et al., 1982). The non-linear breakage encountered could be defined as first-order breakage with subsequent accelerated or decelerated first-order breakage as shown in Figure 2.2.

The non-linearity in breakage rates could arise from environmental effects inside ball mill or material effects or complex interaction of both. A number of possible reasons for non-linearity are given by Austin et al. (1984) as the following:

-Stronger fractions might increase in unbroken material as grinding continues.

-The unbroken material might not get broken with successive impacts, yet, get weakened with time.

-Harder component might be liberated which facilitates the grinding of softer component.

-Fines accumulated in the mill pack around coarse particles, preventing breakage of coarse sizes.

-Fines accumulated in the mill adversely affect the tumbling action inside mill, which results in a decrease in energy input and number of impacts.

-Fines might agglomerate inside the mill forming large particles as grinding continues.

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Figure 2.2. Non-linear deviations observed in breakage rates (Bilgili et al., 2006)

The other breakage parameter in kinetic modeling is the primary breakage distribution function. For a given size interval, it is defined as the progeny size distribution of broken fragments at primary breakage. Considering that particles might re-break as grinding proceeds, primary distribution function should be estimated at the point where no re-breakage of particles occurs. Elements of the breakage distribution function are shown as b_ijwhich is the mass fraction of the broken fragments in size interval “j” which appears in size interval “i”, where size

“i” is smaller than size “j”. The breakage distribution matrix is illustrated in Table 2.1 for a set of N size intervals where 1 is the top size interval and N is the residue.

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Table 2.1. Breakage distribution functions in a matrix form

j=1 j=2 j=3 . j=N-1 j=N

i=1 0 0 0 . 0 0

i=2 b21 0 0 . 0 0

i=3 b31 b32 0 . 0 0

. . . .

i=N b_N1 b_N2 b_N3 . b_N(N-1) 0

By definition, the sum of each column is equal to 1.

∑^N_i=j+1 b_ij=1 (8)

Another form of representation for the primary breakage distribution is the cumulative breakage distribution function, B_ij, which is the cumulative mass fraction of material broken from size “j” which appears in size intervals less than the upper limit of the size interval “i”:

B_ij= ∑^N_k=i b_kj

i j

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The transformation between B and b values can be shown as:

b_ij=B_ij-B_(i+1)j (10)

and, by definition:

b_N=B_j , B_(j+1)j=1 (11)

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13

In principle, B values for monosize feeds should be estimated from short time grinding data in order to prevent re-breakage of fragments. However, it is difficult to get accurate size distribution at small degrees of breakage. As a result, a method named the BII method was developed based on the solution of the batch grinding equation which was based on compensation condition and claimed to correct for secondary breakage (Austin et al., 1984). Then, for a monosize feed having a size index of 1, Bi1 can be estimated as:

( -P_i(0)) ( -P_i(t)) ( -P₂(0) ) ( -P₂(t)) (12)

where P_i(t) and P_i(0) are the cum. mass fraction passing upper size of the size interval “i” at time t and 0, respectively. This equation is known as the BII method.

Moreover, B_i1 values can be fitted to the following functional form:

B_i1=Ф₁( _i-1 ₁)^+(1-Ф₁)( _i-1 ₁) (13)

where x_iis the upper size limit of size interval “i”, Ф₁,  and  are functional parameters. Plotting left-hand side of Equation 13 against (xi-1/x1) gives sum of two straight lines. As given in Figure 2.3, the parameters of  and Ф₁ is the slope and intercept of the small end of the plot, respectively. After estimating  and Ф1,  can be estimated by rearranging Equation 13 such that:

B_i1-Ф₁( _i-1 ₁)^ (1-Ф₁)=( _i-1 ₁) (14)

plotting left-hand side of Equation 14 against (xi-1/x1) in log-log scale will give the slope of .

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14

Figure 2.3. Graphical procedure for estimating parameters of  and Ф1 in functional form of Bi1

2.2.2 Single Particle Breakage Tests

Grinding in a ball mill involves a complex interaction between material effects, stressing conditions and environmental effects inside the mill which, in overall, determines the product size distribution and product quality. In this aspect, single particle breakage tests provide insight to understand breakage process in microscale event basis. Single particle breakage tests are classified with respect to the mode of loading: Single particle will be broken either by impact or compression or shearing.

The following can be estimated from single particle breakage data:

-Functional relationship between specific impact energy and product size distribution (Napier-Munn et al., 1996)

-Specific fracture energy of a single particle (J/g) and specific fracture energy or fracture strength distribution of a given material (Bourgeois et al., 1992; Tavares and King, 1998; Tavares, 2007)