Primary Breakage Distribution Functions

Although higher breakage rates in HPGR product show significant weakening with respect to HPGR feed, the primary breakage distribution functions of batch grinding HPGR product are coarser than those of the HPGR feed for each combination of size fraction and ball size, which are shown in Figure 4.50 through Figure 4.58.

However, breakage distribution function of HPGR product is slightly coarser than that of HPGR feed at batch grinding of -3.35+2.36 mm with 19.05 mm ball.

68

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)

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)

69

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

of material (Raw data at Table C.15, Table C.18 in Appendix C, and Table D.15, Table D.18 in Appendix D)

Figure 4.53. Primary breakage distribution functions after batch grinding of -2.36+1.7 mm of HPGR product and HPGR feed; dB =19.05 mm, ɸBall =0.35, 633 g

of material (Raw data at Table C.7, Table C.10 in Appendix C, and Table D.7, Table D.10 in Appendix D)

70

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

of material (Raw data at Table C.8, Table C.11 in Appendix C, and Table D.8, Table D.11 in Appendix D)

Figure 4.55. Primary breakage distribution functions 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 C.9, Table C.12 in Appendix C, and Table D.9, Table D.12 in Appendix D)

71

Figure 4.56. Primary breakage distribution functions after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; d_B=19.05 mm, ɸBall=0.35, 720 g of material (Raw data at Table C.1, Table C.4 in Appendix C, and Table D.1, Table

D.4 in Appendix D)

Figure 4.57. Primary breakage distribution functions 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 C.2, Table C.5 in Appendix C, and Table D.2, Table

D.5 in Appendix D)

72

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)

It is of the interest to check whether breakage distribution functions of HPGR product and HPGR feed are normalizable with respect to parent size interval at the same ball loading condition. As shown in Figure 4.59 through Figure 4.64, the breakage distribution functions of HPGR product and HPGR feed are non-normalizable. In fact, it was previously found that the batch grinding of coarse feeds gave non-normalizable breakage distribution functions (Austin et al., 1981; Austin et al., 1982). For HPGR product, it is clear that the proportion of fines increase in breakage distribution function as the size interval gets coarser. Actually, this was previously observed and linked to chipping and abrasion action inside the mill that provide a larger proportion of fines with increasing feed size (Austin et al., 1984).

On the other hand, this pattern is not observed in HPGR feed. In this case, batch grinding of -3.35+2.36 mm HPGR feed gives the highest proportion of fines in breakage distribution function. Meanwhile, batch grinding of -2.36+1.7 mm and -1.7+1.18 mm HPGR feed exhibit nearly normalizable breakage distribution function although they seem to be in abnormal breakage region.

73

Figure 4.59. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR product; d_B = 19.05 mm, ɸ_Ball = 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)

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)

74

Figure 4.61. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR product; d_B = 31.75 mm, ɸ_Ball = 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)

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)

75

Figure 4.63. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR feed; d_B = 25.4 mm, ɸ_Ball = 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)

Figure 4.64. Primary breakage distribution functions after batch grinding of three monosize fractions of HPGR feed; dB = 31.75 mm, ɸBall = 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)

76 CHAPTER 5

CONCLUSIONS

Clinker broken in HPGR was found to be weaker than unbroken clinker considering higher breakage probabilities and higher breakage rates encountered. This could be attributed to the existence of cracks in clinker induced by HPGR. However, no coarser than those of HPGR feed at coarse and fine size ranges. Moreover, coarse clinker in HPGR product and in HPGR feed gave nearly the same fragment size distribution at excessive impact energies due to rebreakage.

Single particle breakage tests on HPGR product and HPGR feed gave non-self-similar product size distributions. However, impact breakage of -4.7+3.35 mm HPGR product and HPGR feed exhibited nearly self-similar breakage behaviour.

Also, at size fractions below 12.7 mm, impact breakage of HPGR product and HPGR feed tended to yield self-similar size distributions at excessive energy levels.

In this case, it was believed that rebreakage of particles might probably yield self-similar size distributions; especially at excessive specific impact energy levels.

Meanwhile, non-self-similar size distributions arise from limited rebreakage of particles.

77

The impact breakage distribution functions of coarse particles were a function of particle size and impact energy (J) both in HPGR product and HPGR feed. For a given particle size, broken fragments became finer with increasing impact energy.

Meanwhile, at a given impact energy, proportion of fines in broken fragments increased with decreasing particle size. In this case, given impact energy would probably be insufficient to generate breakage within coarser particles.

The batch grinding tests showed that at a given size fraction, the product size distribution of HPGR product was slightly finer than HPGR feed for the same ball loading and material loading conditions. This was due to the fact that cracks induced in clinker by HPGR facilitate breakage, leading to finer product size distributions in HPGR product. However, the product size distributions of HPGR product and HPGR feed tended to become similar at long grinding times, indicating disappearance of cracks with increasing grinding time. Also, time of disappearance of cracks tended to decrease with larger balls, probably due to higher grinding energies generated with larger balls.

Specific breakage rates of HPGR product and HPGR feed followed a non-linear elimination of cracks, hence, disappearance of weaker particles. All size fractions of HPGR product and HPGR feed ground were in the abnormal breakage zone, that is, the three ball sizes used were smaller related to particle size such that coarse particles could not be broken efficiently inside the mill.

Breakage distribution functions of HPGR product and HPGR feed were non-normalizable with respect to particle size. In HPGR product, batch grinding of particles yielded high proportion of fines with increasing particle size. However, in

78

HPGR feed, breakage distribution function of -3.35+2.36 mm contained the largest proportion of fines while -2.36+1.7 mm and -1.7+1.18 mm exhibited the same breakage pattern. It is believed that the chipping and abrasion inside the mill was responsible for generating more fines in the coarsest feed size.

79 REFERENCES

Aman, S., Tomas, J., & Kalman, H. (2010). Breakage probability of irregularly shaped particles. Chemical Engineering Science, 65(5), 1503–1512.

Austin, L. G., Shoji, K., & Luckie, P. T. (1976). The effect of ball size on mill performance. Powder Technology, 14(1), 71–79.

Austin, L. G. , & Bagga, P. (1981). An analysis of fine dry grinding in ball mills.

Powder Technology, 28(1), 83–90.

Austin, L. G., Bagga, P., & Celik, M. (1981). Breakage properties of some materials in a laboratory ball mill. Powder Technology, 28(2), 235–243.

Austin, L. G., Shoji, K., & Bell, D. (1982). Rate equations for non-linear breakage in mills due to material effects. Powder Technology, 31(1), 127–133.

Austin, L. G., Klimpel, R. R., & Luckie, P. T. (1984). Process engineering of size reduction: ball milling (pp. 61–204). New York: SME/AIME.

Avşar, Ç. (2003). Breakage Characteristics of Cement Components (Ph.D. Thesis, Middle East Technical University, Ankara, Turkey). Retrieved from http://etd.lib.metu.edu.tr/upload/2/587147/index.pdf.

Bilgili, E., Yepes, J., & Scarlett, B. (2006). Formulation of a non-linear framework for population balance modeling of batch grinding: Beyond first-order kinetics.

Chemical Engineering Science, 61(1), 33–44.

Bourgeois, F. S., King, R. P., & Herbst, J. A. (1992). Low-impact-energy single-particle fracture. In S. K. Kawatra (Ed.), Comminution-Theory and Practice (pp.

99–108). Littleton: Society for Mining, Metallurgy, and Exploration, Inc.

Bourgeois, Florent Stephane. (1993). Single-particle fracture as a basis for microscale modeling of comminution processes (Ph.D. Thesis, The University of Utah, Salt Lake City, United States). Retrieved from ProQuest Dissertations and Theses database (Order No. 9406111).

Datta, A., & Rajamani, R. K. (2002). A direct approach of modeling batch grinding in ball mills using population balance principles and impact energy distribution.

International Journal of Mineral Processing, 64, 181–200.

80

De, A. K. (1995). Modeling and optimization of fine grinding of minerals in high-pressure roll mill - ball mill hybrid comminution circuits (Ph.D. Thesis, University of California, Berkeley, United States). Retrieved from ProQuest Dissertations and Theses (Order No. 9602527).

Fuerstenau, D. W., Kapur, P. C., Schoenert, K., & Marktscheffel, M. (1990).

Comparison of energy consumption in the breakage of single particles in a rigidly mounted roll mill with ball mill grinding. International Journal of Mineral Processing, 28(1-2), 109–125.

Fuerstenau, D. W., Kapur, P. C., & Gutsche, O. (1993). Comminution of single particles in a rigidly-mounted roll mill part 1: mill torque model and energy investment. Powder Technology, 76(3), 253–262.

Fuerstenau, D. W., & Vazquez-Favela, J. (1997). On assessing and enhancing the energy efficiency of comminution processes. Minerals and Metallurgical Processing, 14(1), 41–48.

Fuerstenau, D. W., Lutch, J. J., & De, A. (1999). The effect of ball size on the energy efficiency of hybrid high-pressure roll mill/ball mill grinding. Powder Technology, 105, 199–204.

Fuerstenau, D. W., De, A., & Kapur, P. C. (2004). Linear and nonlinear particle breakage processes in comminution systems. International Journal of Mineral Processing, 74, S317–S327.

Gutsche, O., Kapur, P. C., & Fuerstenau, D. W. (1993). Comminution of single particles in a rigidly-mounted roll mill part 2: product size distribution and energy utilization. Powder Technology, 76(3), 263–270.

Jankovic, A., Valery, W., & Davis, E. (2004). Cement grinding optimisation.

Minerals Engineering, 17(11-12), 1075–1081.

Kapur, P. C. (1972). Self-preserving size spectra of comminuted particles. Chemical Engineering Science, 27(2), 425–431.

Kapur, P.C., Pande, D., & Fuerstenau, D. W. (1997). Analysis of single-particle breakage by impact grinding. Materials Science, 49, 223–236.

Krogh, S. R. (1980). Crushing Characteristics. Powder Technology, 27, 171–181.

Lynch, A. J. (1977). Mineral Crushing and Grinding Circuits. Amsterdam: Elsevier Scientific Publishing Company.

81

Napier-Munn, T. J., Morrell, S., Morrison, R. D., & Kojovic, T. (1996). Rock Testing - Determining the Material - Specific Breakage Function. In T. J. Napier-Munn (Ed.), Mineral Comminution Circuits Their Operation and Optimization (pp.

49–94). Indooroopilly, Qld.: Julius Kruttschnitt Mineral Research Centre.

Patzelt, N. (1992). High-pressure grinding rolls, a survey of experience. Cement Industry Technical Conference (pp. 149–181). Dallas: IEEE.

Patzelt, N., Knecht, H., & Baum, W. (1995). Case made for high-pressure-roll-grinding in gold plants. Mining Engineering, 47(6), 524–529.

Schönert, K. (1988). A first survey of grinding with high-compression roller mills.

International Journal of Mineral Processing, 22(1-4), 401–412.

Tavares, L. M., & King, R. P. (1998). Single-particle fracture under impact loading.

International Journal of Mineral Processing, 54, 1–28.

Tavares, L. M. (2005). Particle weakening in high-pressure roll grinding. Minerals Engineering, 18(7), 651–657.

Tavares, L. M. (2007). Breakage of Single Particles : Quasi-Static. In A. D. Salman, M. Ghadiri, & M. J. Hounslow (Eds.), Handbook of Powder Technology (pp. 3–68).

Elsevier Science B.V.

Tromans, D. (2008). Mineral comminution: Energy efficiency considerations.

Minerals Engineering, 21(8), 613–620.

Tuzcu, E. T., & Rajamani, R. K. (2011). Modeling breakage rates in mills with impact energy spectra and ultra fast load cell data. Minerals Engineering, 24(3-4), 252–260.

Von Seebach, H. M., Neumann, E., & Lohnherr, L. (1996). State-of-the-art of energy-efficient grinding systems. ZKG, 49(2), 61–67.

82 APPENDIX A