Specific Rates of Breakage

Breakage rate plots of each size fraction of HPGR product and HPGR feed for each ball size are compared in Figure 4.38 through Figure 4.46. Breakage rate plots of HPGR product and HPGR feed show non-linear breakage which can be represented as a fast initial breakage zone (S₁) and a subsequent slow breakage zone (S₂). The estimated values of S₁ and S₂ are given in Table 4.1. In the fast breakage zone, breakage rates of HPGR product are significantly higher than those of HPGR feed for a given feed size. On the other hand, in the slow breakage zone, this difference tends to diminish or breakage rates of HPGR feed become slightly higher than those of the HPGR product. Significantly higher breakage rates in HPGR product may be resulted from flaws and cracks induced in clinker as these may weaken the particle, increasing the fracture probability with respect to HPGR feed upon the same degree of impact. However, as grinding time increases, the cracks induced by HPGR will

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be eliminated and breakage rates of HPGR product change into breakage rates of HPGR feed.

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)

Size Fraction Ball Size (mm)

Size Fraction Ball Size (mm)

Size Fraction Ball Size (mm)

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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)

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)

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Figure 4.40. Breakage rate plots 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 4.41. Breakage rate plots 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)

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Figure 4.42. Breakage rate plots 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 4.43. Breakage rate plots 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)

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Figure 4.44. Breakage rate plots after batch grinding of -3.35+2.36 mm of HPGR product and HPGR feed; d_B = 19.05 mm, ɸ_Ball =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 4.45. Breakage rate plots 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)

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Figure 4.46. Breakage rate plots 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)

Beside the significant weakening observed in particles broken by HPGR, non-linear breakage rates of HPGR product and HPGR feed may also be the result of inefficient breakage of coarse sizes. In previous studies, it has been found that breakage of a coarse feed above a maximum particle size become abnormal which yields non-linear breakage rate including a faster initial breakage rate and a slower following breakage rate (Austin et al., 1984). In this case, particles that are too big in a given coarse size fraction cannot be efficiently fractured by balls, leading to non-first order breakage. Also, it has been experimentally shown that breakage rates in batch grinding of fine size fractions increase with increasing feed size; whereas, the breakage rates in abnormal breakage of coarse sizes decrease with increasing feed size (Austin et al., 1981; Austin et al., 1976; Austin et al., 1982). Regarding this, for a given ball size, faster and slower breakage rates of each size interval of HPGR product and HPGR feed were plotted against the top size of the corresponding size interval (µm) in log-log plot, so as to compare the variation of breakage rates with particle size. As shown in Figure 4.47 through Figure 4.49, breakage rates of HPGR product and HPGR feed decrease with increasing particle

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size, showing abnormal breakage behavior. Moreover, the plots indicate the presence of a maximum particle size between 2.36 and 1.7 mm above which the S₁ of HPGR product and HPGR feed decrease.

Figure 4.47. Variation of S₁ and S₂ with particle size in batch grinding of HPGR product and HPGR feed (d_B = 19.05 mm)

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)

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Figure 4.49. Variation of S1 and S2 with particle size in batch grinding of HPGR product and HPGR feed (dB = 31.75 mm)

One noteworthy observation is that the S1 and S2 of HPGR product and HPGR feed mostly increase with increasing ball size, as shown in Table 4.1. Actually, for a given ball loading, it has been shown that decrease in ball size would increase the number of ball-on-ball contacts which would result in higher breakage rates in batch grinding of fine material. On the contrary, in abnormal breakage region of coarse feeds, larger ball sizes gave higher breakage rates since smaller balls became insufficient to fracture coarse particles (Austin et al., 1984). Regarding this, it is probable that the breakage rates of HPGR product and HPGR feed decrease with smaller ball size due to insufficient breakage of coarse particles.