Miguel Becerra
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How Standard is The Standard Bond Test?
Miguel Becerra
Peter Amelunxen
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Grinding Technology, 1930
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Minas Britania, Colombia Británica c. 1930’s
1200 tpd Cu/Au/Zn
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Introduction
• The Bond test existed for many years before the
Bond equation
• The work index is an empirical unit of measure
• Differences in test equipment, procedures, and
calculation methods between the variouslaboratories have emerged over the many years
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Variations in Mill Dimensions
• Lab 1 and 2: 12 inches diameter by 12 inches in
length
• Lab 3: 12.125 inches diameter by 12.125 inches in
length
• Lab 4: 12 inches in diameter by 11.875 inches inlength
• Lab 5: 12 inches in diameter by 11.5 inches long
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Variations in Mill Dimensions
• This Figure shows drum interior after polishing the
surface to avoid the effect of imperfections in the
cylinder
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Variations in Ball Charge
Nominal Size Real Size Quantity TotalWeight SuperficialArea
inch CmMax
(inch)
Min
(inch)
Max
(cm)
Min
(cm)N° gr inch
2
1,45 3,68 1,50 1,25 3,81 3,18 43 8800 284,84
1,17 2,97 1,25 1,12 3,18 2,84 67 7209 289,11
1,00 2,54 1,12 0,875 2,84 2,22 10 672 31,52
0,75 1,91 0,875 0,625 2,22 1,59 71 2012 125,88
0,61 1,55 0,625 0,500 1,59 1,27 94 1432 110,18
TOTAL 285 20125 841,55
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Variations in Ball Charge (*)
(*) Reproducibility of Bond Work Index with Different Standard Balls Mills, Kaya E. , Fletcher P.C &
Thompson P., SME Annual Meeting, 2002
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Variations in The Interpolation Procedure
• Lab 1 : Cubic Spline
• Lab 2: Quadratic Log
• Lab 3: Linear
• Lab 4: Swebrec
• Lab 5: Rosin Rammler
• Lab 6: Modified Rosin Rammler
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Example: Variations in The Interpolation Procedure
• These differences can translate into approximately
2.3% difference in the work index
F80 P80 WI WI Calculation
(mm) (mm) kWh/st kWh/mt Method
2.323 2202 174 11.9 13.2 Cubic Spline
2.323 2243 175 11.9 13.2 Quadratic Log
2.323 2258 171 11.7 12.9 Linear
2.323 2225 171 11.8 13.0 Swebrec
2.323 2217 170 11.7 12.9 Rosin-Rammler
2.323 2197 169 11.7 12.9 Rosin-Rammler Modif
Gpr
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Modified Bond Test
• The standard Bond test usually requires 6-7 kilos of
minus 6-mesh sample and requires approximately 6
hours, for a skilled technician
• The length of the test is a result of the original
procedures, designed to reproduce the continuousclosed circuit configuration of the ball mill circuits in
use during the 1930’s
• To simplify the laboratory procedures, and to make it
more practical, it was designed as a locked cycle testusing a dry charge, rather than as a wet, continuous,
closed loop test
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Modified Bond Test
• The test is deemed an empirical test, as it does not
provide any scalable breakage or fracture kinetics
that can be inserted into an accepted plant-scale
phenomenological model
• For this reason, researchers have been proposingalternative Bond test procedures
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Modified Bond Test : Empirical Method
y = 1.0012x
R² = 0.9219
02
46
810
1214
16
1820
222426
28
30
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
S
t a n d a r d B o n d W
i ( k W h / m t )
Modified Bond Wi (kWh/mt)
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Modified Bond Test : Phenomenological Model (1)
y = 0.9852x
R² = 0.6529
0
2
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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
W o r k I n d e x ( S t a
n d a r ) , k W h / s t
Work Index (Modified), kWh/st
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Modified Bond Test : Phenomenological Model (2)
y = 0.9721x
R² = 0.9812
0
2
4
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0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
W o r k I n d e x ( S t a n d a r ) , k W h / s t
Work Index (Modified), kWh/st
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Modified Bond Test : Semi - Empirical Model
y = 1.0059x
R² = 0.9203
0
2
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30
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
W o r k I n d e x ( S t a n
d a r ) , k W h / s t
Work Index (Modified), kWh/st
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Conclusions
• A survey of Bond mill dimensions was conducted, indicating
that Bond mills vary in diameter and length, sometimessignificantly so. Errors of up to 10% between Bond mills may
result from this variation
• Variations in the method used to interpolate the F80 and P80
values was found to contribute up to 2.3% error to the Bondwork index
• It was found that either the completely empirical approach,
or the semi-empirical method, yields Bond work index
precisions that are adequate for typical geo-metallurgical
programs
• Fully phenomenological models require further development
and will be the subject of future research
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Conclusions
• The modified method allows for 7 tests per day
per mill (a team of two)
• Aminpro Chile has completed a study of 500
tests in almost 6 weeks