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DEVELOPMENT OF A TOWER MILL MODEL USING HARDGROVE MILL TESTS
by
Monong Huang
B.Eng., Central South University, 2014
A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF
THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in
THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES
(Mining Engineering)
THE UNIVERSITY OF BRITISH COLUMBIA
(Vancouver)
March 2018
© Monong Huang, 2018
ii
Abstract
The gravity-induced low speed stirred milling technology, commonly referred to as tower mills,
are widely used for fine grinding due to their high energy efficiency compared to conventional
tumbling mills. Moreover, the lower operating cost, shorter installation period and simpler
operating strategy make it attractive for many mines. Researchers have attempted to develop an
ore characterization method and mathematical models for tower mills. However, there is no well-
established universal fine material characterization method for both the grindability assessment
and modeling of tower mills.
In this study, a modified Hardgrove mill fine material characterization method was developed for
the tower mill grindability assessment. The test result was integrated into the fmat breakage model,
which incorporates both the effect of specific energy and particle size. Several industrial tower
mill grinding circuit surveys were conducted to provide the information regarding the operating
conditions and grinding product size distribution. The ore breakage model, the size specific energy
level model, internal classification model and tower mill power models were integrated into a
mass-size balance model to simulate the tower mill performance. A sensitivity analysis was
conducted to simulate the tower mill performance under varied stirrer speed and media charge.
Results obtained from the model and simulation work show that the developed model is capable
of predicting the tower mill grinding product size distribution with adequate accuracy. The
sensitivity analysis indicated a new opportunity to control the tower mill performance by adjusting
the stirrer speed rather than by the conventional media addition strategy.
iii
Lay Summary
The purpose of this research was to develop a mathematical model for tower mill grinding process
which can be used for grinding performance prediction and process optimization. To develop and
validate such a model, the breakage properties of the samples were measured by a new modified
Hardgrove mill fine material characterization method. Furthermore, several industrial tower mill
grinding circuit surveys were conducted to provide the operating information and allow assessment
of the model. Such a model that incorporates both the ore breakage characteristics and the grinding
operating condition is proven to be able to predict the grinding product size distribution with
adequate accuracy.
iv
Preface
This study is part of the Application of Variable Speed Drives in Ball mills and Tower mills project
at UBC Norman B. Keevil Institute of Mining Engineering supported by Ingeteam Power
Technology, BC Hydro, New Afton Mine, Copper Mountain Mine and Mitacs.
Some of the results presented in this document were presented in abbreviated form in the Canadian
Mineral Processors BC/Yukon Branch Conference 2017:
Huang, M., Cebeci, T., Wang, F., Liu, S., & Klein, B. (2017). Application of variable speed drives
for improved grinding energy efficiency at New Afton mine. Canadian Mineral Processors
BC/Yukon Branch conference 2017, Vancouver, BC, Canada.
I was responsible for developing the test program, conducting the test work and interpreting the
results, under the supervision of Dr. Bern Klein, Professor of the Norman B. Keevil Institute of
Mining Engineering, University of British Columbia.
Mr. Stefan Nadolski assisted with the test program design. Mr. Chengtie Wang, Mr. Sijia Liu, Ms.
Ayse Tugba Cebeci and New Afton Mine Metallurgical Technical team assisted with the New
Afton mine grinding circuit survey.
v
Table of Contents
Abstract .......................................................................................................................................... ii
Lay Summary ............................................................................................................................... iii
Preface ........................................................................................................................................... iv
Table of Contents ...........................................................................................................................v
List of Tables .............................................................................................................................. viii
List of Figures .................................................................................................................................x
List of Symbols ........................................................................................................................... xiv
List of Abbreviations ................................................................................................................ xvii
Acknowledgements .................................................................................................................. xviii
Chapter 1: Introduction ............................................................................................................... 1
1.1 Background ................................................................................................................. 1
1.2 Thesis Objectives ........................................................................................................ 3
1.3 Thesis Structure .......................................................................................................... 4
Chapter 2: Literature Review ...................................................................................................... 5
2.1 Introduction of Tower Mill ......................................................................................... 5
2.2 Operating Variables .................................................................................................... 9
2.3 Mathematic Models for Tower Mill ......................................................................... 14
2.4 Ore Characterization Methods .................................................................................. 36
2.5 Review Summary ...................................................................................................... 46
Chapter 3: Operation Survey .................................................................................................... 48
3.1 Operation Background .............................................................................................. 48
vi
3.2 Survey methodology ................................................................................................. 50
3.3 Survey Results .......................................................................................................... 53
Chapter 4: Test Methodology .................................................................................................... 58
4.1 Jar Mill Test .............................................................................................................. 58
4.2 Bond Ball Mill Work Index test ................................................................................ 63
4.3 Hardgrove Mill Fine Material Characterization Test ................................................ 66
4.4 Comparison of Results .............................................................................................. 79
Chapter 5: Model Development ................................................................................................. 81
5.1 Model Structure ........................................................................................................ 83
5.2 Sub-models ............................................................................................................... 85
5.3 Model Algorithms ..................................................................................................... 91
5.4 Model Fitting ............................................................................................................ 93
5.5 Model Validation .................................................................................................... 101
Chapter 6: Sensitivity Analysis ................................................................................................ 106
6.1 Power Draw ............................................................................................................ 106
6.2 Specific Energy Consumption ................................................................................ 107
6.3 Size Specific Energy Consumption ........................................................................ 108
6.4 Product Size P80 ..................................................................................................... 109
6.5 Size Reduction Ratio ............................................................................................... 110
Chapter 7: Conclusion and Recommendation ....................................................................... 112
7.1 Conclusions ............................................................................................................. 112
7.2 Main Contributions ................................................................................................. 114
7.3 Recommendations ................................................................................................... 115
vii
Bibliography ...............................................................................................................................116
Appendices ..................................................................................................................................122
Appendix A ......................................................................................................................... 122
Appendix B ......................................................................................................................... 129
Appendix C ......................................................................................................................... 142
viii
List of Tables
Table 2-1: Constants value for the model fitting in 50% and 80% passing (Duffy, 1994) .......... 23
Table 2-2: Comparison of plant data with results of the grindability test (Levin, 1989) ............. 39
Table 3-1: Equipment specifications ............................................................................................ 50
Table 3-2: Grinding circuit survey period .................................................................................... 51
Table 3-3: Tertiary grinding circuit result summary (Survey #1) ................................................. 54
Table 3-4: Tertiary grinding circuit result summary (Survey #2) ................................................. 55
Table 3-5: SABC-VTM circuit result summary (Survey #3) ....................................................... 55
Table 3-6: SABC-VTM circuit result summary (Survey #4) ....................................................... 56
Table 3-7: Tertiary grinding circuit result summary (Survey #5) ................................................. 57
Table 3-8: Tertiary grinding circuit survey summary at New Afton Mine ................................... 57
Table 4-1: Jar Mill test particle size distribution of feed material ................................................ 59
Table 4-2: Jar mill test grinding condition .................................................................................... 60
Table 4-3: Jar mill test product size distribution .......................................................................... 61
Table 4-4: Jar mill test predicted specific energy consumption for target grind size ................... 62
Table 4-5: The media charge requirement for standard Bond ball mill test ................................. 63
Table 4-6: BBWI result summary ................................................................................................. 65
Table 4-7: Screens used for Hardgrove mill test .......................................................................... 67
Table 4-8: Samples summary for Hardgrove mill grinding tests .................................................. 68
Table 4-9: Sample volume and revolutions for each test .............................................................. 71
Table 4-10: Axb breakage model parameters for sample #1 (VTM feed in survey #3) ............... 74
Table 4-11: Axb breakage model parameters for sample #2 (VTM feed in survey #4) ............... 75
ix
Table 4-12: fmat breakage model parameters for sample #1 (VTM feed in survey #3) ................ 77
Table 4-13: fmat breakage model parameters for sample #1 (VTM feed in survey #3) ................ 78
Table 4-14: Ore grinding test results summary ............................................................................. 79
Table 5-1: Breakage model parameters for sample in survey #4 .................................................. 93
Table 5-2: Fitted model parameters for selection function ........................................................... 95
Table 5-3: Selection function for full sizes ................................................................................... 95
Table 5-4: Fitted model parameters for classification function .................................................... 96
Table 5-5: Classification function for full sizes ............................................................................ 97
Table 5-6: Comparison between the measured and modelled PSD for survey #4 ........................ 98
Table 5-7: Breakage model parameters for sample in survey #3 ................................................ 101
Table 5-8: Comparison between the measured and modelled PSD for survey #3 ...................... 104
x
List of Figures
Figure 2-1: General view of Vertimill® (Kitanoski, 2012) ............................................................ 6
Figure 2-2: Stirrer shapes for different gravity-induced stirred mills: (1) Vertimill® from Metso
(courtesy of Metso), (2) MaxxMill from Eirich (courtesy of Eirich), (3) HIG mill from Outotec
(courtesy of Outotec), (4) VXP Mill from FLSmidth (courtesy of FLSmidth) .............................. 7
Figure 2-3: Media velocity profiles: a) media motion, side and top view; b) angular and c) vertical
velocity profiles (Jankovic, A., & Morrell, S., 1997) ..................................................................... 8
Figure 2-4: Effect of the stirrer speed on laboratory mill power draw (Jankovic, A., & Morrell, S.,
1997) ............................................................................................................................................. 10
Figure 2-5: Media size effect on pilot Tower mill efficiency (Jankovic, Mathematical modelling
of stirred mills. Ph.D. Thesis., 1999) ............................................................................................ 11
Figure 2-6: Media charge effect on power draw for different stirrer types .................................. 12
Figure 2-7: Slurry % solids effect on pilot tower mill efficiency (Hasan, 2016) ......................... 13
Figure 2-8: Comparison with actual and calculated power draw (Nitta, S., Furuyama, T.,
Bissombolo, A., & Mori, S., 2006) ............................................................................................... 17
Figure 2-9: Relationship between amount of balls and power draw in Tower mill KW-1500 (Nitta,
S., Furuyama, T., Bissombolo, A., & Mori, S., 2006) .................................................................. 17
Figure 2-10: Towel mill power model structure (Jankovic, A., & Morrell, S., 1997) .................. 18
Figure 2-11: Comparison between rated and estimated power for various Vertimill® sizes
(Radziszewski, 2014) .................................................................................................................... 22
Figure 2-12: Single size fraction mass balance ............................................................................. 24
xi
Figure 2-13: Breakage function and energy specific selection function (Mazzinghy, D.B., Lichter,
J., Schneider, C.L., Galery, R., & Russo, J.F.C., 2017) ................................................................ 30
Figure 2-14: Measured and simulated (predicted) size distributions around the grinding circuit,
with known classification parameters for the hydrocyclones. (Mazzinghy, D.B., Lichter, J.,
Schneider, C.L., Galery, R., & Russo, J.F.C., 2017) .................................................................... 30
Figure 2-15: Appearance function for iron ore tested (Mazzinghy, D.B. & Russo, J.F.C., 2014) 31
Figure 2-16: Direct circuit (right) and reverse circuit (left) simulations. (Mazzinghy, D.B. &
Russo, J.F.C., 2014) ...................................................................................................................... 32
Figure 2-17: Grinding product size at 20 kWh/t energy input as a function of stress intensity
(Jankovic, 2003) ............................................................................................................................ 34
Figure 2-18: The universal Hargrove mill with the effective grinding work measuring device
(Mucsi, 2008) ................................................................................................................................ 40
Figure 2-19: Relationship between median of ground alumina—x50 and specific grinding work—
WS. (Mucsi, 2008) ........................................................................................................................ 42
Figure 2-20: JKFBC testing rig with a torque recording system for coal breakage characterization
(Shi, F., & Zuo, W., 2014) ............................................................................................................ 43
Figure 2-21: Metso Jar mill test rig (Metso, 2018) ....................................................................... 45
Figure 3-1: Location of New Afton Mine (New Afton Mine, 2015) ............................................ 48
Figure 3-2: Comminution circuit in New Afton Mine concentrator ............................................. 50
Figure 3-3: Sampling points in the SABC-VTM comminution circuit ........................................ 52
Figure 3-4: Sampling points in the tertiary grinding circuit ......................................................... 52
Figure 3-5: High pressure filter (left) and oven (right) ................................................................. 54
Figure 3-6: Ro-tap and US standard screens ................................................................................. 54
xii
Figure 4-1: Jar mill test rig (Metso, 2018) .................................................................................... 58
Figure 4-2: Jar mill test grinding product size distribution ........................................................... 61
Figure 4-3: Specific energy vs. product size P80 ......................................................................... 62
Figure 4-4: Bond ball mill test rig (left) and Rop-tap testing sieve shaker & Screens (right) ...... 64
Figure 4-5: Hardgrove mill at UBC Center for Coal and Mineral Processing ............................. 67
Figure 4-6: Power meter (left) and data logger software (right) ................................................... 68
Figure 4-7: Prepared narrow size fraction particles ...................................................................... 69
Figure 4-8: Bulk density measuring rig ........................................................................................ 70
Figure 4-9: Hardgrove mill ore characterisation test procedure ................................................... 71
Figure 4-10: Grinding product particle size distribution analysis for Vertimill® feed in survey #3
....................................................................................................................................................... 72
Figure 4-11: Grinding product particle size distribution analysis for Vertimill® feed in survey #4
....................................................................................................................................................... 73
Figure 4-12: Relationship between the Ecs and t4 for sample #1 (VTM feed in survey #3) ........ 74
Figure 4-13: Relationship between the Ecs and t4 for sample #2 (VTM feed in survey #4) ........ 75
Figure 4-14: fmat breakage model fitted curve for sample #1 (VTM feed in survey #3) .............. 77
Figure 4-15: fmat breakage model fitted curve for sample #2 (VTM feed in survey #4) .............. 78
Figure 5-1: Scope of the Vertimill® model .................................................................................. 82
Figure 5-2: Vertimill® model structure ........................................................................................ 83
Figure 5-3: Vertimill® grinding and classification zones (Mazzinghy, D.B., Russo, J.F.C., Lichter,
J., Schneider, C.L., Sepúlveda, J., & Videla, A., 2015) ................................................................ 89
Figure 5-4: Model algorithm flowsheet ........................................................................................ 92
Figure 5-5: t4-tn family curves for survey #4 Vertimill® feed ...................................................... 94
xiii
Figure 5-6: Selection function for full sizes ................................................................................. 96
Figure 5-7: Classification function for full sizes .......................................................................... 97
Figure 5-8: Transfer matrix (mij) for Vertimill® feed in survey #4 ............................................. 98
Figure 5-9: Comparison between the measured and modelled product size distribution for survey
#4................................................................................................................................................... 99
Figure 5-10: t4-tn family curves for survey #3 Vertimill® feed .................................................. 102
Figure 5-11: Transfer matrix (mij) for survey #3 ........................................................................ 103
Figure 5-12: Comparison between the measured and modelled product size distribution for survey
#3................................................................................................................................................. 104
Figure 6-1: Vertimill® power draw vs. Stirrer speed/Ball charge .............................................. 107
Figure 6-2: Specific energy vs. Stirrer speed/Ball charge .......................................................... 108
Figure 6-3: Size (75µm) specific energy vs. Stirrer speed/Ball charge ...................................... 109
Figure 6-4: Vertimill® product P80 size vs. Stirrer speed/Ball charge ...................................... 110
Figure 6-5: Size reduction ratio vs. Stirrer speed/Ball charge .................................................... 111
Figure 7-1: Tower mill model development approach for a new operation ............................... 114
xiv
List of Symbols
Symbol Description
F80 particle size at which 80% of particles pass in feed
P80 particle size at which 80% of particles pass in product
P50 particle size at which 50% of particles pass in product
P20 particle size at which 20% of particles pass in product
F75 percentage of particles passing 75 µm in the feed
P75 percentage of particles passing 75 µm in the product
F25 percentage of particles passing 25 µm in the feed
P25 percentage of particles passing 25 µm in the product
SE specific energy (kWh/t)
SSE75 size specific energy of 75 µm (kWh/t)
SSE25 size specific energy of 25 µm (kWh/t)
Ecs specific energy consumption in the size reduction process (kWh/t)
E mean specific energy (kWh/t)
Ei specific energy of size i (kWh/t)
Si selection function describing the specific energy level in size i
t time
P1 closing screen size
Gpr average grams of undersize product per revolution from the last three cycles in
the BBWI test
xv
fi mass fraction of size i in the feed
fi,GZ mass fraction of size i in the tower mill grinding zone feed
pi mass fraction of size i in the product
pi,GZ mass fraction of size i in the tower mill grinding zone product
mij mass transfer matrix in developed tower mill model
C classification efficiency matrix
I identity matrix
t10 the cumulative passing % of the particle size that is 1/10th of the initial geometric
mean particle size after breakage (%)
t4 the cumulative passing % of the particle size that is 1/4th of the initial geometric
mean particle size after breakage (%)
tn the cumulative passing % of the particle size that is 1/nth of the initial geometric
mean particle size after breakage (%)
SMi stirred mill breakage index
SMi150µm stirred mill breakage index at 150 µm
M, fmat, n model parameters in fmat breakage model
x geometric mean particle size (µm)
A, b ore impact breakage parameters
Axb impact breakage index
Emin threshold energy for breakge (kWh/t)
k the successive number of impacts with single impact energy
α1, α2,⋯,αk the knots in cubic spline regression function
xvi
β1, β2, βk the coefficients in cubic spline regression function
Cmax maximum probability of particles reporting to the fine component in internal
classification (%)
α sharpness of the internal classifier
d50c corrected cut size of the internal classifier, at which the corrected classification
efficiency is 50%
di size of interest in internal classificaiton model (µm)
P electric power of tower mill motor (kW)
H height of the media ball inside tower mill chamber (m)
S outside diameter of tower mill (m)
D gap between screw and wall of mill (m)
N stirrer speed of tower mill (rps)
xvii
List of Abbreviations
Abbreviation Description
BBWI Bond ball mill work index
CMP Coal and Mineral Processing Center
CYC hydrocyclone
DCS distributed control system
JKDWT JK Drop Weight
JKMRC Julius Kruttschnitt Mineral Research Center
JKRBT JK Rotary Breakage Test
JMGT Jar mill grinding test
O/F hydrocyclone overflow
R2 coefficient of determination
SABC SAG mill, Ball mill and Pebble crusher grinding circuit
SAG mill semi-autogenous mill
SSQ sum of squares
U/F hydrocyclone underflow
Vertimill® a type of gravity-induced low speed stirred mill manufactured by Metso
VSD Variable Speed Drives
VTM Vertimill®
xviii
Acknowledgements
I would like to express my sincere gratitude to my supervisor, Dr. Bern Klein for his patient
guidance and continuous support throughout my master research period. I also want to thank Mr.
Stefan Nadolski for his guidance, encouragement, and help throughout my master study.
I want to thank my sponsors, Ingeteam Power Technology, B.C Hydro and Mitacs Accelerate, for
the research grant and New Afton mine for samples, process data, and technical support.
I also want to say thank you to my great team members, Mr. Chengtie Wang, Mr. Sijia Liu and
Ms. Ayse Tugba Cebeci, for their support during the research period. Many thanks to Mr. Amit
Kumar, Mr. Aron Hope and Mr. Libing Tong for their help at CMP lab.
Last but not the least, I would like to thank my parents, whose love and guidance are with me in
whatever I pursue. Special thanks to Jialan, who always provides me inspiration and support.
1
Chapter 1: Introduction
1.1 Background
The stirred milling technology has been increasingly promoted due to its outstanding milling
performance for fine grinding. Compared to the conventional tubular tumbling mill technology,
stirred milling technologies have established themselves as an energy-efficient alternative with
lower installation and operating costs and lower energy consumption (Allen, 2013).
Generally, there are two categories of stirred mill technologies: fluidized-media stirred mills and
gravity-induced stirred mills (Ntsele, C., & Allen, J., 2012). Gravity-induced stirred mills initiate
a ball charge motion via rotational movement of a screw to provide a size reduction mechanism
while fluidized stirred mills use a rotational movement to fluidize a media-slurry mixture to
achieve size reduction. Gravity-induced stirred mills have been successfully applied in secondary,
tertiary and regrinding stages in many concentrators with obvious advantages over ball mills,
particularly higher energy efficiency (Ntsele, C., & Allen, J., 2012). The Metso Vertimill® is a
typical gravity induced low speed stirred mill with 440 units installed globally with approximately
300,000 kW of installed power (Metso, 2018). Compared to other stirred milling technologies, the
gravity-induced low speed stirred mills (Tower Mill or Vertimill®) operate at a relatively low
speed (tip speed about 3m/s) with high density steel ball media (around 7.85 t/m3).
Since there is an increasing demand to apply gravity-induced stirred mills in mineral processing
operations, it is necessary to develop a reliable mathematical model to simulate the Vertimill®
performance.
The population balance model (PBM) methodology has been reported by many researchers
(Mazzinghy, D.B., Schneider, C.L., Alves, V.K., & Galery, R., 2015; Duffy, 1994; Tuzun, 1993).
The PBM can simulate the stirred milling process and predict product size distribution. However,
2
the method used to generate the parameters for the breakage and selection functions varies from
case to case. Furthermore, the parameters measured or calculated are hard to use to evaluate the
hardness of the fine material.
Thus, there is a need to develop an ore characterization methodology that can generate a breakage
index for hardness assessment for fine materials. Also, a more robust tower mill model that can
incorporate both the breakage index and account for the grinding conditions should be developed,
in which the product size distribution for different feed materials under different operating
conditions can be predicted.
3
1.2 Thesis Objectives
The result of research presented in this thesis is part of a larger project funded by Mitacs with
Ingeteam Power Technology and BC Hydro that focused on the application of variable speed
drives (VSD) for ball mills and tower mills. The main objective of this research is to develop a
mathematical model that can predict industrial scale tower mill performance in terms of the
relationship between the energy input and product particle size, specifically for the Vertimill®
(VTM-3000-WB). To achieve the main objective, the following secondary objectives are listed.
Sub-objectives:
1) Develop an ore breakage characterization method for fine materials using the Hardgrove mill,
from which a breakage index can be generated to quantitively represent the hardness of the
tested sample.
2) Integrate the ore characterization test results with the existing breakage model that incorporates
both the specific energy effect and particle size effect.
3) Develop a size reduction model for the tower mill (Vertimill®) that can predict the grinding
product size distribution based on ore breakage properties and operating conditions (energy
input).
4
1.3 Thesis Structure
This thesis consists of 7 chapters, including this introduction Chapter 1.
Chapter 2 reviews the stirred milling technology, including the working principle of the gravity-
induced stirred mill, operating variables affecting the mill performance and the mathematical
models. Furthermore, existing ore characterization methods for fine materials are also discussed
in this chapter.
Chapter 3 introduces the industrial tower mill integrated comminution circuit in New Afton
copper-gold mine concentrator located in Kamloops, British Columbia, Canada. The detailed
survey methods and the grinding circuit survey results are presented and discussed.
Chapter 4 describes the ore characterization methods, including the standard Bond ball mill work
index test and the Hardgrove mill test that was developed in this research program. The Hargrove
mill test was developed for fine material characterization and was adapted to assess the hardness
of the samples and generate breakage model parameters.
Chapter 5 details the structure of the tower mill model and its integrated sub-models, including the
breakage model, the selection function and the classification function. The predicted product
particle size distributions are compared to measured size distributions for model validation.
Chapter 6 presents the results of a sensitivity analysis regarding the effect of the stirrer speed and
ball charge on the tower mill key operating indicators, including the product size, specific energy,
size specific energy and size reduction ratio.
Chapter 7 summarizes the main outcomes and conclusions from this study and recommends the
opportunities for the future research investigations.
5
Chapter 2: Literature Review
2.1 Introduction of Tower Mill
The Tower Mill was invented in Japan by Dr. Kawabata in the 1950’s (Kemal, M., Arslan, V., &
Canbazoglu, M., 1996). After this technology was imported to North American, the Vertimill®,
which is a modified Tower Mill developed by Metso, was introduced to the mining industry. To
date, over 440 Vertimills® have been installed globally with over 300,000 kW total power (Metso,
2018). Compared to ball mills, Tower mills (Vertimill®) have higher grinding energy efficiency
requiring about 30% to 40% less energy for fine grinding (Nesset, 2006). The Vertimill® can
accept feed particle sizes up to 6 mm and can grind to below 15 µm. During operation, high density
grinding media (steel balls) with sizes ranging from 5 to 38 mm are used while the stirrer tip speed
is kept constant to around 3m/s. These operating conditions result in lower stress intensities when
compared to other high intensity horizontal stirred milling technologies. Thus, a lower wear and a
lower media consumption are reported when compared to high speed mills. In comparison to
conventional tumbling mills, the Vertimills® have lower operating costs, a lower installation cost,
require a relatively simple foundation and less floor space.
Figure 2-1 shows a typical Vertimill® which includes a cylinder section at the bottom which is the
main grinding zone, an internal stirrer used to rotate the grinding balls and a separation tank for
classification of the ground product. During operation of the Vertimill®, the material is fed into
the mill chamber through the feed chute and the particles are ground due to the interaction with
the grinding media. The ground product is transported to the top of the chamber by the internal
lifting force generated by the stirrer and overflows to the separating tank for size classification.
The overflow (fine particles) from the separating tank reports to the hydrocyclones for re-
6
classification while the underflow (coarse particles) is pumped back to the mill chamber for further
grinding.
Figure 2-1: General view of Vertimill® (Kitanoski, 2012)
As shown in Figure 2-2, one distinguishing feature of the Tower Mill (Vertimill®) when compared
to the other vertical stirred milling technologies is the shape of the stirrer, which is a helical screw
rather than discs (VXP and HIG mills) or pins (SMD and MaxxMill).
7
(1)
(2)
(3)
(4)
Figure 2-2: Stirrer shapes for different gravity-induced stirred mills: (1) Vertimill® from Metso (courtesy
of Metso), (2) MaxxMill from Eirich (courtesy of Eirich), (3) HIG mill from Outotec (courtesy of Outotec),
(4) VXP Mill from FLSmidth (courtesy of FLSmidth)
Considering the design of the helical screw, the media inside the mill is subject to both lifting and
rotating motion that generates two zones inside the mill referred to as the lifting zone and the tip
8
zone (Jankovic, A., & Morrell, S., 1997). The grinding balls within the central screw (shaft to
stirrer tip) are carried upward by the screw flights at a specific radial position. The rotating charge
ascends the screw column at the same angle as the screw flights. When the grinding media nears
the top of the charge, they disperse towards the outer wall and spiral downward within the annular
region between stirrer tip and the wall maintaining their radial position.
Figure 2-3: Media velocity profiles: a) media motion, side and top view; b) angular and c) vertical velocity
profiles (Jankovic, A., & Morrell, S., 1997)
9
2.2 Operating Variables
The grinding performance of Tower Mills is influenced by many operating variables, including
stirrer speed, media size, media density, media charge, solid content and feed particle size
(Jankovic, 2003; Kwade, 1999; Mankosa, M.J., Adel, G.T., & Yoon, R.H., 1989; Jankovic, 2001).
It is reported that the stress intensity of the grinding media that combines the effect of these
operating variables can be used to optimise the stirred milling process (Jankovic, 2003).
2.2.1 Mill Stirrer Speed
The stirrer speed is a significant operating parameter in the stirred mill operation and has been
studied by many researchers, (Jankovic, 2003; Jankovic, A., & Morrell, S., 1997; Hasan, 2016).
Laboratory size tower mill tests were carried out by Jankovic (1997) with varied stirrer speeds. It
is considered that an increased stirred speed leads to an increased media velocity inside the mill
and a positive proportional trend was observed between the stirrer speed and the gross power draw
of the Tower Mill. This phenomenon was further validated by Hasan (2016) who observed a
nonlinear increase in torque as the stirrer tip speed increased from 2 to 3 m/s in batch tower mill
tests. Meanwhile, Hasan also claimed that further increase of the screw rotational speed fluidizes
the media, exerting less force on the screw that reduces the required torque to stir the media.
Pilot Tower Mill tests with tip speeds of 0.37 m/s, 0.74 m/s, and 1.1 m/s were carried out by
Jankovic (2003). The results indicated that the energy efficiency was higher at lower stirrer tip
speeds.
10
Figure 2-4: Effect of the stirrer speed on laboratory mill power draw (Jankovic, A., & Morrell, S., 1997)
2.2.2 Media Size
The media ball size will affect the grinding efficiency and the fineness of the grinding product.
Bond (1952) stated that, “the general principle of selection should be that the proper size of make-
up grinding media is the size which will just break the largest feed particles.”
In Tower mills or Vertimills®, the unique screw stirring action provides better mixing of the
grinding media than conventional ball mills. A smaller make-up ball size (less than 25 mm) is
found to be viable, which is not common for conventional tumbling mills.
Pilot Tower mill tests were carried by Jankovic (1999) on calcite samples, which showed (Figure
2-5) that smaller medium produces a finer product size. Jankovic (2003) stated that there exists an
“optimum media size” for a particular stirrer speed, beyond which the mill efficiency will
deteriorate.
11
Figure 2-5: Media size effect on pilot Tower mill efficiency (Jankovic, Mathematical modelling of stirred
mills. Ph.D. Thesis., 1999)
The effect of media size was validated by a detailed test study conducted at the Mount Isa LGM
regrinding circuit, consisting of two ball mills (Pfaller, 1990). The study showed that the pilot scale
tower mill is more efficient than existing ball mills with a specific energy consumption of 3.6
kWh/t and 12.5 kWh/t, respectively for the same particle size reduction from a F80 = 70 µm to a
P80 = 49 µm. This significant improvement in energy efficiency was considered to come from the
smaller grinding medium size (6 mm in the pilot tower mill versus 38 mm in the regrinding ball
mills).
The results of batch vertical stirred mill tests carried by Hasan (2016) indicated that the effect of
media size on torque (power draw) was prominent in small mills and a higher torque was always
required to stir the coarser media compared to the finer one due to the interlocking effect of the
coarse media at the bottom of the mill. Based on Metso’s datasheet, Hasan also stated the effect
of media size was not observed in the production scale mill, where mill power draw is a function
of the mass of grinding media rather than the media size.
12
2.2.3 Media Density
The grinding media usually have a heavier density than the slurry density to provide adequate
breakage energy. In the Vertimill®, steel grinding balls are used because this media has a high
density and generates higher stress intensity at low speeds (He, 2007).
2.2.4 Media Charge
During Vertimill® operation, media is added to maintain the power draw to control the grinding
product size. Several researchers have found that the media charge is proportional to the mill power
draw (Jankovic, A., & Morrell, S., 1997; Hasan, 2016).
Jankovic et al (1997) conducted laboratory and pilot scale tower mill tests and found that the net
power draw was directly proportional to the media level. In contrast, for mills with pin and
cylindrical disc stirrers, the mill power increased exponentially with media level. The screw design
of the tower mill has a “lifting” action and most of the media is placed inside the screw, resulting
in a linear relationship between the power draw and media charge.
Figure 2-6: Media charge effect on power draw for different stirrer types
a. Laboratory scale units – same, 115 rpm, b. pilot Sala 250 rpm and tower mill 100 rpm (Jankovic,
A., & Morrell, S., 1997)
13
2.2.5 Slurry Density
The slurry density or solid content is reported to affect the grinding performance of stirred mills
(Toraman, O.Y., & Katircioglu, D., 2011; Jankovic, 2003). Based on the pilot scale tower mill
tests, Jankovic (2003) found that a higher slurry density will benefit the grinding efficiency and
achieve a finer product size at the same specific energy consumption. The increase in grinding
efficiency at higher solid content can be explained by a drop-in power draw due to buoyancy
effects (Jankovic, 2003). Conversely, Hasan (2016) observed a higher torque measurement at a
high solid content (70% solids) when compared operation at the low solid content (50% solids).
This observation is believed to be caused by the combined effect of higher solid content and newly
generated fines in the slurry that affect the rheology. In other word, the fine particles increase
viscosity which leads to an increased torque at the mill shaft.
Figure 2-7: Slurry % solids effect on pilot tower mill efficiency (Hasan, 2016)
14
2.3 Mathematic Models for Tower Mill
To evaluate and optimize the tower mill operations, various modelling approaches have been
utilized to represent the phenomenon inside the mill. These mathematical models can be
categorized based on their purposes, including power estimation, size reduction and efficiency.
2.3.1 Power Models
2.3.1.1 Empirical Approach
2.3.1.1.1 Tuzun (1993)
Tuzun (1993) stated that power draw of a stirred mill is related to the power needed to overcome
the friction at the walls and bottom of the mill. An empirical modelling approach was applied to
relate power draw to experimental data by regression analysis.
The stirred mill power estimation equation was developed as below:
P = 0.105 ∙ N ∙ Bc ∙ (ρeff ∙ H ∙ D2 ∙ (k′ ∙ (D
3+ H) + k′′ ∙ V2)) Equation 2-1
Where
P : mill net power draw (W)
D : mill diameter (m)
V : stirrer tip speed (m/s)
H : media height (m)
B : ball size (mm)
ρeff : charge effective density (t/m3)
c, k′, k′′ : model constants
15
2.3.1.1.2 Duffy (1994)
Duffy (1994) introduced a power model structure for the tower mill that includes no-load power
draw and net power draw. The model structure is shown below:
Gross Power = No Load Power + Net Power Equation 2-2
No load power is related to the mass of the screw and speed of the stirrer in the following manner:
No Load Power (kW) = 0.000134 ∙ Ns ∙ Ws ∙ Ds0.57 Equation 2-3
Where
Ns : speed of stirrer (rpm)
Ws : weight of the screw (kgs)
Ds : diameter of the stirrer (m)
The net power draw is related to both the geometry of the tower mill and the operating conditions.
Thus, the net power can be expressed in Equation 2-4.
Net Power (kW) = 0.0743 ∙ Nb ∙ Ns ∙ ρc ∙ Db0.111 ∙ Ds
3.057 ∙ T0.572 Equation 2-4
Where
k : calibration constant
Hb : height of ball charge (m)
N𝑠 : helical screw stirred speed (𝑟𝑝m)
ρc : charge density (𝑡𝑜𝑛𝑛𝑒𝑠/m3)
Ds : helical screw diameter (m)
T : number of turns of the helical screw per start
Db : mean ball size (mm)
16
The net power can be easily determined by subtracting the no-load power from the gross power
draw. The net power consumed in the grinding process represents the power that can be used for
size reduction.
2.3.1.1.3 Nitta (2006)
The authors (Nitta, S., Furuyama, T., Bissombolo, A., & Mori, S., 2006) proposed a pragmatic
approach to calculate the Tower mill motor power by analyzing industrial operational data using
dimensional analysis. The tower mill motor power estimation equation was developed as below:
P = 312 ∙ H0.884 ∙ S2.232 ∙ D ∙ N1.232 Equation 2-5
Where
P : electric power of tower mill motor (kg ∙ m2/s3)
H : height of the ball charge (m)
S : outside diameter of mill (m)
D : gap between screw and wall of mill (m)
N : Screw speed (rps)
The power of the tower mill motors in this study ranged from 37 kW to 526 kW. The comparison
between the power draw predicted from the expression and the actual power draw is shown in
Figure 2-8 and shows good agreement.
17
Figure 2-8: Comparison with actual and calculated power draw (Nitta, S., Furuyama, T., Bissombolo, A.,
& Mori, S., 2006)
A further validation of this model was conducted by comparing the actual power draw of the KW-
1500 tower mill powered by an 1120 kW motor with the calculated power draw, see Figure 2-9. It
shows a good agreement between these two data sets, with a tendency for the error to reduce as
ball mass increases.
Figure 2-9: Relationship between amount of balls and power draw in Tower mill KW-1500 (Nitta, S.,
Furuyama, T., Bissombolo, A., & Mori, S., 2006)
18
This power model represents an empirical approach to estimate the Tower mill power based on
several assumptions while ignoring the effect of rheology on milling performance. Also, the data
collected for developing this model represented a relatively small power range.
2.3.1.2 Mechanical Approach
2.3.1.2.1 Jankovic and Morrell (1997)
Jankovic and Morrell (1997) proposed to model the Tower mill by using the physics-based model.
The friction is considered to be the major energy consumer in a stirred mill, where friction forces
are dependent primarily on the distribution of gravitational and centrifugal forces. Generally, the
media motion within the tower mill is classified into two parts: the media motion inside the screw
and the media motion outside of the screw in the gap between the screw and the wall. The sum of
the power draw from each region is the total tower mill power draw.
There are several forces assumed to affect the forces in a vertical stirred mill: gravitational force,
centrifugal force and frictional force. The power model structure is shown in Figure 2-10.
Figure 2-10: Towel mill power model structure (Jankovic, A., & Morrell, S., 1997)
The power to initiate media motion inside the screw can be calculated using the analogy with
power screws:
19
𝑃𝑖 = 𝑇𝑖 ∙ 𝜔𝑠 = 𝐹𝑏 ∙𝑑𝑚
2∙
𝑡𝑎𝑛(𝛼)+𝜇
1−𝜇∙𝑡𝑎𝑛(𝛼)∙ 𝜔𝑠 Equation 2-6
Where
Pi : power needed to move the media inside the screw (𝑊)
Ti : lifting torque (𝑁𝑚)
ωs : screw angular velocity (1/𝑠)
Fb : gravitational force (media weight) (𝑁)
dm : screw mean diameter (𝑚)
α : helix angle of the screw (°)
μ : coefficient of friction
The power required to rotate the media outside the screw can be calculated based on the friction
between the balls. Friction between two balls is determined by the pressure from the load over the
balls and centrifugal force. The friction force multiplied by the ball velocity is the power needed
to rotate the media between the screw and the wall:
𝑃𝑜 = ∑(𝐹𝑔 + 𝐹𝑐) ∙ 𝜇 ∙ 𝑣𝑟 Equation 2-7
Where
Po : power needed to rotate the media outside the screw (𝑊)
Fg : gravitational force at the ball contact (N)
Fc : centrifugal force at the ball contact (N)
vr : relative velocity between two balls (m/s)
Therefore, the total tower mill power draw can be calculated the sum these two parts:
20
𝑃𝑡 = 𝑃𝑖 + 𝑃𝑜 Equation 2-8
This mechanistic model incorporates the stirrer design and geometry and provides the information
about media collision rate and energy. It can easily be incorporated into a generic breakage model.
2.3.1.2.2 Radziszewski and Allen (2014)
A shear based stirred mill power model was proposed by Radziszewski et al. (2014) that assumes
that the shear is the predominant if not only mechanism that determines stirred mill power
consumption.
Based on this assumption, a viscometer can represent the stirred milling process. The shear stress
experienced by the turning surface is represented by the slurry viscosity (µ), the gap between two
surfaces (y) and the speed of the sliding surface (𝑢 = 𝜔 ∙ 𝑟).
𝜏 = 𝜇 ∙𝑢
𝑦= 𝜇 ∙
𝜔∙𝑟
𝑦 Equation 2-9
Where
𝜏 : shear stress
𝜇 : slurry viscosity
𝜇 : the linear velocity of the sliding surface
𝜔 : the angular velocity of the sliding surface
𝑟 : the radius of the cylinder
𝑦 : gap between two surface (m)
The screw torque can be obtained from the shear stress (𝑇 = 𝜏 ∙ 𝐴 ∙ 𝑟) and the power consumption
can be calculated by combining all the components.
21
𝑃𝜏 = 𝑇 ∙ 𝜔 = 𝜇 ∙ 𝜔2 ∙ 𝐴 ∙𝑟2
𝑦= 𝜇 ∙ 𝜔2 ∙ 𝑉𝜏 Equation 2-10
Where
𝑃𝜏 : power draw of the stirred mill
𝑇 : Torque of the screw
𝜇 : slurry viscosity
𝑢 : the linear velocity of the sliding surface
𝜔 : the angular velocity of the sliding surface
𝐴 : the area of the cylinder cross-section surface
𝑦 : gap between two surface (m)
𝑉𝜏 : shear volume
The application of the analogy between a viscometer and stirred mills requires a viscosity model
with model parameters calibrated by power. The viscosity equation is shown in the equation below.
Equation 2-11
Validation of this model was achieved by applying this analogue stirred mill power model to
Metso’s Vertimill® databased with some adjustments. From Figure 2-11, although the comparison
22
between the predicted and measured power draw is not perfect, the model does predict the mill
power draw for the Vertimill®.
Figure 2-11: Comparison between rated and estimated power for various Vertimill® sizes (Radziszewski,
2014)
2.3.2 Size Reduction Model
2.3.2.1 Empirical Approach
2.3.2.1.1 Duffy (1994)
An empirical model was developed by Duffy (1994) to describe the relationship between size
reduction ratio and process variables. Pilot scale Tower Mill data was collected at the Hilton Mine
near Mount Isa to develop the model, which is represented by Equation 2-12.
𝑅𝑅𝑐 = 𝐾𝑐 ∙ (𝐸𝑖)𝑥 ∙ (𝑏𝑠𝑖𝑧𝑒)𝑦(𝐹𝑐)𝑧 Equation 2-12
where
RRc : size reduction ratio
Ei : input energy (kWh/t)
23
bsize : ball size (mm)
Fc : feed size (μm)
Kc : constants
x, y, z : constant
The fitted values for the coefficients in Equation 2-12 are shown in Table 2-1. The model predicts
the product size from the Tower Mill with a reasonable degree of accuracy, however, the model
accuracy is site specific.
Table 2-1: Constants value for the model fitting in 50% and 80% passing (Duffy, 1994)
RRc (% Passing) 50% 80%
Kc 0.031 0.182
x 0.264 0.28
y -0.376 -0.494
z 1.220 0.706
2.3.2.2 Population Balance Approach
The population balance model approach was introduced by Epstein (1947) with further
development by several researchers, including Whiten (1974), Herbst and Fuerstenau (1980) and
Austin et al (1984). This modelling method was widely applied simulation of grinding processes.
The model is easy to understand by considering the mass balance around a single size fraction in
the breakage process as shown in Figure 2-12.
24
Product of millFeed
Sifi pi
Breakage in
Breakage out
Figure 2-12: Single size fraction mass balance
This process can be expressed using the following expression:
Feed in + Breakage in = Product out + Breakage out
In the breakage model, the particles are assumed to follow first order breakage rates. Thus, there
is a rate constant ki for each size fraction, which characterizes its rate of disappearance. In addition
to the rate of breakage (ki), a breakage function (bij), describes the fraction of size range j which
reports to size range i after breakage.
The balance equation can be rewritten as:
𝑓𝑖 + ∑ 𝑏𝑖𝑗𝑘𝑗𝑠𝑗𝑖−1𝑗=1 = 𝑝𝑖 + 𝑘𝑖 ∙ 𝑠𝑖 Equation 2-13
Where
𝑓𝑖: mass fraction for size range i in the feed
𝑝𝑖: mass fraction for size range i in the product
𝑘𝑖 or 𝑘𝑗: the rate of breakage for size range i or size range j
𝑆𝑖 or 𝑆𝑗: mass fraction for size range i or size range j in the mill
𝑏𝑖𝑗: the fraction of size range j which reports to size range i after breakage
This equation can be re-arranged to the following expression to estimate the mass fraction for size
range i in the product:
25
𝑝𝑖 = 𝑓𝑖 + ∑ 𝑏𝑖𝑗𝑘𝑗𝑠𝑗𝑖−1𝑗=1 − 𝑘𝑖 ∙ 𝑠𝑖 Equation 2-14
Derived from the same basic approach, several different types of population balance models were
developed. There is a time-based population balance model developed by Austin et al (1984) and
a specific energy-based population balance model by Herbst and Fuerstenau (1980) and an
alternative perfect mixing model developed by Whiten (1974).
Austin et al (1984) applied a first order kinetic model to the population balance model and assumed
all the particles follow the first order breakage rates. The product size distribution can be calculated
from the feed particle size distribution, the breakage rate, breakage distribution and the residence
time. The form of the time-based population balance model is shown in Equation 2-15:
𝑑𝑚𝑖(𝑡)
𝑑𝑡= −𝑆𝐼𝑚𝑖(𝑡) + ∑ 𝑏𝑖,𝑗𝑆𝐽𝑚𝑗(𝑡)𝑖−1
𝑗=1,𝑖>1 Equation 2-15
Where
𝑚𝑖(𝑡): mass fraction for size range i
t : grinding time
Sj : selection function for size range j
bi,j : breakage function
Herbst & Fuerstenau (1980) observed that the values of the selection function for each size class,
Si, present a proportionality relationship with the power consumed by the grinding action
according to Equation 2-16:
𝑆𝑖𝐸 = 𝑆𝑖[
𝐻
𝑃] Equation 2-16
Where
𝑆𝑖𝐸: specific energy based breakage rate or selection function for size range i
Si : selection function for size range i
26
H : mill hold-up
P : power input to the mill
Thus, the form of the specific energy based population balance model can be expressed by the
following equation:
𝑑𝑚𝑖(𝐸)
𝑑𝑡= −𝑆𝑖𝑚𝑖(𝐸) + ∑ 𝑏𝑖,𝑗𝑆𝐽𝑚𝑗(𝐸)𝑖−1
𝑗=1,𝑖>1 Equation 2-17
Where,
E: specific energy input to the mill (kWh/t)
Although derived independently, the perfect mixing model proposed by Whiten (1974) is similar
to the general population balance model. The advantage of the perfect mixing model is that the
assumption of a perfectly mixed mill removes complexities in the general population balance
model. The form of the perfect mixing model can be expressed by the following equation:
𝑝𝑖 = 𝑓𝑖 − 𝑟𝑖𝑠𝑖 + ∑ 𝑎𝑖,𝑗𝑟𝑗𝑠𝑗𝑖−1𝑗=1,𝑖>1 Equation 2-18
Where,
𝑝𝑖: mass flow rate of size range i in the mill discharge (t/h)
𝑓𝑖: mass flow rate of size range i in the mill feed (t/h)
𝑟𝑖: the rate of breakage for size range i (ℎ−1)
𝑠𝑖: mass flow rate of size range i in the mill (t/h)
𝑎𝑖,𝑗: appearance function – mass fraction of the size range j that appears at size i fraction after
breakage
As the mill is perfectly mixed, the mill contents are related to mill product with a discharge rate,
di, for each size fraction.
27
𝑝𝑖 = 𝑑𝑖 ∙ 𝑠𝑖 or 𝑠𝑖 =𝑝𝑖
𝑑𝑖 Equation 2-19
The balance equation can be re-written as
𝑝𝑖 = 𝑓𝑖 − (𝑟𝑖
𝑑𝑖)𝑝𝑖 + ∑ 𝑎𝑖,𝑗(
𝑟𝑖
𝑑𝑖)𝑝𝑖
𝑖−1𝑗=1,𝑖>1 Equation 2-20
Where
𝑑𝑖: discharge rate of size range i (ℎ−1)
These models have been successfully applied to tumbling mills and are able to predict the product
size distribution and required power consumption. Recently, this approach was used to model and
simulate the stirred mill technology.
2.3.2.2.1 Mazzinghy (2012 - 2017)
Mazzinghy et al (2012; 2014; 2015) pioneered the population balance approach for modelling and
simulation of the Vertimill®. Both the Austin et al (1984) time-based population balance model
and the Herbst et al (1980) specific energy-based population balance model were used to model
the pilot scale Vertimill®.
In their experimental program, different samples were tested in a pilot scale Vertimill®. The feed
samples were pre-crushed to meet the feed particle size requirements and the media ball size and
distribution inside the mill were adjusted according to the top up feed size and distribution for
different samples. During the pilot tests, samples were collected from the circuit streams for solid
concentration and particle size distribution analysis. The parameters for the selection function and
breakage function were determined through a series of batch tube mill grinding test with different
grinding intervals. The energy specific selection function 𝑆𝑖𝐸 is independent of the dimensions of
the mill and can be modeled by using equations from either Rajamani and Herbst (1984) or from
Austin et al (1984).
28
𝑆𝑖𝐸 = 𝑆1𝐸𝑒𝑥𝑝 {𝜁1 ln (
𝑑𝑖
𝑑1) + 𝜁2 [ln (
𝑑𝑖
𝑑1)]
2} Equation 2-21
Where
𝑆𝑖𝐸: energy specific breakage rate for size range i
𝑑𝑖
𝑑1: the dimensionless particle size (usually normalized at 1 mm)
𝑆1𝐸 , 𝜁1, 𝜁2 : model parameters
𝑆𝑖𝐸 = 𝑆1𝐸 (
𝑑𝑖
𝑑1)
𝛼 1
1+(𝑑𝑖𝜇
)Λ Equation 2-22
Where
𝑆𝑖𝐸: energy specific breakage rate for size range i
𝑑𝑖
𝑑1: the dimensionless particle size (usually normalized at 1 mm)
𝑆1𝐸 , 𝛼, Λ, μ : model parameters
The model parameters in both equations are characteristic of the material and the grinding
conditions. The breakage function can be described by Austin et al (1984) as shown in Equation
2-23 or by the truncated Rosin-Rammler breakage function model developed by King (2012) as
showed in Equation 2-24:
𝐵𝑖,𝑗 = 𝜙(𝑥𝑖−1
𝑥𝑗)𝛾 + (1 − 𝜙)(
𝑥𝑖−1
𝑥𝑗)𝛽 Equation 2-23
Where,
𝐵𝑖,𝑗: the cumulative breakage function
𝜙, 𝛾, 𝛽: model parameters
𝐵𝑖,𝑗 = 1 − (1 − 𝑡10)
(9
(𝑥𝑗𝑥𝑖
)−1)𝛾
Equation 2-24
Where,
29
Bi,j: cumulative breakage function
γ, t10: model parameters characteristic of the ore
The model parameters in both equations are characteristic of the material.
The predictions of the product size distribution obtained by the simulation are very close to the
experimental data. Six different hypothesis tests (t-test, F-test, Kolmogorov-Smirnov test, and
Number of runs test, media test and Mann-Whitney-Wilcoxon test) were applied to compare the
measured and predicted particle size distributions. The distributions were found to be identical
with 95% confidence for most of the samples tested.
This approach was further validated by Mazzinghy et al (2017) by modelling and simulation of
the industrial Vertimill® operations. A comprehensive sampling campaign was conducted around
the regrind circuit at the Minas-Rio operation to collect the energy consumption, particle size
distribution and solids concentration data. A series of batch tube mill grinding tests were conducted
on the mill feed to obtain the model parameters for both the selection function and breakage
function. The resulting energy specific selection function 𝑆𝑖𝐸 and the breakage function 𝐵𝑖,𝑗 are
show in Figure 2-13.
The simulation work was done by using the ModsimTM plant wide simulator in comparison with
the sampling data from the industrial circuit. The results of the measured and simulated size
distributions are compared in Figure 2-14. The comparison shows that the batch tube mill
grindability test along with the population balance model can simulate an industrial Vertimill®
with reasonable accuracy.
30
Figure 2-13: Breakage function and energy specific selection function (Mazzinghy, D.B., Lichter, J.,
Schneider, C.L., Galery, R., & Russo, J.F.C., 2017)
Figure 2-14: Measured and simulated (predicted) size distributions around the grinding circuit, with
known classification parameters for the hydrocyclones. (Mazzinghy, D.B., Lichter, J., Schneider, C.L.,
Galery, R., & Russo, J.F.C., 2017)
2.3.2.2.2 Mazzinghy (2014)
Mazzinghy et al (2014) used the perfect mixing modelling approach to model and simulate the
pilot scale Vertimill® performance. A pilot scale Vertimill® test was conducted on an iron ore
31
sample in closed circuit with a high frequency screen. The samples from each flow stream of the
circuit were collected during the tests for solids concentration and particle size distribution
analysis. The appearance function of the sample was determined through a series of batch tube
mill grinding tests on a wet basis (70% solids concentration). The appearance function was
described by a truncated Rosin-Rammler breakage function model, defined in Equation 2-25:
𝐵𝑖,𝑗 = 1 − (1 − 𝑡10)
(9
(𝑥𝑗𝑥𝑖
)−1)𝛾
Equation 2-25
Where,
Bi,j: cumulative breakage function
γ, t10: model parameters characteristic of the ore
The generated appearance function for the iron ore is shown in Figure 2-15.
Figure 2-15: Appearance function for iron ore tested (Mazzinghy, D.B. & Russo, J.F.C., 2014)
Data from each test was used to perform simulations using the perfect mixing model.
32
Figure 2-16: Direct circuit (right) and reverse circuit (left) simulations. (Mazzinghy, D.B. & Russo, J.F.C.,
2014)
The simulation results show that the perfect mixing model with appearance function obtained from
a batch tube mill grindability test can predict the product size distribution with good accuracy
when compared to the pilot Vertimill® test. Furthermore, it also shows that direct and reverse
circuit configurations are not significantly different.
2.3.3 Efficiency Model
2.3.3.1 Stress Intensity Approach
The stress intensity approach was developed by Kwade (1999) and originally used for modelling
horizontal stirred mills. This approach calculates the number of grinding events and energy per
event in a stirred milling operation to optimize the operating conditions, such as the stirrer tip
speed, grinding media size, and grinding media density.
The original stress intensity model was modified by Jankovic (2003) by integrating the
gravitational force into the model to model the vertical stirred mill technology. The proposed
gravitational stress intensity of the grinding media for the Tower mill was expressed as follows:
33
𝑆𝐼𝑔𝑚 = 𝐾𝐷𝑚2 (𝐷−𝐷𝑆)(𝜌𝑔𝑚−𝜌)
4𝜇 Equation 2-26
Where
𝑆𝐼𝑔𝑚: gravitational stress intensity of the grinding media (Nm)
D : mill diameter (m)
𝐷𝑆 : screw diameter (m)
µ : coefficient of friction
𝜌 : slurry density (kg/m3)
𝜌𝑔𝑚 : grinding media density (kg/m3)
K : ratio between vertical and horizontal media pressure
The test results from the pilot scale Tower mill (Jankovic, 2001) indicate that the media stress
intensity is an important grinding parameter in low speed vertical stirred mills. For a particular
mill design, there is an optimum stress intensity that would produce the finest product for a given
energy consumption. However, the stress intensity approach is mainly used for the grinding
condition optimization and it cannot provide the product size distribution information. Thus, it is
hard to apply for continuous circuit modelling.
34
Figure 2-17: Grinding product size at 20 kWh/t energy input as a function of stress intensity (Jankovic,
2003)
35
2.3.4 Models comparison
Model Approach Advantages Disadvantages
Power model
Empirical approach
- Tuzun (1993)
- Duffy (1994)
- Nitta (2006)
1. Predict the power consumption
2. Integrate operating variables
3. Able to integrate with PSD model
1. Indirect relationship established by regression
2. Model parameters may vary from case to case
Mechanistic approach
- Jankovic & Morrell (1997)
- Radziszewski & Allen (2014)
1. Predict the power consumption
2. Integrate operating variables
3. Able to integrate with PSD model
4. Based on physical mechanism
1. Require details regarding the mill geometry and
operating conditions
2. Experiment may be required to characterize
slurry property (viscosity)
Size reduction model
Empirical approach
- Duffy (1994)
1. Simple and easy to use
2. Establish relationship between energy input
and size reduction
1. Not able to predict full PSD
2. Model parameters are site specific
Population balance approach
- Mazzinghy (2012 – 2017)
1. Able to predict the full PSD
2. Establish relationship between energy and
size reduction
3. Easy to integrate with process simulation
1. Parameters of material, machine and condition
are usually lumped
Perfect mixing approach
- Mazzinghy (2014)
1. Able to predict the full PSD
2. Establish relationship between energy and
size reduction
3. Easy to be integrated in process simulation
1. Parameters of material, machine and condition
are usually lumped
Efficiency model
Stress intensity approach
- Jankovic (2003)
1. Useful for grinding media selection
2. Optimize the grinding performance
1. Not able to generate PSD
2. Hard to be integrated in process simulation
36
2.4 Ore Characterization Methods
Vertimills® are normally sized using existing ball mill operating information. In general, the
Vertimill® can be conservatively sized at 70% of the normal tumbling mill power required for the
same duty. If similar ball mill operating data is not available, ore grindability tests can be used for
the Vertimill® sizing, including the Metso Jar mill test, the standard Bond Ball Mill Work Index
test and the pilot scale Vertimill® test.
2.4.1 Bond Ball Mill Work Index
The standard Bond Ball Mill Work index (BBWI) test was developed by Fred Bond (1952) in
1952. The test is widely used to characterize the hardness of materials and predicts the energy
requirement for the grinding process, the ball mill sizing and the grinding circuit efficiency
assessment. The standard Bond ball mill is 30.5 cm inside diameter and 30.5 cm inside length,
with rounded corners. It is smooth except for the door hole used for charging. The grinding charge
consists of 285 iron or steel balls (43 @ 36.8 mm diameter, 67 @ 29.7 mm diameter, 10 @ 25.4
mm diameter, 71 @ 19.1 mm diameter, and 94 @ 15.5 mm diameter) weighing a total of 20,125
g. The ball charge surface area is 5,432 cm2. The mill runs at 70 rpm and has a revolution counter.
A sieve analysis is used to determine the particle size distribution of the test feed, test product, and
circulating load (screen oversize) material. Dry screening on one or more sieves is done between
grinding cycles when the closing screen aperture chosen for is 75 μm (200 mesh) or coarser. Wet
screening between grind cycles is used when the closing screen is 53 μm (270 mesh) or finer.
A sampling weighting about 10 kg is crushed down to 100% <3350 µm (-6 US Mesh No.), and a
700-ml portion material is charged into the mill for grinding. The ground product is then screened
and used for calculating the circulating load, the required fresh feed material and the revolutions
to achieve a circulation load of 250% for the next cycle. The cycle is repeated five times or until
37
the grams per revolution value becomes constant. The following equation is used to calculate the
Bond Ball Mill Work Index for the tested sample:
𝐵𝐵𝑊𝐼 =44.5
𝑃10.23×𝐺𝑝𝑟0.82×(
10
√𝑃10−
10
√𝐹10)
× 1.103 Equation 2-27
Where,
BBWI: Bond Ball Mill Work Index value (kWh/t)
P1 : Aperture of the closing screen size (µm)
Gpr : average grams of undersize product per revolution from the last three cycles
P80 : Size at which 80 percent of the undersize product passes (µm)
F80 : Size at which 80 percent of the feed passes (µm)
This test can be used for the energy consumption estimation and mill sizing for Vertimill® in
coarse grinding operations by incorporating an energy efficiency factor when the pilot scale
Vertimill® test is not available.
2.4.2 Levin Grindability Test
The standard Bond Ball Mill Work Index test requires feed materials with the following particle
size requirements:
• Particle size 100% less than 3.35 mm
• P80 is between 1.8 and 2.5 mm
• P20 is larger than the closing screen size
Therefore, fine materials such as cleaner flotation tailings or middling streams may not be suitable
for the standard Bond Ball Mill Work Index test due to the unavailability of suitable feed materials
with the required size range. An alternative approach is to grind the unknown material and provide
a similar reference material (known BBWI) with the same operating time and number of
38
revolutions, from which the work input can be assumed to be consistent, and the BBWI for the
unknown material can be calculated by the following equation:
𝑊𝑖𝑢 [1
√𝑃𝑢80−
1
√𝐹𝑢80] = 𝑊𝑖𝑘 [
1
√𝑃𝑘80−
1
√𝐹𝑘80] Equation 2-28
Where
𝑊𝑖𝑢 : the BBWI for reference material
𝑊𝑖𝑘 : the BBWI for unknown material
Pu80 : 80% passing size of the product for unknown material (µm)
Pk80 : 80% passing size of the product for reference material (µm)
Fu80 : Size at which 80 percent of the feed passes for unknown material (µm)
Fk80 : Size at which 80 percent of the feed passes for reference material (µm)
However, a suitable reference material is not easily obtained. Thus, a grindability test that does
not depend on reference material is needed. Levin (1984) proposed a grindability test for fine
material, referred to as the Levin test, to estimate the energy requirement for fine grinding. For
the Levin test, a mass of fine material is ground in Bond ball mill for various time intervals (e.g.
1, 3, 5, 10 min) and the particle size distribution is determined for the feed and product. From the
particle size distribution of each ground product, the mass percentage of materials below 75 µm is
determined and plotted against grind time. From this graph, the grinding time required to grind a
specific percentage of material smaller than 75 µm can be determined. The corresponding specific
energy required to achieve the required target size can be calculated according to Equation 2-29:
𝐸𝑛𝑒𝑟𝑔𝑦 𝑐𝑜𝑛𝑠𝑢𝑚𝑒𝑑 =𝑡
𝑚× 106 × 𝐸 Equation 2-29
Where
t : grinding time (minutes)
39
m: mass of material reduced to certain percent passing 75 µm in t minutes (g)
E : equivalent energy consumption per minute = 1425 x 10-6 (kWh/t)
This method is mainly applied for regrind ball mill sizing. Table 2-2 compares energy
consumptions predicted from the Levin grindability test to plant operating results. The accuracy
of the specific energy consumption generated from Levin test is considered satisfactory when
considering several possible sources of error, such as the representativeness of the samples and
reliability of the correction factors.
Table 2-2: Comparison of plant data with results of the grindability test (Levin, 1989)
Further research was conducted by T. Partyka et al (2007) who considered the effect of media size
on Levin test results. The results indicate smaller grinding balls are more suitable for fine feeds,
while larger balls are suited to coarse feed. Therefore, the media size distribution should be
modified for the Levin test when treating different feed size materials.
40
2.4.3 Modified Hardgrove Grindability Test
Gábor Musci (2008) proposed a fast test method using a modified Universal Hardgrove mill to
characterize the grindability of fine materials. The modified Hardgrove mill is equipped with
torque and power input measuring instruments (torque meter, electric energy meter).
Figure 2-18: The universal Hargrove mill with the effective grinding work measuring device (Mucsi, 2008)
The modified Hardgrove mill test differs from the standard test, which is only based on the fines
produced for a given number of revolutions. The modified method considers other factors, such
as frictional, cohesive, adhesive properties and flow characteristics of the bulk material by
measuring torque with and without materials present. The specific grinding work was calculated
using the following equation. The no-load energy (torque) measurement had to be subtracted from
the gross energy measurement to determine the net specific comminution energy.
𝑊𝑠.𝐻 =∫ 2𝜋𝑛[𝑀(𝑡)−𝑀0]
𝜏0 𝑑𝑡
𝑚 Equation 2-30
Where,
𝑊𝑠.𝐻 : the specific grinding work of the material (kWh/t)
41
M(t) : the torque with material and balls
M0 : the torque with balls
N : revolution number
τ : the grinding time
m : the mass of sample below the closing sieve size (75 µm)
The generated specific grinding work can be used for the calculation of the Bond Ball Mill Work
Index through the following equation:
𝑊𝐼𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 =𝑊𝑠,𝐻
10
√𝑃80−
10
√𝐹80
Equation 2-31
Where
𝑊𝐼𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑜𝑛 : the operational work index from (kWh/t)
𝑃80 : 80% passing size of the product (µm)
𝐹80 : 80% passing size of the feed (µm)
This method has been further validated by conducting the grindability test on fine alumina material
and compared with industrial ball mill performance. A standard Bond Ball Mill Work Index test
was also conducted for comparison of results. The result shows that the modified Hardgrove mill
test provides a more accurate energy prediction than standard Bond Ball Mill Work Index test for
grinding fine materials.
42
Figure 2-19: Relationship between median of ground alumina—x50 and specific grinding work—WS.
(Mucsi, 2008)
2.4.4 JK Fine Breakage Characterization Test
To characterize the breakage properties of fine materials, Shi et al (2014) developed a new fine
material breakage characterization test with a modified Hardgrove mill. The testing rig consists
of a drive system on the top, a precision torque meter T20WN connected to the drive shaft, a shaft
coupling mechanism, lead plates on top of the grinding element, and a standard HGI mill grinding
element comprising a grinding bowl and eight steel balls. A computer interface system with LJ
logger V1.12 software was employed to log the torque measurement data during the test (see
Figure 2-20).
43
Figure 2-20: JKFBC testing rig with a torque recording system for coal breakage characterization (Shi,
F., & Zuo, W., 2014)
The developed method was originally used for coal breakage characterization (Shi, F., & Zuo, W.,
2014) and later was successfully applied to the ore grinding performance for ball mill operation
(Shi, F., & Xie, W., 2015; Shi, F., & Xie, W., 2016). During the test, the materials were screened
into narrow size particles and ground for different time intervals. The ground product was
subjected to standard particle size analysis, which was used to determine a fineness parameter t10.
The recorded torque measurements were used to calculate the specific energy consumption using
Equation 2-32:
𝐸𝑐𝑠 =∫ 𝜋∙
𝜔
30[𝑇(𝑡)−𝑇0]𝑑𝑡
𝜏0
3600∙𝑚 Equation 2-32
Where,
Ecs: specific energy consumption (kWh/t)
ω : the mill rotational speed (rpm)
44
T(t): the measured instantaneous torque (Nm)
T0 : the no-load torque from the calibration (Nm)
τ : the total grinding time (second)
m : the material mass tested (kg)
The determined t10 value was analyzed along with the measured Ecs and fitted into a size-
dependent breakage model. The product particle size distribution results from each narrow size
test were used to establish t10-tn family curves.
𝑡10 = 𝑀 ∙ {1 − exp [−𝑓𝑚𝑎𝑡 ∙ 𝑥 ∙ 𝐸]} Equation 2-33
Where,
t10 : cumulative passing percentage of the 1/10 initial particle size (%)
M : the maximum t10 for a material subject to breakage (%)
fmat : the material breakage property (kg/J·m)
x : the initial particle size (m)
E : the mass-specific energy (J/kg)
Once the parameters of the size dependent breakage model were fitted to the test data, the model
was used to simulate the ball mill performance. The method was successfully applied to batch ball
mills (Shi, F., & Xie, W., 2015) and for continuous ball mill modelling (Shi, F., & Xie, W., 2016).
In addition to the success in ball mill modelling and simulation, this method was extended to
characterize the materials for the gravity-induced stirred mill feed (Palaniandy, 2017).
2.4.5 Metso Jar Mill Test
The Metso Jar Mill test was developed specifically for the selection of Tower Mill or Vertimill®.
A 8 (ID) x 10 (length) inch jar mill (Figure 2-21) charged with 15.9 kg of 19 mm steel balls is
operated at 71.3 rpm in this test. A series of operating parameters are assessed in the test, including
45
the required target grind size, the feed solids content and the ore type. The test is run for various
times and the product size distribution determined to establish the specific energy (kWh/t) versus
grind size relationship (Gupta, A., Yan, D.S., 2016). The measured energy is multiplied by 0.65
(VTM factor) to predict the energy required for a Vertimill® (Wills, B.A., Finch, J.A., 2016).
Figure 2-21: Metso Jar mill test rig (Metso, 2018)
46
2.5 Review Summary
Researchers have conducted extensive studies on the stirred milling technology and related
operations. It was proven that many operating variables, including stirrer speed, media ball size
and slurry density will affect the gravity induced stirred mill performance (Jankovic, 2003). The
smaller media ball size was found to be the main variable leading to a higher grinding efficiency
for stirred mills when compared to tumbling mills through many batch scaled stirred mill tests.
However, the media charge rather than the media size was found to be the main variable affecting
the grinding performance (Hasan, 2016). Thus, media charge is commonly used as the control
parameter for maintaining industrial Vertimill® performance. In contrast, the stirrer speed is rarely
used for control.
The power draw of tower mills was successfully modelled by using empirical and mechanistic
modelling methods with adequate accuracy (Tuzun, 1993; Duffy, 1994; Nitta, S., Furuyama, T.,
Bissombolo, A., & Mori, S., 2006; Jankovic, A., & Morrell, S., 1997). The particle size distribution
of the mill grinding product is usually modelled by applying the population balance or perfect
mixing modelling methods using a batch ball mill (Mazzinghy, D.B., Schneider, C.L., Alves, V.K.,
& Galery, R., 2015; Mazzinghy, D.B., Galery, R., Schneider, C.L., & Alves, V.K., 2014) or a
vertical stirred mill (Hasan, 2016). The stress intensity approach can be used for grinding
efficiency optimization but it is hard to be used for process simulation since no PSD data is
generated from this model (Jankovic, 2001).
Several fine material characterization methods were discussed in this chapter. For most of the
cases, a batch tumbling mill grinding test was used for ore breakage property characterisation,
which was used as the input for Tower Mill or Vertimill® modelling. However, different breakage
mechanisms have been pointed out for these two types of mills, where tumbling mills use both
47
impact and shear energy, while stirred mills use predominately shear energy (Wills, B.A., Finch,
J.A., 2016). Thus, there are doubts about the suitability of test methods that use batch tumbling
mills for modeling the Tower Mill performance. The modified JK fine breakage characterization
test has been used to characterize fine materials and generate the breakage parameters, which has
been successfully applied to continuous industrial ball mill modelling (Shi, F., & Xie, W., 2016).
The similarity of the breakage mechanism between the Hardgrove mill and Tower Mill has been
reported by Palaniandy (2017). Therefore, there is an opportunity to model the Tower Mill by
characterizing the ore breakage property using the Hardgrove mill. Thus, the Tower mill model
based on the grindability test should be able to predict the grinding product particle size
distribution for ore with different hardness and in grinding environments.
48
Chapter 3: Operation Survey
A study was conducted on the Vertimill® grinding circuit at the New Afton mine, British
Columbia, Canada. A model VTM-3000-WB Vertimill® unit was installed for tertiary grinding at
the New Afton concentrator. The mill was operated in a reverse closed-circuit configuration with
33-inch diameter hydrocyclones. A series of circuit survey activities were conducted between 2016
and 2017 to collect representative samples for ore characterization tests and to assess the circuit
energy efficiency.
3.1 Operation Background
The New Afton copper-gold mine is located 10 km west of Kamloops, British Columbia. The
concentrator includes a SAG (semi-autogenous) mill, a ball mill, and a Vertimill® along with
gravity separation and flotation to process 15,000 tpd of porphyry ores, producing copper
concentrates (Bergen, R.D., Krutzelmann, H. & Rennie, D.W., 2015).
Figure 3-1: Location of New Afton Mine (New Afton Mine, 2015)
49
The plant uses a conventional SABC circuit with an 8.3 m diameter × 4.0 m long, 5,222 kW SAG
mill in closed-circuit with a single deck vibrating screen and a cone crusher. The cone crusher
product discharges directly on to the SAG mill feed conveyor. Secondary grinding circuits consists
of a 5.5 m diameter × 9.8 m long, 5,222 kW ball mill in closed circuit with the hydrocyclones.
The SAG discharge screen undersize and ball mill discharge are pumped to the hydrocyclones.
The cyclone underflow distributes the slurry to the flash flotation cell and the ball mill. A mill
expansion project, completed in 2015, installed a 2,237 kW Vertimill® (VTM-3000 WB) as the
tertiary grinding mill in closed-circuit with a 76 cm hydrocyclones. The secondary grinding circuit
product, ball mill cyclone overflow, diverts to the tertiary pumpbox and is pumped to the tertiary
hydrocyclones. The cyclone underflow flows by gravity to the Vertimill® for additional grinding.
The Vertimill® discharge flows back to the tertiary pumpbox for size classification in the tertiary
hydrocyclones. The tertiary cyclone overflow reports to the rougher flotation circuit. The
flowsheet of the grinding circuit in New Afton mine is shown in Figure 3-2. The expansion project
also integrated additional cleaner flotation cells to increase the cleaner flotation capacity, which
contributes to an approximate 15% capacity increase of the mill along with the extra grinding
power from the tertiary grinding unit installation.
50
VTM-3000-WB3,000 hp
18'Ø x 32' Ball Mill7,000 hp
28'Ø x 13' SAG 7,000 hp
Raptor XL600
Flash Flotation cell
SecondaryCyclopac
TertiaryCyclopac
SecondaryPumpbox
TertiaryPumpbox
Rougher Flotation
Figure 3-2: Comminution circuit in New Afton Mine concentrator
Table 3-1: Equipment specifications
Design parameters Unit SAG mill Pebble Crusher Ball mill Vertimill®
Number of mills [-] 1 1 1 1
Dimensions [ft] 28Ø × 13 - 18Ø × 32 22Ø × 17
Models [-] - Raptor XL600 - VTM-3000-WB
Design Power Draw [kW] 5,222 447.4 5,222 2,237
3.2 Survey methodology
A series of comminution circuit survey activities were conducted from 2016 to 2017 to determine
the grinding circuit performance and collect the required data for circuit modelling and simulation.
In March 2016, as part of the mine to mill project, one entire grinding circuit survey was conducted
along with two additional surveys for the tertiary grinding circuit. As part of the study to assess
the potential benefits of variable speed drives (VSD) on ball mills and tower mills, a sampling
campaign was conducted in February 2017 for the entire grinding circuit with an additional survey
on the tertiary grinding circuit. The detailed survey arrangement is listed in the table below.
51
Table 3-2: Grinding circuit survey period
# Date Time Scope
1 March 15, 2016 15:15 to 16:15 Tertiary grinding circuit
2 March 15, 2016 17:00 to 18:00 Tertiary grinding circuit
3 March 16, 2016 12:40 to 13:40 SABC and VTM circuit
4 February 7, 2017 15:20 to 16:20 SABC and VTM circuit
5 February 8, 2017 15:10 to 16:10 Tertiary grinding circuit
The grinding circuit sampling and survey method was adjusted based on the guidelines developed
by the Global Mining Standards and Guidelines Group (The Sampling and Surveying Sub-
Committee of the Industrial Comminution Efficiency Working Group, 2016). For the overall
grinding circuit (SABC + VTM circuit) survey, 14 streams were sampled. Three duplicate samples
were collected over a period of an hour for each stream (excluding the SAG feed belt cut, Pebble
crusher feed and product and cyclone feed samples). The hydrocyclones feed samples were
collected at the end of the survey period. After all the slurry samples were collected, the SAG feed,
pebble crusher feed and product belts were stopped for the collection of the samples. The grinding
circuit survey sampling points are presented in Figure 3-3.
52
Sump Tertiary cyclone feed pump
Hydrocyclone
VTM-3000-WB
Ball Mill
Hydrocyclone
Sump
VibrationScreen
SAG Mill
Pebble Crusher
SAG Feed Belt
Stockpile
Flash Flotation
BM U/F
BM O/F
VTM O/F
VTM U/F
VTM Product
VTM Cyc. Feed
BM
Cy
c. Fee
dBM Product
Coarse Tail
Flash Flot. Fine Tail
Flash Flot. Conc.
SAG Fresh Feed
Pebble Product
Screen U/S
Pebble Feed
SAG Product1
2
3
4
5
6
7
8
9
10
12
14
13
11
Figure 3-3: Sampling points in the SABC-VTM comminution circuit
For the tertiary grinding circuit survey, samples of 5 streams were collected. Three duplicate
samples were collected over a period of an hour for each stream (excluding the cyclone feed
samples). The cyclone feed samples were collected at the end of the survey period. The grinding
circuit flowsheet and sampling points are presented in Figure 3-4.
Sump
Tertiary cyclone feed pump
Hydrocyclone
VTM-3000-WB
VTM CYC O/F
VTM CYC U/F
VTM Product
VTM CYC Feed
BM CYC O/F
1
2
3
4
5
Figure 3-4: Sampling points in the tertiary grinding circuit
53
Samples from New Afton were received at the UBC Center for Coal and Mineral Processing in
March 2017. For the grinding circuit, a 1107 kg SAG belt cut sample was provided in barrels along
with the representative wet slurry sample collected within a one-hour period for each stream in
buckets. In addition to the ore and slurry samples from the grinding circuit, the DCS data reflecting
the grinding circuit performance during the survey period were collected for circuit assessment.
3.3 Survey Results
The slurry samples collected during the surveys were analyzed at the Center for Coal and Mineral
Processing at the UBC Department of Mining Engineering. The solids content of each stream was
measured by weighing the wet and dry weights after drying the material in the oven. To analyze
the particle size distribution, 300 to 500 g sub-samples were split from the dried stream sample
using the riffle splitter for sieve analysis. The detailed sample preparation and sizing procedure is
presented in Appendix A. The survey results from each grinding circuit survey are summarized in
Table 3-3. Detailed particle size distribution data are presented in Appendix A. Other than the
particle size distribution results, the Distributed Control System (DCS) recorded comminution
circuit throughput and Vertimill® power draw were summarized in Table 3-8. The survey results
were used for circuit mass balance and worked as inputs for unit operation model fitting and
grinding circuit simulation.
54
Figure 3-5: High pressure filter (left) and oven (right)
Figure 3-6: Ro-tap and US standard screens
Table 3-3: Tertiary grinding circuit result summary (Survey #1)
No. Sample Name Wet Sample
Weight (kg)
Dry Sample
Weight (kg)
Solid Content
(%)
Particle Size
P80 (µm)
1 Ball Mill Cyclone O/F 13.10 5.50 42% 289
2 Vertimill® Cyclone Feed - - 48%*1 -
3 Vertimill® Product 32.02 21.70 68% 341
4 Vertimill® Cyclone O/F 23.92 8.50 36% 155
5 Vertimill® Cyclone U/F 28.22 19.30 68% 387
Notes: *1. The solids content of the hydrocyclone feed is the average of DCS measurements during the survey period.
55
2. Particle sizing and solids content are collected based on the homogenized sample from the three duplicated
samples within the one-hour period for the same stream.
Table 3-4: Tertiary grinding circuit result summary (Survey #2)
No. Sample Name Wet Sample
Weight (kg)
Dry Sample
Weight (kg)
Solid Content
(%)
Particle Size
P80 (µm)
1 Ball Mill Cyclone O/F 14.32 5.90 41.2% 290
2 Vertimill® Cyclone Feed - - 47.6%*1 -
3 Vertimill® Product 31.72 21.40 67.5% 340
4 Vertimill® Cyclone O/F 19.22 6.80 35.4% 147
5 Vertimill® Cyclone U/F 28.82 19.50 67.7% 390
Notes: *1. The solids content of the hydrocyclone feed is the average of DCS measurements during the survey period.
2. Particle sizing and solids content are collected based on the homogenized sample from the three duplicated
samples within the one-hour period for the same stream.
Table 3-5: SABC-VTM circuit result summary (Survey #3)
No. Sample Name Wet Sample
Weight (kg)
Dry Sample
Weight (kg)
Solid Content
(%)
Particle
P80 (µm)
Solids
SG
1 SAG Feed Belt Cut 2237.0 2156.0 96.4% 66854 2.75
2 SAG Mill Discharge 61.8 49.1 79.5% 15834 -
3 Pebble Crusher Feed 323.5 319.1 98.6% 33747 -
4 Pebble Crusher Product - - - - -
5 Ball Mill Cyclone Feed - - 57.52%*1 - -
6 Ball Mill Product 29.8 20.1 67.4% -
7 Ball Mill Cyclone U/F 33.9 26.8 79.1% - -
8 Ball Mill Cyclone O/F 16.6 6.1 36.6% 289 -
9 Flash flotation Concentrate - - - - -
10 Flash flotation Fine Tails - - - - -
11 Vertimill® Cyclone Feed - - 47.9%*1 - -
12 Vertimill® Product 32.9 22.3 67.8% 338 -
13 Vertimill® Cyclone O/F 20.9 7.4 35.2% 150 -
14 Vertimill® Cyclone U/F 29.3 19.9 67.9% 392 -
Notes: *1. The solids content of the hydrocyclone feed is the average of DCS measurements during the survey period.
56
2. Particle sizing and solids content are collected based on the homogenized sample from the three duplicated
samples within the one-hour period for the same stream.
Table 3-6: SABC-VTM circuit result summary (Survey #4)
No. Sample Name Wet Sample
Weight (kg)
Dry Sample
Weight (kg)
Solid Content
(%)
Particle
P80 (µm)
Solids
SG
1 SAG Feed Belt Cut - 1107.15 - 58664 2.72
2 SAG Mill Discharge 147.22 112.1 76% 4146 -
3 Pebble Crusher Feed 70.52 66.04 94% 25696 -
4 Pebble Crusher Product 70.27 66.46 95% 24082*1 -
5 Ball Mill Cyclone Feed 46.36 31.92 69%*2 3835 -
6 Ball Mill Product 110.83 73.55 66% 2331 -
7 Ball Mill Cyclone U/F 99.38 75.37 76% 3264 -
8 Ball Mill Cyclone O/F 85.36 31.60 37% 287 -
9 Flash flotation Concentrate 44.8 5.33 12% 213 -
10 Flash flotation Fine Tails 43.97 7.39 17% 180 -
11 Vertimill® Cyclone Feed 30.65 8.40 27%*2 328 -
12 Vertimill® Product 35.76 24.46 68% 340 -
13 Vertimill® Cyclone O/F 36.13 7.68 32% 152 -
14 Vertimill® Cyclone U/F 123.52 85.34 69% 394 -
Notes: *1. The pebble crusher product was mixed with a portion of the SAG feed sample during the survey, which
may not represent the actual size distribution.
*2. Ball Mill Cyclone Feed and Vertimill® Cyclone Feed were sampled from the pump suction by-pass line
at the end of the survey period. Despite the representation of the collected samples, those were the best
available sampling points. The resulted data should be treated with caution.
57
Table 3-7: Tertiary grinding circuit result summary (Survey #5)
No. Sample Name Wet Sample
Weight (kg)
Dry Sample
Weight (kg)
Solid Content
(%)
Particle Size
P80 (µm)
1 Ball Mill Cyclone O/F 79.91 30.34 38% 289
2 Vertimill® Cyclone Feed 44.86 22.64 50% 324
3 Vertimill® Product 38.29 27.49 72% 374
4 Vertimill® Cyclone O/F 29.69 9.29 31% 147
5 Vertimill® Cyclone U/F 65.62 45.13 69% 391
Notes: Particle sizing and solids content are collected based on the homogenized sample from the three duplicated
samples within the one-hour period for the same stream.
Table 3-8: Tertiary grinding circuit survey summary at New Afton Mine
Survey Throughput
(Dry)
Circuit Feed
P80
Circuit
Product P80
VertiMill®
Power
Specific
Energy SSE75 WIoperation
# tph µm µm kW kWh/t kWh/t kWh/t
1 692 289 155 2088 3.02 23.63 13.89
2 698 290 147 2073 2.97 17.88 12.56
3 700 289 150 2090 2.99 20.29 13.14
4 706 287 152 2172 3.08 23.82 13.56
5 707 289 147 2172 3.07 24.07 12.99
58
Chapter 4: Test Methodology
Grinding studies were carried out at the UBC Center for Coal and Mineral Processing and Metso
York Testing Laboratory to develop a laboratory test procedure to model the Vertimill® energy
consumption and particle breakage relationship. The grinding tests include the Metso Jar Mill test,
the standard Bond Ball Mill Work Index test and the modified Hardgrove mill test. The Hardgrove
mill test was used to characterize breakage property of the Vertimill® feed. The energy
consumption, as well as the feed and product particle size distribution, were recorded and analyzed
to develop the model to predict the Vertimill® performance at the industrial scale.
4.1 Jar Mill Test
The Jar Mill Test is Metso’s grindability test to size and design Vertimill® grinding circuits. The
test produces a signature plot showing the energy consumption required to grind to target particle
sizes. The test can assess parameters such as the required target grind size, the feed solids content
and the ore type. The test is run for various time periods and the product size distribution is
determined to establish the energy input (kWh/t) versus grind size relationship.
4.1.1 Apparatus
The Jar Mill test rig consists of a 203 mm (Inner diameter) x 254 mm steel jar charged with 15.9
kg of 19 mm steel balls. The mill is rotated at 71.3 rpm (76% critical speed).
Figure 4-1: Jar mill test rig (Metso, 2018)
59
4.1.2 Material
The Jar Mill test requires a 15 to 20 kg sample with particle finer than 2360 µm (8 mesh).
One copper concentrate sample from New Afton mine was shipped to the Metso York Test Plant
on October 20, 2013, for the Jar Mill testing. The particle size distribution of the feed material is
shown in Table 4-1.
Table 4-1: Jar Mill test particle size distribution of feed material
Mesh Microns %Passing
6 3327 100.0
8 2362 99.8
10 1651 99.8
14 1168 99.8
20 833 99.7
28 589 99.2
35 417 95.7
48 295 86.8
65 208 76.4
100 147 64.7
150 104 55.8
200 74 47
270 53 40.9
325 44 37.6
400 37 35.3
500 25 30.9
D80 µm 235.9
4.1.3 Test Method
A representative sample was split from the as-received material and used to determine the bulk
density and particle size distribution. The solids and water required for the desired solids
concentration was calculated and charged to the mill for each Jar Mill test. The material was milled
for a predetermined time-period and then discharged. The Jar Mill product was split and then
dewatered and dried to obtain a sample for particle size analysis for the ground product. The
60
process was repeated until the desired product size specification was achieved. The grinding
conditions and target size are summarized in Table 4-2.
Table 4-2: Jar mill test grinding condition
Test Jar Mill Test
Material Copper Concentrate
Top Size Media 19 mm Steel Balls
Description of Media 15.9 kg of Monosize Balls
Ore Bulk Density 1527.1 g/L
Solids Charged 2170.1 g
Water Charged 1446.7 g
Solids Concentration 60% (by weight)
New Power Draw 0.0383 kW
Product Size Specification 80% Passing 150 µm
4.1.4 Result Analysis
The Jar Mill test was repeated three times using different grinding periods. For each test, a product
particle size distribution and energy consumption were determined, and the target product particle
size (150 µm) was between the product size of test 1 and test 2. Thus, the required specific energy
to grind the material to the target size (150 µm) can be calculated by interpolation. From Figure 4-
3, it is clear that to grind the feed material (F80 = 235.9 µm) to the target grind size (P80 = 150
µm), the specific energy will be 0.91 kWh/t.
61
Table 4-3: Jar mill test product size distribution
Tyler Microns Feed 1 2 3
6 3327 100.0 100.0 100.0 100.0
8 2362 99.8 99.9 99.9 100.0
10 1651 99.8 99.8 99.8 100.0
14 1168 99.8 99.8 99.7 100.0
20 833 99.7 99.8 99.7 100.0
28 589 99.2 99.6 99.6 100.0
35 417 95.7 98.9 99.3 100.0
48 295 86.8 95.2 97.4 99.8
65 208 76.4 87.0 91.9 99.4
100 147 64.7 74.1 80.0 97.2
150 104 55.8 62.9 67.8 90.4
200 74 47.0 52.0 55.5 76.5
270 53 40.9 44.7 47.4 63.8
325 44 37.6 40.8 43.2 57.1
400 37 35.3 37.9 40.2 52.4
500 25 30.9 32.9 35.0 44.5
d80 (µm) 235.9 173.5 147.2 81.1
Specific Energy
(kWh/mt) 0.0 0.6 1.0 2.9
Figure 4-2: Jar mill test grinding product size distribution
0.0
20.0
40.0
60.0
80.0
100.0
10 100 1000 10000
Cu
mu
lati
ve P
erc
en
t P
assi
ng
Particle Size (µm)
Cumulative Percent Passing Vs. Particle Size (µm)
Jar Mill Feed
1
2
3
62
Figure 4-3: Specific energy vs. product size P80
Table 4-4: Jar mill test predicted specific energy consumption for target grind size
Test F80 (µm) P80 (µm) Specific Energy
(kWh/mt)
Jar Mill 235.9 150 0.91
Generally, the Jar Mill Grinding Test (JMGT) is used to estimate energy consumption for an
industrial Vertimill® in the regrinding stage. The measured energy should be multiplied by 0.65
(VTM factor) to predict the energy required by a Vertimill®. However, it has been reported that
the Jar Mill Grinding Test is not suitable for the tertiary grinding circuit energy study due to the
coarseness of the feed and the low reduction ratio (Nadolski, 2015).
10.0
100.0
1000.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Eigh
ty P
erc
en
t P
assi
ng
Size
(μ
m)
Specific Energy (kWhr/mt)
Eighty Percent Passing Size (μm) Vs. Specific Energy (kWhr/mt)
Vertimill Specific Energy Requirements with19 mm Monosize Charge at 60% SolidsP80 Spec. Pt. (0.91 kWh/mt, 150 microns)
63
4.2 Bond Ball Mill Work Index test
The Bond Ball Mill Work Index test is a conventional grindability test, developed by F.C. Bond
(1952), which is used to estimate the grinding hardness of ores, estimate the energy consumption
and size ball mills. Intrinsically, it is an empirical approach to predict the energy consumption for
industrial ball mills operation by testing in a laboratory scale ball mill with a series empirical
correction factors. It has two engineering advantages:
1) It is very simple
2) Experience shows that it works for many (not all) circumstances
This test has been used to size and predict the Vertimill® power draw by considering the energy
efficiency factors (0.6 for regrinding and 0.7~0.75 for tertiary grinding) compared to conventional
ball mills.
4.2.1 Apparatus
A standard Bond ball mill, installed at the Center for Coal and Mineral Processing was used for
ore grindability test work. The standard cylindrical test mill of 305 mm diameter by 305 mm length
operated at a fixed speed of 70 rpm (85% of the critical speed). The media ball charge consists of
a specified number of balls ranging from 15.2 mm to 44.4 mm diameter with the total ball load
weighing 20.1 kg. The detailed media ball charge information is listed in the table below.
Table 4-5: The media charge requirement for standard Bond ball mill test
Ball size Ball size Number Weight Per Ball Total Weight
mm inch - g kg
36.8 1.5 43 204.9 8.809
29.7 1.17 67 107.7 7.215
25.4 1 10 67.0 0.670
19.1 0.75 71 28.2 2.003
15.5 0.61 94 15.2 1.428
Total 285 20.125
64
Figure 4-4: Bond ball mill test rig (left) and Rop-tap testing sieve shaker & Screens (right)
4.2.2 Material
For BBWI testing, samples were obtained from the SAG mill feed belt cut collected during plant
surveys between the years 2016 and 2017. Around 10 kg of dry ore was stage crushed to 100%
minus 6 mesh (3.35 mm), with the following particle size requirements:
1) Particle size P80 between 1.8 and 2.5 mm
2) Particle size P20 larger than the closing screen size
The 10 kg sample was riffle split into 12 sub-samples and bagged prior to testing.
4.2.3 Test Method
The feed material bulk density was measured by filling a 1-liter measuring cylinder and vibrating
on the sieve shaker pad for 10 minutes. The sample mass and volume were used to calculate the
feed bulk density. A 700 cm3 (mass calculated from material bulk density) sample of the feed
material was ground in the Bond ball mill for 100 revolutions and the product was sieved using
the closing size screen to remove the undersize. Fresh feed was added to replace the undersize
weight to the original feed weight. The reconstituted feed (oversize and compensation material)
was reground and the process was repeated using the net production of undersize per revolution to
65
estimate suitable grinding revolution until a constant 250% load (mass of oversize versus mass of
undersize) was reached. The particle size analysis was conducted on the final product (undersize
material).
4.2.4 Result Analysis
After the test work, the BBWI can be calculated using the Equation 4-1.
𝑩𝑩𝑾𝑰 =𝟒𝟒.𝟓
𝑷𝟏𝟎.𝟐𝟑×𝑮𝒑𝒓𝟎.𝟖𝟐×(
𝟏𝟎
√𝑷𝟖𝟎−
𝟏𝟎
√𝑭𝟖𝟎)
× 𝟏. 𝟏𝟎𝟑 Equation 4-1
Where
BBWI: Bond Ball Mill Work Index value (kWh/t)
P1 : closing screen size (µm)
Gpr : average grams of undersize product per revolution from the last three cycles
P80 : Size at which 80 percent of the undersize product passes (µm)
F80 : Size at which 80 percent of the feed passes (µm)
The test results are summarized in the table below, please refer to Appendix B for details.
Table 4-6: BBWI result summary
Survey # Date Closing Screen size (µm) BBWI (kWh/t)
3 March 16, 2016 150 18.4
4 February 7, 2017 212 19.4
Note: the BBWI in 2016 referred to Cave to Mill Project (Nadolski, Cave-to-Mill research program report,
2017)
From Table 4-6, there is a 5% difference when comparing the BBWI indices from SAG mill feed
samples in 2016 and 2017 even though different closing screen sizes were used in these two BBWI
tests.
66
4.3 Hardgrove Mill Fine Material Characterization Test
A Hardgrove mill grindability test, originally used for coal hardness testing, was modified and
applied for the fine material breakage characterization study. This method incorporates a fine
material breakage characterization test, that was modified from the standard Hardgrove mill test.
For the test a precision power meter is used to record energy consumption. It also integrates a
breakage model that characterizes the energy-size reduction relationship for various particle sizes.
The Hardgrove mill fine material characterization test is relevant to Vertimill® milling in terms
of:
1) Both use steel balls as grinding media.
2) Breakage takes place in a compression bed mode.
3) Dominant breakage mechanism is attrition in both the Hardgrove mill and Vertimill®.
4) The particle size (600 – 150 µm) tested in the Hardgrove mill represents approximately 70% –
80% of particles by mass feeding to the tertiary grinding Vertimill® operation at New Afton
mine.
4.3.1 Apparatus
1) Standard sieves - circular, standard testing sieves, which are 200 mm [8 in.] in diameter and
conform to Specification E11 or ISO 3310-1, series R 40/3, with the following sizes, together
with cover and catch pan were used (receiver) (United States of America Patent No.
Designation: D409/D409M - 16, 2016):
67
Table 4-7: Screens used for Hardgrove mill test
10 The U.S.A. Standard Sieve
Series Designation
3350 µm No. 6
2360 µm No. 8
1700 µm No. 12
1180 µm No. 16
850 µm No. 20
600 µm No. 30
425 µm No. 40
300 µm No. 50
212 µm No. 70
150 µm No. 100
106 µm No. 140
75 µm No. 200
53 µm No. 270
38 µm No. 400
20 µm No. 635
2) Grinding machine - The Hardgrove Grindability Machine as shown in Figure 4-5 was used.
The grindability machine includes a stationary grinding bowl of polished cast iron, with a
circular horizontal track that holds nine polished steel balls, each 25.4 ± 0.13 mm in diameter.
Figure 4-5: Hardgrove mill at UBC Center for Coal and Mineral Processing
68
3) Power meter –Power meter is shown in Figure 4-6. The Watts Up USB Data Logger software
was installed in the computer for data recording and downloading.
Figure 4-6: Power meter (left) and data logger software (right)
4.3.2 Material
Samples were collected from the hydrocyclone underflow stream in the Vertimill® tertiary
grinding circuit during the plant survey. The sample was regarded as representative for the
Vertimill® feed at the time of sampling. After the slurry samples were shipped to the UBC Center
for Coal and Mineral Processing, material was dried and split to obtain a 5 kg sample for the
Hardgrove mill grinding test.
Table 4-8: Samples summary for Hardgrove mill grinding tests
No. Survey Sample Stream Mass (kg)
1 Survey #3 Vertimill® Feed ~ 5
2 Survey #4 Vertimill® Feed ~ 5
4.3.3 Testing method
The prepared Hardgrove mill grinding test samples went through dry and wet screening processes
to obtain narrow size fraction sub-samples. The materials from four narrow size fractions were
69
selected for the grinding tests, including 600-425 µm, 425-300 µm, 300-212 µm and 212-150 µm,
the mass of which account for over 70% of the Vertimill® feed.
Figure 4-7: Prepared narrow size fraction particles
In the standard Hardgrove Grindability Index (HGI) test, a consistent mass of 50 g air-dried
material with particle size between 1180 and 600 microns is ground during the test. The consistent
mass-based test has been questioned due to the variety of the densities for different materials
(Prasher, 1987).
In this modified Hardgrove mill grinding tests, a constant volume of 30 ml material was used in
the grinding tests. To obtain the constant volume material, a bulk density test has been conducted
before the grinding test for particles in each size fraction by shaking the material filled in a
transparent measuring cylinder on a vibrating shaker for 15 minutes (see Figure 4-8).
70
Figure 4-8: Bulk density measuring rig
The required mass for the narrow size fraction grinding test can be calculated using the following
equation:
𝑀𝑎𝑠𝑠𝑖 = 𝐵. 𝐷.𝑖 × 30 Equation 4-2
Where
Massi: the required mass for particles in size i (g)
B.D.i : the bulk density for particles in size i (g/ml)
During the Hardgrove mill grinding tests, the material in each size fraction was subjected to four
different numbers of revolutions (20, 40, 80, 160) representing four different energy inputs.
Meanwhile, the no-load energy input was also recorded by running the Hardgrove mill machine
for the same revolutions (20, 40, 80, 160) without material loaded. Thus, the net energy input can
be calculated using the following expression:
71
Net Energy Input = Load Energy Input – No-load Energy Input Equation 4-3
Table 4-9: Sample volume and revolutions for each test
Size fraction Volume Revolutions
(µm) (ml) -
600 x 425 30 20 40 80 160
425 x 300 30 20 40 80 160
300 x 212 30 20 40 80 160
212 x 150 30 20 40 80 160
The grinding products under different energy inputs were then analyzed for particle size
distribution by wet and dry screening. In a summary, the test procedure for the developed
Hardgrove mill ore characterisation test can be expressed using the following flowsheet.
~ 5kg
Vertimill Feed
No-Load Test
(20, 40, 80, 160)
Size Fraction
600 x 425
Size Fraction
425 x 300
Size Fraction
300 x 212
Size Fraction
212 x 150
Load Test
(20, 40, 80, 160)
Bulk Density
Test & Split
Screen & Split
PSD Analysis
Same as
Size Fraction
600 x425
Figure 4-9: Hardgrove mill ore characterisation test procedure
72
4.3.4 Result Analysis
The grinding product particle size distribution analysis results for the sample #1 (Vertimill® feed
in survey#3) are shown in the following figures, for the detailed particle size distribution results,
please refer to Appendix B.
Figure 4-10: Grinding product particle size distribution analysis for Vertimill® feed in survey #3
The grinding product particle size distribution analysis results for the sample #2 (Vertimill® feed
in survey#4) are shown in the following figures, for the detailed particle size distribution results,
please refer to Appendix B.
73
Figure 4-11: Grinding product particle size distribution analysis for Vertimill® feed in survey #4
To compare the Hardgrove mill grinding test results for each sample, breakage models were used
to fit the data and generate the corresponding breakage index.
1) Axb breakage model (Napier-Munn, Timothy J., Morrell, S., Morrison, Robert D. & Kojovic,
T., 1996)
The Axb breakage model was originally used in the JK Drop Weight Test for the SAG mill
comminution process modelling. This model can present the relationship between the specific
energy and the breakage product fineness index t10 and generate a breakage index Axb, which is
used to assess the competency of the tested sample. In this study, t4 was used as the breakage
product fineness index since it is easier to measure and closer to the required product size (150
µm) than the t10. The Axb value is used to represent the hardness of the Vertimill® feed samples.
Thus, the breakage model can be expressed using the Equation 4-4.
74
𝑡4 = 𝐴 ∙ (1 − 𝑒−𝑏∙𝐸𝐶𝑆) Equation 4-4
Where:
t4 : the cumulative passing % of the particle size that is 1/4th of the initial geometric mean particle
size after size reduction (%)
Ecs : the specific energy consumption in the size reduction process (kWh/t)
A, b: the ore impact breakage parameters
• Sample #1 (Vertimill® feed in survey #3)
The breakage model of sample #1 can be represented by Equation 4-5.
𝑡4 = 20.2 ∙ (1 − 𝑒−0.12∙𝐸𝐶𝑆) Equation 4-5
Table 4-10: Axb breakage model parameters for sample #1 (VTM feed in survey #3)
Parameters Value
A 20.2
b 0.12
Axb 2.43
Figure 4-12: Relationship between the Ecs and t4 for sample #1 (VTM feed in survey #3)
75
The Axb value generated from the Hardgrove mill grinding test can be used as a breakage index
to assess the hardness of the tested material. A strong particle size effect was observed in Figure
4-12 which shows that finer particles are harder to break under the same breakage energy input.
• Sample #2 (Vertimill® feed in survey #4)
The breakage model of sample #2 can be represented by Equation 4-6.
𝑡4 = 19.5 ∙ (1 − 𝑒−0.12∙𝐸𝐶𝑆) Equation 4-6
Table 4-11: Axb breakage model parameters for sample #2 (VTM feed in survey #4)
Parameters Value
A 19.5
b 0.12
Axb 2.25
Figure 4-13: Relationship between the Ecs and t4 for sample #2 (VTM feed in survey #4)
Similarly, a strong particle size effect was also observed for sample #2 in the Hardgrove mill
grinding test.
2) fmat breakage model
76
To incorporate the particle size effect, a fmat breakage model was used to analyze the Hardgrove
mill grinding test results. This model can be represented using the following equation. Please refer
to Chapter 5 for the detailed discussion regarding this breakage model.
𝑡4 = 𝑀 ∙ {1 − exp [−𝑓𝑚𝑎𝑡 ∙ 𝑥𝑛 ∙ (𝐸𝑐𝑠 − 𝐸𝑚𝑖𝑛)]} Equation 4-7
Where:
t4 : the cumulative passing % of the particle size that is 1/4th of the initial geometric mean particle
size after size reduction (%)
M : the maximum t4 (%)
Ecs : the mass specific energy input (kWh/t)
Emin : the threshold energy (kWh/t)
fmat : the material breakage property (t/kWh·µm-n)
x : the geometric mean initial particle size (µm)
n : an exponent for the initial particle size and is ore-specific
The threshold energy, Emin, of the tested fine particles is set to 0 kWh/t considering its negligible
magnitude compared to specific energy input during the grinding test.
An ore hardness index SMi, proposed by Palaniandy (2017) was obtained and used to represent
the fine material breakage properties. Generally, a higher SMi value indicates a softer ore whilst a
lower SMi value indicates a harder ore. The SMi value can be calculated using the following
equation.
𝑆𝑀𝑖𝑥 = 𝑀 ∙ 𝑓𝑚𝑎𝑡 ∙ 𝑥𝑛 Equation 4-8
Instead of 106 µm size as suggested by Palaniandy (2017), 150 µm was used as the specific size
for the SMi hardness index, as 150 µm is the target product P80 size for the tertiary grinding circuit
77
at New Afton Mine. Similarly, if a much finer product size is required, such as 50 µm, a smaller x
value is suggested to calculate the SMi hardness index.
• Sample #1 (Vertimill® feed in survey #3)
The breakage model of sample #1 can be represented by Equation 4-9.
𝑡4 = 24.3 ∙ {1 − exp[−0.0016 ∙ 𝑥0.71 ∙ 𝐸𝑐𝑠]} Equation 4-9
Table 4-12: fmat breakage model parameters for sample #1 (VTM feed in survey #3)
Parameters Value
M 24.3
fmat 0.0016
n 0.71
Emin 0
SMi150µm 1.40
Figure 4-14: fmat breakage model fitted curve for sample #1 (VTM feed in survey #3)
78
According to Figure 4-14, the fmat breakage model fit well to the Hardgrove mill grinding test
results for sample #1. The model incorporates both the particle size effect and specific energy
effect on the breakage product fineness.
• Sample #2 (Vertimill® feed in survey #4)
The breakage model of sample #2 can be represented by Equation 4-10.
𝑡4 = 27.6 ∙ {1 − exp [−0.0010 ∙ 𝑥0.75 ∙ 𝐸𝑐𝑠]} Equation 4-10
Table 4-13: fmat breakage model parameters for sample #1 (VTM feed in survey #3)
Parameters Value
M 27.6
fmat 0.0010
n 0.75
Emin 0
SMi150µm 1.19
Figure 4-15: fmat breakage model fitted curve for sample #2 (VTM feed in survey #4)
79
Similarly, the fmat breakage model fits the results better for sample #2 than the Axb breakage
model.
In summary, compared to Axb breakage model, the fmat breakage model fits the grinding test results
better. Thus, the generated hardness index SMi150µm from the fmat breakage model is more reliable
than the averaged Axb value from Axb breakage model.
4.4 Comparison of Results
The grinding tests described above provide information regarding the ore hardness and the
expected power consumption to grind the material to required product size (150 µm). The Jar mill
test was conducted by Metso and was intended for the equipment sizing, and no hardness index
was generated from this test. Thus, it was not discussed in the comparison. The modified
Hardgrove mill fine material characterization test results and the conventional Bond ball mill work
index test results are summarized in Table 4-9 along with the Axb value generated from the
standard JK Drop Weight test.
Table 4-14: Ore grinding test results summary
Sample Axb (DWT) BBWI SMi150µm Axb (HGM) S.E. (DCS) SSE75 (DCS)
SAG mill feed (S#3) 39.2* 18.4* - - 2.99 20.29
VTM Feed (survey #3) - - 1.40 2.43
SAG mill feed (S#4) 40.7 19.4 - - 3.08 24.47
VTM Feed (survey #4) - - 1.19 2.25
*： The ore characterization results referred to Cave to Mill project (Nadolski, Cave-to-Mill research program report,
2017)
The JK DWT generated Axb shows no big difference in the competency for the SAG mill feed
samples in 2016 and 2017. However, there exit some differences when comparing the standard
Bond Ball Mil Work Index and the DCS recorded energy consumption indices (S.E. and SEE75).
80
When comparing the Hardgrove mill grinding test results to the standard BBWI test and the
calculated specific energy from DCS data, the results show a good consistency such that harder
ore has a higher Bond ball mill work index, high specific energy consumption and a lower SMi150µm
value. Therefore, it is reasonable to deduce that the SMi150µm value can represent the ore hardness
for fine materials. Considering the limited quantity of the database used in fine material ore
characterization tests, more samples should be tested to provide a more robust relationship between
the BBWI and SMi150µm.
81
Chapter 5: Model Development
Various tower mill modelling and simulation approaches were described in Chapter 2. There were
several attempts to model and simulate the Vertimill® product particle size distribution using the
population balance modelling approach (Mazzinghy, D.B., Galery, R., Schneider, C.L., & Alves,
V.K., 2014; Mazzinghy, D.B., Russo, J.F.C., Galery, R., & Schneider, C.L., 2015; Mazzinghy,
D.B., Schneider, C.L., Alves, V.K., & Galery, R., 2015; Hasan, 2016). Usually, a batch ball mill
or a batch stirred mill is used to generate the required model parameters which integrate both the
ore characteristics and operating conditions. The Hardgrove mill applies similar breakage
mechanisms to those in gravity-induced low speed stirred milling and was therefore regarded as a
potential device for fine material characterization (Palaniandy, 2017). A modified Hardgrove mill
test was successfully applied to model and simulate the batch ball mill and industrial ball mill
operations (Shi, F., & Xie, W., 2015; Shi, F., & Xie, W., 2016).
In this study, the mass-size balance method was chosen to model and simulate the Vertimill®
performance by integrating ore breakage model, size specific energy selection function and
classification model. This approach enables the hardness assessment of fine materials
characterized by a generated hardness index SMi150µm from the Hardgrove mill grinding test. The
full particle size distribution of the Vertimill® grinding product under certain operating condition
can be simulated using this systematic method. In the present study a programmed Microsoft
Excel-based tool was developed for modelling and simulation of Vertimill®. The three tools that
were developed are:
• Fine material breakage characterization tool used to generate the breakage model parameters
from the modified Hardgrove mill fine material characterization test
82
• Vertimill® Model parameters generator for the selection function from the grinding circuit
survey result
• Vertimill® Simulator used to predict the product particle size distribution
The scope of the Vertimill® modelling is shown in Figure 5-1.
Ball mill cyclone overflow
Sump
Tertiary cyclone feed pump
Cyclone underflow
Cyclone overflow
Vertimill discharge
Hydrocyclone
VTM-3000-WB
Figure 5-1: Scope of the Vertimill® model
83
5.1 Model Structure
The proposed Vertimill model consists of four sub-models: ore breakage model (fmat ore breakage
model), size specific energy level model (selection function), internal classification model
(Whiten’s classification model) and tower mill power model (Nitta’s empirical power model).
In the simulation, the Vertimill model can calculate the breakage index t4 based on the ore breakage
property and size specific energy input. Then, the product size distribution can be reconstructed
through the t4-tn family of curves generated from the Hardgrove mill grinding test and the mass-
size balance method. This methodology was effective for both batch and continuous ball mill
modelling (Shi, F., & Xie, W., 2015; Shi, F., & Xie, W., 2016). Furthermore, an internal
classification effect has been incorporated into the grinding process since it is considered a
classification zone has been identified in the gravity-induced stirred milling technology. A similar
model structure was successfully applied in tumbling mill simulation (Herbst J.A., & Fuerstenau,
D.W., 1980). This is the first time this approach was used for the industrial scale Vertimill®
modelling. Generally, the model structure can be expressed by using the diagram below:
Vertimill
mij
Internal
Classification
Cfi pifi,GZ
pi,GZ
Figure 5-2: Vertimill® model structure
Herbst and Fuerstenau (1980) proposed the solution for pi for this internal classification integrated
grinding product, which is shown in the equation below:
84
𝑝𝑖 = [𝐼 − 𝐶] ∙ 𝑚𝑖𝑗 ∙ ⌈𝐼 − 𝐶 ∙ 𝑚𝑖𝑗⌉−1
∙ 𝑓𝑖 Equation 5-1
Where:
fi : the mass fraction of size i in the feed
pi : the mass fraction of size i in the product
mij : transfer matrix describing the mass fraction distribution during the grinding process for all
the particle sizes under certain condition
C : classification efficiency matrix
I : identity matrix
The key component of this mass-size balance model is the transfer matrix which represents the
mass distribution for the all the materials in each size fraction after the size reduction process. This
transfer matrix not only depends on the breakage properties of the ore sample which can be
represented by the fmat breakage model, but also the size-specific energy function that is related to
the energy level for each size and the energy efficiency between the ore characterization machine
(Hardgrove mill) and the industrial Vertimill® machine (VTM-3000-WB).
85
5.2 Sub-models
5.2.1 Ore Breakage Model
The JKMRC (Julius Kruttschnitt Mineral Research Center) uses the JK breakage model for SAG
mill modelling along with ore characterization methods such as JK Drop Weight (JKDWT) test
and the JK Rotary Breakage Test (JKRBT) (Napier-Munn, Timothy J., Morrell, S., Morrison,
Robert D. & Kojovic, T., 1996). The JK breakage model can be expressed by the following
equation:
𝑡10 = 𝐴 ∙ (1 − 𝑒−𝑏∙𝐸𝐶𝑆) Equation 5-2
Where:
t10 : the cumulative passing % of the particle size that is 1/10th of the initial geometric mean
particle size after size reduction (%)
Ecs : the specific energy consumption in the size reduction process (kWh/t)
A, b: the ore impact breakage parameters
Although the JK breakage model has been widely used for AG/SAG mill modelling, there are
deficiencies that have been identified by researchers, one of which is the lack of recognition of the
size effect on the breakage performance. Many previous studies have shown that the crack density
of larger particles is much greater than that for smaller particles (Tavares, 1998). Therefore, the
coarser particles tend to be weaker and easier to break than smaller particles. Also, it has been
stated that the particle size must be considered when determining the breakage function
(Norazirah, A., Fuad, S.H.S., & Hazizan, M.H.M., 2016). However, the JK A and b breakage
model only presents the average relationship between the comminution specific energy and the
breakage index t10 for all sizes. This “average” set of A and b parameters are then used for the AG
and SAG mill modeling assuming particles of different sizes would break in the same manner
86
when subject to the same specific energy input during size reduction, which is questionable,
especially for a wide feed particle size range.
To incorporate the particle size effect to breakage, Shi and Kojovic (2007) modified Vogel and
Peukert’s breakage probability model (Vogel, L. & Peukert, W., 2003) to describe the relationship
between the breakage index, t10, and the comminution specific energy, Ecs. Furthermore, in the
validation of the proposed new breakage model proposed by Shi and Kojovic (2007), it was found
that the effect of particle size on breakage was not adequately represented by the term x (particle
size) alone. Thus, an upgraded breakage model was proposed by Bonfils and Powell (2013) by
adding a power function to the size term as shown in Equation 5-3.
𝑡10 = 𝑀{1 − exp [−𝑓𝑚𝑎𝑡 ∙ 𝑥𝑛 ∙ 𝑘 ∙ (𝐸𝑐𝑠 − 𝐸𝑚𝑖𝑛)]} Equation 5-3
Where:
t10 : the cumulative passing % of the particle size that is 1/10th of the initial geometric mean
particle size after size reduction (%)
M : the maximum t10 (%)
Ecs : the mass specific impact energy (kWh/t)
Emin : the threshold energy (kWh/t)
fmat : the material breakage property (kg·J-1·m-1)
x : the geometric mean initial particle size (m)
k : the successive number of impacts with single impact energy
n : an exponent for the initial particle size and is ore-specific
Since only fine particles ranging from 150 µm to 600 µm were tested for the ore characterization
purpose, the threshold energy is low and negligible compared to the input energy, which was also
observed by S. Panlaniandy (2017).
87
In this study, t4, defined as cumulative percentage of product passing 1/4th of initial particle size,
was used, instead of the commonly used t10, as the breakage index in this ore breakage model.
From the modelling perspective, the particle sizes of t4 (126 µm, 89 µm, 63 µm and 45 µm) are
closer to the size of interest, 150 µm, which is the target product P80 size in the tertiary grinding
circuit. From the availability perspective, t4 is easier to obtain rather than t10 since the tested
particles in this study are much finer than the t10 integrated breakage test, such as JKDWT or
JKRBT. Similar comments were reported by Shi (2016) in a research project undertaken within
ACARP (the Australian Coal Association Research Program) to develop a unified coke strength
index from the various drum testing materials. It is also recommended that tn should be carefully
selected according to the size of interest and the availability of the index.
The breakage model can be expressed using the following equation:
𝑡4 = 𝑀 ∙ {1 − exp [−𝑓𝑚𝑎𝑡 ∙ 𝑥𝑛 ∙ 𝐸𝑐𝑠]} Equation 5-4
Where:
t4 : the cumulative passing % of the particle size that is 1/4th of the initial geometric mean particle
size after size reduction (%)
M : the maximum t4 (%)
Ecs : the mass specific energy (kWh/t)
fmat : the material breakage property (t/kWh·µm-n)
x : the geometric mean initial particle size (µm)
n : model parameter
It was found that the breakage index, t10, generated from the ore characterization tests is uniquely
related to other tn points for a family of particle size distribution curves, with tn defined as the
cumulative percentage of product passing a given fraction of the initial size, x/n (Narayanan, S.,
88
& Whiten, W.J., 1988). Similarly, the breakage index, t4, rather than t10 was used in this study to
represent the product fineness after the size reduction process. Generally, a larger t4 value
represents a finer product size while a smaller t4 indicates a coarser product. A similar t4-tn
relationship was discovered and employed to reconstruct the product size distribution curve by
using the cubic spline regression method.
5.2.2 Size Specific Energy Model
The size specific energy was first proposed by (Shi, F., & Xie, W., 2015) in their batch ball mill
modelling study as an important input to determine particle size reduction. It is hypothesized that
the mean specific energy E is not evenly applied to all sizes in the Vertimill®. There should be a
selection function describing the size-specific energy level recognizing that some particle sizes
receive more specific energy while some others receive less. Furthermore, an energy efficiency
difference is believed to exist between the industrial scale Vertimill® and the batch Hardgrove
mill when determining the breakage model that illustrates the breakage index, t4 and specific
energy input, which is also integrated into the selection function. The size-specific energy can be
expressed using the following equation:
𝐸𝑖 = 𝑆𝑖 ∙ 𝐸 Equation 5-5
Where:
Ei : size-based specific energy (kWh/t)
Si : selection function describing the specific energy level in different sizes
E : mean specific energy (kWh/t)
To generate the selection function, Shi and Xie (2015) proposed to use the cubic spline regression
method to fit three Si-values at three size knots, by which the full size selection function can be
developed accordingly. The cubic spline regression fits cubic functions that are joined at a series
89
of k knots. Thus, the first and second derivatives at these knots are the same for the piecewise
functions. Such a function follows the form:
𝐸(𝑌|𝑋) = 𝛽0 + 𝛽1𝑥 + 𝛽2𝑥2 + 𝛽3𝑥3 + 𝛽4(𝑥 − 𝛼1)3 + 𝛽5(𝑥 − 𝛼2)3 + ⋯ + 𝛽𝑘+3(𝑥 − 𝛼𝑘)3 +
Equation 5-6
Where
𝛼1, 𝛼2, ⋯ , 𝛼𝑘: the knots
5.2.3 Internal Classification Model
There are two clearly defined zones inside the Vertimill® chamber: the grinding zone and the
classification zone as shown in Figure 5-3 (Mazzinghy, D.B., Russo, J.F.C., Lichter, J., Schneider,
C.L., Sepúlveda, J., & Videla, A., 2015).
Figure 5-3: Vertimill® grinding and classification zones (Mazzinghy, D.B., Russo, J.F.C., Lichter, J.,
Schneider, C.L., Sepúlveda, J., & Videla, A., 2015)
Therefore, a classification sub-model was incorporated into the Vertimill® size reduction model.
In this study, the Whiten classification model (Svarovsky, L., & Thew, M.T., 1992) was used to
fit the discharge efficiency of the grinding product for each size fraction. The function is shown
below:
90
𝐶 = 𝐶𝑚𝑎𝑥 (𝑒𝛼−1
𝑒𝛼𝑑𝑖 𝑑50𝑐⁄ +𝑒𝛼−2) Equation 5-7
Where:
C : classification efficiency of size of interest
Cmax: maximum probability of particles reporting to the fine component
α : sharpness of the internal classifier
d50c: corrected cut size of the internal classifier, at which the corrected classification efficiency is
0.5
di : size of interest
5.2.4 Nitta Tower Mill Power Model
A power model proposed by Nitta (2006) was found to align with the DCS recorded mill power
draw well and has was incorporated into the Moly-Cop 3.0 tools for the Vertimill® power
estimation. As an empirical model, it considers key operating variables, such as media charge,
stirrer speed and mill geometry. In this study, this Tower Mill power model was used for the
Vertimill® power consumption modelling and simulation. The tower mill motor power estimation
equation was shown as below:
P = 312 ∙ H0.884 ∙ S2.232 ∙ D ∙ N1.232 Equation 5-8
Where
P : electric power of tower mill motor (kW)
H : height of the ball (m)
S : outside diameter of mill (m)
D : gap between screw and wall of mill (m)
N : Screw speed (rps)
91
5.3 Model Algorithms
The model algorithm can be illustrated as shown in Figure 5-4. The samples from survey #4 was
tested using the developed Hardgrove mill grinding test. The related breakage model parameters
(M, fmat, n) and the t4-tn family curves can be generated from the test results. The operating
conditions including the throughput, circulating load, and mill power draw are input into the model
to calculate the mean specific energy. The model parameters for the selection function and
classification function are then back-calculated by applying the GRG non-linear regression
algorithm. This modelling fitting step is aimed generating the model parameters.
For model validation, the fitted selection function and classification function along with the
breakage model generated from the ore characterization results for Vertimill® feed in survey #3
were inputted into the Vertimill® simulation tool. The simulated Vertimill® grinding product
particle size distribution was compared with the measured product size distribution during the
circuit survey. Statistical analysis was conducted to evaluate the accuracy of the simulation result.
92
Modified Hardgrove mill fine material test
Breakage model parametersM, fmat, n
DCS Vertimill Power DrawOperating Condition
Mean specific energyS.E.
Size specific energy- Selection function
t4-tn family curves
Classification efficiencyd50c, C, α
Estimated Vertimill product PSD
Pi=[I-C]· mij· [I-C· mij]-1· fi
Breakage modelt4i=M· (1-exp(-fmat· x
n· Ei)
Measured Vertimill product PSD from circuit survey
Initial guess on selection function parameters () & classification parameters
(d50c, C, α)
Check the difference < convergence
Breakage model parametersM, fmat, n
Fitted selection function & classification function
t4-tn family curves
New Operating Condition
Feed size distributionfi
Feed size distributionfi
Modified Hardgrove mill fine material test
Simulate Vertimill product PSD
Nitta Vertimill Power Model
Grind product simulation
Model fitting
Figure 5-4: Model algorithm flowsheet
93
5.4 Model Fitting
5.4.1 Material
The material tested was collected from the tertiary grinding circuit, equipped with VTM-3000 WB
Vertimill® and hydrocyclones at the New Afton mine as described in Chapter 1. The tested
material is the feed to the Vertimill® unit, which is the hydrocyclone underflow stream in the
tertiary grinding circuit. The sample used for model fitting is the Vertimill® feed from survey #4
as described in Chapter 3.
5.4.2 Breakage Model
To evaluate the ore characteristics and generate the parameters for the breakage model, the
modified Hardgrove mill grinding test was used as described in Chapter 4. The fitted model
parameters from the test results are listed in the following Table 5-1.
Table 5-1: Breakage model parameters for sample in survey #4
Model Parameter
M 27.64
fmat 0.0010
n 0.75
Thus, the ore breakage model for the Vertimill® feed material (survey #4) can be represented by
Equation 5-9:
𝑡4𝑖 = 27.64 ∙ (1 − 𝑒−0.0010∙𝑥0.75∙𝐸𝑖) Equation 5-9
Where
t4i : the cumulative passing % of the particle size that is 1/4th of the initial particle geometric mean
size after grinding (%)
Ei : the size-based specific energy consumption in the size reduction process (kWh/t)
94
Similar to the t10-tn family curves, the t4-tn family curves can also be developed from the ore
characterization test results by applying the polynomial “least squares” method. Figure 5-5
presenting the t4-tn family curves are shown below.
Figure 5-5: t4-tn family curves for survey #4 Vertimill® feed
5.4.3 Selection Function and Classification Function Fitting
The selection function is used to describe the specific energy level for each particle size in the mill
feed while the classification function represents the discharge rate of the particles in the grinding
mill product. The parameters for the selection and classification functions were back calculated by
using the Vertimill® feed product particle size distribution that measured after the Vertimill®
circuit survey. Three size knots were chosen for the selection function fitting using the cubic spline
method. The selected size knots and fitted values are listed in Table 5-2.
95
Table 5-2: Fitted model parameters for selection function
Size (µm) Parameters
2003 1.6
505 2.1
126 0.8
The selection function for the full sizes is presented in Table 5-3 and Figure 5-6.
Table 5-3: Selection function for full sizes
Size Geo-mean Spline
(µm) (µm) Si
3350
2360 2812 0.50
1700 2003 1.61
1180 1416 2.54
850 1001 2.76
600 714 2.53
425 505 2.10
300 357 1.66
212 252 1.29
150 178 1.01
106 126 0.82
75 89 0.68
53 63 0.58
0 27 0.45
96
Figure 5-6: Selection function for full sizes
The fitted classification model parameters are listed in Table 5-4.
Table 5-4: Fitted model parameters for classification function
Classification model parameters
D50c 250
α 0.49
Cmax 68%
0.10
1.00
10.00
10 100 1000 10000
Si
Particle size (µm)
Spline Si
Spline Regression
97
The discharge efficiency for the full grinding product sizes are listed in Table 5-5 and Figure 5-7.
Table 5-5: Classification function for full sizes
Size Geo-mean Classification efficiency
(µm) (µm) C
3350
2360 2812 0.0017
1700 2003 0.0084
1180 1416 0.0271
850 1001 0.0634
600 714 0.1167
425 505 0.1858
300 357 0.2626
212 252 0.3402
150 178 0.4119
106 126 0.4743
75 89 0.5258
53 63 0.5667
0 27 0.6313
Figure 5-7: Classification function for full sizes
0%
10%
20%
30%
40%
50%
60%
70%
10 100 1000 10000
Cla
ssif
ica
tio
n e
ffic
ien
cy
Particle size (µm)
98
5.4.4 Transfer Matrix – mij
From the developed specific energy-size reduction model and the modelled fitted size specific
energy function, a transfer matrix can be generated as shown below:
Figure 5-8: Transfer matrix (mij) for Vertimill® feed in survey #4
The transfer matrix is the key component in the size reduction model for the Vertimill® and it
indicates the mass distribution of each particle size at different comminution specific energy levels
following the size reduction process.
5.4.5 Model Fitting Results and Analysis
An Excel-based Vertimill® modelling and simulation tool was developed by integrating the
breakage model, selection function, and classification function. After inputting the Vertimill® feed
size distribution and operating conditions (throughput, solids %, circulating load and power
consumption) into the simulator, the corresponding grinding product size distribution can be
generated by solving the minimum SSQ of the difference between the estimated product size
distribution and the measured product size distribution. For more details about the simulator,
please refer to Appendix C. The modelling results for the Vertimill® feed material in survey #4
are shown in Table 5-6 and Figure 5-9.
Table 5-6: Comparison between the measured and modelled PSD for survey #4
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1700 0.16 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1180 0.08 0.20 0.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
850 0.02 0.08 0.19 0.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
600 0.02 0.04 0.10 0.19 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
425 0.01 0.03 0.05 0.09 0.18 0.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00
300 0.01 0.02 0.03 0.04 0.08 0.17 0.69 0.00 0.00 0.00 0.00 0.00 0.00
212 0.01 0.02 0.03 0.03 0.03 0.07 0.15 0.77 0.00 0.00 0.00 0.00 0.00
150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.84 0.00 0.00 0.00 0.00
106 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.05 0.08 0.89 0.00 0.00 0.00
75 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.06 0.93 0.00 0.00
53 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.00
0 0.03 0.07 0.09 0.09 0.09 0.07 0.06 0.04 0.03 0.03 0.03 0.05 1.00
99
Cumulative Percent Passing, %
Size VTM Feed VTM Product VTM Product
(µm) (measured) (measured) (simulated)
3350 100 100 100
2360 100 100 100
1700 100 100 100
1180 100 100 100
850 99 99 99
600 95 97 97
425 86 90 91
300 62 75 75
212 37 53 53
150 24 36 37
106 17 27 27
75 13 21 21
53 11 17 17
P80 (µm) 394 340 338
P50 (µm) 260 200 202
Figure 5-9: Comparison between the measured and modelled product size distribution for survey #4
0
10
20
30
40
50
60
70
80
90
100
10 100 1000 10000
Cu
m. P
ass
ing
(%
)
Particle size (µm)
VTM Product (simulated)
VTM Feed
VTM Product
100
The deviation between the predicted size distribution and the measured size distribution was
calculated using the following equation.
𝑆𝑆𝑄 = ∑ [𝐶𝑢𝑚. 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)𝑖 − 𝐶𝑢𝑚. 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 (𝑚𝑜𝑑𝑒𝑙𝑙𝑒𝑑)𝑖]2𝑘𝑖=1 Equation 5-10
The coefficient of determination, R2, of the predicted the measured product particle size
distribution was also calculated and used for model assessment. These statistics results are listed
in the table below.
SSQ 1.8792
R2 0.9999
According to the statistical analysis, the size reduction model with the fitted selection and
classification functions accurately predicts the Vertimill® product size distribution.
101
5.5 Model Validation
To validate the Vertimill® model and establish the basis for the simulation work in Chapter 6, a
sample was collected from Vertimill® feed during sampling program ion March 16, 2016. The
sample was tested using the modified Hardgrove mill fine material characterization method as
described in Chapter 4. The selection and classification functions were regarded as the properties
of the Vertimill® unit under similar operation conditions, which was employed directly from the
previous sample (survey #4) model fitting results.
5.5.1 Material
The material tested was collected from the tertiary grinding circuit, equipped with VTM-3000 WB
Vertimill® and hydrocyclones at the New Afton mine concentrator during the tertiary grinding
circuit study (survey #3) as described in Chapter 1. The tested material is the feed to the Vertimill®
unit collected during survey #3 as described in Chapter 3.
5.5.2 Breakage model
The Vertimill® feed sample from survey #3 was also characterized using the modified Hardgrove
mill test as described in Chapter 4. The fitted model parameters from the test results are listed in
the following Table 5-7.
Table 5-7: Breakage model parameters for sample in survey #3
Model Parameter
M 24.33
fmat 0.0016
n 0.71
By substituting the terms with generated model parameters, the ore breakage model for the
Vertimill® feed material (survey #3) can be shown in the equation below:
102
𝑡4𝑖 = 24.33 ∙ (1 − 𝑒−0.0016∙𝑥0.71∙𝐸𝑖) Equation 5-11
Where
t4i : the cumulative passing % of the particle size that is 1/4th of the initial particle geometric mean
size after grinding (%)
Ei : the size-based specific energy consumption in the size reduction process (kWh/t)
Similar to the t10-tn family curves, the t4-tn family curves can also be developed from the ore
characterization test results by applying polynomial “least squares” method. Figure 5-10
presenting the t4-tn curves are shown below:
Figure 5-10: t4-tn family curves for survey #3 Vertimill® feed
5.5.3 Selection function and classification function
It is hypothesized that the selection and classification functions should be consistent for the same
grinding unit (VTM-3000-WB) under similar operating condition. Therefore, the selection
103
function and classification function generated from the former survey result were used for the
model validation purpose.
5.5.4 Transfer Matrix – mij
The transfer matrix was generated using the ore specific breakage model and the selection function.
The matrix for the sample from survey #3 is shown below:
Figure 5-11: Transfer matrix (mij) for survey #3
5.5.5 Modelling Results and Analysis
After inputting the model parameters and operating conditions into the developed simulator, the
Vertimill® product size distribution is generated. The simulated grinding product particle size
distribution results are shown in Table 5-8 and Figure 5-12.
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1700 0.15 0.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1180 0.07 0.20 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
850 0.02 0.08 0.18 0.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
600 0.01 0.04 0.09 0.19 0.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
425 0.01 0.02 0.04 0.09 0.18 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00
300 0.01 0.02 0.02 0.04 0.08 0.17 0.71 0.00 0.00 0.00 0.00 0.00 0.00
212 0.01 0.02 0.02 0.02 0.03 0.07 0.14 0.79 0.00 0.00 0.00 0.00 0.00
150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.85 0.00 0.00 0.00 0.00
106 0.00 0.01 0.02 0.02 0.02 0.02 0.02 0.04 0.08 0.90 0.00 0.00 0.00
75 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.03 0.05 0.93 0.00 0.00
53 0.00 0.01 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.00
0 0.03 0.05 0.07 0.07 0.07 0.06 0.05 0.04 0.03 0.03 0.03 0.05 1.00
104
Table 5-8: Comparison between the measured and modelled PSD for survey #3
Cumulative Percent Passing, %
Size (µm) VTM Feed VTM Product VTM Product (measured) (measured) (simulated)
3350 100 100 100
2360 100 100 100
1700 100 100 100
1180 99 100 100
850 99 99 99
600 95 97 97
425 85 90 90
300 66 75 76
212 44 56 57
150 28 40 40
106 21 30 29
75 16 24 23
53 13 20 19
P80 (µm) 392 338 331
P50 (µm) 237 189 188
Figure 5-12: Comparison between the measured and modelled product size distribution for survey #3
0
10
20
30
40
50
60
70
80
90
100
10 100 1000 10000
Cu
m. P
ass
ing
(%
)
Particle size (µm)
VTM Product (simulated)
VTM Feed
VTM Product
105
The deviation between the predicted and the measured particle size distributions was calculated
using the following equation.
𝑆𝑆𝑄 = ∑ [𝐶𝑢𝑚. 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 (𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑑)𝑖 − 𝐶𝑢𝑚. 𝑃𝑎𝑠𝑠𝑖𝑛𝑔 (𝑚𝑜𝑑𝑒𝑙𝑙𝑒𝑑)𝑖]2𝑘𝑖=1 Equation 5-12
The coefficient of determination, R2, of the predicted the measured product particle size
distribution was also calculated and used for model assessment.
These statistical results are listed in the table below.
SSQ 7.6405
R2 0.9998
According to the statistical analysis, the simulated Vertimill® product size distribution aligned
well with the measured product size distribution from the circuit survey. It is rational to conclude
that the fitted selection and classification function can represent the Vertimill® unit grinding
properties.
106
Chapter 6: Sensitivity Analysis
Operating variables, such as the stirrer speed and media charge, will affect the performance of the
gravity induced stirred mills, including grinding product size distribution and specific energy
consumption or size specific energy consumption. As discussed in Chapter 2, a higher stirrer speed
and a higher media charge will consume more energy and create a more intensive breakage
environment inside the mill chamber. Simulation was used to assess the sensitivity of the effect of
stirrer speed and ball charge on key operating parameters including product size P80, size
reduction ratio, specific energy, and size specific energy (SSE75).
A sensitivity analysis was conducted to evaluate the effect of stirrer speed and media charge on
the Vertimill® performance. Since the model is only for the Vertimill® and not for the complete
reverse-closed circuit tertiary grinding, the sensitivity analysis was limited to the scope of the
Vertimill® unit (VTM-3000-WB) as shown in Figure 5-1. The simulation work was conducted on
the Vertimill® feed sample from survey #4 and it was assumed that the particle size distribution
of the feed, the throughput and the energy efficiency were constant.
6.1 Power Draw
The relationship between the power draw, stirrer speed and media charge is shown in Figure 6-1.
The power draw is directly proportional to both the stirrer speed and media charge. However,
usually only the media charge is adjusted to maintain the consistent power draw during the
operation. The results indicate stirred speed can be used as an alternative approach to control the
power draw.
107
Figure 6-1: Vertimill® power draw vs. Stirrer speed/Ball charge
6.2 Specific Energy Consumption
Specific energy is one of most common key operating indicators when assessing the comminution
circuit energy efficiency and energy requirement. It can be calculated using Equation 6-1.
𝑆𝐸 =𝑀𝑖𝑙𝑙 𝑝𝑜𝑤𝑒𝑟 𝑑𝑟𝑎𝑤 (𝑘𝑊)
𝑇ℎ𝑟𝑜𝑢𝑔ℎ𝑝𝑢𝑡 (𝑡/ℎ) Equation 6-1
As found for the power draw, the specific energy consumption is a directly proportional to stirrer
speed or media charge.
1000
1500
2000
2500
3000
Vert
imill®
Po
wer
dra
w, kW
Vertimill® Power Draw
1000-1500 1500-2000 2000-2500 2500-3000
108
Figure 6-2: Specific energy vs. Stirrer speed/Ball charge
6.3 Size Specific Energy Consumption
The size specific energy concept was proposed by Palaniandy et. al (2015) to assess the energy
requirement for the size reduction in the Vertimill®. It can be represented by Equation 6-2 or
Equation 6-3 for secondary and tertiary, and regrind applications, respectively. It is suggested that
SSE75 is used for secondary and tertiary grind circuits while the SSE25 is for regrind circuits as the
particle size varies a lot in different grinding stages (Palaniandy, S., Powell, M., Hilden, M., Allen,
J., Kermanshahi, K., Oats, B., & Lollback, M., 2015). Therefore, SSE75 was used for the
Vertimill® energy consumption analysis in this study.
𝑆𝑆𝐸75 =𝑆𝐸
(𝑃75−𝐹75)/100 (For secondary and tertiary grind) Equation 6-2
𝑆𝑆𝐸25 =𝑆𝐸
(𝑃25−𝐹25)/100 (For regrind) Equation 6-3
1.00
1.50
2.00
2.50
3.00
Sp
ecif
ic e
nerg
y, kW
h/t
Specific Energy, kWh/t
1.00-1.50 1.50-2.00 2.00-2.50 2.50-3.00
109
The relationship between the SSE75 and stirrer speed / media charge is shown in Figure 6-3. It is
observed that SS75 increases along with the increase in stirrer speed and media charge. Furthermore,
the SSE75 is found to be more sensitive to the stirrer speed at a higher media charge and more
sensitive to the media charge in a higher stirrer speed conditions.
Figure 6-3: Size (75µm) specific energy vs. Stirrer speed/Ball charge
6.4 Product Size P80
Figure 6-4 presents the change of the grinding product particle size P80 under different operating
conditions (different stirrer speed and media charge) for the same feed particle size P80 = 394 µm.
Based on the simulation results, the product particle size P80 decreases along with the increase of
the stirrer speed and media charge. The product particle size P80 is found to be more sensitive to
the stirrer speed with a higher media charge and more sensitive to the media charge at a higher
stirrer speed conditions.
26.0
26.5
27.0
27.5
28.0
28.5
29.0
SS
E75, kW
h/t
Size (75µm) Specific Energy, kWh/t
26.0-26.5 26.5-27.0 27.0-27.5 27.5-28.0 28.0-28.5 28.5-29.0
110
These results indicate the opportunity to develop a control strategy for a target product size that
can be controlled not only by adding the grinding media but also adjusting the stirrer speed of the
mill.
Figure 6-4: Vertimill® product P80 size vs. Stirrer speed/Ball charge
6.5 Size Reduction Ratio
The size reduction ratio of the Vertimill® feed and product is calculated as Equation 6-4.
𝑆𝑖𝑧𝑒 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑖𝑜 =𝐹80
𝑃80 Equation 6-4
Where,
F80: particle size at which 80% of particles pass in feed
P80: particle size at which 80% of particles pass in product
Similar to the other responses, the size reduction ratio is influenced by stirrer speed and media
charge. Higher stirrer speed or higher media charge always leads to a higher size reduction
320
325
330
335
340
345
350
Vert
imill®
pro
du
ct
P80, µ
m
Vertimill® Product P80
320-325 325-330 330-335 335-340 340-345 345-350
111
ratio. It is important to note that the size reduction ratio for the tertiary grinding unit at the
New Afton Mine is low at <1.5, which is one reason that the Jar mill is not suitable for energy
estimation.
Figure 6-5: Size reduction ratio vs. Stirrer speed/Ball charge
In a summary, both the stirrer speed and the ball charge have large effects on the Vertimill® key
operating parameters. Generally, a higher stirrer speed and a higher ball charge lead to a higher
Vertimill® power draw, specific energy, and size specific energy (SSE75). Conversely, the
Vertimill® grinding product size decreases along with the increase of mill speed and media charge
that results to a higher size reduction ratio. The results demonstrate that there is an opportunity to
develop a novel control strategy that uses stirred speed to achieve operating goals.
1.12
1.14
1.16
1.18
1.20
Siz
e R
ed
ucto
in R
ati
o
Size Reduction Ratio
1.12-1.14 1.14-1.16 1.16-1.18 1.18-1.20 1.20-1.21
112
Chapter 7: Conclusion and Recommendation
7.1 Conclusions
This study focused on the tower milling technology, particularly for the Vertimill® application in
the tertiary grinding circuit when treating copper-gold hard-rock ores. The main target is to develop
a size reduction model for Vertimill® operation unit that can predict the grinding product particle
size distribution when treating ores with different hardness. To achieve this target, a
comprehensive literature review has been completed to understand the current stage of the tower
modelling study. Several industrial tower tertiary grinding circuit surveys in New Afton mine
concentrator have been done to snapshot the current operating condition and tower performance.
Moreover, conventional ore characterization method (Bond Ball mill work index test) and
developed fine material breakage characterization test were conducted to assess the hardness of
the sample and generate the corresponding breakage index. The developed model is able to predict
the tower product size distribution by integrating the ore specific breakage index and the grinding
environment specific selection function and classification function. The detailed conclusions are
summarized as follows,
1) The developed Hardgrove mill fine material characterization method incorporates the particle
size effect and specific energy effect on the breakage property of ores. The test results can be
represented by using the fmat breakage model, from which a breakage index, SMi150µm,
representing the hardness of this fine material can be generated. Generally, the smaller the
SMi150µm value is, the harder the ore is. When comparing SMi150µm with the conventional
grindability test results, Bond Ball Mill Work Index, for these two tested samples, it shows a
good consistency that harder ore owns a higher BBWI and a smaller SMi150µm.
113
2) The mass-size balance method is proven by this work to be an effective method to model the
Vertimill® (tower mill) performance. The model parameters for the selection function and
classification were back calculated using the industrial Vertimill® circuit survey results, which
can be used to represent the grinding and classification performance inside the mill chamber.
The further validation was conducted by using the previously fitted model parameters for
selection and classification function and inputting the tested breakage model parameters for
the new sample. The statistical analysis of the simulated product size distribution and the
measured product size distribution has shown a good result with a low SSQ and high R2.
Therefore, it is rational to say the tower mill size reduction model can predict the product size
distribution well with certain accuracy.
3) From the sensitivity analysis results, it is obvious that both the stirrer speed and the ball charge
has a great influence on the Vertimill® performance. Generally, for the same material and
consistent operating condition (throughput, solid %, media size), a higher stirrer speed and/or
a higher ball charge result in finer grinding product size, higher specific energy consumption
and higher size specific energy consumption.
114
7.2 Main Contributions
1) Developed a breakage index SMi150µm that is generated from the modified Hardgrove mil
grinding tests. The SMi150µm can be used to assess the hardness of fine materials. it allows
variability testing on different ore types to predict their performance in tower mill grinding
using the proposed Hardgrove mill tests.
2) Developed a novel modelling approach for tower mills using input parameters from Hardgrove
mill grinding tests. It is suggested the following procedures to be followed to apply this
modelling approach for a new ore or circuit.
2. Ore characterisation
• Vertimill feed sample
• Hardgrove mill grinding test
1. Circuit Survey
• Stream Sampling
• DCS data collection
• Machine geometry & operating conditions
3. Ore breakage model
Circuit condition
• Circuit throughput
• Mill power draw
• Operating conditions
4. Machine and Condition Model
• Size specific energy level model
• Internal Classification model
5. Tower mill model
6. Simulation
Figure 7-1: Tower mill model development approach for a new operation
115
3) Demonstrated alternative control approach for the tower mills by adjusting the stirrer speed
rather than the conventional approach of adding grinding media. It also informs operators how
to adjust the Vertimill® operating parameters in respect to changes in ore breakage properties.
7.3 Recommendations
1) The classification function was model-fitted by using the industrial Vertimill® operation
survey results. A systematic classification experiment should be developed to generate model
parameters for the internal classification effect to replace the model-fitting method.
2) The selection function describes the size specific energy level for different sizes inside the mill
chamber. This function may vary in different machines or grinding environments. Instead of
the model fitting method, a mechanical or empirical model should be developed to generate
the selection function for certain grinding environment or equipment.
116
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Appendices
Appendix A
A.1 Sub-Appendix
SAG Mill Feed Belt Cut Sample Preparation
Figure A-1 shows the sample preparation procedures used to complete the particle size distribution
analysis for the SAG mill feed and prepare appropriate samples for specific gravity and ore
breakage characterisation tests.
SAG Belt Cut Sample
Sample Air Dried
Screen at 31.5 mm
Coarse Sizing+ 63 mm+ 50 mm+ 45 mm+ 31.5 mm
+ 31.5 mm
Sizing+ 26.3 mm+ 22.4 mm+ 19.0 mm+ 16.0 mm+ 13.2 mm+ 9.5 mm+ 6.7 mm+ 4.76 mm+ 3.35 mm- 3.35 mm
- 31.5 mm
Fine Sizing+ 2360 µm+ 1700 µm+ 1180 µm+ 850 µm+ 600 µm+ 425 µm+ 300 µm+ 212 µm+ 150 µm+ 106 µm+ 75 µm+ 53 µm- 53 µm
Split Split
BBWI~ 60 kg
DWT
BBWI
BBWI
DWT
DWT
Left over+31.5 mm
Left Over
Left over+3.35 mm- 31.5 mm
Split
Representative Sample
Left Over
Left Over
Left over-3.35 mm
Figure A-1: SAG belt cut sample preparation
123
Grinding Circuit Slurry Sample Analysis
Figure A-2 presents the procedure for the slurry samples analysis for the solids content and particle
size distribution.
Slurry Sample
Weight the wet material
Dry and weight
Split
Particle Size AnalysisBack Up
Figure A-2: Grinding circuit slurry sample analysis
124
A.2 Sub-Appendix
New Afton Mine Tertiary Grinding Circuit - Survey #1
Survey:
Date:
Time:
Sample origin
Net Wet Weight (g)
Net Dry Weight (g)
%Solids
Mesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing
6 3350 0% 100% 0% 100% 0% 100% 0% 100%
8 2360 0% 100% 0% 100% 0% 100% 0% 100%
12 1700 0% 100% 0% 100% 0% 100% 0% 100%
16 1180 0% 100% 0% 100% 0% 100% 0% 100%
20 850 1% 99% 1% 99% 0% 100% 1% 99%
30 600 2% 97% 2% 97% 0% 100% 3% 96%
40 425 6% 91% 7% 90% 0% 100% 10% 86%
50 300 10% 81% 16% 75% 2% 98% 20% 66%
70 212 11% 70% 20% 55% 7% 91% 22% 44%
100 150 11% 59% 16% 38% 12% 79% 16% 28%
140 106 9% 50% 10% 28% 13% 66% 8% 20%
200 75 7% 43% 6% 22% 10% 56% 5% 15%
270 53 6% 37% 4% 18% 8% 48% 3% 12%
-270 -53 37% 18% 48% 12%
P50 104 P50 194 P50 58 P50 238
P80 289 P80 341 P80 155 P80 387
42% 68% 36% 68%
13.1 32.0 23.9 28.2
5.5 21.7 8.5 19.3
#1 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #1)
15-Mar-16
15:15 to 16:15
Ball Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000 10000
Cu
mm
ula
tive P
ass
ing (
%)
Particle Size (um)
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #1)
Ball Mill Cyclone O/F
Vertimill Cyclone O/F
Vertimill Cyclone U/F
Vertimill Product
125
New Afton Mine Tertiary Grinding Circuit - Survey #2
Survey:
Date:
Time:
Sample origin
Net Wet Weight (g)
Net Dry Weight (g)
%Solids
Mesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing
6 3350 0% 100% 0% 100% 0% 100% 0% 100%
8 2360 0% 100% 0% 100% 0% 100% 0% 100%
12 1700 0% 100% 0% 100% 0% 100% 0% 100%
16 1180 0% 100% 0% 100% 0% 100% 0% 100%
20 850 1% 99% 1% 99% 0% 100% 1% 99%
30 600 2% 97% 2% 97% 0% 100% 3% 96%
40 425 6% 91% 7% 90% 0% 100% 10% 86%
50 300 10% 81% 16% 75% 2% 98% 20% 65%
70 212 11% 70% 20% 55% 6% 92% 23% 43%
100 150 10% 59% 16% 38% 11% 81% 15% 27%
140 106 10% 49% 10% 28% 12% 69% 8% 20%
200 75 7% 42% 6% 22% 10% 58% 4% 15%
270 53 6% 36% 5% 18% 8% 50% 3% 12%
-270 -53 36% 18% 50% 12%
P50 110 P50 195 P50 53 P50 241
P80 290 P80 340 P80 147 P80 390
41% 67% 35% 68%
14.3 31.7 19.2 28.8
5.9 21.4 6.8 19.5
#2 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #2)
15-Mar-16
17:00 to 18:00
Ball Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000 10000
Cu
mm
ula
tive P
ass
ing (
%)
Particle Size (um)
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #2)
Ball Mill Cyclone O/F
Vertimill Cyclone O/F
Vertimill Cyclone U/F
Vertimill Product
126
New Afton Mine Tertiary Grinding Circuit - Survey #3
Survey:
Date:
Time:
Sample origin
Net Wet Weight (g)
Net Dry Weight (g)
%Solids
Mesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing
6 3350 0% 100% 0% 100% 0% 100% 0% 100%
8 2360 0% 100% 0% 100% 0% 100% 0% 100%
12 1700 0% 100% 0% 100% 0% 100% 0% 100%
16 1180 0% 100% 0% 100% 0% 100% 0% 99%
20 850 1% 99% 1% 99% 0% 100% 1% 99%
30 600 2% 97% 2% 97% 0% 100% 4% 95%
40 425 6% 91% 7% 90% 0% 100% 10% 85%
50 300 10% 81% 15% 75% 2% 97% 19% 66%
70 212 11% 70% 19% 56% 7% 91% 22% 44%
100 150 10% 60% 16% 40% 11% 80% 16% 28%
140 106 9% 51% 9% 30% 12% 68% 7% 21%
200 75 7% 44% 6% 24% 10% 59% 4% 16%
270 53 6% 38% 4% 20% 8% 51% 3% 13%
-270 -53 38% 20% 51% 13%
P50 102 P50 189 P50 51 P50 237
P80 289 P80 338 P80 150 P80 392
6.1 22.3 7.4 19.9
37% 68% 35% 68%
Vertimill Cyclone O/F Vertimill Cyclone U/F
16.6 32.9 20.9 29.3
#3 Survey
16-Mar-16
12:40 to 13:40
Ball Mill Cyclone O/F Vertimill Product
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #3)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000 10000
Cu
mm
ula
tive P
ass
ing (
%)
Particle Size (um)
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #3)
Ball Mill Cyclone O/F
Vertimill Cyclone O/F
Vertimill Cyclone U/F
Vertimill Product
127
New Afton Mine Tertiary Grinding Circuit - Survey #4
Survey:
Date:
Time:
Sample origin
Net Wet Weight (g)
Net Dry Weight (g)
%Solids
Mesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing
6 3350 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
8 2360 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
12 1700 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
16 1180 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
20 850 0% 99% 1% 99% 1% 99% 0% 100% 1% 99%
30 600 2% 98% 2% 97% 2% 97% 0% 100% 3% 95%
40 425 6% 92% 6% 91% 7% 90% 0% 100% 10% 86%
50 300 11% 81% 14% 77% 16% 75% 1% 99% 24% 62%
70 212 11% 70% 18% 58% 21% 53% 6% 92% 25% 37%
100 150 9% 61% 12% 46% 17% 36% 13% 80% 13% 24%
140 106 8% 52% 6% 40% 9% 27% 11% 69% 7% 17%
200 75 6% 46% 4% 36% 6% 21% 10% 59% 4% 13%
270 53 6% 40% 3% 33% 4% 17% 8% 51% 2% 11%
-270 -53 40% 33% 17% 51% 11%
P50 93 P50 169 P50 200 P50 50 P50 260
P80 287 P80 328 P80 340 P80 152 P80 394
39% 68% 32% 69%
Vertimill Cyclone Feed
30.7
8.4
49%
80.5 35.8 33.7 123.5
31.6 24.5 7.7 85.3
#4 Survey
7-Feb-17
3:20 pm to 4:20 pm
Ball Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #4)
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000 10000
Cu
mm
ula
tive P
ass
ing (
%)
Particle Size (um)
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #4)
Ball Mill Cyclone O/F
Vertimill Cyclone O/F
Vertimill Cyclone U/F
Vertimill Product
Vertimill Cyclone Feed
128
New Afton Mine Tertiary Grinding Circuit - Survey #5
Survey:
Date:
Time:
Sample origin
Net Wet Weight (g)
Net Dry Weight (g)
%Solids
Mesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing
6 3350 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
8 2360 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
12 1700 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
16 1180 0% 100% 0% 100% 0% 100% 0% 100% 0% 100%
20 850 0% 100% 1% 99% 1% 99% 0% 100% 1% 99%
30 600 2% 98% 2% 97% 3% 96% 0% 100% 3% 95%
40 425 5% 92% 6% 91% 9% 87% 0% 100% 9% 86%
50 300 11% 81% 14% 77% 18% 69% 1% 99% 23% 63%
70 212 12% 70% 19% 58% 21% 48% 6% 93% 25% 38%
100 150 10% 60% 13% 45% 15% 33% 13% 81% 14% 24%
140 106 9% 51% 9% 36% 8% 25% 11% 70% 7% 17%
200 75 6% 45% 6% 30% 5% 20% 10% 60% 3% 13%
270 53 6% 39% 4% 26% 3% 16% 8% 52% 2% 11%
-270 -53 39% 26% 16% 52% 11%
P50 98 P50 173 P50 221 P50 48 P50 256
P80 289 P80 324 P80 374 P80 147 P80 391
38% 50% 72% 31% 69%
79.9 44.9 38.3 29.7 65.6
30.3 22.6 27.5 9.3 45.1
#5 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #5)
8-Feb-17
3:10 pm to 4:10 pm
Ball Mill Cyclone O/F Vertimill Cyclone Feed Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000 10000
Cu
mm
ula
tive P
ass
ing (
%)
Particle Size (um)
PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #5)
Ball Mill Cyclone O/F
Vertimill Cyclone O/F
Vertimill Cyclone U/F
Vertimill Product
Vertimill Cyclone Feed
129
Appendix B
B.1 Sub-Appendix
BOND GRINDABILITY TEST
SAG FEED BELT CUT (S#4)
Weight of 700 ml Sample: 1322.2 gram Aperture test Sieve: 212 µm
Bulk Density: 1.89 g/mL Percent Undersize: 15.9%
Cycle Weight of
New Feed
Number of
Revolutions.
Weight
of
Oversize
Weight of Undersize
Feed Discharge Net Product Net / Rev CLR
1 1322.2 100 1012.6 209.7 309.6 99.9 0.999 327
2 309.6 329 911.1 49.1 411.1 362.0 1.101 222
3 411.1 284 938.5 65.2 383.7 318.5 1.122 245
4 383.7 283 931.3 60.8 390.9 330.1 1.168 238
5 390.9 270 940.7 62.0 381.5 319.5 1.182 247
6 381.5 268 942.9 60.5 379.3 318.8 1.187 249
BONDS WORK INDEX FORMULA
Wi = 44.5 / (Pi^0.23 Gpb^0.82 (10/ – 10/ ))
Pi = Sieve Size Tested 212 µm
Gbp = Net undersize produced per revolution of mill 1.179 g/rev.
P = 80% Passing size of test product 140 µm
F = 80% Passing size of test feed 2422 µm
WORK INDEX (Wi)
17.63 kw-hr/ton
19.44 kw-hr/tonne
NB: Gbp = Average of last 3 Net/Rev Cycles
130
Feed Product
Size Cum.
Passing
Cum.
Passing
[mesh] [um] [%] [%]
8 3350 99.9
12 2360 78.7
10 1700 59.0
16 1180 45.6
20 850 36.9
30 600 29.9
40 425 24.1
50 300 19.6
70 212 15.9 100.0
100 150 82.7
150 106 68.0
200 75 57.2
270 53 48.9
400 38 42.1
Passing 80% (microns) 2422.3
0
10
20
30
40
50
60
70
80
90
100
10 100 1000 10000
Cu
m.
perc
en
t p
assin
g,
%
Particle size, microns
Feed
Product
131
B.2 Sub-Appendix
JK DROP WEIGHT TEST
SAG FEED BELT CUT (S#4)
Table B2-1: SAG/Autogenous Mill Parameters from DW Test Results
A b A*b ta
58.2 0.70 40.74 0.29
The t10 versus Ecs relationship for sample SAG Feed Belt Cut is given in Figure B2-1.
Figure B2-1: t10/Ecs Relationship for SAG Feed Belt Cut
SAG Feed Belt Cut has an A*b value of 40.7, which puts this material in the moderate hard range
of resistance to impact breakage. With a ta of 0.29, SAG Feed Belt Cut falls into the hard abrasion
range.
0
10
20
30
40
50
60
70
80
90
100
0 0.5 1 1.5 2 2.5 3 3.5 4
t10 (
%)
Ecs (kWh/t)
SAG Feed Belt Cut
Weighted Fit
63 x 53
45 x 37.5
31.5 x 26.5
22.4 x 19
16 x 13.2
A = 58.2, b = 0.70 and Axb = 40.7 (Wtd Fit)
132
Table B2-2: Crusher Model Parameters for SAG Feed Belt Cut
Size Relative to Initial Size
t75 t50 t25 t4 t2
t10 cumulative percent passing
10.0 2.4 3.1 4.9 25.6 58.2
20.0 4.7 6.1 9.9 48.1 87.3
30.0 7.1 9.3 15.1 67.0 97.2
Table B2-3: Specific Comminution Energy
Initial Particle Size, mm
+13.2, -16.0 +19.0, -22.4 +26.5, -31.5 +37.5, -45.0 +53.0, -63.0
14.53 20.63 28.89 41.08 57.78
t10 Ecs, (kWh/t)
10 0.41 0.34 0.30 0.17 0.16
20 0.88 0.73 0.65 0.40 0.36
30 1.43 1.20 1.05 0.76 0.61
The data in Table 2B indicates that for particles of SAG Feed Belt Cut of up to 63 mm, there is
some increase in impact resistance with decreasing particle size.
133
Figure B2-2: Variation of Impact Resistance with Particle Size - SAG Feed Belt Cut
The data graphed in Figure 2 are the t10 values for up to 5 different particle sizes from SAG Feed
Belt Cut, all broken with the very similar specific comminution energies (0.25 kWh/t, 1.0 kWh/t
and 2.5 kWh/t). The data for SAG Feed Belt Cut partially follow the frequently observed trend of
decreasing slope with decreasing energy (Ecs values).
0
10
20
30
40
50
60
70
80
90
100
10 15 20 25 30 35 40 45 50 55 60
t10 (
%)
Particle Size (mm)
SAG Feed Belt Cut
2.5
1.0
0.25
134
Table B2-4 - Relative Density Measurements for 30 Particles for SAG Feed Belt Cut
2.78 2.75 2.68 2.71 2.85
2.60 2.67 2.73 2.76 2.66
2.70 2.71 2.71 2.73 2.66
2.73 2.75 2.64 2.67 2.82
2.69 2.80 2.70 2.66 2.67
2.76 2.84 2.85 2.85 2.61
Mean 2.72
Standard Deviation
0.07
Maximum
2.85
Minimum 2.60
Figure B2-3: Histogram of the Relative Density Measurements for 30 Particles for SAG Feed Belt Cut
0
5
10
15
20
25
< 2
.2
< 2
.4
< 2
.6
< 2
.8
< 3
.0
< 3
.2
< 3
.4
< 3
.6
< 3
.8
< 4
.0
< 4
.2
< 4
.4
< 4
.6
< 4
.8
< 5
.0
Num
ber
of
Part
icle
s
Relative Density (top of Range)
SAG Feed Belt Cut
135
The SAG Feed Belt Cut data contain no evidence of bimodality in the relative density distribution,
that is, no evidence of a dense component that could concentrate in the mill load and cause power
problems, resulting in a loss of throughput.
136
B.3 Sub-Appendix
HARDGROVE MILL FINE MATERIAL CHARACTERIZATION TEST
VERTIMILL® FEED (S#3)
Table B3-1: Breakage Parameters from HGMFC Test Results
M fmat n SMi150µm
24.3 0.0016 0.71 1.40
The t4 versus fmat·xn·(Ecs-Emin) relationship for Vertimill® feed sample in survey #3 is given in
Figure B3-1.
Figure B3-1: t4/fmat·xn·(Ecs-Emin) relationship for VTM feed (S#3)
0
5
10
15
20
25
0.00 0.50 1.00 1.50 2.00
Bre
akag
e Index, t 4
[%]
fmat.xn.(Ecs-Emin)
New Afton Vertimill® Feed (survey #3) - fmat model
505.0 357.1 252.2 178.3
137
The t4 versus Ecs relationship for single size fraction is given in Figure B3-2.
Figure B3-2: t10/Ecs relationship for VTM feed (S#3)
The t4-tn family curves generated from the test is given in Figure B3-3.
Figure B3-3: t4-tn family curves for VTM feed (S#3)
0
5
10
15
20
25
0.00 5.00 10.00 15.00
Bre
akag
e Index, t 4
[%]
Ecs [kWh/t]
600 x 425 425 x 300 300 x 212 212 x 150
600 x 425 425 x 300 300 x 212 212 x 150
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0.0 5.0 10.0 15.0 20.0 25.0
t n(%
)
t4 (%)
t1.2
t2
t4
t8
t25
138
The particle size distribution and the specific energy results are shown in Figure B3-4.
Figure B3-4: Particle size distribution and specific energy record (S#3)
Enter your data in the blue fields only
Client:
Uni of BC Project Name or Number:
Deposit / Sample Source:
Client Sample Identification:
Size [µm]
No. of revolutions - 40 80 160 320 40 80 160 320 40 80 160 320 40 80 160 320
Time [second] 54 109 220 442 54 109 220 442 54 109 220 442 54 109 220 442
Mass [g] 44.6 44.6 44.6 44.6 44.3 44.3 44.3 44.3 44.6 44.6 44.6 44.6 45.0 45.0 45.0 45.0
Edle Energy [kWh] 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013
Load Energy [kWh] 0.002 0.003 0.007 0.014 0.002 0.003 0.007 0.014 0.002 0.003 0.007 0.014 0.002 0.003 0.007 0.014
Net Energy [kWh] 6.52E-05 1.07E-04 2.57E-04 5.07E-04 6.62E-05 1.22E-04 2.86E-04 5.35E-04 7.48E-05 1.45E-04 2.65E-04 5.82E-04 8.75E-05 1.36E-04 2.86E-04 5.95E-04
Spec. Energy [kWh/t] 1.46 2.40 5.76 11.37 1.50 2.76 6.45 12.09 1.68 3.26 5.94 13.06 1.94 3.02 6.35 13.21
600 x 425 Geo-mean 505
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
600 30 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
425 40 67.1 78% 22% 57.2 67% 33% 44.3 53% 47% 32.1 38% 62%
300 50 10.3 12% 10% 14.6 17% 16% 18.2 22% 25% 20.4 24% 37%
212 70 3.0 3% 7% 4.5 5% 11% 6.0 7% 18% 7.3 9% 28%
150 100 1.4 2% 5% 2.5 3% 8% 3.4 4% 14% 4.3 5% 23%
106 140 0.9 1% 4% 1.6 2% 6% 2.4 3% 11% 3.1 4% 20%
75 200 0.6 1% 3% 1.1 1% 5% 1.7 2% 9% 2.4 3% 17%
53 270 0.3 0% 3% 0.7 1% 4% 1.3 2% 8% 1.8 2% 15%
38 400 0.2 0% 3% 0.5 1% 4% 0.9 1% 7% 1.6 2% 13%
20 635 0.2 0% 2% 0.7 1% 3% 1.4 2% 5% 2.5 3% 10%
Pan Pan 2.1 2% 2.3 3% 4.1 5% 8.1 10%
86.1 85.7 83.7 83.6
425 x 300 Geo-mean 357
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
425 40 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
300 50 67.9 81% 19% 59.7 72% 28% 49.5 60% 40% 39.7 48% 52%
212 70 9.4 11% 8% 12.9 15% 13% 15.9 19% 20% 18.2 22% 29%
150 100 2.0 2% 5% 3.2 4% 9% 4.2 5% 15% 5.2 6% 23%
106 140 1.2 1% 4% 1.9 2% 7% 2.7 3% 12% 3.2 4% 19%
75 200 0.7 1% 3% 1.2 1% 5% 1.7 2% 10% 2.4 3% 16%
53 270 0.5 1% 2% 0.9 1% 4% 1.3 2% 8% 1.8 2% 14%
38 400 0.3 0% 2% 0.6 1% 4% 1.0 1% 7% 1.5 2% 12%
20 635 0.4 0% 2% 0.8 1% 3% 1.5 2% 5% 2.3 3% 9%
Pan Pan 1.3 2% 2.2 3% 4.2 5% 7.7 9%
83.7 83.4 82.0 82.0
300 x 212 Geo-mean 252
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
300 50 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
212 70 69.8 81% 19% 61.8 75% 25% 52.6 64% 36% 45.3 54% 46%
150 100 10.2 12% 7% 12.1 15% 10% 15.0 18% 18% 17.7 21% 25%
106 140 1.9 2% 5% 2.2 3% 7% 3.7 4% 13% 4.5 5% 20%
75 200 1.0 1% 4% 1.3 2% 6% 2.3 3% 11% 2.8 3% 17%
53 270 0.6 1% 3% 0.8 1% 5% 1.6 2% 9% 2.0 2% 14%
38 400 0.4 0% 3% 0.6 1% 4% 1.1 1% 7% 1.6 2% 12%
20 635 0.5 1% 2% 0.8 1% 3% 1.6 2% 5% 2.4 3% 9%
Pan Pan 1.8 2% 2.6 3% 4.5 5% 7.9 9%
86.2 82.2 82.4 84.2
212 x 150 Geo-mean 178
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
212 70 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
150 100 66.9 81% 19% 60.0 72% 28% 55.3 66% 34% 49.0 59% 41%
106 140 10.1 12% 7% 13.8 17% 11% 14.9 18% 16% 17.3 21% 20%
75 200 1.6 2% 5% 2.8 3% 8% 3.4 4% 12% 3.7 4% 16%
53 270 0.9 1% 4% 1.5 2% 6% 1.9 2% 10% 2.1 3% 13%
38 400 0.5 1% 3% 1.0 1% 5% 1.3 2% 8% 1.5 2% 12%
20 635 0.6 1% 2% 1.2 1% 3% 1.9 2% 6% 2.1 3% 9%
Pan Pan 1.9 2% 2.9 3% 4.9 6% 7.6 9%
82.5 83.2 83.6 83.3
Size Distribution
After Wet-Screen Sample Weights (g) 80.6 80.3 78.7 75.7
After Wet-Screen Sample Weights (g) 82.4 81.2 77.8 74.3
13.21
Original Sample Weights (g) 82.5 83.2 83.6 83.3
84.2
Totals
Totals
Specific Energy (kWh/t)
Totals
Vertimill Model Development
New Afton Mine
Cu-Gold
NA S#3 VTM CYC U/F
Specific Energy (kWh/t) 1.94 3.02
Original Sample Weights (g) 86.2 82.2
2.40
425 x 300
6.35
82.4
6.45
1.68 3.26 5.94 13.06
After Wet-Screen Sample Weights (g) 84.4 79.6 77.9 76.3
Size Distribution
Original Sample Weights (g) 83.7 83.4 82.0 82.0
UBC Hardgrove Mill Fine Material Charaterisation TestTest Result Entry
600 x 425
12.092.76Specific Energy (kWh/t) 1.50
300 x 212
Totals
After Wet-Screen Sample Weights (g) 84.0 83.4 79.6 75.5
Size Distribution
Size Distribution
212 x 150
Specific Energy (kWh/t) 5.76 11.37
85.7 83.7 83.6Original Sample Weights (g)
1.46
86.1
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
assi
ng
(%)
Particle Size (µm)
Sizings from breakage of 600 x 425 fraction
1.46
2.40
5.76
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
assi
ng
(%)
Particle Size (µm)
Sizings from breakage of 425 x 300 fraction
1.50
2.76
6.45
12.09
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
assi
ng
(%)
Particle Size (µm)
Sizings from breakage of 300 x 212 fraction
1.68
3.26
5.94
13.06
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
assi
ng
(%)
Particle Size (µm)
Sizings from breakage of 212 x 150 fraction
1.94
3.02
6.35
13.21
139
HARDGROVE MILL FINE MATERIAL CHARACTERIZATION TEST
VERTIMILL® FEED (S#4)
Table B3-2: Breakage Parameters from HGMFC Test Results
M fmat n SMi150µm
27.6 0.0010 0.75 1.19
The t4 versus fmat·xn·Ecs relationship for Vertimill®® feed sample in survey #4 is given in Figure
B3-5.
Figure B3-5: t4/fmat·xn·(Ecs-Emin) relationship for VTM feed (S#4)
0
5
10
15
20
25
0.00 0.50 1.00 1.50 2.00
Bre
akag
e Index, t 4
[%]
fmat.xn.(Ecs-Emin)
New Afton Vertimill® Feed (survey #4) - fmat model
505.0 357.1 252.2 178.3
140
The t4 versus Ecs relationship for single size fraction is given in Figure B3-6.
Figure B3-6: t10/Ecs relationship for VTM feed (S#4)
The t4-tn family curves generated from the test is given in Figure B3-7.
Figure B3-7: t4-tn family curves for VTM feed (S#4)
0
5
10
15
20
25
0.00 5.00 10.00 15.00 20.00
Bre
akage I
nd
ex, t 4
[%]
Ecs [kWh/t]
600 x 425 425 x 300 300 x 212 212 x 150
505.0 357.1 252.2 178.3
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
0.0 5.0 10.0 15.0 20.0 25.0
t n(%
)
t4 (%)
t1.2
t2
t4
t8
t25
141
The particle size distribution and the specific energy consumption is shown in Figure B3-8.
Figure B3-8: Particle size distribution and specific energy record (S#4)
Enter your data in the blue fields only
Client:
Uni of BC Project Name or Number:
Deposit / Sample Source:
Client Sample Identification:
Size [µm]
No. of revolutions - 20 40 80 160 20 40 80 160 20 40 80 160 20 40 80 160
Time [seconds] 53 109 220 442 53 110 220 443 54 110 220 443 54 109 220 442
Mass [g] 44.6 44.6 44.6 44.6 44.5 44.5 44.5 44.5 44.4 44.4 44.4 44.4 44.9 44.9 44.9 44.9
Edle Energy [kWh] 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.013
Load Energy [kWh] 0.002 0.003 0.007 0.013 0.002 0.003 0.007 0.014 0.002 0.003 0.007 0.014 0.002 0.003 0.007 0.014
Net Energy [kWh] 6.55E-05 1.32E-04 2.67E-04 5.03E-04 6.82E-05 1.33E-04 2.87E-04 5.62E-04 7.13E-05 1.59E-04 2.84E-04 6.02E-04 8.00E-05 1.72E-04 3.45E-04 6.90E-04
Spec. Energy [kWh/t] 1.47 2.96 5.98 11.28 1.53 3.00 6.46 12.64 1.61 3.58 6.39 13.57 1.78 3.84 7.68 15.36
600 x 425 Geo-mean 505
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
600 30 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
425 40 64.3 78% 22% 57.1 67% 33% 44.6 53% 47% 32.5 39% 61%
300 50 10.3 12% 10% 14.2 17% 16% 18.4 22% 25% 19.6 24% 37%
212 70 3.2 4% 6% 4.4 5% 11% 5.9 7% 18% 7.1 9% 29%
150 100 1.5 2% 4% 2.4 3% 8% 3.3 4% 14% 4.2 5% 23%
106 140 0.9 1% 3% 1.5 2% 6% 2.2 3% 11% 3.0 4% 20%
75 200 0.6 1% 2% 1.0 1% 5% 1.6 2% 10% 2.4 3% 17%
53 270 0.4 0% 2% 0.7 1% 4% 1.2 1% 8% 1.8 2% 15%
38 400 0.3 0% 2% 0.5 1% 3% 0.9 1% 7% 1.6 2% 13%
20 635 0.3 0% 1% 0.6 1% 3% 1.3 2% 5% 2.4 3% 10%
Pan Pan 1.0 1% 2.3 3% 4.6 5% 8.2 10%
82.8 84.7 84 82.8
425 x 300 Geo-mean 357
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
425 40 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
300 50 68.0 81% 19% 59.0 71% 29% 49.9 60% 40% 40.7 49% 51%
212 70 9.6 11% 7% 13.2 16% 13% 16.7 20% 20% 17.9 22% 29%
150 100 2.0 2% 5% 3.1 4% 9% 4.3 5% 15% 5.0 6% 23%
106 140 1.0 1% 4% 1.8 2% 7% 2.6 3% 12% 3.1 4% 19%
75 200 0.7 1% 3% 1.2 1% 5% 1.8 2% 9% 2.3 3% 16%
53 270 0.4 0% 2% 0.8 1% 4% 1.3 2% 8% 1.7 2% 14%
38 400 0.2 0% 2% 0.6 1% 4% 1.0 1% 7% 1.4 2% 13%
20 635 0.2 0% 2% 0.7 1% 3% 1.3 2% 5% 2.3 3% 10%
Pan Pan 1.6 2% 2.4 3% 4.3 5% 8.0 10%
83.7 82.8 83.2 82.4
300 x 212 Geo-mean 252
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
300 50 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
212 70 68.7 82% 18% 62.2 75% 25% 54.9 66% 34% 46.7 56% 44%
150 100 8.8 11% 7% 11.1 13% 11% 14.2 17% 17% 15.5 19% 25%
106 140 1.7 2% 5% 2.6 3% 8% 3.5 4% 13% 4.2 5% 20%
75 200 0.9 1% 4% 1.5 2% 6% 2.2 3% 10% 2.7 3% 17%
53 270 0.6 1% 3% 1.0 1% 5% 1.5 2% 8% 1.9 2% 14%
38 400 0.4 0% 3% 0.7 1% 4% 1.1 1% 7% 1.5 2% 13%
20 635 0.4 0% 2% 0.9 1% 3% 1.6 2% 5% 2.4 3% 10%
Pan Pan 2.0 2% 2.7 3% 4.0 5% 8.1 10%
83.5 82.7 83.0 83.0
212 x 150 Geo-mean 178
Size (µm) Tyler MeshWeight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
Weight Ret
(g)% Ret.
Cum. %
Pass.
212 70 0.0 0% 100% 0.0 0% 100% 0.0 0% 100% 0.0 0% 100%
150 100 69.0 84% 16% 61.8 75% 25% 59.0 70% 30% 50.4 60% 40%
106 140 8.2 10% 6% 12.1 15% 10% 12.6 15% 15% 16.0 19% 21%
75 200 1.6 2% 4% 2.4 3% 8% 2.9 3% 11% 3.8 5% 16%
53 270 0.8 1% 3% 1.3 2% 6% 1.7 2% 9% 2.1 3% 14%
38 400 0.5 1% 3% 0.9 1% 5% 1.1 1% 8% 1.6 2% 12%
20 635 0.6 1% 2% 1.0 1% 4% 1.6 2% 6% 2.0 2% 10%
Pan Pan 1.7 2% 3.0 4% 5.1 6% 8.0 10%
82.4 82.5 84.0 83.9
Size Distribution
212 x 150
Specific Energy (kWh/t) 5.98 11.28
84.7 84.0 82.8Original Sample Weights (g)
1.47
82.8
82.4
UBC Hardgrove Mill Fine Material Charaterisation TestTest Result Entry
600 x 425
12.643.00Specific Energy (kWh/t) 1.53
300 x 212
Totals
After Wet-Screen Sample Weights (g) 81.8 82.4 79.4 74.6
Size Distribution
Size Distribution
Original Sample Weights (g) 83.7 82.8 83.2
1.61 3.58 6.39 13.57
After Wet-Screen Sample Weights (g) 81.5 80.0 79.0 74.9
Totals
Vertimill Model Development
New Afton Mine
Cu-Gold
NA S#4 VTM CYC U/F
Specific Energy (kWh/t) 1.78 3.84
Original Sample Weights (g) 83.5 82.7
2.96
425 x 300
7.68
83.0
6.46
75.9
After Wet-Screen Sample Weights (g) 82.1 80.4 78.9 74.4
15.36
Original Sample Weights (g) 82.4 82.5 84.0 83.9
83.0
Totals
Totals
Specific Energy (kWh/t)
Size Distribution
After Wet-Screen Sample Weights (g) 80.7 79.5 78.9
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
ass
ing (
%)
Particle Size (µm)
Sizings from breakage of 600 x 425 fraction
1.47
2.96
5.98
11.28
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
ass
ing (
%)
Particle Size (µm)
Sizings from breakage of 425 x 300 fraction
1.53
3.00
6.46
12.64
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
ass
ing (
%)
Particle Size (µm)
Sizings from breakage of 300 x 212 fraction
1.61
3.58
6.39
13.57
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
10 100 1000
Cu
m. P
ass
ing (
%)
Particle Size (µm)
Sizings from breakage of 212 x 150 fraction
1.78
3.84
7.68
15.36
142
Appendix C
The modelling & simulation tool is detailed in this section.
The main control panel of the simulation tool is shown in Figure C-1.
Figure C-1: control panel
Model M 27.6408 d50c 250 t1.2 0.0088 -0.3538 6.3051
fmat 0.0010 α 0.49 t2 0.0019 -0.0671 2.0855
Chamber diameter (inner) 6.10 m n 0.7476 C 68% t8 -0.0005 0.0172 0.5987
Chamber height 5.00 m t25 -0.0004 0.0152 0.2955
Screw diameter 4.83 m
Wall/Screw Gap 0.637 m
Screw speed 12.0 rpm Size VTM Feed VTM Product VTM Product
Screw tip speed 3.0 m/s Deviation (µm) (measured) (measured) (simulated)
Balls filling 52.0 % 0.00 3350 100.00 100 100
Ball diameter 0.75 inch 0.00 2360 100.00 100 100
Ball density 7.85 kg/m3 0.00 1700 99.79 100 100
0.00 1180 99.60 100 100
0.00 850 98.59 99 99
New Feed (Dry) 953 t/h 0.00 600 95.30 97 97
Moisture Content 3.6 % 0.82 425 85.80 90 91
New Feed (Wet) 732 t/h 0.00 300 62.04 75 75
Circulating Load 135% 0.60 212 36.97 53 53
Solids Density (SG) 2.75 t/m3 0.44 150 23.71 36 37
Water Density (SG) 1 t/m3 0.00 106 16.71 27 27
Mill Power Draw 2171 kWh 0.00 75 13.16 21 21
Energy Efficiency 90% 0.01 53 10.81 17 17
Specific Energy 2.28 kWh/t 1.8792 0 0 0 0
SSE75 28.49 kWh/t P80 (µm) 394 340 338
0.9999 P50 (µm) 260 200 202
P75 (%) 13 21
Operating Condition
Classification Model ParameterBreakage Model Parameter Appearance FunctionVertiMill
VTM-3000-WB
Dimension
Operating parameters Particle Size Distribution
0
10
20
30
40
50
60
70
80
90
100
10 100 1000 10000
Cum
. P
ass
ing
(%
)
Particle size (µm)
VTM Product (simulated)
VTM Feed
VTM Product
143
The tower mill power model panel is shown in Figure C-2.
Figure C-2: Power model panel
The selection function panel is shown in Figure C-3.
Figure C-3: selection function panel
Pnet Pgross h DG H S N Jb K
kW kW % m m m rps %
1954 2171 0.90 0.637 5.00 4.83 0.2 52 312
Pnet = h Pgross = K (H*Jb)0.884
S2.232
DG N1.232
Where:
Pgross kW gross power draw of mill = Pnet/h
h % electrical and power transmission efficiencty
DG m effective gap between the mill wall and the screw
H m effective mill charge chamber height
N rps rotation speed of the screw
S m rotating screw diameter
Jb %
K - power constant
Tower Mill Power Estimation Model (Nitta)
ball volumetric fractional mill filling (including the balls and the interstitial voids in
between such balls)
Size Geo-mean Spline
(µm) (µm) Si 0
3350 Size (µm) Parameters 0
2360 2812 0.50 2003 1.6 0 0
1700 2003 1.61 505 2.1 0
1180 1416 2.54 126 0.8 0
850 1001 2.76
600 714 2.53
425 505 2.10
300 357 1.66
212 252 1.29
150 178 1.01
106 126 0.82
75 89 0.68
53 63 0.58
0 27 0.45
Spline Regression
0.10
1.00
10.00
10 100 1000 10000
Particle size (µm)
Si
Spline Regression
Spline Si
Solver Si(Spline)
144
The classification panel is shown in Figure C-4.
Figure C-4: classification function panel
The transfer matrix panel is shown in Figure C-5.
Figure C-5: transfer matrix panel
d50c 249.85
α 0.49
C 68%
Size Geo-mean Classifier Efficiency
(µm) (µm) C I-C
3350
2360 2812 0.0017 0.9983
1700 2003 0.0084 0.9916
1180 1416 0.0271 0.9729
850 1001 0.0634 0.9366
600 714 0.1167 0.8833
425 505 0.1858 0.8142
300 357 0.2626 0.7374
212 252 0.3402 0.6598
150 178 0.4119 0.5881
106 126 0.4743 0.5257
75 89 0.5258 0.4742
53 63 0.5667 0.4333
0 27 0.6313 0.3687
Classification Model Parameter
0%
10%
20%
30%
40%
50%
60%
70%
10 100 1000 10000
Cla
ssif
icati
on
eff
icie
ncy
Particle size (µm)
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1700 0.16 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
1180 0.08 0.20 0.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
850 0.02 0.08 0.19 0.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
600 0.02 0.04 0.10 0.19 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
425 0.01 0.03 0.05 0.09 0.18 0.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00
300 0.01 0.02 0.03 0.04 0.08 0.17 0.69 0.00 0.00 0.00 0.00 0.00 0.00
212 0.01 0.02 0.03 0.03 0.03 0.07 0.15 0.77 0.00 0.00 0.00 0.00 0.00
150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.84 0.00 0.00 0.00 0.00
106 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.05 0.08 0.89 0.00 0.00 0.00
75 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.06 0.93 0.00 0.00
53 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.00
0 0.03 0.07 0.09 0.09 0.09 0.07 0.06 0.04 0.03 0.03 0.03 0.05 1.00
1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000
145
The calculation matrixes are listed below.
C·mij matrix
I-C·mij matrix
[I-C·mij]-1 matrix
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.001063534 0 0 0 0 0 0 0 0 0 0 0 0
1700 0.001311353 0.003989 0 0 0 0 0 0 0 0 0 0 0
1180 0.002077449 0.005366 0.011969 0 0 0 0 0 0 0 0 0 0
850 0.001555895 0.00539 0.012101 0.030008 0 0 0 0 0 0 0 0 0
600 0.001812969 0.00479 0.011806 0.02247 0.063696 0 0 0 0 0 0 0 0
425 0.002532626 0.004798 0.008578 0.017131 0.032752 0.113441 0 0 0 0 0 0 0
300 0.003452377 0.006127 0.007899 0.01091 0.021482 0.044454 0.180656 0 0 0 0 0 0
212 0.003759012 0.007747 0.008895 0.008963 0.011391 0.02505 0.050218 0.261723 0 0 0 0 0
150 0.003413602 0.007977 0.010219 0.009655 0.008599 0.011226 0.025713 0.047206 0.345791 0 0 0 0
106 0.002837448 0.006961 0.009947 0.010902 0.009141 0.00783 0.010283 0.022866 0.039003 0.422897 0 0 0
75 0.002215007 0.005534 0.008264 0.010268 0.010054 0.007849 0.006669 0.008412 0.017933 0.029574 0.487395 0 0
53 0.001682838 0.004229 0.006427 0.008384 0.009312 0.008227 0.006281 0.005256 0.00635 0.013272 0.021735 0.538537 0
0 0.020282774 0.047077 0.057649 0.059088 0.05494 0.046226 0.035738 0.02686 0.020795 0.018083 0.021889 0.031362 0.631281
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.998936466 0 0 0 0 0 0 0 0 0 0 0 0
1700 -0.001311353 0.996011 0 0 0 0 0 0 0 0 0 0 0
1180 -0.002077449 -0.00537 0.988031 0 0 0 0 0 0 0 0 0 0
850 -0.001555895 -0.00539 -0.0121 0.969992 0 0 0 0 0 0 0 0 0
600 -0.001812969 -0.00479 -0.01181 -0.02247 0.936304 0 0 0 0 0 0 0 0
425 -0.002532626 -0.0048 -0.00858 -0.01713 -0.03275 0.886559 0 0 0 0 0 0 0
300 -0.003452377 -0.00613 -0.0079 -0.01091 -0.02148 -0.04445 0.819344 0 0 0 0 0 0
212 -0.003759012 -0.00775 -0.00889 -0.00896 -0.01139 -0.02505 -0.05022 0.738277 0 0 0 0 0
150 -0.003413602 -0.00798 -0.01022 -0.00965 -0.0086 -0.01123 -0.02571 -0.04721 0.654209 0 0 0 0
106 -0.002837448 -0.00696 -0.00995 -0.0109 -0.00914 -0.00783 -0.01028 -0.02287 -0.039 0.577103 0 0 0
75 -0.002215007 -0.00553 -0.00826 -0.01027 -0.01005 -0.00785 -0.00667 -0.00841 -0.01793 -0.02957 0.512605 0 0
53 -0.001682838 -0.00423 -0.00643 -0.00838 -0.00931 -0.00823 -0.00628 -0.00526 -0.00635 -0.01327 -0.02174 0.461463 0
0 -0.020282774 -0.04708 -0.05765 -0.05909 -0.05494 -0.04623 -0.03574 -0.02686 -0.02079 -0.01808 -0.02189 -0.03136 0.368719
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 1.001064667 0 0 0 0 0 0 0 0 0 0 0 0
1700 0.001318007 1.004005 0 0 0 0 0 0 0 0 0 0 0
1180 0.002112011 0.005453 1.012114 0 0 0 0 0 0 0 0 0 0
850 0.001639408 0.005647 0.012627 1.030936 0 0 0 0 0 0 0 0 0
600 0.002011084 0.005341 0.013065 0.024741 1.068029 0 0 0 0 0 0 0 0
425 0.002993276 0.005793 0.010519 0.020835 0.039456 1.127957 0 0 0 0 0 0 0
300 0.00448525 0.00809 0.010839 0.015506 0.030143 0.061198 1.220489 0 0 0 0 0 0
212 0.005593883 0.0115 0.013643 0.014659 0.019868 0.042435 0.083018 1.354505 0 0 0 0 0
150 0.005954442 0.013728 0.017758 0.017565 0.017333 0.024822 0.05396 0.097738 1.528564 0 0 0 0
106 0.005781662 0.014001 0.019967 0.022195 0.019948 0.019752 0.028683 0.060273 0.103305 1.732794 0 0 0
75 0.005184105 0.012816 0.019126 0.023792 0.024027 0.020772 0.020783 0.029126 0.059436 0.099971 1.950821 0 0
53 0.004433009 0.011028 0.0168 0.02198 0.024835 0.023314 0.020104 0.019878 0.026804 0.054545 0.091885 2.167021 0
0 0.05864989 0.136251 0.170121 0.179441 0.173948 0.15602 0.131737 0.110561 0.097081 0.095553 0.123627 0.184322 2.712094
146
[I-C]·mij matrix
[I-C]·mij·[I-C·mij]-1 matrix
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.63387202 0 0 0 0 0 0 0 0 0 0 0 0
1700 0.155643942 0.473502 0 0 0 0 0 0 0 0 0 0 0
1180 0.074562047 0.192605 0.429566 0 0 0 0 0 0 0 0 0 0
850 0.022970978 0.079571 0.178658 0.443031 0 0 0 0 0 0 0 0 0
600 0.01371869 0.036247 0.089337 0.170032 0.481987 0 0 0 0 0 0 0 0
425 0.011100583 0.021031 0.037598 0.075087 0.143551 0.497217 0 0 0 0 0 0 0
300 0.009693424 0.017202 0.022179 0.030632 0.060317 0.124816 0.507238 0 0 0 0 0 0
212 0.00729092 0.015027 0.017252 0.017384 0.022093 0.048587 0.097402 0.507634 0 0 0 0 0
150 0.004873927 0.01139 0.01459 0.013785 0.012277 0.016028 0.036713 0.067401 0.493719 0 0 0 0
106 0.003145381 0.007716 0.011026 0.012086 0.010133 0.008679 0.011399 0.025347 0.043235 0.468792 0 0 0
75 0.001997688 0.004991 0.007453 0.009261 0.009067 0.007079 0.006014 0.007587 0.016174 0.026672 0.439576 0 0
53 0.00128675 0.003234 0.004915 0.006411 0.00712 0.006291 0.004803 0.004019 0.004855 0.010148 0.016619 0.411782 0
0 0.011846766 0.027497 0.033671 0.034512 0.032089 0.027 0.020874 0.015689 0.012146 0.010562 0.012785 0.018318 0.368719
Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 0
2360 0.634546882 0 0 0 0 0 0 0 0 0 0 0 0
1700 0.156433729 0.475398 0 0 0 0 0 0 0 0 0 0 0
1180 0.075802534 0.195719 0.43477 0 0 0 0 0 0 0 0 0 0
850 0.024203947 0.083366 0.186416 0.456737 0 0 0 0 0 0 0 0 0
600 0.015217817 0.040413 0.098864 0.187217 0.514776 0 0 0 0 0 0 0 0
425 0.013119626 0.025391 0.046107 0.091321 0.172935 0.560839 0 0 0 0 0 0 0
300 0.012593478 0.022714 0.030434 0.043537 0.084634 0.171829 0.619079 0 0 0 0 0 0
212 0.010849807 0.022304 0.026462 0.028433 0.038535 0.082307 0.161021 0.687592 0 0 0 0 0
150 0.008501728 0.019601 0.025355 0.025079 0.024748 0.035441 0.077044 0.13955 0.754681 0 0 0 0
106 0.006409115 0.015521 0.022134 0.024604 0.022113 0.021896 0.031796 0.066814 0.114517 0.81232 0 0 0
75 0.004675481 0.011559 0.017249 0.021458 0.02167 0.018734 0.018744 0.026268 0.053604 0.090162 0.857534 0 0
53 0.003389617 0.008432 0.012846 0.016807 0.01899 0.017826 0.015372 0.015199 0.020495 0.041707 0.070258 0.892341 0
0 0.034256238 0.079581 0.099364 0.104808 0.1016 0.091128 0.076945 0.064576 0.056703 0.055811 0.072208 0.107659 1
