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Development of a tower mill model using hardgrove mill tests Huang, Monong 2018

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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′ ∙ (D3+ 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 ∙ Ds3.057 ∙ 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 ∙𝑑𝑚2∙𝑡𝑎𝑛(𝛼)+𝜇1−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 ∙𝑢𝑦= 𝜇 ∙𝜔∙𝑟𝑦                                     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 ∙𝑟2𝑦= 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 millFeedSifi piBreakage inBreakage 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−1𝑗=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[𝐻𝑃]                                       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−1𝑗=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 =𝑝𝑖𝑑𝑖                              Equation 2-19  The balance equation can be re-written as 𝑝𝑖 = 𝑓𝑖 − (𝑟𝑖𝑑𝑖)𝑝𝑖 + ∑ 𝑎𝑖,𝑗(𝑟𝑖𝑑𝑖)𝑝𝑖𝑖−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 (𝑑𝑖𝑑1) + 𝜁2 [ln (𝑑𝑖𝑑1)]2}           Equation 2-21 Where 𝑆𝑖𝐸: energy specific breakage rate for size range i 𝑑𝑖𝑑1: the dimensionless particle size (usually normalized at 1 mm) 𝑆1𝐸 , 𝜁1, 𝜁2 : model parameters 𝑆𝑖𝐸 = 𝑆1𝐸 (𝑑𝑖𝑑1)𝛼 11+(𝑑𝑖𝜇)Λ                          Equation 2-22 Where 𝑆𝑖𝐸: energy specific breakage rate for size range i 𝑑𝑖𝑑1: 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−1𝑥𝑗)𝛾 + (1 − 𝜙)(𝑥𝑖−1𝑥𝑗)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 =44.5𝑃10.23×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 =𝑡𝑚× 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 𝑑𝑡𝑚                              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,𝐻10√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∙𝜔30[𝑇(𝑡)−𝑇0]𝑑𝑡𝜏03600∙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 hp18'Ø x 32' Ball Mill7,000 hp28'Ø x 13' SAG 7,000 hpRaptor XL600Flash Flotation cellSecondaryCyclopacTertiaryCyclopacSecondaryPumpboxTertiaryPumpboxRougher 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 pumpHydrocycloneVTM-3000-WBBall MillHydrocycloneSumpVibrationScreenSAG MillPebble CrusherSAG Feed BeltStockpileFlash FlotationBM U/FBM O/FVTM O/FVTM U/FVTM ProductVTM Cyc. FeedBM Cyc. FeedBM ProductCoarse TailFlash Flot. Fine TailFlash Flot. Conc.SAG Fresh FeedPebble ProductScreen U/SPebble FeedSAG Product1234567891012141311 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. SumpTertiary cyclone feed pumpHydrocycloneVTM-3000-WBVTM CYC O/FVTM CYC U/FVTM ProductVTM CYC FeedBM CYC O/F12345 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 0.020.040.060.080.0100.010 100 1000 10000Cumulative Percent PassingParticle Size (µm)Cumulative Percent Passing Vs. Particle Size (µm)Jar Mill Feed12362   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).   10.0100.01000.00.0 0.5 1.0 1.5 2.0 2.5 3.0Eighty Percent Passing Size (μm)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 =𝟒𝟒.𝟓𝑷𝟏𝟎.𝟐𝟑×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 FeedNo-Load Test(20, 40, 80, 160)Size Fraction600 x 425Size Fraction425 x 300Size Fraction300 x 212Size Fraction212 x 150Load Test(20, 40, 80, 160)Bulk Density Test & SplitScreen & SplitPSD AnalysisSame 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 overflowSumpTertiary cyclone feed pumpCyclone underflowCyclone overflowVertimill dischargeHydrocycloneVTM-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: VertimillmijInternal ClassificationCfi 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−1𝑒𝛼𝑑𝑖 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 testBreakage model parametersM, fmat, n DCS Vertimill Power DrawOperating ConditionMean specific energyS.E.Size specific energy- Selection functiont4-tn family curvesClassification efficiencyd50c, C, αEstimated Vertimill product PSDPi=[I-C]· mij· [I-C· mij]-1· fiBreakage modelt4i=M· (1-exp(-fmat· xn· Ei)Measured Vertimill product PSD from circuit surveyInitial guess on selection function parameters () & classification parameters (d50c, C, α)Check the difference < convergenceBreakage model parametersM, fmat, n Fitted selection function & classification functiont4-tn family curvesNew Operating ConditionFeed size distributionfiFeed size distributionfiModified Hardgrove mill fine material testSimulate Vertimill product PSDNitta Vertimill Power ModelGrind product simulationModel 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%    0.101.0010.0010 100 1000 10000SiParticle size (µm)Spline SiSpline Regression97  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 10000Classification efficiencyParticle 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 02360 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001700 0.16 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001180 0.08 0.20 0.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00850 0.02 0.08 0.19 0.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00600 0.02 0.04 0.10 0.19 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00425 0.01 0.03 0.05 0.09 0.18 0.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00300 0.01 0.02 0.03 0.04 0.08 0.17 0.69 0.00 0.00 0.00 0.00 0.00 0.00212 0.01 0.02 0.03 0.03 0.03 0.07 0.15 0.77 0.00 0.00 0.00 0.00 0.00150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.84 0.00 0.00 0.00 0.00106 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.05 0.08 0.89 0.00 0.00 0.0075 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.06 0.93 0.00 0.0053 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.000 0.03 0.07 0.09 0.09 0.09 0.07 0.06 0.04 0.03 0.03 0.03 0.05 1.0099   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 010203040506070809010010 100 1000 10000Cum. Passing (%)Particle size (µm)VTM Product (simulated)VTM FeedVTM Product100  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 02360 0.67 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001700 0.15 0.52 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001180 0.07 0.20 0.50 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00850 0.02 0.08 0.18 0.51 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00600 0.01 0.04 0.09 0.19 0.57 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00425 0.01 0.02 0.04 0.09 0.18 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00300 0.01 0.02 0.02 0.04 0.08 0.17 0.71 0.00 0.00 0.00 0.00 0.00 0.00212 0.01 0.02 0.02 0.02 0.03 0.07 0.14 0.79 0.00 0.00 0.00 0.00 0.00150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.85 0.00 0.00 0.00 0.00106 0.00 0.01 0.02 0.02 0.02 0.02 0.02 0.04 0.08 0.90 0.00 0.00 0.0075 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.01 0.03 0.05 0.93 0.00 0.0053 0.00 0.01 0.01 0.02 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.000 0.03 0.05 0.07 0.07 0.07 0.06 0.05 0.04 0.03 0.03 0.03 0.05 1.00104  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 010203040506070809010010 100 1000 10000Cum. Passing (%)Particle size (µm)VTM Product (simulated)VTM FeedVTM Product105  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. 10001500200025003000Vertimill® Power draw, kWVertimill® Power Draw1000-1500 1500-2000 2000-2500 2500-3000108   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 1.001.502.002.503.00Specific energy, kWh/tSpecific Energy, kWh/t1.00-1.50 1.50-2.00 2.00-2.50 2.50-3.00109  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. 26.026.527.027.528.028.529.0SSE75, kWh/tSize (75µm) Specific Energy, kWh/t26.0-26.5 26.5-27.0 27.0-27.5 27.5-28.0 28.0-28.5 28.5-29.0110  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 =𝐹80𝑃80                          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 320325330335340345350Vertimill® product P80, µmVertimill® Product P80320-325 325-330 330-335 335-340 340-345 345-350111  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.  1.121.141.161.181.20Size Reductoin RatioSize Reduction Ratio1.12-1.14 1.14-1.16 1.16-1.18 1.18-1.20 1.20-1.21112  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 test1. Circuit Survey• Stream Sampling• DCS data collection• Machine geometry & operating conditions3. Ore breakage modelCircuit condition• Circuit throughput• Mill power draw• Operating conditions4. Machine and Condition Model• Size specific energy level model• Internal Classification model5. Tower mill model6. 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. 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Oxford, UK: Elsevier.  122  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 SampleSample Air DriedScreen at 31.5 mmCoarse Sizing+ 63 mm+ 50 mm+ 45 mm+ 31.5 mm+ 31.5 mmSizing+ 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 mmFine 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 µmSplit SplitBBWI~ 60 kgDWTBBWIBBWIDWTDWTLeft over+31.5 mmLeft OverLeft over+3.35 mm- 31.5 mmSplitRepresentative SampleLeft OverLeft OverLeft 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 SampleWeight the wet materialDry and weightSplitParticle 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 originNet Wet Weight (g)Net Dry Weight (g)%SolidsMesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing6 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 238P80 289 P80 341 P80 155 P80 38742% 68% 36% 68%13.1 32.0 23.9 28.25.5 21.7 8.5 19.3#1 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #1)15-Mar-1615:15 to 16:15Ball Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F0%10%20%30%40%50%60%70%80%90%100%10 100 1000 10000Cummulative Passing (%)Particle Size (um)PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #1)Ball Mill Cyclone O/FVertimill Cyclone O/FVertimill Cyclone U/FVertimill Product125  New Afton Mine Tertiary Grinding Circuit - Survey #2  Survey:Date:Time:Sample originNet Wet Weight (g)Net Dry Weight (g)%SolidsMesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing6 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 241P80 290 P80 340 P80 147 P80 39041% 67% 35% 68%14.3 31.7 19.2 28.85.9 21.4 6.8 19.5#2 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #2)15-Mar-1617:00 to 18:00Ball Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F0%10%20%30%40%50%60%70%80%90%100%10 100 1000 10000Cummulative Passing (%)Particle Size (um)PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #2)Ball Mill Cyclone O/FVertimill Cyclone O/FVertimill Cyclone U/FVertimill Product126  New Afton Mine Tertiary Grinding Circuit - Survey #3    Survey:Date:Time:Sample originNet Wet Weight (g)Net Dry Weight (g)%SolidsMesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing6 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 237P80 289 P80 338 P80 150 P80 3926.1 22.3 7.4 19.937% 68% 35% 68%Vertimill Cyclone O/F Vertimill Cyclone U/F16.6 32.9 20.9 29.3#3 Survey16-Mar-1612:40 to 13:40Ball 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 10000Cummulative Passing (%)Particle Size (um)PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #3)Ball Mill Cyclone O/FVertimill Cyclone O/FVertimill Cyclone U/FVertimill Product127  New Afton Mine Tertiary Grinding Circuit - Survey #4   Survey:Date:Time:Sample originNet Wet Weight (g)Net Dry Weight (g)%SolidsMesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing6 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 260P80 287 P80 328 P80 340 P80 152 P80 39439% 68% 32% 69%Vertimill Cyclone Feed30.78.449%80.5 35.8 33.7 123.531.6 24.5 7.7 85.3#4 Survey7-Feb-173:20 pm to 4:20 pmBall Mill Cyclone O/F Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/FPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #4)0%10%20%30%40%50%60%70%80%90%100%10 100 1000 10000Cummulative Passing (%)Particle Size (um)PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #4)Ball Mill Cyclone O/FVertimill Cyclone O/FVertimill Cyclone U/FVertimill ProductVertimill Cyclone Feed128  New Afton Mine Tertiary Grinding Circuit - Survey #5    Survey:Date:Time:Sample originNet Wet Weight (g)Net Dry Weight (g)%SolidsMesh Opening (µm) %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing %Retained %Passing6 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 256P80 289 P80 324 P80 374 P80 147 P80 39138% 50% 72% 31% 69%79.9 44.9 38.3 29.7 65.630.3 22.6 27.5 9.3 45.1#5 SurveyPARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #5)8-Feb-173:10 pm to 4:10 pmBall Mill Cyclone O/F Vertimill Cyclone Feed Vertimill Product Vertimill Cyclone O/F Vertimill Cyclone U/F0%10%20%30%40%50%60%70%80%90%100%10 100 1000 10000Cummulative Passing (%)Particle Size (um)PARTICLE SIZE DISTRIBUTION ANALYSIS (SURVEY #5)Ball Mill Cyclone O/FVertimill Cyclone O/FVertimill Cyclone U/FVertimill ProductVertimill Cyclone Feed129  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   010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeedProduct131  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.  01020304050607080901000 0.5 1 1.5 2 2.5 3 3.5 4t10 (%)Ecs  (kWh/t)SAG Feed Belt CutWeighted Fit63 x 5345 x 37.531.5 x 26.522.4 x 1916 x 13.2A = 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).   010203040506070809010010 15 20 25 30 35 40 45 50 55 60t10 (%)Particle Size (mm)SAG Feed Belt Cut2.51.00.25134  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 0510152025< 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< 5.0Number of ParticlesRelative Density (top of Range)SAG Feed Belt Cut135  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)   05101520250.00 0.50 1.00 1.50 2.00Breakage Index, t 4[%]fmat.xn.(Ecs-Emin)New Afton Vertimill® Feed (survey #3) - fmat model505.0 357.1 252.2 178.3137  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)  05101520250.00 5.00 10.00 15.00Breakage Index, t 4[%]Ecs [kWh/t]600 x 425 425 x 300 300 x 212 212 x 150600 x 425 425 x 300 300 x 212 212 x 1500.05.010.015.020.025.030.035.040.045.050.00.0 5.0 10.0 15.0 20.0 25.0t n(%)t4 (%)t1.2t2t4t8t25138  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 onlyClient: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 320Time [second] 54 109 220 442 54 109 220 442 54 109 220 442 54 109 220 442Mass [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 45.0Edle 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 0.013Load 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 0.014Net 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-04Spec. 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 13.21600 x 425 Geo-mean 505Size (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 83.6425 x 300 Geo-mean 357Size (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 82.0300 x 212 Geo-mean 252Size (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 84.2212 x 150 Geo-mean 178Size (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 83.3Size DistributionAfter Wet-Screen Sample Weights (g) 80.6 80.3 78.7 75.7After Wet-Screen Sample Weights (g) 82.4 81.2 77.8 74.313.21Original Sample Weights (g) 82.5 83.2 83.6 83.384.2TotalsTotalsSpecific Energy (kWh/t)TotalsVertimill Model DevelopmentNew Afton MineCu-GoldNA S#3 VTM CYC U/FSpecific Energy (kWh/t) 1.94 3.02Original Sample Weights (g) 86.2 82.22.40425 x 3006.3582.46.451.68 3.26 5.94 13.06After Wet-Screen Sample Weights (g) 84.4 79.6 77.9 76.3Size DistributionOriginal Sample Weights (g) 83.7 83.4 82.0 82.0UBC Hardgrove Mill Fine Material Charaterisation TestTest Result Entry600 x 42512.092.76Specific Energy (kWh/t) 1.50300 x 212TotalsAfter Wet-Screen Sample Weights (g) 84.0 83.4 79.6 75.5Size DistributionSize Distribution212 x 150Specific Energy (kWh/t) 5.76 11.3785.7 83.7 83.6Original Sample Weights (g)1.4686.10%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 600 x 425 fraction1.462.405.760%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 425 x 300 fraction1.502.766.4512.090%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 300 x 212 fraction1.683.265.9413.060%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 212 x 150 fraction1.943.026.3513.21139  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)     05101520250.00 0.50 1.00 1.50 2.00Breakage Index, t 4[%]fmat.xn.(Ecs-Emin)New Afton Vertimill® Feed (survey #4) - fmat model505.0 357.1 252.2 178.3140  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) 05101520250.00 5.00 10.00 15.00 20.00Breakage Index, t 4[%]Ecs [kWh/t]600 x 425 425 x 300 300 x 212 212 x 150505.0 357.1 252.2 178.30.05.010.015.020.025.030.035.040.045.050.00.0 5.0 10.0 15.0 20.0 25.0t n(%)t4 (%)t1.2t2t4t8t25141  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 onlyClient: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 160Time [seconds] 53 109 220 442 53 110 220 443 54 110 220 443 54 109 220 442Mass [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 44.9Edle 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 0.013Load 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 0.014Net 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-04Spec. 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 15.36600 x 425 Geo-mean 505Size (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 82.8425 x 300 Geo-mean 357Size (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 82.4300 x 212 Geo-mean 252Size (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 83.0212 x 150 Geo-mean 178Size (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 83.9Size Distribution212 x 150Specific Energy (kWh/t) 5.98 11.2884.7 84.0 82.8Original Sample Weights (g)1.4782.882.4UBC Hardgrove Mill Fine Material Charaterisation TestTest Result Entry600 x 42512.643.00Specific Energy (kWh/t) 1.53300 x 212TotalsAfter Wet-Screen Sample Weights (g) 81.8 82.4 79.4 74.6Size DistributionSize DistributionOriginal Sample Weights (g) 83.7 82.8 83.21.61 3.58 6.39 13.57After Wet-Screen Sample Weights (g) 81.5 80.0 79.0 74.9TotalsVertimill Model DevelopmentNew Afton MineCu-GoldNA S#4 VTM CYC U/FSpecific Energy (kWh/t) 1.78 3.84Original Sample Weights (g) 83.5 82.72.96425 x 3007.6883.06.4675.9After Wet-Screen Sample Weights (g) 82.1 80.4 78.9 74.415.36Original Sample Weights (g) 82.4 82.5 84.0 83.983.0TotalsTotalsSpecific Energy (kWh/t)Size DistributionAfter Wet-Screen Sample Weights (g) 80.7 79.5 78.90%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 600 x 425 fraction1.472.965.9811.280%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 425 x 300 fraction1.533.006.4612.640%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 300 x 212 fraction1.613.586.3913.570%10%20%30%40%50%60%70%80%90%100%10 100 1000Cum. Passing (%)Particle Size (µm)Sizings from breakage of 212 x 150 fraction1.783.847.6815.36142  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 6.3051fmat 0.0010 α 0.49 t2 0.0019 -0.0671 2.0855Chamber diameter (inner) 6.10 m n 0.7476 C 68% t8 -0.0005 0.0172 0.5987Chamber height 5.00 m t25 -0.0004 0.0152 0.2955Screw diameter 4.83 mWall/Screw Gap 0.637 mScrew speed 12.0 rpm Size VTM Feed VTM Product VTM ProductScrew tip speed 3.0 m/s Deviation  (µm) (measured) (measured) (simulated)Balls filling 52.0 % 0.00 3350 100.00 100 100Ball diameter 0.75 inch 0.00 2360 100.00 100 100Ball density 7.85 kg/m3 0.00 1700 99.79 100 1000.00 1180 99.60 100 1000.00 850 98.59 99 99New Feed (Dry) 953 t/h 0.00 600 95.30 97 97Moisture Content 3.6 % 0.82 425 85.80 90 91New Feed (Wet) 732 t/h 0.00 300 62.04 75 75Circulating Load 135% 0.60 212 36.97 53 53Solids Density (SG) 2.75 t/m3 0.44 150 23.71 36 37Water Density (SG) 1 t/m3 0.00 106 16.71 27 27Mill Power Draw 2171 kWh 0.00 75 13.16 21 21Energy Efficiency 90% 0.01 53 10.81 17 17Specific Energy 2.28 kWh/t 1.8792 0 0 0 0SSE75 28.49 kWh/t P80 (µm) 394 340 3380.9999 P50 (µm) 260 200 202P75 (%) 13 21Operating ConditionClassification Model ParameterBreakage Model Parameter Appearance FunctionVertiMillVTM-3000-WBDimensionOperating parameters Particle Size Distribution010203040506070809010010 100 1000 10000Cum. Passing (%)Particle size (µm)VTM Product (simulated)VTM FeedVTM Product143  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 KkW kW % m m m rps %1954 2171 0.90 0.637 5.00 4.83 0.2 52 312Pnet  =  h Pgross  =  K (H*Jb)0.884 S2.232 DG N1.232Where:Pgross kW gross power draw of mill = Pnet/hh % electrical and power transmission efficienctyDG m effective gap between the mill wall and the screwH m effective mill charge chamber heightN rps rotation speed of the screwS m rotating screw diameterJb %K - power constantTower 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 03350 Size (µm) Parameters 02360 2812 0.50 2003 1.6 0 01700 2003 1.61 505 2.1 01180 1416 2.54 126 0.8 0850 1001 2.76600 714 2.53425 505 2.10300 357 1.66212 252 1.29150 178 1.01106 126 0.8275 89 0.6853 63 0.580 27 0.45Spline Regression0.101.0010.0010 100 1000 10000Particle size (µm)SiSpline RegressionSpline SiSolver 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 249.85α 0.49C 68%Size Geo-mean Classifier Efficiency (µm)  (µm) C I-C33502360 2812 0.0017 0.99831700 2003 0.0084 0.99161180 1416 0.0271 0.9729850 1001 0.0634 0.9366600 714 0.1167 0.8833425 505 0.1858 0.8142300 357 0.2626 0.7374212 252 0.3402 0.6598150 178 0.4119 0.5881106 126 0.4743 0.525775 89 0.5258 0.474253 63 0.5667 0.43330 27 0.6313 0.3687Classification Model Parameter0%10%20%30%40%50%60%70%10 100 1000 10000Classification efficiencyParticle size (µm)Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 02360 0.63 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001700 0.16 0.48 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.001180 0.08 0.20 0.44 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00850 0.02 0.08 0.19 0.47 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00600 0.02 0.04 0.10 0.19 0.55 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00425 0.01 0.03 0.05 0.09 0.18 0.61 0.00 0.00 0.00 0.00 0.00 0.00 0.00300 0.01 0.02 0.03 0.04 0.08 0.17 0.69 0.00 0.00 0.00 0.00 0.00 0.00212 0.01 0.02 0.03 0.03 0.03 0.07 0.15 0.77 0.00 0.00 0.00 0.00 0.00150 0.01 0.02 0.02 0.02 0.02 0.03 0.06 0.11 0.84 0.00 0.00 0.00 0.00106 0.01 0.01 0.02 0.02 0.02 0.02 0.02 0.05 0.08 0.89 0.00 0.00 0.0075 0.00 0.01 0.02 0.02 0.02 0.01 0.01 0.02 0.03 0.06 0.93 0.00 0.0053 0.00 0.01 0.01 0.01 0.02 0.01 0.01 0.01 0.01 0.02 0.04 0.95 0.000 0.03 0.07 0.09 0.09 0.09 0.07 0.06 0.04 0.03 0.03 0.03 0.05 1.001.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000145  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 02360 0.001063534 0 0 0 0 0 0 0 0 0 0 0 01700 0.001311353 0.003989 0 0 0 0 0 0 0 0 0 0 01180 0.002077449 0.005366 0.011969 0 0 0 0 0 0 0 0 0 0850 0.001555895 0.00539 0.012101 0.030008 0 0 0 0 0 0 0 0 0600 0.001812969 0.00479 0.011806 0.02247 0.063696 0 0 0 0 0 0 0 0425 0.002532626 0.004798 0.008578 0.017131 0.032752 0.113441 0 0 0 0 0 0 0300 0.003452377 0.006127 0.007899 0.01091 0.021482 0.044454 0.180656 0 0 0 0 0 0212 0.003759012 0.007747 0.008895 0.008963 0.011391 0.02505 0.050218 0.261723 0 0 0 0 0150 0.003413602 0.007977 0.010219 0.009655 0.008599 0.011226 0.025713 0.047206 0.345791 0 0 0 0106 0.002837448 0.006961 0.009947 0.010902 0.009141 0.00783 0.010283 0.022866 0.039003 0.422897 0 0 075 0.002215007 0.005534 0.008264 0.010268 0.010054 0.007849 0.006669 0.008412 0.017933 0.029574 0.487395 0 053 0.001682838 0.004229 0.006427 0.008384 0.009312 0.008227 0.006281 0.005256 0.00635 0.013272 0.021735 0.538537 00 0.020282774 0.047077 0.057649 0.059088 0.05494 0.046226 0.035738 0.02686 0.020795 0.018083 0.021889 0.031362 0.631281Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 02360 0.998936466 0 0 0 0 0 0 0 0 0 0 0 01700 -0.001311353 0.996011 0 0 0 0 0 0 0 0 0 0 01180 -0.002077449 -0.00537 0.988031 0 0 0 0 0 0 0 0 0 0850 -0.001555895 -0.00539 -0.0121 0.969992 0 0 0 0 0 0 0 0 0600 -0.001812969 -0.00479 -0.01181 -0.02247 0.936304 0 0 0 0 0 0 0 0425 -0.002532626 -0.0048 -0.00858 -0.01713 -0.03275 0.886559 0 0 0 0 0 0 0300 -0.003452377 -0.00613 -0.0079 -0.01091 -0.02148 -0.04445 0.819344 0 0 0 0 0 0212 -0.003759012 -0.00775 -0.00889 -0.00896 -0.01139 -0.02505 -0.05022 0.738277 0 0 0 0 0150 -0.003413602 -0.00798 -0.01022 -0.00965 -0.0086 -0.01123 -0.02571 -0.04721 0.654209 0 0 0 0106 -0.002837448 -0.00696 -0.00995 -0.0109 -0.00914 -0.00783 -0.01028 -0.02287 -0.039 0.577103 0 0 075 -0.002215007 -0.00553 -0.00826 -0.01027 -0.01005 -0.00785 -0.00667 -0.00841 -0.01793 -0.02957 0.512605 0 053 -0.001682838 -0.00423 -0.00643 -0.00838 -0.00931 -0.00823 -0.00628 -0.00526 -0.00635 -0.01327 -0.02174 0.461463 00 -0.020282774 -0.04708 -0.05765 -0.05909 -0.05494 -0.04623 -0.03574 -0.02686 -0.02079 -0.01808 -0.02189 -0.03136 0.368719Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 02360 1.001064667 0 0 0 0 0 0 0 0 0 0 0 01700 0.001318007 1.004005 0 0 0 0 0 0 0 0 0 0 01180 0.002112011 0.005453 1.012114 0 0 0 0 0 0 0 0 0 0850 0.001639408 0.005647 0.012627 1.030936 0 0 0 0 0 0 0 0 0600 0.002011084 0.005341 0.013065 0.024741 1.068029 0 0 0 0 0 0 0 0425 0.002993276 0.005793 0.010519 0.020835 0.039456 1.127957 0 0 0 0 0 0 0300 0.00448525 0.00809 0.010839 0.015506 0.030143 0.061198 1.220489 0 0 0 0 0 0212 0.005593883 0.0115 0.013643 0.014659 0.019868 0.042435 0.083018 1.354505 0 0 0 0 0150 0.005954442 0.013728 0.017758 0.017565 0.017333 0.024822 0.05396 0.097738 1.528564 0 0 0 0106 0.005781662 0.014001 0.019967 0.022195 0.019948 0.019752 0.028683 0.060273 0.103305 1.732794 0 0 075 0.005184105 0.012816 0.019126 0.023792 0.024027 0.020772 0.020783 0.029126 0.059436 0.099971 1.950821 0 053 0.004433009 0.011028 0.0168 0.02198 0.024835 0.023314 0.020104 0.019878 0.026804 0.054545 0.091885 2.167021 00 0.05864989 0.136251 0.170121 0.179441 0.173948 0.15602 0.131737 0.110561 0.097081 0.095553 0.123627 0.184322 2.712094146  [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 02360 0.63387202 0 0 0 0 0 0 0 0 0 0 0 01700 0.155643942 0.473502 0 0 0 0 0 0 0 0 0 0 01180 0.074562047 0.192605 0.429566 0 0 0 0 0 0 0 0 0 0850 0.022970978 0.079571 0.178658 0.443031 0 0 0 0 0 0 0 0 0600 0.01371869 0.036247 0.089337 0.170032 0.481987 0 0 0 0 0 0 0 0425 0.011100583 0.021031 0.037598 0.075087 0.143551 0.497217 0 0 0 0 0 0 0300 0.009693424 0.017202 0.022179 0.030632 0.060317 0.124816 0.507238 0 0 0 0 0 0212 0.00729092 0.015027 0.017252 0.017384 0.022093 0.048587 0.097402 0.507634 0 0 0 0 0150 0.004873927 0.01139 0.01459 0.013785 0.012277 0.016028 0.036713 0.067401 0.493719 0 0 0 0106 0.003145381 0.007716 0.011026 0.012086 0.010133 0.008679 0.011399 0.025347 0.043235 0.468792 0 0 075 0.001997688 0.004991 0.007453 0.009261 0.009067 0.007079 0.006014 0.007587 0.016174 0.026672 0.439576 0 053 0.00128675 0.003234 0.004915 0.006411 0.00712 0.006291 0.004803 0.004019 0.004855 0.010148 0.016619 0.411782 00 0.011846766 0.027497 0.033671 0.034512 0.032089 0.027 0.020874 0.015689 0.012146 0.010562 0.012785 0.018318 0.368719Size (µm) 2360 1700 1180 850 600 425 300 212 150 106 75 53 02360 0.634546882 0 0 0 0 0 0 0 0 0 0 0 01700 0.156433729 0.475398 0 0 0 0 0 0 0 0 0 0 01180 0.075802534 0.195719 0.43477 0 0 0 0 0 0 0 0 0 0850 0.024203947 0.083366 0.186416 0.456737 0 0 0 0 0 0 0 0 0600 0.015217817 0.040413 0.098864 0.187217 0.514776 0 0 0 0 0 0 0 0425 0.013119626 0.025391 0.046107 0.091321 0.172935 0.560839 0 0 0 0 0 0 0300 0.012593478 0.022714 0.030434 0.043537 0.084634 0.171829 0.619079 0 0 0 0 0 0212 0.010849807 0.022304 0.026462 0.028433 0.038535 0.082307 0.161021 0.687592 0 0 0 0 0150 0.008501728 0.019601 0.025355 0.025079 0.024748 0.035441 0.077044 0.13955 0.754681 0 0 0 0106 0.006409115 0.015521 0.022134 0.024604 0.022113 0.021896 0.031796 0.066814 0.114517 0.81232 0 0 075 0.004675481 0.011559 0.017249 0.021458 0.02167 0.018734 0.018744 0.026268 0.053604 0.090162 0.857534 0 053 0.003389617 0.008432 0.012846 0.016807 0.01899 0.017826 0.015372 0.015199 0.020495 0.041707 0.070258 0.892341 00 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

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