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Development of operation strategies for variable speed ball mills Liu, Sijia 2018

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DEVELOPMENT OF OPERATION STRATEGIES FOR VARIABLE SPEED BALL MILLS   by  Sijia Liu  B.Eng., Central South University, 2012  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)  April 2018  © Sijia Liu, 2018 ii  The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, a thesis/dissertation entitled: Development of Operation Strategies for Variable Speed Ball Mills  submitted by Sijia Liu  in partial fulfillment of the requirements for the degree of Master of Applied Science in Mining Engineering  Examining Committee: Dr. Bern Klein, Mining Engineering Supervisor  Dr. Scott Dunbar, Mining Engineering Supervisory Committee Member  Dr. Sanja Miskovic, Mining Engineering Supervisory Committee Member  Additional Examiner   Additional Supervisory Committee Members:  Supervisory Committee Member  Supervisory Committee Member iii  Abstract Mineral processing productivity relates to a range of operating parameters, including production rate, product grind size, and energy efficiency. Variations in ore properties and operating conditions change the comminution dynamics, resulting in a constant deviation from operational goals. Although most processing facilities currently use fixed speed grinding mills, variable speed drive is considered to provide an important control variable that can contribute to achieving operational objectives.   This thesis examines variable speed ball mill performance under changing operating conditions to recommend operating conditions for the Copper Mountain Mine. JK SimMet, a very powerful predictive tool, was used to estimate grinding circuit performance and mill power consumption. Samples and operating data were collected directly from the Copper Mountain Mine to build a calibrated model. Appearance (breakage distribution) functions of different geo-samples were measured and used to predict plant performance under different ore property variations.  The results indicate that higher mill speed and lower ball load operating strategies are preferable with respect to energy savings in variable speed ball mill operations. Ore characteristic variations at the Copper Mountain Mine are significant and can cause large oscillations within mill operations. Thus, ore blending in Copper Mountain should be done carefully and cautiously. However, in combination with traditional optimization methods, ball mill grinding speed can be used to control energy input and offset the influences of ore variability. Optimum ball mill operating conditions can be determined based on circuit design and operating dynamics for any given run-of-mine ore.  iv  Lay Summary Grinding is an important process in the mining industry that is used to break ore to a targeted size. Grinding conditions are not constant during production, and can be affected by changes in ore types and operating conditions. As drive technology develops, variable speed drives are gradually being accepted into the mining industry and are now considered an important mill speed control that can contribute to maintaining a steady product size.   In this thesis, adequate variable speed ball mill operation strategies are developed based on JK SimMet simulation results. The results indicate that variable speed drives can be used effectively as a means of controlling energy input to offset the influences of ore variability with improved comminution energy efficiency.   v  Preface This research has been developed through the UBC Variable Speed Drive Project and was supported by Ingeteam Power Technology, BC Hydro, and Mitacs. Some of the test results have been summarized in the Copper Mountain VSD project report.  Under the supervision of Dr. Bern Klein, professor at the Norman B. Keevil Institute of Mining Engineering at the University of British Columbia, I was responsible for developing and conducting appearance (breakage distribution) function measurements, building JK SimMet models, running the simulations and interpreting the results.  The survey samples were collected and analyzed by Dr. Sanja Miskovic, Chengtie Wang, Ayse Tugbe Cebeci, Monong Huang and myself.   vi  Table of Contents Abstract ......................................................................................................................................... iii Lay Summary ............................................................................................................................... iv Preface .............................................................................................................................................v Table of Contents ......................................................................................................................... vi List of Tables ..................................................................................................................................x List of Figures .............................................................................................................................. xii List of Symbols .............................................................................................................................xv List of Abbreviations ................................................................................................................ xvii Acknowledgements .................................................................................................................. xviii Dedication ................................................................................................................................... xix Chapter 1: Introduction ................................................................................................................1 1.1 Background ..................................................................................................................... 1 1.2 Thesis objectives ............................................................................................................. 3 1.3 Thesis outline .................................................................................................................. 3 Chapter 2: Literature review ........................................................................................................5 2.1 Introduction ..................................................................................................................... 5 2.2 Ball mill .......................................................................................................................... 6 2.2.1 Ball mill history .......................................................................................................... 7 2.2.2 Configuration and classification ................................................................................. 7 2.2.3 Breakage mechanism and theory ................................................................................ 9 2.2.4 Variables in ball mills ............................................................................................... 11 2.3 Variable speed ball mills ............................................................................................... 14 vii  2.3.1 Variable speed drive ................................................................................................. 14 2.3.2 Effects of speed ......................................................................................................... 15 2.3.3 Benefits of variable speed ball mills ......................................................................... 20 2.4 JK SimMet simulation .................................................................................................. 23 2.4.1 Introduction ............................................................................................................... 23 2.4.2 Ball mill model ......................................................................................................... 24 2.4.3 Appearance (breakage distribution) function measurement ..................................... 28 2.4.4 Power model ............................................................................................................. 29 2.4.5 JK SimMet applications ............................................................................................ 32 2.5 Summary of literature review ....................................................................................... 33 Chapter 3: Experimental program.............................................................................................35 3.1 Methodology ................................................................................................................. 35 3.2 Copper Mountain mine ................................................................................................. 36 3.3 Sample description ........................................................................................................ 37 3.3.1 Survey samples ......................................................................................................... 37 3.3.2 Geo-metallurgical samples........................................................................................ 38 3.3.3 Sample preparation ................................................................................................... 41 3.4 Ore characterization ...................................................................................................... 43 3.4.1 Bond ball mill work index (BBWI) test .................................................................... 43 3.4.2 JK drop weight test ................................................................................................... 44 3.4.3 Appearance (breakage distribution) function measurement ..................................... 45 3.5 JK SimMet model set-up .............................................................................................. 48 3.5.1 Model configuration .................................................................................................. 49 viii  3.5.2 Mass balance ............................................................................................................. 49 3.5.3 Model fit.................................................................................................................... 51 3.6 Simulation ..................................................................................................................... 55 3.6.1 Mill speed and mill load ........................................................................................... 55 3.6.2 Water addition ........................................................................................................... 56 3.6.3 Target grinding size achievement ............................................................................. 57 3.6.4 Ore type ..................................................................................................................... 57 Chapter 4: Test results and discussion ......................................................................................58 4.1 Ore characterization results ........................................................................................... 58 4.2 Ball mill appearance function ....................................................................................... 60 4.3 JK SimMet model set-up .............................................................................................. 67 4.3.1 Mass balance ............................................................................................................. 67 4.3.2 Model fit.................................................................................................................... 69 4.4 Simulation and optimization ......................................................................................... 73 4.4.1 Mill speed and mill load ........................................................................................... 73 4.4.2 Water addition and addition points ........................................................................... 80 4.4.3 Target grind size achievement .................................................................................. 83 4.4.4 Ore types ................................................................................................................... 88 4.4.5 Discussion ................................................................................................................. 92 Chapter 5: Conclusions and recommendations ........................................................................94 5.1 Conclusions ................................................................................................................... 94 5.2 Recommendations for future work ............................................................................... 96 Bibliography .................................................................................................................................98 ix  Appendices ..................................................................................................................................104 Appendix A Survey data summaries ....................................................................................... 104 A.1 DCS data ................................................................................................................. 104 A.2 Survey data.............................................................................................................. 105 Appendix B BBWI test results ................................................................................................ 109 B.1 SAG feed ................................................................................................................. 109 B.2 Geo-sample #1 ........................................................................................................ 110 B.3 Geo-sample #2 ........................................................................................................ 111 B.4 Geo-sample #3 ........................................................................................................ 112 B.5 Geo-sample #4 ........................................................................................................ 113 B.6 Geo-sample #5 ........................................................................................................ 114 B.7 Geo-sample #6 ........................................................................................................ 115  x  List of Tables Table 2-1 Comparison of overflow and grate discharge ball mils .................................................. 9 Table 2-2 Overall system efficiency for 16 MW ball mill ............................................................ 15 Table 3-1 Detailed equipment information in Copper Mountain Mine ........................................ 37 Table 3-2 Qualitative interpretation of DWT results as defined by JKMRC ............................... 45 Table 3-3 Drop weight test specification ...................................................................................... 48 Table 3-4 Ball mill model parameters .......................................................................................... 52 Table 3-5 Cyclone model parameters ........................................................................................... 53 Table 3-6 Template used for sensitivity analysis of mill speed and mill load .............................. 55 Table 3-7 Effects of water adding points assessment ................................................................... 57 Table 4-1 Ore characterization results .......................................................................................... 58 Table 4-2 Hardness classification based on BBWI ....................................................................... 58 Table 4-3 Competency classification based on JK DWT ............................................................. 58 Table 4-4 Particle size distribution ............................................................................................... 61 Table 4-5 Mass loss assessment .................................................................................................... 62 Table 4-6 Fitted parameters and R squared .................................................................................. 65 Table 4-7 Appearance function of various samples ...................................................................... 66 Table 4-8 Fitted ball mill parameters ............................................................................................ 69 Table 4-9 Fitted cyclone parameters ............................................................................................. 70 Table 4-10 Comparison of fitted key operation parameters and experimental parameters .......... 70 Table 4-11 Optimal operating conditions vs final fitted operating conditions ............................. 79 Table 4-12 Sensitivity analysis of water addition ......................................................................... 82 Table 4-13 Sensitivity analysis of water adding points ................................................................ 82 xi  Table 4-14 Power consumptions of BM 1 and BM 2 with targeted grinding size of 212 µm ...... 85 Table 4-15 Fitted final cyclone O/F PSD ..................................................................................... 86 Table 4-16 Mills operating conditions with achieved target grind size ........................................ 87 Table 4-17 Final product sizes of various geo-samples with identical operating conditions ....... 88 Table 4-18 Theoretical maximum mill throughput of various geo-samples with detailed operating conditions ...................................................................................................................................... 89 Table 4-19 Theoretical power consumptions of various geo-samples with required target grind size ................................................................................................................................................ 91  xii  List of Figures Figure 1-1 Energy distribution of various comminution equipment types ..................................... 1 Figure 1-2 Cost distribution in an SABC circuit ............................................................................ 2 Figure 2-1 Theoretical size reduction for different grinding mills ................................................. 6 Figure 2-2 Ball mill structure .......................................................................................................... 8 Figure 2-3 Breakage mechanisms: (a) Impact or compression, (b) Chipping or attrition, and (c) Abrasion .......................................................................................................................................... 9 Figure 2-4 Charge motion with increasing mill speed .................................................................. 10 Figure 2-5 Effects of mill filling on net power draw .................................................................... 13 Figure 2-6 Toe and shoulder positions of load at various speed and mill fillings ........................ 17 Figure 2-7 Effect of mill speed on breakage rate .......................................................................... 18 Figure 2-8 Power variation with mill speed and charge filling .................................................... 19 Figure 2-9 Variation of torque with speed and filling .................................................................. 19 Figure 2-10 Grinding cost contributed by liner, media, and energy ............................................. 23 Figure 2-11 Fundamental principle of perfect mixing model ....................................................... 24 Figure 2-12 Mechanisms of the perfect mixing ball mill model .................................................. 25 Figure 2-13 Variation of parameter r/d* with particle size ........................................................... 26 Figure 2-14 Simplified charge shape for grate (left) and overflow mills (right) .......................... 30 Figure 2-15 Schematic of mill charge for energy balance approach ............................................ 30 Figure 3-1 Experimental program flowsheet ................................................................................ 36 Figure 3-2 Copper Mountain Circuit Schematic ........................................................................... 38 Figure 3-3: Geo-sample receipt (Top Geo-unit 1-3, Bottom Geo-unit 4-6) ................................. 39 Figure 3-4: Locations of Geo-samples .......................................................................................... 39 xiii  Figure 3-5 Sample preparation flowsheet ..................................................................................... 42 Figure 3-6 Bond ball mill work index test equipment .................................................................. 43 Figure 3-7 JK drop weight tester (left), abrasion tester (right) ..................................................... 44 Figure 3-8 r/d values obtained with default appearance function ................................................. 46 Figure 3-9 Appearance function comparison ................................................................................ 47 Figure 3-10 Ball mill circuit configuration ................................................................................... 49 Figure 3-11 Mass balance process block diagram ........................................................................ 51 Figure 3-12 Model fit process block diagram ............................................................................... 54 Figure 4-1 Ore classification ......................................................................................................... 59 Figure 4-2 SAG feed normalization and comparison ................................................................... 63 Figure 4-3 Geo-sample #1 normalization and comparison ........................................................... 63 Figure 4-4 Geo-sample #2 normalization and comparison ........................................................... 64 Figure 4-5 Geo-sample #4 normalization and comparison ........................................................... 64 Figure 4-6 Geo-sample #6 normalization and comparison ........................................................... 65 Figure 4-7 Ball mill circuit 1 - stream PSDs................................................................................. 67 Figure 4-8 Ball mill circuit 2 - stream PSDs................................................................................. 68 Figure 4-9 Ball mill circuit 1- experimental data vs balanced data .............................................. 68 Figure 4-10 Ball mill circuit 2- experimental data vs balanced data ............................................ 69 Figure 4-11 BM 1 PSD comparison (balanced vs fitted) .............................................................. 71 Figure 4-12 BM 2 PSD comparison (balanced vs fitted) .............................................................. 71 Figure 4-13 Comparison of r/d* 1 and r/d* 2 ............................................................................... 72 Figure 4-14 Relationship between mill speed and r/d* ................................................................ 73 Figure 4-15 Relationship between mill load and r/d* ................................................................... 74 xiv  Figure 4-16 Sensitivity analysis of BM circuit 1 .......................................................................... 75 Figure 4-17 Sensitivity analysis of BM circuit 2 .......................................................................... 76 Figure 4-18 BM 1 power draw under various operating conditions ............................................. 78 Figure 4-19 BM 2 power draw under various operating conditions ............................................. 78 Figure 4-20 Water adding points .................................................................................................. 81 Figure 4-21 Split ratio of each size fraction accounted for BM circuit 1 ..................................... 84 Figure 4-22 Theoretical maximum throughputs of various geo-metallurgical samples ............... 90  xv  List of Symbols Symbol   Description Nc    Critical speed D    Mill diameter db    Ball diameter dbmax    Maximum ball diameter d    Top size of the ore  d95    Particle size at which 95% of particles pass d80   Particle size at which 80% of particles pass Q   Total mill volumetric discharge Qm    Mill discharge flowrate through grinding media Qt    Mill discharge flowrate through slurry pool at the toe of charge A   Total discharge grate open area γ    Grate design parameter ɸ    Critical mill speed percentage (%) Jpm    Frictional slurry hold up in the grinding media (%) Jpt    Fractional slurry hold up in the slurry pool (%) fi,   mass of ith size fraction in the feed si    mass of ith size fraction in the mill pi    mass of ith size fraction in the product aij,  appearance (breakage distribution) function (describe the fraction of size range j which reports to size range i after breakage) xvi  rj Rate of breakage per unit time that characterizes the rate of disappearance in the size fraction j di    Discharge rate of size fraction i L    Mill length tn   Percentage passing 1 𝑛⁄  of the original particle size Nm    Rotational rate at the mill shell liner wear face rm    Mill radius at the mill shell liner wear face ri Charge inner surface radius which marks the boundary between the active part of the charge and the inactive kidney  Jt    Fractional mill filling ρp    Slurry density ρc    Grinding charge density ƟTO    Slurry toe angle for overflow discharge mill ƟT    Charge toe angle Ɵs    Charge shoulder angle  xvii  List of Abbreviations Symbol   Description AG   Autogenous grinding BBWI   Bond ball mill work index BM   Ball mill CS   Fraction critical speed CYC   Hydrocyclone DCS   Data collection system DEM   Discrete element method FIT   Fitted conditions GMD   Gearless mill drive LF    Mill load fraction  PSD   Particle size distribution ROM   Run of mine SAG   Semi-autogenous grinding SIM   Simulated condition VSD   Variable speed drive WI    Work index     xviii  Acknowledgements I would like to express my gratitude to my supervisory committee, and especially to my supervisor Professor Bern Klein, for his supervision, support, and guidance throughout this research project. It is he who sparked my ideas, broadened my views and provided me with the opportunity to study this topic. I would also like to express my sincere thanks to Chengtie Wang, as my best friend and workmate, who was always willing to help and gave me many useful suggestions for my research and with respect to my life.  I would like to express my appreciation to Ingeteam Power Technology and Mitacs for the financial support of my study. I would like to acknowledge Copper Mountain Mine for providing test samples, on-site information, and DCS data. I am also deeply thankful to my group members Ayse Tugbe Cebeci and Monong Huang for their support with respect to sample collection and data analysis. I further want to recognize and thank Ayse Tugbe Cebeci and Stefan Nadolski for their guidance on the use of the JK SimMet software.  I would like to acknowledge Amit Kumar and Genzhuang Li for providing me with emotional support and assistance during my life in Vancouver. I would also like to express my gratitude to Pius Lo, Libin Tong and Aaron Hope for providing me with the lab facilities for my research. Finally, I would like to convey my sincere appreciation to my dear parents, my cousin Jiayu Guo and mother teacher Maren Klein for their love, encouragement, and support throughout my graduate life.  xix  Dedication  To my parents:  Without your support, encouragement and understanding, this work would never have been finished. 1  Chapter 1: Introduction 1.1 Background Comminution is a crucial process in the mineral processing industry that consists of blasting, crushing and grinding. By applying mechanical forces and energy, run of mine (ROM) ore size is reduced to a targeted size in order to separate valuable minerals from gangue (waste) minerals. It is commonly agreed that comminution is an energy-intensive process. It consumes approximately 3% of the total energy produced in the world (Pease, 2007), and accounts for approximately 50-80% of the total energy consumed in a mill concentrator (Abouzeid & Fuerstenau, 2009). Of the various comminution components, grinding takes around 90% of total energy used (Ballantyne & Powell, 2015). Detailed power consumption distributions according to various types of equipment (Figure 1-1), and cost distributions in a traditional comminution circuit (Figure 1-2) illustrate this intense resource consumption.  Figure 1-1 Energy distribution of various comminution equipment types (Ballantyne & Powell, 2015)  2   Figure 1-2 Cost distribution in an SABC circuit (Costello & Brown, 2015) Moreover, comminution is low in energy efficiency. Only 1-2% of the energy consumed can be used for breakage (Alvarado, Algüerno, Auracher, & Casali, 1998; Whittles, Kingman, Lowndes, & Jackson, 2006; Zadeh, 2012). Considering this large energy consumption rate, even a 1-2% efficiency improvement during grinding could achieve enormous energy savings. After years of mining exploitation, remaining ore bodies become more complex, rendering grinding increasingly more challenging (Yang, Jayasundara, Yu, & Curry, 2006). Finding a reliable and efficient method for grinding ores is crucial, and needs to be developed as soon as possible.  The growing adoption of variable speed drives has created opportunities for mill operation optimization. They provide greater operational flexibility for mill operators and require less maintenance. However, quite a few mines are aware of these potential benefits and fixed speed motors are still used in most mills. Traditional operation parameters such as water addition, throughput, and ball load are usually adjusted instead of mill speed to minimize the influences of feed material changes and to optimize mill performance. However, these adjustments are time-consuming and usually result in unavoidable wear increase and unquantified final grind size (Atutxa & Legarra, 2015). 3  1.2 Thesis objectives This study attempts to gain a better understanding of variable speed ball mills performance under constantly changing mill operating conditions. The primary objective of this research is to develop adequate variable speed ball mill operation strategies with regard to energy consumption and changes in ore characteristics. To achieve this objective, the following intermediate objectives were set: • Conduct an on-site mill survey to collect representative samples and DCS (data collection system) data. • Analyze survey samples and generate datasets (BBWI, PSD, solid percentage) for JK SimMet models. • Conduct drop weight tests and collect appearance functions for representative geo-samples • Develop the JK SimMet model using collected data and fitted machine parameters • Conduct mill speed, mill load and water addition sensitivity analysis on onsite mill performance and provide reasonable operation strategies based on the results. • Assess the effects of ore variations on the comminution process and recommend potential energy savings that could be achieved within reasonable operating conditions, specifically by adjusting mill speed. 1.3 Thesis outline This thesis consists of six chapters.  Chapter 1 introduces the background and objectives of this research. 4  Chapter 2 provides a literature review of ball mill technology and its applications. A description of variable speed ball mills and their potential benefits are provided. This chapter also introduces the JK SimMet software and illustrates principles of its ball mill breakage and power models. Chapter 3 details the overall experimental program. The sampling method, ore characterization (appearance function and BBWI), and JK simulation plan are discussed. Relative test procedures are also described in detail. Chapter 4 presents the results of mill survey, lab test work and a discussion of the JK simulation results, as well as mill optimization strategies. Chapter 5 covers the key findings and recommendations for future work based on the test results of this research. 5  Chapter 2: Literature review  2.1 Introduction It is widely known that most minerals are finely disseminated amongst gangue materials. To efficiently recover valuable minerals, comminution has been employed to break Run of Mine (ROM) ore to its targeted liberation size. This process usually consists of two stages: crushing and grinding. Crushing is the first mechanical stage in the comminution process and is used to break down ROM ore as large as 1.5m. (Wills & Finch, 2015). Following the crushing stage, the material is transported to the grinding section through belt conveyors. Based on their charge motions, grinding mills can be classified into either tumbling or stirred mills (Wills & Finch, 2015). The theoretical size reductions and power ranges for different grinding mills are shown in Figure 2-1. As a common and widely used piece of equipment for grinding in the mining industry, tumbling mills are made up of a rotating metallic cylindrical drum and grinding media, and can be classified into 4 main types based on their media: rod mills, ball mills, AG mills and SAG mills (Wang, 2013). Known for their low efficiency, most of the input energy for grinding mills is wasted in the form of heat and noise (Zadeh, 2012). Driven by a desire to exploit lower grade mineral resources, investors have gradually favored larger mining and mineral processing operations. To minimize the total operation units required in higher capacity plants, comminution equipment has become larger and larger, requiring higher levels of power to operate. Consequently, grinding efficiency becomes lower as mill size increases (Lynch & Rowland, 2005).  6   Figure 2-1 Theoretical size reduction for different grinding mills (Metso, 2015) To improve mill efficiency, mining groups have conducted extensive research with a variety of equipment and technologies. As VSD technologies developed, variable speed mills provided new opportunities for mill operation and optimization. In particular, variable speed mills can provide flexible operating conditions that offset the dynamic changes of ore properties, while maintaining product quality.  2.2 Ball mill In mill operations, variable speed SAG mill has been well accepted and gradually adapted to maintain a stable mill product size and provide flexible mill operations. However, quite little attention have been paid to variable speed ball mills, and they are usually treated as a nice-to-have feature (Vijfeijken, Filidore, Walbert, & Marks, 2012). To evaluate variable speed ball mills, a relative literature review has been conducted. This section consists of ball mill history, ball mill classification, breakage mechanism and operation variables. 7  2.2.1 Ball mill history The first ball mill was used for fine grinding in the cement industry in 1876; however, it was not accepted by the industry until 1885 (Lynch & Rowland, 2005). Following the development of the flotation technology, ball mills quickly spread into the metal mining field at the beginning of the 20th century (Lynch & Rowland, 2005). The original ball mill, only 0.9-1.5 m in diameter, has since evolved to a recent 6.7m diameter with 15 MW motor power (Lynch & Rowland, 2005). The appearance and development of ball mill technology have contributed significantly to the area of fine grinding and occupies a vital position in the comminution system. Currently, the ball mill technology is being widely used in the cement, mining, painting, pyrotechnic, ceramic and selective laser sintering industries (Wikipedia, 2018). 2.2.2 Configuration and classification The ball mill, which is named as its grinding media, is usually used for wet or dry fine grinding. A typical ball mill configuration is shown in Figure 2-2. When the mill shell starts to rotate, the motion is imparted to the charge via the mill shell (Wills & Finch, 2015). The material is fed from one end of the ball mill, and the product is discharged from the other end of the equipment after it has been given a reasonable grinding time. Ball mills are usually used with hydro cyclones (CYC) that assist in separating fine materials and returning coarse materials back to the ball mill.   8   Figure 2-2 Ball mill structure (Bailing Machinery, 2003) Ball mills can be classified into two types according to their length and diameter ratios. The term ‘ball mill’ is only used for mills with a length to diameter ratio of between 2 to 1, and the mills with a ratio of 3 to 5 are known as tube mills (Wills & Finch, 2015). They can also be classified according to their mill discharge methods, as overflow ball mill and grate discharge ball mill respectively. Grate discharge ball mills consume 15% more power than overflow ball mills with the same size reduction and similar grinding efficiency (Lewis, Coburn, & Bhappu, 1976; Wills & Finch, 2015). Key features of these two kinds of ball mills are summarized in Table 2-1.     9  Table 2-1 Comparison of overflow and grate discharge ball mils (Metso, 2015) Overflow ball mill Grate discharge ball mill Wet only Dry or wet Robust and simple Discharge end more complicated Mostly in closed circuit (secondary) Mostly in closed circuit (secondary) Finer grind (longer retention time) Coarser grind (shorter retention time) Higher risk for over-grinding Lower risk for over-grinding Ball charge 35-40% Can take about 5-10% more ball with correspondingly higher throughput  2.2.3 Breakage mechanism and theory Within the ball mill, the grinding process involves three main breakage mechanisms: impact or compression, chipping or attrition and abrasion (Figure 2-3). “These mechanisms distort the particles and change their shape beyond certain limits determined by their degree of elasticity, which causes them to break” (Wills & Finch, 2015).  Figure 2-3 Breakage mechanisms: (a) Impact or compression, (b) Chipping or attrition, and (c) Abrasion (Wills & Finch, 2015) When a ball mill starts to roll, the mill power is transferred into kinetic energy and potential energy of the grinding media through the friction between the mill liners and ball load. The shape of the ball load changes according to the mill rotation speed (Figure 2-4). When the speed is low (stage 10  d), steel balls will gradually roll down from one side to another in a cascading motion, and attrition and abrasion breakage mechanisms play primary roles during this stage. When speed is increased gradually, some of the loads will separate from the cascading media and be lifted and thrown into the empty zone of the chamber. This part of the load will form a trajectory and finally fall back on the charge in what is called a cataracting motion. All three breakage mechanisms contribute to the particle breakage during this stage (stage e). When the rotation speed is higher than the critical speed (Equation 2-1), the load will be forced against the shell and centrifuging will occur without any particle breakage (stage f). Cascading causes attrition and abrasion producing fine particles and cataracting results in impact for of coarser particles (Wills & Finch, 2015). As such, changes in the ball mill speed can have a significant effect on particle breakage mechanisms and product size distribution. In real operations, impact is used to break big particles down and abrasion is used to reduce material to a target grinding size.  Figure 2-4 Charge motion with increasing mill speed (Richter, Govender, Parker, Richardson, & Mainza, 2015) 11  Mill critical speed can be described by Equation 2-1 (Gupta & Yan, 2016), and mill speed is usually demonstrated as a % of critical speed (Cs).  𝑁𝐶 =42.3√𝐷 − 𝑑 Equation 2-1 where,  Nc is critical speed (rev/min) D is mill diameter (m)  d is ball diameter (m) 2.2.4 Variables in ball mills Ball mill performance is affected by many associated variables. These variables can be classified into the categories of material variables and mill configuration. Material variables include feed throughput and particle size distribution, ore hardness, and slurry characteristics. Mill configuration variables include mill speed, grinding media (shape, size, and density), and ball load. All of these variables can be utilized to optimize mill operations and to improve grinding efficiency (Hou, 2014). In fact, variables in a ball mill do not occur individually, but rather, take place together. When evaluating their effects, two or more factors need to be considered in conjunction.  The effects of the main variables on ball mill performance are summarized in the following sections. Feed variables Grinding consists of a series of individual breakage events, and the breakage probability for each particle depends on its size, breakage rate and retention time (Runge, Tabosa, & Jankovic, 2013). The shape of the breakage rate curve is calculated based on the relationship between particles sizes and their corresponding breakage rate (Erdem, Ergun, & Benzer, 2009). This relationship was 12  described in detail in 1984 by Austin et al. (Austin, Klimpel, & Luckie, 1984), and later confirmed by DEM simulation tests conducted by de Carvalho and Tavares (2013). The simulation results clearly demonstrated that the breakage rate increases along with particle size increase until a maximum point is reached, and then decreases as the particles become coarser. Thus, under a configured ball mill with a specific ball size, the mill performance will be affected by various feed particles. In terms of ore properties, it will not only determine ore specific appearance function but also affects the breakage rate in the mill simulation (Austin et al., 1984; Herbst & Fuerstenau, 1980). Normally, under the same grinding conditions, the increases in ore coarseness, hardness, and mill throughput will result in coarser ball mill products. In mill operations, although feed material characteristics are hard to control, feed coarseness and PSD can still be manipulated by using screens. (Rahal, Roberts, & Rivett, 2011) Pulp density Pulp density is another operation factor that can have a large impact on ball mill operations (Bazin & Obiang, 2007; Mulenga & Moys, 2014). As long as slurry can easily pass through the mill, pulp density should be maintained at high levels during operations. Wills and Finch (2015) point out that “it is essential that the balls are coated with a layer of ore; too dilute a pulp increases metal-to-metal contact, giving increased steel consumption and reduced efficiency. Ball mills should operate between 65% and 80% solids by weight, depending on the ore.” If the slurry density is too high, particle breakage that results from the impact mechanism will be weakened (Mulenga & Moys, 2014; Rajamani, Songfack, & Mishra, 2000).   13  Mill charge Mill charge volume is another sensitive factor affecting mill performance. “Ball mill charge filling is usually about 30-45% of the internal volume, about 40% of this being void space” (Wills & Finch, 2015). It is reported that with a given mill speed, lower mill loadings (11-19%) show more cataracting action than higher loadings (23-29%), and result in  lower grinding efficiency (Fortsch, 2006). When the mill load is lower than 25%, specific energy consumption may increase by up to 25% and produces a higher mill capital cost. However, mill charge can also not be too high. With too much mill loading, lift distance will be greatly reduced and the impact mechanism will be weakened in ball mill grinding (Mulenga & Moys, 2014).  The relationship between charge filling and net power draw is shown in Figure 2-5, the maximum net power draw takes place at around 45% mill filling. Either an increase or decrease in mill filling will result in reduced mill power draw. In mill operations, 45% mill filling is the industrial ball mill operation limit (Wills & Finch, 2015) and no mills should be operated beyond this point.  Figure 2-5 Effects of mill filling on net power draw (Wills & Finch, 2015) 14  2.3 Variable speed ball mills As a large energy consumer within the industry, mill availability and efficiency always represent an important issue. Since the ball mill was introduced into the mining industry, fixed speed motors have been commonly used in most mines. To minimize the influence of ore characteristic variations, and to gain optimum mill performance, traditional operation parameters such as water addition and ball load are usually adjusted. However, these adjustments are time-consuming and usually result in unavoidable medium wear as well as a higher risk of unqualified target grind size (Atutxa & Legarra, 2015). The development and application of variable speed ball mills greatly simplify mill operations by allowing quick responses to mill variations. They also provide greater operational flexibility and freedom to mill operators. Because of their simplified structure, variable speed drives (VSD) also require less maintenance, which greatly reduces operating costs and increases ball mill availability (Ahrens & Gonser, 2007; Atutxa & Legarra, 2015; Ow & Bomvisinho, 2010; Tozlu, Lim, Castillo, & Sobil). In addition to being used in new mills, VSDs can also easily be adapted to old fixed ball mills through simplified modifications. During real mill operations, typical VSD ball mills usually operate from 65% to 85% of critical speed (Egbe, 2013; Wills & Finch, 2015), yet fixed speed ball mill can be only operated at the designed fixed speed.  2.3.1 Variable speed drive The grades of ore deposits have decreased in recent years (Batterham & Elvish, 2009). To maximize mill throughput and increase economic benefits, larger machines with higher power requirements have been developed and installed. Significant progress and development have taken place in motor technology to meet the higher power draw demand. Since the development of the first fixed speed synchronous or wound motor with only 2MW power, to the recent Gearless Mill Drive (GMD) ball mills with 22 MW power, it took less than 50 years (Ow & Bomvisinho, 2010). 15  Motors used in the mining industry can be roughly classified into three groups: high speed, low speed, and gearless mill drives (Atutxa & Legarra, 2015; Tozlu et al.). Squirrel cage induction motors are the most common high-speed motors, and synchronous motors are the most common low-speed motors (Ow & Bomvisinho, 2010). Both are typically found in one or two pinion configurations (Doll & Barratt, 2010). High-speed motors tend to have lower initial costs but have higher maintenance costs and are less efficient (Atutxa & Legarra, 2015; Tozlu et al.). GMD is the most efficient, but also incur the highest capital costs and longest installation time (Wills & Finch, 2015). Typical efficiencies of these motors in 16 MW ball mills are shown in Table 2-2. Table 2-2 Overall system efficiency for 16 MW ball mill (Ow & Bomvisinho, 2010) - VSD (High speed) VSD (Low speed) VSD (GMD) Transformer 99.1% 99.1% 99.1% Converter 98.6% 98.6% 99.2% Motor 97.2% 97.2% 96.8% Gear reducer 98.5% n/a n/a Ring-gear 98.0% 98.0% n/a Overall efficiency 91.7% 93.1% 95.2%  2.3.2 Effects of speed As a vital control variable, mill speed has been studied and evaluated by numerous researchers. Its effects on the mill performances can be classified into four parts: volumetric discharge, charge shape, specific breakage rate and mill power and torque. 16  Volumetric discharge Mill speed has a direct effect on the material discharge rate in the ball mill. It has been reported that total volumetric discharge can be separated into flowrate through the grinding media and flowrate through the slurry pool (Atutxa & Legarra, 2015). The relationships between mill speed and two different discharge flowrates are shown in Equation 2-3 and Equation 2-4, respectively (King, 2012).  𝑄 = 𝑄𝑚 + 𝑄𝑡 Equation 2-2  𝑄𝑚 = 6100 𝐽𝑝𝑚2 𝛾2.5 𝐴 Φ−1.38𝐷0.5 Equation 2-3  𝑄𝑡 = 935 𝐽𝑝𝑡 𝛾2 𝐴 𝐷0.5 Equation 2-4 where, Q = Total mill volumetric discharge (m3/h) Qm = mill discharge flowrate through grinding media (m3/h) Qt = mill discharge flowrate through slurry pool at the toe of charge (m3/h) A = total discharge grate open area (m2) D = mill inside diameter (m) γ = grate design parameter ɸ = critical mill speed percentage (%) Jpm = fractional slurry hold up in the grinding media (%) Jpt = fractional slurry hold up in the slurry pool (%) Charge shape Mill speed has a large impact on the shape of mill charge, and it is also the most feasible way to change the charge shape within a short period of time during mill operation. The detailed 17  relationship between mill speed and charge shape are shown in Figure 2-6. Thus, the toe and shoulder which are used to define charge shapes also change with the increase of mill speed. Many studies have shown that the toe angle increases slightly with mill speed until 85-87% of critical speed, at which the toe angle will quickly drop back because of centrifuging (Mulenga & Moys, 2014). However, the shoulder angle keeps increasing with mill speed, and in comparison, is affected more than the toe angle (Lameck, 2005b; Liddell & Moys, 1988; Moys & Skorupa, 1993). The relationship between mill speed and toe and shoulder angles is shown in Figure 2-6.   Figure 2-6 Toe and shoulder positions of load at various speed and mill fillings (Liddell & Moys, 1988) Specific breakage rate As an operational variable, mill speed has a significant effect on breakage rates. As discussed in Section 2.2.3, ball mill grinding consists of three different breakage mechanisms: impact, abrasion, and attrition. The breakage contributed to by these three mechanisms will change at different mill speeds. Some researchers believe that the rise of mill speed will promote a cataracting action (impact mechanism) of grinding media and lead to a more efficient size reduction of coarse 18  particles (Austin et al., 1984; McIvor, 1983). This relationship was confirmed by de Carvalho and Tavares (2013) and the test result is summarized in Figure 2-7.  Figure 2-7 Effect of mill speed on breakage rate (de Carvalho & Tavares, 2013) Mill power and torque Speed can affect mill power in two ways. First, speed has a linear relationship to mill power when torque is held constant. Second, torque will change with the rise of mill speed. Since the ball mill begins at a lower speed, power is found to be almost linear as the increase of mill speed, as power is influenced more significantly by mill speed than increased torque. However, as the mill speed increases, the center of gravity of the mill charge shifts gradually towards the mill’s center and derives a gradually decreased torque, thus functioning to reduce mill power. So mill power increases with increased mill speed until a maximum point, and then drops as speed increases until the whole charge is centrifuging when the net power drops to zero (Atutxa & Legarra, 2015; King, 2012). Tests conducted by several researchers (Lameck, 2005b; Liddell & Moys, 1988; Moys & Skorupa, 1993) confirm the relationship between mill speed with power and torque. Selected results are displayed in Figure 2-8 and Figure 2-9.  19   Figure 2-8 Power variation with mill speed and charge filling (Lameck, 2005a)  Figure 2-9 Variation of torque with speed and filling (Liddell & Moys, 1988)   20  2.3.3 Benefits of variable speed ball mills Process optimization and flexibility Mill optimization usually consists of throughput improvement, final PSD stability, power draw and media wear minimization (Ow & Bomvisinho, 2010). Without tonnage constraints, fixed speed ball mills are usually used with a maximum ball charge and a higher fixed mill speed (Ahrens & Gonser, 2007). The effects of most ore characteristic changes are assigned to be offset by the VSD SAG mill (Ahrens & Gonser, 2007), giving a constant feed size to the ball mill circuit.  However, this action usually results in the development of two issues. The first is that even with a similar feed PSD, the ball mill circuit still faces issues that result from ore hardness. Fixed speed ball mill optimization is limited by traditional time-consuming control variables when feed material changes (hardness and feed size) are encountered. Without a speed control strategy, operators would have to optimize the process by adjusting ball loads, changing levels of water addition, or even shut down the ball mills (Vijfeijken et al., 2012). These strategies would inevitably result in the production of unsatisfactory products and lower grinding availability. The second issue is that the process does not always take place as expected. For instance, if ore characteristics are outside the control range of SAG speed, without a quick and efficient response, changed SAG product sizes will bring big impacts on the ball mill and flotation performance. Speed control can be used as a quick and efficient tool to find the optimal operational point while maintaining a constant product size (Ow & Bomvisinho, 2010), which in turn provides additional freedom for operators. By combing ball load and other control variables, mill power can be utilized more wisely, and energy savings could be realized.   21  Electrical friendliness Mining operations are typically developed in remote areas where it is harder and more expensive to access power and infrastructure (Atutxa & Legarra, 2015). High starting currents that result from fixed speed motors will cause high stress on the network and endanger other power consumers in the plant (Ow & Bomvisinho, 2010). In contrast, VSD provides a soft mill start with a low starting current, something that significantly avoids the shutdown and voltage dips brought about by fixed speed motors. Additionally, the VSD can be operated under low voltage conditions with a lower speed and torque. The drive will not turn off until it encounters a long-time power loss or dangerous situation, which is very useful in remote areas where networks are weak (Ow & Bomvisinho, 2010). Maintenance and operational friendliness Maintenance and operational friendliness are the other benefits derived from the variable speed ball mills. With soft machine start and stop sequences, VSD greatly relieves the stress and damage suffered by motor mechanical systems compared to the direct motor starts of fixed speed drives (Atutxa & Legarra, 2015).  When the mill comes to rest, the material inside the mill tends to settle down and solidify, forming frozen charge (Ahrens & Gonser, 2007; Tozlu et al.). When the mill re-starts, the frozen charge will stick to and go up with the mill shell to a large angle (90 to 180º), where the charge will break from the shell, fall through the mill and land heavily on the mill chamber (Ahrens & Gonser, 2007). The frozen charge detection capability provided by VSD solves this problem. After the mill starts, the position of the charge and torque are calculated in real time, and will slowly increase the mill angle to a position where the charge starts to cascade. The mill will then begin to accelerate to the 22  designated mill speed. If the charge does not cascade before a certain critical angle, the mill will stop and then start to inch very slowly to loosen the frozen charge. This frozen charge detection procedure is repeated until the mill can start safely (Atutxa & Legarra, 2015).  This action can not only save a large amount of time on mechanical arrangements but also greatly reduce severe damage to the mill shell, bearings and liners. Reliability and availability are very critical for grinding operations and have strong effects on mill productivity. In addition to all the other factors of influence, “liner replacement represents a major cause of mill shutdown” (Ow & Bomvisinho, 2010) and traditional replacement methods are usually unreliable and time-consuming. VSD can easily solve this problem by accurately and quickly turning the mill to the specific angle (specific line position) needed with no torque left on the bearing (Ahrens & Gonser, 2007; Atutxa & Legarra, 2015; Ow & Bomvisinho, 2010). As well, under a balanced load condition, operators can conduct maintenance in a much safer manner.  In addition, the landing point and impact energy of mill trajectory largely depend on mill speed, and liner and ball wear can be greatly reduced through the usage of mill speed. Considering the costs of liners and media (Figure 2-10) and the improvement of mill availability, the benefits of using variable speed ball mills are considerable.  23   Figure 2-10 Grinding cost contributed by liner, media, and energy (Metso, 2015) The variable speed solution can also provide flexible operating conditions during the process of commissioning and startup, filling, emptying, and process interruption. In some cases, there will be no ore feed to the ball mill because of a short shut down of the SAG mill. Without a variable speed solution, the ball mill should either be washed out of samples and stopped or be kept running while grinding its own balls (Vijfeijken et al., 2012). VSD allows the ball mill to be operated at a relatively lower speed where no grinding takes place, and the charges are just tumbling. When the SAG mill recovers, the ball mill can immediately be accelerated to normal speed, resulting in a significantly reduced operation downtime (Vijfeijken et al., 2012).  2.4 JK SimMet simulation 2.4.1 Introduction JK SimMet was originally developed by JKMRC in 1982 based on their more than 50 years of studies in the area of comminution (Bailey, Lane, Morrell, & Staples, 2009; McKee & Napier-Munn, 1990). “It is a steady-state software which allows users to mass balance, model fit, and to simulate the comminution circuits” (Schwarz & Richardson, 2013) and “it integrates all tasks 24  associated with data analysis, design, and optimization” (Split Engineering LLC, 2018). Because of its simplicity, effectiveness, and user-friendliness, JK SimMet has become the most widely accepted simulation software, with over 350 software packages in use around the world (Bailey et al., 2009).   JK SimMet decouples ore characteristics from machine characteristics (Schwarz & Richardson, 2013). Ore characteristics can be represented by the ore-specific appearance function and be independently obtained using the JK drop weight test. Machine-related characteristics can be derived by non-linear least squares model fitting to the operating data (Napier-Munn, Morrell, Morrison, & Kojovic, 1996).  2.4.2 Ball mill model  Perfect mixing model Ball mill models can be classified into two groups: one group are black box models that aim to build the relationships between feed and product PSDs, and the other group are referred as fundamental models (e.g. DEM) that calculate movements and breakage events for each particle within the process (Napier-Munn et al., 1996). The perfect mixing model developed by Whitten (Whitten, 1976) belongs to the first group and is utilized for ball mill modelling in JK SimMet. The perfect mixing model presumes the ball mill as a perfectly mixed container, and the process can be described in Figure 2-11. Sifi pi Figure 2-11 Fundamental principle of perfect mixing model fi, si and pi are mass of ith size fraction in the feed, mill, and product, respectively.  25  When the mill operates at steady state, the mass of a single size fraction, i, should be balanced and can be represented by the following equation: Feed in + breaking in = Product out + Breakage out  𝑓𝑖 + ∑𝑎𝑖𝑗𝑟𝑗𝑝𝑗𝑑𝑗= 𝑝𝑖 +𝑟𝑖𝑝𝑖𝑑𝑖 𝑖𝑗=1 Equation 2-5 where, aij is appearance function (describes the fraction of size range j which reports to size range i after breakage) ri and rj are rates of breakage per unit of time that characterizes the rates of disappearance in the size fraction i and j, respectively di is discharge rate of size fraction i From Equation 2-5, it is clear that the ri/di ratio can be calculated for each size fraction if the feed size distribution, production size distribution and reasonable appearance function are provided. Detailed mechanisms of the perfect mixing ball mill model are shown in Figure 2-12.  Figure 2-12 Mechanisms of the perfect mixing ball mill model (Napier-Munn et al., 1996) 26  Considering that mill retention time is influenced by mill volume and volumetric feed rate (Q), the di can be corrected to di* using Equation 2-6.  𝑑𝑖∗ = (𝐷2𝐿4𝑄) 𝑑𝑖 Equation 2-6 where, di* is corrected di D and L are mill diameter and length in meter The typical discharge rate remains almost constant for small particles and then decreases quickly when it approaches grate size. As described in Section 2.2.4, typical breakage rates first increase with particle size and then decrease after passing their maximum point.  Then, based on the corrected equation, the relationship between feed PSD and product PSD can be built using a full set of r/ d* ratios. In JK SimMet, the r/ d* function is represented by a cubic spline function and can be derived by fitting the ball mill model to operational data with only 3 to 4 points (knots) (Napier-Munn & Lynch, 1992; Napier-Munn et al., 1996).  Figure 2-13 Variation of parameter r/d* with particle size (Napier-Munn & Lynch, 1992) 27  Scaling the ball mill model In JK SimMet, “the ball mill can be scaled for mill size, speed, load and even the make-up ball size and it can be achieved by modifying the fitted r/d* function according to mill dimensions and operating conditions as described in the equation below” (Napier-Munn et al., 1996). [𝑟𝑑]∗𝑆𝐼𝑀= [𝑟𝑑]∗𝐹𝐼𝑇[𝑑𝑆𝐼𝑀𝑑𝐹𝐼𝑇]0.5[(1 − 𝐿𝐹𝑆𝐼𝑀)𝐿𝐹𝑆𝐼𝑀(1 − 𝐿𝐹𝐹𝐼𝑇)𝐿𝐹𝐹𝐼𝑇] [𝐶𝑆𝑆𝐼𝑀𝐶𝑆𝐹𝐼𝑇] [𝑊𝐼𝐹𝐼𝑇𝑊𝐼𝑆𝐼𝑀]0.8 Equation 2-7 where,  d = mill diameters  LF = mill load fraction (0.3 to 0.45 after grinding out)  CS = fraction critical speed (0.55 to 0.80) WI = work index - either measured or operating may be used for scaling, provided both                        are of the same type.  FIT identifies the base case (“fitted” conditions)  SIM identifies the scaled case (“simulated” conditions) When changing the mill operating conditions, the r/d* will change correspondingly using Equation 2-7. Thus, the ball mill product size distributions under various operating conditions can be predicted from the changed r/d* value and measured appearance function by using Equation 2-5. Besides, when input new WI values, new ore performance in the ball mill can be predicted with their corresponding ore-specific appearance functions and predicted r/d* function (Napier-Munn et al., 1996).    28  2.4.3 Appearance (breakage distribution) function measurement Appearance function is assumed to only be related to material properties and can be independently derived from the complete product size distribution that results from a single breakage event (Narayanan, 1987; Narayanan, 1985). Many studies have already proven that the breakage distribution function derived from a single breakage event can be used to accurately describe the performance of comminution equipment. (Narayanan, 1987; Narayanan, 1985; Rumpf, 1973; Schonert, 1979, 1981). There are three common single particle breakage test methods: dynamic loading (drop weight test), slow compression and single impact. After reviewing the tests’ principles and simulating the appearance functions derived from different test methods in comminution models, the research concludes that final product size distributions are very similar (Awachie, 1983; Narayanan, 1987; Narayanan, Lira, & Rong, 1988). As described in JK ball mill models (Napier-Munn et al., 1996), the ore appearance function is  measured through dynamic loading method using either a drop weight tester or pendulum breakage tester. The drop weight tester marks the benefits of providing a wider energy input range, has a wider test ore size range, shorter test duration, and greater precision than the traditional pendulum test machine (Napier-Munn et al., 1996). It usually consists of a steel drop weight and a steel anvil where the test ore can be placed. By changing the release height and the mass of the drop weight, the input energy can be controlled within a wide range. This method usually involves conducting drop weight tests on a narrow range of ore size fractions under various input energies and analyzing the resulting particles PSDs using screens in a √2 series of screen apertures (Napier-Munn et al., 1996; Narayanan, 1988).  29  Appearance function is affected by input energy and particle size. To find a suitable input energy and test particle size, Narayanan tested 3 narrow sized fractions ranging from 9.5 mm to 2.36 mm with three various input energy levels on two different samples (Narayanan, 1987; Narayanan, 1985). The test results show that particle size distribution remains the same with same specific comminution energy, and breakage distribution is normalized with respect to particle size (Narayanan, 1987; Narayanan, 1985). Thus, Narayanan concluded that “the product size distribution of a certain particle size at a standard level of input energy can be used for the determination of the breakage distribution function” (Narayanan, 1985). Based on the JK SimMet manual, in this study the ball mill ore-specific appearance function is determined using a standard input energy of 41.788 kg × cm, applied to the -5.6+4.75 mm size fraction (Napier-Munn et al., 1996). The effects of the breakage distribution functions derived from various input energy levels on the breakage rate function have also been evaluated by Narayanan (Narayanan, 1985). The test results show that the breakage rate parameters change in a relatively similar manner to compensate for the change in breakage distribution function. Therefore, the choice of the input energy does not influence the relative nature of the variation of breakage rate parameters with particle size. 2.4.4 Power model A power model is used to predict the ball mill power consumptions under various operating conditions. In JK SimMet, the ball mill power model was developed primarily based on studies conducted by Morrel (Morrell, 1993; Morrell, 1996a, 1996b; Morrell, Napier-Munn, & Andersen, 1992). It has proven to be very accurate by comparing model-predicted power with the real power of 82 datasets of ball mills, SAG and AG mills ranging from 6.2 to 10000 kW (Morrell, 1996b). 30  However, recent research shows that this model will lose its predictive accuracy when used for the mill speed higher than 90% Cs and for tube mills (Mulenga & Moys, 2014). In this power model, charge toe (Ɵt) and shoulder (Ɵs) are used to define the mill charge position They are recorded with an angular displacement method, measured in an anti-clockwise direction from the 3 o’clock position (0 degrees) (Morrell et al., 1992; Napier-Munn et al., 1996). The assumed charge shapes for grate mills and overflow mills are shown in Figure 2-14.  Figure 2-14 Simplified charge shape for grate (left) and overflow mills (right) (Morrell et al., 1992)  Figure 2-15 Schematic of mill charge for energy balance approach (Morrell, 1996b) Based on reasonable charge motion and charge shape (Figure 2-15) assumption, the final overflow ball mill net power draw is given by Morrell (1996b). 31  𝑃𝑛𝑒𝑡 =𝜋𝑔𝐿𝑁𝑚𝑟𝑚3(𝑟𝑚 − 𝑧𝑟𝑖){2𝑟𝑚3 − 3𝑧𝑟𝑚2𝑟𝑖 + 𝑟𝑖3(3𝑧 − 2)}  {𝜌𝑐(sin 𝜃𝑆 − sin 𝜃𝑇) + 𝜌𝑝(sin 𝜃𝑇 − sin 𝜃𝑇𝑂)}+ 𝐿𝜌𝑐 {𝑁𝑚𝑟𝑚𝜋(𝑟𝑚 − 𝑧𝑟𝑖)}3{(𝑟𝑚 − 𝑧𝑟𝑖)4 − 𝑟𝑖4(𝑧 − 1)4} Equation 2-8 where, L = mill charge length Nm =rotational rate at the mill shell liner wear face rm = mill radius at the mill shell liner wear face ri= charge of inner surface radius which marks the boundary between the active part of the charge and the inactive kidney (see the mill charge shape in Figure 2-14) Z= (1-Jt)0.4532 Jt = fractional mill filling ρp = slurry density ρc = grinding charge density ƟTO = slurry toe angle for overflow discharge mill ƟT = charge toe angle Ɵs = charge shoulder angle Based on the net power equation, gross power can be calculated as ((Napier-Munn et al., 1996) Gross power = no-load power + (k × charge motion power) Equation 2-9 where, Gross power                   = power input to the motor no-load power                = power input to the motor when the mill is empty 32  charge motion power     = power associated with charge motion k × charge motion power = net power net power                       = total power input to the charge k                                     = lumped parameter which accounts for heat losses and energy                                            consumption, plus inaccuracies associated with assumptions                                                and measurements Based on Equation 2-8 and Equation 2-9, the ball mill power under various operating conditions can be predicted. With the predicted product sizes and mill power consumptions, reasonable VSD ball mill operating conditions that are responsive to changing ore characteristics can be obtained.  2.4.5 JK SimMet applications JK SimMet has been widely used for flowsheet design and plant optimization. It usually employs the following steps: feed ore characterization with single particle drop weight test, mass-balance flowsheet, and model fit specific equipment using known plant and test information. (Nikkhah & Anderson, 2001). JK SimMet can be used as a valuable tool for accurately representing specific comminution configurations with mathematical models and predicting the “what-if” scenarios for the existing or green-filled plants (Nikkhah & Anderson, 2001; Pokrajcic, 2008; Runge, Tabosa, Holtham, & Valle; Valery et al., 2007). It also marks the benefits of ease of access and installation, no powerful computer requirements, no user programming capacity requirements, permission of input engineering knowledge, flexible adaption to various plant capacities and flowsheets (Napier-Munn & Lynch, 1992). JK SimMet has proven to be an asset for understanding the process of comminution with decoupled ore characterization and machine characterization (Schwarz & Richardson, 2013), and has been 33  successfully applied many times in mill power predictions, mill optimizations and mill designs (Jankovic, Valery, & Davis, 2004; McKee & Napier-Munn, 1990; Morrell, Johnson, & Revy, 1991; Pokrajcic, 2008; Runge et al.; Schwarz & Richardson, 2013; Zhang, 2016). Because of its proven practical applications in optimizing mill performance, JK SimMet was chosen for simulating and developing recommendations for Copper Mountain Mine. 2.5 Summary of literature review Since their first application in the mid of 19th century, ball mills have been widely applied in the mining industry and have played a vital role in comminution. Driven by a desire to exploit lower grade mineral resources, ball mills have increased from initial 0.9 m in diameter with only 2MW power to the recent 6.7m with 22 MW power. As a major energy consumer, optimizing operational power efficiency in ball mills has drawn a great deal of attention from the mining industry. Discovering new and efficient ways to operate ball mills and improve their power efficiency has become a hot topic.  Ball mill operation is a complex process and there are many variables, which can bring deviations to the target product size. However, traditional operation strategies (ball load and water adjustments) are time-consuming and can always result in unqualified products. The development and application of speed control represent one approach that has potential to upgrade a grinding process to achieve a higher level of productivity and profitability with less energy consumption. Speed control can not only provide additional degrees of freedom for operators but also support mill maintenance and increase overall system availability.  JK SimMet is a simple yet powerful tool for studying what-if questions in the comminution circuit. Due to its ore characteristics consideration, it has been used widely for mill simulation and 34  optimization in comminution circuits. Because of its proven practical applications in optimizing mill performance, the performance of variable speed ball mills in Copper Mountain Mine will be analyzed using this software. With perfect mixing model and power draw prediction method in JK SimMet, the ball mill circuit product size distribution and power consumption will be analyzed under various operating conditions (various mill speed, mill load, and ore characteristics). Based on the simulation results, reasonable and effective operational strategies under various operational conditions will be proposed based on simulation results.    35  Chapter 3: Experimental program The primary objective of this research is to gain a better understanding of the performance of variable speed ball mills within constantly changing mill operating conditions and to provide adequate optimization suggestions for the Copper Mountain Mine based on the study’s results. To meet this objective, the research was divided into two parts. The first part involved collecting representative mill and geo-metallurgical samples at the Copper Mountain Mine and gathering ore characterization data by conducting relative ore characterization tests (BBWI and single particle drop weight tests) in the lab. The second part involved running simulation software by utilizing the data obtained to predict the performance of the ball mill-cyclone close circuit. In the first half of this chapter, detailed methodology, sample description, and ore characterization tests are introduced. In the second half, the JK model construction and simulation will be described. 3.1 Methodology All the samples and data collected from the mill survey were classified and analyzed in three different flowsheets. The first set, DCS (data collection system) data, included equipment dimensions, operation parameters, mill power and throughput. The second contained all the stream samples, which were first dried in the oven, and then subjected to a particle size analysis on the separated representative samples using screens with a √2 series of screen apertures. The third group consisted of SAG feed sample and all the geo-samples which were characterized by BBWI and drop weight tests. Based on the collected data, JK SimMet models were built and used for simulation and optimization. The main structure of the test methodology is shown in Figure 3-1.  36  Sample and Data CollectionDCS Data Mill Survey Samples Geo-metallurgical SamplesEquipment ParametersCyclone Operating Pressure Volumetric FlowMill PowerSolid Percentage (%)Size DistributionOre Characterization:BBWISingle Particle Drop Weight TestJK Model Development & SimulationCircuit IdentificationAnalysis Analysis Analysis Figure 3-1 Experimental program flowsheet 3.2 Copper Mountain mine The Copper Mountain Mine is located 15 km south of Princeton, British Columbia. 75% of the Project is owned by Copper Mountain Mining Corporation and 25% by Mitsubishi Materials Corporation (Vijfeijken et al., 2012). The mill throughput is around 40,000 tpd and the main product is copper concentrate. Copper Mountain consists of one SAG circuit and two ball mill circuits and all mills have variable speed drives. The detailed equipment information is summarized in Table 3-1. 37  Table 3-1 Detailed equipment information in Copper Mountain Mine (Vijfeijken et al., 2012) Design parameters Unit SAG mill Ball mill Number of mills [-] 1 2 Dimensions [ft] 34 × 20 24 × 39.5 Installed power [kW] 12,800 (13,800*)  12,800  3.3 Sample description There were two groups of samples which were collected at Copper Mountain Mine. The first one consisted of 12 samples, collected from different streams of the onsite comminution circuits. The second one consisted of onsite SAG mill feed and 6 representative geo-samples. A detailed description will be given in the following sections. 3.3.1 Survey samples To evaluate the effects of the variable speed drive on the comminution optimization, a sampling survey around the whole grinding circuit was conducted by Copper Mountain Technical Group and UBC Mining VSD Research Group on May 18th, 2017. Samples from 12 streams were collected during this survey. When the mill performance was at steady state, three duplicate samples were collected simultaneously over an hour period for each stream during mill operations. The SAG feed conveyer belt was then shut down for sampling. Cyclone feed samples were collected from a by-pass pipe connected to the cyclo-pack distribution head. The detailed grinding circuit flowsheet and sampling points were shown in Figure 3-2.  38  Ball MillHydrocycloneSplit BoxVibration ScreenSAG MillPebble CrusherSAG Feed BeltStockpileBM U/FBM O/FBM Cyc. FeedBM ProductSAG Fresh FeedPebble ProductScreen U/SScreen O/SSAG ProductBall MillHydrocycloneBM U/FBM O/FBM Cyc. FeedBM ProductSumpSump# 1# 2SAG Mill shutdown to measure the ball charge Figure 3-2 Copper Mountain Circuit Schematic 3.3.2 Geo-metallurgical samples There were six types of representative geo-metallurgical samples (Figure 3-3), which were collected by geologists at the Copper Mountain Mine and were analyzed by the VSD group. Geo-sample #1 and geo-sample #6 were collected from pit 3, and the other geo-samples were collected from pit 2. Detailed location information for each geo-metallurgical sample is shown in Figure 3-4, and detailed sample descriptions will also be included in this section. 39   Figure 3-3: Geo-sample receipt (Top Geo-unit 1-3, Bottom Geo-unit 4-6)  Figure 3-4: Locations of Geo-samples    40  Geo-sample #1: Albite>Hornfels (Very hard) This sample was mainly albite with weak hornfels alteration. It was a very hard, clean ore with very fine to fine-grained (assumed 120 microns grind) chalcopyrite and a lot of pyrite. It also contained traces of chlorite. Geo-sample #2: Potassic>Albite (Hard) This sample was potassic and albitic alterations. It was a hard, clean ore with medium grained (assumed 290 microns grind) chalcopyrite. Geo-sample #3: Albite>Potassic (Hard) This sample was mainly albite with weak potassic alteration. It was also a hard ore, with traces of oxidization and with medium grained (assumed 290 microns grind) chalcopyrite and coarse pyrite, located inside the high pyrite zone. Geo-sample #4: Potassic (Medium hardness) This sample had strong potassic alteration, medium hardness, and was a clean ore with coarse-grained (assumed 320 microns grind) chalcopyrite. Geo-sample #5: Potassic>Argillic (Soft-medium) This ore had potassic alteration with a slight argillic alteration. It had soft to medium hardness, and medium to coarse-grained (assumed 290-320 microns grind) chalcopyrite mineralization. Geo-sample #6: Volcanic Hornfels (Very hard) This ore was mainly hornfels altered volcanic. It was very hard, possessing very fine to fine-grained (assume 120 microns grind) disseminated chalcopyrite and pyrite, and narrow (1 mm) chalcopyrite veins. 41  As can be seen from the sample description, the mineral compositions and target grinding size are totally different for different geo-samples. The distinct ore properties may bring variations in mill product size, mill throughput, and mill operation efficiency and thus create operation challenges. 3.3.3 Sample preparation After completing the mill survey and collecting representative geo-samples, adequate sample preparation was conducted using the flowsheet shown in Figure 3-5.  For SAG feed sample, it was firstly split by using Rotary Splitter and then two representative samples were collected. Corresponding particle size analysis was conducted on one representative split sample by using Gilson testing screens. After obtained the SAG feed PSD, this representative sample was separated into different narrow size fractions and was ready for JK drop weight test and appearance function measurement. Another SAG feed representative sample was crushed down to 3.35 mm for BBWI measurement.  To obtain representative sub-samples, each geo-sample was crushed down to 63 mm by using the jaw crusher installed at UBC. Then they were split into two parts. The first part represented 3/4 of the total materials and was used for JK drop weight test and appearance function measurement. Before conducting the tests, adequate crushing and screening processes were needed to separate the materials into various required narrow size fractions. The second part represented 1/4 of the total materials and was crushed down to 3.35 mm for BBWI measurement.   42  Geo-Sample #1Geo-Sample #2Geo-Sample #3Geo-Sample #4Geo-Sample #5Geo-Sample #6Screen at 63 mmJaw Crusher+ 63 mm materialSplitting- 63 mm materialBBWISingle Particle Drop Weight Test¼ material¾ materialA and b measurementsAppearance function measurementJaw CrusherScreeningCone CrusherJaw CrusherCone CrusherScreening- 3.35 mm material+ 3.35 mm materialSAG Belt Cut SamplesSplittingOther PurposesRepresentive Samples  Figure 3-5 Sample preparation flowsheet 43  3.4 Ore characterization In this section, three different types of ore characterization methods will be described in detail: the BBWI test, the JK drop weight test and the appearance measurement. They were employed to characterize ore hardness, ore competency, and ore breakage properties, respectively.  3.4.1 Bond ball mill work index (BBWI) test  Figure 3-6 Bond ball mill work index test equipment All the spilt representative samples were first crushed to -3.35 mm with the jaw crusher and cone crusher installed at UBC. Then, the standard Bond ball mill work index test procedure was followed using 212 microns as the closing screen size. Bond ball mill work indices for the SAG belt cut sample and each geo-metallurgical sample are summarized and analyzed in the next chapter and detailed test work data are shown in Appendix B.      44  3.4.2 JK drop weight test   Figure 3-7 JK drop weight tester (left), abrasion tester (right) The drop weight testing was performed using the JK drop weight tester installed at UBC (Figure 3-7 left). After screening the samples into different size ranges, particles were randomly picked from each size range and stored in individual bags. Each set of particles was tested under one specific energy level, and all crushed samples were collected in individual bags per set. Detailed particle requirements and specific energy levels are shown in Table 3-2.  A standard abrasion test (Figure 3-7 right) was performed using a 300 mm diameter ×300 mm long tumbling mill. A 3kg portion of -55+38 mm ore was ground for 10 minutes at 53 rpm (70% of critical speed) (Napier-Munn et al., 1996). All the samples that were tested using the JK drop weight tester and the abrasion tester were size-analyzed using standard JK screens on a √2 series of sieves. Based on the size distributions, A, b and ta parameters were derived. In this research, test samples included SAG feed, Geo-unit 1, Geo-unit 2, Geo-unit 3, Geo-unit 4, Geo-unit 5 and Geo-unit 6 samples.  45  Table 3-2 Qualitative interpretation of DWT results as defined by JKMRC (Napier-Munn et al., 1996) Size range, mm No. of particles Expected Ecs Upper Lower Per set KWh/t 63.0 53.9 10 0.1 0.25 0.40   45.0 37.5 15 0.1 0.25  1.0  31.5 26.5 30  0.25  1.0 2.5 22.4 19.0 30  0.25  1.0 2.5 16.0 13.2 30  0.25  1.0 2.5  3.4.3 Appearance (breakage distribution) function measurement As mentioned in Chapter 2, the r/d* values (machine characteristics) can be generated based on the operation data and appearance function (ore characteristics). The effects of mill operating conditions changes can be demonstrated by scaling up the r/d* values. Thus, it is very important to obtain a set of accurate r/d* values. Considering that survey data is constant, the reliability of the appearance function becomes essential.  In the JK SimMet application, the machine related characteristics (r/d*) are usually calculated based on the JK default appearance function. Based on the survey data conducted in Copper Mountain Mine in January 2017 and May 2017, the corresponding r/d* values of ball mill 1 are calculated by using the default appearance function. The test results are shown in Figure 3-8. It can be seen that although ball mill 1 keeps similar in the operating conditions, the r/d* values which are supposed to be very similar are totally different. It is obvious that the ore properties have already changed significantly during the four months’ operations. With a constant default 46  appearance function, the calculated r/d* values are not reliable. Thus, the default appearance function provided by JK SimMet cannot be used in this study.  Figure 3-8 r/d values obtained with default appearance function The Moly-Cop tools employ the population balance model which is quite similar to the perfect mixing model used in JK SimMet. In Moly-Cop tools, the appearance function can be predicted directly based on onsite mill data. So, the appearance function generated by using Moly-Cop tools was evaluated. The calculated appearance functions of BM 1 by using Moly-Cop tool were compared with a few ore appearance functions measured by JK SimMet, and the results are shown in Figure 3-9. The test results illustrate that the predicted appearance functions in Moly-Cop are much coarser than those measured in JK SimMet. If these two different appearance functions are used, the predicted r/d* values will be very different. Thus, the appearance function predicted by Moly-cop cannot be used in this study.  Therefore, it was decided that the appearance functions for the Copper Mountain ores should be determined experimentally rather than by using the default values provided by JK SimMet or the values predicted by Moly-Cop Tools. 47   Figure 3-9 Appearance function comparison As mentioned in Chapter 2, the ore-specific appearance function can be measured independently by using the drop weight test machine. Although not used commonly in JK SimMet applications, the single particle drop weight test method developed by Narayanan (1987) was accepted by JKMRC and was used to measure ore-specific appearance functions. In this study, this method is adopted and the ore-specific appearance function is determined using a standard input energy of 41.788 kg ×cm (drop weight (kg) × height of drop (cm); 1kg × cm = 0.0981 joules), applied to the -5.6+4.75 mm size fraction (Napier-Munn et al., 1996). According to the standard particle size test method, if the maximum particle size is 4.75 mm, a minimum 200g sample is needed to accurately represent the sample size distribution with results reported to the nearest 0.1% (ASTM International, 2009). Considering that all the samples will pass through the 4.75 mm screen after breakage, the whole size distribution for a standard energy input was measured using 200g samples. The resulting particle size distribution was analyzed by using JK screens on a √2 series of sieves.  48  Breakage size distributions resulting from single drop weight test are assumed to follow the Rosin-Rammler model (Narayanan, 1987). Thus, all the breakage distribution functions were examined using the Rosin-Rammler equation (ROSIN & RAMMLER, 1933) log [ln11 − 𝑌] = 𝑛 log 𝑥 − 𝑛 log 𝑥′ Equation 3-1 where, Y = cumulative fraction finer than x (or cumulative fraction passing/undersize) x = particle size x’ = size modulus (theoretical maximum particle size) n = distribution modulus (spread of the distribution) From Equation 3-1, it can be concluded that if the PSDs derived from single particle drop weight tests fit this relationship very well, the parameters “n” and “x'” can be calculated to predict more size interval particle size distributions. Drop weight and drop height used during the test to input the standard energy are shown in Table 3-3. Table 3-3 Drop weight test specification Head weight (kg) Height (cm) Input energy (kg × cm) 2.6248 15.92 41.788  3.5 JK SimMet model set-up After inputting the survey data and test results, JK SimMet was used to model and simulate the ball mill and cyclone circuit. There are three main components included in JK SimMet, which are 49  the mass balance function, the model fit function, and the simulation function. The theories that these three functions are based on will be illustrated in the following sections. 3.5.1 Model configuration The Copper Mountain Mine process plant consists of one SAG mill-pebble crusher in closed-circuit and two ball mill-cyclone closed-circuits. The product of the SAG mill is classified by a vibrating screen, and screen underflow is split by a split-box and separated into two ball mill circuits. The configured ball mill circuits constructed by JK SimMet are shown in Figure 3-10.  Figure 3-10 Ball mill circuit configuration 3.5.2 Mass balance In JK SimMet, the mass balance accounts for all the related streams and is used to make calculations based on the smallest set of data adjustments. Users can define the accuracy (SD: standard deviation) for the data of each (tonnage, solid percentage, and PSD) through their understanding of the survey. Based on various defined accuracy, the mass balanced flowsheet will change accordingly giving different weights to the data of each stream. The final mass balanced 50  flowsheet is obtained using the least weighted sum of squares values (WSSQ) between the measured data and balanced data.  In this section, all the stream-related data were input into JK models, including solid content, particle size distribution, and mill throughput. As restricted by JK SimMet software, only 1 cyclone O/F PSD and 1 cyclone U/F PSD can be input to the software. To represent all O/F and U/F cyclone streams, input PSDs for cyclone U/F and O/F are calculated based on the average retained percentages of all 8 cyclone O/F streams and 8 U/F streams respectively. Detailed survey data are summarized in Appendix A.  The procedure of mass balance used in this study is described as follows: 1. Input all the stream information (tonnage, solid percentage, and PSDs) into the software 2. Define accuracy for each tonnage, solid percentage, and PSDs 3. Select the equipment, steams and size intervals that need to be mass balanced 4. Set “Tonnage” and “Sizes” as “Adjust” and leave “% solid” and “water tonnage” as “unused” 5. Start iteration, check convergence and compare balanced data with experimental data 6. Set “Tonnage” and “Sizes” as “Fixed” and change “water tonnage” as “Adjust” and “% solid” as “Influence” 7. Start iteration, and check convergence and balanced data 8. If the balanced results are not satisfied, adjust accuracy for specific data and run iteration again 9. Repeat step 8 until a final desired mass balance result is achieved The logic diagram of mass balance is shown in Figure 3-11. 51  Mass balanceStream informationCompared with measured dataWeight coefficient for each class of dataFinal resultsBalanced resultsAdjust coefficientSum of squares Figure 3-11 Mass balance process block diagram 3.5.3 Model fit Model fit is an important section in JK SimMet that characterizes comminution equipment models to represent real mill configurations. In this section, several groups of parameters are used as model inputs, which are machine-dependent parameters, ore-dependent parameters, mass balanced PSDs, 52  tonnages and solid percentages. Model fit is similar to the mass balance section in that the final fitted parameters depend on the least weighted sum of squares value (WSSQ) between fitted data and balanced data. The detailed ball mill and cyclone parameters are summarized in Table 3-4 and Table 3-5. Ore dependent parameters are appearance functions that are measured in Section 3.4.3. Table 3-4 Ball mill model parameters Ball mill parameters Ball mill circuit 1 Ball mill circuit 2 Internal Diameter (m) 7.086 7.135 Internal Length (m) 11.80 11.84 Fraction Critical Speed 0.7760 0.7762 Load Fraction 0.3190 0.3056 Ore Work Index [kWh/t] 24.29 24.29 Max Breakage Rate Factor - K 0.00044 0.00044 Original Mill Ball Top Size (mm) 69.85 69.85 Feed Cone Angle (Flat = 0) 22.5 22.5 Discharge Cone Angle (Flat = 0) 22.5 22.5 Trunion Diameter (m) 1.9 1.9 Ball SG 7.75 7.75       53  Table 3-5 Cyclone model parameters Cyclone parameters Ball mill circuit 1 Ball mill circuit 2 Cyclone Diameter - Dc (m) 0.838 0.838 Inlet Diameter - Di (m) 0.278 0.278 Vortex Finder Diameter - Do (m) 0.356 0.356 Spigot Diameter - Du (m) 0.179 0.187 Cylinder Length - Lc (m) 0.673 0.673 Cone Angle - Theta (degree) 20 20  The procedure of model fit used in this study is described as follows: 1. Replace all the stream information (tonnage, solid percentage, and PSDs) with balanced data 2. Define accuracies for each tonnage, solid percentage and PSD 3. Input machine-dependent parameters and ore-dependent parameters 4. Select the equipment and related steams that need to be model fitted 5. Estimate model parameters (usually starting with default values) 6. Start iteration, check fitted results (residual error and fitted SDs) and compare fitted data with balanced data 7. If the fitted results are not satisfied, adjust estimated model parameters and run iteration again 8. Repeat step 7 until a final desired set of model parameters that can conform fitted data well to the balanced data is acheived. 54  9. If the desired set of model parameters cannot be achieved, repeat the mass balance procedure by giving new accuracy for each tonnage, solid percentage, and PSDs 10. After obtained a new balanced flowsheet and repeat steps 1-8 again until a final desired model fit result is achieved The logic diagram of model fit is shown in Figure 3-12. SimulatorFeed descriptionCircuit configurationPredicted products and streamsModel fitBalanced dataModel parameter estimateAdjusted model parametersSum of squareBest fitted parameters Figure 3-12 Model fit process block diagram 55  3.6 Simulation After completing model fitting, the simulation can be conducted based on the obtained ball mill and cyclone models. As mentioned in Chapter 2, JK SimMet models are very powerful and can accurately predict “what-if” situations.  In order to build adequate variable speed ball mill operation strategies, a sensitivity analysis was conducted and analyzed. The chosen factors included were mill speed (%Cs), mill load (%), water addition and ore types. This selection was based on key findings in the literature review, and the practical requirements of the Copper Mountain Mine’s onsite operations. 3.6.1 Mill speed and mill load Sensitivity analysis of mill speed and mill load were evaluated first due to their importance in mill optimizations. The mill speed was tested in the range of 65% to 80% critical speed and mill load was tested in the range of 25% to 45% mill filling. The template used in this study was shown in Table 3-6. When mill speed and mill load changed, corresponding cyclone O/F P80, mill power draw, and specific energy were recorded. Table 3-6 Template used for sensitivity analysis of mill speed and mill load P80/ Mill power/ Specific energy Mill speed/ % Cs 65 70 75 80 Ball load/ % 25     30     35     40     45      56  Based on the collected data, two 3D graphs were built. The first describes the relationship between cyclone O/F P80 and both mill speed and mill load. The second shows the relationship between mill power draw, mill speed, and mill load. Since the onsite grind size is measured, all mill speed and mill load combinations used to achieve the same product size can be referenced in the first graph. Under these operating conditions, the required mill power draw can be generated from the second graph.  To evaluate on-site mill performance and operating efficiency, the final product sizes for both circuits were set to be the same as those measured at the Copper Mountain Mine. All speed and load combinations that could achieve the same grinding sizes were recorded, and the correlated mill power was analyzed. Based on the results, optimal operating conditions with the lowest power consumption can be obtained. Finally, by comparing optimal conditions to on-site mill operations, the Copper Mountain mill performance can be evaluated.  3.6.2 Water addition Water addition has historically been used for optimization of mill operations. Thus, the effects of water addition and addition points were evaluated based on optimal mill speed and mill load operating conditions. At Copper Mountain, there are two water addition points (pump sump and ball mill feed), and the pump sump adding point is usually used for mill optimization. Based on this information, the water addition effect was evaluated from 200t/h to 700t/h at pump sump. The effect of the water addition points was assessed by gradually changing the water distribution at these two adding points while maintaining the same total amount of water addition. Detailed test information is summarized in Table 3-7. Based on the simulation results, the effects of water addition can be evaluated and adequate operation strategies can be obtained.  57  Table 3-7 Effects of water adding points assessment Water addition at Ball mill feed (t/h) 0 100 200 320.65 Water addition at pump sump (t/h) 320.65 220.65 120.65 0  3.6.3 Target grinding size achievement The simulation results show that onsite mill product size is coarser than target grinding size. Based on the obtained optimal operation strategies of mill speed, mill load, and water addition, reasonable operating conditions, that could be used to achieve the target grinding size, can be obtained by using JK simulation. However, the uneven split feed issue at Copper Mountain Mine requires different grinding tasks for these two grinding circuits. In this section, the effect of uneven split feed issue will be analyzed. Based on the analysis results, adequate operation strategies will be suggested so as to minimize the effects of uneven split feed while achieving a required targeted grinding size.  3.6.4 Ore type With measured ore-specific appearance functions, influences caused by ore type changes can be examined in this section. First, the final circuit product sizes for various ore types were monitored, while all the other operating conditions were kept constant. Then, the theoretical maximum throughput for each ore type was simulated at maximum mill power. Finally, theoretical mill power draw for each ore type was predicted under optimal onsite operating conditions (onsite throughput with optimal mill speed, mill load and water addition operating conditions). Based on these simulation results, a comprehensive data sets can be provided to Copper Mountain Mine for their ore blending.  58  Chapter 4: Test results and discussion 4.1 Ore characterization results The ore characteristics for each sample tested are summarized in Table 4-1. Standard ore hardness and competency classifications are shown in Table 4-2 and Table 4-3, respectively. Table 4-1 Ore characterization results Sample no. Alternation/rock type DWT ta BBWI A b Axb (kWh/t) SAG feed Composite 51.23 0.64 32.79 0.09 24.29 Geo#1 Albite > Hornfel 67.44 0.46 30.85 0.19 22.20 Geo#2 Potassic > Albite 60.76 0.59 36.12 0.22 23.39 Geo#3 Albite > Pottasic 59.25 0.67 39.71 0.15 27.47 Geo#4 Potassic 66.65 0.48 31.66 0.18 20.12 Geo#5 Potassic with slight Argillic 62.73 0.47 29.17 0.26 26.88 Geo#6 Volcanic Hornfels 66.55 0.43 28.81 0.20 21.18 Table 4-2 Hardness classification based on BBWI (Bueno, Foggiatto, & Lane, 2015) Property Soft Moderate Hard Very hard BWI (kWh/t) <10 10 - 15 15 - 20 >20 Table 4-3 Competency classification based on JK DWT (Napier-Munn et al., 1996) Impact resistance parameter Very hard Hard Mod. hard Medium Mod. soft Soft Very soft High energy parameters, A·b <30 30-38 38-43 43-56 56-67 67-127 >127  59  Based on ore hardness and competency classification, all the test samples are categorized in Figure 4-1. To assess the ore properties variations with the changes of time, the historical data which was used for mill design is also shown in this Figure.  Figure 4-1 Ore classification It can be seen that ore properties at Copper Mountain vary significantly. Furthermore, compared to the historical data (pit 2 and 3 in 2011), ore currently being processed is less competent. Most ore types can be classified as very hard ores, with BBWI values ranging from 20 kWh/t to 27.5kWh/t, and A×b values ranging from 39.71, which is moderate competent, to 28.81, which is very competent. As mentioned in Chapter 3, complex ore hardness will have a significant impact on the product size, mill throughput, and mill operation efficiency and thus create many challenges 60  for mill operations. To maintain a consistent mill operation, appropriate operation strategies that are flexible to changing ore types need to be considered.  4.2 Ball mill appearance function JK SimMet can only simulate ball mill comminution for ores with BBWI values below 25 kWh/t.  Since Geo-sample 3 and Geo-sample 5 have BBWI values of 27.47 kWh/t and 26.88 kWh/t, respectively, which exceeds the JK limits, they will not be considered in this study.  The ball mill ore-specific appearance function is determined using a standard input energy of 41.788 kg ×cm, applied to the -5.6+4.75 mm size fraction. For each geo-sample, approximately 200g samples were tested using the single particle drop weight test method, and the resulting particle size distribution was analyzed using JK screens in a √2 sieve series. In JK, it is assumed that no particles will be left in the original size range after the breakage event, thus the daughter particles start from the next size range down. The test results confirmed this assumption, with all the particles having passed a 4.75mm aperture size. The distribution of the daughter particles is shown in Table 4-4.            61  Table 4-4 Particle size distribution Screen (mm) SAG feed Geo # 1 Geo # 2 Geo # 4 Geo # 6 3.35 99.5% 99.9% 99.9% 100.0% 99.9% 2.36 96.6% 98.5% 98.9% 99.2% 98.8% 1.70 87.8% 94.2% 95.4% 95.9% 94.7% 1.18 70.0% 82.1% 85.0% 85.6% 82.4% 0.850 53.8% 67.8% 71.2% 71.7% 67.3% 0.600 40.5% 53.6% 56.7% 57.1% 52.7% 0.425 30.1% 41.3% 43.7% 44.3% 40.4% 0.300 22.7% 32.2% 33.7% 34.6% 31.6% 0.212 17.4% 25.6% 26.4% 27.6% 25.3% 0.150 13.1% 20.1% 20.2% 21.8% 20.3% 0.106 10.0% 16.1% 15.8% 17.5% 16.7% 0.075 7.7% 12.8% 12.1% 13.8% 13.8% 0.053 5.6% 9.8% 9.1% 10.6% 11.1% 0.038 3.7% 7.2% 6.6% 7.8% 8.4%  Materials can easily be lost during the process of single drop weight test. If too much is lost, the final size distribution will be inaccurate and thus affects the reliability of JK models. It can be seen from Table 4-5 that the total material loss during testing were only around 2%, which is within the expected error range.   62  Table 4-5 Mass loss assessment Sample No. SAG feed Geo # 1 Geo # 2 Geo # 4 Geo # 6 Weight before test (g) 214.7 203.9 205.2 205.7 208.9 Weight after test (g) 209.1 200.1 201.3 201.0 204.6 Mass lost percentage (%) 2.61 1.86 1.90 2.28 2.06  As mentioned in Chapter 2, the appearance function and selection function are used to build the relationship between mill feed and mill product. Thus, the number of appearance function size intervals should be consistent with the number of size intervals in the mill feed and product. For all the measured PSDs of the stream samples, there are 20 size intervals with a √2 series of screen sieves, which means 20 size intervals are also required in the breakage distribution function. However, there are 6 size intervals of all geo-samples which are too fine to be accurately measured by Ro-tap screens and can only be obtained by using reasonable predictions.  According to the Rosin-Rammler equation mentioned in Chapter 3, the size distributions of the missing 6 intervals were calculated. The fitted results are shown from Figure 4-2 to Figure 4-6. The fitted parameters and coefficients of determination (R squared) are shown in Table 4-6.  63   Figure 4-2 SAG feed normalization and comparison  Figure 4-3 Geo-sample #1 normalization and comparison 64   Figure 4-4 Geo-sample #2 normalization and comparison  Figure 4-5 Geo-sample #4 normalization and comparison 65   Figure 4-6 Geo-sample #6 normalization and comparison Table 4-6 Fitted parameters and R squared Sample No. SAG feed Geo # 1 Geo # 2 Geo # 4 Geo # 6 n 1.066 0.989 1.020 0.997 0.957 x’ 909 632 610 571 630 R squared 0.9881 0.9830 0.9920 0.9836 0.9765  As Table 4-6 shows, all tested size distributions fit the Rosin-Rammler relationship very well, with only around 2% deviations. Thus, the missing six intervals were accurately predicted based on the known parameters of “n” and “x'”. The final appearance functions are listed in the form of percentage retained in each size interval in Table 4-7.  66  Table 4-7 Appearance function of various samples No. SAG feed Geo # 1 Geo # 2 Geo # 4 Geo # 6 1 0.005 0.001 0.001 0.000 0.001 2 0.030 0.014 0.010 0.007 0.011 3 0.088 0.044 0.035 0.033 0.040 4 0.177 0.121 0.103 0.103 0.123 5 0.162 0.142 0.138 0.139 0.151 6 0.133 0.143 0.145 0.146 0.147 7 0.105 0.123 0.130 0.128 0.123 8 0.074 0.091 0.100 0.096 0.088 9 0.053 0.066 0.073 0.070 0.062 10 0.043 0.055 0.062 0.059 0.051 11 0.031 0.040 0.044 0.043 0.036 12 0.023 0.033 0.036 0.036 0.029 13 0.020 0.030 0.030 0.032 0.027 14 0.019 0.0261 0.025 0.028 0.026 15 0.010 0.017 0.017 0.019 0.018 16 0.007 0.012 0.012 0.013 0.013 17 0.005 0.009 0.008 0.010 0.010 18 0.003 0.006 0.006 0.007 0.007 19 0.002 0.005 0.004 0.005 0.005 20 0.002 0.003 0.003 0.003 0.004  67  4.3 JK SimMet model set-up 4.3.1 Mass balance As mentioned in Chapter 3, the final mass balance flowsheet is determined through a repetitive iterative process of adjusting the standard deviations of each stream and examining the errors between the experimental data and balanced data. As seen in Figure 4-7 and Figure 4-8, the collected ball mill discharge PSDs are even coarser than the cyclone U/F PSDs in the large size range, which means that the experimental data of the ball mill discharges are poor. Besides, restricted by the sampling points of cyclone feed, the accuracy of the cyclone feed PSDs is also questionable. The mass balance was conducted in light of these findings, the mass balance was conducted and the final balanced flowsheets are shown in Figure 4-9 and Figure 4-10. Although given the same input feed tonnages, the final balanced results show that the feed of BM circuit 2 is lower in tonnage but coarser in coarseness than that found in BM circuit 1. This finding matches real mill operations, and so provides a good marker of balanced results. However, the balanced data still needed to be rechecked with model fitting in the next section.   Figure 4-7 Ball mill circuit 1 - stream PSDs 68   Figure 4-8 Ball mill circuit 2 - stream PSDs   Figure 4-9 Ball mill circuit 1- experimental data vs balanced data 69   Figure 4-10 Ball mill circuit 2- experimental data vs balanced data 4.3.2 Model fit After inputting required machine-dependent parameters, ore-dependent parameters, mass balanced PSDs, tonnages and solid percentages, two ball mill-cyclone closed circuits were built and fitted successfully. The fitted model parameters are shown in Table 4-8 and Table 4-9, and the comparison between fitted data and balanced data are shown in Table 4-10, Figure 4-11 and Figure 4-12. Table 4-8 Fitted ball mill parameters Knot Size (mm) BM 1 BM 2 Ln R/D*  Ln R/D*  1 0.1 0.50 0.55 2 1 1.70 1.70 3 3 2.43 2.54 4 12.5 0.98 1.11  70  Table 4-9 Fitted cyclone parameters  Parameters Cyclone 1 Cyclone 2 D50 Constant - KD0 0.0000248 0.0000255 Capacity Constant - KQ0 745.3 778.3 Volume Split Constant - KV1 12.19 10.85 Water Split Constant - KW1 11.4 9.7 Sharpness of Efficiency Curve - Alpha 2.3 2.9 Initial Dip in Efficiency Curve - Beta 0 0 Calculated Value Beta* 1 1  Table 4-10 Comparison of fitted key operation parameters and experimental parameters Compared parameter BM 1 BM 2 Experimental  Fitted Experimental Fitted Feed Tonnage (t/h) 891.85 898.27 891.85 878.11 P80 (mm) 5.866 5.798 6.247 6.132 Cyclone feed (t/h) 7234.00 7196.60 6834.40 6996.85 Cyclone Pressure (kPa) 48.86 46.70 39.94 40.30 CYC O/F solid Percentage (%) 43.205 43.171 44.448 44.284 CYC O/F P80 (mm) 0.211 0.215 0.192 0.209 Mill Power (kw) 12569.28 12561.89 12401.71 12401.09  71   Figure 4-11 BM 1 PSD comparison (balanced vs fitted)  Figure 4-12 BM 2 PSD comparison (balanced vs fitted) Comparison of the results indicates that the fitted models correlate well with mill operational data and balanced PSDs. As mentioned in Chapter 2, JK SimMet decouples ore characteristics from 72  machine characteristics. The appearance function represents ore characteristics and r/d* represents machine characteristics. To validate JK ball mill models, the typical method is to conduct a second mill survey and the obtained r/d* values from the first survey should fit the second set of survey data. If the test result is good, then the models are successfully validated and can be used for simulation. At Copper Mountain, there are two ball mills which are very similar in their mill dimensions and operating conditions, although they are operating with different throughputs, ore coarseness, and solid percentages. Thus, they can be treated as two individual mill surveys and can be used to validate each other if they have similar r/d* values. Models for these two ball mill circuits were fitted and a comparison of r/d* values is presented in  Figure 4-13. The test results show that the r/d* values for both ball mills are similar for a wide range of particles sizes. The cumulative comparison results indicate that the two BM-CYC closed circuit models fit well and can be used for further simulation.  Figure 4-13 Comparison of r/d* 1 and r/d* 2 73  4.4 Simulation and optimization Mill operation is a dynamically changing process. Traditional mill optimization methods include mill load and water addition adjustments. In this section, these traditional methods and mill speed are evaluated according to their optimization performances. The effects of ore characteristics on mill performance are also assessed, not only in terms of their theoretical maximum throughputs but also in terms of their theoretical power consumptions under onsite mill throughput and target grind size. 4.4.1 Mill speed and mill load Sensitivity analysis Due to the similarities between BM circuit 1 and BM circuit 2, the effects of mill speed and mill load on the ball mill models were only evaluated using fitted BM 1 circuit. Both were simulated while keeping the rest of the parameters constant. Based on information gained from the literature review, mill speed was tested in the range of 65% to 80% critical speed and mill load was tested in the range of 25% to 45%. The test results are shown in Figure 4-14 and Figure 4-15, respectively.   Figure 4-14 Relationship between mill speed and r/d* 74   Figure 4-15 Relationship between mill load and r/d* As shown in Figure 4-14 and Figure 4-15, one can conclude that the ratios of breakage rate and the discharge rate increases with the increases of mill speed within the full range of tested particle sizes, signifying that as mill speed and mill load increase, the probability of ore breakage improves accordingly. Sensitivity analysis of BM circuit 1 and BM circuit 2 was conducted based on the results with respect to changes in mill speed and mill load.           75     Figure 4-16 Sensitivity analysis of BM circuit 1  76      Figure 4-17 Sensitivity analysis of BM circuit 2 77  Figure 4-16 and Figure 4-17 show that as ball mill speed and mill load increase, the cyclone O/F P80 decreases accordingly, with gradually increased mill power. However, when the material becomes finer, even if increased same mill speed (5%) or mill load (5%), achieved size reduction becomes smaller.  As can be seen from the second graph of Figure 4-16, there should be a series of combinations of mill speed and mill load which can be used to achieve a same target grind size. With this series of combinations of mill speed and mill load, a line can be found on the power draw surface in the first graph of Figure 4-16. Therefore, to achieve the same grinding size, the power consumption varies with the different combinations of mill speed and mill load. If the corresponding line on the power draw surface could be found, the optimal point (blue dot) with the least power consumption could be obtained. This point represents the optimal operating conditions for BM 1 of Copper Mountain Mine. The same optimal point could also be found for BM 2 by using Figure 4-17.  Assessment and optimization For BM circuit 1 and BM circuit 2, on-site cyclone O/F p80s are 215 µm and 209 µm, respectively.  Based on these two targeted grinding sizes, two power consumption lines were derived with two series of mill speed and mill load operating conditions. The effects of different combinations on mill power are shown in Figure 4-18 and Figure 4-19.  78   Figure 4-18 BM 1 power draw under various operating conditions   Figure 4-19 BM 2 power draw under various operating conditions optimal Fitted Fitted Optimal 79  Figure 4-18 and Figure 4-19 clearly reveal that with the same circuit product size, mill power draws are significantly lower with higher mill speed and lower ball load operating conditions. Comparing with the largest power consumption with the lowest ones, the power saving could be as large as 320 kW and 440 kW for BM 1 and BM 2 circuits, respectively. Thus, the operation strategies of a higher mill speed and a lower ball load should be used in the mill operation. However, as mill speed increases and mill load decreases, the probability of grinding balls landing on the mill shell increases as well. The issue of the position of the ball trajectory to avoid impact the mill liner restricts the mill operation range and affects the optimal operating conditions which will need to be studied in the future work. In this study, it is assumed that all mill load combinations of 30-45% with mill speeds of 65%-80% are safe and no steel balls will land on the mill liner. Under this assumption, the best-operating conditions for BM 1 and BM 2 are obtained and are compared with the final fitted BM operating conditions are summarized in Table 4-11.  Table 4-11 Optimal operating conditions vs final fitted operating conditions   Mill speed (% Cs) Mill load (%) Mill power draw (kW)  Specific energy (kWh/t) Operation work index (kWh/t) BM 1 (optimal) 80.0 30.1 12475.48 13.89 25.22 BM 1 (fitted) 77.6 31.9 12561.89 13.98 25.40 BM 2 (optimal) 78.3 30.0 12357.78 14.07 24.96 BM 2 (fitted) 77.6 30.6 12401.09 14.12 25.05  80  Based on information summarized in Table 4-11, the optimal conditions and fitted conditions are marked as blue dots and red dots on Figure 4-18 and Figure 4-19. It can be seen that mill speeds of BM 1 and BM 2 are almost at the maximum mill speed (80% of Cs). Since the ore properties vary frequently at the Copper Mountain, mill speed can respond more quickly to changes in properties than by attempting to change the mill load. Using the maximum mill speed will restrict the flexibility of mill operations. The red dots represent the onsite mill operating conditions. Comparing with the optimal operating conditions, the conditions represented by the red dots results in slightly higher power consumptions but the conditions allow benefits of operating flexibility. Based on this conclusion, the Copper Mountain’s mill operating conditions are reasonable. Corresponding mill speed adjustment need to be made at Copper Mountain Mine when the ore type changes are detected.  Compared with a maximum power draw of 12800kW, both ball mills almost reach their maximum capacities. When comparing fitted operation work indexes with measured BWI values (24.29 kWh/t), the operating efficiencies for the two ball mill circuits are good and can be improved by decreasing mill throughput.  4.4.2 Water addition and addition points A suitable solid percentage value of cyclone O/F is very important. If solid density is too high or too low, flotation recovery will be significantly impaired. Water addition is also known as a traditional control variable which is usually used to optimize ball mill grinding performance. Therefore, the effects of water addition and addition points were evaluated in this study. There are two water addition points at Copper Mountain Mine, one is at the pump sump and the other is at ball mill feed. The detailed circuit information is shown in Figure 4-20. 81   Figure 4-20 Water adding points Since these two circuits are similar, the effects of water addition and addition points were evaluated using the BM circuit 1 with optimal ball load and mill speed (optimal operating conditions). At Copper Mountain Mine, the normal water addition point is at the pump sump. Thus, the effects of water addition from 200-700t/h were evaluated at this water addition point. The test results are shown in Table 4-12. The effects of water addition points were also evaluated while keeping total circuit water addition constant. The detailed test conditions and test results are summarized in and Table 4-13.      82  Table 4-12 Sensitivity analysis of water addition Water addition  (t/h) 200 300 400 500 600 700  O/F Solid percentage (%) 45.82 43.60 41.58 39.74 38.06 36.51 O/F P80  (mm) 0.225 0.217 0.209 0.202 0.196 0.190 Mill power  (kW) 12476.09 12475.59 12475.03 12474.42 12473.78 12473.10 U/F solid percentage (%) 82.57 82.77 83.01 83.26 83.52 83.79 Underflow tonnage (t/h) 6192.85 6280.10 6375.41 6477.05 6583.79 6694.13  Table 4-13 Sensitivity analysis of water adding points Water addition at Ball mill feed (t/h) 0.00 100.00 200.00 320.65 Water addition at pump sump (t/h) 320.65 220.65 120.65 0.00  O/F Solid percentage (%) 43.172 43.172 43.172 43.172 O/F P80 (mm) 0.215 0.221 0.227 0.233 Mill power (kW) 12475.48 12477.50 12479.43 12481.63 U/F solid percentage (%) 82.82 83.04 83.25 83.49 Underflow tonnage (t/h) 6299.13 6360.69 6418.73 6486.78  Table 4-12 shows that as water addition at the pump sump increases from 200 t/h to 700t/h, the P80 of cyclone O/F decreases dramatically from 225µm to 190µm with a nearly consistent mill 83  power. Based on the test results, increased water addition at the pump sump could be used as an effective method to control the final circuit product. However, it should also be noted that higher water addition incurs a higher circulating load and a higher solid percentage in the ball mill, which results in a greater risk of ball mill overloading. Considering the distinct benefits of more water additions, as long as the mill is not overloaded, the water addition should be maintained at a higher level. In this research, both the cyclone O/F solid percentages and the circulating loads are already very high, thus either increasing or decreasing the water addition need to be considered cautiously. And the optimal water addition needs to be obtained based on the real variability tests in the mill. In this study, onsite water addition will be treated as the optimal condition and relative water control strategies will not be considered. From Table 4-13, it is clear that both cyclone O/F P80 and mill power draw increase as water addition at the pump sump point decreases. Thus, the best water addition point is at pump sump. With the exception of controlling for ball mill grinding solid percentages, no water should be added at the ball mill feed.  4.4.3 Target grind size achievement To achieve the required target grind size, BM circuit 1 and BM circuit 2 need to be operated together and should be assigned various tasks based on their own capacities. As can be seen in the mass balance results in Section 4.3.1, the feed of the two ball mill circuits is split unevenly, that will result in different grinding capacities for each of these two ball mills. To evaluate the effects caused by this issue, the split ratio of each size fraction was analyzed. The ratio taken up by BM circuit 1 is shown in Figure 4-21. 84   Figure 4-21 Split ratio of each size fraction accounted for BM circuit 1 Figure 4-21 demonstrates that around 55% of materials in the screen underflow under 1 mm were split into BM circuit 1. In contrast, materials in the 1-5 mm range were split more into BM circuit 2, with a minimum split ratio taking place at 2.36 mm (0.4). For coarse fractions that range from 5 mm to 16 mm, the split ratio is relatively stable between the two circuits and levels off at 0.5. Because of the uneven split, the feed P80s of BM circuit 1 and BM circuit 2 are 5.80 mm and 6.13 mm, respectively, and the tonnage of BM circuit 1 is 20 t/h larger than BM circuit 2.  To achieve the final grinding objectives, the differences between the two feeds will contribute different grinding attributes for these two ball mill circuits. To compare the grinding abilities of these two circuits, an identical grind size of 212 µm was set up and the energy consumption of both circuits was analyzed and compared. The test results are summarized in Table 4-14.    85  Table 4-14 Power consumptions of BM 1 and BM 2 with targeted grinding size of 212 µm  Mill speed/ % Mill load/ % Mill power/ kW Mill 1 79.9 31 12750.5 Mill 2 77.2 30 12131.6  To achieve the final grinding size of 212 µm, BM 1 and BM2 need to be operated with different mill speeds and mill loads. The operating conditions were optimized for this grind size (212 µm) by using higher mill speed and lower mill load operating strategies. The simulation results show that BM circuit 2 consumes around 600 kW less power than BM circuit 1 for the same grind size, which means BM 2 has more energy potential to contribute a finer grind size.  At Copper Mountain, products from BM circuits 1 and 2 are combined and then are fed into the flotation circuit together. The target grinding size for the whole ball mill circuit is 210 µm. Based on JK fitted data, the final onsite mill grinding circuit fineness is 212 µm, which is slightly higher than the required grinding size. The particle size distribution of ball mill circuits product is calculated based on the PSDs of BM circuit 1 product and BM circuit 2 product and is presented in Table 4-15.        86  Table 4-15 Fitted final cyclone O/F PSD Screen size/ mm BM1 BM2 Total 1.180 100.00 100.00 100.00 0.850 99.97 99.99 99.98 0.600 99.50 99.75 99.63 0.425 96.52 97.40 96.96 0.300 89.29 90.27 89.77 0.212 79.53 80.43 79.97 0.150 68.84 69.61 69.22 0.106 58.47 59.15 58.81 0.075 48.80 49.49 49.14 0.053 40.63 41.31 40.97 0.038 34.87 35.39 35.12 0.025 29.23 29.53 29.38  To achieve the target grinding size (210 µm), BM 1 and BM 2 operating conditions were tuned to achieve a finer product. Corresponding simulations were conducted considering the higher speed and lower load operation strategies. The test results are summarized in Table 4-16.      87  Table 4-16 Mills operating conditions with achieved target grind size   Mill speed/ % Mill load/ % Mill power/ kW P80/ mm Total power/ kW Optimal conditions Mill 1 80.00 30.10 12475.48 0.215 24833.26 Mill 2 78.30 30.00 12357.78 0.209 Tune BM 1 Mill 1 80.00 31.09 12799.67 0.212 25173.81 Mill 2 78.38 30.00 12374.14 0.209 Tune BM 2 Mill 1 80.00 30.10 12475.48 0.215 25149.74 Mill 2 79.86 30.00 12674.26 0.205  Based on the fitted results, the product P80s of BM circuit 1 and BM circuit 2 were 215 µm and 209 µm, respectively. The optimal conditions were derived with these two grinding sizes by using a higher mill speed and a lower mill load. To achieve the target grinding size (210 µm), BM 1 and BM 2 were tested separately by changing their operating conditions.  Simulation results show that BM 1 has already achieved its maximum mill speed (80% of Cs). Restricted by mill power, mill load of BM 1 can only be increased from 30.1% to 31.09% with 80% Cs. However, even if the BM 1 has achieved its maximum mill power (12800 kW), the final target grind size could not be achieved. By increasing the mill speed from 78.30 to 78.38% Cs for BM 2, the target grind size was achieved with a total mill power of 25173 kW. However, considering the BM 1 power draw has already reached its maximum power (12800 kW), it is difficult to realize this in the real mill operations. When only BM 2 was tuned, the final targeted grind size was reached by increasing the mill speed from 78.3% to 79.86% Cs, with a final total 88  mill power of 25149 kW. The latter option consumes less power and can be more realistically achieved in the real mill operations. 4.4.4 Ore types The effects of ore characteristics on SAG mill circuit product size distribution were simulated through JK SimMet. The test results show that as the classification of the SAG discharge screen and vibrating screen, PSD oscillations brought on by ore changes are quite small. By inputting these slightly changed particle size distributions, ball mill operations could also be evaluated. The simulation results show that final ball mill product sizes are not affected much by these variations. As such, the effects of ore variations on upstream PSD changes were not considered. Under the same feed characteristics and operating conditions with those at Copper Mountain Mine, product sizes for various geo-samples in the two circuits are summarized (Table 4-17). Test results reveal that changes in ore properties have large impacts on final product sizes in the ball mill circuit. As well, the final product size correlates well with its BBWI values, in that the higher the BBWI value, the coarser the final product size. It can also be seen that Geo #1 and Geo #6 are coarser than their targeted grinding size, yet Geo #2 and Geo #4 are finer than their target grinding size. Table 4-17 Final product sizes of various geo-samples with identical operating conditions   SAG 1 2 4 6 BBWI /kWh/t 24.29 22.20 23.39 20.12 21.18 Target grind size/ mm 0.210 0.120 0.290 0.320 0.120 Circuit 1-P80 /mm 0.215 0.169 0.171 0.149 0.162 Circuit 2-P80 /mm 0.209 0.163 0.165 0.144 0.157  89  Based on the target grind sizes, the theoretical maximum throughputs for the 4 different geo-metallurgical samples were determined using the simulation.  As can be seen in Table 4-18, for the maximum power draw, the mill speeds are almost at the maximum mill speed (80% Cs). The theoretical maximum mill throughputs for the various geo samples are compared to the operating mill throughput in Figure 4-22. The results show that the mill throughput is affected significantly by changes in ore characteristics. The maximum throughput of geo sample #4 is around 4500 t/h, which is nearly 4 times that of geo sample #1 and geo sample #6. The maximum throughput of geo sample #2 is also remarkable at around 3200 t/h.  Table 4-18 Theoretical maximum mill throughput of various geo-samples with detailed operating conditions   Mill speed/ % Ball load/ % P80/ µm Power/ kW Tonnage/ t/h Geo #1 BM 1 80.0 31.0 120 12799.4 632.0 BM 2 76.3 30.0 120 11967.2 617.8 Geo #2 BM 1 80.0 31.1 290 12792.1 1661.0 BM 2 76.5 30.0 290 11959.3 1623.7 Geo #4 BM 1 80.0 31.1 320 12787.2 2200.0 BM 2 76.4 30.0 320 11925.6 2150.6 Geo #6 BM 1 80.0 31.0 120 12799.1 660.0 BM 2 76.3 30.0 120 11996.3 645.2  90   Figure 4-22 Theoretical maximum throughputs of various geo-metallurgical samples To maintain a relatively constant mill throughput at Copper Mountain Mine, different geo-metallurgical samples are blended and processed together with the same target grinding size (P80=210 µm). To provide reasonable blending suggestions, the theoretical mill power consumptions of various ore types are assessed according to target the mill grind sizes and onsite mill throughput. A sensitivity analysis was conducted at 30-45% of ball load and 65-80% of Cs speed. During simulation of the power consumption, the operating conditions already exceeded this range. Therefore, to reasonably compare the power consumption of various ore types, the power simulation was conducted based on the same lower mill load (30%) with different mill speeds. The simulated operating conditions and results are summarized in Table 4-19. Test results show that mill speed changes according to the ore types, ranging from 57.2 % to 64.9 % Cs. Considerable energy savings can be obtained if these geo samples are processed in the mill individually. Especially for geo-sample #4, the theoretical power saving can be as large as 9000 kW. However, due to limitations of the JK SimMet software, geo-sample #3 and geo-sample #5 91  could not be evaluated. If the performances of these two ores could be analyzed, the ore blending ratios could be calculated based on provided mill powers and required liberation sizes.  Table 4-19 Theoretical power consumptions of various geo-samples with required target grind size     Speed/ %Cs Mill Load/ % Energy/ kW Geo 1 BM 1 64.9 30.0 9345.90 BM 2 61.0 30.0 8721.38 Geo 2 BM 1 65.7 30.0 9510.81 BM 2 61.7 30.0 8867.32 Geo 4 BM 1 60.0 30.0 7850.14 BM 2 57.2 30.0 7305.96 Geo 6 BM 1 62.4 30.0 8830.25 BM 2 60.0 30.0 8312.02  However, ore blending is not always a good method to deal with the issues of ore property variations. As described in Chapter 3, the liberation sizes of various geo-samples are totally different. With blended ore feed, all the materials are required to be ground down to 210 µm. In this case, some ore types have already been over-ground, yet some ore types have not been liberated. With unsatisfactory liberation size, these ore types cannot gain satisfactory flotation recoveries. Although ore blending has the benefit of relative stable mill throughput, the improved copper recovery resulted by processing individual ore types is also quite notable. Thus, some trade-off studies need to be conducted to analyze the benefits of mill throughput and copper recoveries. 92  4.4.5 Discussion Based on the simulation results, operating strategies that involve controlling mill speed are proposed.  In general, higher mill speeds and lower ball loads are preferred with regards to power consumption. Onsite mill speed and mill load are already close to the optimal operating conditions. Though onsite operating conditions consume slightly more power, there are benefits of operating flexibility and responsiveness to changes with ore types by adjusting mill speed.  Test results show that increasing the water addition at the pump sump can reduce the product P80 without sacrificing mill power. Therefor water addition at the pump sump can be used as an effective approach to optimize the ball mill grinding circuit. If the final product P80 is kept constant, onsite mill throughput can be improved by adding more water to the pump sump. As long as the ball mills are not overloaded, a higher water addition is recommended. Since the increase of water addition increase the risk of ball mill overloading, the optimal water addition needs to be determined based on onsite variability tests. When simulating the maximum mill throughput and mill power consumption for each ore type, the water addition was maintained according to present mill operating practices. If water addition was changed according the results presented above, the results for each geo sample would change accordingly.  For a target grinding size, mill performance can be optimized by applying a higher mill speed and lower ball load. If the geo-samples are processed individually, a maximum usage of mill speed with a lower mill load strategy can assist in achieving the maximum mill throughput. Due to uneven splitting of feed to the two ball mills, the feed to the BM 1 circuit is different than the feed to BM 2, resulting in different grinding tasks for each circuit. Based on simulation results, the grinding ability of BM 2 is greater than BM 1. For the same target grinding size, the simulated 93  power consumption for BM 2 is less than that for BM 1. When mill throughput is at its maximum, the mill speed of BM 2 can still be adjusted to offset the feed property changes. Samples Geo 3 and Geo 5 are very hard ores, and they are processed together with other ore types during the mills’ operation. After blending with other ore types, they increase overall hardness and result in a higher power consumption with the same target grinding size (210 µm). Based on the targeted liberation size of these two geo-samples (290-320 µm), the power saving will be notable if both were could be process individually. Based on the simulation, power savings can also be realized for other ore types if they are processed individually. Thus, a trade-off study needs to be conducted to assess the benefits of a stable mill throughput and improved copper recoveries and reduced power consumption.  94  Chapter 5: Conclusions and recommendations 5.1 Conclusions This research attempts to gain a more complete understanding of the performance of variable speed ball mills within the context of constantly changing mill operations. The core research objective was to develop adequate variable speed ball mill operation strategies regarding energy consumption when ore specification changes. Based on mill survey and DCS data, reliable JK SimMet models were built to achieve this objective. Mill performance under different operating conditions was simulated and analyzed. Finally, adequate operation strategies and optimization suggestions were developed based on the results and will be provided to Copper Mountain mill. The following six conclusions are derived from the literature review, lab tests, model buildup and simulation results conducted throughout the duration of the study. • The variation of ore characteristics at Copper Mountain mine is significant according in term of ore competency, hardness and grain size, which suggests that mill operations will face many challenges with changes in mill feed. According to the ore characterization test results, Axb value ranges from 28 to 40, signifying that the SAG feed and 6 geo-units are still competent, even though it seems less competent than historical data measured in 2011. According to their BBWI values, the SAG feed and 6 geo-units are quite hard ores that range from 20 to 28 kWh/t. The variety of ore types leads to potential instabilities for the mill operations. • Although default appearance function is widely used in JK SimMet applications, it cannot be used to assess different ore types in a specific mill operation. Although Moly-Cop is quite similar with JK SimMet in their model theories, the appearance function derived from 95  Moly-Cop cannot be used in JK simulations. To evaluate the performance of various ore types in a specific mill, relative ore-specific appearance functions need to be determined by using the method developed by Narayanan. • Based on the DCS, survey and ore characterization data, BM circuit 1 and BM circuit 2 were successfully balanced and fitted. The final flowsheet matches well with the experimental data and has the all the characteristics marks of real mill operations. Although the two experimental datasets were different, the final fitted results showed that BM 1 has similar R/D* values to BM 2. This match allows the mills to validate one another, and proves that simulation models developed for this study are quite reliable.  • Based on the JK SimMet simulations, ball mill speed was shown to be a valuable control for optimizing the comminution circuit, while considering power consumption, mill throughput and grain size. For designated mill throughput and ore characteristics, higher ball mill speed and lower mill load operation strategies should be applied. For a specific target grind size, the energy difference between the higher speed/lower load operation and the lower speed/higher load operation can be as large as 760 kW for on-site mill operations. • Increasing water addition at pump sump can be used to optimize cyclone separation efficiency and achieve a finer product size without consuming additional mill power. In contrast, water addition at the ball mill feed does not have any benefits on the mill performance. Without adjusting mill grinding solid density, water should not be added at this point. However, increasing water addition will also result in a higher circulating load and mill feed density, which will in turn result in a higher likelihood of mill over-loading. Thus, higher water addition should be considered providing the ball mill could handle a 96  higher grinding tonnage. This method needs to be considered carefully, and optimal addition tonnage should be obtained via trial and error testing in real mill operations. • Copper Mountain Mine has already arrived at its maximum throughput based on its recent ore type samples. Its operating conditions are reasonable, and very close to optimal levels. That said, the uneven split ratio requires a different set of grinding attributes for each ball mill circuit, and in general BM 2 has more energy potential for creating a finer grind size. According to the simulation results, the speed of BM 2 can be increased slightly to achieve a finer target grind size. • Differing ore types are likely to have a large impact on mill operations, not only because of their own characteristics, but also because of their various targeted grinding sizes. The theoretical maximum throughputs for geo-sample #2 and geo-sample #4 can be as large as 3200t/h and 4500 t/h, respectively, but for geo-sample #1 and geo-sample #6, they are only around 1000 t/h of what can be achieved. Under the same target grind size (210 µm), mill throughput, and feed PSDs, mill power consumption could vary significantly according to the various types of ores. The softest ores theoretically have higher energy saving potentials. This is especially true for geo-sample #4, for which power savings could theoretically reach 9000 kW. 5.2 Recommendations for future work Based on the study findings, some future opportunities are proposed as follows: • JK SimMet cannot be used to predict the mill trajectory under various mill load and liner wear conditions. With accurate mill trajectory predictions, mill speed operation ranges will be more accurate under various conditions. Combined with JK simulation results, more 97  specific operation recommendations can be generated that not only in consideration of power consumption, but also with respect to media consumption and liner wear.  • In this study, mill speed and mill load were chosen as control variables to offset mill feed characteristic changes. There are other control variables that can be analyzed and used to optimize mill operations, such as ball size, cyclone dimensions, and cyclone numbers. • When the expected mill feed property variations occur, relative mill operations strategies should be conducted based on simulated results to double-check the predicted results.  • Due to limitations in the JK SimMet software, the performances of geo-sample #3 and geo-sample#5 cannot be predicted in this research. If other methods could be used to predict their power consumptions and theoretical mill throughputs, the ore blending ratios could be calculated based on the provided mill powers and required liberation sizes. • Ore blending is not always a good solution to the issues brought by ore variations. Although it has the benefits of a stable mill throughput, the copper recovery is sacrificed because of the unsatisfactory liberation sizes for various ores. 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Minerals Engineering, 19(10), 984-994.  Zadeh, A. B. M. (2012). Improvements in comminution efficiency through high velocity impact. (Master), University of British Columbia, Vancouver.  Zhang, W. (2016). Optimizing Performance of SABC Comminution Circuit of the Wushan Porphyry Copper Mine—A Practical Approach. Minerals, 6(4), 127.   104  Appendices Appendix A  Survey data summaries A.1 DCS data Description Units Measured Fresh feed throughput [mtph] 1783.99 SAG mill total motor power [kW] 12038.10 Pebble crusher throughput [mtph] 387.91 Pebble crusher power [kW] 417.02 Ball mill 1 motor power [kW] 12569.28 Ball mill 2 motor power [kW] 12401.71 Total equipment power [kW] 37,426 Total specific energy [kW/t] 20.98 BM circuit 1 cyclone pressure [kPa] 48.86 BM circuit 1 cyclone pressure [kPa] 39.94 BM1 CYC. Feed flow rate [m3/h] 5478.41 BM2 CYC. Feed flow rate [m3/h] 5304.64 BM 1speed [rpm] 12.33 BM 2 speed [rpm] 12.34       105  A.2 Survey data Ball mill circuit 1 No. Sample Name Dry Weight (g) Density wt.% Solid Particle Size P80 µm  1 Splitter Box 15689 51.0% 5924.61 2 CYC Feed 22143 71.7% 4128.92 3 BM Discharge 30208 79.8% 4420.64 4 OSA Flot. Feed 6255 45.2% 210.98 5 Cyclone 1 O/F 5855 43.6% 242.75 6 Cyclone 2 O/F 3880 45.0% 232.95 7 Cyclone 3 O/F 2970 46.6% 230.49 8 Cyclone 4 O/F 4608 42.9% 215.23 9 Cyclone 5 O/F 4570 42.0% 189.55 10 Cyclone 6 O/F 3853 44.1% 220.60 11 Cyclone 7 O/F 3670 40.5% 174.50 12 Cyclone 8 O/F 4070 40.8% 191.92 13 Cyclone 1 U/F 12476 82.3% 3591.05 14 Cyclone 2 U/F 13657 83.1% 4765.22 15 Cyclone 3 U/F 12576 79.4% 4151.72 16 Cyclone 4 U/F 14639 80.3% 5378.05 17 Cyclone 5 U/F 12278 82.2% 5129.84 18 Cyclone 6 U/F 9809 78.9% 3217.44 19 Cyclone 7 U/F 11423 81.4% 3462.27 20 Cyclone 8 U/F 11267 81.3% 3320.36   106  Screen Size (mm) Split-box Cyclone feed Ball discharge Cyclone O/F Cyclone U/F 16.000 99.90% 99.98% 99.94% 100.00% 99.91% 13.500 99.53% 99.11% 99.19% 100.00% 99.38% 9.500 94.70% 94.52% 93.60% 100.00% 94.69% 6.730 83.03% 86.09% 85.10% 100.00% 86.50% 4.760 75.05% 81.80% 80.85% 100.00% 81.90% 3.350 65.57% 77.43% 76.90% 100.00% 77.05% 2.360 59.27% 73.33% 73.55% 100.00% 71.77% 1.700 52.42% 69.52% 69.91% 100.00% 66.34% 1.180 44.38% 65.10% 64.56% 99.99% 59.37% 0.850 37.92% 60.31% 58.90% 99.93% 52.39% 0.600 31.95% 52.46% 50.91% 99.53% 42.86% 0.425 27.05% 42.64% 39.88% 97.39% 31.29% 0.300 22.97% 32.01% 28.96% 91.09% 20.33% 0.212 19.68% 24.34% 21.58% 80.11% 13.64% 0.150 16.80% 19.22% 16.73% 68.10% 9.92% 0.106 14.58% 15.93% 13.84% 58.67% 7.90% 0.075 12.58% 13.50% 11.75% 50.62% 6.62% 0.053 10.94% 11.74% 10.17% 44.13% 5.73% 0.038 10.94% 10.17% 10.17% 42.30% 5.56% 0.025 10.94% 8.54% 10.17% 39.72% 5.41%      107  BM circuit 2 No. Sample Name Dry Weight (g) Density wt.% Solid Particle Size P80 µm  1 Splitter Box 19213 53.264% 6289.02 2 CYC Feed 47389 70.729% 2985.65 3 BM Discharge 26491 80.323% 6106.12 4 OSA Flot. Feed 6255 45.225% 210.98 5 Cyclone 1 O/F 5314 43.740% 204.37 6 Cyclone 2 O/F 5679 43.620% 183.68 7 Cyclone 3 O/F 5231 43.774% 180.84 8 Cyclone 4 O/F 5881 46.972% 198.74 9 Cyclone 5 O/F 5369 42.440% 178.00 10 Cyclone 6 O/F 5709 46.227% 218.39 11 Cyclone 7 O/F 6191 45.454% 205.41 12 Cyclone 8 O/F 5979 43.357% 183.74 13 Cyclone 1 U/F 12750 81.993% 4530.60 14 Cyclone 2 U/F 11204 82.081% 5381.77 15 Cyclone 3 U/F 14283 82.320% 4614.10 16 Cyclone 4 U/F 11228 81.658% 5361.57 17 Cyclone 5 U/F 10697 82.604% 4808.85 18 Cyclone 6 U/F 9239 78.627% 4983.45 19 Cyclone 7 U/F 11533 80.367% 4600.48 20 Cyclone 8 U/F 13721 81.433% 3818.05     108  Screen Size (mm) Split-box Cyclone feed Ball discharge Cyclone O/F Cyclone U/F 16 99.93% 99.93% 99.88% 100.00% 99.92% 13.5 99.55% 99.51% 99.10% 100.00% 99.13% 9.5 94.37% 96.18% 92.48% 100.00% 94.05% 6.73 81.67% 89.64% 81.48% 100.00% 85.30% 4.76 73.50% 85.86% 76.32% 100.00% 80.22% 3.35 64.12% 81.59% 71.48% 100.00% 74.97% 2.36 52.88% 76.85% 66.56% 99.99% 70.22% 1.7 44.43% 72.29% 62.30% 99.98% 65.60% 1.18 36.37% 67.01% 56.96% 99.95% 59.45% 0.85 31.14% 61.83% 51.43% 99.90% 53.09% 0.6 26.66% 53.72% 44.00% 99.64% 44.28% 0.425 22.73% 44.07% 34.99% 98.23% 32.91% 0.3 19.55% 33.47% 25.57% 92.93% 21.44% 0.212 16.92% 25.76% 19.19% 83.07% 14.46% 0.15 14.54% 20.92% 15.13% 71.69% 10.64% 0.106 12.69% 17.79% 12.71% 62.42% 8.61% 0.075 11.08% 15.56% 10.90% 54.71% 7.23% 0.053 9.73% 13.73% 9.54% 48.79% 6.23% 0.038 9.73% 12.11% 9.54% 47.45% 6.05% 0.025 9.73% 10.44% 9.54% 45.83% 5.83%      109  Appendix B  BBWI test results B.1 SAG feed        Sample Name: Cu Mountain sag cut - mid blend Mass: 1341.1 gramsBulk Density: 1.92 Volume: 700.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.912 2360 72.610 1700 50.216 1180 37.420 850 29.630 600 23.640 425 18.950 300 15.270 212 12.4 100.0100 150 10.0 80.8150 106 8.0 65.0200 75 6.4 53.3270 53 44.4400 38 37.32627.2 147.8Feed Discharge Net Product Net / Rev CLR1 1341.1 250 952.0 165.7 389.1 223.4 0.894 2452 389.1 375 947.2 48.1 393.9 345.8 0.922 2403 393.9 363 952.7 48.7 388.4 339.7 0.937 2454 388.4 358 950.2 48.0 390.9 342.9 0.958 2435 390.9 349 936.8 48.3 404.3 356.0 1.019 2326 404.3 327 972.0 49.9 369.1 319.2 0.976 2637 369.1 346 975.3 45.6 365.8 320.2 0.926 2678 365.8 365 957.5 45.2 383.6 338.4 0.927 2500.926269.99 22.03 kw-hr/ton24.29 kw-hr/tonne   Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs. Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product110  B.2 Geo-sample #1          Sample Name: Copper Mountain Mine, Geo-Met #1 Mass: 1124.0 gramsBulk Density: 1.87 Volume: 600.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.912 2360 72.110 1700 47.116 1180 30.520 850 21.730 600 15.640 425 11.450 300 8.670 212 6.7 99.5100 150 79.0150 106 62.7200 75 50.8270 53 42.3400 38 35.02640.3 153.0Feed Discharge Net Product Net / Rev CLR1 1311.3 300 943.6 87.3 367.7 280.4 0.935 2572 367.7 375 913.6 24.5 397.7 373.2 0.996 2303 397.7 350 919.1 26.5 392.2 365.7 1.046 2344 392.2 333 927.6 26.1 383.7 357.6 1.074 2425 383.7 325 940.0 25.6 371.3 345.8 1.063 253598.1 20.14 kw-hr/ton22.20 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs. Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product111  B.3 Geo-sample #2         Sample Name: Copper Mountain Mine, Geo-Met #2 Mass: 1279.5 gramsBulk Density: 1.75 Volume: 730.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.912 2360 70.510 1700 45.616 1180 29.720 850 21.730 600 16.340 425 12.550 300 9.870 212 7.6 99.8100 150 80.6150 106 63.3200 75 50.9270 53 42.0400 38 34.92679.1 148.4Feed Discharge Net Product Net / Rev CLR1 1226.9 300 883.7 93.8 343.2 249.4 0.831 2572 343.2 390 843.8 26.2 383.1 356.9 0.915 2203 383.1 351 855.3 29.3 371.6 342.3 0.975 2304 371.6 330 878.8 28.4 348.1 319.7 0.968 2525 348.1 335 877.5 26.6 349.4 322.8 0.964 251598.1 21.22 kw-hr/ton23.39 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs. Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product112  B.4 Geo-sample #3       Sample Name: Copper Mountain Mine, Geo-Met #3 Mass: 1269.0 gramsBulk Density: 1.80 Volume: 705.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.812 2360 71.710 1700 44.416 1180 26.320 850 16.830 600 10.440 425 6.250 300 3.770 212 2.2 99.8100 150 79.3150 106 61.3200 75 48.6270 53 39.8400 38 32.92651.9 152.1Feed Discharge Net Product Net / Rev CLR1 1260.0 300 1010.9 27.5 249.1 221.6 0.739 4062 249.1 480 897.8 5.4 362.2 356.8 0.743 2483 362.2 474 879.3 7.9 380.7 372.8 0.787 2314 380.7 447 891.7 8.3 368.3 360.0 0.806 2425 368.3 437 892.9 8.0 367.1 359.1 0.822 2436 367.1 428 903.2 8.0 356.8 348.8 0.814 253598.1 24.92 kw-hr/ton27.47 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs.Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product113  B.5 Geo-sample #4       Sample Name: Copper Mountain Mine, Geo-Met #4 Mass: 977.7 gramsBulk Density: 1.92 Volume: 510.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.812 2360 66.710 1700 43.216 1180 29.220 850 21.630 600 16.340 425 12.450 300 9.770 212 7.8 99.3100 150 79.2150 106 62.6200 75 50.4270 53 41.5400 38 33.72758.7 152.6 Feed Discharge Net Product Net / Rev CLR1 1341.9 100 1172.8 104.9 169.1 64.3 0.643 6932 169.1 576 719.2 13.2 622.7 609.5 1.059 1153 622.7 316 929.2 48.7 412.7 364.1 1.151 2254 412.7 305 952.0 32.2 389.9 357.7 1.173 2445 389.9 301 955.7 30.5 386.2 355.8 1.182 2476 386.2 299 954.2 30.2 387.7 357.6 1.197 24618.26 kw-hr/ton20.12 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs.Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product114  B.6 Geo-sample #5        Sample Name: Copper Mountain Mine, Geo-Met #5 Mass: 1413.1 gramsBulk Density: 1.79 Volume: 790.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.812 2360 68.610 1700 44.916 1180 29.420 850 21.030 600 14.840 425 10.350 300 7.070 212 4.5 99.7100 150 81.8150 106 65.6200 75 53.5270 53 45.0400 38 37.92721.2 145.2Feed Discharge Net Product Net / Rev CLR1 1252.1 100 1103.6 56.6 148.5 91.9 0.919 7432 148.5 382 950.8 6.7 301.3 294.6 0.771 3163 301.3 446 886.3 13.6 365.8 352.2 0.789 2424 365.8 432 886.3 16.5 365.8 349.3 0.808 2425 365.8 422 894.5 16.5 357.6 341.1 0.808 250598.1 24.38 kw-hr/ton26.88 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs.Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product115  B.7 Geo-sample #6       Sample Name: Copper Mountain Mine, Geo-Met #6 Mass: 752.5 gramsBulk Density: 1.93 Volume: 390.0 mLFeed ProductCum.  Passing Cum.  Passing[mesh] [um] [%] [%]8 3350 99.512 2360 66.010 1700 45.116 1180 31.020 850 23.330 600 17.640 425 13.350 300 10.370 212 8.0 99.2100 150 80.5150 106 65.2200 75 53.9270 53 45.6400 38 37.92773.5 148.5Feed Discharge Net Product Net / Rev CLR1 1350.6 100 1131.5 107.5 219.1 111.6 1.116 5162 219.1 330 1007.0 17.4 343.6 326.2 0.988 2933 343.6 363 954.4 27.4 396.2 368.9 1.016 2414 396.2 349 939.6 31.6 411.0 379.5 1.089 2295 411.0 324 965.4 32.7 385.2 352.5 1.087 2516 385.2 327 964.3 30.7 386.3 355.7 1.088 250598.1 19.21 kw-hr/ton21.18 kw-hr/tonne Wi = 44.5 / (P1^.23 x Gbp^.82 x (10/√P - 10/√F))WORK INDEX (Wi)Standard Bond Ball Mill Grindability TestSizePassing 80% (microns)Cycle Test Feed Added Number of Revs.Weight of OversizeWeight of Undersize010203040506070809010010 100 1000 10000Cum. percent passing, %Particle size, micronsFeed Product

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