THE EFFECT OF STIRRED MILL OPERATION ON PARTICLES BREAKAGE MECHANISM AND THEIR MORPHOLOGICAL FEATURES by REEM ADEL ROUFAIL B.Sc., The American University in Cairo, 1992 M.Sc., The American University in Cairo, 1997 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Mining Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2011 © Reem Adel Roufail, 2011 Abstract Stirred milling is a grinding tool that is used extensively for mineral liberation, in order to achieve successful downstream processing such as flotation or leaching. The focus of this research is to understand the effect of different operating parameters on particle breakage mechanism. Operating parameters could be summarized as stress intensity on the particles which are varied by changing the mill’s agitator speed, and different ground material properties such as extreme hard/low density minerals like quartz versus soft/high density minerals like galena. Grinding performance is assessed by analysing particle size reduction and energy consumption. Breakage mechanism is evaluated using the state of the art morphological analysis and liberation. Finally, theoretical evaluation of particles flow, types of forces and energy distribution across the mill are investigated using Discrete Element Modelling (DEM). It is observed that breakage mechanisms are affected by the type of mineral and stress intensities (agitator speed) in the mill. For example, galena, the soft/high density mineral, reaches its grinding limit very fast at high agitator speed and specific energy consumption increases exponentially with the increase of the agitator speed. On the other hand, for quartz, the hard/low density mineral, the breakage rate is very slow at low agitator speed and the specific energy consumption increases linearly with the increase of the agitator speed. Fracture mechanism of the particles is also function of the agitator speed and type of mineral. At high agitator speed, galena fractures mostly along the grain boundaries, whereas quartz breaks across the grains, which is abrasion. The morphology observation is confirmed by the DEM model, which conveyed that at higher agitator speed, the normal forces were higher than tangential forces on the galena particles compared to the ceramic grinding media particles. The core of this research is the morphology analysis, which is a novel approach to studying particle breakage mechanisms. More work is recommended in the field of morphology with other types of minerals to confirm the findings of this research. 3D liberation analysis was introduced in this research; a correlation to the conventional liberation methodology would be a major addition to the industry. ii Preface The research results presented in this thesis represent work conducted by the author with input and advice from the supervisory committee. Thus far the research has generated two publications. The first publication titled ―Mineral Liberation and Particle Breakage in Stirred Mills‖ was presented at the 43rd Conference of Metallurgists in Sudbury in 2009. It was then re-published by the Canadian Metallurgical Quarterly (Vol. 49, No4, pp 419-428, 2010). This publication was coauthored by Professor B. Klein. I was responsible for developing the methodology to analyse the morphological features and their parameters from Scanning Electron Microscope images. I was responsible for developing the concepts and writing the paper, with advice of the coauthor. The second publication titled, ―Effect of Grinding Operation and Product Morphology in Stirred Mill‖ was coauthored by B. Klein and R. Blaskovich and was presented and published at the 43rd Annual Meeting of the Canadian Mineral Processor in Ottawa, 2011. I was responsible for performing the experiments, defining the morphological features to be analysed, compiling the data and writing the publication. B. Klein advised on and reviewed this publication and R. Blaskovich acquired the SEM images and generated the fundamental data for analysis. The results presented in the publication were included in chapters 2, 3 and 4 of this document. iii Table of Contents Abstract ..................................................................................................................................... ii Preface ...................................................................................................................................... iii Table of Contents ...................................................................................................................... iv List of Tables .......................................................................................................................... viii List of Symbols ....................................................................................................................... xiii Acknowledgments ....................................................................................................................xvi Dedication.............................................................................................................................. xvii 1. 2. Introduction .........................................................................................................................1 1.1 Stirred Mills ..................................................................................................................1 1.2 Research Objective .......................................................................................................4 1.3 Thesis Outline ...............................................................................................................5 Literature Review ................................................................................................................7 2.1 Mill Operation and Particle Size Distribution ................................................................7 2.2 Failure Analysis – Brittle and Fatigue Fractures ............................................................9 2.3 Morphology ................................................................................................................ 14 2.3.1 Morphological Features of Fractured Surfaces ..................................................... 14 2.3.2 Morphological Features and Comminution ........................................................... 17 2.4 Computer Model and Mill Simulation ......................................................................... 20 2.4.1 2.5 3. Power Model ....................................................................................................... 25 Conclusion .................................................................................................................. 26 Grinding Studies ................................................................................................................ 28 3.1 Introduction ................................................................................................................ 28 3.2 Grinding Test Material ................................................................................................ 28 3.3 Procedures .................................................................................................................. 30 3.3.1 Material Preparation Procedure ............................................................................ 31 3.3.2 Grinding Procedure .............................................................................................. 33 3.3.3 Particle Size Analysis Procedure .......................................................................... 35 3.3.4 Preparation of Test Products ................................................................................ 36 3.4 Grinding Results ......................................................................................................... 38 3.4.1 Particle Size Distribution ..................................................................................... 38 3.4.2 Breakage Rate ...................................................................................................... 47 iv Initial Breakage Rate..................................................................................... 54 3.4.2.2 Average Breakage Rate ................................................................................. 55 3.4.3 Energy Consumption............................................................................................ 56 3.4.4 Effective Energy .................................................................................................. 62 3.4.5 Specific Breakage Energy .................................................................................... 65 3.5 4. 3.4.2.1 Conclusion .................................................................................................................. 66 Morphology and Liberation ............................................................................................... 69 4.1 Introduction ................................................................................................................ 69 4.1.1 Morphology Definition ........................................................................................ 69 4.1.2 Morphology Evaluation ....................................................................................... 69 4.1.3 Sample Description for Morphology .................................................................... 71 4.2 Clemex Method .......................................................................................................... 72 4.3 Manual Point Counting Method .................................................................................. 74 4.3.1 4.4 Liberation Methodology .............................................................................................. 76 4.5 Morphology and Liberation Results ............................................................................ 77 4.5.1 Manual Point Counting Results ............................................................................ 78 4.5.2 Pearson’s Correlation ........................................................................................... 79 4.5.3 Stacked Charts Analysis ....................................................................................... 90 4.5.4 Shattered Particles Feature ................................................................................. 104 4.5.5 Automated Quantitative Morphological Analysis ............................................... 105 4.5.6 Liberation Analysis Results ................................................................................ 110 4.5.7 Liberation versus Agitator Speed ....................................................................... 111 4.5.8 Particle Mount versus Polished Samples ............................................................ 117 4.6 5. Point Counting Sensitivity Analysis ..................................................................... 76 Conclusion ................................................................................................................ 120 Computer Modeling and Simulation of Stirred Mill ......................................................... 123 5.1 EDEM Software........................................................................................................ 125 5.2 DEM Simulation Limitations .................................................................................... 129 5.3 IsaMill Model Geometry ........................................................................................... 131 5.3.1 Number of Particles ........................................................................................... 134 5.3.2 Triangular versus Circular Discs ........................................................................ 135 5.3.3 Effect of Drag Forces ......................................................................................... 138 5.3.4 Material Properties ............................................................................................. 144 v 5.3.5 5.4 5.3.5.1 Fixed Parameters ........................................................................................ 147 5.3.5.2 Variable Parameters .................................................................................... 149 Computer Model Results ........................................................................................... 150 5.4.1 6. Media Particles Runs ......................................................................................... 150 5.4.1.1 Particle Distribution .................................................................................... 150 5.4.1.2 Energy Distribution..................................................................................... 153 5.4.1.3 Forces Distribution ..................................................................................... 159 5.4.1.4 Average Force Distribution ......................................................................... 160 5.4.2 5.5 Model Parameters .............................................................................................. 147 Galena and Media Particles Runs ....................................................................... 166 5.4.2.1 Particle Distribution .................................................................................... 166 5.4.2.2 Maximum Forces Distribution .................................................................... 170 5.4.2.3 Average Force Distribution ......................................................................... 171 Conclusion ................................................................................................................ 172 Conclusions and Recommendations ................................................................................. 175 6.1 Conclusions .............................................................................................................. 175 6.1.2 Experimental Work ............................................................................................ 176 6.1.3 Morphology ....................................................................................................... 178 6.1.4 Computer Model ................................................................................................ 180 6.2 Recommendations ..................................................................................................... 183 6.2.1 Experimental and Morphology ........................................................................... 183 6.2.2 Computer Modeling ........................................................................................... 184 References .............................................................................................................................. 185 Appendix A: Experimental Data...................................................................................................... 199 Appendix A1: MSDS Sheets ............................................................................................ 199 Appendix A2: Assay Analysis .......................................................................................... 213 Appendix A3: Measured Specific Gravity, SG ................................................................. 214 Appendix A4: Experimental Data ..................................................................................... 215 Appendix A5: Cyclone Correlation Factor ........................................................................ 226 Appendix B: Experimental Results ................................................................................................. 227 Appendix B1: Mass of Solids Calculations Based on Volume Percent .............................. 227 Appendix B2: Rosin Rammler Fit and Parameters ............................................................ 228 vi Appendix B3: Correlation between Measured and Calculated P80 .................................... 239 Appendix B4: Energy Breakage vs. Particle Size P80 (m) .............................................. 243 Appendix C: Morphology ................................................................................................................ 245 Appendix C1: Manual Point Counting Sub-Routine ......................................................... 245 Appendix C2: Snap Shot of the Manual Point Counting Screen ........................................ 246 Appendix C3: Manual Point Counting Sensitivity Analysis .............................................. 247 Appendix C4: Clemex Routine ......................................................................................... 248 Appendix C5: Morphology Point Counting Data .............................................................. 250 Appendix C6: List of Morphology Samples ...................................................................... 265 vii List of Tables Table 3-1: Properties of Material Tested and Percent Solid by Mass ...................................................... 30 Table 3-2: Percent Solids by Volume and Weight for the Experimental Samples Tested......................... 33 Table 3-3: Morphology Sample Size Fractions and Geometric Mean Size .............................................. 37 Table 3-4: Size Distribution of the Samples as Received ........................................................................ 39 Table 3-5: R-Squared Values for Linear and Exponential Data Fit ......................................................... 52 Table 3-6: Initial and Average Breakage at Different Agitator Speed ..................................................... 54 Table 3-7: R2 Values for Specific Energy vs. Size Reduction Using Power and Exponential Equations ... 57 Table 3-8: Specific Breakage Energy (kJ/m) ........................................................................................ 66 Table 4-1: Morphology Roughness Level Definitions and Illustration .................................................... 75 Table 4-2: Breakage Mode versus Roughness Level .............................................................................. 78 Table 4-3: Morphological Statistical Analysis of Galena Concentrate Sample ..................................... 108 Table 4-4: Morphological Statistical Analysis of Quartz ...................................................................... 109 Table 4-5: Morphological Statistical Analysis of Mixed Quartz and Galena Concentrate Sample ......... 110 Table 4-6: Feed Sample – Difference in Distribution Between Polished and Particle Mount Samples ... 119 Table 4-7: Lead-Zinc Ore Sample 1500-P1 Sample – Difference in Distribution Between Polished and Particle Mount Samples ....................................................................................................................... 119 Table 4-8: Lead-zinc ore sample 1500-P2 Sample – Difference in Distribution between Polished and Particle Mount Samples ....................................................................................................................... 119 Table 4-9: Lead-zinc ore sample 1500-P3 Sample – Difference in Distribution between Polished and Particle Mount Samples ....................................................................................................................... 119 Table 5-1: Benchmark Material Properties ........................................................................................... 144 Table 5-2: Effect of Material Properties on Run Time, Forces and Energy Efficiency .......................... 147 Table 5-3: Material Properties - Fixed Parameters ................................................................................ 148 Table 5-4: Particles and Mill Component Interactions .......................................................................... 149 Table 5-5 : Maximum Normal and Tangential Forces .......................................................................... 160 Table 5-6: Normal Forces Distribution Across the Mill at 1000, 1500 and 2000 rpm Agitator Speed .... 165 Table 5-7: Mixed Media and Galena Particles Distribution at 1500 rpm ............................................... 169 Table 5-8: Mixed Media and Galena Particles Distribution at 2000 rpm ............................................... 170 Table 5-9: Maximum Normal and Tangential Forces Distribution ........................................................ 171 Table A4-1: Quartz Experimental Data at 1000 rpm............................................................................. 215 Table A4-2: Quartz Experimental Data at 1500 rpm............................................................................. 216 Table A4-3: Quartz Experimental Data at 2000 rpm............................................................................. 217 Table A4-4: Galena Concentrate Experimental Data at 1000 rpm ......................................................... 218 viii Table A4-5: Galena Concentrate Experimental Data 1500 rpm ............................................................ 219 Table A4-6: Galena Concentrate Experimental Data at 2000 rpm ......................................................... 220 Table A4-7: Mix Quartz and Galena Concentrate Experimental Data at 1000 rpm................................ 221 Table A4-8: Mix Quartz and Galena Concentrate Experimental Data at 2000 rpm................................ 222 Table A4-9: Lead-Zinc Ore Experimental Data at 1000 rpm ................................................................ 223 Table A4-10: Lead-Zinc Ore Experimental Data at 1500 rpm .............................................................. 224 Table A4-11: Lead-Zinc Ore Experimental Data at 2000 rpm .............................................................. 225 Table C5-66-12C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Quartz + Galena Counts), ................................................................................................................................... 261 ix List of Figures Figure 1-1: Reported Specific Energy per Mill Type, (Wang and Forssberg, 2007) .................................. 2 Figure 1-2: Verti Mill and SMD Mill, (Metso, 2010 [Brochure]) .............................................................. 3 Figure 1-3: IsaMill, (Gao, and Holmes, 2007) .......................................................................................... 3 Figure 2-1: Fracture Toughness Versus Material Thickness; After Farag (1989)..................................... 11 Figure 2-2: Fracture Toughness of Ductile and Brittle Material .............................................................. 11 Figure 2-3: (a) Typical Particle Shapes; (b) Perfect Circle Particle ......................................................... 13 Figure 2-4: Schematic Diagram Subjected to Compressive Force P, a) flaw inclined at angle with respect to loading axis, b) flaw parallel to loading axis =0); After Tromans and Meech (2001).......13 Figure 2-5: Cleavage in a Low Carbon Steel Impact Fractured at Liquid Nitrogen Temperature. ............ 15 Figure 2-6: Fatigue Striation in a Low Carbon Steel Fractured Sample (Zone II). ................................... 16 Figure 2-7: Intergranular Fracture and Grain Boundary Separation for Low Alloy Steel. ........................ 16 Figure 2-8: SEM Image - 53 m Fraction; (a) BM; (b) HPGR................................................................ 19 Figure 2-9: SEM Image of Dense Packed Sand Grain Subjected ............................................................ 19 Figure 2-10: (a) Ball Mill, (b) Rod Mill, (c) SEM Micrograph of Ball Mill, .......................................... 19 Figure 2-11: Morphology of Gold Particles Generated by (a) Hammer Milling, (b) Disc Milling, ........... 20 Figure 3-1: Sample Preparation Flow Diagram ...................................................................................... 32 Figure 3-2: Schematic Diagram of Experimental Flow ........................................................................... 35 Figure 3-3: Correlation Coefficient versus Size Reduction ..................................................................... 40 Figure 3-4: Correlation Coefficient versus Modulus of Distribution ....................................................... 40 Figure 3-5: Rosin Rammler Modulus of Distribution versus Size Reduction .......................................... 41 Figure 3-6: Quartz Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm........................................... 43 Figure 3-7: Galena Concentrate Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm ....................... 44 Figure 3-8: Mixed Quartz and Galena Sample Passing Percent for ......................................................... 45 Figure 3-9: Lead-Zinc Ore Sample Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm .................. 46 Figure 3-10: Quartz (a) Linear and (b) Linearized Exponential Fitting Data ........................................... 48 Figure 3-11: Galena Concentrate (a) Linear and (b) Linearized Exponential Fitting Data ....................... 49 Figure 3-12: Mixed Quartz and Galena Sample (a) Linear and ............................................................... 50 Figure 3-13: Lead-Zinc Ore Sample (a) Linear and ................................................................................ 51 Figure 3-14: Correlation Between Measured and Calculated P80 for ...................................................... 53 Figure 3-15: Quartz Signature Plot – (a) Exponential and (b) Power Fit ................................................. 58 Figure 3-16: Galena Concentrate Signature Plot – (a) Exponential and (b) Power Fit ............................. 59 Figure 3-17: Mixed Quartz and Galena Sample Signature Plot ............................................................... 60 Figure 3-18: Lead-Zinc Ore Sample Signature Plot – (a) Exponential and (b) Power Fit ......................... 61 x Figure 3-19: Grinding Effective Energy for (a) Quartz, (b) Galena Concentrate, .................................... 64 Figure 4-1 Particle Perimeter and Hull Perimeter ................................................................................... 70 Figure 4-2: (a) Particle ID 39 Roughness value was 0.9; ........................................................................ 73 Figure 4-3: Pearson’s Time Correlation vs. Roughness Level Count ...................................................... 81 Figure 4-4: Pearson’s Time Correlation and Roughness Level Count for Quartz, ................................... 83 Figure 4-5: Pearson’s Time Correlation and Roughness Level Count for Quartz in................................. 85 Figure 4-6: Pearson’s Time Correlation and Roughness Level Count for Galena in ................................ 86 Figure 4-7: Pearson’s Time Correlation and Roughness Level Count for Cumulative ............................. 87 Figure 4-8: Pearson’s Time Correlation and Roughness Level Count for Lead-Zinc Ore Sample ............ 89 Figure 4-9: Quartz Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes 1000rpm, (b) 1500rpm, (c) 2000rpm ...................................................................................................... 94 Figure 4-10: Roughness Trend of Quartz for (a) Coarse, (b) Medium (c) Fine Fractions ......................... 95 Figure 4-11: Galena Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes 1000rpm, (b) 1500 rpm, (c) 2000rpm ..................................................................................................... 96 Figure 4-12: Roughness Trend of Galena Concentrate for (a) Coarse, (b) Medium (c) Fine Fractions ..... 97 Figure 4-13: Mixed Quartz and Galena Sample Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes (a) 1000rpm, (b) 2000rpm ............................................................................ 98 Figure 4-14: Roughness Trend of Mixed Quartz and Galena Concentrate ............................................... 99 Figure 4-15: Lead-Zinc Ore Sample Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes (a) 1000rpm, (b) 1500rpm, (c) 2000rpm ..................................................................... 100 Figure 4-16: Roughness Trend of Lead-Zinc Ore for (a) Coarse, (b) Medium (c) Fine Fractions........... 101 Figure 4-17: Overall Roughness Trend for Quartz Sample ................................................................... 102 Figure 4-18: Overall Roughness Trend for Galena Concentrate Sample ............................................... 102 Figure 4-19: Overall Roughness Trend for the Mixed Quartz and Galena Concentrate Sample ............. 103 Figure 4-20: Overall Roughness Trend for Lead – Zinc Ore Sample.................................................... 103 Figure 4-21: Individual Quartz Particles Broken, Shattered .................................................................. 105 Figure 4-22: Individual Galena Particles Broken, Shattered ................................................................. 105 Figure 4-23: Feed Liberation ............................................................................................................... 111 Figure 4-24: Lead-Zinc Ore Sample 1000 rpm - Pass1 Liberation ........................................................ 112 Figure 4-25: Lead-Zinc Ore Sample 1500 rpm - Pass1 Liberation ........................................................ 113 Figure 4-26: Lead-Zinc Ore Sample 2000 rpm - Pass1 Liberation ........................................................ 114 Figure 5-1: Schematic Diagram of Hertz Mindlin Contact Model, EDEM Training Manual, 2009 ........ 126 Figure 5-2: Schematic Diagram of Circular Agitator, Dimensions were mm ......................................... 132 Figure 5-3: Schematic Diagram of Triangular Discs Agitator ............................................................... 132 Figure 5-4: Cross Section of Particles Factory Surrounding 3 Discs ..................................................... 133 Figure 5-5: Initial Setting of the Particles in the 3 Sections at Time Zero .............................................. 135 xi Figure 5-6: Particle Distribution in 3 Sections for Circular and Triangular Discs .................................. 137 Figure 5-7: Fluid Flow Effect with No Drag Flow at 1500 rpm Agitator Speed .................................... 140 Figure 5-8: Drag Flow Force Effect on Particle Distribution Across the Mill ........................................ 142 Figure 5-9: Particle Distribution Across the Mill: ................................................................................. 143 Figure 5-10: Particle Distribution vs. Simulation Time ........................................................................ 152 Figure 5-11: Output vs. Input Energies for Media Runs ....................................................................... 154 Figure 5-12: Media Effective Energy Ratio vs. Simulation Time.......................................................... 156 Figure 5-13: Torque vs. Simulation Time............................................................................................. 158 Figure 5-14: Instantaneous Energy vs. Time Simulation, a) Input Energy, b) Output Energy ................ 158 Figure 5-15: Mill Cross Section .......................................................................................................... 161 Figure 5-16: (a) Normal and (b) Tangential Forces Distribution in Section A-A for 1000 rpm run ........ 162 Figure 5-17: (a) Normal and (b) Tangential Forces Distribution in Section B-B for 1000 rpm .............. 163 Figure 5-18: Number of Particles Distribution Across the Mill: ............................................................ 167 Figure 5-19: Initial Particle Distribution at Time Zero: (a) Radial Direction, section B-B; (b) Linear Direction, section A-A, (c) Isometric corss section............................................................................... 168 Figure 5-20: Normal Forces Distribution at 1500 rpm (a) Section A-A; (b) Section B-B ...................... 172 Figure 5-21: Normal Forces Distribution at 2000 rpm (a) Section A-A; (b) Section B-B ...................... 172 xii List of Symbols K KI KC KIC Y a B σ i, j Vi ωi Ii Ri µr Fn E* R* δ Ei, Ej Vi, Vj Ri, Rj P80 c tr Wr X a: b: R2 S A C c’ tr Psp Po S fracture toughness, when the sample has a thickness less than B stress intensity factor critical intensity factor fracture toughness value of the material constant related to crack geometry crack length (surface crack), one half crack length (internal crack) (m) material/particle thickness facing the crack stress applied to the material (MPa) particles interacting transitional velocity angular velocity moment of inertia particle radius (vector starting at center of particle) normal contact force tangential contact force coefficient of rolling friction normal force equivalent Young’s modulus equivalent radius overlap particles on contact Young’s modulus for particles i and j Poisson ratio for particles i and j radius of each particle i and j 80% passing specific breakage rate (min-1) residence time weight % retained particle size represents the size at which 36.79% of the weight was retained distribution modulus correlation coefficient size P80 (µm) size P80 at residence time zero, which was feed size specific breakage rate (min-1) breakage rate (m/min) residence time specific power (KWhr/ton) specific power at size zero; hypothetical size P80 (m) xiii D Xi Yi X, Y L W A P HP AR S Vs g dp ρp ρw SEn Fr Df Di Fn Y* R* δn M* β , Sn e Ft G* St i µr Ri ωi specific power per size reduction residence time number of particles counted per degree of roughness mean values for residence time and number of particles length width area perimeter hull perimeter aspect ratio sphericity settling velocity gravity particle diameter particle density water density viscosity surface energy per unit mass surface roughness surface energy (1/2 crack energy) particle final diameter particle initial diameter normal force equivalent Young’s modulus equivalent radius normal overlay normal damping forces equivalent mass relative normal velocity normal stiffness coefficient of restitution tangential force equivalent shear modulus tangential damping force tangential stiffness relative tangential velocity rolling friction coefficient of rolling friction distance of contact point from object center mass angular velocity at contact point xiv Ks C δn E* rpm EI T t PSD SEM BM HPGR DEM CFD PEPT MSDS SG HP MLA CAD CFD API linear spring stiffness dashpot coefficient overlap overlap velocity equivalent Modulus of elasticity revolution per minute input energy torque time particle size distribution scanning electron microscope ball mill high pressure grinding roll discrete element modeling method computer fluid dynamics positron emission particles tomography material safety data sheet specific gravity hull perimeter mineral liberation analysis computer aided design computational fluid dynamics application programming interface xv Acknowledgments I would like to express my gratitude to the following people who without them, this work would have been impossible to achieve. First, I would like to thank professor, Bern Klein for his support and guidance throughout this research. I have immensely learned from your knowledge in the field of comminution and mineral processing and gave me the freedom and confidence to try and learn new things. I would like to extend my thankfulness to my co-advisors, professor, Peter Radziszewski for his valuable support and technical advice in the modeling segment of this work. Your patience and advice was highly appreciated. Also Dr. Andy Stradling, my industrial advisor and committee member, I really appreciate your guidance and assistance that helped me to stay on track. Professor, Marek Pawlik, committee member, your input added depth and value to my work, thank you. I would also like to thank Teck Cominco Ltd., ART staff for their enthusiastic support in capturing the SEM images, Clemex data and their technical input. I am also grateful for the support of G&T Metallurgical Services Ltd. and High Way Technical Engineering Services Ltd. for allowing me to use their labs for sample preparation. I would like to thank the mining engineering department’s staff and my colleagues for all the support they’ve given me throughout the experimental process. I can’t forget my family, especially my beloved husband and lovely children who were holding on and gave me an enormous tangible and emotional support all through the 5 years. I couldn’t have done it without you. Finally, the first man in my life, my father, who believed in me, more than I believed in myself, wished you were here to witness this. xvi Dedication To My Family xvii 1. Introduction Ultra fine grinding and stirred mills are widely considered in mining operations since the mineralogical complexity of the available ore bodies is increasing. In many cases, particles need to be ground to 10m to liberate minerals. Over the past couple decades studies were performed to investigate the relationship between energy, stress intensity and product particle size (Blecher et al., 1996). Several studies focused on mill design and/or stress intensity distribution in the grinding mill (Kwade et al., 1996; Jie et al., 1996; Kwade, 1999a). Other studies considered the effect of the mechanical properties of the grinding media and ground material on the comminution process (Peukert, 2004; Becker et al., 2001; Kwade and Schwedes, 2002) 1.1 Stirred Mills Grinding is the largest energy consuming operation in mineral processing. About 50% of the energy consumed in mining operation is consumed in comminution operation (Botin, 2009). High speed stirred milling is the only technology that is employed in metal mining to grind particles down to ultrafine particle sizes (below 10m). The ability to grind to this particle size range relates to the power intensity in stirred mills which is about 300 kW/m3, compared to ball mills and tower mills that are 20 kW/m3 and 40 kW/m3, respectively (Pease et al., 2006). Despite the high power intensity, the overall power consumption of high speed stirred mills is lower due to their high specific throughput reflected by short retention times. Figure 1-1 compares the specific energy input and particle size reduction for different types of mills. Stirred mills have the highest specific energy input, but are the only mills that have the capability to grind particles below 5 microns. 1 Figure 1-1: Reported Specific Energy per Mill Type, (Wang and Forssberg, 2007) The main types of stirred mills used in the mining industry are the IsaMill, the Stirred Media Detritor (SMD) and the Verti mill. The IsaMill and SMD are high speed mills and the Verti mill is a low speed mill. The IsaMill is horizontally oriented and the latter two mills are vertically oriented. Another difference is the agitator type. The SMD uses pin agitator; the Verti mill uses a helical agitator (Figure 1-2) and the IsaMill employs discs (Figure 1-3). The power intensity of the IsaMill is 400 kW/m3 compared to 150 kW/m3 of the SMD mill, 19 kW/m3 of the ball mill and 4 kW/m3 for the Verti-Tower mill (Xstrata Technology 2010). 2 Figure 1-2: Verti Mill and SMD Mill, (Metso, 2010 [Brochure]) Figure 1-3: IsaMill, (Gao, and Holmes, 2007) Another difference between high speed mills and both the Verti mills and ball mills is that high speed mills are typically run in open circuit (no size classification). Over the past few decades research studies, such as those by Kwade and Becker (2001), were performed to relate different 3 forms of energy (input energy, specific energy, volume / mass specific energies), stress intensity and the final product particle size. Other studies focused on mill design and/or stress intensity distribution in the grinding mill (Becker et al., 1996, Kwade, 1999, 1996, Blecher et al, 1996, Partyka and Yan, 2007, Stender et al., 2004). The mechanical properties of the grinding media and ground material on the comminution process were also considered (Peukert, 2004). Stress intensity and energy in stirred mills were extensively researched. Attrition was considered to be the main breakage mechanism; however the actual breakage mechanisms encountered in the stirred mills are not well understood. 1.2 Research Objective The primary objective of this research is to gain an understanding of how operating parameters affect breakage mechanism. The objective is achieved via theoretical and experimental work. The secondary objective is to develop an understanding of the grinding mechanism of stirred mills via studying the state of the art researches performed on stirred mills using different tools including particle breakage analysis, morphology and computer modeling techniques. Specific objectives of the research were: To study the effect of different operating conditions and different material properties on grinding performance via analysing particle size reduction and energy consumption. To develop an understanding of the effect of breakage mechanism under varying mill operating conditions as well as mechanical material properties on particle morphology and liberation. To create a computer model that simulates particle flow, forces and energy distribution across the mill under different operating conditions. 4 1.3 Thesis Outline The state of the art literature is reviewed in chapter 2. The published literature reviews information about stirred mill operation and summarises the topics of failure analysis, types of fracture, morphology analysis, Discrete Element Modeling (DEM) and simulation. The results of the research are presented in three chapters, relating to grinding studies, morphological analysis and DEM. In chapter 3, test procedures and results of grinding studies are presented. Criteria for selecting material are reviewed. Material preparation and grinding procedures are outlined. Grinding results such as particle size distribution, breakage rates, Rosin Rammler fit and energy consumptions are summarized. In chapter 4, morphology definitions and analysis procedures are validated. Morphological analysis procedures are performed via manual point counting and pre-programmed image analysis software. The effect of residence time on the degree of roughness is analysed both statistically and cumulatively. Manual point count data are statistically analysed using Pearson’s Correlation, and cumulatively analyzed using stacked charts and degree of roughness trends. Whereas, the pre-programmed data, acquired via image analysis software, are analysed using general descriptive statistics. Liberation analysis of a lead-zinc ore sample, at three agitator speeds, is also addressed in chapter 4. In chapter 5, the discrete element modeling technique (DEM), the software utilizing (EDEM), the equations employed and the operating parameters are summarized. The simulation runs are analysed across the mill based on three criteria; number of particles, energy distribution and types and magnitude of forces the particles generated. 5 Finally chapter 6 presents the main findings and conclusions of the research. Recommendations for future research are also presented in the same chapter. 6 2. Literature Review The Literature review covers three main areas, the relationship between mill operation and size reduction, morphology analysis and discrete element modeling (DEM). Despite all the researches and studies performed on stirred mills, the operation and performance of these mills were only empirically understood. Particle breakage mechanism versus operating conditions of the mill was rarely studied. In this research, a comprehensive understanding of the fundamental mill operation and its products (ground particles) were explored, focusing on particle breakage mechanisms. The use of morphological analysis to understand the breakage mode of the particles under different grinding mechanisms represents a novel approach. The literature was reviewed to summarize the relationship between breakage mode and surface texture (morphology features). In order to simulate breakage in stirred mills, the modeling should accurately simulate particle motion and forces in the mill. However, it was recognised that limitations to modeling existed, which leads to oversimplification of the system. A summary of computer modeling (DEM) of stirred mills was included in this chapter. 2.1 Mill Operation and Particle Size Distribution Stirred mills, by definition, are mills that stir particles which are usually in slurry form and need to be ground. Grinding media could be natural sand, steel slag or ceramic beads. The stirred mills are classified according to their orientation i.e. vertical or horizontal. Examples of vertical mills are tower mills, pin mills and the stirred media detritor (SMD), whereas the IsaMill is a horizontal mill. A vast number of researchers (Gao and Forssberg, 1993, Blecher et al., 1996, Kwade et al, 1996, Zheng, et al., 1996 , Gao et. al, 1996, Varinot et. al, 1999, Kwade, 1999, 7 2004, Wang and Forssberg, 2000, Becker et al., 2001, Kwade and Schwededs, 2002, Jankovic, 2003, Stender, et al., 2004, Yue, and Klein, 2005, Parry, 2006, Gao and Holmes, 2007, Shi, et al., 2009, Ye, et al., 2010, Pease, et al., 2010, Vizcarra et al., 2010, Celep et al., 2011, and others) investigated different types of stirred mills operation, stress energy distribution, stress types, energy consumption, breakage kinetics, mineral liberation, product size distribution, mineral flotation performance and other parameters. Particle size distribution (PSD) is one of the initial parameters to be checked after a grinding operation which is essential in mineral processing. PSD affects the behaviour of the particles in subsequent operations, such as flotation or leaching that require adequate mineral liberation. Furthermore, dewatering processes such as thickening and filtering are affected by the PSD. In general, a narrow PSD is preferred over a wide PSD. Jankovic and Sinclair (2006) investigated the role of media size and the mechanical properties of the minerals using different types of stirred mills. They concluded that grinding hard minerals produced a narrower particle size distribution compared to soft minerals; whereas the media size had no significant effect on PSD. Parry (2006) investigated the behaviour of different material properties at different mill stress intensities and concluded that softer minerals were ground faster at lower stress intensities than harder minerals. Jankovic and Sinclair (2006) agreed with Yue and Klein (2004) and Tromans and Meech (2004) that below a specific particle size, the breakage behaviour would change. Yue and Klein (2004) when reduction ratio reached 1, no grinding would take place i.e. grinding limit was reached. Close to the grinding limit, the breakage mechanism would change from massive fracture to attrition (abrasion). On the other hand, Jankovic and Sinclair (2006) speculated that the size limit 8 below which the PSD gets narrower due to particles hardening was below P80 20 m. Tromans and Meech (2004) based their suggestions on a mathematical model, where they stated that there was a limiting size beyond which grinding would not reduce the particle size any further. They claimed that the limiting size was associated with the critical stress intensity factor of the particle. Smaller particles would exhibit fewer and smaller flaw sizes and cracks, therefore would require a high stress intensity to exceed the critical stress intensity and propagate the crack. In an attempt to build a more comprehensive picture of stirred mill grinding operation with respect to particle breakage, it was important to understand the basics of failure analysis and particularly brittle and fatigue failure fractures. Brittle and fatigue fractures are most relevant because rocks and minerals are brittle. During comminution, such minerals and rocks are exposed to multiple impacts, compressive and shear loadings which would lead to a typical fatigue fracture. 2.2 Failure Analysis – Brittle and Fatigue Fractures The science of failure analysis has emerged to study different mechanisms of failure or fracture (breakage) of a work piece that was made of metal, ceramic, rubber, polymer and other materials (Farag, 1989). The information can be used to improve design and thereby prevent failure. On the other hand, particle breakage is the objective of comminution in mineral processing. Comminution involves mechanical loading of particles either by impact, compression or abrasion until the target particles break (fail). According to Farag (1989), failure results when a component does not perform its intended function. Failure that would lead to fracture is due to static overloading that could be either ductile or brittle. Fatigue fractures are usually sudden without visual signs and due to multiple impact loadings. In order to quantitatively predict the 9 fracture strength of a component, the fracture stress can be calculated. Fracture stress according to Griffith’s (1921) equation for glass (Farag, 1989), is a function of crack length for edge cracks or half crack length for center cracks, Young’s modulus of the material, and energy required to extend the crack by unit area. The energy required to propagate a crack in a component needs to exceed its plastic deformation energy. Therefore, fracture toughness of a material is proportional to energy consumed in plastic deformation i.e. stress intensity factor KI. The stress intensity factor value is the level of stress at the tip of the crack. It is a function of crack geometry and is material independent. When the stress intensity (KI) exceeds the limits for the material, unstable fracture occurs. This is called the critical intensity factor value Kc, which is a thickness dependent value. As the material thickness increases, the K c decreases until it reaches a minimum value which is the fracture toughness value of the material (KIc) as shown in Figure 2-1 . Fracture toughness of a material is the total energy required to fracture the material. It is the area under the curve of a stress-strain plot as shown in Figure 2-2. The value of fracture toughness is a function of applied stress, geometry factor of the crack (thickness and width), and crack size (2a for center crack and a for edge crack), Equation 2-1 (Farag, 1989) below: K Y a Equation 2-1 Where: K = fracture toughness, when the sample has a thickness less than B (MPa √m) Y = constant related to crack geometry (-) a = crack length (surface crack), one half crack length (internal crack) (m) = stress applied to the material (MPa) 10 Figure 2-1: Fracture Toughness versus Material Thickness; After Farag (1989) Figure 2-2: Fracture Toughness of Ductile and Brittle Material A higher fracture toughness value signifies more energy absorbed by the material before fracture. A comparison of the area under the stress strain curve of brittle and ductile materials in Figure 2-2 shows that ductile material absorbs more energy before fracture compared to brittle material. Another definition for ductile and brittle fracture is the extent of macroscopic or microscopic 11 plastic deformation which precedes fracture. By analysing fracture surface texture (morphology), the mode of breakage can be identified. In the grinding process, breakage is the intentional fracture of the particles. Accordingly, parameters such as particle shape and means of loading directly affect the grinding performance. For example, if the particles are not perfectly round in shape i.e. have sharp edges or corners as highlighted in Figure 2-3(a), then high stress concentration zones are present and the particles might also have internal hair cracks. At such stress concentration zones, the (KI) stress intensity factor reaches its critical value which will ultimately propagate the fracture with minimum loading. The smaller the particle thickness facing the propagation direction of the crack, the higher the critical stress factor value (Kc). In other words, less energy is required for the fracture to propagate. The fracture toughness of the minerals (K Ic) is a material property, which is determined based on the largest particle size facing crack propagation direction. Whitney, Broz, & Cook (2007) studied the effect of hardness values, toughness and modulus of some common metamorphic minerals (mohs and Vickers hardness). Particles that are perfectly circular as in Figure 2-3(b) will possess a lower stress intensity factor due to the absence of stress raisers. However, they posses inherent flaws that via fatigue loading through multi impact or multi compression loading would cause the micro cracks to either initiate or propagate and eventually fracture. Particle size has a major effect on the type of stress that causes fracture initiation and propagation. The larger the particle beyond a certain thickness threshold (B: material/particle thickness facing the crack), fracture toughness (KIc) which is a mineral property, will be the cause of fracture initiation and/or propagation. The smaller the particle size than the thickness (B) threshold, the critical stress intensity factor (Kc) which is inversely proportional to the thickness, will be the cause of fracture initiation and/or propagation, (Figure 2-1). 12 (a) (b) Figure 2-3: (a) Typical Particle Shapes; (b) Perfect Circle Particle Fracture toughness of minerals was studied by Tromans & Meech (2001). Fracture toughness of 48 minerals (oxides, sulphides, and silicates) was theoretically modeled based on their ionic crystal bonding. Tromans and Meech (2001) concluded that transgranular fracture toughness for pure single phase minerals was about 10-14% higher than the intergranular fracture toughness. Tromans and Meech (2001) stated that in a ball or rod mill, the impact efficiency was directly related to the loading force on the particles as well as the flaw size and orientation relative to the loading axis and critical stress intensity factor, as shown in Figure 2-4. Figure 2-4: Schematic Diagram Subjected to Compressive Force P, a) flaw inclined at angle with respect to loading axis, b) flaw parallel to loading axis =0); After Tromans & Meech (2001). 13 The material science discipline and physical metallurgy relates the microstructure of the material to its physical and mechanical properties. Metallography is a tool used in material science to evaluate the material microstructure using optical and electronic microscopes by which images could be captured and analyzed. The failure analysis is a branched discipline from the material science where metallography is further developed and morphological analyses of fractured surfaces have emerged. Fracture morphology is an expression that emerged about three decades ago as per researches published by the American Society of Testing and Materials, (Srauss and Cullen, 1978). Fracture types are either brittle or ductile depending on the type of material. Morphology is a powerful tool that is often used to recognise the different types of fractured surfaces. Ductile fracture morphology is not addressed in this review since the focus of this research is on grinding minerals which are brittle by nature. A particle could be exposed to multiple impacts until it fractures open, which if morphologically examined, would possess features of fatigue fracture. 2.3 Morphology 2.3.1 Morphological Features of Fractured Surfaces Typical brittle fracture occurs at low plastic deformation at low energy absorption. The preexisting crack propagates very fast when exposed to a constant stress that could be less than the yield strength of the material. Brittle fracture usually initiates at stress raisers such as defects, fatigue cracks, inclusions, notches and sharp corners or cleavage faces as in mineral crystal structure boundaries. Breakage surface and its morphology are indications of the type of fracture. For example, brittle fracture surface shows bright granular appearance. Brittle fracture mechanisms are either transgranular (cleavage) or intergranular. 14 Transgranular fracture mode propagates the crack through the grains and they are typically along cleavage planes. Visual characteristics of the fracture are bright, reflecting facets. SEM images of the transgranular fracture appear as flat surface and river patterns which are identified at higher magnification as shown in Figure 2-5. Figure 2-5: Cleavage in a Low Carbon Steel Impact Fractured at Liquid Nitrogen Temperature. After Gabriel (1985) Fatigue fracture is usually categorized as brittle fracture with cyclic loading, which is usually due to stress cycles. A fracture possesses three zones. Zone I is the initiation zone which is usually near or at the surface where the cyclic load is high and is usually brittle transgranular fracture. Zone II is the propagation zone which appears as parallel plateaus separated by longitudinal ridges which are called clamshell marks and fatigue striations. The clamshell marks and striations are very significant in the case of a uniformly applied load. If the loading is not uniform, at very high magnifications, clamshells and striation features can show up at different angles due to the multi angle loading, as shown in Figure 2-6. Zone III is the unstable fast fracture zone. This zone is the smallest cross sectional area of the component that cannot withstand the applied load. Unstable fracture can exhibit a coalescence-ductile feature or brittle fracture. 15 Figure 2-6: Fatigue Striation in a Low Carbon Steel Fractured Sample (Zone II). After Gabriel (1985) Intergranular fracture mode propagates along grain boundaries. Its visual appearance is rockcandy or faceted. Intergranular fracture arises when there are significant differences between the grain properties. It also occurs when the intergranular matrix is environmentally attacked via corrosion, or grain boundary embrittlement. Creep loading could also lead to intergranular fracture mode. Typical intergranular fracture is shown in Figure 2-7. Figure 2-7: Intergranular Fracture and Grain Boundary Separation for Low Alloy Steel. After Gabriel (1985) 16 Fracture analysis methodology starts by examining the fractured surface for basic morphological features, such as brightness or dullness, roughness or smoothness, striation lines and their direction. In order to detect the type of failure, the fractured surfaces are examined at different levels of magnification. The particles broken via grinding have more than one fracture surface. The type and number of fractured surfaces depend on the mode of loading that the particles are subjected to. Other morphological features such as sphericity, elongation and convexity which are indications of particle elongation and surface roughness are employed to identify the breakage mode of the particles. Image analysis software follows standard mathematical principals for measuring these parameters. To determine sphericity, the circumference of the equivalent area of the circle is divided by the actual perimeter of the particle. Particle elongation is the inverse of the aspect ratio (length divided by width). Convexity reflects particle roughness and is mathematically calculated by dividing the convex hull perimeter by the actual particle perimeter. The values for each parameter are between 0 and 1. The value closer to 1 indicates that the particle is almost perfectly circular or equiaxed (not elongated) or the surface is extremely smooth. 2.3.2 Morphological Features and Comminution Morphological features of rocks agree with the general material science concepts and failure analysis as revealed in the study performed by Celik and Oner (2006) where the ball mill (BM) and high pressure grinding roll mill (HPGR) were compared. Celik and Oner (2006) observed from the surface texture images captured by SEM that the BM consistently produced smooth surfaces compared to the HPGR as shown in Figure 2-8. They concluded that HPGR produced intergranular breakage due to its compression loading mechanism, whereas the BM produced transgranular breakage due to the impact and shear loading. Guimaraes, et al., (2007) deduced 17 conclusions on breakage mechanism versus particle packing (loose and dense packing) under one dimensional compression loading using morphological texture analysis. Their results showed that loose packing of particles exhibited splitting and massive breakage, rougher surfaces, which implied crushing and intergranular breakage. On the other hand, the dense packing experienced local damage at contact with multiple fresh faces as shown in Figure 2-9. They also observed that sphericity and roundness decreased as the particle size decreased. The type of grinding mill dictates the roundness and elongation shapes of the fractured particles as per the research performed by Hiçyilmaz, et al., (2004) on ball and rod mills (Figure 2-10). Ahmed (2010) compared dry versus wet grinding. He concluded that dry grinding produced rough surfaces compared to wet grinding and added that impact crushing produced rougher, fragmented particles compared to the particles produced via rotary mills. Frances, et. al., (2001), also studied the effect of wet and dry grinding using four different types of mills, which are tumble mills, shaker mills, air jet mills and stirred bead mills on gibbsite’s morphology. They concluded that in comminution, the characteristics of the ground material and type of mill dictated the particle shape and fracture features. Similar conclusions were earlier reached by Lecoq, et al., (1999) who found that under similar grinding conditions the type of ground material would determine the type of breakage. They added that the higher the particles complexity, the more resistant it will be to breakage via attrition. Alex, et al., (2008) studied the effect of residence time on the morphological features of gibbsite in a stirred mill. Their observations were visually analysed where they concluded that the particles started to break at grain boundaries, producing platelet like particles. On the other hand, if the same particles were exposed to longer grinding, the produced particles would have a more complex shape and the platelet shaped particles would disappear. 18 (a) (b) Figure 2-8: SEM Image - 53 m Fraction; (a) BM; (b) HPGR. After Celik & Oner (2006) Figure 2-9: SEM Image of Dense Packed Sand Grain Subjected to One Dimensional Compression Load. After Guimaraes et al. (2007). Figure 2-10: (a) Ball Mill, (b) Rod Mill, (c) SEM Micrograph of Ball Mill, (d) SEM Micrograph of Rod Mill. After Hiçyilmaz et al. (2004). Ofori-Sarpong and Amankway (2011), agreed with Frances, et al., (2001), that the type of grinding machine would dictate the shape of the particles produced as shown in Figure 2-11. 19 Ofori-Sarpong and Amankway (2011) focused on gold particle morphology on gravity concentration performance. They concluded that fine spherical particles settle faster than coarser flaky cigar-shaped particles. Accordingly, they recommended choosing a grinding mill which would produce coarse round gold particles for gravity concentration. Figure 2-11: Morphology of Gold Particles Generated by (a) Hammer Milling, (b) Disc Milling, (c) Pulverising (d) Ball Milling, After Ofori-Sarpong and Amankway (2011) The effect of particle morphology on flotation was studied by Ahmed, (2010). He concluded that the particle’s roughness had more influence on flotation than the particle’s shape. He added that the rough surface had faster flotation kinetics than smooth surfaces. 2.4 Computer Model and Mill Simulation To obtain a comprehensive understanding of the grinding operation after physically analysing its products, a mathematical quantitative analysis was essential. Accordingly, part of this research was dedicated to creating a Discrete Element Model (DEM) of the IsaMill that would address some of the questions raised by the objectives of the study. DEM was used to help assess the effect of different operating conditions of the mill on the flow of the material and distribution of different types of forces across the mill chamber. 20 Computer simulation is a technique used to model a real life machine or situation, so that it can be further understood. Simulation assists in understanding how a system works and how variables would affect its performance. A model was described by a set of equations and variables that are controlled by their inputs. The outputs are further analyzed in order to optimize the system. Comminution modeling has been extensively studied for different grinding mills including SAG mills, ball mills, vertical and horizontal stirred mills. Various approaches exist in implementing a model such as mathematical models or computer simulation models. Radziszewski and Morrell (1998) developed a mathematical model for ball mills, Datta and Rajamani (2002) also modeled ball mills but used two dimensional Discrete Element Modeling (DEM). Govender and Powell (2006), empirically modeled the power derived from three dimensional particle tracking experiments. Zhao et al., (2006) modeled granular material in three dimension via discrete simulation. Gui and Fan (2009), studied the motion of rigid spherical particles in a rotating tumbling mill. Gers et al., (2010), numerically modeled stirred media mills and studied grinding operation and hydrodynamics and collision characteristics. Mannheim (2011) recently used an empirical mathematical modeling procedure to scale up stirred ball mills. Modelling of stirred mills were performed by Cleary et al., (2006a), and Sinnott et al., (2006b) on tower and pin vertical stirred mills using DEM. They studied the media flow, mixing and force network in the mill. Positron Emission Particles Tomography (PEPT) technology was used to visualize the motion of particles in the mill. The PEPT was used as a research tool on a vertical stirred mill by Conway-Baker et al., (2002) and Barley et al., (2004) and on horizontal stirred mill by Jayasundara, et al., (2011). In literature, the IsaMill has been modeled mostly using DEM; however, most of the models were developed on an over simplified version of the mill. Typical simplified models included only 3 agitator discs, oversized particles and no fluid 21 dynamics for slurry flow in the mill. Examples of the first DEM models of the IsaMill were developed by Jayasundara et al., (2006 and 2008). In an attempt to take the DEM modelling of the IsaMill closer to a real case scenario, a computer fluid dynamics (CFD) was coupled with the standard DEM modeling by Jayasundara et al., (2009) and Jayasundara et al. (2010). Almost all modelling researches assessed the particle velocity pattern in the mill and they agreed that high velocity patterns were close to the discs and the highest velocities were observed at the discs holes. Jayasundara, et al., (2006) DEM simulation results agreed with Westhuizen, et al., (2011), tracking the media particles using the Positron Emission Particles Tomography (PEPT) technology. They found that the discs have a major effect on the particles flow pattern in the mill. There were fewer particles within the discs region, but the particle distribution was packed between discs and near the chamber wall. However, Westhuizen et al., (2010) studies contradicted the findings by Jayasundara et al., (2008) on the effect of particle density on velocity. Jayasundara, et al., (2008) stated that particle density did not affect velocities, but particles would exhibit a high number of collisions, higher collision energies and would require a higher input power. Conversely, Westhuizen et al., (2010) concluded, through using the PEPT tracking experiments, that the denser the particles, the lower their acceleration. Other parameters investigated included the effect of media loading and agitator speed. Jayasundara et al., (2010) and Yang et al., (2006 and 2008) concluded that increasing agitator tip speed increased particle velocity, which in turn increased impact energies, compressive forces and power draw. On the other hand, by increasing media loading, particle agitation became more vigorous as the collision frequency increased. However, by increasing media loading, the collision energy decreased and impact energy and compressive loading increased, which in turn 22 increased power draw. Jayasundara et. al, (2011) investigated the effect of fluid flow on a simplified ISAMill using a coupling of DEM and Computer Fluid Dynamics (CFD) software. Jayasundara et al., (2011) concluded that the flow pattern and media velocities in the mill were similar to the model with no fluid dynamics effect, with minor change in velocity between the tip of the disc and mill’s chamber. In spite of the vast number of studies performed on the IsaMill, which contributed to the knowledge of the mill operation, there is still a gap in the understanding of the mill operation and stress intensity distributions. The effects of different types of particles, with different material properties, on each other in the mill have not been investigated. A simulation that would include more features of a real mill needs to be investigated. The IsaMill classifier should be included to assist in understanding the actual flow dynamics of the particles throughout the mill length. As well as, careful choice of material properties for the different parts of the mill and the particles would bring the DEM model closer to a real mill performance. Discrete Element modeling, according to DEM Solutions, is a computer program that treats the particles as discrete bodies. DEM allows the particles to be displaced, rotate and detach. The interactions between the particles and their surroundings before and after contacts are calculated. Each particle movement is modeled. The basic mechanics of discrete element modeling is founded on Newton’s second law of motion as per Equation 2-2. 23 & Equation 2-2 i and j were particles interacting vi : transitional velocity i: angular velocity Ii: moment of inertia Ri: particle radius (vector starting at center of particle) Fnij: normal contact force Ftij: tangential contact force r: coefficient of rolling friction torque due to tangential forces Rolling friction torque arising from elastic hysteresis loss or viscous dissipation The EDEM software has multiple built in contact stress models to choose from. The closest model to the comminution application is the Hertz Mindlin contact model. Hertz Mindlin calculates localized stresses that develop at two curved surfaces that come in contact. The contact stress is a function of the normal contact force, the radii of curvature of both bodies and the modulus of elasticity of both bodies, as per Equation 2-3. 24 Equation 2-3 Where Fn = normal force E* = equivalent Young’s modulus R* = equivalent radius = overlap particles in contact Equation 2-4 Equation 2-5 Where: Ei, Ej = Young’s modulus for particles i and j vi, vj = Poisson ratio for particles i and j Ri, Rj = radius of each particle i and j DEM is limited due to its intensive computation requirement. Accordingly, simulating a mill with actual number of particles, actual particle size and imperfect shapes rather than perfect spheres, is not achievable with the available computing tools used in this research. 2.4.1 Power Model Most computer models have focused on the stirred mill’s qualitative performance such as the distribution of particles and their velocities across the mill at different operating conditions. Quantitative analysis is addressed in this research to understand the type of forces (normal and tangential), power and energy distributions under different operating conditions, such as different 25 agitator speeds. Quantitative analysis was performed via mathematical and empirical methodologies (Herbst and Sepulveda, 1978). A recent mathematical model that empirically relates the power to agitator speed and other parameters was the model developed by Gao et al., (1996) as per Equation 2-6 Equation 2-6 Where: P: power (kW) N: stirrer speed (rpm) ρs: slurry density (% solids) ρb: media density (gm/cm3) d: dispersant dosage (%) Gao et. al (1996) concluded that the mill’s stirrer speed was a leading factor affecting the power consumption and the relationship between stirrer speed and power was significantly non linear. They also added that the higher the power input, the size reduction process would accelerate significantly with minimum change in energy efficiency. 2.5 Conclusion Stirred mills are used by mineral industry to liberate valuable minerals for downstream operations. In many cases, this is not achievable unless the particles are ground to below 10 m. The only mills that can accomplish such fine grinding are high speed stirred mills such as the IsaMill. Many studies and researches on stirred mills state that stirred mills grind via attrition (abrasion). There is a gap in the existing researches that points to particle breakage in stirred mill under different operating conditions, particularly from the morphology and surface texture point of view. Furthermore, the interaction between particles with different mechanical properties 26 versus mill operating conditions needs further investigation. There is a relationship between particle breakage mechanism and their morphology features which if understood, will provide an insight onto how mill performance can be improved. In this study, such relationship is quantitatively evaluated rather than qualitative analysis as per literature. Discrete element modeling has been applied on stirred mills in general and particularly on the IsaMill. The DEM assists in understanding the effect of the different media types, agitator speed, media loading and fluid dynamics on mill performance and operation. However, none of the models performed to date could relate the effect of different particle mechanical properties on each other. Also, all the models developed for the IsaMill were over simplified. The effect of the media classifier on the particles flow and distribution has not been investigated. The research in this thesis attempts to bridge some of the knowledge gaps. In particular, DEM is used to better understand the relationship between the mill operating parameters and possible breakage methodology from the force distribution standpoint in the mill. A correlation between predicted particle breakage mechanism which are acquired via DEM model and actual ground particle morphology are addressed. In this study, The IsaMill was chosen as a tool for stirred mill grinding. 27 3. Grinding Studies 3.1 Introduction The objective of the experimental work was to understand the effect of varying mill operating parameters and different material properties on breakage mechanism. To meet the objective, the experimental work was conducted on four samples. Two samples contain pure minerals with distinct mechanical properties, the third sample is a mixture of the two pure minerals and the fourth sample is an ore sample which is similar in mineralogical composition to the mixed sample. The variable parameters tested were material type, agitator speed and residence time and results were analysed based on: - Particle size distribution (PSD) - Particle breakage rate - Energy consumption 3.2 Grinding Test Material Four different samples were selected for the test program: - Quartz (silica sand Target Industrial Minerals) - Galena concentrate (supplied by Pend Oreille mine) - Mixed galena concentrate and quartz (ratio of 1 to 6 by volume) - Lead-Zinc Ore (Red Dog SAG mill discharge). The quartz and galena concentrate samples were selected based on their mechanical and physical properties. The Mohs hardness value for the galena is about 2.5 (very soft) while quartz is close to 7.0 (very hard) according to literature. The galena concentrate has a high specific gravity (SG) compared to quartz. The measured SG of the galena concentrate is 7.19, while quartz is 2.63. 28 Fracture surfaces are different. The mineral galena has distinct cubical cleavage planes whereas quartz has a conchoidal fracture surface. In addition, galena is a sulphide mineral and quartz is an oxide mineral. According to the assay analysis (Appendix A2), the quartz sample consists of mainly silica, 92% silicon dioxide. The average chemical composition of the galena concentrate sample is 83% lead, 1.5% zinc, 0.26% iron, and 0.34% silicon dioxide. The average chemical composition of the lead zinc ore sample is 20% zinc, 9.3% lead, 32% silicon dioxide and 7% iron. The modal mineralogy distribution of the feed was performed on one size fraction with a geometric means size of 63m. This size fraction is used for liberation analysis as discussed in section 4.5.7. The minerals modal distribution included galena, sphalerite, pyrite and quartz minerals, which were 6%, 33%, 15% and 31%, respectively for the of 63m size fraction. Since ores are composed of mixtures of minerals, that can possess extreme mechanical and physical properties, it was important to understand the impact of these mixtures on grinding. Accordingly, a mixture of galena and quartz (concentrate) was prepared for testing. The mixture was based on 1:6 volume ratio of galena to quartz concentrate. The mixture was prepared on a volume basis rather than a weight basis because the pulp rheology is directly affected by volume solids content, (Yue and Klein, 2004). Since the two materials tested were liberated, it was reasonable to take the experimental work to the next level and study the effect of similar operating parameters on an ore sample similar to the mixed sample. The lead-zinc concentrate sample was selected because it consisted of a mixture of non-liberated quartz and galena minerals with a similar ratio to the mixed quartz-galena concentrate sample. The response of locked particles under similar operating conditions would give a real representation of the effect of the different operating conditions on mineral breakage behaviour. 29 Based on typical stirred mill grinding operation recommendation, the mixed mineral slurry suspension with an average solids SG between 3.0 and 4.0, pulp densities should be between 40 and 50% by weight. This corresponds to an average volume solids content of 14.3%. Accordingly the percent solid by volume was chosen as 14.3% for the experimental work. The SG of the four samples used in the study was determined as per ASTM D854-06 procedures. Detailed calculations of the mass for each material tested and operating parameter are found in Appendix A-3. The Mohs hardness values, measured specific gravity, and calculated percent solids by mass for the materials used in the experimental work are presented in Table 3-1. For the mixed sample, the ratio of galena to quartz was selected to be 1:6 by volume to be comparable to the lead-zinc ore sample. Table 3-1: Properties of Material Tested and Percent Solid by Mass 3.3 Material Mohs Hardness Value Specific Gravity (SG) % Solids by mass Quartz 7.0 2.63 30.5 Galena 2.5 7.19 54.4 Mixed (Galena : Quartz; 1:6) -- 3.30 36.0 Lead-Zinc Ore SAG Discharge – -- 3.66 37.9 Procedures A systematic procedure was followed in preparing the four materials for the series of experiments conducted in this study. Similar grinding procedure and mill operating conditions were followed for the four materials to guarantee comparability of results. The same size analysis and sample preparation procedures were also applied. 30 3.3.1 Material Preparation Procedure The four materials chosen for this research showed a wide variation of particle size distribution and top size. For the sake of comparison, it was important to bring the four materials top size and PSD close to similar. Specific surface area (size per mass) is an ideal measurement and indication of particle size reduction for the entire sample. However, typical industrial practice reports size reduction as 80% pass (P80). Therefore, in this research, particle size and its reduction are reported as P80. The 80% pass (P80) sizes of galena concentrate, quartz and lead-zinc ore were 234.4, 134.1 and 326.3 m respectively. The distribution modulus according to the Rosin Rammler equation for the galena concentrate, quartz and lead-zinc ore were 2.14, 2.4 and 0.7, respectively. Quartz had the narrowest size distribution and as expected the SAG discharge of the ore had the widest size distribution. In order to bring the three materials close to similar top size and PSD, they were screened on a 150 mesh (106 m) sieve. The +106 m quartz and galena concentrate were ground in a laboratory rod mill and wet screened on the same 150 mesh sieve. The -106 m rod mill products were dried, and then mixed with the pre-screened -106m material and riffled into 5 kg charges for stirred mill grinding tests. A sample preparation flow chart is shown in Figure 3-1. As mentioned in section 3.2, the galena concentrate and quartz (-106m size fraction) were mixed with a ratio of 1:6 by volume to create the mix product for testing. The lead-zinc ore sample (SAG discharge; -106m size fraction) was assayed for chemical composition. The detailed assay analysis is presented in Appendix A2. The major elements were 20% zinc, 9.3% lead, 32% silicon dioxide and 10.4% iron III oxide. The particle size distribution of the feed product from the -106m size fraction are presented in section 3.4. 31 Rod Mill +106 m 150 m mesh +106 m 150 mesh -106m Discard m -106m Drying Oven Riffle Splitte r 5 kg sample 5 kg sample IsaMill Figure 3-1: Sample Preparation Flow Diagram The specific gravity (SG) for each material prepared was tested according to ASTM D854-06 procedures. The SG’s of quartz, galena concentrate, mixed quartz and galena sample and leadzinc ore sample were measured to be 2.63, 7.19, 3.30 and 3.66, respectively. Since the minerals chosen have a wide range of SG’s, grinding tests were conducted at solid content based on volume rather than weight to guarantee similar pulp flow behaviour in the mill. In industrial operations, pulp densities refer to solid concentrations by mass, which range between 35% and 65%, depending on the SG’s of the mineral constituents. The solid content chosen for the research test program was 14.3% solids by volume, based on a typical specific gravity of 4.00. Accordingly, the percent solids by mass for quartz, galena concentrate, mixed quartz and galena concentrate sample and lead-zinc ore sample were 30.5%, and 54.4%, 36% and 38%, respectively as shown in Table 3-2. 32 Table 3-2: Percent Solids by Volume and Weight for the Experimental Samples Tested Sample Specific Gravity % Solids by Volume % Solids by Weight Quartz 2.63 14.3 30.5 7.19 14.3 54.5 3.30 14.3 37.9 3.66 14.3 35.5 Galena Concentrate Mixed Quartz & Galena Lead-Zinc Ore 3.3.2 Grinding Procedure A 4 litre Netzsch (ISA) Mill was used for the grinding tests. The 4 litre mills are commonly used for pilot scale testing. Figure 3-2 is a schematic diagram showing the ISA mill, feed tank and product tank and illustrates the pulp flow of a 5 pass test run. Three grinding tests were performed for each material using grinding speeds of 1000, 1500 and 2000 rpm. The pulp flow rate was set at the highest possible setting, 3.5L/min. A high flow rate was chosen to estimate the initial breakage of the particles. The effect of residence time was studied by running the material through the mill 5 times (5 passes) in order to study the secondary breakage behaviour of the particles when given more time and to determine the energy usage and product size relationship. For each test run, five samples were produced for PSD and morphology analysis. The grinding media used was the MT1 ceramic beads single size ( 2mm). 33 The detailed testing procedure was as follows: Turn on the mill agitator at 1000, 1500 and 2000 rpm, empty (no media or slurry), and record the power consumed at no load. Turn off the mill agitator. Pre-fill the mill with the required amount of grinding media, which was set at 80% by volume of the effective grinding mill volume. The effective grinding volume is the inner chamber volume minus classifier section, agitator and discs volume. Fill Tank 1 with the required amount of water then turn on the pump to circulate the water within the same tank. Add solids slowly to the desired pulp density. Change valve positions so that pulp flows through the mill with no agitation. Once the pulp filled the mill and started to discharge, turn on the mill agitator to the desired speed e.g. 1000, 1500 or 2000 rpm. Operate the mill until a steady state was achieved (first 60 seconds). Product generated during the first 60 seconds was rejected from the circuit. Change valve position such that the product was sent to Tank 2. Check flow rate using a graduated cylinder and stopwatch. The flow rate of the pulp was initially set at the highest possible rate which was 3.5 L/min. Once approximately half of the feed had passed through mill, collect about 300 mL samples for analyses. Once Tank 1 was empty, change valve positions such that Tank 2 would be the feed tank and Tank 1 would be the collection tank. Repeat the above cycle 5 times and collect 5 products for analysis. 34 Note: The test run for the quartz and galena mixed material was performed only at two agitator speeds (1000 and 2000 rpm) due to the shortage of available material. In Figure 3-2, the white arrows show the flow direction for passes 1, 3 and 5 and the blue arrows indicate direction for passes 2 and 4. Detailed data collected for each test run are presented in Appendix A4. Tank 1 Tank 2 Passes 1, 3, 5 Passes 2, 4 Figure 3-2: Schematic Diagram of Experimental Flow 3.3.3 Particle Size Analysis Procedure Particle size analysis was performed using sieve analysis/cyclosizing and laser sizing. Both particle size analysis methods were used in this study. Laser sizing was used to study the effect of different operating conditions on PSD and sieve screening was used to create particles for morphology analysis. For sieve analysis, a representative sample was collected, dried, weighed and then screened using sieve series. Weights retained on each screen were recorded and size versus percent passing or retained was plotted. The PSD’s were also determined by using laser sizing. The laser sizing 35 technology was based on the physics of light scattering (Malvern Instruments, 2009). According to Malvern innovative solution in material characterization website (2010), Rodrı´guez and Uriarte (2009), Dishman et al., (1993), laser diffraction technology measures the particle equivalent spherical size based on the particle’s volume, whereas, sieve screens allow the elongated particles to pass through the screens and report to the smaller size fraction. Therefore, results from laser sizing would be biased to upper size values compared to sieve screens. 3.3.4 Preparation of Test Products Five samples were collected for each test run, totalling 55 samples. Power consumption was recorded for each test and the 55 samples were prepared for size distribution analysis, breakage rate calculations and morphology analysis. Samples collected in slurry form were sized using a Malvern Laser Sizer. However, galena concentrate and quartz samples were sized using dry sieving. Then the -53 m fraction was cyclosized and finally the –C6 fraction was laser sized and weighted size fractions were added to the distribution to get a complete size distribution spectrum. This procedure was changed for the mixed quartz and galena sample and lead-zinc ore sample to a laser sizing of the slurry product before dry screening. Sizing results were used for particle size distribution analysis and energy analysis. The remaining of the samples was dried and screened into size fractions (+106m), (-106 +75 m), (-75 +53m) and (-53 m). The -53 m portions were cyclosized to produce the finer fractions. The fractions chosen for morphology analysis were defined as coarse, medium and fine. The coarse fractions were (-75 +53m) for all materials tested, which was equivalent to geometric mean size of 63m. The other products were created using the cyclosizer. Cyclosizer technology 36 is based on particles specific gravity and their free falling velocities in a given fluid. Therefore, the particle size of the four materials, measured using the cyclosizer, varied based on their SG values. The medium and fine cyclone product size fractions and their equivalent geometric mean size are chosen based on the actual measured particle size rather than a specific cyclosizer. Product particle size and their cyclone are listed in Table 3-3. Table 3-3: Morphology Sample Size Fractions and Geometric Mean Size Quartz Reference Size Galena Concentrate Mixed Quartz and Galena Concentrate Lead Zinc Ore Size Fraction (m) Geometric Mean Size (m) Size Fraction (m) Geometric Mean Size (m) Size Fraction (m) Geometric Mean Size (m) Size Fraction (m) Geometric Mean Size (m) Coarse -75 +53 63 -75 +53 63 -75 +53 63 -75 +53 63 Medium -42 +27 (C3) 34 -53 +26 (C2) 37 -42 +31 (C2) 36 -38 +28 (C2) 33 Fine -17 +13 (C5) 15 -20 +14 (C1) 17 -22 +14 (C4) 18 -20 +13 (C4) 16 To obtain sub sample for morphology analysis, each size fraction was spread out onto a glass sheet to produce a monolayer of particles. The particles were captured on double graphite sticky paper, and placed on a scanning electron microscope (SEM) stub mount. Scanning Electron Microscope (SEM) in Secondary Emission Mode was used to capture high resolution 3D images. Images were analysed for roughness values using manual point count based on roughness level as explained in details in chapter 4: Morphology and Liberation. 37 3.4 Grinding Results 3.4.1 Particle Size Distribution The materials chosen for this study were significantly different in chemical, physical and mechanical aspects as well as breakage behaviour. The particle size distribution versus stress intensity and energy input relationship was determined by varying the agitator speed (rpm). Product particle size was characterized according to the Rosin Rammler equation (Rosin, and Rammler, 1933, Harriz, 1971) and the 80 percent passing size (P80). The results of the particle size analyses of each sample and the grinding test products are presented in Figures 3.3, 3.4, 3.5 and 3.6. Equation 3.1 is the Rosin Rammler equation. Equation 3-1 Where: Wr : weight % retained X : particle size a : represents the size at which 36.79% of the weight was retained. b: distribution modulus. Applying the Rosin-Rammler equation to the feed showed that the distribution modulus coefficient for the quartz, galena concentrate, mixed quartz and galena concentrate sample and lead-zinc ore sample were 4.42, 1.34, 1.46 and 1.12 respectively. This reflected the fact that quartz started with a narrower size distribution than other materials and the lead-zinc ore sample had the widest size distribution of the four materials tested. However, the 80% passing (P 80) sizes were close, 97.4 m for the quartz, 96.6m for the galena concentrate, 122.8 m for the mixed quartz and galena concentrate sample and 96.2 m for the lead-zinc ore sample as shown in 38 Table 3-4. As mentioned in section 3.3.2, the sizing procedure followed for the mixed sample and lead-zinc ore sample was by laser sizing (Malvern); accordingly data were biased to an upper size limit due to difference in sizing technology. Table 3-4: Size Distribution of the Samples as Received Rosin Rammler Distribution Modulus (b) Rosin Rammler Size Coefficient (a) (m) 80% pass size P80 (m) Quartz 4.42 75 97.4 Galena Concentrate 1.34 60 96.6 Mixed Quartz & Galena 1.46 109 122.8 Lead-Zinc Ore 1.12 60 96.2 Sample The Rosin Rammler equation was also fit to all grinding test products. The complete Rosin Rammler data for all test products are presented in Appendix B2. The correlation coefficient R 2, which related the best data fit to a fitted regression line, was calculated for the PSD and Rosin Rammler fit. A plot of R2 against P80 showed that the equation fited the coarser products better than the fine products as shown in Figure 3-3. 39 Figure 3-3: Correlation Coefficient versus Size Reduction Fitting correlation coefficient (R2) to modulus of distribution (b), as in Figure 3-4, showed that the narrower the size distribution, the better the fit to Rosin Rammler equation. Figure 3-4: Correlation Coefficient versus Modulus of Distribution 40 The minerals used for this research was received with a wide range of modulus values. Quartz had the highest modulus value 4.42 which indicated a narrow size distribution. The other three minerals, galena concentrate, mixed quartz and galena concentrate and the lead-zinc ore, had wider size distributions with modulus values of 1.34, 1.46 and 1.12, respectively. Decreasing particle size via grinding had decreased the modulus of distribution minimally as shown in Figure 3-5. Figure 3-5: Rosin Rammler Modulus of Distribution versus Size Reduction Comparison of Figure 3-6 (a) and Figure 3-8 (a) showed that for grinding tests at 1000 rpm, the particle size distribution for the quartz and the mixed quartz and galena samples are similar. The mixed sample contained mostly quartz (86% quartz), therefore, it was not surprising that the two samples responded in a similar manner. At higher stirrer speeds, the plots showed greater size reduction. While it was intuitive that at low energy input hard minerals would grind slower, the relatively small changes in particle size following each pass of grinding implied that there was a minimum grinding energy input required to initiate breakage. The plots showed that particle size 41 reduction increased as the stirrer speed (energy input) increased which indicated that the threshold energy for breakage was exceeded by increasing the stirrer speed. Grinding tests on the galena concentrate (Figure 3-7) showed that after the first pass through the mill, there was a large reduction in particle size. However in subsequent passes through the mill, the size reduction was small indicating that a grinding limit was approached. This response was most pronounced at high stirrer speeds where following the first pass there was almost no change in the product particle size with each subsequent pass. For the quartz (Figure 3-6), mixed quartz and galena (Figure 3-8) and lead-zinc ore sample (Figure 3-9), the product particle size decreased after each stage of grinding at all stirrer speeds indicating that the grinding limit was not reached for these samples. PSD analysis is performed on the entire sample. It is well known that the grinding limit depends on the size of grinding media such that finer media will grind to a smaller particle size. For hard minerals, such as quartz, a low speed did not result in significant size reduction which implied that the grinding limit would be quite coarse. However, at high speed, there was significant size reduction. These results suggested that the grinding limit did not only depend on bead size but also on stirrer speed and mineral type. 42 (a) (b) (c) Figure 3-6: Quartz Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm 43 (a) (b) (c) Figure 3-7: Galena Concentrate Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm 44 (a) (b) Figure 3-8: Mixed Quartz and Galena Sample Passing Percent for (a) 1000 and (b) 2000 rpm 45 (a) (b) (c) Figure 3-9: Lead-Zinc Ore Sample Passing Percent for (a) 1000, (b) 1500 and (c) 2000 rpm 46 3.4.2 Breakage Rate Breakage rate was analysed for the four materials tested via relating residence time to the 80% pass in size. Residence time was calculated based on the flow rate and mill volume. For the purpose of this study, the ―initial breakage rate‖ was defined as the change in the 80% passing size divided by the residence time from the first pass through the mill. Further breakage was defined as the change in the 80% passing size beyond the first pass through the mill; that was between pass 1 and 5 (P1-P5) and is referred to in this study as the ―average breakage rate‖. The ―overall breakage rate‖ was also determined based on the change in the 80% passing size divided by the total residence time of all passes through the mill. Specific breakage rate can be expressed in units of inverse seconds (Yue and Klein, 2004) as well as inverse minutes (Hogg, 1999). In this study, the specific breakage rates were expressed in units of inverse minutes. Plots of 80% passing size versus residence time are presented in Figure 3-10 to Figure 3-13 for the four materials tested. Linear (Equation 3.2) and exponential (Equation 3.3) functions were fit to the results in order to characterize the size reduction responses. The fits were compared based on the coefficient of determination (R2) as summarized in Table 3-5. Equation 3-2 Equation 3-3 Where: S: size P80 (m), A: size P80 at residence time zero, which was feed size, c: specific breakage rate (min-1) c’: breakage rate (m/min) tr: residence time 47 The overall coefficient of determination (average) was higher for the linear model than the exponential model for quartz and mixed quartz and galena sample. On the other hand, the R 2 value for exponential model was higher than the linear model for the galena concentrate sample and slightly higher for lead-zinc ore sample. This implied that the type of mineral had an effect on the breakage rate trend, linear versus exponential. Linear Quartz (a) P80 (m) 100 80 Feed 60 Q1000 40 Q1500 20 Q2000 0 0 1 2 3 4 5 6 Residence Time (min) Linearized Quartz (b) 5.0 Ln P80 (m) 4.0 Feed 3.0 Q1000 2.0 Q1500 1.0 Q2000 0.0 0 1 2 3 4 5 6 Residence Time (min) Figure 3-10: Quartz (a) Linear and (b) Linearized Exponential Fitting Data 48 Linear Galena Concentrate (a) P80 (m) 100 80 Feed 60 G1000 G1500 40 G2000 20 0 0 1 2 3 4 5 6 Reidence Time (min) (b) Linearized Galena Concentrate Ln P80 (m) 5.0 4.0 Feed 3.0 G1000 G1500 2.0 G2000 1.0 0.0 0 1 2 3 4 Residence Time (min) 5 6 Figure 3-11: Galena Concentrate (a) Linear and (b) Linearized Exponential Fitting Data 49 (a) Linear Mixed Sample 140 120 P80 (m) 100 Feed 80 60 M1000 40 M2000 20 0 0 1 2 3 4 5 6 Residence Time (min) (b) Linearized Mixed Sample 6.0 5.0 Ln P80 4.0 Feed 3.0 M1000 2.0 M2000 1.0 0.0 0 1 2 3 4 5 Residence Time (min) 6 Figure 3-12: Mixed Quartz and Galena Sample (a) Linear and (b) Linearized Exponential Fitting Data 50 Linear Lead-Zinc Ore (a) P80 (m) 100 80 Feed 60 O1000 40 O1500 O2000 20 0 0 2 4 6 Residnece Time (min) Linearized Lead-Zinc Ore (b) Ln P80 (m) 5.0 4.0 Feed 3.0 O1000 2.0 O1500 O2000 1.0 0.0 0 1 2 3 4 5 Residence Time (min) 6 Figure 3-13: Lead-Zinc Ore Sample (a) Linear and (b) Linearized Exponential Fitting Data 51 Table 3-5: R-Squared Values for Linear and Exponential Data Fit Linear Fitting – R2 Exponential Fitting – R2 0.948 0.819 0.987 0.903 0.959 0.995 0.964 0.906 0.873 0.977 0.966 0.937 0.824 0.921 0.888 0.945 0.945 0.850 0.895 0.984 0.920 0.917 Lead-Zinc Ore 1000 rpm 0.976 0.793 Lead-Zinc Ore* 1500 rpm 0.947 0.976 Lead-Zinc Ore* 2000 rpm 0.814 0.991 Lead-Zinc Ore Average 0.912 0.920 Experimental Data Quartz 1000 rpm Quartz 1500 rpm Quartz* 2000 rpm Quartz – Average Galena Concentrate* 1000 rpm Galena Concentrate 1500 rpm Galena Concentrate* 2000 rpm Galena – Average Mixed Quartz and Galena 1000 rpm Mixed Quartz and Galena* 2000 rpm Mixed Quartz & Galena Average Note: * Exponential fitting is better than the Linear fitting 52 Data correlation charts for overall breakage rate are presented in Figure 3.14. Initial breakage fit equally well for both linear and exponential. The average breakage fitted reasonably well with both the linear and exponential equations, (Appendix B3). Analysis of the overall breakage showed a better exponential rate fit compared to the linear fit. The galena concentrate and the lead-zinc ore had the poorest fit, particularly at higher agitator speeds. The reason for the poor data fit was that the product reached its grinding limit faster than the other material tested. Therefore, the calculated data points don’t have a matching experimental, measured value. (a) (c) (b) (d) Figure 3-14: Correlation Between Measured and Calculated P80 for Overall Breakage Rate Data; (a) Quartz, (b) Galena Concentrate, (c) Mixed Quartz and Galena Concentrate Sample and (d) Lead-Zinc Ore Sample Note: The initial and average breakage rate correlation plots are presented on Appendix B3 53 3.4.2.1 Initial Breakage Rate Since initial breakage showed a different trend than the average breakage, breakage rate values were calculated for both, and presented in Table 3-6. The trend showed that quartz, galena concentrate, mixed quartz and galena sample and lead-zinc ore sample initial breakage rates increased linearly with the increase of input energy (agitator speed). Softer mineral breakage rate values were higher than the harder ones by approximately one order of magnitude. For example, the galena concentrate breakage rate at 1000 rpm was 0.78min-1 compared to the quartz which was only 0.07min-1. It was also observed that the mixed quartz and galena sample breakage rate was closer to the pure quartz than the pure galena concentrate samples. Also, at the lowest stirrer speed (1000 rpm) the breakage rate for both the quartz and the mixed quartz and galena samples was low which reflected that the energy input was not sufficient to promote breakage. The initial breakage rate for softer minerals was faster than for the harder minerals at the three agitator speeds tested. Table 3-6: Initial and Average Breakage at Different Agitator Speed Specific Breakage Rate (min-1) RPM Quartz Initial Galena Concentrate Mixed Sample Lead-Zinc Ore Average Average Average Average Initial Initial Initial Breakage Breakage Breakage Breakage 1000 0.07 0.05 0.78 0.25 0.02 0.05 0.63 0.22 1500 0.18 0.22 1.34 0.16 --- --- 0.90 0.34 2000 0.35 0.32 1.82 0.02 0.36 0.37 1.34 0.32 54 3.4.2.2 Average Breakage Rate The effect of the increasing grinding residence time on breakage rate was represented by the average breakage rate. Increasing the grinding residence time had a minimal effect on breakage rate for quartz and mixed quartz and galena sample, but decreased for the galena concentrate sample and the lead-zinc ore sample. Residence time and agitator speed were directly proportional to the average breakage rate for the quartz and mixed sample, but inversely proportional for the galena concentrate sample. For the lead-zinc ore sample, average breakage rate increased with the increase of the agitator speed from 1000 to 1500 rpm and then decreased slightly at the 2000 rpm agitator speed. The average breakage rate was affected by the grinding limits for the materials and test conditions. The softer samples (galena concentrate and to some extent the lead-zinc ore samples) had high initial breakage rates and therefore approached their grinding limit faster than harder minerals. Parry (2006) stated that soft minerals broke faster at lower agitator speeds than hard minerals, but the breakage rates for hard and soft minerals converge at very high agitator speed. Similar conclusions could be deduced from the data obtained from this set of experiments. For the quartz sample, the breakage rate curve changed from linear to exponential when increasing the stirrer speed from 1500 rpm to 2000 rpm. For the galena, the breakage rate data fit the non-linear breakage equation at a lower agitator speed of 1000 rpm. Therefore, both the hard and soft minerals responded in a similar manner, but at different stirrer speeds. The breakage rate values could lead to a preliminary conclusion that if the target was to grind the softer mineral in a mix of hard and soft minerals, then the choices would either be to operate the mill at a low agitator speed, such that, the soft mineral would break and the hard mineral would not, or operate the mill at a higher agitator speed for a shorter residence time. Similar conclusion 55 is observed by Parry (2006), who tested quartz and magnetite as hard minerals and calcite as soft mineral, and concluded that soft minerals do break faster as lower agitator speeds than hard minerals. 3.4.3 Energy Consumption The grinding mechanism in the stirred mill is through agitating the slurry material in the mill using agitator discs. Accordingly, energy is transmitted from the agitator to the grinding media and the slurry. Then abrasion, compression and impact loadings are applied to the particles. In other words, kinetic energy was transmitted from the shaft to the particles in the mill (media and minerals). Thus increasing or decreasing the agitator speed (kinetic energy input) directly affects the amount and type of loading applied on the particles which would consequently lead to particle breakage and size reduction. Specific energy is calculated by subtracting the power of the mill with no load from the power of the mill with load, multiplied by the residence time per mill volume. The powers used in the calculations are read from the agitator panel, which is the input power direct to the agitator with and without load. This is a typical industrial practice to scale up stirred mills based on energy versus size reduction. The log-log plot of the specific energy input versus size reduction (P80) produces linearized data which fit a power equation that is called a signature plot. Signature plots are used for scaling up stirred mill machines from a lab scale to an industrial scale. Most of the data have a curve trend which could fit either to a power or exponential fit equation as per equation 3-4 or equation 3-5, respectively. For the power function, a variable base is raised to a fixed exponent, whereas for the exponential function, a fixed base is raised to a variable exponent. 56 Equation 3-4 Equation 3-5 Where: Psp: specific power (KWhr/ton) Po: specific power at size zero; hypothetical S: size P80 (m), d: specific power per size reduction Experimental data did not fit the power equation as well as expected for all test runs. Therefore, data were also fit to the exponential equation for comparison. As presented in Table 3-7, when comparing the coefficient of determination (R2 values) for both types of equation fittings, it showed that the exponential equations fit better than the power equation for the four materials tested at low and medium agitator speeds, 1000 and 1500 rpm, respectively. At a higher agitator speed of 2000 rpm, the power equation fit the data slightly better. Table 3-7: R2 Values for Specific Energy vs. Size Reduction Using Power and Exponential Equations Quartz Agitator Speed (rpm) Galena Mix Ore Power Exponential Power Exponential Power Exponential Power Exponential 1000 RPM 0.821 0.835 0.978 0.988 0.879 0.883 0.796 0.851 1500 RPM 0.880 0.937 0.940 0.965 --- --- 0.972 1.000 2000 RPM 0.996 0.986 0.920 0.918 0.978 0.994 0.990 0.954 Combined 0.829 0.915 0.897 0.805 0.900 0.971 0.939 0.963 Power and exponential equation fits were plotted for quartz, galena concentrate, mixed quartz and galena concentrate sample, and lead-zinc ore sample, as shown in Figure 3-15, Figure 3-16, 57 Figure 3-17 and Figure 3-18, respectively. The cumulative data trend combined for the three agitator speeds per each material type were also plotted. (a) (b) Data Overlap Figure 3-15: Quartz Signature Plot – (a) Exponential and (b) Power Fit The quartz signature plot results supported the interpretation of PSD plot for the 1000 rpm test. It indicated that the agitator speed had a limiting grinding ability, as shown in Figure 3-6(a) no matter how much more input power was given to the material. The exponential equations for all cumulative data from the three agitator speeds fit the data better than the power equations. This was identified by a higher R2 value (0.915) for the exponential equation, compared to the power equation R2 value, which was 0.829, as illustrated in Figure 3-15. It was also noticed that the specific energy required to target a certain size reduction (P80) was overlapping among the three agitator speeds. The 1500 rpm initial breakage (1st pass) overlapped with the 1000 rpm at the 4th pass. The 2nd pass of the 1500 rpm was overlapping with the 2000 rpm at the 1 st pass. The overlap between data at the three agitator speeds indicated that the effect of the agitator speed on the signature plot was insignificant, compared to the breakage rate effect. 58 Galena Concentrate - Power (a) (b) Specific Energy (kWhr/ton) 100 y = 11238x-2.459 R² = 0.8966 10 y = 3657.7x-2.124 R² = 0.9547 1 10 G1000 Size P80 (m) G1500 G2000 Power (Cumulative) 100 Power (Cumulative 1000 & 1500) Figure 3-16: Galena Concentrate Signature Plot – (a) Exponential and (b) Power Fit The galena concentrate signature plot also helped to explain the PSD results at 2000 rpm, where the grinding limit was reached immediately after the first pass (54 seconds residence time). Increasing power input, in the form of increasing residence time, did not significantly affect particle size reduction at the high agitator speed (2000 rpm). For the low agitator speed (1000 rpm), the last two passes (4th and 5th) showed similar size values, with minor increase in energy input. This implied that grinding limit had been reached using a low agitator speed. However, if additional runs were done, it would have confirmed the grinding limit of the galena; it is expected that the energy consumption would have increased without a reduction in product particle size. The galena concentrate (soft) responded in an opposite manner to that of quartz (hard). The combined R2 value for galena concentrate fitted the power equation better than the exponential equation while for quartz the combined R2 values fitted the exponential equation better than the power equation. It was also noticed that the combined R2 value for both the power and exponential equations for galena concentrate were consistently lower than the individual R2 for 59 each agitator speed. Similarly, the quartz followed the same trend as the galena concentrate except for the low agitator speed (1000 rpm), which had a lower R2 value compared to the combined values as per Table 3-7. Such results would imply that the individual set of data for each agitator speed created a different trend. Such an observation was graphically confirmed in Figure 3-16. The high speed (2000 rpm) data were excluded from the combined analysis because the grinding limit was reached almost immediately after the first pass. The results showed that changing the stirrer speed shifted the signature plot. For example, at about 5kwhr/t specific energy, the lower agitator speed (1000 rpm) created finer product than the same specific energy for the intermediate agitator speed (1500 rpm). If the grinding process was targeting a certain size fraction, such as 13m, the high agitator speed (2000 rpm) would consume more specific energy (19 kwhr/t) compared to the intermediate agitator speed, which consumed 15 kwhr/t. The agitator speed had a significant effect on the signature plot and breakage rates of the galena concentrate material. (a) (b) Figure 3-17: Mixed Quartz and Galena Sample Signature Plot (a) Exponential and (b) Power Fit 60 Due to a shortage in material availability, the mixed quartz and galena sample test runs were executed on only the extreme agitator speeds, 1000 and 2000 rpm. The exponential equation fit the data slightly better than the power equation in terms of their R2 values, 0.971 and 0.900, respectively. The cumulative trend, as in Figure 3-17, showed that there was a potential for continuity between the two agitator speeds, despite the gap between them. This gap could have been covered by increasing the residence time of the particles in the mill, especially for the 1000 rpm test run. The mixed quartz and galena concentrate sample trend was similar to the trend for the quartz material. (a) Target size ~ 17m (b) Data Overlap Data Overlap Figure 3-18: Lead-Zinc Ore Sample Signature Plot – (a) Exponential and (b) Power Fit For the lead-zinc ore sample, specific energy versus size reduction followed a continuous pattern, except for the fifth pass for the 1000 and 1500 rpm test runs. The exponential equation fit the data slightly better than the power equation, as shown by the R2 values, which were 0.9634 and 0.9393, respectively. The combined R 2 values for power and exponential equations were higher than the individual R2 values for the low agitator speed (1000 rpm), which indicated a trend for low agitator speeds that deviated from the other two agitator speeds. The plots 61 showed that there was a minor overlap between the data at the three agitator speeds. The overlaps were identified at the initial breakage (1st pass) of the intermediate agitator speed (1500 rpm), and the 4th pass of the lower agitator speed (1000 rpm), as shown in Figure 3-18(a). Similar overlap was noticed at the initial breakage (1 st pass) of the high agitator speed (2000 rpm), and the 2nd pass of the intermediate agitator speed (1500 rpm). Overlap was also noticed at the 2nd pass and the 4th pass of the high agitator speed (2000 rpm), and intermediate agitator speed (1500 rpm), as shown in Figure 3-18(b), respectively. The lower agitator speed reached a similar size at a lower specific energy input, as with the 17m target size shown in Figure 319(a). The specific energy analysis showed that there was overlapping in the energy required versus targeted size reduction between the different agitator speeds; however, the overlap was not consistent. The analysis also demonstrated that the data fit differently to the power and exponential equations, based on the type of material and agitator speed selected for grinding. The effect of the agitator speed on the signature plot was a function of the material type. It was believed that the grinding limit was not reached for all the test runs carried out on the 4 materials tested and at the agitator speeds chosen. If more passes were performed, a complete analysis could have been achieved. However, reaching the grinding limit was not the scope of this research. The amount of samples collected were enough for the scope and focus of this study which is the morphology analysis. 3.4.4 Effective Energy Energy usage that is transmitted from the agitator discs into stirring of the slurry is the effective energy which creates the particles dynamics in the mill. The particles dynamics in the mill generates the forces that are translated into stresses. When the stresses exceed the critical stress 62 intensity values, breakage initiates or propagates. The net energy is the total energy consumed by the mill with-load minus the energy consumed with no-load. The ―no load‖ energy is the energy required to rotate the agitator of the mill with no media or slurry. The net energy is the energy needed to agitate the slurry and break particles. The ratio of the net energy to the total energy input to the system is an indication of the effective energy applied to the slurry. The unit of the effective energy was reported in this study as Joules. Similar comparison was attempted using a DEM computer model of the IsaMill, which is described in details in chapter 5. The net energy from the experimental work was equivalent to the total kinetic plus rotational kinetic energies of the particles captured at each time step of the simulation runs. In the computer model, such energy was referred to as the output energy. The total energy from the experiments was equivalent to the input energy to the mill from the computer model, which was the cumulative agitator torque for all time steps. Section 5.4.1.2 further describes the energy distribution in the mill using DEM. The net energies versus total energies are plotted in Figure 3-19. The slopes signified the effective energy ratio. 63 (a) (c) (b) (d) Figure 3-19: Grinding Effective Energy for (a) Quartz, (b) Galena Concentrate, (c) Mixed Sample and (d) Lead-Zinc Ore Sample According to the plots in Figure 3-19, the agitator speed had a more considerable effect on the energy ratio than type of material being ground. It was observed that the higher the agitator speed, the higher the effective energy ratio. The average effective energy ratio values for the four materials tested were 0.3, 0.5 and 0.6 for agitator speeds 1000, 1500 and 2000 rpm, respectively. The higher the agitator speed, the better use of the energy input to the mill during the grinding process. The effective energy analysis indicated that it is a function of agitator speed rather than material being ground. 64 3.4.5 Specific Breakage Energy For the purpose of this study, specific breakage energy is presented as the amount of energy required to reduce a particle size by one micron. The net energy was plotted versus particle size (P80) for each material tested at different agitator speeds (Appendix B4). The slope is the ratio of the net energy input per particle breakage. The specific breakage energy values are listed in Table 3-8. The initial breakage energy for quartz, a hard mineral, increased linearly with the increase of the agitator speed. On the other hand, the initial breakage energy for galena, a soft mineral, increased exponentially with the increase of the agitator speed. Comparing the same agitator speeds showed that galena consumed about 5.5 times less energy per particle breakage than the quartz at low agitator speed (1000 rpm). At intermediate agitator speed (1500 rpm), galena consumed about 3 times less energy per particle than quartz and at the high agitator speed (2000 rpm), galena consumed 2 times less energy per particle breakage than quartz. This implied that for initial breakage, the galena consumed less energy to break at all agitator speeds. The average specific breakage energy is the specific energy after 5 passes, which corresponds to a longer residence time of the material in the mill. The average specific breakage energy showed that galena consumed about 2.3 times less energy per particle breakage than quartz. Whereas at intermediate agitator speed (1500 rpm), galena consumed 4.4 times more energy per particle breakage than quartz, and at high agitator speed (2000 rpm) galena consumed 52 times more energy per particle breakage than quartz. The reason for the increase of energy consumption per particle by galena was that it reached its grinding limit early in the grinding process, mostly during the initial breakage. If the particles were exposed to more grinding by increasing their residence time in the mill, after reaching their grinding limit, it would lead to useless energy consumption. 65 The mixed quartz and galena sample responded in similar manner to the quartz at a high agitator speed (2000 rpm) for both initial and average breakage. At a low agitator speed (1000 rpm), the initial breakage seemed to consume higher energy than both galena and quartz, which implied that there was hardly any breakage occurring. The specific breakage energy of the lead-zinc ore sample was increasing with the increase of the agitator speed, but showed lower values than the galena concentrate sample. This implied that the effect of the mix of minerals in the ore had a significant effect on the amount of energy required per unit micron breakage. Table 3-8: Specific Breakage Energy (kJ/m) Agitator Speed (rpm) Galena Lead-Zinc Ore Mixed sample Concentrate Sample (kJ/m) (kJ/m) (kJ/m) Initial Average Initial Average Initial Average Initial Average Quartz (kJ/m) 1000 1.83 2.79 0.33 1.18 6.82 1.74 0.24 1.08 1500 2.94 3.47 0.96 15.3 --- --- 0.78 3.93 2000 3.40 6.05 1.85 314.0 3.11 5.06 1.42 11.4 3.5 Conclusion The effect of the material properties, mill input energy in the form of agitator speeds, and residence time was investigated through a series of experiments. Results showed that the material type had a major effect on particle size distribution and size reduction at the three agitator speeds evaluated. Quartz did not break efficiently at the 1000 rpm agitator speed, which indicated that there was a minimum energy input required to initiate the breakage. On the other hand, 1000 rpm was enough for the galena concentrate to break. The extreme agitator speed, 2000 rpm, broke the galena concentrate particles down to its grinding limit after the first pass through the mill. For the mixed sample, the quartz breakage mechanism 66 effect was dominant over the galena due to the higher content of quartz in the mix compared to galena, 6:1 ratio. Initial breakage rates of the 4 materials tested increased linearly with the increase of the agitator speed. However, breakage rates were almost one order of magnitude higher for the soft minerals than the hard minerals. Average breakage values were directly affected by how close the particle sizes were from their grinding limit. Breakage rate decreased once it reached the grinding limit of the material. The breakage rate was linear for most of the grinds except for quartz at 2000 rpm, galena concentrate at 1000 rpm, mixed quartz and galena sample at 2000 rpm and lead-zinc ore sample at 1500 and 2000 rpm. The aforementioned test runs and material exhibited a nonlinear breakage rate. This observation indicated that breakage rate trend is non-linear when it approaches the grinding limit of the material. Energy consumption was evaluated using typical signature plots, which are specific energy versus size reduction (P80). It was observed that there was some overlapping in the energy required versus targeted size between the different agitator speeds; however, the overlapping was not consistent. The analysis also revealed that the data fit differently to the power and exponential equations, based on the type of material and agitator speed selected for grinding. It was also observed that the effective energy ratio of the mill was not affected by the type of material as much as it was affected by the agitator speed. The highest effective energy ratio was observed at the highest agitator speed. On the other hand, the amount of energy required to break one micron was directly affected by the type of material being ground. Soft minerals required 67 less energy per micron at all agitator speeds. Thus, the softer minerals would break faster at lower agitator speed than harder minerals and vice versa. 68 4. Morphology and Liberation 4.1 Introduction 4.1.1 Morphology Definition Morphology is the study of particle shape and texture. Particle shape is a factor of equivalent diameter, sphericity, convexity, aspect ratio and roughness. Morphology analysis software measures basic parameters such as particle length, width, perimeter from pre-captured images, either through optical microscopes or scanning electron microscopes (SEM). Software such as Clemex uses standard mathematical equations to deduce more complex morphological parameters, such as sphericity, elongation, aspect ratio, roughness and others. 4.1.2 Morphology Evaluation Studies performed on particle morphology analysis for different grinding processes have been addressed by Gabriel (1985), Pons et. al. (1999), Hiçyilmaz et al. (2004), Yekler et. al. (2004), Ulusoy and Yekeler (2005), Celik & Oner (2006); Kursun and Ulusoy (2006), Guimaraes et al. (2007), Tavares and Das Neves (2008), Hasanpour and Choupani (2009). These analyses were either qualitative or quantitative. Qualitative analysis is a visual comparison of captured high resolution images via SEM, such as the stirred bead mill of gibbsite research performed by Alex, et. al. (2008), and a study on aggregate production during rock crushing by Guimaraes, et. al.(2007). For quantitative analysis, morphological parameters are measured such as elongation, sphericity, and roughness as those performed by Lecoq et. al (1999) and Donskoi et al. (2007). 69 Typical equations used for quantitative morphology analysis are as follows, Clemex Technologies Inc. (2009): Equation 4-1 Equation 4-2 Equation 4-3 Equation 4-4 Elongation = 1 / AR Equation 4-5 Note: Sphericity is the circularity squared, which is the equivalent circumference squared (perimeter squared) of a measured surface area, divided by the actual perimeter. Convexity is a parameter used to evaluate particle roughness. Convexity is the ratio between the hull perimeter and the actual measured perimeter. The hull perimeter (HP) is the measure of the contour of the extrude edges of the particle as shown in Figure 4-1 HP P Figure 4-1 Particle Perimeter and Hull Perimeter Equation 4-6 Where: L: length P: perimeter W: width HP: hull perimeter A: area AR: aspect ratio S: sphericity 70 The major parameters of interest for this research were roughness, sphericity and elongation values. The values of such parameters range from zero to one. For roughness, a value of one reflects a perfectly smooth particle, since the hull perimeter would coincide with the actual perimeter. Similarly, if the sphericity value is one, then the calculated perimeter from the surface area would be equivalent to the actual measured perimeter. For elongation, a value of one reflects an equiaxed particle since the particle’s width would be equal to its length. Values close to zero, for all three parameters, means that the particles are rougher, less circular and more elongated. The roughness level assessed using pre-programmed morphology software (Clemex) was not precise enough for 3D images captured via SEM when compared to 2D images. The software evaluated the outer contour of the particles, ignoring the surface texture. Accordingly, the values were biased towards smooth particles rather than rough particles. Therefore, the manual point count methodology was developed. Since roughness was the major parameter to be assessed in this research, both methodologies were evaluated and compared. 4.1.3 Sample Description for Morphology The samples used for morphology analysis were classified according to their size fraction, as coarse, medium and fine. The coarse fraction was a product of screening, and the geometric mean particle size was 63m for the four materials analysed: quartz, galena concentrate, mixed quartz and galena concentrate, and lead-zinc ore. The medium and fine fractions were produced via Cyclosizer, which resulted in different size fractions based on the mineral density. For the sake of comparison, the size fraction for each material was chosen based on the particle size, rather than the Cyclosizer cyclone number. Therefore, the geometric mean size for quartz, galena concentrate, mixed quartz and galena sample, and lead-zinc ore samples were 34, 37, 36 and 71 33m for the medium size fraction and 15, 17, 18 and 16m for the fine size fraction, respectively. Details on sample preparation of size fractions are presented in chapter 3, section 3.3.4. 4.2 Clemex Method The roughness of the particles suggests the mode of particle breakage. It could be due to impact, abrasion or compression loading. If the particles are exposed to abrasion, they would exhibit smoother and more rounded surfaces. On the other hand, if they are exposed to compression or impact loading, they would reveal rougher and less round surfaces. The theory is that if the particles are exposed to enough impact or compression forces, they would break along their weakest planes, that is their grain boundaries, and show intergranular breakage. Abrasion, on the other hand, would cause a polishing effect, creating smooth particles with breakage across the grains – transgranular breakage. The procedure followed to evaluate the particles’ morphology features started by capturing high resolution 3D images via SEM - back scatter beam. Images were then imported into the Clemex software, followed by running a routine that recognizes the particles, and calculates their main morphology parameters (sphericity, elongation and roughness). Measured and calculated data were then exported to an excel format for further analysis. The detailed Clemex routine is provided in Appendix C4. By assessing the values of roughness, it was noticed that the Clemex results were biased towards higher values, indicating smoother particles, as compared to visual observation. For example, the particles that were given a roughness value of 0.9 (closer to a smooth value) were visually identified to have exhibited extremely rough surfaces. An example of this observation is 72 presented in Figure 4-2. The particles in this figure are from the +53m fraction of the quartz sample prior to stirred milling. The Clemex identified their roughness values as 0.9 and 1.0, which would be categorized as smooth particles, whereas visual examination would identify their roughness values as 5 and 4, which would categorize them as very rough particles. There could be two possible reasons for this observation. Either the Clemex recognised the particles in 2-D (outer contour of the particles), and ignored their actual surface texture, or the software overiterated the convex perimeter (Feret Iteration), which ended up very close to the particles’ actual perimeter. a b Figure 4-2: (a) Particle ID 39 Roughness value was 0.9; (b) Particle ID 14 Roughness value was 1.0 Feret is a measure of the distance between two parallel tangent lines at a defined angle. The convex perimeter is the measure of a rubber band around all the ferets. The greater the number of ferets measured at multiple angles, the closer the hull perimeter value would be to the actual perimeter. This measurement would return a roughness value closer to 1 (smooth particle). Therefore, a manual point counting methodology was introduced and tested in this study. 73 4.3 Manual Point Counting Method As an alternative to the Clemex software, manual point counting was tested. The roughness values were set to 5 levels: R1, R2, R3, R4, and R5. The roughest particle was given a value of 5, where as the smoothest particle was given a value of 2. The degree of roughness increased from 2 to 5. Roughness level 1 was given to surfaces that were round, with no sharp edges, but had a hammered surface. It was speculated that the same particle was exposed to some type of compressive loading. Detailed definitions and illustrations of roughness levels for quartz and galena are presented in Table 4-1. An excel macro subroutine was built using visual basic to assist in the counting process, and its details are given in Appendix C1 and C2. The subroutine accumulated the counts for the roughness values between 1 and 5. After the counter was familiarized with the definitions of the roughness levels for the particles, a grid was placed on the SEM printed images in order to assist in tracing and counting the particles’ degree of roughness. 74 Table 4-1: Morphology Roughness Level Definitions and Illustration Roughness Level Illustration Definition Quartz R1 Hammered Round but hammered surface. R2 Smoothest Round and less rough surfaces. R3 Semi-Rough Partially round, partially angled and partially rough surfaces. R4 Rougher R5 Roughest Galena - For quartz: partially round and rougher surfaces. - For Galena: square edges Rough and sharp angled surfaces. 75 4.3.1 Point Counting Sensitivity Analysis To assess sensitivity, three counters were trained on evaluating the particles’ degree of roughness. Each performed the counting procedure on the same sample, and results were then compared. The first counting attempt showed that the degree of roughness definition for R2, R3 and R4 was not adequately identified by the counters. The roughness level definitions were fine tuned and re-defined, as per Table 4-1, and the counting procedure was repeated. Results were compared among the three counters, and results showed that a very close match between the three individuals was achieved, with a maximum difference of 6%. The process was repeated on different size fractions in order to verify the results (53m and 14m particles). Detailed counting results of the sensitivity analysis are presented in Appendix C3. 4.4 Liberation Methodology The fourth material tested was the lead-zinc ore sample, which was a complex ore that has similar mineral composition to that of the synthesised mixed quartz and galena sample. However, it contained un-liberated composite particles. The objective of this part of the study was to understand the liberation behaviour of the minerals under different stress intensity input (i.e. different agitator speeds). The Mineral Liberation Analyser (MLA) is a conventional tool used for liberation analysis. A representative sample is placed in an epoxy resin, which is then ground and polished, in order to expose a monolayer of the particles in a 2D format. This process creates a cross section surface through the particles. The samples are then placed in an SEM, which is equipped with Mineral Liberation Analysis software (MLA) that scans and analyses the identified mineral particles and their associations. The MLA process was costly and time consuming. Furthermore, this research was focused on analysing the particles as fractured, without sectioning them, since morphology was the core of 76 this study. Accordingly, liberation analysis was performed on a stud sample where the particles were first spread on a glass sheet in order to create a monolayer. The particles were then pickedup on a double graphite sticky sheet on a stud. The sampling type was called ―as mount‖ samples. The same analysis procedure using the SEM-MLA was performed. Analysis was performed following the first stage of grinding for the lead-zinc ore samples from the three agitator speed grinds (O1000-P1, O1500-P1 and O2000-P1). The size fraction tested was -75m +53m. Since the ―as mount‖ procedure was not a conventional method, it was important to compare the conventional, resin mount polished sample with the ―as mount‖ procedures. Samples used for comparison were the -75m +53m size fraction, which has a geometric mean size of 63m from the 1500 rpm stirrer speed test run. Sample from 3 passes through the mill were enough to compare the trend of the ―as mount‖ to the conventional method. 4.5 Morphology and Liberation Results The effect of mineral properties and mill operation on breakage mechanisms could be identified by analysing the product morphology. Due to the biased results of the pre-programmed image analysis software, explained in section 4.2, manual point counting and automated (preprogrammed) morphology analysis were both performed, for the sake of comparison and confirmation of the outcome results. Manual point counting was executed on 3 size fractions for each material (coarse, medium and fine), and the automated morphology analysis was executed on the coarse size fraction (geometric mean size is 63m). 77 4.5.1 Manual Point Counting Results Manual point counting was based on five levels of roughness as described in section 4.3. Roughness levels start with R1 as a round and hammered surface, R2 as the smoothest, round particles, R3 as the bridge between the smooth and rough particles which was labelled as semirough particles, R4 as a rough particle with few round surfaces, and R5 as the roughest particle with all sharp and angled surfaces. Detailed roughness levels and their descriptions are presented in Table 4-1. Relationships between the roughness level and mode of breakage were predicted such that the rougher the particles, the higher the potential for intergranular breakage was to occur. One could reasonably suggest that for smoother particles, the breakage mode was abrasion (transgranular), whereas for rougher particles, the breakage mode could be fracture via impact or compression loading (intergranular – along grain boundaries). Detailed breakage modes versus roughness levels are outlined in Table 4-2. Table 4-2: Breakage Mode versus Roughness Level Roughness Level Breakage Mode R2 Smoothest - Started Abrasion (Transgranular) - Then Exposed to Impact (Indents on Surface) Abrasion (Transgranular) R3 Semi-Rough Exposed to both Abrasion and Fracture (Transgranular and Intergranular) R4 Rougher Fracture (Intergranular) R5 Roughest Fracture (Intergranular) R1 Hammered 78 4.5.2 Pearson’s Correlation Correlation coefficient measures the strength of the linear association between two variables, relative to their standard deviation. This is also known as Pearson’s correlation, as per Equation 4-7, (Freedman, D., Pisani, R and Purves, R, 1998). The correlation returns a unitless value (r) between -1 and +1. If the correlation value is positive, it indicates that the two variables are increasing together. A negative correlation signifies that as one variable increases, the other variable decreases. A correlation magnitude (r) close to zero indicates that the strength of the correlation between the variables is weak. The effect of grinding time (residence time) on the product roughness level were the two variables that were statistically correlated using Pearson’s correlation (r) as per Equation 4-7; where Xi is the residence time, and Yi is the number of particles counted per degree of roughness, R1, R2, R3, R4 and R5. X and Y are the mean values for residence time and number of particles, respectively. – Equation 4-7 If Pearson’s correlation value (r) is close to -1, this indicates that the number of particles counted for a specific roughness level is decreasing with time. It is indicated on the charts as disappearing. On the other hand, if the correlation is closer to +1, it signifies that the number of particles counted for a specific roughness level is increasing with time. It is indicated on the charts as appearing. Correlation values between -0.5 and +0.5 reflect no significant effect of time on the appearance or disappearance of a particular level of roughness. Charts which correlate time versus roughness were plotted, in order to visualise their relationships. Error bars were 79 presented on the cumulative data, in order to demonstrate the statistical confidence of the results. However, the objective of the time correlation charts was to illustrate the trend, rather than present discrete values. Galena Pearson’s correlation for galena concentrate sample as in Figure 4-3 showed that at a higher agitator speed, the smoothest particles (R2), and hammered particles (R1), increased and appeared more in the count as the residence time increased. Whereas the rougher particles (R4), and roughest particles (R5) were less counted and disappeared as the residence time increased. Although the correlation was similar for the three agitator speeds tested, the trend was more evident for the highest agitator speed of 2000 rpm. The disappearance of rough particles and the appearance of smooth and hammered particles would imply that the breakage mode in the mill was abrasion rather than fracture. An exception was the fine fraction, with a geometric mean size of 17m, where higher roughness level of R4 appeared more often as the agitator speed increased. A similar exception was noted for the quartz fine fraction, with a geometric mean size of 15m at the highest roughness level of R5, (Figure 4-4). This implied that the smaller size fraction could be exposed to a different breakage mode, compared to the coarser size fraction for both soft and hard minerals. 80 Galena Concentrate - 1000 rpm (a) 1.0 Appear ( R1 R2 R3 R4 R5 -0.5 --- 0.0 Disappear Time Correlation 0.5 -1.0 -1.5 63 um 37um 17um Cumulative Galena Concentrate - 1500 rpm (b) Appear (a) ( --- 0.5 0.0 R1 R2 R3 R4 R5 -0.5 ( Disappear Time Correlation 1.0 -1.0 63 um 37um 17um Cumulative (c) Galena Concentrate - 2000 rpm Appear --- 0.5 ( 0.0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1.0 -1.0 63 um 37um 17um Cumulative Figure 4-3: Pearson’s Time Correlation vs. Roughness Level Count for Galena Concentrate Sample, (a) 1000rpm, (b) 1500rpm, (c) 2000rpm 81 Quartz Morphological fracture features of quartz were affected to a greater extent by the agitator speed compared to galena, which coincided with the PSD results presented in Chapter 3. As shown in Figure 4-4, the 1000 rpm test demonstrated that the hammered particles, R1, increased and appeared more often as residence time increased, and rougher particles, R4, decreased and disappeared more often with time. However, the roughest particles, R5, consistently existed in the count and were not affected by the increase of the residence time of particles in the mill. This implied that although the main fracture mode was speculated to be abrasion, other fracture modes were taking place that generated the roughest particles. Increasing the agitator speed to 1500 rpm generated a dominant abrasion breakage mode in the mill. Smoother particles were increasing and appearing in the counts as residence time was increasing, as presented by the R2 and R1 correlation values which were closer to +1. Rougher particles were decreasing and disappearing in the counts with the increase of residence time, as presented by the R4 and R5 correlation values which were closer to -1. Semi-rough particles, R3, came into view, reflecting that there were quite a number of particles that were in the intermediate phase between smooth and rough levels. Increasing the agitator speed to 2000 rpm seemed to push the rougher, smooth and semi-rough, R4, R2 and R3, particles towards the weak correlation zone (i.e. particle counts were not affected by the increase of the residence time). Roughness levels that were dominantly on the ―appear‖ side of the chart, such as R2 and R3 at the low input energy intensity (i.e. agitator speed 1000rpm), moved towards the ―disappear‖ side of the chart, and the weak correlation, when the input energy intensity increased to 2000 rpm and vice versa. This implied that particles were equally exposed to both abrasion and fracture loading at the higher agitator speed. 82 Quartz - 1000 rpm (a) Appear --- 0.5 0.0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1.0 -1.0 63 um 34um 15um Cumulative Quartz - 1500 rpm (b) Appear --- 0.5 0.0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1.0 -1.0 63 um 34um 15um Cumulative (c) Quartz - 2000 rpm Appear --- 0.5 0.0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1.0 -1.0 63 um 34um 15um Cumulative Figure 4-4: Pearson’s Time Correlation and Roughness Level Count for Quartz, 1000rpm, (b) 1500rpm, (c) 2000rpm 83 Mixed Quartz and Galena Sample The mixed quartz and galena sample were counted on two stages, where quartz and galena were counted separately, since the difference in particle type and shape were easy to recognize. Quartz was counted per image, followed by counting the galena particles. Data counts for both galena and quartz were added in order to analyze the entire sample. Quartz had a similar pattern to that of the pure quartz sample, (compare Figure 4-4 and Figure 4-5 for the 1000 and 2000 rpm). The results indicated that the presence of galena in the mix had a negligible effect on the breakage behaviour of the quartz. On the other hand, galena counts in the mix sample showed fewer appearances of smoother particles than the pure galena, at both 1000 and 2000 rpm (Figure 4-6). This result implied that galena was exposed to both modes of breakage, fracture and abrasion, in the presence of quartz. In this case, quartz may have behaved as a grinding media for the galena. The other obvious phenomena was the disappearance of galena particles from the (-75m +53m) fraction. 84 (a) Mix Sample - Quartz - 1000 rpm Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63um 36um 18um Cumulative Mix Sample - Quartz - 2000 rpm (b) Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63um 36um 18um Cumulative Figure 4-5: Pearson’s Time Correlation and Roughness Level Count for Quartz in Mixed Sample (a) 1000rpm, (b) 2000rpm The cumulative point count data for the mixed quartz and galena sample demonstrated that at a low agitator speed (1000 rpm) the smoothest particles (R2) were increasing in counts and appeared more often as residence time increased. On the other hand, the rougher and roughest particles, R4 and R5, disappeared with the increase of the residence time at the higher agitator speed (2000 rpm) when compared to the lower agitator speed (1000 rpm). This implied that both breakage mechanisms existed at both agitator speeds, with different intensities. The intermediate roughness, R3, at the low agitator speed (1000 rpm) was slightly lower in counts and disappeared 85 more often as residence time increased, although it increased in counts and appeared more often for the higher agitator speed (2000 rpm). This indicated that grinding time was insufficient for the rough particles to become smooth via abrasion; nevertheless, fracture breakage was taking place simultaneously with abrasion breakage. (a) Mix Sample - Galena - 1000 rpm Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63um 36um 18um Cumulative (b) Mix Sample - Galena - 2000 rpm Appear 0 R1 R2 R3 R4 R5 -0.5 --- 0.5 Disappear Time Correlation 1 -1 -1.5 63um 36um 18um Cumulative Figure 4-6: Pearson’s Time Correlation and Roughness Level Count for Galena in Mixed Sample (a) 1000rpm, (b) 2000rpm 86 (a) Mix Sample - 1000 rpm Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63 um 36um 18um Cumulative (b) Mix Sample - 2000 rpm Appea r --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappea r Time Correlation 1 -1 63 um 36um 18um Cumulative Figure 4-7: Pearson’s Time Correlation and Roughness Level Count for Cumulative Mixed Sample (a) 1000rpm, (b) 2000rpm Lead-Zinc Ore Sample The quartz and galena concentrate samples contained liberated minerals with a single mineral in the slurry in each test run. In order to understand the behaviour of a real ore with locked minerals, a lead-zinc ore sample was chosen for analysis. The lead-zinc ore sample is a Red Dog SAG mill discharge, which was the closest in composition to the synthesized minerals tested. The average chemical composition of the feed, according to assay analysis (Appendix A2), was 87 as follows: lead was 9.3%, zinc was 20%, iron was 7.0% and silica was approximately 32%. The ratio of the hard minerals, pyrite and silica, to soft the minerals, sphalerite and galena, was about 1.33:1. Breakage of the lead-zinc ore particles at higher agitator speeds revealed a similar pattern with time as the mixed quartz and galena sample, except for the hammered particles, R1. The R1 correlation was mostly between the -0.5 and +0.5 range, which meant that R1 was consistently existing in the counts. The majority of the particles that appeared in the count were the smoothest and intermediate rough particles, R2 and R3. The rough particles, R4 and R5, for the 2000 rpm and 1500 rpm agitator speeds were disappearing at a slower rate than the pure galena. On the other hand, at low agitator speed, 1000 rpm, the intermediate and rough particles, R3, R4 and R5 were showing a weak correlation with residence time. This correlation could be interpreted as constant existence of these types of roughness levels, with a minimum effect of residence time on their appearance or disappearance. This implied that the intermediate agitator speed was creating a breakage mode of fracture when compared to the higher agitator speed. At 1500 rpm, the breakage mode trend was inclined towards abrasion, whereas at 2000 rpm there was a mixed mode of breakage, abrasion and fracture. 88 (a) Lead-Zinc Ore Sample - 1000 rpm 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 0.5 --- Appear 1 -1 -1.5 63 um 33um 16um Cumulative (b) Lead-Zinc Ore Sample - 1500 rpm Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63 um 33um 16um Cumulative Lead-Zinc Ore Sample - 2000 rpm (c) Appear --- 0.5 0 R1 R2 R3 R4 R5 -0.5 Disappear Time Correlation 1 -1 63 um 33um 16um Cumulative Figure 4-8: Pearson’s Time Correlation and Roughness Level Count for Lead-Zinc Ore Sample 1000rpm, (b) 1500rpm, (c) 2000rpm 89 4.5.3 Stacked Charts Analysis The general belief is that stirred mills predominantly break particles via attrition, which in morphology analysis should be confirmed by the presence of mostly smooth particles. Morphology results provided evidence to support some researchers’ speculations including those by Jankovic and Sinclair (2006), Yue and Klein (2004) and Tromans and Meech (2004). They agreed that the breakage mechanism changed below a specific size limit. The specific limit could be either a specific particle size, such as 20m, or below the grinding limit of the material with respect to a set of operating conditions (media size, stirrer speed). During the manual point counting, it was observed that the high roughness levels (R4 and R5) were dominant. This trend was opposite to the time correlation that showed a consistent increase in the appearance of smooth particles. In order to quantify the results, particle roughness levels per pass for each test run were presented in standard stacked charts. The stacked charts showed the distribution of the different levels of roughness per pass for each test run. Each section in the stack represented the distribution percentage of the roughness level counted for the cumulative of the three size fractions prepared for morphology analysis, coarse, medium and fine fractions. Stacked charts for quartz, galena, mixed quartz and galena sample as shown in Figure 4-9, Figure 4-11, and Figure 4-13 confirmed that the majority of the particle counts had high roughness levels of R4 and R5, where their added percentages were between 80% and 43% of the total particles counted. On the other hand, the distributions of the smooth particles R1 and R2 were between 41% and 8%. This implied that the majority of the counted particles were rough. A comparison of the overall trends between rough, R4+R5, and smooth, R1+R2, particles showed that the number of rough particles decreased and the number of smooth particles 90 increased per pass through the mill. This comparison implied that attrition breakage was increasing with time. Overall trends are presented in Figure 4-17, Figure 4-18, Figure 4-19 and Figure 4-20. The trends showed that the number of rough particles were consistently higher than the smooth particles at all agitator speeds. Also, there were more rough particles than smooth particles, even after 5 passes through the mill. Such results implied that breakage via fracture was also occurring after long residence time. The new particles generated per pass were new particles that could be considered as the progeny of the coarser fractions from the previous pass. The trends for the rough (R4+R5) and smooth (R1+R2) particles for the three size fractions used for morphology analysis were plotted separately, against grinding passes, as shown in Figure 4-10, Figure 4-12, Figure 4-14 and Figure 4-16 for quartz, galena, mixed quartz and galena and lead-zinc ore samples, respectively. The three fractions (coarse, medium and fine) had geometric mean sizes of 63m, 34m and 15m for the quartz, 63m, 37m and 17m for the galena, 63m, 36m and 18m for the mixed quartz and galena concentrate sample, and 63m, 36m and 18m for the lead-zinc ore sample. The trend showed that the fine products (15m, 17m and 18m for quartz, galena and mix, respectively) had consistently higher numbers of rough particles than smooth particles for the five passes. The rough particles were about 60% of the total particles counted, whereas the smooth particles were about 30%. This observation indicated that the finer products, which should contain a significant progeny from coarser fractions, were consistently broken via fracture. The coarse and medium size fractions were also showing significant amounts of coarse particles compared to the smooth particles. However, the trend demonstrated that the smooth particles increased and the rough particles decreased with increasing residence time. This trend implied that fracture breakage occurred and may be the 91 predominant breakage mechanism in stirred mills. For coarse particles, attrition was the main type of breakage as residence time increased. When comparing the distribution of the different roughness levels for the two pure mineral samples, quartz and galena concentrate, at each agitator speed versus each pass, the data revealed that the percentage of smooth particles of the galena concentrate sample increased per pass more than the quartz sample, Figure 4-11, and Figure 4-9, respectively. This relationship implied that as residence time increased, galena concentrate particles were increasingly breaking across their grains via abrasion, transgranular. Whereas the quartz particles were consistently breaking along their grain boundaries via fracture, intergranular, and residence time did not have an effect on the type of breakage. The initial breakage (P1) of the galena concentrate sample at a high agitator speed (2000 rpm) generated similar amounts of rough particles as at low agitator speed (1000 rpm). The galena concentrate sample generated 73% rough particles (R4, R5) at high agitator speed (2000 rpm), compared to 71% at a low agitator speed (1000 rpm). Quartz, on the other hand, showed an opposite trend to the galena concentrate. Quartz generated 61% rough particles (R4, R5) at high agitator speed (2000 rpm), compared to 78% rough particles (R4, R5) at a low agitator speed (1000 rpm). This result indicated that the initial breakage of galena concentrate particles was via fracture at a high agitator speed, 2000 rpm, whereas for the quartz sample there was less fracture. As shown in Figure 4-13, the mixed quartz and galena sample followed the quartz breakage pattern more closely than that of the galena, which demonstrated that the quartz had a more dominant effect on the breakage mode in the mill. The lead-zinc ore sample had the same decreasing pattern of rough particles (R4 and R5) percentage per pass, Figure 4-15. The hammered and smoothed particles, R1 and R2, increased up to the 3rd pass, and then decreased. It was speculated that the particles started to break via 92 fracture, and then turned to abrasion at later passes. Since the particles of the lead-zinc ore are complex consisting of un-liberated composite particles with more than one mineral, at different grinding stages, the type and amount of mineral particles liberated and locked would vary per pass. Accordingly, it was presumed that the breakage mechanism would also vary according to the grinding passes, agitator speeds and types of composite particles. 93 Q - 1000 RPM (a) Cumulative Roughness % 100% 21 21 21 24 27 20 80% 44 60% 59 57 58 53 R4 50 40% 16 20% 0% 8 6 6 feed 8 5 9 P1 5 6 10 P2 7 8 8 P3 8 5 10 P4 R5 11 10 R3 R2 R1 P5 Grinding Passes Q - 1500 RPM Cumulative Roughness % 100% 21 24 (b) 12 13 13 10 54 53 45 50 80% 60% 59 R4 55 40% 20% 0% 8 6 6 feed 12 4 4 P1 R5 17 17 10 7 10 7 P2 P3 20 15 R3 12 9 12 R2 12 R1 P4 P5 Grinding Passes Q - 2000 RPM Cumulative Roughness % 100% 21 19 23 18 (c) 16 14 39 41 15 15 R3 15 13 R2 16 17 R1 80% 42 60% 59 44 40% 23 20% 0% 8 6 6 feed 10 6 P1 14 9 10 P2 44 R5 R4 13 11 13 P3 P4 P5 Grinding Passes Figure 4-9: Quartz Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes 1000rpm, (b) 1500rpm, (c) 2000rpm 94 Coarse Fraction (63m) (a) 100 Q1000 - R1+R2 Roughness % 80 Q1000 - R4+R5 60 Q1500 - R1+R2 40 Q1500 - R4+R5 Q2000 - R1+R2 20 Q2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 (b) Medium Fraction (34m) 100 Q1000 - R1+R2 Roughness % 80 Q1000 - R4+R5 60 Q1500 - R1+R2 40 Q1500 - R4+R5 20 Q2000 - R1+R2 Q2000 - R4+R5 0 P1 P2 P3 P4 P5 Grinding Passes (c) Fine Fraction (15m) 100 Q1000 - R1+R2 Roughness % 80 Q1000 - R4_R5 60 Q1500 - R1+R2 40 Q1500 - R4+R5 Q2000 - R1+R2 20 Q2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 Figure 4-10: Roughness Trend of Quartz for (a) Coarse, (b) Medium (c) Fine Fractions 95 (a) (b) G - 2000 RPM Cumulative Roughness % 100% 80% 35 60% 40% 20% 0% 24 49 21 14 3 5 feed P1 15 14 14 39 35 36 9 11 11 31 24 44 42 9 8 10 (c) 9 14 13 P2 9 12 24 P3 P4 15 R5 R4 R3 R2 R1 P5 Grinding Passes Figure 4-11: Galena Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes 1000rpm, (b) 1500 rpm, (c) 2000rpm 96 Coarse Fraction (63m) (a) 100 G1000 0 R1+R2 Roughness % 80 G1000 - R4+R5 60 G1500 - R1+R2 40 G1500 - R4+R5 20 G2000 - R1+R2 0 G2000 - R4+R5 P1 P2 P3 P4 Grinding Passes P5 (b) Medium Fraction (37m) 100 G1000 - R1+R2 Roughness % 80 G1000 - R4+R5 60 G1500 - R1+R2 40 G1500 - R4+R5 20 G2000 - R1+R2 G2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 (c) Fine Fraction (17m) 100 G1000 - R1+R2 Roughness % 80 G1000 - R4_R5 60 G1500 - R1+R2 40 G1500 - R4+R5 20 G2000 - R1+R2 G2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 Figure 4-12: Roughness Trend of Galena Concentrate for (a) Coarse, (b) Medium (c) Fine Fractions 97 M - 1000 RPM Cumulative Roughness % 100% 24 21 24 13 (a) 21 16 80% 60% 48 44 49 20% 0% 16 10 2 feed 12 3 P1 38 48 14 10 5 P2 R5 R4 40% 20 37 17 20 12 9 14 9 P3 P4 15 R3 21 R2 11 R1 P5 Grinding Passes M - 2000 RPM Cumulative Roughness % 100% 24 13 11 5 6 5 38 44 40 39 40 80% 60% (b) R5 48 40% 21 20% 16 17 0% 10 2 9 feed P1 R4 19 20 23 21 20 20 19 23 R2 12 12 12 12 R1 P2 P3 P4 R3 P5 Grinding Passes Figure 4-13: Mixed Quartz and Galena Sample Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes (a) 1000rpm, (b) 2000rpm 98 Coarse Fraction (63m) (a) 100 Roughness % 80 M1000 - R1+R2 60 M1000 - R4+R5 40 M2000 - R1+R2 20 M2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 (b) Medium Fraction (36m) Roughness % 100 80 M1000 - R1+R2 60 M1000 - R4+R5 40 M2000 - R1+R2 20 M2000 - R4+R5 0 P1 P2 P3 P4 Grinding Passes P5 Fine Fraction (18m) (c) Roughness % 100 80 M1000 - R1+R2 60 M1000 - R4+R5 M2000 - R1+R2 40 M2000 - R4+R5 20 0 P1 P2 P3 P4 Grinding Passes P5 Figure 4-14: Roughness Trend of Mixed Quartz and Galena Concentrate for (a) Coarse, (b) Medium (c) Fine Fractions 99 (a) O - 1500 RPM Cumulative Roughness % 100% 12 80% 40 5 40 60% 40% 3 4 1 2 32 34 34 33 19 24 23 25 25 16 18 16 15 17 23 13 18 20 19 20% (b) 27 R5 19 24 R4 R3 R2 R1 0% feed P1 P2 P3 P4 P5 Grinding Passes O - 2000 RPM Cumulative Roughness % 100% (c) 3 3 2 4 4 36 33 34 31 34 18 20 18 20 17 21 20 24 26 25 feed P1 P2 12 80% 40 60% 40% 15 13 20% 12 R5 14 27 20 26 28 R4 R3 R2 R1 0% P3 P4 P5 Grinding Passes Figure 4-15: Lead-Zinc Ore Sample Stacked Chart of Cumulative Roughness Percent Point Count vs. Grinding Passes (a) 1000rpm, (b) 1500rpm, (c) 2000rpm 100 Coarse Fraction (63m) Roughness % 100 (a) O1000 0 R1+R2 80 O1000 - R4+R5 60 O1500 - R1+R2 40 O1500 - R4+R5 20 O2000 - R1+R2 0 O2000 - R4+R5 P1 P2 P3 P4 P5 Grinding Passes Medium Fraction (33m) (b) Roughness % 100 80 O1000 - R1+R2 60 O1000 - R4+R5 40 O1500 - R1+R2 20 O1500 - R4+R5 0 P1 P2 P3 P4 P5 O2000 - R1+R2 O2000 - R4+R5 Grinding Passes Fine Fraction (16m) (c) Roughness % 100 O1000 - R1+R2 80 O1000 - R4_R5 60 O1500 - R1+R2 40 O1500 - R4+R5 20 O2000 - R1+R2 0 O2000 - R4+R5 P1 P2 P3 P4 P5 Grinding Passes Figure 4-16: Roughness Trend of Lead-Zinc Ore for (a) Coarse, (b) Medium (c) Fine Fractions 101 100 Roughness % 80 Quartz 1000 - R1+R2 60 Quartz 1000 - R4+R5 Quartz 1500- R1+R2 40 Quartz 1500- R4+R5 20 Quartz 2000- R1+R2 Quartz 2000- R4+R5 0 P1 P2 P3 P4 P5 Grinding Passes Figure 4-17: Overall Roughness Trend for Quartz Sample 100 Roughness % 80 Galena 1000 - R1+R2 60 Galena 1000 - R4+R5 Galena 1500 - R1+R2 40 Galena 1500 - R4+R5 20 Galena 2000 - R1+R2 Galena 2000 R4+R5 0 P1 P2 P3 P4 P5 Grinding Passes Figure 4-18: Overall Roughness Trend for Galena Concentrate Sample 102 100 Roughness % 80 60 Mix 1000- R1+R2 Mix 1000 - R4+R5 40 Mix 2000 - R1+R2 20 Mix 2000 - R4+R5 0 P1 P2 P3 P4 P5 Grinding Passes Figure 4-19: Overall Roughness Trend for the Mixed Quartz and Galena Concentrate Sample 100 Roughness % 80 Ore 1000 - R1+R2 60 Ore 1000 - R4+R5 Ore 1500 - R1+R2 40 Ore 1500 - R4+R5 20 Ore 2000 - R1+R2 Ore 2000- R4+R5 0 P1 P2 P3 P4 P5 Grinding Passes Figure 4-20: Overall Roughness Trend for Lead – Zinc Ore Sample 103 The time correlation for the 4 materials tested implied that the smoother particles were appearing in the counts as the stress intensity increased by increasing the grinding residence time, which would in turn imply that the breakage mode was more transgranular (abrasion). However, the actual majority of the counts as presented in the stacked charts and breakage trend charts showed that more than 50% of the counts had rough surfaces (R4 and R5), implying that fracture breakage was also occurring 4.5.4 Shattered Particles Feature The scanning electron microscope (SEM) images revealed that some particles had a fractured and shattered appearance. It seemed that the particles were shattered in place while capturing the SEM images. It could be presumed that some type of load was applied on the particles, during or after mounting, that shattered those particles into smaller pieces. It should be noted that these types of particles were excluded from point counting. The galena concentrate particles that possessed this feature were mostly in the 63m fraction, from the 4th and 5th passes through the mill, and at 1000 rpm agitator speed. The higher the agitator speed, the earlier this feature appeared, as early as the 1st pass of the 2000 rpm test run. This feature also appeared at the 37m size fraction, but only at the higher speed and at higher passes. For the quartz samples, the shattering feature became visible only at the highest agitator speed, 2000 rpm, during the 4th and 5th passes. Examples of shattered particles are shown in Figure 4-21 for quartz and Figure 4-22 for galena. This phenomenon did not appear in the mixed quartz and galena sample or the leadzinc ore samples. It was speculated that cracks were initiated during the grinding process, but did not fracture the particles completely. The crack lengths were large enough to propagate with minimum stress 104 applied on the particles. Recall that critical stress intensity is a function of crack length and stress applied on the particle. Figure 4-21: Individual Quartz Particles Broken, Shattered Figure 4-22: Individual Galena Particles Broken, Shattered 4.5.5 Automated Quantitative Morphological Analysis Morphology analysis includes particle shape and texture analysis. The particles sphericity and elongation are two other parameters that would provide further understanding of breakage mechanisms. Sphericity determines the roundness of particles and is calculated by dividing the circumference of an equivalent circular area by the actual measured particle perimeter. The perfect circle should return a value of one and the less circular, the particle should return a value 105 closer to zero. The elongation is a measure of length to width relationship and is equal to the inverse of the aspect ratio. An elongated particle will return a value close to zero, and an equiaxed particle will return a value close to 1.0. Sphericity is inversely proportional to elongation. It was speculated that an increase in abrasion breakage in the mill would result in more circular, less elongated, and smoother particles. The Clemex readings are based on the outer contour of the particles. Accordingly, the roughness readings were biased toward smoother readings. Manual point counting has therefore been used to evaluate roughness. For the sake of comparison between the manual point counting and the Clemex roughness evaluation, Clemex roughness values were also generated and statistically analysed. Statistical analysis was performed on the quartz, galena concentrate, and mixed quartz and galena samples at the first and fifth passes, to assess the effect of residence time on morphological features. Analyses were performed on the coarse fraction, 63m. The lead-zinc ore sample was excluded from the analysis due to the existence of multiple minerals which would require an advanced analyses procedure to identify each mineral separately. The statistical analysis showed a small standard deviation, as well as a narrow 95% confidence interval. The data were better represented by the most abundant response, rather than the mean response, which depended on the data distribution. Skewness measures the degree to which the statistical distribution is unbalanced around the mean. Positive skewness represents data that are biased above the mean value. Negative skewness on the other hand, represents data that are biased below the mean value. In other words, predominant parameters are better recognized using skewness, rather than mean. For example, in the case of abrasion breakage, where the particles were more circular, less elongated, and had smooth surface, the skewness values should follow the following trend: 106 - Sphericity data would give a higher negative skewness which would mean that the majority of the readings were skewed towards the round particles. - Elongation data should be negatively skewed where the particles were more equiaxed than elongated. - Roughness data would be negatively skewed which would reflect smoother surfaces. The skewness trends of the data were predominantly negative for the three parameters in question, which suggested that the particles were mostly smooth. This agreed with the Pearson’s time correlation data. However, as mentioned earlier, actual visual point counting proved that this was just a trend, and according to the stacked charts, there were consistently more rough particles than smooth particles. The trend and intensity of the skewness versus the agitator speed and retention time in the mill served to complete the morphology analysis. Galena Concentrate Sample Detailed statistical data for galena concentrate are shown in Table 4-3. For the low agitator speed (G1000-P1), sphericity, elongation and roughness skewness values were -0.45, -0.77 and -1.29, respectively, compared to the higher agitator speed skewness values (G2000-P1), of 0, -0.61 and -0.55 for sphericity, elongation and roughness, respectively. The higher negative values at low speed imply that the lower agitator speed (1000 rpm) created abrasion breakage more than the higher agitator speed (2000 rpm). With increasing residence time, the abrasion breakage mode became more evident. For example, sphericity, elongation and roughness values from pass 5 at low agitator speed (1000 rpm) were -0.69, -0.78 and -1.53, respectively as per G1000-P5 data, whereas the values from pass 4 for 2000 rpm were -0.45, -1.22 and -1.06, respectively for G2000-P4 data. 107 Table 4-3: Morphological Statistical Analysis of Galena Concentrate Sample Statistical Criteria Sample Sphericity Elongation Roughness Mean 0.61 0.70 0.92 Standard Deviation 0.10 0.10 Skewness Sample Sphericity Elongation Roughness 0.61 0.71 0.91 0.08 0.12 0.12 0.09 -1.26 -0.69 -0.45 -0.77 -0.78 -1.53 Minimum 0.30 0.31 0.59 0.09 0.25 0.47 Maximum 0.90 0.90 1.00 1.00 1.00 1.00 Confidence Level(95.0%) 0.01 0.01 0.01 0.01 0.01 0.01 Mean 0.57 0.71 0.77 0.56 0.71 0.88 Standard Deviation 0.13 0.12 0.17 0.12 0.12 0.11 -0.55 -0.43 G1000-P1 Skewness G1000-P5 0.00 -0.61 -1.22 -1.06 Minimum 0.10 0.31 0.27 0.18 0.14 0.46 Maximum 1.00 1.00 1.00 0.82 0.90 1.00 Confidence Level(95.0%) 0.01 0.01 0.02 0.01 0.01 0.01 G2000-P1 G2000-P4 Quartz Sample The morphological statistical analysis for the quartz sample is presented in Table 4-4. The quartz sample had a different breakage mode versus agitator speed than that of galena concentrate. The initial quartz breakage, data from pass 1, showed an abrasion breakage mode for the higher agitator speed (2000 rpm), with more spherical, less elongated and smoother particles (-0.20, -0.61 and -2.0, respectively). On the other hand, the lower agitator speed (1000 rpm) showed less abrasion features (+0.79, -0.13 and -0.9 for sphericity, elongation and roughness, respectively). Similar to the galena concentrate, a longer residence time promoted abrasion breakage for the quartz sample. A comparison of the data from the 5th pass at both low agitator speed (1000 rpm) and high agitator speed (2000 rpm) for Q1000-P5 and Q2000-P5 samples are shown in Table 4-4. 108 Table 4-4: Morphological Statistical Analysis of Quartz Statistical Criteria Sample Sphericity Elongation Roughness Mean 0.60 0.69 0.94 Standard Deviation 0.15 0.14 Skewness Sample Sphericity Elongation Roughness 0.59 0.69 0.94 0.05 0.10 0.11 0.04 -0.90 -0.18 0.79 -0.13 -0.36 -1.49 Minimum 0.18 0.22 0.73 0.35 0.37 0.71 Maximum 1.00 1.00 1.00 0.81 0.93 1.00 Confidence Level(95.0%) 0.01 0.01 0.00 0.01 0.01 0.00 Mean 0.59 0.69 0.96 0.61 0.71 0.94 Standard Deviation 0.11 0.11 0.05 0.12 0.13 0.09 -2.00 -0.61 Q1000-P1 Skewness Q1000-P5 -0.20 -0.61 -0.91 -3.06 Minimum 0.26 0.33 0.68 0.14 0.20 0.43 Maximum 1.00 1.00 1.00 1.00 1.00 1.00 Confidence Level(95.0%) 0.01 0.01 0.01 0.01 0.01 0.01 Q2000-P1 Q2000-P5 Mixed quartz and galena Concentrate Sample The results of the morphological analysis for the mixed quartz and galena concentrate are presented in Table 4-5. The agitator speed did not have an effect on the breakage mode of the mixed quartz and galena sample. At both agitator speeds, abrasion was the main breakage mode in the mill. This was demonstrated by similar negative skewness values for the sphericity, elongation and roughness. It was speculated that the quartz in the mixed sample behaved as a grinding media to the galena. Therefore, galena particles in the mixed sample showed abrasion features at a high agitator speed, opposite to the breakage trend of the galena concentrate sample at a similar agitator speed. Since the low agitator speed promoted abrasion for both types of minerals with different intensities, the overall breakage mode at low speed for the mixed quartz and galena was dominantly abrasion. 109 Table 4-5: Morphological Statistical Analysis of Mixed Quartz and Galena Concentrate Sample Statistical Criteria Sample Sphericity Elongation Roughness Mean 0.60 0.68 0.91 Standard Deviation 0.14 0.12 Skewness Sample Sphericity Elongation Roughness 0.59 0.69 0.88 0.12 0.11 0.11 0.08 -1.33 -0.30 -0.14 -0.55 -0.60 -0.60 Minimum 0.16 0.27 0.47 0.09 0.23 0.53 Maximum 0.82 0.92 1.00 0.81 0.90 1.00 Confidence Level(95.0%) 0.01 0.01 0.01 0.01 0.01 0.01 Mean 0.62 0.71 0.92 0.64 0.71 0.94 Standard Deviation 0.12 0.11 0.06 0.12 0.11 0.08 -1.36 -0.29 M1000-P1 Skewness M1000-P5 -0.14 -0.50 -0.77 -1.58 Minimum 0.24 0.26 0.67 0.22 0.31 0.63 Maximum 0.90 0.94 1.00 1.00 1.00 1.00 Confidence Level(95.0%) 0.01 0.01 0.01 0.01 0.01 0.01 M2000-P1 M2000-P5 4.5.6 Liberation Analysis Results The objective of the morphology study was to identify operating conditions in the mill that would enhance liberation via promoting breakage along grain boundaries, rather than across the grains. It was important to relate breakage mode to liberation through studying the liberation of the lead-zinc ore sample that was used for morphology analysis. The conventional sample preparation for liberation analysis is to generate a 2 dimensional surface of the particle by sectioning the particles through grinding and polishing. In order to study the mineral liberation of particles in 3-dimension (3D), particles generated from grinding were mounted on a graphite sticky paper, on a stud that could be placed in the SEM without grinding or polishing. In this study such particles were referred to as ―particle mount‖ samples. Liberation analyses of the ―particle mount‖ samples were compared to the conventional samples, using the Mineral Liberation Analyser (MLA). 110 4.5.7 Liberation versus Agitator Speed Due to the high cost of such analysis using an expensive tool as the MLA, it was important to carefully choose the minimum number of samples for liberation analyse that will give a significant analytical trend. Therefore, the samples were chosen from the initial breakage (pass 1) for the three agitator speeds tested, 1000, 1500 and 2000 rpm, with a geometric mean size of 63m (coarse fraction). The main minerals in the lead-zinc ore sample that were analysed for liberation included galena, sphalerite, pyrite and quartz. The modal mineralogy distribution of the feed for the galena, sphalerite, pyrite and quartz were 6%, 33%, 15% and 31%, respectively. Since the analysis was performed on only one size fraction, the distributions of the minerals differed with respect to the agitator speed. Galena - Feed 8% 27% Sphalerite Pyrite 43% 15% 7% Quartz Galena Other Figure 4-23: Feed Liberation 111 Liberation and locking analysis are presented in pie-charts where each sector color represents a mineral. Each pi-chart represents a mineral type, its liberation and locking with the other minerals associated with it. For example, the feed sample presented in Figure 4-23 shows four pi-charts for galena, sphalerite, pyrite and quartz. The galena chart shows that 43% of the galena was liberated, 27% was locked with sphalerite, 15% was locked with pyrite, 7% locked with quartz and 8% locked with other types of minerals. Similar types of distribution were represented for the sphalerite liberation and its locking with the minerals in question, as well as the pyrite and quartz. Similar liberation/locking Pi-charts data for the 1000 rpm, 1500 rpm and 2000 rpm agitator speeds were repeated, following the first grinding for each stirrer speed. These results are presented in Figure 4-24, Figure 4-25 and Figure 4-26. Galena - Feed 8% 27% Sphalerite Pyrite 43% 15% 7% Quartz Galena Other Figure 4-24: Lead-Zinc Ore Sample 1000 rpm - Pass1 Liberation 112 Mineral liberation trends were assessed and generally showed that the percentage of liberated minerals decreased with the increase of agitator speed for galena, sphalerite and pyrite. On the other hand, liberation of quartz increased slightly with the increase of the agitator speed. It was also observed that the sulphide locking with quartz increased with stirrer speed. For example, the percentage of galena-quartz composite particles was 9% in the feed, and increased to 22% after grinding at a stirrer speed of 2000 rpm. The analysis was not comprehensive for the entire feed sample, and is based on the analysis of one size fraction (63m -geometric mean size). Therefore, the analysis did not balance the liberation and locking distribution of the minerals across all size fractions. The percentage retained on the -75m +53m sieve (63m -geometric mean size) accounted for 15% of the feed sample, 11% for the 1000 rpm-Pass 1 sample, 8% for the 1500 rpm-Pass 1 sample and only 4% for the 2000 rpm–Pass 1 sample. Galena - Feed 8% 27% Sphalerite Pyrite 43% 15% 7% Quartz Galena Other Figure 4-25: Lead-Zinc Ore Sample 1500 rpm - Pass1 Liberation 113 Galena - Feed 8% 27% Sphalerite Pyrite 43% 15% 7% Quartz Galena Other Figure 4-26: Lead-Zinc Ore Sample 2000 rpm - Pass1 Liberation According to the PSD analysis, the higher the agitator speed, the finer the products. This conclusion implied that the liberated particles were broken, and as a result passed the size fraction under investigation (63m) to the next smaller fractions. The percentage of liberated minerals on the -75m +53m size fraction sieve (63m – geometric mean size) therefore, decreased with the increase of the agitator speed. On the other hand, quartz liberation increased with the increase of the agitator speed, implying that quartz was being liberated and behaving differently than the other three minerals in question. This result can be partly explained by the relative hardness of the quartz, in comparison to the other minerals. The hard quartz would have greater resistance to grinding in comparison to the softer sulphide minerals. 114 The minerals analysed could be classified according to two physical properties, either their hardness or their specific gravities. Quartz and pyrite have similar Mohs hardness values of 7 and 6, respectively. Nevertheless, the pyrite followed similar liberation patterns as galena and sphalerite. Specific gravity, on the other hand, differentiates quartz from the other three minerals galena, sphalerite and pyrite. Quartz is the lightest mineral in the mix with an SG of 2.65. However, this information was not enough to account for the increase of the percentage of quartz on increasing the agitator speed. Looking back to the breakage rates of the quartz and galena concentrate samples (Chapter 3), it was evident that quartz had a significantly lower breakage rate, compared to galena. The initial breakage rate of quartz at 1000 rpm was 0.07 min-1, compared to 0.78 min-1 for the galena concentrate, and at 2000 rpm, the quartz initial breakage rate was 0.35 min-1, compared to 1.82 min-1 for galena concentrate. The breakage rate of both minerals in the lead-zinc ore sample increased with the increase of the agitator speed. However, the breakage rate for galena was significantly faster than for quartz. The percentage of quartz in the size fraction increased with the increase of the agitator speed, which indicated that quartz lagged in breakage when compared to galena. The flow dynamics and breakage mechanism of different types of minerals in stirred mills, based on their material properties, has not been investigated. Particles gain kinetic energy and momentum from the agitator speed; the higher the speed, the higher the kinetic energy. The kinetic energy and momentum relate to the particle velocities. Typical particle velocities in slurry, under stationary conditions for settling, are a function of particle size, particle density and slurry viscosity, as per Stoke’s equation (Equation 4-8). Since particle size and slurry viscosity are similar for all types of mineral particles in the mill, density is then the only remaining 115 parameter that controls the effect of particle velocities. This would imply that the dynamics and kinetics of mixed mineral particles in the mill would be a function of the density of the particles. Equation 4-8 Where: Vs: settling velocity g: gravity dp: particle diameter ρp: particle density ρw: water density : viscosity Particles’ fracture surface energy is function of particle properties as seen in the studies by Tromans and Meech (2002, 2004). Tromans and Meech’s (2002) calculated the theoretical fracture toughness and surface energies of minerals. They also calculated the energy required to create new surfaces using ionic bond models as per Equation 4-9, where the surface energy per unit mass (SEn) was a function of the surface energy (), surface roughness (Fr), and was inversely proportional to mineral density (ρ) and final and initial particle size (Df, Di). Equation 4-9 The mineral density would therefore have an effect on the behaviour of the particles in the mill from the agitation and breakage energy point of views. For example, less dense particles would agitate freely, relative to the agitator speed, since the settling velocity effect would have less impact on the particle’s resulting velocity. The heavier minerals would settle faster, relative to 116 the agitator speed, and would be exposed to more complex types of forces, relative to the flow dynamics of the slurry in the mill. Also, according to the surface energy per unit mass equation, the less dense particles would require more surface energy per unit mass to create new surfaces, compared to denser particles. Since quartz has the lowest density value compared to the other minerals in the mill, it could be deduced that the SG of the quartz was the main reason for its distinctive performance, as compared to the other minerals. Similarly, the percentage of locked minerals with quartz increased. As quartz was locked with another heavier mineral, depending on the relative size of both minerals, it would decrease the overall SG of the particle. Hence, the flow dynamics of the locked particles with quartz would be similar to that of the liberated quartz particles. 4.5.8 Particle Mount versus Polished Samples Since this research focused primarily on the effect of particle morphology on liberation it was important to investigate the particle liberation in a 3D format, without slicing the particles via grinding and polishing. Samples available for this type of analysis were from the test runs performed at an agitator speed of 1500 rpm, for the first three passes through the mill as well as the feed. Samples were mounted in a resin, ground and polished. These samples were referred to as ―Polished‖ samples. The polished sections represent a 2D plane cut through the particles. They were compared to the same set of samples, but were mounted on the stud as 3D particles with no grinding or polishing. They were referred to as ―Particle mount‖ samples. Similar liberation analysis procedures were followed using the MLA-Analyzer. As expected, liberation results were not identical. The difference between liberation results of the ―Particle Mount‖ and ―Polished‖ samples were calculated by subtracting the percentage of 117 ―Polished‖ liberated/locked samples from the percentage of the ―Particle Mount‖ liberated/locked samples. Results are presented in Table 4-7, Table 4-8 and Figure 4-8. The majority of the values were positive, which meant that the ―Polished‖ samples were overestimating the liberation compared to the ―Particle Mount‖ samples. The highest and lowest difference between the ―Polished‖ and the ―Particle Mount‖ samples were -19.3% for sphalerite locked with the other minerals in the feed sample, 21.6% for liberated sphalerite after the first pass, 21.4% for pyrite locked with quartz after the second pass, and 25.1% for pyrite locked with quartz after the third pass. 118 Table 4-6: Feed Sample – Difference in Distribution Between Polished and Particle Mount Samples Table 4-7: Lead-Zinc Ore Sample 1500-P1 Sample – Difference in Distribution Between Polished and Particle Mount Samples Table 4-8: Lead-zinc ore sample 1500-P2 Sample – Difference in Distribution between Polished and Particle Mount Samples Table 4-9: Lead-zinc ore sample 1500-P3 Sample – Difference in Distribution between Polished and Particle Mount Samples 119 The liberation differences ranged from 0.2% to 25%. This was a considerable difference in values and would require further investigation. However, this study indicated that there is a potential for analysing liberation in a short time with less cost if needed. It was understood that the choice of liberation procedure performed in this study would have a large margin of error of up to +/-25%, while using the ―Particle mount‖ methodology. However, the main objective of the study was to understand trends, rather than create discrete liberation values. 4.6 Conclusion Morphology analysis was the focus of this research, which assisted in understanding the breakage behaviour of the different material properties at different stress intensity inputs. The major morphology features analysed were the surface roughness, roundness and elongation of the particles. Surface roughness dictated the type of breakage, whether it was along the grain boundaries or across them. The breakage along the grain boundaries should create rougher surfaces and less circular particles. It would have been more convenient if the analysis was based on pre-programmed software and would follow a standard procedure. However, pre-assessment of the results showed that the morphology analysis software was biased toward smooth counts. As a result, a manual point counting method was developed and tested. In spite of the fact that there was about 6% difference between personnel counters based on their judgement of the degree of roughness of the particles, the trend of the data of the manual point count and Clemex software were similar and correlated. Initial breakage results using Clemex roughness analysis and manual point counting, along with stacked charts were coinciding. Galena concentrate had a trend of fracture breakage, along their 120 grain boundaries, at higher agitator speed, 2000 rpm, whereas quartz had a trend of abrasion breakage, across the grains, at the same agitator speed. This suggested that if the target was to break and liberate minerals similar to galena, then a higher agitator speed would be recommended. The effect of residence time reflected the same trend for Clemex analysis and manual point counting (Pearson’s time correlation). Both materials demonstrated a higher abrasion trend when the particles were exposed to grinding for longer time. This indicated that increasing the residence time of the mineral in the mill created smoother particles. Particles broke across their grain boundaries. The trends of rough (R4+R5) and smooth (R1+R2) particles versus grinding passes - as shown in Figure 4-17, Figure 4-18, Figure 4-19, for quartz, galena concentrate and mixed quartz and galena concentrate samples, respectively - demonstrated the stirred mill breakage patterns for the different types of minerals. Visual observations and trends of counts showed that stirred mills broke particles via both abrasion and fracture. Abrasion became more evident as residence time increased. The trends showed that the longer the time the particles were exposed to grinding, the amount of smooth particles (R1+R2) would increase, while the amount of rough (R4+R5) particles would decrease. However, the overall trends for both types of materials (quartz, and galena concentrate) demonstrated that the amount of rough particles was always higher than the amount of smooth particles. The results suggested that fracture was the dominant breakage mode in the grinding system. The hypothesis was built on the observation that the particles’ size decreased during the grinding process, as per the PSD analysis. Therefore, it is safe to speculate that the particles analyzed were the progeny created during the grinding process. The trends demonstrated that abrasion is an important breakage mechanism and increases with residence 121 time, but that fracture is also important, if not dominant during the initial stage of breakage in the mill. Liberation analysis was performed on a single size fraction, which was considered to be incomplete analysis; nevertheless, conclusions can be deduced from the results. Results supported the theory that the flow dynamics of minerals in the mill are not dependent on their hardness. For example, pyrite and quartz were close in hardness, but behaved quite differently. Conversely, the flow dynamics seemed to be somewhat dependent on the mineral specific gravity. Results from this research demonstrated that there was potential to understand grinding versus liberation beyond the well-known relationship between liberation and particle size. The morphology analysis revealed that minerals, with a high SG such as galena, would break faster at lower agitator speed. However, breakage would be via abrasion. In order to impose intergranular breakage on minerals similar to galena, a higher agitator speed and shorter residence time is recommended. In other words, the mode of breakage should be a priority over the breakage rate in order to promote liberation. Further analysis of the performance of the different mineral properties, particularly their specific gravity and surface energy versus breakage mode (intergranular-transgranular), should be investigated. 122 5. Computer Modeling and Simulation of Stirred Mill The objective of this part of the research was to create a computer model that would simulate particle flow, forces and energy distribution across the IsaMill under different operating conditions. The experimental work performed on the IsaMill in this research shed some light on the mill grinding operation and particle breakage behaviour. However, the distribution of energies and types of stresses in the mill were quite ambiguous. Discrete Element Modeling (DEM) is a numerical method that computes the motion and interaction of particles against each other and their boundaries (Cundall and Stack, 1979). At every time step, the DEM software searches for contacts (particle-particle or particle-boundaries), then it calculates all contact forces and integrates equations of motion for each particle, which in turn identifies the resultant velocities, directions and positions of those particles for the next time step. The theory of discrete element modeling was founded on Newton’s laws of physics. The software used in this study is EDEM. The EDEM model has standard steps to set up the simulation model: Configure and define the contact physics of the model, particle to particle and particle to geometry interaction. If there is an external force applied on the particles, they can be further defined as particle body forces, which are fluid drag forces, and typical gravity force effects on the system. Define the material properties for the different parts of the mill and their interactions. Create the geometry of the system to be modeled, which includes the model boundaries and input dynamics for the particles. In this research, the IsaMill agitator shaft, along with the discs, separator/classifier, and the mill chamber surrounding the agitator account for the 123 geometry parts of the system. Assign the pre-defined materials to the mill parts and their dynamics (rotational or translational). Define the domain size, which is the volume where all simulation is taking place, and if particles move outside the domain, they will not be tracked. In this simulation, the domain included all the IsaMill geometry parts. Define the particle properties, size, material properties and total number of particles to be created. Create a particle factory, which is a virtual geometry that generates the particles and defines whether to use a continuous particle generation, or a specific number of particles. Set time step, simulation time, and divide the domain into grid cells with a size of 4 times the minimum particle radius. Run the simulation. The analyst is a tool used to review the simulation and analyse the generated interaction between the particles and their boundaries. The important parameters for this research were the agitator speed and interaction between the different types of materials, such as the grinding media and galena particles. The responses of such parameters were summarized as the energies generated in the mill, and the types of forces the particles were exposed to. Since breakage was the main focus of this research, and the model could not simulate particle breakage, the types of forces would indicate the type of breakage the particles could be exposed to during the grinding process. 124 5.1 EDEM Software EDEM software was produced by DEM Solutions in 2005 (DEM Solutions, 2011). The EDEM software is a simplified simulation of material flow. It analyses and tracks the interaction of individual particles with each other and their boundaries by analyzing the individual contacts. When two elements overlap, a contact is recognized, along with its properties, particle size, material properties, and relative velocity, which is further used to calculate the contact forces. As a result, particles and geometric elements are re-positioned. Contact data intervals are saved based on the user choice. In EDEM the model geometry and particles are in a domain that has geometrical limits in space, X, Y and Z directions. The domain is the region where EDEM performs all the contact calculations. If the user defines a domain size smaller than the designed system, the contact calculations beyond the domain zone are ignored. The domain is divided into grids, from 2 to 6 times the minimum particle radius. It is the user’s choice to decide on the number of grids created. The smaller the grid size, the larger the number of grids created which would require a higher computing memory, and would therefore slow down the iteration speed. EDEM has multiple pre-built integrated contact models. Typical contact models used by DEM simulation for particles in motion are Hertz Mindlin or linear spring. Both contact models calculate normal forces and tangential forces of particles colliding at an initial velocity. Both models include the spring stiffness and damping coefficient (dashpot). However, the Hertz Mindlin contact model is more detailed and complicated, when compared to the linear spring model. A detailed schematic diagram of the Hertz Mindlin model is shown in Figure 5-1, and the model equivalent normal forces, tangential forces and rolling friction equations are given in Equations 5-1 to Equation 5-7, respectively. The force equations for the linear spring model are given in Equation 5-8 to Equation 5-10. The Hertz Mindlin model includes the static friction and 125 rolling friction in its calculations, which is ignored by the linear spring model. Consequently, according to the calculated forces, the Hertz Mindlin model represents a more realistic case scenario than the linear spring model. However, Hertz Mindlin produces a default smaller time step which slows the simulation speed. Figure 5-1: Schematic Diagram of Hertz Mindlin Contact Model, EDEM Training Manual, 2009 Hertz Mindlin normal forces are a function of material properties, particle size, damping normal forces, relative normal forces and stiffness as per Equation 5-1, Equation 5-2 and Equation 5-3, (EDEM Training Manual, 2009). Equation 5-1 Equation 5-2 Equation 5-3 126 Where: Fn : normal force Y*: equivalent Young’s modulus m*: equivalent mass R*: equivalent radius n: normal overlap and Sn: normal stiffness e: coefficient of restitution The Hertz Mindlin tangential forces are a function of shear modulus of the material, tangential damping force, relative tangential velocities and tangential stiffness, but exclude the coefficient of restitution as per Equation 5-4, Equation 5-5 and Equation 5-6 (EDEM Training Manual, 2009). Equation 5-4 Equation 5-5 Equation 5-6 Where: Ft : tangential force G*: equivalent shear modulus St: tangential stiffness Hertz Mindlin has a rolling friction parameter, which is function of rolling friction and angular velocities at contact, as per Equation 5-7 (EDEM Training Manual, 2009). 127 Equation 5-7 Where: i : rolling friction r: coefficient of rolling friction Ri: distance of contact point from object center mass i: angular velocity at contact point Linear spring normal forces are simpler than the Hertz Mindlin normal forces. Linear spring normal forces are function of the material properties, linear spring stiffness, dash pot coefficient and overlap velocities, as shown in Equation 5-8, Equation 5-9 and Equation 5-10 as per EDEM Training Manual (2009). Tangential force equations are similar to the normal force equations. Equation 5-8 Equation 5-9 Equation 5-10 Where: Fn : normal force K: linear spring stiffness C: dashpot coefficient n: overlap : overlap velocity E : equivalent modulus of elasticity R*: equivalent radius * 128 The Hertz Mindlin model was chosen to model the IsaMill because the quantitative analysis would assist in understanding the particle breakage mechanism by analysing the forces that the particles would be exposed to, at different agitator speeds. 5.2 DEM Simulation Limitations It is almost impossible to model a complete mill with the actual number of grinding media and mineral particles using DEM, since such modeling requires a high intensive computational program. It requires some sort of compromise in either the number of particles or simulation lengths in regard to speed simulation runs. Most of the model studies performed on the IsaMill have compromised the mill design by simulating three discs instead of eight, and excluding the classifier section. Consequently, the number of particles simulated were less, and the flow pattern of the particles was also compromised (Jayasundara, Yang, Yu, and Curry, 2006, and 2008; Jayasundara, Yang, Guo, Yu and Rubenstein, 2009). Another method to increase the speed of the simulation process is to limit the length of the simulation time. The majority of the researchers have either run the simulation for a very short time or they neglected to mention the simulation length. The model by Jayasundara et al. (2006) was simulated for only 1.5 seconds. The assigned material property of the different parts of the mill has a direct effect on the simulation iteration time, which will eventually affect total time required to run the simulation. Typical media used in stirred mills are ceramic beads MT1, (accuratus, 2009), which are mainly composed of aluminum oxide, zirconium oxide and silica. The density, Young’s modulus and shear modulus of ceramic beads is about 3700kg/m, 290 GPa and 120 GPa, respectively. Actual properties of ceramic media have not been used in simulations by DEM model researchers. The highest Young’s modulus value for grinding media particles that has been researched is 0.2 GPa (Yang et. al, 2006), which is three orders of magnitude less than the actual MT1 grinding media. 129 According to EDEM’s manual (2009), the higher the stiffness of the material, the higher the forces and stresses which would lead to a lower time step to capture these high forces. Stiffness of the material is directly proportional to its mechanical properties, Young’s modulus. The model used in this research was compromised by limiting the number of particles in the mill, and controlling the stiffness effect of the grinding media by assigning 2 orders of magnitude less for its shear modulus (1.2 GPa). The number of particles was limited by modeling only three discs and the classifier, instead of a full mill that consisted of eight discs and a classifier. The number of particles simulated was also limited, by choosing a reasonable media size and similar galena size (3mm each) that would occupy the mill’s empty volume, as per typical IsaMill operations. Detailed simulation parameters and criteria are discussed in detail later in this chapter. The computer for this research was a DELL Mobile Precision M6400 Quad Core; 2.53 GHz; 4GB MEM-1066MHz; 64 bit operating system. Although this was the highest processor speed available in a portable computing machine at the time, its computational capabilities were limited. The above mentioned constraints would limit the ability to validate the model relative to experimental full scale mill. However, it is a feasible tool that throws a shadow of knowledge on particles flow and their forces in the mill when exposed to different agitator speeds. Qualitative trends such as types of forces (tangential versus compressive) were used to validate the model relative to the experimental morphological results (across versus along grain boundaries breakage). All simulation models studied the effect of particle flow within the range of three discs, excluding the classifier section. The classifier section in the mill was meant to keep the media in the grinding zone of the mill, and to segregate the fine particles (Xstrata [IsaMill Brochure], 2009). In other words, no grinding action was to take place in the classifier zone. Since the main 130 objective of this part of the research was to bring the computer model as close as possible to real case scenario, it was important to include the classifier section in order to simulate the actual particle flow along the mill length. It was also noticed that the agitator design had changed in the past decade, from triangular discs to circular discs. Running a preliminary model using circular discs showed that the particles spread out along the mill, up to the classifier zone and eventually became evenly distributed along the mill after about 10 seconds. The spread of the particles along the mill did not agree with a video of a simulation of the IsaMill that was running with a clear chamber that was provided by J. Rubenstein, 2010 (Rubenstein, J., personal communication, March 04, 2010). When the video was carefully examined, it was noticed that the agitator discs were triangular rather than circular. Therefore, it was essential to compare the triangular discs versus circular discs in terms of their distribution of the particles along the mill’s length. 5.3 IsaMill Model Geometry The model creates particles within boundaries of a system which can contain stationary and/or moving parts. The system was geometrically designed similar to the structure of the actual machine, and the moving parts were assigned the magnitude and direction of the dynamics of motion, which could be rotational, translational or combined. If the geometry of the system were composed of simple cylinders, cubes and cuboids, this system could then be created within EDEM software. However, if the parts were more complicated, then they would need to be imported from a computer aided design software (CAD), where the geometry were pre-drafted. In this research, the mill geometry and dimensions were based on those of the M4-IsaMill. The dimensions of the agitator shaft and discs are shown in Figure 5-2. The mill chamber was a 131 simple closed cylinder, with an inner diameter of 135 mm. An agitator was drawn with triangular discs instead of circular discs, as shown in Figure 5-3. Side View Front View Figure 5-2: Schematic Diagram of Circular Agitator, Dimensions were mm Side View Front View Figure 5-3: Schematic Diagram of Triangular Discs Agitator 132 The geometry of the mill’s agitator was drafted using SolidWorks CAD software, which was then imported in the EDEM as the agitator geometry component of the mill. The mill chamber was drafted within the EDEM software, using a simple closed cylinder geometry that surrounded the agitator. The Particles factory was a virtual geometry which surrounded the three discs of the agitator. Its function was to create the particles inside the mill chamber, at random positions around the agitator and the three discs. The factory was pre-drafted using the same CAD software (SolidWorks), which was a negative image of the 3 discs on the left of the agitator. A cross section of the agitator and the factory surrounding the first three discs is shown in Figure 5-4. The factory had no physical effect on particle interaction during simulation. The only force applied on the particles as they were generating was the force due to gravity. The agitator was stationary for 2 seconds of the simulation time, in order to allow the particles to settle under the effect of gravity. Particles Factory Agitator Figure 5-4: Cross Section of Particles Factory Surrounding 3 Discs 133 5.3.1 Number of Particles It is recommended by the manufacturers of the IsaMill to load the mill with the grinding media to 80% of its effective volume. The definition of effective volume is the volume of the grinding chamber, which includes the agitator and grinding discs, excluding the last disc and fingers zone (classifier zone). The effective volume was calculated using the dimensions of the mill chamber and subtracting the agitator volume. 80% of the net volume was then available to be filled with grinding media. The packing of the grinding media particles was assumed to be 40% voids. If the actual size of the grinding media particles were to be simulated, this would lead to generating an enormous number of particles, in the order of millions (10 6). If mineral particles were to be added to the grinding system, with an optimum size ration of 20:1 for media to minerals as suggested by Mankosa et. al. (1986), then the number of particles to be generated would be in the order of gega (109) particles. The realistic number of particles that can be modeled should be less than (105) particles. Consequently, particle diameter is fixed to 3mm for both media and mineral particles in order to minimize the number of particles simulated. The total number of media particles, according to the above mentioned criteria, was 44,775. Computer simulation runs were performed on pure media at three agitator speeds (1000, 1500 and 2000 rpm). Since it was not possible to simulate a real case, a simplified model was implemented, in order to understand the interaction between two different types of particle in the mill both on each other and their boundaries. Accordingly, simulation of the mill at two agitator speeds (1500 and 2000 rpm) was executed, with material properties close to galena added to the system. The number of galena particles was 19,407, which made the combined total of 64,191 particles simulated. The ratio of the number of galena to media particles in the mill was 1 to 2.3. 134 5.3.2 Triangular versus Circular Discs The effect of triangular versus circular discs on particle distribution across the mill was studied. Only media particles were used in the mill (total number of 44,785) for each model run. For the sake of analysis, the model domain was split into 3 sections, in the x-direction, Section A, Section B and Section C, as shown in Figure 5-5. Section A was the end part of the modeled mill, which was close to where the actual feed of media particles was located in a real M4IsaMill. Section B was the middle section, which included the narrow gap between the two end discs. Section C was the separator/classifier zone. Section A Section B Section C Figure 5-5: Initial Setting of the Particles in the 3 Sections at Time Zero Similar sections were created for the triangular discs. The model was simulated for 120 seconds for each disc type. Particle distribution across the mill was analysed and showed a similar pattern to that of the circular discs. At time zero, after the particles had settled due to gravity, particle distribution across the three sections was approximately 21,000 at section A, 17,600 at section B and 6,000 at section C. Once the agitator started rotating at 1500 rpm, the particles spread out so 135 that the highest particle population, sections A and B, decreased, and the less populated section C increased until stability was reached. Stability was reached when no more change in the distribution of the number of particles across the mill was observed. The middle section, section B, reached its stable conditions almost instantly, within about 2 seconds. The number of particles increased by approximately 7 000 and stabilized at a total of 15 000 particles, for both circular and triangular discs. The end sections, sections A and C, reached their stable conditions after about 5 seconds for the triangular discs, whereas the circular discs took more than double the time to get to the same stable conditions (11 seconds). The number of particles in section A decreased by 8 000 particles, and stabilized at a total of 13 000 particles. Section C increased by 10 000 particles and stabilized at a total of 16 500 particles. The number of distributed particles along the mill length was similar for both the circular and triangular discs. Particle distribution patterns across the mill over the 120 second run are presented in Figure 5-6. The initial particle distribution pattern before the agitator started rotating was 47% particles in section A, 39% in section B and 14% in section C. At stable conditions, the particle distribution pattern across the mill was 30% in section A, 33% in section B and 37% in section C. In other words, section C, the classifier section, was occupied with more particles than sections A and B. 136 (a) (b) Figure 5-6: Particle Distribution in 3 Sections for Circular and Triangular Discs Despite the fact that the triangular discs distributed the particles across the mill faster than the circular discs, both types of discs reached a similar particle distribution pattern within a reasonable time span. As a result, the circular discs were chosen for the model runs, since such design is used in the current IsaMill. 137 5.3.3 Effect of Drag Forces The actual IsaMill has a fluid flow effect on the particles, since the particles are pumped into the mill in a slurry form. In order to analyse the effect of slurry flow on the particles, a coupling with the Computational Fluid Dynamics (CFD) was required. There is a simpler Application Programming Interface (API) body particle force module available in the EDEM software, which would analyse the effect of drag forces on the particles. The equation that EDEM utilises for drag force is a function of the particle coefficient of friction (CD), a particle’s cross section area (A), fluid density (ρ), and velocity of the fluid flow past the particle (v), as shown in Equation 5-11. Equation 5-11 The input data required for the particle body drag forces routine were: Stream input in X, Y and Z directions, end side of section A. Stream outlet in X, Y and Z directions, end side of section C. Stream diameter, which was the mill inner chamber diameter, 135 mm. Fluid velocity, 0.00408 m/sec, which was equivalent to the 3.5 L/min was used in experimental work. Drag coefficient was based on particle shape. It was 0.47 for spheres. Fluid density for water, which was 1000 kg/m3. The fact that the particles spread throughout the mill, as explained earlier, required further investigation of the effect of back drag force on the particles, in an opposite direction to the inlet stream flow. The drag forces in the mill were classified as the fluid flow, due to the slurry being pumped into the mill, and an opposite drag flow, which was due to the possible reverse fluid 138 dynamics at the exit end of the mill. The flow from the inlet to the exit direction of the mill was called ―fluid flow‖, which was assigned a flow rate value of 0.00408 m/second, which is equivalent to the experimental flow rate 3.5 L/min. The opposite flow, from the exit to the inlet direction, from section C to section A in the x-direction, was called ―drag flow‖. The effect of the drag flow on the particles distribution was tested at different percentages from the fluid flow: 0, 1.6%, 25%, 50%, 100% and 200%. Fluid flow created forces that prevented the particles from flowing freely around the mill. An example of this behaviour is shown in the snap shot images of 100% drag flow in Figure 5-7. Particles behaved in a similar manner for all the drag flow percentages modeled. Figure 5-7 and Figure 5-9 represent the grinding ceramic media particles in the mill and the color codes represent the particles velocity (m/s) at the current simulation time step. The particle distribution across the mill for each drag flow versus time is plotted in Figure 5-8. 139 5 Seconds 11 Seconds Figure 5-7: Fluid Flow Effect with No Drag Flow at 1500 rpm Agitator Speed 140 Drag flow had no effect on particle distribution across the mill. The particle distribution was more affected with the presence or absence of fluid flow, as shown in Figure 5-8. The fluid flow slowed down the distribution of the particles across the mill. However, the model did not perform as expected where the particles did not rotate freely around the inner chamber walls along with the agitator rotation. The drag forces did not properly represent the complex fluid dynamics effect that was supposed to occur in the mill, such as vortex effects. Therefore, the y and z components of the fluid forces on the particles were excluded, and only the x component of the fluid forces was simulated. The effect of the pump on directing the particles through the mill was speculated to emphasize the effect of the x component of the fluid forces more than the y and z components. It is presumed that the y and z components of the fluid forces were overestimated, which led to the abnormal behaviour of the particles during agitation. It could be concluded that the x-component of the drag forces had a more dominant effect over the y and z components. Discarding the effect of the y and z component of drag forces gave the particles a higher degree of freedom to flow while under the effect of the agitator rotation as presented in Figure 5-8 and Figure 5-9. 141 Figure 5-8: Drag Flow Force Effect on Particle Distribution Across the Mill 142 a b c Figure 5-9: Particle Distribution Across the Mill: a) Initial Distribution at Time Zero b) Drag Forces (fluid flow) in x, y and z Direction c) Drag Forces (fluid flow) in x Direction 143 5.3.4 Material Properties A series of simulation runs were performed in order to assess the effect of material properties on the time iteration, particles behaviour, and their resultant forces, for the different components of the mill. The different components of the mill including the agitator, chamber and most importantly the particles, have unique mechanical properties that were pre-defined by the user. The mechanical properties of the mill parts and particles have a direct effect on the behaviour of the particles and their resultant forces. The goal was to create a model that was as close to the real case as possible. The material properties of the IsaMill, presented in Table 5-1, were considered as the benchmark properties. The material parameters that EDEM defines and utilises are Poisson’s ratio, shear modulus and density, (Gercek, 2007). Table 5-1: Benchmark Material Properties Mill Parts Density (kg/m3) Young’s Modulus (Y) (Pa) Shear Modulus (G) (Pa) Poisson’s Ratio (υ) Mill Chamber Steel 8000 19.24 x 1010 7.40 x 1010 0.30 Agitator Polyurethane 1250 25.80 x 106 8.60 x 106 0.50 Agitator (calculated) Polyurethane+ Steel 4625 --- 8.60 x 108 0.4 Media Ceramic MT1 3700 2.90 x 1011 1.20 x 1011 0.21 Particles Galena 7190 8.102 x 1010 3.19 x 1010 0.27 144 Iteration rate of the model was a main concern, since simulating a one second run, should not require an enormous time to iterate. Iteration rate is defined as the number of iteration hours per one second of simulation. The media particles were assigned the benchmark material properties for the first simulation run, which produced a very slow run, with a very slow iteration rate (27.6 hours to simulate a one second run). A series of simulation runs were performed in order to analyse the effect of material properties on particles behaviour and simulation iteration time. The runs were simplified by excluding all drag forces. A simulation was performed with material properties from the different parts of the mill, dropped to two orders of magnitude relative to their benchmark values, where G value for media was 1.2x109, agitator was 8.6x104, and mill chamber was 7.4x108 (simulation run a). The simulation iteration rate increased significantly to 8.78 hours for one second simulation. However, the particles did not agitate properly. Through analysis of the forces created in the mill, it was noticed that the force values were relatively high, compared to the other simulation runs (Table 5-2). The next two simulation runs were performed using the material properties of the agitator and mill chamber materials similar to the benchmark, as well as decreased the shear modulus for the grinding media to one and two orders of magnitude, (simulation runs b, and c, consecutively). The particle flow in the mill was closer to normal, but for simulation run b, the particles’ shear modulus was not small enough to increase the iteration rate (20.8 hrs for each simulated second). Simulation run c showed a better response in terms of speeding up the simulation run time. The iteration rate of simulation run c was 7.1 hrs for each simulated second. The fourth model run was performed with the agitator material properties defined as steel, similar to the chamber property, which were two orders of magnitude less than the benchmark 145 values (simulation run d). The simulation iteration rate was close to that of simulation run c (6.9 hrs for each simulated second). Other parameters that were affected by the material properties of the mill parts were the maximum forces generated in the mill and the effective energy consumed by the particles. The effective energy was calculated based on the ratio of output to input energy. The input energy was calculated from the agitator torque values, and the output energy was the total kinetic and rotational kinetic energies of the particles created in the simulation run by the agitator rotation. As presented in Table 5-2, the steel agitator created a high value of maximum normal force, especially in section A, and the effective energy was 7.9%, which was the highest compared to the other simulation runs. At this point, it was noticed that the model deviated from the initial objective, which was to create a computer model that was similar to the real case scenario. One of the advantages of stirred mills is their inert environment for grinding, where the agitator is not steel. The M4-IsaMill agitator used in the experiments carried out in this research was made of steel, covered with a layer of polyurethane. The material properties of steel-covered polyurethane were calculated. Simulation run e was then performed on an agitator shaft that was assigned the calculated material properties of the mixed steel and polyurethane, and results were reasonable. Finally, a similar run was conducted using the mixed steel-polyurethane agitator, and fluid drag forces were included in the x-direction, using EDEM built-in particle body forces (simulation run f). Simulation iteration rate was reasonable (8.3 hours for each simulated second), effective energy percent ratio was 4%, and the force values were reasonable when compared to the previous runs. 146 Table 5-2: Effect of Material Properties on Run Time, Forces and Energy Efficiency Simulation Runs Iteration Rate (hrs/second) Maximum Normal Forces Maximum Tangential Forces A B C A B C Effective Energy (%) (a) 2 Order Mag-All parts 8.8 4.86 2.86 1.26 1.26 0.55 0.26 3.9 (b) 1 Order MagMedia 20.8 1.16 0.89 0.12 0.21 0.17 0.02 3.5 (c) 2 Order Mag – Media 7.1 1.76 1.25 0.94 0.34 0.24 0.18 3.5 (d) Steel-Agitator 6.9 2.58 2.07 1.01 0.61 0.38 0.22 7.9 (e) Steel +PolyAgitator 7.2 1.50 2.23 1.96 0.27 0.34 0.36 2.9 (f) Steel + Poly Agitator & Drag Force 8.3 2.04 1.95 1.69 0.40 0.36 0.32 4.0 5.3.5 Model Parameters Since the model simulations were aimed at understanding the behaviour of the particles in the mill at different operating conditions, as well as the effect of the different particle properties on each other, the parameters were classified as fixed and variable. 5.3.5.1 Fixed Parameters The fixed parameters were mill design, material properties, contact forces model, number of particles and external body forces acting on the particles. The fixed parameters had to be compromised in order to achieve a realistic simulation based on reasonable values of the iterated parameters. 147 The fixed parameters were summarized as follows: Mill agitator discs were circular. Material properties input to the EDEM software are as listed in Table 5-3. Particles and mill components interactions were coefficient of restitution, a coefficient of static friction, and a coefficient of rolling friction. Table 5-4 lists coefficient values which were based on similar values for similar material from the websites rocscience, 2010, roymech, 2010, accuratus, 2010 and efunda, 2010. Particle size was 3 mm for both media and galena. Number of particles simulated was: media 44,775 and galena 19,407. The contact force model was the Hertz Mindlin model. An external body force was applied in the form of drag force (x-axis component) in the direction of fluid flow from section A towards section C. Table 5-3: Material Properties - Fixed Parameters Mill Parts Density (kg/m3) Shear Modulus (G) (Pa) Poisson’s Ratio (υ) Mill Chamber Steel 8000 7.40 x 1010 0.30 Agitator (calculated) Polyurethane+ Steel 4625 8.60 x 108 0.4 3700 1.20 x 109 0.21 7190 3.19 x 1010 0.27 Media Ceramic MT1 Particles Galena 148 Table 5-4: Particles and Mill Component Interactions Media Mill Component Galena COR COSF CORF COR COSF CORF Agitator 0.4 0.2 0.01 0.35 0.35 0.01 Chamber 0.5 0.4 0.01 0.45 0.5 0.01 Media Particles 0.5 0.2 0.01 0.45 0.3 0.01 Note: COR : Coefficient of Restitution COSF: Coefficient of Static Friction CORF: Coefficient of Rolling Friction 5.3.5.2 Variable Parameters The main objective of the simulation was to visualize the behaviour of the particles across the mill length, and to quantify the forces that the different types of particles were exposed to at different agitator speeds. The variables tested were the agitator speed and material properties, including ceramic media and galena like minerals. The effect of the agitator speed on a single material type in the mill, namely the ceramic media particles, were tested via a series of simulation runs at 3 agitator speeds, 1000, 1500 and 2000 rpm. Then the effect of galena particles on the system performance was modeled at intermediate agitator speed (1500 rpm) and high agitator speed (2000 rpm). The responses were quantified by varying the agitator speed and analysing the responses. It was possible to quantify the rate at which the particles spread across the mill, as well as the type (normal/tangential) and magnitude of forces generated at different input energies. 149 5.4 Computer Model Results The core objective of this research was to further understand the effect of different high speed stirred mill operating conditions (energy input via agitator speed) and the interactions between different material types. Experimental work tested three agitator speeds (1000, 1500 and 2000 rpm), and their effect on extreme material properties (quartz and galena). For the sake of comparison, the model runs were chosen to simulate conditions close to actual grinding operation. To understand the effect of different simulation parameters on the modeled system, each parameter had to be tested individually before simulating a complex system. Therefore, it was important to start the model runs with one type of particle in the system (media particles) and study the effect of the different agitator speeds on particle behaviour and forces generated. Then a more complex model was generated by adding galena particles to the system and the effect of medium and high agitator speeds were investigated. Fixed parameters for the five runs are presented in Table 5-3 and Table 5-4. 5.4.1 Media Particles Runs According to the particle distribution analysis shown in Figure 5-8 and Figure 5-9, the mill reached its stable state at about the 12th second. As a result, the simulation was run for 15 seconds to assure stable conditions were reached. The particle, forces and energy distributions were analysed. 5.4.1.1 Particle Distribution For the sake of comparison, the total number of particles was fixed for all simulation runs. Particle distribution across the mill was an initial sign of system stability. Since agitator speed dictated the energy input to the particles, it was important to evaluate the effect of the agitator speed on stability. As shown in Figure 5-10, particle distribution across the mill was similar for 150 the three agitator speeds tested. By the 12th second, the number of particles at the three sections tended to approach the 15 000 particles in each section. Sections A and B started with a higher number of particles at time zero. The number of particles decreased in section A by about 9% and by 6% in section B, but increased by 14% in section C. 151 (a) (b) (c) Figure 5-10: Particle Distribution vs. Simulation Time (a)1000rpm, (b) 1500rpm, (c) 2000rpm 152 The initial particle distribution was 47% in section A, 39% in section B and 14% in section C. At stable conditions (at the 12th second), the particle distribution was 38% in section A, 34% in section B and 28% in section C. Section C had the least number of particles in the system. Fluid flow slowed down the particle spread across the mill as shown in Figure 5-8 and Figure 5-10. Therefore, fluid flow drag forces were incorporated in the simulation. The material properties chosen and the number of particles distributed across the mill length were minimum at the classifier section, bringing the model closer to the actual mill operation. 5.4.1.2 Energy Distribution The stirred mill dynamics can be summarized as an input energy to the system via rotation of an agitator (torque), which in turn transmits the energy to the particles in contact with the agitator. Such particles gain kinetic and rotational kinetic energies, which are in turn transmitted to the neighbouring particles via contacts and impacts. Hence, the energies can be summarized as input energy via the agitator’s torque, and output energies which are the particles’ kinetic energies plus rotational kinetic energies. Although the agitator rotation speed was pre-defined to be 1000 rpm (5m/s), 1500 rpm (8m/s) and 2000 rpm (10m/s), the lifting and agitation of the particles created resistance, which in turn changed the agitator’s torque values per time step. In order to trace the effect of lifting and agitation on torque values, the agitator torque value was saved after every iteration interval, as well as total kinetic energies and rotational kinetic energies of all the particles for each section in the mill (A, B and C). Energy values were exported to a spread sheet for analysis. Input energy from the agitator was calculated using the torque values, as per Equation 5-12. Output energies were the sum of all the kinetic and rotational kinetic energies for all the particles, as per sections A, B and C. Output versus input energies were plotted, and the slopes of the lines were the effective energy ratio in the mill, as shown in Figure 5-11. 153 Equation 5-12 Where: EI: input energy T: torque rpm: revolution per minute t: time (a) (b) (c) (d) Figure 5-11: Output vs. Input Energies for Media Runs (a)1000rpm, (b) 1500rpm, (c) 2000rpm, (d) Full Mill 154 The energy distribution differed in the three sections of the mill according to the agitator speed. Section C was exposed to the least energy for the three agitator speeds. Section A and B had similar energy distribution throughout the simulation time at 1500 rpm, Figure 5-11(b). The sections also had similar energy distributions up to an input energy of 400 J for the 2000 rpm (Figure 5-11(c)). Beyond an input energy of 400 J at 2000 rpm, section B showed a steeper slope than section A (Figure 5-11(c)), which implied that the same input energy in section B was better utilized by the particles than that in section A. The commencement of the run showed similar particle behaviour in sections A and B at 1000 rpm (Figure 5-11(a)). The overall effective energy percent ratio (ratio of output to input) for the three agitator speeds were 4.9% for 1000 rpm, 4% for 1500 rpm and 4.4% for 2000 rpm as in Figure 5-11(d). The experimental and theoretical (computer model) effective energies could not be compared directly, since the energies encountered in the actual mill had complex parameters that were not addressed by the computer model. The dynamics of a continuous flow of slurry through the mill, the actual particle breakage versus time, the particle size distribution in the slurry mix, were all parameters that were not considered in this research. To evaluate the energy balance across the mill, effective energy ratio was plotted versus simulation time Figure 5-12. The effective energy ratio consistently increased in section C at a higher rate for the higher agitator speed. For sections A and B during the first two seconds of the run, the mill experienced a disturbance at the three agitator speeds. Then the effective energy ratio stabilized according to the agitator speed. The effective energy ratio stabilized when it did not change with time, which implied that the particles gained their inertia relative to the mill agitator rotation, and that the effect of lifting and falling of the particles versus energy consumption during the agitation was not changing with time. The effective energy ratio in 155 sections A and B coincided after the first 2 seconds at 2000 rpm, they converged at the 8th second at 1500 rpm, and they were almost parallel at 1000 rpm. The effective energy ratio was highest at the lowest agitator speed (1000 rpm), followed by the 2000 rpm, and the lowest effective energy ratio was at the 1500 rpm. The results could be explained by particles dynamic in the mill relative to the agitator torque and individual particles’ kinetic flow. The agitator torque was directly affected by the number of particles resting on the agitator, which in turn affected the center of mass of the particles that the agitator was lifting. Cumulative energy trends were further evaluated. 1500 RPM (a) 0.07 0.07 0.06 0.06 0.05 Section A 0.04 Section B 0.03 Section C 0.02 0.01 Effective Energy Ra tio Effective Energy Ratio 1000 RPM 0.05 0.04 Section A 0.03 Section B 0.02 Section C 0.01 0.00 0.00 0 2 4 6 8 10 12 14 16 0 2 4 6 Time (sec) 8 10 12 14 16 Time (sec) 2000 RPM Full Mill Energy Efficiency (c) 0.07 (d) 0.14 0.12 0.05 0.04 Section A 0.03 Section B Section C 0.02 0.01 Effective Energy Ratio 0.06 Effective Energy Ratio (b) 0.10 1000RPM 0.08 1500RPM 0.06 2000RPM 0.04 0.02 0.00 0.00 0 2 4 6 8 Time (sec) 10 12 14 16 0 2 4 6 8 10 12 14 16 Time (sec) Figure 5-12: Media Effective Energy Ratio vs. Simulation Time 156 The cumulative energy trends did not follow the agitator speed. The intermediate agitator speed, 1500 rpm, had the lowest effective energy ratio, and the lowest agitator speed had the highest as shown in Figure 5-12 (d). Therefore, instantaneous torque, input and output energies were further investigated. The torque trend showed similarity for the three agitator speeds as presented in Figure 5-13. The standard deviation of the average torque among the three agitator speeds was only 0.0081, which showed that the torque was quite constant for the three agitator speeds. This observation contradicted the expected torque values relative to the agitator speed. The simple equation for torque was the tangential force multiplied by the radius on which the force was acting. The torque on the agitator, calculated by EDEM, was the tangential contact force, multiplied by the distance from the center of mass of the particles resting on the agitator, to the contact point. Therefore, the amount of stationary particles on the agitator dictated the distance to be multiplied by the tangential contact force, which in turn affected the torque value during agitation. The average number of particles in contact with the agitator was inversely proportional to the agitator speeds. The number of particles in contact with the agitator was 508, 412 and 387 at agitator speeds 1000, 1500 and 2000 rpm, respectively. This implied that the torque values should have an order similar to the number of contact particles, where the lowest agitator speed should posses the highest torque value and the highest agitator speed should have the highest torque values. In order to translate the torque into input energy, the torque values were multiplied by the agitator speed, which created the proportional differences of the input energy curves, relative to the agitator speeds as shown in Figure 5-14(a). On the other hand, the output energies, kinetic and rotational energies were individually calculated by EDEM based on the particle velocities and rotational velocities. The proportional differences of the output energy curves, relative to the 157 agitator speeds, as shown in Figure 5-14(b) were similar to the input energy, Figure 5-14(a). The results agreed with the empirical power equation of Gao’s et al. (1996), (Equation 2-4). This equation related the mill power consumption to the agitator speed to the power of 1.429, where . Since power is the product of torque and agitator speed ( direct substitution, ( 0.429 ( ), then with , the torque would be directly proportional to the power of ). This implied that the effect of the agitator speed (N) on the power/energy was more significant when compared to its effect on torque, which explained the insignificant response of the torque to the agitator speed when compared to the power. 0.40 0.35 Torque (Nm) 0.30 0.25 0.20 0.15 0.10 0.05 0.00 0 5 10 15 Time (sec) 15 per. Mov. Avg. (1000) 15 per. Mov. Avg. (1500) 15 per. Mov. Avg. (2000) Figure 5-13: Torque vs. Simulation Time 8.0 (a) (b) 0.25 0.20 6.0 Output Energy Input Energy 7.0 5.0 4.0 3.0 2.0 0.15 0.10 0.05 1.0 0.0 0.00 0 5 10 15 0 Time (sec) 15 per. Mov. Avg. (1000) 15 per. Mov. Avg. (1500) 5 10 15 Time (sec) 15 per. Mov. Avg. (2000) 15 per. Mov. Avg. (1000) 15 per. Mov. Avg. (1500) 15 per. Mov. Avg. (2000) Figure 5-14: Instantaneous Energy vs. Time Simulation, a) Input Energy, b) Output Energy 158 Despite the fact that the model agreed with other empirical mathematical models that related the power to agitator speed (Gao’s et al., 1996), the relationship between energy utilization and types of forces was not entirely understood. Energy input was utilised as friction, impact, linear and rolling velocities, tangential forces and normal forces. From the effective energy percent ratio plots for the three agitator speeds in Figure 5-11(d), it could be deduced that at a speed of 1500 rpm, the energy input was used differently than at other agitator speeds. EDEM would track and save the tangential and normal forces, which were then exported for further analysis. 5.4.1.3 Forces Distribution Stirred milling exposes the particles to both fracture and attrition. Fracture is due to impact and compressive forces, which could be translated using a computer model into the normal component of the forces applied on the particles. Attrition breakage is due to abrasion, which could be identified in a computer model as the tangential component of the forces applied on the particles. Maximum normal and tangential forces, for each time step, and at each section in the mill (sections A, B and C) were exported, and their averages were calculated over the total simulation time. The highest normal and tangential forces occurred primarily in section A, due to the highest number of particles in this section. A higher agitator speed generated consistent higher normal forces in all three sections of the mill. Tangential force values were not significantly different between the three agitator speeds; however, there was a trend where the agitator speed of 1500 rpm produced higher tangential forces than the 1000 and 2000 rpm. The magnitude of the average normal forces were approximately 6.8 and 7.3 times more than the tangential forces for 1000 and 2000 rpm, respectively, while normal forces for the 1500 rpm were 5.2 times more than the tangential forces. Detailed force values are shown in Table 5-5. 159 Table 5-5 : Maximum Normal and Tangential Forces Maximum Normal Forces (N) Maximum Tangential Forces (N) RPM A B C A B C 1000 2.0 1.6 0.8 0.3 0.2 0.1 1500 2.3 1.9 1.2 0.5 0.4 0.2 2000 2.7 2.3 1.7 0.4 0.3 0.2 The results indicated that an agitator speed of 1500 rpm would expose the particles to about 26% more tangential forces than normal forces, compared to the 1000 and 2000 rpm. This indicated that more abrasion was likely occurring at 1500 rpm than the lower or higher agitator speeds. Since the energy input to the mill was not fully utilized by the particles at 1500 rpm (less energy efficiency), the particle dynamics at 1500 rpm were different than at the other agitator speeds. As for the 1000 and 2000 rpm, the dominant forces were the compressive forces, which would be translated to fracture breakages rather than abrasion in actual grinding operation. 5.4.1.4 Average Force Distribution The force distribution across the mill was assessed qualitatively via snap shot images at instantaneous times. The images were along section A-A of the mill or across the center between the discs, section B-B, as shown in Figure 5-15(a) and (b). 160 A (a) A B (b) B Figure 5-15: Mill Cross Section (a) Along the Mill A-A (b) Across the Center Between the Discs B-B As shown in Figure 5-12, the effective energy ratio versus residence time response stabilized at the 8th second, at an agitator speed of 1000 rpm, and at the 5th second at the agitator speeds of 1500 rpm and 2000 rpm. The normal and tangential forces were similarly distributed across the mill, but the magnitude of the maximum normal forces was five times more than the tangential forces. An example of the normal and tangential forces distribution, both along and across the mill, are shown in Figure 5-16 and Figure 5-17. 161 (a) (b) Figure 5-16: (a) Normal and (b) Tangential Forces Distribution in Section A-A for 1000 rpm run 162 (a) Lifting Section (b) Figure 5-17: (a) Normal and (b) Tangential Forces Distribution in Section B-B for 1000 rpm 163 The effect of the agitator speed on normal force distribution is presented in Table 5-6. The higher agitator speed would drive the particles out and away from the agitator towards the inner wall of the mill chamber, via centrifugal acceleration forces, as shown in section A-A. The forces were higher in the middle section between the discs at the medium agitator speed, 1500 rpm. The radial distribution of the normal forces, section B-B, was similar for the three agitator speeds. The forces in the lifting section possessed average values of 3x10-3 N normal forces and 6x10 -4 N tangential force, whereas the highest force values were closer to the inner chamber wall, with different intensities according to the agitator speed. The force distribution dissipated at the classifier section, but did not completely disappear. In other words, grinding occurred throughout the mill, but the highest grinding forces were between the discs. 164 Table 5-6: Normal Forces Distribution Across the Mill at 1000, 1500 and 2000 rpm Agitator Speed 1000 rpm Section A-A Section B-B 1500 rpm 2000 rpm 165 5.4.2 Galena and Media Particles Runs Since this study incorporated the effect of different material properties on the mill performance, 19,407 particles similar to galena properties were added to the system. The total number of media plus galena particles in the system totalled 64,182 particles. Accordingly, the iteration time of the simulation run increased drastically, due to the increased number of particles in the system. Therefore, the simulation runs were shortened to 5 seconds instead of 15 seconds, and only 2 agitator speeds were tested, 1500 and 2000 rpm. 5.4.2.1 Particle Distribution The particle distribution across the mill was evaluated separately, based on the type of particles. After running the model on the mixed media plus galena, the media particles were distributed across the three sections of the mill with the same distribution as the run with only media. The spread of the particles across the three sections was faster with the presence of galena in the system compared to media-only runs (Figure 5-18, a, c). For the galena run at 1500 rpm, the number of particles in section A did not change much by the 5 th second. The number of galena particles at the same agitator speed in sections B and C were equal by the 2nd second, with 60 000 particles in each section, (Figure 5-18 b). At 2000 rpm (Figure 5-18d), the number of galena particles in section C was greater than in section B. 166 (a) 25000 10000 20000 8000 A 15000 B C 10000 5000 6000 A 4000 B C 2000 0 0 0 1 2 3 4 0 5 1 2 3 4 5 Time (sec) Time (sec) G2000 RPM - Media G2000 RPM - Galena (c) 25000 10000 20000 8000 A 15000 B C 10000 5000 Number of Particles Number of Particles (b) G1500 RPM - Galena Number of Particles Number of Particles G1500 RPM - Media (d) (a) 6000 A 4000 B C 2000 0 0 0 1 2 3 4 5 0 1 2 3 4 5 Time (sec) Time (sec) Figure 5-18: Number of Particles Distribution Across the Mill: (a) Media distribution at 1500 rpm; (b) Galena distribution at 1500 rpm; (c) Media distribution at 2000 rpm; (d) Galena distribution at 2000 rpm 167 Galena (a) Media (b) Media (c) Figure 5-19: Initial Particle Distribution at Time Zero: (a) Radial Direction, section B-B; (b) Linear Direction, section A-A, (c) Isometric corss section Visual evaluation of the galena particle mixing showed that the distribution became more homogenous by the end of the 5th second. It was presumed that 5 seconds were not enough for complete homogenization and proper mixing of the galena and media particles. Agitator speed did not show a major effect on mixing and homogenizing the two types of particles (Table 5-7 and Table 5-8). 168 Table 5-7: Mixed Media and Galena Particles Distribution at 1500 rpm Simulation Time Radial Section B-B Linear Section A-A Isometric 1st Second 1500 rpm 2.5th Second 1500 rpm 5th Second 1500 rpm 169 Table 5-8: Mixed Media and Galena Particles Distribution at 2000 rpm Simulation Time 1st Second 2.5th Second 5th Second 2000 rpm 5.4.2.2 Maximum Forces Distribution The maximum normal and tangential forces over the 5 second simulation run were exported for media and galena particles for agitator speeds tested, 1500 and 2000 rpm. Galena particles possessed the highest force values for both speeds. The detailed force distribution is shown in Table 5-9. Both the tangential and normal forces on the galena particles were higher than on the media particles. The average tangential forces of the galena particles were 24% and 31% higher than media particles for the agitator speeds 1500 and 2000 rpm, respectively. The average normal forces of the galena particles were 4% and 8% higher than the media particles for the agitator speeds 1500 and 2000 rpm, respectively. The agitator speed had a direct effect on the forces encountered by the particles, based on the particle type. By increasing the agitator speed, the average increase of the tangential forces of the galena particles, relative to the media particles, was 24%. On the other hand, the average increase of the normal forces of the galena particles, relative to the media particles, was 50%. The data implied that the major breakage mode of galena particles was abrasion, since tangential forces were dominant. By increasing the agitator speed, the average increase of the normal forces 170 on the galena particles relative to the media particles was almost double. The data agreed with the morphology results, where the galena concentrate breakage mode was dominantly abrasion at low agitator speed, and turned into fracture at a higher agitator speed. Table 5-9: Maximum Normal and Tangential Forces Distribution Maximum Normal Forces (N) Maximum Tangential Forces (N) RPM A B C A B C 1500 Media 4.4 3.5 4.7 1.1 0.9 1.1 1500 Galena 4.7 4.1 4.3 1.6 1.4 1.2 2000 Media 4.5 4.4 4.1 1.0 1.1 1.0 2000 Galena 5.4 3.7 5.0 1.8 1.1 1.5 5.4.2.3 Average Force Distribution Quantitative analysis of the force distribution across the mill showed that grinding occurred throughout the mill, and that it increased at the classifier section. The media-only runs showed no grinding occurring at the classifier section for both agitator speeds (1500 and 2000 rpm), as shown in Figure 5-20 and Figure 5-21. The classifier section was populated by a higher number of particles, especially galena, by the 2nd second, which in turn created more interaction between the particles. The galena particles were heavier than the media, which created a higher inertia once the particles were put in motion. The inertia was in addition to the overall higher number of particles in the mill that affected the particle kinematics within the same volume of the mill chamber. At high agitator speed (2000 rpm) the particles spread towards the inner walls of the mill chamber with high values of normal forces, (Figure 5-21 a). The highest values of normal forces were under the agitator discs, and the particles were cascading closer to the agitator shaft 171 than was the case with media runs, as shown in Figure 5-20b, Figure 5-21b and section B-B in Table 5-6. (a) (b) Figure 5-20: Normal Forces Distribution at 1500 rpm (a) Section A-A; (b) Section B-B (a) (b) Figure 5-21: Normal Forces Distribution at 2000 rpm (a) Section A-A; (b) Section B-B 5.5 Conclusion A computer simulation of the Isa-Mill was included in this research in order to further understand the forces, energies and particle distribution across the mill at different operating conditions, as well as the interaction of the particles relative to each other using the Discrete Element Method. 172 Almost all computer models require a degree of compromise and deviation from an actual system, due to the intensive computational requirements of such models. It was believed that the parameters chosen for the basic simulation runs were the most appropriate based on the computational abilities of the computer. The parameters chosen were based on a series of simulation runs which evaluated each parameter individually. The parameter levels selected brought the model close to a real IsaMill operation. The simulation runs had very good association with the particle breakage mechanisms observed in the morphology study. The types of forces encountered in the model were correlated to the type of particle breakages presented by the morphology analysis. It was observed that the agitator speed 1500 rpm exposed the media particles to 26% more tangential forces than normal forces when compared to agitator speeds of 1000 and 2000 rpm. This observation was similar to morphology results for quartz, where abrasion was dominant at the medium agitator speed of 1500 rpm. On the other hand, the dominant forces at 1000 and 2000 rpm agitator speeds were normal, compressive forces, which were equivalent to fracture breakage in an actual grinding process. It was also concluded that the media particle dynamics at 1500 rpm were different, as the effective energy ratio was the lowest at this agitator speed, when compared with 1000 and 2000 rpm. In order to understand the effect of the different particle properties on the forces generated and their dynamics in the mill, particles whose properties were similar to galena properties were added to the system. However, due to the vast number of particles in the system which were drastically hindering the simulation time iteration, media and galena runs were limited to 5 seconds. It was observed that the media particle distribution across the mill over the 5 seconds 173 was similar to the runs with only media particles in the system. The galena particles behaved differently. The number of galena particles in the first section of the mill, section A, slightly decreased as time elapsed. Whereas for the medium agitator speed (1500 rpm) the particles in the middle and classifier sections, sections B and C, increased up to an equal number of particles, 60 000, by the 2nd second. At the high agitator speed (2000 rpm), the number of particles in section C was slightly more than the number of particles in section B. Visual examination of media and galena particles mixing and homogenizing showed that five seconds were not quite enough time in order to reach a stable, homogenized system. On the other hand, quantitative analysis of the media and galena particle forces provided some insight into the type of breakage that the different types of particles were exposed to in the mill at different agitator speeds. The data agreed with the morphology results, that the major breakage mode of galena particles was abrasion, since tangential forces were dominant. Morphology results also showed that by increasing the agitator speed, a fracture breakage mode started to show, and this breakage along grain boundaries. Those results complied with the model findings, which demonstrated that at the higher agitator speed, the normal forces of the galena particles, relative to the media particles, increased by 50%. Normal forces were translated into compressive forces that would consequently impose fracture breakage along the grain boundaries. The coherent findings of the DEM model, with the equivalent observations of the morphology analysis, contributed to the understanding of the particle breakage mode and mechanism. Thus, a DEM model could be used to predict types of particle breakages in stirred milling, based on the material properties of the particles and mill operating conditions. 174 6. Conclusions and Recommendations 6.1 Conclusions The major objective of this research was to gain a comprehensive understanding of how operating parameters would affect particle breakage mechanisms in stirred mills. In order to achieve the objective, state of the art researches performed on stirred mills were reviewed. It was recognised that the operation and performance of these mills was only empirically understood. Breakage modes of the particles under different grinding mechanisms were morphologically analysed. The literature was reviewed in order to summarize the relationship between breakage mode and surface texture (morphology features). The effect of different operating conditions and different material properties on grinding performance was analysed via particle size reduction analysis and energy consumption. Experimental results were supported by discrete element modeling (DEM). None of the models performed to date related the effect of different particle properties on each other. The computer simulation models performed on the IsaMill were over simplified. The effect of the media classifier, and the classifier on the particle flow and distribution were not investigated. The computer model in this study was designed to be as close as possible to the real case scenario, so that the forces and energy distributions across the mill were quantitatively analysed. 175 The conclusions of the experimental work can be summarized as follows: 6.1.1 Experimental Work The parameters addressed in the experimental work were material properties, machine input energy, in the form of different agitator speeds, and residence time effect on breakage behaviour. The materials chosen for the set of experiments were quartz and galena concentrate that were extreme in their hardness values as well as their specific gravity. The other two materials chosen were a mixed sample of galena and quartz with a ratio of 1:6, and a similar but locked lead-zinc ore sample from the SAG discharge of Red Dog mine. The machine input energy was defined by three agitator speeds which were 1000, 1500 and 2000 rpm. The residence time effect on grinding was studied by circulating the material into the mill five times, so that the same particles would be exposed to the same grinding mechanism for a longer time. The flow rate was set at 3.5 L/min, which was the highest flow rate the machine could handle. Material type had a major effect on particle size distribution and size reduction at the three agitator speeds evaluated. Quartz did not break efficiently at the 1000 rpm agitator speed, which indicated that there was a minimum energy input required to initiate and break the quartz particles. On the other hand, the 1000 rpm was enough for the galena to break. The extreme agitator speed of 2000 rpm, broke the galena particles down to their grinding limit after the first pass through the mill. 176 The effect of the quartz breakage mechanism was dominant over the galena, due to the higher content of quartz compared to galena, ratio of 6:1. The initial breakage rate of the 4 materials tested increased linearly with the increase of the agitator speed. However, breakage rates were almost one order of magnitude higher for the soft minerals than the hard minerals. Average breakages were directly affected by how close the particle sizes were to their grinding limit. Breakage rate decreased once it reached the grinding limit of the material. The breakage rate was linear for most of the grinds, except for the quartz at 2000 rpm, the galena concentrate at 1000 rpm, the mix at 2000 rpm and the lead-zinc ore sample at 1500 and 2000 rpm. At these agitator speeds an exponential breakage rate trend was revealed. This observation indicated that quartz, the harder mineral would break faster at the higher agitator speed, whereas galena, the soft mineral, would break faster at a lower agitator speed. The breakage mechanism of the mix quartz and galena sample followed the harder mineral mechanism rather than the softer mineral. As for the leadzinc ore sample breakage rate, it was faster at the 1500 and 2000 rpm, which indicated that it had a high content of hard minerals, as well as a reasonable amount of soft minerals. The hard minerals lead to fast breakage rate at high agitator speed and the soft minerals lead to fast breakage rate at intermediate agitator speed. Energy consumption was evaluated using the typical signature plots. There was some overlap in the energy required versus targeted size between the different agitator speeds; however, the overlap was not consistent. The analysis also revealed that the data fit differently to the power and exponential equations, based on the type of material and agitator speed selected for grinding. 177 The agitator speed has a higher effect on the mill’s effective energy ratio than the type of mineral it is grinding. The higher the agitator speed, the better use of the energy input to the mill during the grinding process. The amount of energy required to break one micron was directly affected by the type of material being ground. Soft minerals required less energy per micron at all agitator speeds. Thus, the softer minerals would break faster at lower agitator speed than harder minerals and vice versa. 6.1.2 Morphology Morphology analysis assists in understanding the breakage behaviour of the different material properties at different stress intensity inputs, in the form of the agitator speeds. Results from this research demonstrated that there was a potential to understand grinding versus liberation, beyond the obvious fact that the smaller the particles, the more the minerals will be liberated. The major morphological features analysed were the surface roughness, roundness and elongation of the particles. Surface roughness dictates the type of breakage, whether it is along the grain boundaries or across them. The breakage along the grain boundaries should create rougher surfaces and less circular particles. Roughness values were assessed using Clemex software, and results were biased to smooth counts. Accordingly, a manual point count method was developed and tested. Despite the fact that there was about 6% difference between counters, based on their judgement of the degree of roughness of the particles, the trends of the data of the manual point count and Clemex software results were similar and correlated. Initial breakage results according to the Clemex analysis coincided with the manual point counting and stacked charts. The galena concentrate had a trend of fracture 178 breakage along grain boundaries, at the higher agitator speed of 2000 rpm, whereas quartz had a trend of abrasion breakage, across grain boundaries, at the same agitator speed. This suggested that if the target was to liberate minerals similar to galena, then a higher agitator speed would be recommended. The effect of residence time reflected a similar trend for Clemex analysis and manual point counting, using Pearson’s time correlation. Increasing residence time promoted abrasion breakage (transgranular breakage) for both galena concentrate and quartz. Visual observations and trends counts of rough (R4+R5) and smooth (R1+R2) particles showed that stirred mills broke the particles via both abrasion and fracture. The overall trends for both types of materials (quartz, and galena concentrate) demonstrated that the amount of rough particles was always higher than smooth particles. This observation could be interpreted as fracture being the breakage mechanism that was dominant in the grinding system, along with some abrasion. This hypothesis was built on the observation that the particles size decreased during the grinding process, as per the PSD analysis. Therefore, in spite of the fact that the size fractions counted were similar, they were the progeny of coarser fractions. The trends proved that an abrasion breakage mechanism increased with time and existed in the stirred milling process, but that fracture was equally present, if not dominant during initial breakages, and for fine fractions. If the target was to liberate, soft mineral such as galena, then higher agitator speed as well as short residence time in the mill would be recommended and vice versa for hard minerals. 179 Flow dynamics in the mill were not exclusively dependent on the hardness of the mineral. Liberation analysis of the lead-zinc ore sample showed that pyrite and quartz were close in hardness values. Mohs hardness values were 6.5 and 7, respectively. Liberation dependent on the specific gravity of the minerals, which dictated the flow dynamics in the mill and surface energy per unit mass. It was learned from the morphology analysis that minerals, similar to galena properties, would break faster at lower agitator speeds. However, breakage would be achieved via abrasion. In order to impose intergranular breakage on minerals similar to galena properties, a higher agitator speed and shorter residence time would be recommended. In other words, mode of breakage should be a priority over breakage rate in order to produce liberated particles. 6.1.3 Computer Model Discrete Element Modeling was utilized in this study to further understand the forces, energies and particle distributions across the mill at different operating conditions. Computer modeling is a data intensive computing system which demands compromise and deviation from the parameters of an actual system. To create a model close to a real IsaMill, a series of simulation runs were performed in order to evaluate each parameter individually. The parameters were: - The number of particles, - Material properties of the mill and of the particles, - Presence versus absence of fluid flow. 180 The computer model simulation runs produced a very good association between the particle breakage mechanisms observed by the morphology results, and the types of forces encountered in the model. A summary of the observations from the simulation runs were as follows: - The medium agitator speed, 1500 rpm, exposed the media particles to 26% more tangential forces than normal forces, when compared to agitator speeds of 1000 and 2000 rpm. This observation was similar to morphology results for quartz, where abrasion was dominant at the medium agitator speed, 1500 rpm. On the other hand, the agitator speeds of 1000 and 2000 rpm as dominant forces were normal, compressive forces. - It was also concluded that the dynamics of the media particles in the mill at 1500 rpm were different than that of the 1000 and 2000 rpm agitator speeds, since the effective energy ratio was the lowest at 1500 rpm agitator speed. Particles with properties similar to galena were added to the system to understand the effect of the different particle properties on the forces generated, and their dynamics in the mill. However, due to the increased number of particles in the system which drastically hindered the simulation time iteration, the mixed particles, media and galena, runs were limited to 5 seconds. The galena and media particle simulation results can be summarized as follows: - Media particle distributions across the mill over the 5 seconds were similar to the runs with only media particles in the system. Galena particle distributions behaved differently. The number of Galena particles in the first section of the mill, section A, slightly decreased as time elapsed for the both agitator speeds, 1500 181 and 2000 rpm. The middle and classifier sections (B and C) both had 60 000 particles at 1500 rpm agitator speed by the 2nd second, but the number of particles increased in section C, compared to section B at the 2000 rpm agitator speed. - Visual examination of media and galena particles mixing and homogenizing showed that the five seconds were not enough to reach a stable, homogenized system. - The quantitative analysis of the type of forces generated by the media and galena particles agreed with the morphology results. The major breakage mode for galena was abrasion, since tangential forces were dominant. Morphology results also showed that by increasing the agitator speed, fracture breakage mode, that is breakage along grain boundaries, started to come into view. Those results complied with the model findings, which demonstrated that the higher agitator speeds increased the average increase of the normal forces of the galena particles relative to the media particles, by 50%. Normal forces were translated into compressive forces that would consequently impose fracture breakage, along the grain boundaries. - The coherent findings of the DEM model, along with the equivalent observations of the morphology analysis, contributed to the understanding of the particle breakage mode and mechanism. Thus, a DEM model could be used to predict types of particle breakages in stirred milling, based on the particle material properties and mill operating conditions. 182 6.2 Recommendations This work was a comprehensive study on the stirred mill operation and particle breakage. Some of the tools utilized in this study were new to the industry, such as the morphology analysis, and other tools were extensively used, such as the computer modeling. However, most of the computer models were analysed qualitatively, rather than quantitatively. Also, the correlation between the experimental and the computer models were rarely addressed in literature. Nevertheless, more work still needs to be performed on morphology, as well as the quantitative computing models is needed in order to fully understand the mill performance and operation so that knowledgeable operating conditions could be employed rather than applying empirical data. Recommendations for further work are summarized as follows: 6.2.1 Experimental and Morphology Perform a similar series of grinding experiments using multi-size grinding media to reach a real grinding limit of the material in question. Further investigation on the actual material properties that cause different types of breakage, fracture, or abrasion, such as hardness, specific gravity and crystal structure of the mineral. A complete, detailed liberation/morphology analysis for all size fractions, so that a proper liberation balance may be performed. 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International Journal for Computer-Aided Engineering and Software, 23(7), 749-770. 197 Appendices 198 Appendix A: Experimental Data Appendix A1: MSDS Sheets A1-1: Lead Concentrate Sample 199 200 201 202 203 A1-2: Quartz Sample 204 205 206 207 208 209 A1-3: SAG Discharge, Lead-Zinc Ore Sample 210 211 212 Appendix A2: Assay Analysis ISO 9001:2008 Certificate No. FS63170 Certificate of Analysis University of British Columbia - KM3009 Date: April 15th, 2011 Sample Silica Sample Galena Concentrate Lead Zinc Ore Silica Sample Galena Concentrate Lead Zinc Ore Pb Zn Fe Al2O3 Elements BaO CaO Cr2O3 Fe2O3 K2O MgO MnO 82.7 9.30 1.49 19.8 0.26 7.00 0.54 0.07 0.83 <0.01 - 0.11 0.03 0.87 0.05 <0.01 0.02 0.52 0.36 10.35 0.18 0.02 0.11 0.03 0.01 0.08 <0.01 <0.01 0.02 Na2O P2O5 SiO2 TiO2 0.19 0.17 0.10 0.05 - 92.1 0.34 31.7 0.06 <0.01 0.02 % % % % % % % % % % % Analytical Laboratory Manager 213 Appendix A3: Measured Specific Gravity, SG 214 Appendix A4: Experimental Data Table A4-1: Quartz Experimental Data at 1000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore SG 2.629 7.19 3.662 3.296 Target RPM 1000 Set Flow rate (L/min): ~ 3.5 77.10% 860 mL 15.03 sec ===> Pass Number Start RPM Cummlative Test Time (min) Test Time (min) 1 1000 6.82 6.82 1.04 2 1000 13.35 6.53 3 1000 19.88 4 1000 5 1000 Feed material type: Starting Flow Rate: Mix 3.433 Residence Time/4L mill Temp (oC) volume (min) Date: Jan 29, '10 Test No: Q1000 L/min Net Calculated Calculate Energy d Power (KWhr) (KW) Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) 21 0.4 0.7 3.43 92.09 0.11 0.023 0.2 2.03 22 0.35 0.7 3.52 92.19 0.10 0.022 0.2 6.53 3.02 22.5 0.4 0.7 3.51 92.29 0.10 0.022 0.2 26.30 6.42 4.00 24 0.4 0.7 3.44 92.38 0.09 0.021 0.2 32.68 6.38 4.97 25 0.4 0.7 3.34 92.47 0.09 0.021 0.2 Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Silica: 30.8% solids wt Solid Mass 10kg + Liquid 22.5L Galena: 54.5% solids wt Solid Mass 10kg + Liquid 8.3L 14.29% solids vol Solid Mass 15kg+Liquid 33.7L 14.29% solids vol Solid Mass 15kg+Liquid 12.5L 215 Solid Mass 5kg+Liquid 11.2L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 91.98 KWhr Table A4-2: Quartz Experimental Data at 1500 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore SG 2.629 7.19 3.662 3.296 Target RPM 1500 77.10% 870 mL 15.06 sec ===> Pass Number Start RPM Cummlative Test Time Test Time 1 1490 6.97 6.97 1.06 2 1490 13.87 6.90 3 1490 20.55 4 1490 5 1490 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Mix Date: Jan 29, '10 Test No: Q1500 ~ 3.5 max 3.466 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Energy (KWhr) Net Calculated Power (KW) 19.00 0.45 1.6 3.43 92.94 0.22 0.093 0.8 2.11 22.50 0.45 1.7 3.45 93.15 0.21 0.104 0.9 6.68 3.13 26.00 0.45 1.7 3.39 93.36 0.21 0.100 0.9 27.02 6.47 4.11 28.00 0.45 1.6 3.41 93.55 0.19 0.086 0.8 33.52 6.50 5.10 30.00 0.45 1.5 3.44 93.74 0.18 0.076 0.7 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Silica: 30.8% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 22.5L Solid Mass 15kg+Liquid 33.7L Solid Mass 5kg+Liquid 11.2L Galena: 54.5% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 8.3L Solid Mass 15kg+Liquid 12.5L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 92.71 KWhr 216 Table A4-3: Quartz Experimental Data at 2000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore SG 2.629 7.19 3.662 3.296 Target RPM 2000 77.00% 965 mL 16.94 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1940 6.92 6.92 1.05 2 1950 13.17 6.25 3 1950 19.42 4 1950 5 1950 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Mix Date: Jan 29, '10 Test No: Q2000 ~ 3.5 max 3.418 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Energy (KWhr) Net Calculated Power (KW) 23.00 0.50 2.7 3.46 95.42 0.34 0.18 1.6 2.00 29.00 0.50 2.5 3.51 95.70 0.28 0.15 1.4 6.25 2.95 31.00 0.55 2.5 3.37 95.98 0.28 0.15 1.4 25.58 6.17 3.89 35.00 0.55 2.5 3.40 96.25 0.27 0.14 1.4 32.10 6.52 4.88 37.00 0.55 2.5 3.52 96.55 0.30 0.15 1.4 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Silica: 30.8% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 22.5L Solid Mass 15kg+Liquid 33.7L Solid Mass 5kg+Liquid 11.2L Galena: 54.5% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 8.3L Solid Mass 15kg+Liquid 12.5L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 95.08 KWhr 217 Table A4-4: Galena Concentrate Experimental Data at 1000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 1000 77.00% 870 mL 14.81 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1000 3.30 3.30 0.90 2 1000 6.73 3.43 3 1000 9.73 4 1000 5 1000 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Jan 30, '10 Test No: G1000 ~ 3.5 max 3.525 Residence Time/4L mill Temp (oC) volume (min) L/min Net Calculated Calculated Power Power (KWhr) (KW) Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) 23.00 0.4 0.8 3.51 98.30 0.06 0.02 0.3 1.85 23.50 0.4 0.8 3.53 98.36 0.05 0.02 0.3 3.00 2.67 24.00 0.4 0.8 3.35 98.40 0.05 0.02 0.3 12.68 2.95 3.48 24.00 0.5 0.7 3.52 98.44 0.04 0.01 0.2 15.55 2.87 4.26 24.50 0.5 0.7 3.39 98.49 0.04 0.01 0.2 Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Silica: 30.8% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 22.5L Solid Mass 15kg+Liquid 33.7L Solid Mass 5kg+Liquid 11.2L Galena: 54.5% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 8.3L Solid Mass 15kg+Liquid 12.5L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 98.24 KWhr 218 Table A4-5: Galena Concentrate Experimental Data 1500 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 1500 77.00% 870 mL 14.69 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1500 3.87 3.87 1.06 2 1500 7.73 3.87 3 1500 11.50 4 1500 5 1500 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Jan 30, '10 Test No: G1500 ~ 3.5 max 3.553 Residence Time/4L mill Temp (oC) volume (min) L/min Net Calculated Calculated Power Power (KWhr) (KW) Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) 21.00 0.70 1.9 3.50 99.61 0.13 0.07 1.10 2.12 23.00 0.80 1.55 3.46 99.72 0.11 0.05 0.75 3.77 3.15 25.50 0.80 1.8 3.48 99.84 0.12 0.06 1.00 15.35 3.85 4.21 27.00 0.60 1.6 3.63 99.95 0.12 0.05 0.80 18.87 3.52 5.17 30.00 0.70 1.6 3.44 100.06 0.11 0.05 0.80 Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Silica: 30.8% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 22.5L Solid Mass 15kg+Liquid 33.7L Solid Mass 5kg+Liquid 11.2L Galena: 54.5% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 8.3L Solid Mass 15kg+Liquid 12.5L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 99.48 KWhr 219 Table A4-6: Galena Concentrate Experimental Data at 2000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 2000 77.00% 880 mL 15.09 sec ===> Pass Number start RPM Cumulative Test Time Test Time 1 2070 * 3.88 3.88 1.06 2 1980 7.48 3.60 3 1980 10.93 4 1980 5 1980 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Jan 30, '10 Test No: G2000 ~ 3.5 max 3.499 Residence Time/4L mill Temp (oC) volume (min) L/min Net Calculated Calculated Power Power (KWhr) (KW) Pressure (bar) Power (KW) Flow Rate (L/min) Cumulative Energy (KWhr) Energy Read (KWhr) 22.00 1.4/2.3 3.50 3.58 101.09 0.22 0.16 2.40 2.05 31.00 1.30 3.20 3.46 101.30 0.21 0.13 2.10 3.45 3.00 34.00 1.10 3.10 -- 101.49 0.19 0.12 2.00 14.52 3.58 3.98 38.00 1.10 3.10 -- 101.68 0.20 0.12 2.00 17.73 3.22 4.86 42.00 1.00 3.10 3.47 101.87 0.18 0.11 2.00 Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear before second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. * The pressure during pass1 was approaching the threshold of the machine (2.6 bar), accordingly the rpm was reduced from 2070 to 1980 to avoid tripping off the machine. Silica: 30.8% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 22.5L Solid Mass 15kg+Liquid 33.7L Galena: 54.5% solids wt 14.29% solids vol Solid Mass 10kg + Liquid 8.3L Solid Mass 15kg+Liquid 12.5L Solid Mass 5kg+Liquid 4.17L Initial Energy @ T0 = 100.872 KWhr 220 Table A4-7: Mix Quartz and Galena Concentrate Experimental Data at 1000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 1000 77.10% 910 mL 15.28 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1000 6.97 6.97 1.09 2 1000 13.17 6.20 3 1000 18.73 4 1000 5 1000 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Test No: M1000 ~ 3.5 max 3.573 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Power (KWhr) Net Calculated Power (KW) 16.00 0.40 0.80 3.49 141.08 0.11 0.03 0.30 2.06 18.00 0.35 0.70 3.35 141.16 0.09 0.02 0.20 5.57 2.93 19.00 0.40 0.70 April, 05, '10 141.24 0.08 0.02 0.20 24.20 5.47 3.79 20.00 0.40 0.70 3.55 141.32 0.08 0.02 0.20 29.55 5.35 4.63 20.00 0.40 0.70 3.57 141.40 0.08 0.02 0.20 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Mix: 36% solids wt 14.29% solids vol April 5, 2010 Solid Mass 12.5kg + Liquid 22.5L Initial Energy @ T0 = 140.96 KWhr 221 Table A4-8: Mix Quartz and Galena Concentrate Experimental Data at 2000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 2000 77.30% 900 mL 15.14 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1950 7.30 7.30 1.11 2 1950 13.87 6.57 3 1950 20.30 4 1950 5 1950 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Test No: M2000 ~ 3.5 max 3.567 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Power (KWhr) Net Calculated Power (KW) 21.00 0.70 3.00 3.57 142.62 0.40 0.23 1.90 2.11 22.00 0.70 3.00 3.51 142.96 0.34 0.21 1.90 6.43 3.09 22.50 0.70 2.70 3.43 143.28 0.31 0.17 1.60 27.47 7.17 4.18 24.00 0.70 2.70 3.61 143.61 0.34 0.19 1.60 33.43 5.97 5.08 25.00 0.70 2.60 3.51 143.89 0.28 0.15 1.50 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Mix: 36% solids wt 14.29% solids vol April 5, 2010 Solid Mass 12.5kg + Liquid 22.5L Initial Energy @ T0 = 142.22 KWhr 222 Table A4-9: Lead-Zinc Ore Experimental Data at 1000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 1000 78.00% 900 mL 15.54 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 980 4.38 4.38 0.67 2 980 8.87 4.48 3 980 12.95 4 980 5 980 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Test No: O1000 ~ 3.5 max 3.475 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Power (KWhr) Net Calculated Power (KW) 16.00 0.40 0.70 3.55 144.06 0.07 0.01 0.20 1.35 17.00 0.40 0.70 --- 144.12 0.07 0.01 0.20 4.08 1.97 19.00 0.40 0.70 3.43 144.18 0.06 0.01 0.20 16.98 4.03 2.58 20.00 0.40 0.70 --- 144.24 0.06 0.01 0.20 20.68 3.70 3.15 21.00 0.40 0.70 3.56 144.30 0.05 0.01 0.20 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Mix: 36% solids wt 14.29% solids vol April 5, 2010 Solid Mass 12.5kg + Liquid 22.5L Initial Energy @ T0 = 143.99 KWhr 223 Table A4-10: Lead-Zinc Ore Experimental Data at 1500 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 1500 78.00% 840 mL 15.47 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1500 5.32 5.32 0.81 2 1510 11.00 5.68 3 1510 15.73 4 1510 5 1510 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Test No: O1500 ~ 3.5 max 3.468 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (kWhr) Calculated Energy (KWhr) Net Calculated Power (KW) 18.00 0.50 1.60 3.49 144.77 0.16 0.07 0.80 1.67 18.00 0.50 1.60 --- 144.94 0.17 0.08 0.80 4.73 2.39 24.00 0.50 1.50 3.58 145.07 0.14 0.06 0.70 20.88 5.15 3.18 26.00 0.50 1.50 --- 145.22 0.14 0.06 0.70 25.40 4.52 3.86 27.00 0.50 1.50 3.24 145.34 0.13 0.05 0.70 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Mix: 36% solids wt 14.29% solids vol April 5, 2010 Solid Mass 12.5kg + Liquid 22.5L Initial Energy @ T0 = 144.61 KWhr 224 Table A4-11: Lead-Zinc Ore Experimental Data at 2000 rpm ISA-Mill Grind Tests Data Sheet Quartz Galena Ore Mix SG 2.629 7.19 3.662 3.296 Target RPM 2000 77.20% 920 mL 15.59 sec ===> Pass Number start RPM Cummlative Test Time Test Time 1 1980 5.08 5.08 0.77 2 1980 10.38 5.30 3 1990 15.22 4 1990 5 1990 Feed material type: Set Flow rate (L/min): Starting Flow Rate: Date: Test No: O2000 ~ 3.5 max 3.541 L/min Pressure (bar) Power (KW) Flow Rate (L/min) Cummulative Energy (KWhr) Energy Read (KWhr) Calculated Energy (KWhr) Net Calculated Power (KW) 23.00 0.60 3.00 3.67 146.09 0.27 0.16 1.90 1.58 26.00 0.70 2.80 --- 146.35 0.27 0.15 1.70 4.83 2.31 31.00 0.70 2.70 --- 146.59 0.23 0.13 1.60 20.05 4.83 3.05 33.00 0.70 2.70 --- 146.92 0.33 0.13 1.60 26.42 6.37 4.02 41.00 0.70 2.70 3.50 147.12 0.21 0.17 1.60 Residence Time/4L mill Temp (oC) volume (min) Discarded first 40 seconds of the first Run. Flush mill with water until water comes out clear beore second Test. Non-stop between passes, consistent flow pattern in the mill. First 30 seconds are in the feed tank, since what is left in the mill is from previous pass. Mix: 36% solids wt 14.29% solids vol April 5, 2010 Solid Mass 12.5kg + Liquid 22.5L Initial Energy @ T0 = 145.82 KWhr 225 Appendix A5: Cyclone Correlation Factor Table A5: Cyclone Correlation Factor for Quartz, Galena Concentra, Mixed Quartz and Galena, Lead-Zinc Ore Samples Temp (oC) Flow Rate (mm/min) Elutriation Time (min) SG Material Total Correction Factor Measure Correction Factor Measure Correction Factor Measure Correction Factor Measure Correction Factor Quartz 5.3 1.225 181 0.992 20 0.995 2.629 1.00 1.161 Galena Concentrate 5.2 1.225 180 0.992 20 0.995 7.19 0.51 0.592 Mixed Quartz and Galena 7.7 1.180 180 0.992 20 0.955 3.296 0.85 0.950 Lead-Zinc Ore 7.8 1.180 180 0.992 20 0.995 3.662 0.77 0.861 226 Appendix B: Experimental Results Appendix B1: Mass of Solids Calculations Based on Volume Percent Target % Solids by Volume = 14.29 % 3 SG = gm/cm (kg/L) SG-Galena = 7.19 kg/L SG-Silica = 2.63 kg/L SG-Ore = 3.662 kg/L SG-Mix = 3.296 kg/L Mass Solids Galena = 27.0 kg Mass Solids Silica = 9.9 12.5 Liter of water 22.5 Liter of water kg ====> % Solids by weight : 54.5 for 15 kg solids => 30.5 for 10 kg solids => 37.9 for 10 kg solids => kg MassSolids Ore = 13.7 16.4 Liter of water Mass Solid Mix = 12.4 kg 35.5 for 10 kg solids => 18.2 Liter of water 227 Appendix B2: Rosin Rammler Fit and Parameters Table B2-1: Rosin Rammler Parameters for Quartz at 1000 rpm Quartz - 1000 RPM Slope (b) (a) P80 R2 Feed 4.42 74.52 97.38 0.98 Q1000-P1 2.26 78.28 90.57 0.94 Q1000-P2 2.20 73.12 87.68 0.94 Q1000-P3 2.13 68.09 86.12 0.94 Q1000-P4 2.08 62.94 78.72 0.95 Q1000-P5 2.05 56.79 74.95 0.93 Pass Quartz - 1000 RPM - Pass 100 % Passing 90 Feed 80 RR-Feed 70 Q1000-P1 60 RR-P1 50 Q1000-P2 RR-P2 40 Q1000-P3 30 RR-P3 20 Q1000-P4 10 RR-P4 0 Q1000-P5 0.1 1 10 100 1000 RR-P5 Size (m) Figure B2-1: Rosin Rammler Fit superimposed on PSD for Quartz at 1000 rpm 228 Table B2-2: Rosin Rammler Parameters for Quartz at 1500 rpm Quartz - 1500 RPM Pass Slope (b) (a) P80 R 2 Q1500-P1 2.06 58.89 80.10 0.93 Q1500-P2 1.86 46.21 67.81 0.95 Q1500-P3 1.82 38.21 55.94 0.95 Q1500-P4 1.80 30.35 40.39 0.93 Q1500-P5 1.67 28.15 34.71 0.93 Quartz - 1500 RPM - Pass % Passing 100 90 Feed 80 RR-Feed 70 Q1500-P1 60 RR-P1 50 Q1500-P2 RR-P2 40 Q1500-P3 30 RR-P3 20 Q1500-P4 10 RR-P4 0 Q1500-P5 0.1 1 10 100 1000 RR-P5 Size (m) Figure B2-2: Rosin Rammler Fit superimposed on PSD for Quartz at 1500 rpm 229 Table B2-3: Rosin Rammler Parameters for Quartz at 2000 rpm Quartz - 2000 RPM Pass Slope (b) (a) P80 R 2 Q2000-P1 1.86 46.66 67.66 0.96 Q2000-P2 1.81 33.36 43.41 0.94 Q2000-P3 1.69 28.09 32.39 0.93 Q2000-P4 1.66 23.56 24.18 0.91 Q2000-P5 1.65 19.80 20.04 0.91 Quartz - 2000 RPM - Pass % Passing 100 90 Feed 80 RR-Feed 70 Q2000-P1 60 RR-P1 50 Q2000-P2 RR-P2 40 Q2000-P3 30 RR-P3 20 Q2000-P4 10 RR-P4 0 Q2000-P5 0.1 1 10 100 1000 RR-P5 Size (m) Figure B2-3: Rosin Rammler Fit superimposed on PSD for Quartz at 2000 rpm 230 Table B2-4: Rosin Rammler Parameters for Galena at 1000 rpm Galena - 1000 RPM Slope (b) (a) P80 R2 Feed 1.34 60 96.6 0.96 G1000-P1 2.01 32 47.7 0.92 G1000-P2 1.69 33 33.8 0.92 G1000-P3 2.07 28 25.3 0.90 G1000-P4-2 2.08 21 21.1 0.91 G1000-P5-2 1.53 22 21.3 0.96 Pass Galena - 1000 RPM Feed % Passing 100 90 RR-Feed 80 G1000-P1 70 RR-P1 60 G1000-P2 RR-P2 50 G1000-P3 40 RR-P3 30 G1000-P4-2 20 RR-P4 10 G1000-P5-2 0 1 10 100 1000 RR-P5 size (m) Figure B2-4: Rosin Rammler Fit superimposed on PSD for Galena at 1000 rpm 231 Table B2-5: Rosin Rammler Parameters for Galena at 1500 rpm Galena - 1500 RPM Pass Slope (b) (a) P80 R 2 G1500-P1 2.02 22 23.4 0.89 G1500-P2 1.95 22 18.7 0.89 G1500-P3 1.99 21 17.2 0.89 G1500-P4 1.84 18 13.1 0.85 G1500-P5 1.75 16 11.9 0.82 Galena - 1500 RPM % Passing 100 Feed 90 RR-Feed 80 G1500-P1 70 RR-P1 60 G1500-P2 RR-P2 50 G1500-P3 40 RR-P3 30 G1500-P4-2 20 RR-P4 10 G1500-P5-2 0 RR-P5 1 10 100 1000 size (m) Figure B2-5: Rosin Rammler Fit superimposed on PSD for Galena at 1500 rpm 232 Table B2-6: Rosin Rammler Parameters for Galena at 2000 rpm Galena - 2000 RPM Pass Slope (b) (a) P80 R 2 G2000-P1 1.62 20 14.0 0.82 G2000-P2 1.69 17 13.2 0.89 G2000-P3-2 1.30 23 13.2 0.84 G2000-P4 1.20 18 12.7 0.84 G2000-P5 1.05 18 12.8 0.84 Galena - 2000 RPM % Passing Feed 100 RR-Feed 90 G2000-P1 80 RR-P1 70 G2000-P2 RR-P2 60 G2000-P3 50 RR-P3 40 G2000-P4 30 RR-P4 20 G2000-P5 10 RR-P5 0 1 10 100 1000 size (m) Figure B2-6: Rosin Rammler Fit superimposed on PSD for Galena at 2000 rpm 233 Table B2-7: Rosin Rammler Parameters for Mixed quartz and galena Sample at 1000 rpm Mix - 1000 Slope (b) (a) P80 R2 Feed 1.46 109.1 122.8 0.92 M1000-P1 1.47 109.5 119.9 0.95 M1000-P2 1.36 110.8 119.4 0.95 M1000-P3 1.32 88.39 109.8 0.97 M1000-P5 1.30 80.09 105.8 0.97 M1000-P4-2 1.35 72.66 100.9 0.96 Pass Mix - 1000 RPM % Passing 100 Feed 90 RR-Feed 80 M1000-P1 70 RR-P1 60 M1000-P2 RR-P2 50 M1000-P3 40 RR-P3 30 M1000-P4 20 RR-P4 10 M1000-P5 0 RR-P5 1 10 100 1000 size (m) Figure B2-7: Rosin Rammler Fit superimposed on PSD for Mixed quartz and galena Sample at 1000 rpm 234 Table B2-8: Rosin Rammler Parameters for Mixed quartz and galena Sample at 2000 rpm Mix - 2000 Pass Slope (b) (a) P80 R M2000-P1 1.22 53.93 82.7 0.98 M2000-P2 1.19 29.94 47.3 0.99 M2000-P3 0.98 27.11 33.9 0.95 M2000-P4 0.85 20.66 22.5 0.89 M2000-P5 1.00 14.99 17.2 0.94 2 Mix - 2000 RPM % Passing 100 Feed 90 RR-Feed 80 M2000-P1 70 RR-P1 60 M2000-P2 RR-P2 50 M2000-P3 40 RR-P3 30 M2000-P4 20 RR-P4 10 M2000-P5 0 RR-P5 1 10 100 1000 size (m) Figure B2-8: Rosin Rammler Parameters for Mixed quartz and galena Sample at 2000 rpm 235 Table B2-9: Rosin Rammler Parameters for Lead-Zinc Ore at 1000 rpm Ore - 1000 Slope (b) a P80 R2 Feed 1.12 59.52 96.2 0.97 O1000-P1 1.20 37.40 63.0 0.97 O1000-P2 1.20 34.30 56.2 0.97 O1000-P3 1.23 33.99 54.1 0.98 O1000-P4 1.20 29.75 44.5 0.98 O1000-P5 1.24 25.44 35.9 0.98 Pass Ore - 1000 RPM % Passing 100 Feed 90 RR-Feed 80 O1000-P1 70 RR-P1 O1000-P2 60 RR-P2 50 O1000-P3 40 RR-P3 30 O1000-P4 20 RR-P4 10 O1000-P5 RR-P5 0 1 10 100 1000 size (mm) Figure B2-9: Rosin Rammler Parameters for Lead-Zinc Ore at 1000 rpm 236 Table B2-10: Rosin Rammler Parameters for Lead-Zinc Ore at 1500 rpm Ore - 1500 Pass Slope (b) a P80 R O1500-P1 1.23 30.33 46.5 0.98 O1500-P2 1.22 24.92 31.9 0.97 O1500-P3 1.00 24.74 25.9 0.92 O1500-P4 0.89 21.03 20.0 0.86 O1500-P5 1.23 14.97 16.3 0.96 2 Ore - 1500 RPM 100 Feed 90 RR-Feed 80 O1500-P1 % Passing 70 RR-P1 60 O1500-P2 50 RR-P2 40 O1500-P3 30 RR-P3 20 O1500-P4 10 RR-P4 0 1 10 100 size (mm) 1000 O1500-P5 RR-P5 Figure B2-10: Rosin Rammler Parameters for Lead-Zinc Ore at 1500 rpm 237 Table B2-11: Rosin Rammler Parameters for Lead-Zinc Ore at 2000 rpm Ore - 2000 Pass Slope (b) a P80 R O2000-P1 1.02 29.39 34.2 0.93 O2000-P2 0.90 21.16 20.0 0.86 O2000-P3 0.90 17.48 16.8 0.85 O2000-P4 0.82 13.90 13.0 0.80 O2000-P5 0.74 13.70 11.7 0.75 2 Ore - 2000 RPM 100 Feed 90 RR-Feed 80 O2000-P1 % Passing 70 RR-P1 60 O2000-P2 50 RR-P2 40 O2000-P3 30 RR-P3 20 O2000-P4 10 RR-P4 0 1 10 100 size (mm) 1000 O2000-P5 RR-P5 Figure B2-11: Rosin Rammler Parameters for Lead-Zinc Ore at 2000 rpm 238 Appendix B3: Correlation between Measured and Calculated P80 (Initial and Post Initial) Data Quartz - Initial (a) 100 Calculated P80 (m) Exponential 1000 90 Linear 1000 Exponenial 1500 80 Linear 1500 Exponential 2000 70 Linear 2000 60 60 70 80 90 100 Measured P80 (m) (b) Quartz - Average Berakage (P1-P5) 100 Calculated P80 (m) 90 Exponential 1000 80 70 Linear 1000 60 Exponential 1500 50 Linear 1500 40 30 Exponential 2000 20 Linear 2000 10 10 20 30 40 50 60 70 80 90 100 Measured P80 (m) Figure B3-1: Quartz Correlation; (a) Initial Breakage; (b) Average breakage 239 (a) Galena Concentrate - Initial Calculated P80 (m) 100 90 Exponential 1000 80 Linear 1000 70 Exponential 1500 60 50 Linear1500 40 Exponential 2000 30 Linear2000 20 10 10 20 30 40 50 60 70 80 90 100 Measured P80 (m) (b) Galena Concentrate Average Berakage (P1-P5) Caclculated P80 (m) 50 Exponential 1000 45 40 Linear 1000 35 Exponential 1500 30 25 Linear 1500 20 Exponential 2000 15 Linear 2000 10 10 20 30 40 50 Measured P80 (m) Figure B3-2: Galena Concentrate Correlation; (a) Initial Breakage; (b) Average breakage 240 (a)(b) Mixed Sample - Initial 130 Exponential 1000 Calculated P80 (m) 120 110 Linear 1000 100 Exponential 2000 90 80 Linear 2000 70 60 60 70 80 90 100 110 120 130 Measured P80 (m) Mixed Sample Average Berakage (P1-P5) (b) Calculated P80 (m) 130 110 Exponential 1000 90 Linear 1000 70 Exponential 2000 50 Linear 2000 30 10 10 30 50 70 90 110 130 Measured P80 (m) Figure B3-3: Mixed Quartz and Galena Correlation; (a) Initial Breakage; (b) Average Breakage 241 (a) Lead-Zinc Ore - Initial Calculated P80 (m) 100 Exponential 1000 90 Linear 1000 80 Exponential 1500 70 60 Linear 1500 50 Exponential 2000 40 Linear 2000 30 30 40 50 60 70 80 90 100 Measured P80 (mm) Lead-Zinc Ore Sample Average Berakage (P1-P5) (b) Calculated P80 (m) 70 65 Exponential 1000 60 55 Linear 1000 50 Exponential 1500 45 Linear 1500 40 Exponential 2000 35 Linear 2000 30 30 35 40 45 50 55 60 65 70 Measured P80 (m) Figure B3-4: Lead-Zinc Ore Correlation; (a) Initial Breakage; (b) Average breakage 242 Appendix B4: Energy Breakage vs. Particle Size P80 (m) Quartz Sample 500 Net Energy (KJ) 400 y = 44285e-0.087x R² = 0.8328 Q1000 300 y = 675.09e -0.029x R² = 0.8681 Q1500 200 Q2000 y = 660.33e -0.029x R² = 0.9748 100 0 1 10 100 Particle Size P80 (m) Figure B4-1: Net Energy vs. Particle Size for Quartz Galena Concentrate Sample 700 Net Energy (KJ) 600 y = 115.99e -0.04x R² = 0.927 500 G1000 y = 932.29e -0.111x R² = 0.8726 400 G1500 300 y = 2E+08e-1.028x R² = 0.9067 200 G2000 100 0 1 10 100 Particle Size P80 (m) Figure B4-2: Net Energy vs. Particle Size for Galena Concentrate 243 Mixed Quartz and Galena Sample 500 Net Energy (KJ) 400 y = 9027.2e -0.05x R² = 0.9695 M1000 300 M2000 y = 640.78e -0.02x R² = 0.9948 200 100 0 1 10 100 1000 Particle Size P80 (m) Figure B4-3: Net Energy vs. Particle Size for Mixed Quartz and Galena Sample Lead-Zinc Ore Sample 500 Net Energy (KJ) 400 y = 303.88e -0.053x R² = 0.8482 O1000 300 y = 345.42e -0.047x R² = 0.9982 O1500 200 O2000 y = 661.48e -0.061x R² = 0.9419 100 0 1 10 100 Particle Size P80 (m) Figure B4-4: Net Energy vs. Particle Size for Lead-Zinc Ore Sample 244 Appendix C: Morphology Appendix C1: Manual Point Counting Sub-Routine Sub Morphology() Dim Roughness As Integer R1 = 0 R2 = 0 R3 = 0 R4 = 0 R5 = 0 Do Roughness = Application.InputBox("Enter Roughness Per Particle-Between 1 and 5", "Roughness Value", "") If Roughness <> False Then If Roughness = 1 Then R1 = R1 + 1 ActiveSheet.Range("rough1").Value = R1 ElseIf Roughness = 2 Then R2 = R2 + 1 ActiveSheet.Range("C3").Value = R2 ElseIf Roughness = 3 Then R3 = R3 + 1 ActiveSheet.Range("D3").Value = R3 ElseIf Roughness = 4 Then R4 = R4 + 1 ActiveSheet.Range("E3").Value = R4 ElseIf Roughness = 5 Then R5 = R5 + 1 ActiveSheet.Range("F3").Value = R5 Else: MsgBox ("Wrong Value") End If End If Loop Until Roughness = False End Sub 245 Appendix C2: Snap Shot of the Manual Point Counting Screen Figure C2-1: Screen Snap Shot of Manual Point Counting and Definition 246 Appendix C3: Manual Point Counting Sensitivity Analysis Table C3-1: Initial Count of 53m Quartz Sample-Feed Count % Roughness level R1 R2 R3 R4 R5 Total Counter 1 1 3 20 43 34 100 Counter 2 2 8 22 50 20 100 Table C3--2: After Fine Tuning Roughness Definition Count of 53m Quartz Sample-Feed Count % Roughness level R1 R2 R3 R4 R5 Total Counter 1 2 7 34 41 18 100 Counter 2 2 7 31 41 21 100 Counter 3 1 5 35 37 23 100 Table C3-3: Count of 13m Quartz Sample-Feed Count % Roughness level R1 R2 R3 R4 R5 Total Counter 1 0 12 20 62 6 100 Counter 2 0 9 26 61 4 100 247 Appendix C4: Clemex Routine 001 ' Morphology - UBC-Reem 002 Set Guard Frame to 0,0 1385x1276 µm Set Guard Frame to 0,0 1000x921 pixels 003 Edit Analysis Property <<Sample>> 004 ' Change stage pattern based on number of images from SEM 005 Load Stage Pattern (should be used in Prolog only) File: UBC Morphology 10 images.stg Path: C:\IaFiles\Pattern End of Prolog 001 Clear => All 002 ' Calibrate Scale. Choose "Edit" 003 ' Drag the Red Scale line to match the Scale from SEM image 004 ' Type Scale from SEM image in the "Caliper Width" 005 ' Image location needs to be changed for each set of samples 006 Load Image '*.jpg' File: *.jpg Path: C:\Documents and Settings\cpollock\Desktop\15 July 2010 UBC Morphology 933540 SEM 15kV CLP\Q1500_P5_53um Use Default Calibration:No 007 ' Save Mosaic to Sample Folder 008 Build Mosaic Max Mosaic Size: 2000 Destination: File "Z:\Clemex\933540 UBC Morphology\25 June 2010\Q1000_P1_53um\Q1000_P1_53um.tif" Overwrite Protection: Yes 009 Gray Threshold BPL1 range 86..247 010 Delineation x2 011 Chord Size, diameter = 10, BPL1 -> None 012 Object Transfer BPL1 -> BPL2 Roughness less than 0.96 013 Copy BPL2 -> BPL3 014 Opening SQR x1 => BPL3 Extend 015 (BPL2 AND BPL3) -> BPL2 016 Combine (BPL1, BPL2) -> BPL1 017 Separate Manually BPL1 Marking plane : BPL4 Editing tool : Line Clear marking bitplane on entry : True Outline thickness : 2 Message: seperate your particles 018 Border Transfer BPL1 (All) -> None 019 Object Measures (BPL1) -> OBJM1 Aspect Ratio 248 Compactness Roughness Roundness Sphericity Length Width Breadth Perimeter Convex Perimeter Area ASTM E112-96 Angular Position Volume : Spherical Volume : Cylindrical Volume : Ellipsoidal Volume : Tetragonal 020 ' Change "FldNo" based on number of images from SEM 021 IF FldNo = 20 THEN Next Section Action: Step out to the Next Section Display Condition in a Message-Box: No End of Field 001 ' Save Data to sample folder 002 Export Data OBJM1 File: Q_1500_P5_53um.xls Path: C:\Documents and Settings\cpollock\Desktop\Q1500 Info Header: Yes Overwrite Protection: Yes End of Epilog 249 Appendix C5: Morphology Point Counting Data Table C5-1A: Morphology Counts for Quartz Sample, Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) Qfeed P1 P2 P3 P4 P5 0.0 1.0 2.0 3.0 4.0 5.0 % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Total # of Particles 13 55 47 42 58 52 14 15 14 34 24 30 28 41 7 29 32 27 162 224 115 132 213 136 96 118 73 131 150 102 313 453 256 368 477 347 Qfeed P1 P2 P3 P4 P5 0.0 1.0 2.0 3.0 4.0 5.0 4 12 18 11 12 15 4 3 5 9 5 9 9 9 3 8 7 8 52 49 45 36 45 39 31 26 29 36 31 29 100 100 100 100 100 100 34 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.0 2.0 3.0 4.0 5.0 25 13 31 31 45 15 32 14 26 15 20 28 43 15 23 27 35 38 297 119 239 191 237 59 91 28 79 68 127 13 488 189 398 332 464 153 34 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.0 2.0 3.0 4.0 5.0 5 7 8 9 10 10 7 7 7 5 4 18 9 8 6 8 8 25 61 63 60 58 51 39 19 15 20 20 27 8 100 100 100 100 100 100 15 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.0 2.0 3.0 4.0 5.0 19 16 12 24 15 6 17 19 11 42 19 19 14 21 16 30 23 45 139 180 167 298 150 114 31 45 33 76 46 24 220 281 239 470 253 208 15 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.0 2.0 3.0 4.0 5.0 9 6 5 5 6 3 8 7 5 9 8 9 6 7 7 6 9 22 63 64 70 63 59 55 14 16 14 16 18 12 100 100 100 100 100 100 250 Table C5-2A: Morphology Counts for Quartz Sample, Test Run at Agitator Speed 1500 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) Qfeed P1 P2 P3 P4 P5 0.0 1.1 2.1 3.1 4.1 5.1 % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles 13 35 18 25 29 29 14 34 27 34 44 32 28 64 33 57 61 50 162 280 107 209 108 136 96 180 41 80 57 31 313 593 226 405 299 278 Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Total # of Particles Qfeed P1 P2 P3 P4 P5 0.0 1.1 2.1 3.1 4.1 5.1 4 6 8 6 10 10 4 6 12 8 15 12 9 11 15 14 20 18 52 47 47 52 36 49 31 30 18 20 19 11 100 100 100 100 100 100 34 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.1 5.1 25 17 41 46 48 61 32 12 48 62 57 55 43 66 94 93 97 63 297 305 239 169 141 101 91 112 55 21 15 16 488 512 477 391 358 296 34 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.1 5.1 5 3 9 12 13 21 7 2 10 16 16 19 9 13 20 24 27 21 61 60 50 43 39 34 19 22 12 5 4 5 100 100 100 100 100 100 15 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.1 5.1 19 0 3 4 8 19 17 6 17 13 7 21 14 16 33 27 21 20 139 96 156 181 157 202 31 10 17 35 48 40 220 128 226 260 241 302 15 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.1 5.1 9 0 1 2 4 6 8 5 8 5 3 7 6 13 15 10 9 7 63 75 69 70 65 67 14 8 8 13 20 13 100 100 100 100 100 100 251 Table C5-3A: Morphology Counts for Quartz Sample, Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction % Roughness 63 microns Size Fraction Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Total # of Particles Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Qfeed P1 P2 P3 P4 P5 0.0 1.1 2.0 3.0 3.9 4.9 13 29 39 51 46 78 14 39 29 39 50 55 28 67 47 34 50 47 162 97 88 76 111 115 96 72 50 32 5 8 313 304 253 232 262 303 Qfeed P1 P2 P3 P4 P5 0.0 1.1 2.0 3.0 3.9 4.9 4 10 15 22 18 26 4 13 11 17 19 18 9 22 19 15 19 16 52 32 35 33 42 38 31 24 20 14 2 3 Total # of Particles 100 100 100 100 100 100 34 microns Size Fraction Qfeed 0.0 P1 1.1 P2 2.0 P3 3.0 P4 3.9 P5 4.9 25 14 39 35 50 21 32 34 37 32 50 12 43 82 54 39 43 22 297 129 145 143 119 75 91 52 84 55 43 34 488 311 359 304 305 164 34 microns Size Fraction 0.0 Qfeed P1 1.1 P2 2.0 P3 3.0 P4 3.9 P5 4.9 5 5 11 12 16 13 7 11 10 11 16 7 9 26 15 13 14 13 61 41 40 47 39 46 19 17 23 18 14 21 100 100 100 100 100 100 15 microns Size Fraction Qfeed 0.0 P1 1.1 P2 2.0 P3 3.0 P4 3.9 P5 4.9 19 6 24 22 28 2 17 11 27 18 17 10 14 50 36 39 26 18 139 131 210 150 75 49 31 41 93 66 79 42 220 239 390 295 225 121 15 microns Size Fraction 0.0 Qfeed P1 1.1 P2 2.0 P3 3.0 P4 3.9 P5 4.9 9 3 6 7 12 2 8 5 7 6 8 8 6 21 9 13 12 15 63 55 54 51 33 40 14 17 24 22 35 35 100 100 100 100 100 100 252 Table C5-1B Morphology Counts for Galena Concentrate Sample, Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 Qfeed 0.00 6 5 P1 0.90 29 8 P2 1.85 14 27 P3 2.67 34 29 P4* 3.48 22 19 P5 4.26 33 29 * Majority is Sphalerite particles - not counted 37 microns Size Fraction Qfeed 25 17 0.00 P1 0.90 47 44 P2 1.85 39 47 P3 2.67 56 78 P4 3.48 43 52 P5 4.26 46 44 17 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.00 0.90 1.85 2.67 3.48 4.26 30 24 52 58 38 68 16 28 53 77 20 76 R3 R4 R5 Total # of Particles 22 35 35 35 20 20 85 127 85 76 57 82 55 74 62 32 36 37 173 273 223 206 154 201 65 66 72 68 64 30 207 239 241 239 226 107 162 159 120 87 116 44 476 555 519 528 501 271 Qfeed 0.00 3 3 P1 0.90 11 3 P2 1.85 6 12 P3 2.67 17 14 P4* 3.48 14 12 P5 4.26 16 14 * Majority is Sphalerite particles - not counted 37 microns Size Fraction 5 Qfeed 0.00 4 P1 0.90 8 8 P2 1.85 8 9 P3 2.67 11 15 P4 3.48 9 10 P5 4.26 17 16 71 35 61 80 34 69 192 119 222 261 112 244 181 67 137 114 63 113 490 273 525 590 267 570 17 microns Size Qfeed P1 P2 P3 P4 P5 Roughness Level Residence Time (min) Fraction 0.00 0.90 1.85 2.67 3.48 4.26 R1 6 9 10 10 14 12 R2 3 10 10 13 7 13 R3 R4 R5 Total # of Particles 13 13 16 17 13 10 49 47 38 37 37 41 32 27 28 16 23 18 100 100 100 100 100 100 14 12 14 13 13 11 43 43 46 45 45 39 34 29 23 16 23 16 100 100 100 100 100 100 14 13 12 14 13 12 39 44 42 44 42 43 37 25 26 19 24 20 100 100 100 100 100 100 253 Table C5-2B: Morphology Counts for Galena Concentrate Sample, Test Run at Agitator Speed 1500 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 Qfeed 0.0 6 5 P1 1.1 29 28 P2 2.1 12 16 P3* 3.2 41 9 P4 4.2 87 22 P5 5.2 All Smashed particles * mostly broken pieces 37 microns Size Fraction Qfeed 0 25 17 P1 1.1 34 25 P2 2.1 54 66 P3 3.2 92 63 P4 4.2 67 64 P5 5.2 181 106 17 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0 1.1 2.1 3.2 4.2 5.2 30 46 47 63 53 30 16 38 47 56 39 31 Total # of Particles Roughness Level Residence Time (min) 55 52 24 7 27 173 209 97 84 204 0 Qfeed P1 P2 P3* P4 P5 0.0 1.1 2.1 3.2 4.2 5.2 207 159 252 191 171 308 162 97 90 61 89 95 476 354 525 475 424 755 37 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0 1.1 2.1 3.2 4.2 5.2 5 10 10 19 16 24 192 173 213 193 132 94 181 114 164 99 77 36 490 412 520 451 324 218 17 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0 1.1 2.1 3.2 4.2 5.2 6 11 9 14 16 14 R3 R4 R5 22 33 12 6 10 85 67 33 21 58 65 39 63 68 33 65 71 41 49 40 23 27 R1 R2 Total # of Particles R3 R4 R5 13 16 12 7 5 49 32 34 25 28 32 25 25 8 13 100 100 100 100 100 0 4 7 13 13 15 14 14 11 12 14 8 9 43 45 48 40 40 41 34 27 17 13 21 13 100 100 100 100 100 100 3 9 9 12 12 14 14 10 9 9 7 12 39 42 41 43 41 43 37 28 32 22 24 17 100 100 100 100 100 100 3 3 14 13 12 16 49 11 43 11 All Smashed particles 254 Table C5-3B: Morphology Counts for Galena Concentrate Sample, Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Total # of Particles Qfeed P1* P2 P3 P4 P5 0.0 1.1 2.1 3.0 4.0 4.9 3 21 0 0 0 0 3 13 0 0 0 0 13 7 0 0 0 0 49 50 0 0 0 0 32 10 0 0 0 0 100 100 0 0 0 0 Qfeed 0.0 P1* 1.1 P2 2.1 P3 3.0 P4 4.0 P5 4.9 * mostly broken pieces 37 microns Size Fraction Qfeed 0.0 P1 1.1 P2 2.1 P3 3.0 P4 4.0 P5 4.9 6 21 0 0 0 0 5 13 0 0 0 0 22 7 0 0 0 0 85 51 0 0 0 0 55 10 0 0 0 0 173 102 0 0 0 0 25 32 56 131 155 95 17 33 52 41 50 40 65 28 27 30 36 25 207 191 161 141 109 85 162 79 61 27 36 27 476 363 357 370 386 272 37 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.0 4.0 4.9 5 9 16 35 40 35 4 9 15 11 13 15 14 8 8 8 9 9 43 53 45 38 28 31 34 22 17 7 9 10 100 100 100 100 100 100 17 microns Size Qfeed P1 P2 P3 P4 P5 30 18 31 24 21 60 16 14 37 39 12 60 71 26 30 30 18 49 192 103 129 112 91 151 181 85 74 68 46 62 490 246 301 273 188 382 17 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.0 4.0 4.9 6 7 10 9 11 16 3 6 12 14 6 16 14 11 10 11 10 13 39 42 43 41 48 40 37 35 25 25 24 16 100 100 100 100 100 100 Fraction 0.0 1.1 2.1 3.0 4.0 4.9 255 Table C5-1C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Quartz Counts), Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 Qfeed 0 4 29 P1 1.1 1 37 P2 2.1 7 24 P3 2.9 37 63 P4* 3.8 26 49 P5 4.6 30 67 * Majority is Sphalerite particles - not counted 36 microns Size Fraction Qfeed 0.0 0 2 P1 1.1 3 7 P2 2.1 1 15 P3 2.9 4 13 P4 3.8 11 31 P5 4.6 18 46 18 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 2.9 3.8 4.6 0 0 0 0 0 5 13 3 5 5 3 19 Total # of Particles Roughness Level Residence Time (min) R3 R4 R5 45 64 28 52 60 45 61 87 51 113 87 69 15 18 28 39 25 154 207 138 265 261 236 3 14 10 26 29 24 8 32 36 45 52 55 3 15 16 14 35 30 16 71 78 102 158 173 Qfeed 0.00 3 19 P1 1.09 0 18 P2 2.06 5 17 P3 2.93 14 24 P4* 3.79 10 19 P5 4.63 13 28 * Majority is Sphalerite particles - not counted 36 microns Size Fraction Qfeed 0.00 0 13 P1 1.09 4 10 P2 2.06 1 19 P3 2.93 4 13 P4 3.79 7 20 P5 4.63 10 27 17 7 8 9 5 15 55 23 22 30 7 49 24 11 9 8 4 17 109 44 44 52 19 105 18 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.00 1.09 2.06 2.93 3.79 4.63 R1 0 0 0 0 0 5 R2 12 7 11 10 16 18 R3 R4 R5 Total # of Particles 29 31 20 20 23 19 40 42 37 43 33 29 10 9 20 0 15 11 100 100 100 100 100 100 19 20 13 25 18 14 50 45 46 44 33 32 19 21 21 14 22 17 100 100 100 100 100 100 16 16 18 17 26 14 50 52 50 58 37 47 22 25 20 15 21 16 100 100 100 100 100 100 256 Table C5-2C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Galena Counts), Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 Qfeed 0.0 2 1 P1 1.1 0 1 P2 2.1 0 0 P3 2.9 0 0 P4* 3.8 0 0 P5 4.6 0 0 * Majority is Sphalerite particles - not counted 316microns Size Fraction Qfeed 0.0 3 8 P1 1.1 6 15 P2 2.1 15 8 P3 2.9 5 7 P4 3.8 11 12 P5 4.6 14 7 18 microns Size Qfeed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 2.9 3.8 4.6 5 8 13 22 24 11 21 22 21 8 20 15 R3 R4 R5 Total # of Particles 3 3 0 0 0 0 7 5 0 0 0 0 5 3 0 0 0 0 18 12 0 0 0 0 20 27 21 26 19 8 95 79 96 73 35 29 76 44 60 35 14 9 202 171 200 146 91 67 Qfeed 0.00 11 6 P1 1.09 0 8 P2 2.06 0 0 P3 2.93 0 0 P4* 3.79 0 0 P5 4.63 0 0 * Majority is Sphalerite particles - not counted 36 microns Size Fraction Qfeed 0.00 1 4 P1 1.09 4 9 P2 2.06 8 4 P3 2.93 3 5 P4 3.79 12 13 P5 4.63 21 10 259 180 304 227 315 157 18 microns Size Qfeed P1 P2 P3 P4 P5 34 21 38 23 52 16 137 78 158 126 130 80 62 51 74 48 89 35 Roughness Level Residence Time (min) Fraction 0.00 1.09 2.06 2.93 3.79 4.63 R1 2 4 4 10 8 7 R2 8 12 7 4 6 10 R3 R4 R5 Total # of Particles 17 25 0 0 0 0 39 42 0 0 0 0 28 25 0 0 0 0 100 100 0 0 0 0 10 16 11 18 21 12 47 46 48 50 38 43 38 26 30 24 15 13 100 100 100 100 100 100 13 12 13 10 17 10 53 43 52 56 41 51 24 28 24 21 28 22 100 100 100 100 100 100 257 Table C5-3C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Quartz + Galena Counts), Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction Roughness Level Residence Time (min) % Roughness 63 microns Size Fraction R1 R2 feed 0.0 6 30 P1 1.1 1 38 P2 2.1 7 24 P3 2.9 37 63 P4* 3.8 26 49 P5 4.6 30 67 * Majority is Sphalerite particles - not counted 36 microns Size Fraction feed 0.0 3 10 P1 1.1 9 22 P2 2.1 16 23 P3 2.9 9 20 P4 3.8 22 43 P5 4.6 32 53 18 microns Size Fraction feed 0.0 P1 1.1 P2 2.1 P3 2.9 P4 3.8 P5 4.6 5 8 13 22 24 16 34 25 26 13 23 34 R3 R4 R5 Total # of Particles Roughness Level Residence Time (min) 48 67 28 52 60 45 68 92 51 113 87 69 20 21 28 0 39 25 172 219 138 265 261 236 23 41 31 52 48 32 103 111 132 118 87 84 79 59 76 49 49 39 218 242 278 248 249 240 feed 0.00 3 17 P1 1.09 0 17 P2 2.06 5 17 P3 2.93 14 24 P4* 3.79 10 19 P5 4.63 13 28 * Majority is Sphalerite particles - not counted 36 microns Size Fraction feed 0.00 1 5 P1 1.09 4 9 P2 2.06 6 8 P3 2.93 4 8 P4 3.79 9 17 P5 4.63 13 22 51 28 46 32 57 31 192 101 180 156 137 129 86 62 83 56 93 52 368 224 348 279 334 262 18 microns Size Fraction feed 0.00 P1 1.09 P2 2.06 P3 2.93 P4 3.79 P5 4.63 R1 1 4 4 8 7 6 R2 9 11 7 5 7 13 R3 R4 R5 28 31 20 20 23 19 40 42 37 43 33 29 12 10 20 0 15 11 Total # of Particles 100 100 100 100 100 100 11 17 11 21 19 13 47 46 47 48 35 35 36 24 27 20 20 16 100 100 100 100 100 100 14 13 13 11 17 12 52 45 52 56 41 49 23 28 24 20 28 20 100 100 100 100 100 100 258 Table C5-4C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Quartz Counts), Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) feed 0.0 P1 1.1 P2 2.1 P3 3.1 P4 4.2 P5 5.1 * mostly broken pieces 36 microns Size Fraction feed 0.0 P1 1.1 P2 2.1 P3 3.1 P4 4.2 P5 5.1 18 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles Roughness Level Residence Time (min) R1 R2 R3 R4 R5 Total # of Particles 4 41 37 41 45 41 29 52 52 70 66 67 45 55 52 45 64 62 61 81 61 77 79 58 15 40 11 2 1 1 154 269 213 235 255 229 feed P1 P2 P3 P4 P5 0.0 1.1 2.1 3.1 4.2 5.1 3 15 17 17 18 18 19 19 24 30 26 29 29 20 24 19 25 27 40 30 29 33 31 25 10 15 5 1 0 0 100 100 100 100 100 100 0 9 10 10 6 11 2 38 42 42 31 66 3 51 37 57 30 47 8 65 54 104 61 93 3 12 15 9 6 6 16 175 158 222 134 223 36 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 0 5 6 5 4 5 13 22 27 19 23 30 19 29 23 26 22 21 50 37 34 47 46 42 19 7 9 4 4 3 100 100 100 100 100 100 0 0 2 4 1 4 13 7 15 12 17 12 17 16 21 20 39 15 55 42 70 60 80 44 24 14 21 13 21 14 109 79 129 109 158 89 18 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 0 0 2 4 1 4 12 9 12 11 11 13 16 20 16 18 25 17 50 53 54 55 51 49 22 18 16 12 13 16 100 100 100 100 100 100 259 Table C5-5C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Galena Counts), Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction Residence Roughness Level Time (min) % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles Roughness Level Residence Time R1(min) R2 feed 0.0 P1* 1.1 P2 2.1 P3 3.1 P4 4.2 P5 5.1 * mostly broken pieces 36 microns Size Fraction feed 0.0 P1 1.1 P2 2.1 P3 3.1 P4 4.2 P5 5.1 2 0 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0 0 7 0 0 0 0 0 5 0 0 0 0 0 18 0 0 0 0 0 3 3 17 10 21 12 8 12 11 6 14 8 20 10 18 8 20 7 95 30 27 15 34 15 76 8 13 2 4 4 202 63 86 41 93 46 36 microns Size feed P1 P2 P3 P4 P5 18 microns Size feed P1 P2 P3 P4 P5 5 19 27 21 25 22 21 19 29 16 19 16 34 29 18 20 29 25 137 84 73 66 63 73 62 23 25 10 14 9 259 174 172 133 150 145 18 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 feed P1* P2 P3 P4 P5 0.0 1.1 2.1 3.1 4.2 5.1 R3 R4 R5 Total # of Particles 11 0 0 0 0 0 6 0 0 0 0 0 17 0 0 0 0 0 39 0 0 0 0 0 28 0 0 0 0 0 100 0 0 0 0 0 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 1 5 20 24 23 26 4 19 13 15 15 17 10 16 21 20 22 15 47 48 31 37 37 33 38 13 15 5 4 9 100 100 100 100 100 100 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 2 11 16 16 17 15 8 11 17 12 13 11 13 17 10 15 19 17 53 48 42 50 42 50 24 13 15 8 9 6 100 100 100 100 100 100 260 Table C5-66-12C: Morphology Counts for Mixed quartz and galena Concentrate Sample (Quartz + Galena Counts), Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) % Roughness 63 microns Size Fraction R1 R2 feed 0.0 6 30 P1 1.1 41 52 P2 2.1 37 52 P3 3.1 41 70 P4* 4.2 45 66 P5 5.1 41 67 * Majority is Sphalerite particles - not counted 36 microns Size Fraction feed 0.0 3 10 P1 1.1 12 50 P2 2.1 27 53 P3 3.1 20 48 P4 4.2 27 45 P5 5.1 23 74 18 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 1.1 2.1 3.1 4.2 5.1 5 19 29 25 26 26 34 26 44 28 36 28 R3 R4 R5 Total # of Particles 48 55 52 45 64 62 68 81 61 77 79 58 20 40 11 2 1 1 172 269 213 235 255 229 23 61 55 65 50 54 103 95 81 119 95 108 79 20 28 11 10 10 218 238 244 263 227 269 feed 0.00 3 17 P1 1.11 15 19 P2 2.11 17 24 P3 3.09 17 30 P4* 4.18 18 26 P5 5.08 18 29 * Majority is Sphalerite particles - not counted 36 microns Size Fraction feed 0.00 1 5 P1 1.11 5 21 P2 2.11 11 22 P3 3.09 8 18 P4 4.18 12 20 P5 5.08 9 28 51 45 39 40 68 40 192 126 143 126 143 117 86 37 46 23 35 23 368 253 301 242 308 234 18 microns Size feed P1 P2 P3 P4 P5 Roughness Residence Level Time (min) Fraction 0.00 1.11 2.11 3.09 4.18 5.08 R1 1 8 10 10 8 11 R2 9 10 15 12 12 12 R3 R4 R5 Total # of Particles 28 20 24 19 25 27 40 30 29 33 31 25 12 15 5 1 0.4 0.4 100 100 100 100 100 100 11 26 23 25 22 20 47 40 33 45 42 40 36 8 11 4 4 4 100 100 100 100 100 100 14 18 13 17 22 17 52 50 48 52 46 50 23 15 15 10 11 10 100 100 100 100 100 100 261 Table C5-1D: Morphology Counts for Lead-Zinc Ore Sample, Test Run at Agitator Speed 1000 rpm Particle Counts 63 microns Size Fraction % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles 36 55 50 74 40 49 34 37 67 70 67 96 35 46 68 54 44 90 86 70 66 80 118 139 18 10 5 15 9 10 209 218 256 293 278 384 Fraction 0.0 0.7 1.3 2.0 2.6 3.1 63 53 48 52 56 56 40 39 52 61 55 61 43 49 40 43 32 39 107 73 93 102 88 89 22 35 11 14 23 10 275 249 244 272 254 255 33 microns Size feed P1 P2 P3 P4 P5 16microns Size Fraction feed 0.0 P1 0.7 P2 1.3 P3 2.0 P4 2.6 P5 3.1 47 57 49 57 65 67 21 39 48 46 44 57 31 43 30 23 43 41 99 106 98 95 101 95 48 18 12 6 23 15 246 263 237 227 276 275 16 microns Size feed P1 P2 P3 P4 P5 Roughness Residence Level Time (min) feed P1 P2 P3 P4 P5 33 microns Size feed P1 P2 P3 P4 P5 0.0 0.7 1.3 2.0 2.6 3.1 R1 R2 R3 R4 R5 Total # of Particles 17 25 20 25 14 13 16 17 26 24 24 25 17 21 27 18 16 23 41 32 26 27 42 36 9 5 2 5 3 3 100 100 100 100 100 100 Fraction 0.0 0.7 1.3 2.0 2.6 3.1 23 21 20 19 22 22 15 16 21 22 22 24 16 20 16 16 13 15 39 29 38 38 35 35 8 14 5 5 9 4 100 100 100 100 100 100 Fraction 0.0 0.7 1.3 2.0 2.6 3.1 19 22 21 25 24 24 9 15 20 20 16 21 13 16 13 10 16 15 40 40 41 42 37 35 20 7 5 3 8 5 100 100 100 100 100 100 Roughness Residence Level Time (min) feed P1 P2 P3 P4 P5 0.0 0.7 1.3 2.0 2.6 3.1 262 Table C5-2D: Morphology Counts for Lead-Zinc Ore Sample, Test Run at Agitator Speed 1500 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) feed 0.0 P1 0.8 P2 1.7 P3* 2.4 P4 3.2 P5 3.9 * mostly broken pieces 33 microns Size Fraction feed 0 P1 0.8 P2 1.7 P3 2.4 P4 3.2 P5 3.9 16 microns Size feed P1 P2 P3 P4 P5 Fraction 0 0.8 1.7 2.4 3.2 3.9 % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles 36 19 89 34 32 49 34 51 80 45 77 85 35 51 44 41 92 69 86 88 80 69 105 83 18 10 3 4 2 2 209 219 296 193 308 288 63 69 63 78 45 37 40 44 54 54 93 39 43 37 42 44 77 48 107 92 85 85 113 71 22 12 4 7 1 7 275 254 248 268 329 202 47 78 58 55 56 39 21 62 42 38 42 50 31 60 37 51 38 41 99 164 80 83 74 77 48 25 16 15 6 3 246 389 233 242 216 210 Roughness Residence Level Time (min) feed P1 P2 P3* P4 P5 0.0 0.8 1.7 2.4 3.2 3.9 33 microns Size Fraction feed 0 P1 0.8 P2 1.7 P3 2.4 P4 3.2 P5 3.9 * mostly broken pieces 16 microns Size Fraction feed 0 P1 0.8 P2 1.7 P3 2.4 P4 3.2 P5 3.9 R1 R2 R3 R4 R5 Total # of Particles 17 9 30 18 10 17 16 23 27 23 25 30 17 23 15 21 30 24 41 40 27 36 34 29 9 5 1 2 1 1 100 100 100 100 100 100 23 27 25 29 14 18 15 17 22 20 28 19 16 15 17 16 23 24 39 36 34 32 34 35 8 5 2 3 0 3 100 100 100 100 100 100 19 20 25 23 26 19 9 16 18 16 19 24 13 15 16 21 18 20 40 42 34 34 34 37 20 6 7 6 3 1 100 100 100 100 100 100 263 Table C5-3D: Morphology Counts for Lead-Zinc Ore Sample, Test Run at Agitator Speed 2000 rpm Particle Counts 63 microns Size Fraction Roughness Residence Level Time (min) feed P1 P2 P3 P4 P5 0.0 0.8 1.6 2.3 3.0 4.0 % Roughness 63 microns Size Fraction R1 R2 R3 R4 R5 Total # of Particles 36 60 70 60 73 0 34 67 53 81 93 0 35 59 44 58 30 0 86 86 120 97 79 0 18 0 4 3 4 0 209 272 291 299 279 0 33 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 0.8 1.6 2.3 3.0 4.0 63 45 75 59 0 0 40 37 44 50 0 0 43 33 60 43 0 0 107 66 77 75 0 0 22 2 5 7 0 0 16 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 0.8 1.6 2.3 3.0 4.0 47 71 106 80 66 88 21 42 69 38 52 61 31 42 92 40 35 44 99 111 119 95 84 106 48 17 23 6 15 13 Roughness Residence Level Time (min) feed P1 P2 P3 P4 P5 0.0 0.8 1.6 2.3 3.0 4.0 R1 R2 R3 R4 R5 Total # of Particles 17 22 24 20 26 0 16 25 18 27 33 0 17 22 15 19 11 0 41 32 41 32 28 0 9 0 1 1 1 0 100 100 100 100 100 0 275 183 261 234 0 0 33 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 0.8 1.6 2.3 3.0 4.0 23 25 29 25 0 0 15 20 17 21 0 0 16 18 23 18 0 0 39 36 30 32 0 0 8 1 2 3 0 0 100 100 100 100 0 0 246 283 409 259 252 312 16 microns Size feed P1 P2 P3 P4 P5 Fraction 0.0 0.8 1.6 2.3 3.0 4.0 19 25 26 31 26 28 9 15 17 15 21 20 13 15 22 15 14 14 40 39 29 37 33 34 20 6 6 2 6 4 100 100 100 100 100 100 264 UBC Morpholgy Appendix C6:Study List- Samples of Morphology Samples Reem Roufail (PhD candidate) Q = Quartz G = Galena M = Mixed Sample of Silica and Galena O = Ore Sample from Red SAG Discharge (Pb-Zn circuit) Sample Q-feed Q1000-P1 Q1000-P2 Q1000-P3 Q1000-P4 Q1000-5 Q1500-P1 Q1500-P2 Q1500-P3 Q1500-P4 Q1500-5 Size Fraction 53 micron C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) Availability Sample G-feed G1000-P1 G1000-P2 G1000-P3 G1000-P4 G1000-5 G1500-P1 G1500-P2 G1500-P3 G1500-P4 G1500-5 Size Fraction Availability 53 micron C1 (26 micron) C3 (14 micron) C2 (31 micron) C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon)* C3 (14 mircon) 53 mircon C1 (26 mircon)* C3 (14 mircon) 53 mircon C1 (26 mircon)* C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) 53 mircon C1 (26 mircon)* C3 (14 mircon) Sample M-feed M1000-P1 M1000-P2 M1000-P3 M1000-P4 M1000-5 M2000-P1 M2000-P2 M2000-P3 M2000-P4 combined with C2 combined with C2 M2000-5 Size Fraction Availability 53 micron C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon C2 (31 micron) C4 (14 mircon) 53 mircon * C2 (31 micron) C4 (14 mircon) 53 mircon * C2 (31 micron)* C4 (14 mircon) 53 mircon * C2 (31 micron)* C4 (14 mircon) 53 mircon * C2 (31 micron)* C4 (14 mircon) Sample O-feed O1500-P4 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron O1500-P5 C2 (28 micron) C4 (13 micron) 53 micron O1000-P1 O1000-P2 O1000-P3 O1000-P4 O1000-5 O1500-P1 O1500-P2 O1500-P3 Size Fraction C2 (28 micron) C4 (13 micron) Availability 265 Sample Size Fraction Q2000-P1 53 mircon C3 (27 micron) C5 (13 micron) Q2000-P2 53 mircon C3 (27 micron) C5 (13 micron) Q2000-P3 53 mircon C3 (27 micron) C5 (13 micron) Q2000-P4 53 mircon Q2000-5 C3 (27 micron) C5 (13 micron) 53 mircon C3 (27 micron) C5 (13 micron) Availability Sample G2000-P1 G2000-P2 G2000-P3 G2000-P4 C1 (26 mircon) C3 (14 mircon) 53 mircon G2000-5 C1 (26 mircon) C3 (14 mircon) 53 mircon Size Fraction Availability 53 mircon C1 (26 mircon)* C3 (14 mircon) 53 mircon C1 (26 mircon)* C3 (14 mircon) 53 mircon C1 (26 mircon) C3 (14 mircon) Sample Size Fraction Availability Sample O2000-P1 O2000-P3 Size Fraction 53 micron C2 (28 micron) C4 (13 micron) 53 micron C2 (28 micron) C4 (13 micron) 53 micron O2000-P4 C2 (28 micron) C4 (13 micron) 53 micron O2000-P5 C2 (28 micron) C4 (13 micron)* 53 micron C2 (28 micron) C4 (13 micron)* O2000-P2 combined with C2 combined with C2 combined with C2 Note: * Total Number of Samples are 169 that need Morphology Analysis * Orange Stars and ALL Ore samples are all that we have i.e. No more Samples : Not generated Availability 266
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The effect of stirred mill operation on particles breakage mechanism and their morphological features Reem, Adel Roufail 2011
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Title | The effect of stirred mill operation on particles breakage mechanism and their morphological features |
Creator |
Reem, Adel Roufail |
Publisher | University of British Columbia |
Date Issued | 2011 |
Description | Stirred milling is a grinding tool that is used extensively for mineral liberation, in order to achieve successful downstream processing such as flotation or leaching. The focus of this research is to understand the effect of different operating parameters on particle breakage mechanism. Operating parameters could be summarized as stress intensity on the particles which are varied by changing the mill’s agitator speed, and different ground material properties such as extreme hard/low density minerals like quartz versus soft/high density minerals like galena. Grinding performance is assessed by analysing particle size reduction and energy consumption. Breakage mechanism is evaluated using the state of the art morphological analysis and liberation. Finally, theoretical evaluation of particles flow, types of forces and energy distribution across the mill are investigated using Discrete Element Modelling (DEM). It is observed that breakage mechanisms are affected by the type of mineral and stress intensities (agitator speed) in the mill. For example, galena, the soft/high density mineral, reaches its grinding limit very fast at high agitator speed and specific energy consumption increases exponentially with the increase of the agitator speed. On the other hand, for quartz, the hard/low density mineral, the breakage rate is very slow at low agitator speed and the specific energy consumption increases linearly with the increase of the agitator speed. Fracture mechanism of the particles is also a function of the agitator speed and type of mineral. At high agitator speed, galena fractures mostly along the grain boundaries, whereas quartz breaks across the grains, which is abrasion. The morphology observation is confirmed by the DEM model, which conveyed that at higher agitator speed, the normal forces were higher than tangential forces on the galena particles compared to the ceramic grinding media particles. The core of this research is the morphology analysis, which is a novel approach to studying particle breakage mechanisms. More work is recommended in the field of morphology with other types of minerals to confirm the findings of this research. 3D liberation analysis was introduced in this research; a correlation to the conventional liberation methodology would be a major addition to the industry. |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2011-10-24 |
Provider | Vancouver : University of British Columbia Library |
Rights | Attribution-NonCommercial-NoDerivatives 4.0 International |
DOI | 10.14288/1.0072358 |
URI | http://hdl.handle.net/2429/38190 |
Degree |
Doctor of Philosophy - PhD |
Program |
Mining Engineering |
Affiliation |
Applied Science, Faculty of Mining Engineering, Keevil Institute of |
Degree Grantor | University of British Columbia |
Graduation Date | 2011-11 |
Campus |
UBCV |
Scholarly Level | Graduate |
Rights URI | http://creativecommons.org/licenses/by-nc-nd/4.0/ |
Aggregated Source Repository | DSpace |
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