An evaluation of the effect of blast-generated fragment size distribution on the unit costs of a mining operation, using modeling and simulation techniques

This research was undertaken to investigate the impacts of finer rock fragmentation (arising from higher energy blasting) on the unit costs of a hard-rock surface mine. The investigation was carried out at a copper operation in southern Utah, which exploits its deposits by conventional methods, including drilling, blasting, loading, and truck haulage. The run of mine is processed in a three-stage crushing circuit and a two-stage grinding circuit, which feed a flotation plant that produces a copper concentrate. The research was carried out using modeling and simulation techniques. Fifty-five blast designs in total were developed for ore and waste units, with energy inputs ranging from 100 kcal/st to 400 kcal/st. For each design, fragmentation was predicted using the Kuz-Ram method. Crushing of the predicted ore fragment size distributions was simulated using MODSIM^TM. Data from pit face imaging and timed motion studies were collected and analyzed for the influence of fragmentation on shovel and truck productivity. Analyses indicated that fragment size distribution alone does not significantly impact this productivity. From simulation of the crushing circuit, it was found that the impact of differences in the blast-generated fragment distribution on the crusher energy is limited to the primary crusher, where a vast range of feed size distributions are introduced. No such relationships were evident at the secondary and tertiary crushers. Energy savings from increasing blasting intensity proved negligible and would not justify the costs of higher energy blasting. There was no evidence from this work that any beneficial influences of blast-generated fragment size distribution reach the grinding mill. Costs were estimated for drilling, blasting, and crushing, which were the principal unit operations inferred to be affected in some meaningful way by the varying intensities of blast energy input. The research shows that, principally as a result of jaw crusher gape restrictions and the significant unit costs of secondary reduction for both ore and waste, the net of all breakage (primary blast, secondary reduction, and crushing) does reduce to a transient minimum before they begin to ramp up again, thus fitting a classical mine-to-mill curve.

AN EVALUATION OF THE EFFECT OF BLAST-GENERATED FRAGMENT SIZE DISTRIBUTION ON THE UNIT COSTS OF A MINING OPERATION, USING MODELING AND SIMULATION TECHNIQUES by Solomon Augustine Tucker A dissertation submitted to the faculty of The University of Utah in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Mining Engineering The University of Utah May 2015 Copyright © Solomon Augustine Tucker 2015 All Rights Reserved The Uni v e r s i t y of Utah Graduat e School STATEMENT OF DISSERTATION APPROVAL The dissertation of Solomon Augustine Tucker has been approved by the following supervisory committee members: Michael K. McCarter Chair 12/19/2014 Date Approved Michael G. Nelson Member 12/19/2014 Date Approved Thomas A. Hethmon Member 12/19/2014 Date Approved Hyung Min Park Member 12/19/2014 Date Approved Raj K. Rajamani Member 12/19/2014 Date Approved and by Michael G. Nelson Chair of the Department of ________________ Mining Engineering and by David B. Kieda, Dean of The Graduate School. ABSTRACT This research was undertaken to investigate the impacts of finer rock fragmentation (arising from higher energy blasting) on the unit costs of a hard-rock surface mine. The investigation was carried out at a copper operation in southern Utah, which exploits its deposits by conventional methods, including drilling, blasting, loading, and truck haulage. The run of mine is processed in a three-stage crushing circuit and a two-stage grinding circuit, which feed a flotation plant that produces a copper concentrate. The research was carried out using modeling and simulation techniques. Fifty-five blast designs in total were developed for ore and waste units, with energy inputs ranging from 100 kcal/st to 400 kcal/st. For each design, fragmentation was predicted using the Kuz-Ram method. Crushing of the predicted ore fragment size distributions was simulated using MODSIM™. Data from pit face imaging and timed motion studies were collected and analyzed for the influence of fragmentation on shovel and truck productivity. Analyses indicated that fragment size distribution alone does not significantly impact this productivity. From simulation of the crushing circuit, it was found that the impact of differences in the blast-generated fragment distribution on the crusher energy is limited to the primary crusher, where a vast range of feed size distributions are introduced. No such relationships were evident at the secondary and tertiary crushers. Energy savings from increasing blasting intensity proved negligible and would not justify the costs of higher energy blasting. There was no evidence from this work that any beneficial influences of blast­generated fragment size distribution reach the grinding mill. Costs were estimated for drilling, blasting, and crushing, which were the principal unit operations inferred to be affected in some meaningful way by the varying intensities of blast energy input. The research shows that, principally as a result of jaw crusher gape restrictions and the significant unit costs of secondary reduction for both ore and waste, the net of all breakage (primary blast, secondary reduction, and crushing) does reduce to a transient minimum before they begin to ramp up again, thus fitting a classical mine-to-mill curve. iv To Yie and Papa TABLE OF CONTENTS ABSTRACT........................................................................................................................... iii ACKNOWLEDGEMENTS.................................................................................................. x CHAPTERS 1. INTRODUCTION........................................................................................................... 1 1.1 Problem statement..................................................................................................... 1 1.2 Hypothesis.................................................................................................................. 2 1.3 Objectives of the research........................................................................................ 3 1.4 Description of the host operation............................................................................ 4 1.5 Scope of the research .............................................................................................. 5 1.6 Units of measure........................................................................................................ 6 2. UNDERSTANDING MINE-TO-MILL PROCESS OPTIMIZATION................... 8 2.1 Overview of mine-to-mill process optimization................................................... 8 2.2 Evolution of mine-to-mill......................................................................................... 9 2.3 "Optimum blasting" not based on cost a lo n e ....................................................... 11 2.4 How blasting influences fragmentation and filters into mine-to-mill............... 12 2.5 The focus of this research......................................................................................... 13 3. PRINCIPLES FOR THE DESIGN, MEASUREMENT, MODELING, AND SIMULATION OF BLAST FRAGMENTATION..................................................... 18 3.1 Introduction................................................................................................................ 18 3.2 Blast design objectives, fundamentals, and methods.......................................... 18 3.2.1 The objectives and fundamentals of blast design..................................... 18 3.2.2 The methods of blast design........................................................................ 19 3.2.3 The Blast Dynamics Energy method......................................................... 22 3.3 Description and modeling of blast fragmentation................................................. 23 3.3.1 An objective description of the degree of fragmentation........................ 24 3.3.2 The modeling of particle size distribution................................................ 26 3.4 The measurement and estimation of blast fragmentation.................................... 28 3.4.1 Photographic granulometry methods......................................................... 28 3.5 The prediction of blast fragmentation.................................................................... .30 3.5.1 Ouchterlony's review................................................................................... .31 3.6 The Kuz-Ram model..................................................................................................32 3.6.1 The Kuznetsov equation.............................................................................. .33 3.6.2 Adoption of the Rosin-Rammler equation................................................ .36 3.6.3 The Uniformity equation............................................................................. .37 3.7 Important limitations to the original Kuz-Ram model......................................... .39 3.7.1 Important changes to the algorithm........................................................... .39 4. PRINCIPLES, TRENDS, AND METHODS FOR COMMINUTION MODELING AND THE SIMULATION OF CRUSHING SYSTEMS.......................................... 46 4.1 Overview......................................................................................................................46 4.2 The discussion and reporting of grinding simulation........................................... .46 4.3 The simulation of mineral processing circuits........................................................47 4.3.1 The Bond model........................................................................................... .48 4.3.2 Justification for the use of modeling and simulation in this research... 49 4.4 The modeling and simulation of crushing systems............................................... 50 4.4.1 The jaw crusher model..................................................................................51 4.4.2 The cone crusher model................................................................................51 4.4.3 Estimation of crusher classification and breakage functions................. .55 4.4.4 Estimating the crusher work index..............................................................56 5. FRAGMENTATION MODELING PARAMETERS, BLAST DESIGNS, AND FRAGMENTATION PREDICTION............................................................................ 58 5.1 Overview..................................................................................................................... 58 5.2 Determination of rock factor, A.............................................................................. 58 5.2.1 Sample collection and preparation...............................................................59 5.2.2 Testing..............................................................................................................61 5.2.3 Computation of rock factor, A......................................................................63 5.3 Blast design................................................................................................................ ..63 5.3.1 Details of blast design.................................................................................. 64 5.4 Prediction of blast fragmentation............................................................................ 64 6. ESTIMATION OF CRUSHER SIMULATION PARAMETERS............................ 83 6.1 Overview..................................................................................................................83 6.2 Estimation of crushing simulation parameters...................................................... ..83 6.2.1 Preliminaries for parameter estimation..................................................... ..84 6.2.2 Crusher and screen settings and characteristics....................................... ..86 6.2.3 The crusher breakage and classification functions.................................. ..86 6.2.4 The crusher work index............................................................................... ..87 6.2.5 Verification of crushing simulation parameters....................................... ..88 vii 7. SIMULATION OF THE CRUSHING OPERATION................................................ 99 7.1 Overview..................................................................................................................... 99 7.2 Simulation setup........................................................................................................ 99 7.2.1 Results............................................................................................................ 101 7.2.2 Performance evaluation criteria.................................................................. 101 7.2.3 Conclusions about the impact on crushing............................................... 103 8. THE INFLUENCE OF FRAGMENTATION ON DRILLING AND BLASTING COSTS AND LOADING AND HAULING PRODUCTIVITY.............................. 111 8.1 Overview..................................................................................................................... 111 8.2 Oversize rock and its implications for secondary breakage and overall costs ...111 8.3 The effect of the degree of fragmentation on the costs of drilling and blasting 112 8.4 Estimation of the costs of drilling and blasting..................................................... 112 8.4.1 Drilling costs................................................................................................. .113 8.4.2 Blasting costs................................................................................................ .114 8.5 The influence of fragment particle size distribution on loading productivity... 116 8.6 Evaluation of the loader cycle/productivity versus fragment size distributions 117 8.7 Results of statistical analysis................................................................................... .118 8.8 Implications................................................................................................................ .120 8.9 Estimation of wear and tear arising from degrees of rock fragmentation......... .121 9. THE RELATIONSHIP OF BLAST-GENERATED FRAGMENT SIZE DISTRIBUTION AND UNIT MINING COSTS........................................................ 151 9.1 Overview: The requirements and scope of evaluation......................................... 151 9.2 The method of economic evaluation....................................................................... 154 9.3 Costs of wear and tear...............................................................................................155 9.4 The effects on slope stability costs......................................................................... 155 9.5 Implications for grade control, ore loss, and dilution.......................................... 156 10. SUMMARY, OBSERVATIONS, RECOMMENDATIONS, AND CONCLUSIONS............................................................................................................... 159 10.1 Summary of research process............................................................................... 159 10.2 Summary of findings............................................................................................. 161 10.3 Other observations................................................................................................. 162 10.4 Discussions.............................................................................................................. 163 10.5 Future research....................................................................................................... 164 APPENDICES A GRINDING REPORT.............................................................................................. 167 viii B A SELECTION OF CONVERSIONS OF THE UNITS USED IN THIS RESEARCH...............................................................................................................218 C DEVELOPMENT OF THE KUZ-RAM ROCK FACTORS..............................220 D CORE DIMENSIONS, SEISMIC VELOCITIES, AND DYNAMIC YOUNG'S MODULI................................................................................................225 E PHOTO OF CORES USED IN ROCK CHARACTERIZATION.....................227 F DENSITY DATA OBTAINED FROM W.U.S. COPPER'S GEOLOGY (ORE CONTROL) SECTION, WITH THOSE ESTIMATED IN THIS RESEARCH AT THE UNIVERSITY OF UTAH (U OF U)..................................................... 229 G A SUMMARY OF DATA OBTAINED FROM UNIAXIAL COMPRESSIVE STRENGTH TESTING OF ROCKS FROM W.U.S. COPPER MINE............ 231 H POINT LOAD DATA USED TO ESTIMATE UNIAXIAL COMPRESSIVE STRENGTHS OF ROCKS...................................................................................... 233 I CRUSHING CIRCUIT CHARACTERISTICS....................................................237 REFERENCES...................................................................................................................... 239 ix ACKNOWLEDGEMENTS Many people contributed in many different ways to make my research possible. I owe these people my sincere thanks. Firstly, my heartfelt thanks to W.U.S. Copper (a pseudonym) for kindly and generously granting me access to their mine and their incredible personnel. My experience with them has built me up in many invaluable ways, and I wish them the success that they work so hard for and that they so greatly deserve. While I would love to name and thank specific persons working at or in relation to this operation, the company's desire for anonymity prevents my saying thanks to these persons by name. However, I say to them a big thank you for all the help, time, and other resources they so graciously gave me. My heartfelt thanks to the Fulbright Program for sponsoring my studies, and to the Institute for International Education (IIE) for stoutly and vigilantly shepherding me through. I am forever grateful for your support. I am indebted to my committee, whose dedicated and thoughtful review of my evolving concepts, thoughts, and drafts made this dissertation possible. Each member gave more support than duty required. As a result, I come out a confident professional in issues of mine-to-mill optimization. Thank you, Dr. Kim McCarter, Dr. Mike Nelson, Dr. Raj Rajamani, Prof. Tom Hethmon, and Dr. Hyung Min Park. I am grateful to Pam Hofmann, Samantha Davis, and Darrel Cameron for their kindness of heart and their stalwart support throughout the course of my studies. Special thanks to Rob Byrnes for patiently giving me guidance in my geotechnical test work. My incredible colleagues and fellow travelers, Mahesh Kumar Shriwas, Siavash Nadimi, Ankit Jha, Anirban Bhattacharyya, Hossein Changani, Kirk Erickson, and Rao Latchireddi, I am grateful to have known you, and to have shared the bond and trials of learning. I thank you, Jessica Wempen, for being such sound counsel and encouragement. Many times, I have wished you were not so uncannily spot-on with your shot-in-the-dark predictions! My family bore the most sacrifice to make my studies possible. The rest of my life is committed to making up for my absence in your lives over this period. Thank you, Annette, Kwame, Hinga, Nyapo, and Ama! My thanks to Chris Adjei, Hannah David, Joseph Morrison, Marie Rogers, Amelia Liberty, Martha Munezhi, Henok Eyob, Michelle Twali, Betty Jonah, John and Amie Tucker, and the Newlove family for giving me socio-psycho-emotional support and succor through this period. I hope I have been a good enough friend and brother, and I dearly look forward to keeping the bond through the rest of our lives. xi CHAPTER 1 INTRODUCTION 1.1 Problem Statement The view is held widely in the mining industry that more intense fragmentation created by blasting yields increasingly better economic benefits to some key aspects of the mine-to-mill value chain (MacKenzie 1966, 1967; Edgar and Pfleider 1972; Workman and Eloranta 2003; Singh and Narendrula 2005; Eloranta et al. 2007; Brandt et al. 2011). Those aspects that are said to benefit from blasting improvement include the load and haul segments (with associated improvement in productivity), crushing, grinding, and general processing throughput potential. However, a closer examination suggests that, while the anticipated benefits may be realized in some specific situations, there may actually not be as much economic merit to increasing blast fragmentation (reducing the particle size distribution) on these elements as the widely held notion suggests. Process performance improvements, such as increased mining productivity, plant throughput and decreased comminution energy consumption, which are conventionally attributed to blast-induced particle size reduction, may actually be due to additional or entirely different causes, such as better-blended ore grades and changing material hardness (Dance et al. 2007). Similarly, the productivity of loading machines may be affected not by particle size distribution alone, but by several other factors, including the looseness, angle of repose, moisture content of the muck pile (Singh and Narendrula 2005), the degree of interlock between fragments, and operator efficiency. Additionally, it is common experience that a wide range of fragmentation size profiles result within the same rock domain (as observed in this research), even when based on a constant level of blast energy infusion. Indeed, such an observation that blasting provides inconsistent particle size distributions and muck pile characteristics further confuses evidence or undermines the prospect that any observed downstream benefits actually would arise directly from blasting alone. The ambiguity therefore triggers the question: how consistent can the effects of blasting be expected to be along the mine-to-mill pathway? The anticipated benefits are sometimes not even necessarily evident, possibly being far too negligible to be considered significant. In effect, the process of physically and objectively tracing the cause-and-effect relationships between the blast results, load and haul productivity, grinding effort (Eloranta 2014), and the overall economics of the operation is often far too fraught with obscurities to provide conclusive results. Thus, it remains a challenge to provide definitive answers to the question: how does blasting and blast-generated particle size distribution affect the economics of a hard-rock operation? 1.2 Hypothesis The hypothesis for this research has been formulated to investigate the validity of the above-described notion which is prevalently held about the mine-to-mill concept, that is: 2 Increased intensity o f blasting leads to reduced particle size distributions which eventually lead to a diminishing and minimization o f net mine-to-mill costs. The alternative proposition to this hypothesis is that the increased energies and reduced particle size distributions do not lead to a reduction and minimization of the net mine-to-mill costs. 1.3 Objectives of the research In pursuit of evidence for the above hypothesis, the following objectives were outlined for this research: 1. Carry out preliminary rock (ore and waste) characterization • From these, generate modeling and simulation parameters (for blasting, crushing, and grinding); 2. Produce a range of blast designs with energy inputs ranging from low to high; 3. For each blast design, predict the resulting particle size distribution (PSD) using the Kuz-Ram model; 4. For each design, estimate the unit costs of all the mining unit operations; 5. Simulate the comminution process for all feed PSDs • Crushing; • Grinding; 6. Evaluate the effect of feed size (PSD) changes on: • Mining : drilling, blasting, loading, hauling; • Energy consumption, throughput/feed rate; • Costs 3 7. Compare the savings/losses from the mine to the mill, based on the changes in energy input into the blast. 1.4 Description of the host operation This research was carried out at the operations of W.U.S. Copper, a private-equity-funded company located in the western United States, whose real name has been disguised in this dissertation for reasons of privacy. Typically, copper, silver, and gold mineralization in the deposits of W.U.S. Copper is associated with low-iron skarn alterations within clastic sedimentary rocks and in limestone lying immediately above a monzonite intrusive stock. The company extracts ore by open pit methods, and employs drilling and blasting techniques to dislodge and fragment ore and waste. Drilling and blasting services are provided by a contractor, based on terms that are reviewed periodically. The mine uses conventional load and haul processes to move ore to the crusher and waste to the adjacent dumps. A three-stage crushing circuit (one jaw and two cone crushers) produces feed for a two-stage grinding plant. At each stage of grinding, there are two ball mills operating in parallel with each other. Each ball mill operates in standard closed circuit configuration. The cyclone product from the first-stage of grinding is screened at 140 Tyler mesh (105 microns), and the screen undersize is caught in a sump that feeds the second-stage ball mill. The screen oversize forms part of the grinding circuit's final product. The P80 size of the final grinding product (screen undersize plus Stage 2 cyclone overflow), combined from the parallel circuits, is 140 Tyler mesh (105 microns). Figure 1.1 is a schematic of 4 the whole comminution circuit. The liberated copper content in the grinding product is recovered in a flotation circuit to form the final product which is a concentrate. The grade of the concentrate is 22% Cu. 1.5 Scope of the research This research focused on the stages from drilling to grinding, and did not consider any of the processes downstream of the comminution circuit, including flotation. The reader may notice that, even though grinding studies are outlined in Section 1.3 as a part of the objectives of this research, the topic of grinding has not been included in the list of chapters. This exclusion was made as a consequence of findings during the research that the crushing product streams remain invariant irrespective of the size profiles generated in the blasting product (crusher head feed). This finding implied that, irrespective of the range of blast energies considered, only a single particle size distribution of feed would be available for a grinding study, and this lack of variety would render pointless the plan to simulate grinding performance for a variety of blast energy-related feed particle size profiles. However, it must be noted that a significant amount of the research time, especially at the early stages, was devoted to studying the grinding characteristics of the ore, in anticipation of using that understanding to assess the effect of blasting. The decision was therefore made to include the grinding report (with the related literature reviews, modeling theory, and a full account of the grinding test procedures) in Appendix A for interested readers. The remark is made in Section 4.2 that the outcomes of the grinding study presented in Appendix A remain valid considerations for a grinding optimization 5 effort at the mine, for as long as the ores being treated in the ball mills remain the same as those that were being treated at the time of the grinding sample collection. Should those ores change, which they will as mining progresses downwards in the pits, fresh samples of crusher product will need to be taken, and the full range of fresh grinding tests performed on the new material. 1.6 Units of measure The primary units of measure in this dissertation are the S.I. units. However, the blasting industry in the United States is solidly based on customary English units, with designs and measurements being prevalently carried out and expressed using the latter. In order to minimize the chances for loss of communication in this operating context, the design procedures have all adhered to the customary practice, and metric equivalents of measure have been provided throughout. Appendix B provides a selection of conversions of the units used in this research. 6 FIGURE 1.1 A schematic layout of the comminution circuit at W.U.S. Copper 7 CHAPTER 2 UNDERSTANDING MINE-TO-MILL PROCESS OPTIMIZATION 2.1 Overview of mine-to-mill process optimization Between 1990 and 2010, the mining industry saw a surge of interest in the field now commonly called mine-to-mill process optimization, mine-to-mill (Julius Kruttschnitt Mineral Research Center, or JKMRC, 2012), mine-to-mill integration, and process improvement and optimization (PIO) (Dance et al. 2007; Mwansa et al. 2010). The basic concept in this field is that the unit processes in the mining and mineral processing phases of mineral extraction are all related and interdependent, and that they should therefore be treated with an integrated approach, rather than as unrelated processes. Accordingly, it is argued that all benefits and costs accruing at each stage should be reckoned and optimized together against (or in), as it were, a unified overall cost center. In the traditional system, which is still practiced in many operations around the world, the optimizations of the mine and mill are done separately, with the following typical characteristics being evident (JKMRC 2012): • mine and mill are under different management structures and cost centers; • each process has production targets and cost budgets that are optimized without due consideration for the implications of this said optimization either upstream or downstream; • in the case of costs, the optimization objective for each cost center is to achieve a minimum, and the production volume objective is a maximum. Thus, effectively, the effort is a bid for quantity rather than quality. Commenting on the traditional approach, Workman and Eloranta (2003) say, "in the past, the primary focus was the ability of the excavation equipment to productively dig the blasted rock and the amount of oversize chunks produced". In an analysis of the syndromes of the traditional approach to mining optimization, the Julius Kruttschnitt Mineral Research Centre (JKMRC 2012) notes that there is often inadequate communication between different processes to understand the interactions and changes. Furthermore, there is usually no incentive to improve the overall efficiency or value added. These commentators describe this approach as mainly cost oriented rather than value oriented, as the key performance indices (KPIs) do not encourage the maximization of the overall economic value across the operation. However, according to JKMRC (2012) "the focus .... (should be) to maximize the overall value of the operation rather than just to minimize the unit costs". 2.2 Evolution of mine-to-mill Although the surge of industry interest in mine-to-mill was seen mostly around the turn of the millennium, focus on the impact of the degree of rock fragmentation on the economics of an operation was brought to the fore much earlier, principally through the writings and conference presentations of MacKenzie (1966, 1967). MacKenzie produced what are now considered the classical curves representing the relationships between the 9 degree of fragmentation and the individual as well as cumulative costs of the various unit processes, from drilling to crushing (Figure 2.1). This set of curves demonstrates the cost dependence of the various mining unit operations on the degree of fragmentation. The costs of these unit operations, namely, drilling, blasting, loading, hauling, and primary crushing, will increase (or decrease) as shown, with the degree of fragmentation. Summing the curves together, the overall cost versus degree-of-fragmentation curve shown last in the set of curves is obtained. This curve has the form of a saddle, indicating that there is a certain set of values of the degree of fragmentation for which the overall cost is a minimum. According to MacKenzie's presentations, the base of the saddle is quite broad, suggesting that the overall costs change little over a wide range of fragmentation. MacKenzie (1966, 1967) and later Hustrulid (1999) explain the logic and mechanism behind MacKenzie's curves in detail. Probably due to the central thought in MacKenzie's presentations, the mining industry has prevalently viewed the concept of mine-to-mill integration as leaning almost entirely on rock fragmentation, especially by blasting. However, this view is misleading. Dance et al. (2007) clarify that it is really about (producing) "a more suitable, higher value or higher quality concentrator feed". They stress that what "higher quality feed" means will vary from operation to operation. "In some cases, it is finer fragmentation, in others it is feed that is well blended for grade and lacking in contaminants; it can even indicate that certain ore types are, in fact, not profitable and should be considered mineralized waste" (Dance et al. 2007). They add that "process improvement and optimization (or mine-to-mill) reflects the fact that optimizing concentrator feed goes beyond run-of-mine (ROM) fragmentation and considers all aspects of improving mill 10 performance from throughput, recovery and final concentrate grade to lower operating costs". Mine-to-mill philosophy follows a more-or-less 5-stage methodology in its implementation that is highly similar to the workflow of the widely known six-sigma process improvement methodology. This protocol typically involves benchmarking, rock characterization, measurements, modeling/simulation and, if necessary, material tracking. 2.3 "Optimum blasting" not based on cost alone MacKenzie (1966, 1967) defined optimum blasting as that blasting practice that gives the degree of fragmentation necessary to obtain the lowest unit cost of the combined operations of drilling, blasting, loading, hauling, and crushing. Quoting a popular saying in mine management at the time of his writing, MacKenzie says: "the place for primary crushing is in the mine, not in the crushing plant". He adds, "It has been known for many years that the key to an efficient, low cost hard rock operation is in the mine" (MacKenzie, 1966). He then goes ahead to state as the objective (of his study) the identification of the minimum cost method for the chain of activities under review. In fact, MacKenzie's focus on mine-to-mill was principally one of cost optimization. He sought to optimize the mine-to-crusher pathway by aggregating the process (unit operation) options which together achieved an overall cost minimum. However, as was later demonstrated by Kanchibotla (2001), this may well lead to a kind of false efficiency, as it overlooks the influence of revenue changes related to various degrees of fragmentation. 11 According to Kanchibotla (2001), revenue is a principal component of the optimization effort. Whilst recognizing that costs for some subprocesses actually need to be increased (rather than decreased) in order to reduce the overall costs of the chain, he notes that the profitability of an operation can be improved either by increasing the revenues or by decreasing the costs, or both. Inherently, he argues, various scenarios exist which shift the optimal choice across a whole spectrum of possible combinations of blasting and processing cost. Some of these scenarios are commodity-specific. As an example, Kanchibotla reports studies he carried out that demonstrate that purely minimizing total operating costs does not necessarily result in optimum solution unless the impact on unit fixed costs and revenues are also considered. Indeed, the optimum, which may be defined as the maximization of profit, may as well occur on either side of the total cost minimum as on it. This reality of uncertain merits and outcomes for a fragmentation objective thus necessitates a systematic study to determine the conceptually more correct notion of value chain optimization. Figures 2.2 and 2.3 demonstrate Kanchibotla's value chain curves. Thus, according to Kanchibotla (referring to the contents of Figure 2.3), "optimum" is where the results deliver the maximum net returns on the investment while maintaining the safety and environmental standards. 2.4 How blasting influences fragmentation and filters into mine-to-mill Various authors have reviewed the nature of rock fragmentation produced by blasting, and opined on the mechanisms by which that fragmentation affects the mine-to-mill pathway (Nielsen and Kristiansen 1996; Hustrulid 1999; Valery and Jankovic 2002; 12 Ouchterlony 2003; Workman and Eloranta 2003; Valery et al. 2004; Eloranta et al. 2007; JKMRC 2012). All views embrace the notion by Workman and Eloranta (2003) that there are two important aspects of blasting effect on fragmentation, namely, the seen and the unseen. The seen part is the size distribution of blasted fragments, and the unseen effect is in the form of fractures or cracks within the blasted fragments. It appears to be a consensus among these commentators that improvements in yield from blasting typically consist of some combination of the following features: • A larger throughput in crushers and mills; • A lower total energy expenditure in the process; • Smaller volumes of worthless or cost-prone fractions like fines and oversize; • A higher ore concentrate grade; • A higher processing recovery arising from improved liberation (Ouchterlony 2003); • An improved or, at least, a maintained fragmentation with a lower consumption of explosives. 2.5 The focus of this research This research focuses principally on the seen aspect of blast fragmentation, namely the particle size distribution. It neither attempts to assess microfractures nor to evaluate the processing impacts of those microfractures on the liberation characteristics of the ore. Liberation requirements that determine the target grind size were previously investigated by the host mine. Based on verbal advice received, and on current practices at the mine, the assumption was made here that maximum liberation of all of the copper 13 ore for economic metallurgical recovery is achieved at a grind of 80% passing size of 105 microns (150 Tyler Mesh or 140 US Mesh). This comminution target is the final grind size at the mill of the host mine. Indeed, this size is the sum of all of the breakage goals, contributed to at each stage of "comminution" from the mine to the mill. 14 15 Fragmentation Fragmentation Fragmentation After Mackenzie 1966, 1967 FIGURE 2.1 The effect of the degree of fragmentation on the individual unit operations and on the overall cost -----------Processing cost Load and haul cost ............. Drill and blast cost ■ ■ " Operating cost ............. Throughput .............Fixed cost ■ Total cost Adapted from Kanchibotla et al. (2001) FIGURE 2.2 An adaptation of MacKenzie's fragmentation curves to account for impact on throughput 91 Final Product Value Revenues - - - - Total cost 3 Cl. - CM3O FIGURE 2.3 An adaptation of MacKenzie's curves to reflect the contribution of revenue and overall value to the determination of optimum blast performance 17 CHAPTER 3 PRINCIPLES FOR THE DESIGN, MEASUREMENT, MODELING, AND SIMULATION OF BLAST FRAGMENTATION 3.1 Introduction In this chapter, the objectives and fundamentals of surface blast design are reviewed briefly, and some key methods of bench blast design are discussed. A justification is provided for the selection of the design method that is used in this research. Methods for the description and measurement of blasting results are reviewed, and the basis is laid out for the techniques used in this work to model and predict or simulate the blasting product particle size distributions. 3.2 Blast design objectives, fundamentals, and methods 3.2.1 The objectives and fundamentals of blast design All blast design efforts for open pit mining seek, partly, to find suitable values for the following geometrical elements: the blast hole diameter (D), the burden (B), the spacing (S), the sub-drill (J) and the stemming (T). Together, these elements define the region of rock space that will be directly impacted by the infusion of chemical energy in the process of blasting. The combination of these dimensions with the choice and characteristics of the explosive, as well as the manner and sequence of initiation of the explosive throughout all or part of the blast, constitute the totality of the blast design. In a bench blast, the burden (B) is defined as the distance between the individual rows of holes (see Figure 3.1). The burden is also usually reckoned as the distance between the front row of holes and the free face. The spacing (S) is the distance between holes in a given row. Typically, the holes are drilled to a finite depth below the desired final grade. This extra depth of drilling is called the sub-drill (J). Generally, a fraction of the length of the drill hole is left uncharged with explosive, and is usually filled with crushed rock or drill chippings, or just simply left unfilled. This fraction is the stemming (T). The drilled length of the blast hole (L) is equal to the bench height (H) plus the sub-drill (J). The total length of the explosive column (Le) equals the hole length (L) less the stemming (T). 3.2.2 The methods of blast design According to Hustrulid (1999), most geometrical designs for a surface mine blast operate, not arbitrarily, but on the basis of some kind of a rational relationship between two or more of the geometric elements listed above, that seeks to optimize energy distribution. He lists the five most fundamental of these relationships as follows: 1 Spacing - Burden S = KsB 19 Where: KS is a constant relating spacing, S, to the burden. B. For a square pattern, KS = 1; it grades into a rectangular pattern for values between 1 to 1.5. For staggered patterns, the best energy distribution is achieved with KS = 1.15. 2 Burden - Diameter B = KbD Where: Kb is a constant relating burden to the hole diameter, and incorporates explosive energy factors and rock density. 3 Subdrill - Burden J = KjB Where: KJ is a constant relating sub-drill to the burden. Values range from 0.23 to 0.32. A typical value is 0.3. 4 Stemming - Burden T = Kt B Where: 20 Kt is a constant relating stemming to the burden. Typically, KT > 0.7 21 5 Bench height - Burden H = KhB Where: Kh is a constant relating bench height to the burden. Typically, Kh > 1, but is more commonly between 1.5 and 2. Hustrulid (1999) combines relationships 2 and 5, and devises the following: H > KbD John Floyd (n.d.) validates this relationship by recommending the following: D(in) < % * H (ft) There are many blast design methods in use in the mining industry today, the most common of which include: Konya's method, Ash's method, Powder Factor method, Blast Dynamics method, and Blast Dynamics Energy method. All of these methods have emerged or evolved from empirical observations and/or rules of thumb, focused on deducing the values for the above-listed ratios which yield the most efficient energy coverage in the mass of rock to be blasted. Details of the various methods are documented in various places (Ash 1963; Konya 1968; Hustrulid 1999; Floyd n.d.). In this dissertation, the method used to design blasts is the Blast Dynamics Energy method. 3.2.3 The Blast Dynamics Energy method This method has been promoted in industry by John Floyd of Blast Dynamics. Like the other methods, it applies suitable values for all of the ratios outlined above that, in the experience of the proponent, enhances explosive energy distribution. The uniqueness of this method is based first on a decision to apply a certain level of energy to the rock. This desired energy infusion is specified in terms of an energy factor (EF), expressed in kcal/st. A list of recommended energy factors, viewed by Floyd as suitable in the described situations, is presented in Table 3.1. Once the energy level is selected, a back-calculation is done (see Equation 3.1) to determine the various dimensions of the design factors that would yield the specified energy input. The advantage of using the Blast Dynamics Energy method is that it gives an excellent index for comparing energy inputs. For example, an EF of 100 kcal/st is clearly smaller than one of 400 kcal/st. This scale then provides an objective means for a systematic investigation like the one in this dissertation, to progressively change blast energy input and assess the key outcomes and impacts. Although it is somewhat similar to the Powder Factor method in terms of the ability to rank levels of explosive energy input into blasts, it differs in the sense that it considers the actual explosive energy input rather than (as in the Powder Factor method) just the weight of the explosive used. Thus, various explosives of different formulations can be compared on a consistent and rational energy-based scale. The design process by this method is as follows (McCarter 2014; Floyd n.d.): i. Calculate stem length, T, by the formula: 22 T = De(22/12) (for explosive density < 0.9 g/ cm3) De(24/12) (for explosive density > 0.9 g/cm3) 23 ii. Calculate: Subdrill, J = De*(7/12) iii. Calculate: Loading density = 0.3405*(Explosive Density)*De iv. Calculate: Charge weight = (H + subdrill - stem length)*(loading density) v. Calculate: Charge energy = 0.454*(charge weight)*(AWS) vi. Calculate: Burden (B in feet) by the formula: B = 1739 * 0.5 Charge Energy .Desired Energy Factor*Rock Density*Bench Height. (3.1) Where: Charge Energy is in kcal/blast hole Desired Energy Factor is in kcal/st 3 Rock Density is in lb/ft3 Bench Height, H, is in ft Hole Diameter, De, is in inches Explosive Density is in g/cm3 AWS is in cal/g vii. Calculate Spacing (S) (ft) = 1.15*B 3.3 Description and modeling of blast fragmentation For many years, an unambiguous representation of blast-related fragmentation outcomes was difficult to produce. This difficulty was closely related to the problem of measuring or evaluating fragmentation outcomes. Aspects of measurement and evaluation are treated in Section 3.4. It is noteworthy that MacKenzie (1966, 1967) in his accounts of the results of his study of fragmentation never stated the difficulty he encountered in evaluating the outcomes. His solution was to represent fragmentation by indirect means. He represented the "degree of fragmentation" by shovel loading speed (exclusive of operating delays). This method to describe fragmentation is classified as indirect, in that it does not really produce an objective quantitative representation of the fragmentation, but instead makes reference to performance values, such as shovel loading speed, that depend on the degree of fragmentation. In addition to this loading rate which MacKenzie favored, other workers (Hustrulid 1999) have indicated other methods such as the quantity of secondary breakage required, secondary breakage costs, bridging delays at the crusher, crusher energy consumption, the type, strength, and size of the feed material, the size of the crushed product, and crusher throughput. The effectiveness of these various means to represent the degree of fragmentation is, at best, left to personal proof. All of those measures are subject to a wide range of extraneous influences. While MacKenzie's shovel productivity may be valid in some situations, it is fraught with a lot of issues such as will be demonstrated in this work (see Sections 8.5 and 8.6). 3.3.1 An objective description of the degree of fragmentation The most common and objective representation of the degree of fragmentation today is the PSD. It is a mathematical description of the fraction of discrete or cumulative mass(es), P, passing a screen with a given size, x. 24 In its simplest form, the PSD is expressed as the equivalent of a frequency table, listing the various fractions of mass appearing in each of a set of discrete size ranges. A suitable graphical representation would be patterned after the frequency distribution model, P(a), such that all size fractions are displayed as size interval-bound frequencies. In its cumulative form (the cumulative distribution function or CDF), it itemizes the probability, P(x), of fractions of the masses in question appearing below (or passing) a specified mesh size, x. The function, P(x) then varies from 0 to 1 or from 0 to 100%. Figure 3.2 is an example of a graphical output from this kind of a function. In relation to Figure 3.2, the following features are relevant to this discussion: X50 is a measure of mean fragmentation, which equates to the mesh size through which half of the muckpile (P = 0.5 or 50%) passes. XN is some other percentage-related fragmentation size, where N = 20, 30, 75, 80, 90, etc. PO is the percentage of fragments larger than a typical size, xO. This percentage is related to the handling of big blocks (or oversize) by trucks or the size of blocks that the primary crusher cannot swallow. PF is the percentage of fine material smaller than a typical size, xF. In certain contexts, this percentage may be related to sizes below which a penalty for the product's generation is accounted. The above method of representation of fragmentation or particle size distribution is very prevalently used in mineral processing. 25 26 3.3.2 The modeling of particle size distribution The CDF discussed in Section 3.3.1 is typically discretized, as it is obtained over a number of fractions, retained or passing specified sizes, from sieving with a finite number of screens. A common related practice is to represent the CDF by a continuous function, P(x). A number of standard continuous functions of this nature are used to model particle size distributions, the most common of which are the Rosin-Rammler function (Rosin and Rammler 1933) and the Gaudin-Schuhmann function (Schuhmann et al. 1940). Both distribution functions will be discussed here. 3.3.2.1 The Rosin-Rammler Distribution function This function is given as follows: Where: Y is the cumulative fraction finer than x x is the particle size xc is the size modulus or characteristic size, or absolute size constant (theoretical maximum particle size) n is the distribution or dispersion modulus (the spread of the distribution) The expression can be transformed to (3.2) (3.3) 27 This model generally fits coarse particle distributions, which is both a strength and a weakness. The model is known to not adequately predict in the fines range. The relationship is relatively linear over the entire range of particle sizes. Other variations of this expression are used in mining and mineral processing, as will be seen in Section 3.6.1.2. 3.3.2.2 The Gaudin-Schuhmann Distribution function This distribution function is more commonly used in mineral processing, and generally fits fine particle distributions, such as a ball mill product. It tends to best fit below the 75 to 80% passing size, and has been used in this dissertation in the description of particle size distributions of test ball mill feed and product streams. The relationship is: Where: Y is the cumulative fraction finer than x x is the particle size k is the size modulus (theoretical maximum particle size) m is the distribution modulus (spread of the distribution) (3.4a) Re-expressed, log Y = m • logx - m • logk (3.4b) 3.4 The measurement and estimation of blast fragmentation The pertinent question is how should the particle size of a muck pile be measured or estimated? Either direct or indirect methods can be used. Direct methods include sieving the whole muck pile, counting boulders, and measuring boulders. Sieving the muck pile is a particularly tedious option that may be impractical or nonviable, and is certainly time-consuming and very costly. Boulder evaluation (counting and measuring) does provide some information, but is restricted to assessing the coarse extremes of the distribution. On the other hand, the indirect methods, which may be somewhat less accurate, are usually the most practical methods. Two categories of viable indirect methods are (1) the photographic (or photogrammetric) methods, and (2) the measurement of parameters that can be quantitatively related to the degree of fragmentation. Both of these methods have been used in this dissertation. Photographic methods have been used to estimate the particle size distribution on the mining face, and time-and-motion studies have been used, with very limited success, to attempt to establish a relationship between the particle size distribution and the rate at which loading of rock is done. The inability, encountered in this work ( Sections 8.4 and 8.5) to establish a statistically significant relationship between loading rate and PSD underscores the unreliability and ineffectiveness of this kind of indirect method. 3.4.1 Photographic granulometry methods The theoretical basis and operating details of photographic methods of size distribution analysis are well documented in literature (Kemeny et al. 1993; Bedair 1996; 28 Maerz 1998; Maerz et al. 1998; Kemeny et al. 2001; Maerz et al. 2001; Palangio et al. 2005; Eloranta et al. 2007; Bobo, n.d.), and will not be given any extensive treatment here. Photographic methods involve less of measurement and more of estimation. However, it is important to note that, imperfect as photographic methods are, they are the speediest, most practical, and most cost-friendly evaluation methods that provide quantitative descriptions of the blast product distribution. In the fast-paced contemporary production environments, these methods can return fairly dependable results in close to real-time, and provide a means for rapid evaluation and pro-active or corrective decision making. Typically, the results of photographic granulometry estimates of particle size distribution are provided in the form of the particle size distributions, as shown in Figure 3.2. A key issue in these techniques is that evaluation of fines can be quite tenuous below a certain size. Only estimates can be made of fines below certain sizes, these size limits being influenced by the capabilities of the specific piece of software in use. Estimates of the particle distribution profile below this cutoff may be done using curve characteristic options, including Rosin-Rammler (Split Desktop and WipFrag software), Gaudin-Schuhmann (in Split Desktop software), or the Swebrec function (WipFrag software). Importantly, photographic methods also provide a means for validation of predictive and simulation models. Without such a practical tool for comparison, and given the impracticality of direct sizing techniques, the predictive models would probably have no means to be validated or checked for effectiveness. 29 3.5 The prediction of blast fragmentation Blasting literature documents various methods that have developed over the years that attempt to predict the size distribution resulting from a blast design (Hall and Brunton 2001; Ouchterlony 2005). According to Cunningham (2005), the majority of these methods generally fall into two categories, empirical and mechanistic modeling techniques. Empirical models are predominantly based on the assumption that increased energy levels result in reduced fragmentation across the whole range of sizes. A broader assessment of the characteristics of these models is provided in a review by Ouchterlony (2005), which is summarized in Section 3.5.1. Mechanistic models track the physics of detonation and the process of energy transfer in a well-defined medium (rock) for specific blast layouts. The models are also able to derive the whole range of blasting results. By its very nature, the mechanistic approach is intrinsically able to map out and demonstrate or "play out" the individual mechanisms in the detonation and breakage process. The approach takes into consideration the physics of both the explosion process and the response characteristics of the blasted medium. Extensive work has been carried out by Dale Preece (2001, 2003, 2008), employing finite element and discrete element methods. Mechanistic models typically entail a visual element to their depiction of the fragmentation outcome, and are therefore very compelling to potential end-users. However, Cunningham (2005) insists that they are not necessarily any more accurate than the more prevalently used empirical models. He outlines the major shortcoming of the mechanistic models as that they are limited in scale, require long run times, and involve 30 great difficulty in collecting adequate data about the detonation, the rock, and the end results. 3.5.1 Ouchterlony' s review At about the same time as Cunningham's analysis above, Ouchterlony (2003) carried out an extensive review of fragmentation prediction models. Quoting Rustan (1981), Ouchterlony concluded that, almost invariably, the existing models, which are predominantly empirical in nature, predict the average fragment size (x50) and how that average size depends on the different factors which govern blasting. Some of the models, in addition, venture to describe the fragment size distribution, P(x). Importantly, Ouchterlony observed that rarely do these models attempt to predict the shape of the fragments or their internal microfracture status. This latter fact is a shortcoming, as it leaves a gap in the full evaluation of blast outcomes. Ouchterlony reports that Rustan (1981) had produced a summary in which he (Rustan) noted that the Kuznetsov formula (which eventually became one element of the Kuz-Ram model) tended to have the best basis of all the methods, with a reported accuracy of ±15%. Ouchterlony observed that the general build up of the x50 equation in all instances contained the three factors in the following structure: x50 = constant*(rock factor)*(geometry factor)*(explosives factor) (3.5) 31 The prediction models listed and discussed by Ouchterlony (2003) are as follows: • SveDeFo's fragmentation equations, based on work by Langefors and Kihlstrom (1963), Holmberg (1974), and Larsson (1974) • The Kou-Rustan fragmentation equation (Saroblast) - (Kou and Rustan 1993) • The Kuz-Ram model (Cunningham 1983, 1987, 2005) • The Chung and Katsabanis model (CK model) - (Chung and Katsabanis 2000) • The model of Bergmann, Riggle, and Wu (BRW model) - (Bergmann et al. 1973) • The models of the Julius Kruttschnitt Mineral Research Center (JKMRC or JK models) (Hall and Brunton, 2001) o The Crush(ed) Zone model (CZM) o The Two-Component model (TCM) • The Swebrec Function (Ouchterlony 2003) • The Natural Breakage Characteristic (NBC) model (Moser 2003). For practical reasons, and given the extent of industry affirmation of the Kuz-Ram model (albeit with some significantly acknowledged shortcomings), only the Kuz-Ram model has been discussed and used in this research work. 3.6 The Kuz-Ram model The Kuz-Ram model is probably the best known and most widely used empirical approach to estimating fragmentation from blasting (Cunningham, 2005). It was introduced by Cunningham (1987), and has undergone a number of modifications and seen several applications since its first introduction. There are three key equations constituting the Kuz-Ram model, namely the adapted Kuznetsov equation, the adapted Rosin-Rammler function, and the uniformity equation. 32 33 The Kuznetsov equation predicts the mean particle size resulting from a given blasting situation as a function of the in situ rock condition and the explosive energy infused into the blast. The Rosin-Rammler function describes the particle size distribution over the entire range of fragmentation to be achieved. The uniformity equation predicts the spread of the distribution around the Rosin-Rammler profile, and is an indicator of the precision or statistical spread of particle sizes around the expected distribution profile. Hustrulid (1999) has provided an account of the relationship developed by Kuznetsov (1973) between the mean fragment size and the blast energy applied per unit volume of rock (powder factor), expressed as a function of rock type. The development below is sourced from Hustrulid (1999). According to Kuznetsov, X is the mean fragment size, cm A is the rock factor. Rock factor is 7 for medium rocks; 10 for hard, highly fissured rocks; 13 for hard, weakly fissured rocks Vo is the rock volume (cubic meters) broken per blast hole. Vo = Burden * Spacing * Bench Height Qt is the mass (kg) of TNT containing the energy equivalent of the explosive charge in each blast hole 3.6.1 The Kuznetsov equation (3.6) Where: Expressing the TNT strength in Equation 3.6 in terms of ANFO strength (where the relative weight strength of TNT compared to ANFO is 115, ANFO relative strength being 100), then: 34 x = a ( Q ) ° > Where: Qe is the mass of explosive being used (kg) Sanfo is the weight strength of the explosive relative to ANFO But: Vo _ 1 Qe K Where: 3 K is the powder factor (or specific charge, in kg/m ) Hence, Equation 3.7 becomes: (3.7) (3.8) X _ A(K)-a8Q1e /6 (VSA^NFyO/ 9730 (3.9) The mean fragment size can, therefore, now be calculated from a given powder factor. This form (Equation 3.9), as well as that in Equation 3.7, is the preferred form employed by Cunningham in the Kuz-Ram model. Various applications have been found for this equation, including the calculation of the quantity of a given explosive required to achieve a certain mean fragmentation from a blast. 3.6.1.1 The rock factor, A Cunningham (1983) reckoned initially that values of rock factor, A, range from 8 to 12, with 8 being the lower limit even for very weak rocks and 12 the upper limit even for hard rocks. Cunningham has since taken several steps to improve estimates of the factor, A. A significant milestone along this path was the adoption and modification of Lilly's Blastability Index (Lilly 1986; Widzyk-Capehart and Lilly 2001). Lilly (1986) defined the Blastability Index (BI) as: BI = 2 [RMD + JPS + JPO + SGI + H] (3.10) Where: RMD is the rock mass description JPS is the joint plane spacing JPO is the joint plane orientation SGI is the specific gravity influence H is rock hardness Values that Lilly provided for the terms in this relationship are given in Table 3.2. 35 Cunningham (1987) initially proposed an adaptation for Lilly's scheme as follows: A = 0.06 x (RMD + JF + RDI + HF) (3.11) Where: JF, the Joint Factor, replaces the Joint Plane Spacing (JPS) and Joint Plane Orientation (JPO) in Lilly's formulation. As will be shown in Equation 3.17, this replacement would be subsequently modified further in Cunningham's revision of the algorithm. 36 3.6.2 Adoption of the Rosin-Rammler equation Cunningham observed that the Rosin Rammler formula (see Equation 3.2) provides a reasonable description of the fragment size distribution in blasted rock, the preferred formulation being: - ( - T R = e (3.12) or Wr = 100e - ((x-c)J n (3.13) Where: R is the proportion of material retained on a given mesh, x Wr is the percentage of the weight retained on that mesh x is a given screen size xc is the characteristic size, a scale factor dictating the size through which 63.2% of the particles pass Cunningham (1983) and Hustrulid (1999) show that xc can be obtained from a rearrangement of Equation 3.12, such that: 37 llnRj (3.14) x x c n Given that the Kuznetsov formula gives the 50%-passing screen size X, then substituting X for x and R = 0.5 in Equation 2.12, then: *<= = i d b * (3-15> The requirement for completeness of the prediction model, then, is to determine "n" the uniformity constant. 3.6.3 The U niformity equation From field results, Cunningham (1987) found that, for a square drilling pattern, 1 , S (2-2 - 1 4D )1? 0 - W)(H) 0.5 (3.16) Where: n B is the burden (m) S is the spacing (m) D is the hole diameter (mm) W is the standard deviation of drilling accuracy (m) L is the total charge length (m) H is the bench height (m) For a staggered pattern, ‘n' increases by 10%. In general, it is desirable to have uniform fragmentation, so high values of ‘n' may be preferred. Cunningham (1987) has observed the following pattern: • The normal range of ‘n' for blasting fragmentation in reasonably competent ground is from 0.75 to 1.5, with the average being around 1.0. More competent rocks have higher values. • Values of ‘n ' below 0.75 represent a situation of "dust and boulders" which, if it occurs on a wide scale in practice, indicates that the rock conditions are not conducive to control of fragmentation through changes in blasting. Cunningham observed that "dust and boulders" typically happens when stripping overburden in weathered ground. • For values below 1, variations in the uniformity index, ‘n', are more critical to oversize and fines. For n = 1.5 and higher, muck pile texture does not change much, and errors in judgment are less punitive. • The rock at a given site will tend to break into a particular shape. These shapes may be loosely termed "cubes", "plates", or "shards". The shape factor has an important influence on the results of sieving tests, as the mesh used is generally 38 square, and will retain the majority of fragments having any dimension greater than the mesh size. 3.7 Important limitations to the original Kuz-Ram model As the mining industry embraced the original Kuz-Ram model, a number of shortcomings became apparent, as shown below. Some of these shortcomings still exist today. i. The model failed to consider the effect of timing on fragmentation (Ouchterlony 2005; Kanchibotla et al. 1999) ii. It did not expressly consider the effect of gas pressure and brisance iii. It did not account for microfractures resulting in the broken rock iv. It did not model fines sufficiently effectively (Ouchterlony 2005) v. It did not account for boosters and primers In the light of some the above limitations, Cunningham (2005) proposed a set of changes to the original Kuz-Ram model. The changes aimed at improving estimation of mean fragmentation X, and uniformity, ‘n', both of which he reckoned were partly outcomes of the initiation methods. He ascribes the possibility of these changes to advancements related to the introduction of electronic delay detonators. 3.7.1 Important changes to the algorithm One significant change in the mean fragmentation algorithm lies in the inclusion of a correction factor, C(A). Need for this correction typically arises when it is apparent that the rock factor, A, is either greater or smaller than the original algorithm dictates. 39 Cunningham (2005) recommends that, rather than tweak the input, thus possibly losing some valid input, a correction factor is applied to the rock factor, to adjust to what is reckoned to be the reasonable value. There is also a minor change in the sub-algorithm to quantify the Joint Plane Angle (JPA) influence. This change is as shown in Table 3.3. The revised algorithm, which has been used in this dissertation, is: A = 0.06(RMD + RDI + HF)C(A) (3.17) 40 C(A) has values well within the range 0.5 to 2. 41 Adapted from Latham et al. (2006) FIGURE 3.1 A schematic of key design features in a bench blast 42 Adapted from Ouchterlony (2003) FIGURE 3.2 An example of a fragmentation curve TABLE 3.1 A list of energy factors recommended for various blasting situations 43 Operating Situation Recommended Energy Factor (kcal/st) Very weak rock 100 Well jointed, harder rock 140 Average rock 180 Hard rock 220 Blocky, very hard rock 250 Mine-to-mill blasting 350 Very high energy blasts 500 Upper limit 1200 Source: J. Floyd, 2012: Efficient Blasting Techniques TABLE 3.2: Ratings for Lilly's rock factor parameters 44 Parameter Description Rating Rock Mass Description (RMD) Powdery/Friable 10 Blocky 20 Totally Massive 50 Joint Plane Spacing (JPS) Close (< 0.1m) 10 Intermediate (0.1 to 1m) 20 Wide (> 1m) 50 Joint Plane Orientation (JPO) Horizontal 10 Dip out of face 20 Strike normal to face 30 Dip into face 40 Specific Gravity Influence (SGI) SGI = 25* SG - 50 (where SG is in t/m3) Hardness (H) Mohr's Hardness 1 to 10 Adapted from Lilly, 1986 45 TABLE 3.3: Modifications to assigned values for joint plane angle (JPA) Direction of rock fabric Value 1987 Value 2005 Dip out of face 20 40 Strike out of face 30 30 Dip into face 40 20 CHAPTER 4 PRINCIPLES, TRENDS, AND METHODS FOR COMMINUTION MODELING AND THE SIMULATION OF CRUSHING SYSTEMS 4.1 Overview In this chapter, the principles and theories behind the range of process simulation models used in this research are reviewed. Because comminution processes are typically supported and accompanied by classification phenomena and processes, the applicable models for these accompanying phenomena and processes have been included in this discussion. 4.2 The discussion and reporting of grinding simulation The original plan for reporting on the outcomes of this research included providing a detailed discussion of the theory of grinding simulation. The plan also included providing a complete account of the grinding work that was carried out as part of this research in anticipation of the need to appraise (by simulation) the grinding performance of various streams of hypothetical mill feed that may arise from crushing simulated fragment size distributions for the range of blast designs considered. In the pursuit of the original research plans, the key findings and conclusions that are presented in Chapters 7, 8, and 9 demonstrated that the initially anticipated analysis of grinding are not justified as a central component of this dissertation. However, in view of the amount of effort devoted to this process, the grinding simulation literature review, the details of the modeling parameter development, and the grinding simulation work itself are included as Appendix A. The outcomes presented in this appendix remain valid considerations for a grinding optimization effort at the mine, for as long as the ores being treated in the ball mills remain the same as those that were being treated at the time of the grinding sample collection. Should those ores change, which they will as mining progresses downwards in the pits, fresh samples of crusher product will need to be taken, and the full range of grinding tests performed on the material. In light of the situation described above, the discussions and reviews in this chapter have been provided with very broad attention to comminution in general, and a very specific focus on crushing. Minimal space is given to grinding considerations in the main text. 4.3 The simulation of mineral processing circuits According to Thomas et al. (2014), "Simulation is the imitation of the operation of a real-world process or system over time. The act of simulating something first requires that a model be developed; this model represents the key characteristics or behaviors/functions of the selected physical or abstract system or process". In mineral processing technology, Lynch and Morrison (1999) maintain that, modeling and simulation are concerned with the design and optimization of circuits. According to them, realistic simulation relies heavily on the availability of accurate and 47 48 physically meaningful mathematical models, of which there are three types: theoretical, empirical, and phenomenological. Detailed discussions about the characteristics and formulation of these models are well dispersed in literature (Mular 1989; Sastry and Lofftus 1989; Sastry 1990; Wills 2006) and will, therefore, not be given further treatment here. Bond's (1952) model is one of three popular empirical energy-size relationships for the modeling and scale up and simulation of comminution systems. The others are by Rittinger (1867) and Kick (1883). According to Bond, the energy required for comminution is proportional to the new crack tip length produced. Reconciling Rittinger's and Kick's laws, a practical form of Bond's law contains three parameters: a feed size parameter, a product size parameter, and a work index, all of which are used to compute the specific energy requirement for a commercial size reduction process. It is given as: 4.3.1 The Bond model (4.1) Where: E is the Specific Energy, (-t-) kWh Wi is the Bond's Work Index P80 is the 80% product passing size F80 is the 80% feed passing size A major problem with Bond's formulation is that it is inherently a gross over­simplification of especially the grinding system (Herbst and Fuerstenau 1968) and is typically in error by large margins, increasing design risk by up to ±20 % (Blasket 1970; Herbst et al. 1977; Smith 1979). The shortcomings in the performance of the Bond model, especially in wet comminution systems, seem to arise from its failure to explicitly account for some important circuit subprocesses in the grinding process (Siddique 1977). Instead, it lumps them all into a single empirical correlation (Herbst and Fuerstenau 1968; Herbst et al. 1983). These important subprocesses include the breakage kinetics, particle transport through the mill, and size classification. Perhaps the most significant detailed phenomenological models for grinding are derived from population balance considerations (Siddique 1977). These models explicitly account for the grinding circuit subprocesses, namely, size reduction kinetics, size classification, and material transport in the mill. By including these critical elements, the population balance models become significantly more effective than the simpler energy-size reduction equations. 4.3.2 Justification for the use of modeling and simulation in this research It is notoriously challenging to include or provide adequately for research work within the normal mining and processing activity of an operation. Even where an operation approves such a project, the demands and pressures of production usually and quickly cause many aspects of such research work to be de-prioritized, and focus tends to 49 be drawn to them only if the production is facing significant enough technical challenges whose solution may lie in the research outcomes. Modeling and simulation are essentially nonobtrusive methods and provide a convenient answer not only for operating mines, but also especially for academic research. In academic research, the objectives and focus may have little overlap with those of a particular mine. By using these techniques, it is usually feasible and convenient to study the processes without necessarily incurring the penalty of the physical outcome of the processes themselves (Tucker 2001). Thus, modeling and simulation methods have been used in this work, to investigate all stages from blasting to grinding. 4.4 The modeling and simulation of crushing systems A variety of models are available in literature for the simulation and modeling of crusher performance (King 2012; Wills 2006). Not all of these models take into consideration the particle size distribution of the feed. To be applicable to this study, only models which are susceptible to effective simulation of input and output particle size distributions are considered. In addition, the particle size distribution of the product from such models would normally be strongly related (directly or indirectly) to the particle size distribution of the feed. Lastly, the product characteristics arising from such a model must also bear evidence of the influences of the comminution system and the prevailing breakage and classification phenomena. 50 4.4.1 The jaw crusher model The jaw crusher model used in this research is the Empirical Model for Jaw and Gyratory Crushers (EMJC)). This model is a simple normalized logarithmic distribution predictor, (Csoke et al. 1996) that is based on the idea that material in the feed smaller than the gap passes straight through the crusher and the larger material is crushed to a predefined size distribution that is modeled by the relation: B(r) = (r/rmax)m Where: B is the size distribution function for product arising from feed with size characteristic "r", which is defined below r = dp/GAP dp is the size of the feed particle being broken rmax = dp(max)/GAP dp(max) is the maximum size of the feed particle in the feed stream GAP is the Open Side Setting (OSS) of the crusher m is the exponent In addition to these inputs into the EJMC model, the impact work index material in this crusher is an important input. 4.4.2 The cone crusher model The cone crusher model selected for use in this research is the Classification- Breakage Cycle Model (or CBCM) (after Whiten 1973). This model provides perhaps 51 (4.2) of the the most effective and useful description of the crushing action of a crusher. Also considered the standard model for crushers (Whiten et al. 1973), the CBCM is developed from population balance considerations, and is amenable to use for jaw, gyratory, and cone crushers. In this work, the CBCM has been used to simulate the performance of only the cone crushers. The model formulation is based on the fact that the operation of a crusher is periodic, with each period consisting of a nipping action and an opening action. In the opening stage of the cycle, some fresh feed is taken in, while material already inside and further up moves downward into the crusher. In the process, some material falls through and out. This set (or cycle) of events can then be described quantitatively in terms of a discrete size distribution for both feed and product. Consider a feed stream with various size classes, i, where i = 1 to n, with class 1 containing the largest particles. Let: pi be the fraction of the product in size class i piF the fraction of feed in size class i M the mass of material held in the crusher bij the fraction of particles breaking in size class j that end up in size class i mi the fraction of material in the crusher in size class i ci = c(di), the fraction of material in size class i that is retained for breakage during the next nip of the crusher W is the mass of total feed that is accepted during a single opening of the crusher, which is also the mass of product discharged from the crusher. 52 53 In this scheme, the size distribution in a product is completely determined from the size distribution in the feed and a knowledge of the classification and breakage functions, ci and bij, respectively. The size distribution in the product can be calculated from the following relationship: An account of the development of this relationship is provided by King (2012). For a specific crusher, this model reduces to the specification of the appropriate classification and breakage functions. These two features are directly related to the characteristics of the crusher, rather than to the characteristics of the material. 4.4.2.1 The crusher classification function For the range d1< dpi < d2, a useful form of the crusher classification function, ci, in Equation 4.3 is typically of the form: (4.4) For dpi <di, ci = 0 For, dpi > d2. ci = 1 Where: 54 d1 is the smallest size particle that can be retained in the crushing zone during the opening phase of the cycle d2 is the largest particle size that can fall through the crushing zone during the opening phase of the cycle The parameters, d1 and d2, are characteristic of the crusher, and are determined primarily by the setting of the crusher. King (2012) reports that data from crushing machines indicate that both of these parameters are proportional to the closed side setting (CSS) of the crusher. For both the standard and short-head Symons cone crushers, the relationship is as follows: In general, ai varies from about 0.5 to 0.95, and a2 varies from about 1.7 to 3.5. The power, n, is usually approximately 2, but can be as low as 1 and as high as 3. The value of d* is normally set to 0. 4.4.2.2 The crusher breakage function According to King (2012), the breakage function that describes crushed product behavior is of the form: di = ai CSS (4.5) d2 = a2 CSS + d (4.6) (4.7) 55 The values of bij are obtained from the cumulative breakage function by the relationship: bij = B(Di-1; dpj) - B(Di; d j (4.8) Where: bij is the fraction of material that enters size interval i from size interval j. The values of bjj are determined from the relationship: bjj = 1-B(Dj; dpj) (4.9) Where: bjj is the fraction of material that remains in size interval j after breakage. 4.4.3 Estimation of crusher classification and breakage functions The parameters in the classification and breakage functions are specific to crusher type and size. According to King (2012), not many studies have been done to establish their values under a range of actual operating conditions using predictive equations. The recommended practical means to estimate these quantities is from measured particle size distributions in the products from operating crushers. However, once established for a particular material in a particular crusher, they remain independent of the CSS. Hence, crusher performance can be simulated as the CSS is varied. This method to estimate selection and breakage functions has been used in this research. 56 4.4.4 Estimating the crusher work index Utley (2002) and Luz and Milhomem (2013) maintain that the classical Bond equation is useful for the estimation of comminution power estimation, including crushing power. However, this procedure has come under criticism from authors such as Magdalinovic (1989, 1990) and Magdalinovic et al. (2011), who proposed a modification (see Jankovic et al., 2004; Luz and Milhomem 2013): A is a material- and crusher-dependent parameter. In the absence of a first-principles approach to the determination of the crusher work index or Magdalinovic's parameter, A, a representative value for the work index can be estimated by more practical ways. Of note is the usefulness of a back-calculation method involving the use of the Operating Work Index (Rajamani 2012; Rowland and McIvor 2009). Based in principle on Bond's original theory (Section 4.3.1), this approach does not involve using conventional testing equipment, but instead relies on actual specific energies expended at the comminution plant (in this case, the crusher) during normal operation. It also relies on measures from actual (or estimated) feed and product 80%- passing particle sizes (P80 and F80). The adapted Bond relationship applied at each crusher in the circuit is as follows (Rajamani 2012; Rowland and McIvor 2009): (4.10) Where: 57 E = F = 10Wb Ff (4.11) Where: kWh. E is the specific energy, (-t-) PC is crusher power, (kW) Ff is fresh feed rate into crusher (tonnes per hour) WB is the Bond's crusher work index (kWh/ton) P80 is the 80% product passing size, (microns) F80 is the 80% feed passing size, (microns) All terms in this relationship, with the exception of the work index, can be obtained from actual operational data. Hence, the operating work index can be estimated. It is noteworthy that the value WB, which is also Bond's crusher work index in so that: B (4.12) Importantly, this relationship makes the value of WB both crusher- and material-dependent, rather than just material-dependent. Indeed, this phenomenon is observed in parameter development in Section 6.2.3. CHAPTER 5 FRAGMENTATION MODELING PARAMETERS, BLAST DESIGNS, AND FRAGMENTATION PREDICTION 5.1 Overview In this chapter, three aspects of this research work are treated. Firstly, the rock characterization procedure used to generate parameters for blast fragmentation modeling and simulation is presented. This stage of work was almost entirely geotechnical in content. The outcome was a set of Kuz-Ram factors for the entire suite of rocks treated in the research. The second stage involved the development of blast designs. All blast designs resulting from that phase of work are presented. The third stage involved prediction of the blast fragment size distributions. 5.2 Determination of rock factor, A Cunningham's formula for rock factor is given in equation 3.17 as: A = 0.06- (RMD + RDI + HF) C(A) (5.1) Where: RMD is the Rock Mass Description RDI is the Rock Density Influence HF is the Hardness Factor C(A) is the Correction Factor In this scheme, the value of RMD is 10 for powdery/friable rock and 50 for massive rock; and RMD is equal to JF, for vertically jointed rock. These values are fixed and there is no gradation between them. The RMD is an in situ rock parameter, and the RDI and HF are laboratory-assessed. The in situ rock characteristics (RDI) were evaluated with the input of the mine geologists at W.U.S. Copper. To aid an unbiased and objective characterization of the in situ rock condition, a questionnaire was developed, based on Cunningham's algorithm. By carefully posing questions related to the rock condition and obtaining answers from the geologists, it was possible to use this questionnaire to evaluate the rock mass description (RMD). Table 5.1 shows a typical form, populated with answers (from both in situ and laboratory-derived data), related to the skarn ore in Bom pit. The forms for the rest of the rock types are presented in Appendix C. 5.2.1 Sample collection and preparation Specimens of rock of various sizes were obtained from selected piles of blasted ore and waste at the mine site of W.U.S. Copper. This selection was guided by W.U.S. Copper personnel, based on the specimens' apparent representativeness of the visually assessed physical characteristics of the rock category of interest. Specimens were 59 obtained from both Bom and Sembehun pits, in dimensions ranging in diameter from a few centimeters (for point load tests) to about a quarter of a meter for coring and use in uniaxial compressive strength and related tests. All tests were carried out in the geotechnical laboratories of the Department of Mining Engineering at the University of Utah. Preparation of the rock specimens intended for compressive strength testing involved the casting of the blocks of rock in concrete, to facilitate good positioning and a firm grip during coring. Four separate blocks of rock (2 ore, 2 waste) were cast in concrete. After curing, these blocks were cored into cylindrical specimens of two main diameters, using the radial drill. Cored specimens were cut to sizes suitable for UCS testing, as specified in ASTM D7012. A total of 17 cores of size NX (nominal 54.7 mm, or 2.16 in.) and six of 31.4 mm nominal size were obtained. Appendix D shows, in addition to other data, details of the dimensions of the specimen cores used in this work. The target Length/Diameter (L/D) ratio was 2:1. However, where it was not possible to achieve that ratio, the specimen was cut to the nearest ratio possible. Appendix E shows selected photos of some of the cores produced. The cut ends of the cylindrical rock cores were ground to achieve smooth and parallel ends to each specimen. The cores of softer rock (particularly from Bom pit) were not subjected to grinding, as it was perceived that this would massively degrade the specimens. Those specimens whose ends were not ground were observed to have markedly irregular ends. To ensure that they had the end-parallelism necessary for the strength tests, the ends of these specimens were lined with a quick-set, epoxy-based filler, and 60 molded between cylinders of stainless steel. Strips of cellophane sheet were used to promote the separation of the samples from the cylinders. Although end-parallelism was still not fully achieved, the samples were significantly better than before. 5.2.2 Testing 5.2.2.1 Density tests All samples were weighed using a Sartorius™ scale model 3713. Their lengths and diameters were determined using digital calipers. The values from these measurements were recorded and used to calculate the density of the rocks. The densities so obtained became key inputs into the derivation of the Kuz-Ram factor. For good comparison of the density values of the rocks, density data were obtained from the Ore Control Section at W.U.S. Copper (Appendix F). Overall, the densities reported by the mine compared well with those calculated. Where differences were apparent, judgment was used to decide which values to use in the determination of the Kuz-Ram rock factor. 5.2.2.2 Ultrasonic velocity testing Ultrasonic velocity testing was carried out on the cylindrical samples. In this procedure, the p- and s-wave velocities of the specimens were obtained by standard ASTM procedures (ASTM D 2845 - 00). Primarily, the purpose of this was to obtain values of the dynamic Young's modulus of these rocks. According to Cunningham, (2005) uniaxial compressive strength values for soft rocks are meaningless as an input to the derivation of rock factor, and should be replaced by the dynamic Young's Modulus in 61 the algorithm (obtained from ultrasonic velocity testing). The data obtained from this process are presented along with the core dimension data in Appendix D. 5.2.2.3 Uniaxial Compressive Strength (UCS) testing UCS tests were performed by standard ASTM methods (ASTM 7012). Two types of testing machine were used, namely, the Rock Mechanics Testing Machine, (RMTS machine) and a testing machine specifically constructed for low-strength samples (a low-strength sample testing machine, or LSTM). The softer samples, predominantly obtained from Bom Pit, were tested using the LSTM. The harder, larger samples, predominantly waste rock from Sembehun Pit, which had been cored with NX bits, were tested using the RMTS machine. The results obtained from the uniaxial compressive strength tests are summarized in Appendix G. 5.2.2.4 Point Load Index (PLI) tests Point load index testing was done on the smaller-sized, irregular-shaped specimens obtained from the mine site. Procedures were based on the ASTM methods (ASTM D5731). The results obtained are presented in Appendix H. The results were used to corroborate UCS values. Where cores were unavailable, the point load test values were used to estimate the UCS values (example, Sembehun low-grade ore). 62 5.2.3 Computation of rock factor, A From the results of the various tests outlined above, and using the forms in Table 5.1 and Appendix C, the rock factor was estimated for the major rocks that are blasted at the mine. The summary of these factors, along with values of various relevant rock parameters used in this research, are shown in Table 5.2. In addition to Cunningham's procedure, Lilly (1986) proposed an alternative method to determine the Kuz-Ram rock factor. According to Lilly's experience in Australia, the rock factor can be obtained from the blastability index by the equation: A = 0.12*(BI) (5.2) Using this scheme, a parallel estimate of the rock factor, A, was obtained (see Table 5.2). These results show remarkable similarity. However, only the results from Cunningham's model were used in blast prediction in this work. 5.3 Blast design Eleven blast designs were developed using the Blast Dynamics Energy Factor method (see Section 3.2.3) (Floyd, n.d.). The base case energy design, which is one of the 11 designs, was that arising from the contract blasting pattern agreed between W.U.S. Copper and the blasting contractor. These contract patterns are approximately replicated in Table 5.3. The differences among the energy factors as shown in the table are accounted for by the differences in design formula used by this researcher and the mine. 63 The researcher retains the use of the Energy Factor method because of its perceived superiority to the Powder Factor method favored by the mine. The following are the characteristics of the blast design exercise and its scope: i. The energy levels chosen for this set of designs range from 100 kcal/st to 400 kcal/st. For each of the six rock categories that are mined by W.U.S. Copper, a blast design has been developed at each of 10 energy levels, based on Equation 3.1. ii. The explosive of choice in each design is bulk ANFO. While ANFO is effective and relatively inexpensive explosive, the peculiar specification of the explosive does not really matter to the investigation concept. The energy factor is the true driver of the investigation. However, the energy factor does not address the issue of differences in certain other strength characteristics such as the brisance and gas-production capacity. The effect of these other characteristics on blasting outcomes is beyond the scope of this investigation. iii. Precise timing has been assumed for NONEL initiation. 5.3.1 Details of blast design Tables 5.4 to 5.8 are summaries of the patterns resulting from the energy factor-driven blast designs for each of the lithologies under consideration. 64 5.4 Prediction of blast fragmentation Using the Kuz-Ram model, predictions of particle size distributions were done. The results of the ore shot size prediction are provided in Table 5.9. Figures 5.1, 5.2, and 5.3 are graphs showing the ore particle size distributions from that prediction. Table 5.10 is the result of the predictions of waste shot particle size distributions. Figures 5.4 and 5.5 are plots of these particle size distributions. 65 % Passing stated size Size (cm) FIGURE 5.1 Plot of fragment size distribution prediction for Bom ore. Fragment size distributions are shown at different blast energies 99 % Passing stated size 120.00% 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% 0.1 0 140 180 - 250 - 35 /in 0 n 10 Size (cm) 100 1000 FIGURE 5.2 Plot of fragment size distribution prediction for Sembehun high-grade ore. Fragment size distributions are shown at different blast energies 1 67 % Passing stated size FIGURE 5.3 Plot of fragment size distribution prediction for Sembehun low-grade ore. Fragment size distributions are shown at different blast energies 89 % Passing stated size FIGURE 5.4 Plot of fragment size distribution prediction for waste rock (limestone). Fragment size distributions are shown at different blast energies 69 % Passing stated size 120.00% 100.00% 80.00% 60.00% 40.00% 20.00% 0.00% / 0 / / ? j r j r / / / J J r > I / / f / j r I f / f f / / / / / f y / V y / / / / / / / A r f / / / /1CH 7^ I f > / > * J f Base Case (164.7) y y / / / / 100 « / >y , f J r / / 1 140 Jf / / 180 AVA\ r J f 4?A/ / / 250 . y r/ rA f\ 350 Va u \ 1 400 ----------- - - --- - - ----------- ---- - - - --- -^ - -- ___ +---------- 1- - - ---- ----------- --- ------ - - --- 0.1 10 Size (cm) 100 1000 FIGURE 5.5 Plot of fragment size distribution prediction for granodiorite. Fragment size distributions are shown at different blast energies 1 70 71 TABLE 5.1 A sample of the form used to compute the Kuz-Ram rock factor, A. Estimation of the Kuz-Ram Rock Factor, A A = 0.06 * (RMD + RDI + HF) * C(A) A = Kuz-Ram Factor RDI = Rock Density Influence Factor RMD = Rock Mass Description________________HF = Hardness Factor C(A) = Correction Factor Rock Tvne: Bom Ore (Soft) Section 1: RMD RMD = 10 for powdery/friable rock; RMD = 50 for massiver Rock; RMD = JF, for vertically jointed Section 1a: Rock Mass Description (RMD) Please choose yes (Y) to only one of the following three questions: i. Is this rock friable (powdery)?(y/n) n ii. Is this rock massive, with no jointing, or with joint spacing > blast hole spacing ? (y/n) iii. Is the rock vertically jointed? (y/n) y n Section 1b: Joint Factor, JF - (Only valid if you answered "Y" to Question iii in Section 1a, above) Note: JF = (JCF * JPS) + JPA JF = Joint Factor JCF = Joint Condition Factor JPA = Vertical Joint Plane Angle Factor JPS = Joint Plane Spacing Factor JCF Range of values: 1 to 2 Describe th joint condition in the box below. Please, choose only one of three options, namely: "Tight", "Relaxed" or "Gouge-filled": if "Tight", input "1"; if "Relaxed", input "1.5"; If joint is "gouge-filled", input "2" What is the condition of the joint? (1, 1.5 or 2) 1.5 JPS Range: 10 to 50 Relevant factors: Reduced Pattern (P) and Joint Spacing (S) P = Reduced Pattern = (B*S)05 What is the average spacing of joints, in meters? 0.25 p = 4.56 What is the blast Burden (in meters)? 4.27 95% P 4.33 What is the blast Spacing (in meters)? 4.88 JPS 20.00 JPA Note that only one answer can be "Yes", although all can be "No" Do the joints dip out of the face at >30o? (Y or N) y Do the joints dip into the face at >30o? (Y or N) n JPA 40 Do the joints Strike out of the face? (Y or N) n RMD 65 Section 2: RDI (Rock Density Influence) Rock Density (kg//m3) 3268 Rock Density Influence Factor (RDI) = 31.7 Section 3: Hardness Factor (HF) Young's Modulus, Y (Gpa) UCS (MPa) 44.56 28.76 Hence, Hardness Factor, HF = 14.85 Kuz-Ram Factor | Uncorrected Kuz-Ram Factor 6.69 Correction 1 Kuz-Ram Factor (Estimate) 6.69 TABLE 5.2 Summary of the estimated rock characteristics Rock SG (t/m3) K-Factor 1 K-Factor2 (Lilly) Blastability Index P-wave vel (km/s) Bom ore (Skarn) 3 . 2 7 6 . 6 9 6 . 9 4 5 7 . 8 5 4 . 4 3 Sembehun high-grade (soft) (Skarn) 2 . 9 7 6 . 51 5 . 4 3 5 4 . 3 3 5 . 3 6 Sembehun low-grade (hard) (Skarn) 2 . 7 2 8 . 4 9 8 . 0 4 5 7 . 0 4 5 . 3 6 Waste (Limestone) 2 . 5 9 8 . 3 3 7 . 9 4 5 6 . 1 9 5 . 9 2 Monzonite 2 . 6 6 8 . 7 2 8 . 0 7 5 7 . 2 4 5 . 9 2 Granodiorite 2 . 5 6 8 . 1 9 6 . 0 9 5 0 . 7 9 5 . 9 2 ZL TABLE 5.3 The contract blast pattern and its approximate representation in this research work. (Note: 1 ft = 0.3048 m) Rock Contract Pattern Research Approximation Burden (ft) Spacing (ft) Powder factor (lb/yd3) Burden (ft) Spacing (ft) Powder factor (lb/yd3) Energy factor (kcal/st) Bom 14 16 0 . 6 1 4 . 0 16 . 1 0 . 9 12 9. 0 Sembehun high-grade 14 16 0 . 6 1 4 . 0 16 . 1 0 . 9 142 . 0 Sembehun low-grade 14 16 0 . 6 1 4 . 0 16 . 1 0 . 9 1 5 5 . 0 Waste 14 16 1 . 2 1 4 . 0 16 . 1 0 . 9 16 2 . 5 Monzonite 12 14 1 . 3 5 12 . 2 1 4 . 0 1. 2 2 1 0 . 2 Granodiorite 14 16 1 . 2 1 4 . 0 16 . 1 0 . 9 16 4 . 5 73 TABLE 5.4 Blast pattern for Bom ore (Note: 1 ft = 0.3048 m) Explosive energy (kcal/st) 129 100 140 160 180 220 250 280 300 350 400 Bench height, L (ft) 20 20 20 20 20 20 20 20 20 20 20 Burden (ft) 1401 15.92 13.45 12.58 1186 10.73 10.07 9 .51 9 .19 8 .51 7 .96 Spacing (ft) 1612 18.30 15.47 14.47 1364 12.34 11.58 10.94 10.57 9 .78 5 15 Subdrill (ft) 394 3 .94 394 3.94 394 3 .94 3 .94 3.94 3 .94 3 .94 3 .94 Stemming (ft) 1238 1238 1238 1238 1238 12 38 1238 1238 1238 1238 1238 T otal hole length (ft) 2394 23.94 23.94 23.94 2394 23.94 23.94 23.94 23.94 23.94 23.94 L/B (Stiffness ratio) 143 1 .26 1.49 1 .59 169 1 .86 1 .99 2 .10 5 18 2 .35 5 51 P owder factor (lb/st) 032 0 .25 035 0.40 5 .45 0 .54 0 .62 0.69 0 .74 0 .87 0 .99 P owder factor (lb/yd3) 5 88 0 .68 095 1 .09 523 1 .50 1.70 1 .91 2.04 2 .39 2 .73 74 TABLE 5.5 Blast pattern for Sembehun high-grade ore (Note: 1 ft = 0.3048 m) Explosive energy (kcal/st) 142 100 140 160 180 220 250 280 300 350 400 Bench height (L) (ft) 20 20 20 20 20 20 20 20 20 20 20 Burden (ft) 1402 16.71 14.12 1321 12.45 11.26 10.57 1 98 9.65 8.93 835 Spacing (ft) 1612 1921 1624 15.19 1432 12.95 12.15 11.48 11.09 10.27 9.61 Subdrill (ft) 394 1 94 3.94 1 94 1 94 1 94 1 94 1 94 1 94 3.94 1 94 Stemming (ft) 1238 1238 1238 1238 1238 1238 1238 1238 1238 1238 1238 Total hole length (ft) 2394 23.94 23.94 23.94 2394 2394 2394 2394 2394 23.94 2394 L/B (Stiffness ratio) 1.43 120 1.42 1.51 161 1.78 1.89 2.00 1 07 2.24 239 Powder factor (lb/st) 035 0.25 1 35 1 .40 0.45 0.54 1 62 1 69 1 .74 0.87 1 99 Powder factor (lb/yd3) 088 062 0.87 1 99 111 136 155 1.73 1.86 2.17 1 .47 75 TABLE 5.6 Blast pattern for Sembehun low-grade ore (Note: 1 ft = 0.3048 m) Explosive Energy (kcal/st) 155 100 140 160 180 220 250 280 300 350 400 Bench Height, L (ft) 20 20 20 20 20 20 20 20 20 20 20 Burden (ft) 14.00 17.44 14.74 13.78 13.00 11.75 11.03 10.42 10.07 9.32 8.72 Spacing (ft) 16.10 20.05 16.95 15.85 14.94 13.52 12.68 11.98 11.58 10.72 10.03 Subdrill (ft) 3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.94 3.94 Stemming (ft) 12.38 12.38 12.38 12.38 12.38 12.38 12.38 12.38 12.38 12.38 12.38 Total Hole length (ft) 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 23.94 L/B (Stiffness ratio) 1.43 1.15 1.36 1.45 1.54 1.70 1.81 1.92 1.99 2.15 2.29 Powder Factor (lb/st) 0.38 0.25 0.35 0.40 0.45 0.54 0.62 0.69 0.74 0.87 0.99 Powder Factor (lb/yd3) 0.88 0.57 0.80 0.91 1.02 1.25 1.42 1.59 1.70 1.99 2.27 9 L TABLE 5.7 Blast pattern for limestone (Note: 1 ft = 0.3048 m) Explosive energy (kcal/st) 162.5 100 140 160 180 220 250 280 300 350 400 B en ch height, L (ft) 20 20 20 20 20 20 20 20 20 20 20 Burden (ft) 14 0 1 17 86 1509 1412 1331 1204 111.30 110.67 10 3 1 1 91.55 8 93 Spacing (ft) 1611 1 0 5 4 17 3 6 16.24 1531 1 3 8 5 112.99 112.27 111.86 110.98 1110.27 Subdrill (ft) 3 9 4 3 94 3 9 4 3 9 4 3 9 4 1 9 4 1 31.94 1 9 4 3 94 1 9 4 1 9 4 Stemming (ft) 1 2 3 8 1238 1238 1 2 3 8 1238 1 2 3 8 1 2 3 8 1238 1238 1238 1 2 3 8 T o ta l hole length (ft) 1 3 9 4 2 3 9 4 1 3 9 4 1 3 9 4 2 3 9 4 2 3 9 4 1 123.94 2 3 9 4 2 3 9 4 2 3 9 4 2 3 9 4 L/B (Stiffness ratio) 1.43 112 132 1.42 150 11.66 1 11.77 1 11.87 1 11.94 21.09 21.24 Powder fa c to r (lb/st) 0.40 0 2 5 0 3 5 0.40 0.45 1 01.54 1 01.62 10.69 10.74 10.87 01.99 P owder fa c to r (lb/yd3) 0 8 8 0 54 0.76 0 8 7 0 9 7 1 11.19 135 111.52 111.62 11.89 1 21.17 77 TABLE 5.8 Blast pattern for granodiorite (Note: 1 ft = 0.3048 m) Explosive energy (kcal/st) 164 7 100 140 160 180 220 250 280 300 350 400 Bench height, L (ft) 20 20 20 20 20 20 20 20 20 20 20 Burden (ft) 14 00 117 97 115 19 14 21 13 .40 12 12 1 111 37 10 74 10 38 19 61 8 9 9 Spacing (ft) 16 10 20 67 117 47 16 34 15 .40 1 113 93 13 07 12 35 111 93 11.05 1033 Subdrill (ft) 3 94 13 94 13 94 3 94 3 94 1 13 94 13 94 13 94 13 94 13.94 3 9 4 Stemming (ft) 12 38 12 38 12 38 12 38 12 38 12 38 12 38 12 38 12 38 1238 1238 Total hole length (ft) 13 94 23 94 23 94 13 94 23 94 13 94 23 94 13 94 23 94 13 94 23 94 L/B (Stiffness ratio) 11 43 11 11 132 141 1 .49 1 11 65 11 76 186 11 93 2 08 2 23 Powder factor (lb/st) 0 .41 0 25 0 35 0 .40 0 45 0 54 0 62 0 69 0 .74 0 87 0 99 Powder factor (lb/yd3) 0 88 0 53 0 75 0 86 0 96 118 11 34 150 1 60 187 2 14 78 TABLE 5.9 Particle size distributions predicted for a range of blasting energy factors within the various ore types E. F a c to r (kcal/st) 129 142 155 100 140 160 180 220 M a te rial - Bum s h g s l g Bum s h g s l g Bum s h g s l g Bum s h g s l g B um s h g s l g Bum s h g s l g Iic h e s cm 384 .00 975 36 100 00% 100 .00% 100 .00% 100 00% 100 00% 100 00% 100 .00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 192 .00 487 68 100 00% 100 .00% 100 .00% 99 99% 99 96% 93 100 .00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 100 00% 96 .00 243 84 99 75% 99 72% 99 42% 98 64% 69 95 19% 99 83% 99 69% 98 94% 99 94% 99 88% 99 53% 99 98% 99 96% 99 80% 100 00% 99 99% 99 97% 48 .00 12192 94 09% 93 82% 89 97% 87 67% 85 51% 236 94 97% 93 56% 87 21% 96 85% 95 78% 90 77% 98 05% 97 26% 93 41% 99 27% 98 87% 96 73% 30 .00 76 20 66 8137% 59 3 332 299 6 58 07% 83 24% 39 89 9687 08% 84 95% 74 73% 90 10% 88 18% 78 90% 62 49 CQ29 85 49% 24 .00 60 96 73 57% 73 35% s46 63 91% 6166% 49 53% 75 31% 2 7 60 53% 79 72% 33 5356 83 41% 8112% 69 96 89 01% 87 02% 77 04% 12 .00 30 48 46 53% 66 4 63 393 37 86% 27 71% 48 02% 46 24% 23 34 52 12% 50 15% 37 59% 55 96% 53 83% 40 78% 87 26 35 6 46 88% 6 .00 15 24 25 52% 25 80% 18 51% 21.47% 21.04% 14 28% 38 62 25 57% 17 31% 28 82% 27 85% 18 91% 31 .2 3 30 11% 20 54% 895 3 34 51% 23 81% 3 .00 26 12 94% 22 13 8 73% 1111% 11.06% 7 05% 13 35% 13 11% 8 24% 14 52% 14 20% 8 90% 15 71% 15 30% 9 60% 18 09% 35 1104% 1 50 3 81 6 31% 6 51% 4 .00% 5 57% 5 65% 3 41% 6 48% 6 47% 3 81% 99 6 396 4 06% 7 50% 7 41% 33 4 8 56% 8 40% 4 90% 0 .75 1 90 3 01% 3 14% 180% 2 75% 2 84% 36 3 08% 3 12% 1.74% 3 28% 3 30% 182% 3 49% 3 50% 192% 393 3 90% 2 13% 0 38 0 95 1.43% 150% 0 81% 135% 1.42% 0 78% 1.45% 150% 0 79% 153% 156% 0 81% 1 61% 164% 0 85% 1.78% 180% 0 92% 0 18 0 48 0 68% 0 73% 0 37% 0 67% 0 71% 0 37% 0 69% 0 72% 63 0 72% 0 74% 0 37% 0 75% 0 77% 0 38% 0 81% 0 83% 0 40% 0 .09 0 24 23 0 35% 0 16% 23 63 0 18% 23 0 34% 0 16% 33 0 35% 0 16% 0 34% 63 0 17% 0 37% 0 38% 0 17% % o / s 18 34% 18 63% 26 41% 27 67% 30 08% 4193% 16 76% 19 07% 30 11% 12 92% 15 05% 25 27% 9 90% 1182% 2110% 5 74% 7 20% 14 51% O/S in C lu s h e r f e ed 21.1% 33.2% 22.0% 17.7% 14 .3% 9 .1% U/S in C ru sh e r F e e d 78.9% 66.8% 78.0% 82 .3% 85 .7% 90 .9% Note: SHG refers to Sembehun high-grade ore; SLG refers to Sembehun low-grade ore. 79 TABLE 5.9 (Continued) E. Factor (kcal/st) 250 280 300 350 400 Material - Bum SHG SLG Bum SHG SLG Bum SHG SLG Bum SHG SLG Bum SHG SLG Inches cm 384 975.36 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 192.00 487.68 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 96.00 243.84 100.00% 100.00% 99.99% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 48.00 121.92 99.66% 99.43% 98.11% 99.84% 99.72% 98.93% 99.91% 99.82% 99.27% 99.98% 99.95% 99.73% 99.99% 99.98% 99.90% 30.00 76.20 96.23% 95.08% 89.16% 97.54% 96.66% 91.97% 98.16% 97.43% 93.45% 99.12% 98.68% 96.12% 99.59% 99.33% 97.74% 24.00 60.96 91.99% 90.27% 81.49% 94.20% 92.74% 85.17% 95.33% 94.04% 87.24% 97.32% 96.40% 91.33% 98.48% 97.84% 94.18% 12.00 30.48 67.43% 65.00% 51.17% 71.49% 69.02% 55.20% 73.93% 71.46% 57.75% 79.23% 76.83% 63.62% 83.53% 81.25% 68.80% 6.00 15.24 39.25% 37.69% 26.25% 42.48% 40.75% 28.67% 44.55% 42.73% 30.26% 49.48% 47.44% 34.17% 54.03% 51.83% 37.95% 3.00 7.62 19.87% 19.19% 12.14% 21.63% 20.85% 13.25% 22.79% 21.94% 14.00% 25.66% 24.65% 15.88% 28.46% 27.29% 17.75% 1.50 3.81 9.37% 9.16% 5.35% 10.18% 9.92% 5.81% 10.73% 10.43% 6.12% 12.09% 11.71% 6.90% 13.44% 12.98% 7.69% 0.75 1.90 4.27% 4.22% 2.30% 4.61% 4.55% 2.48% 4.84% 4.76% 2.60% 5.42% 5.31% 2.90% 6.01% 5.87% 3.22% 0.38 0.95 1.92% 1.92% 0.98% 2.06% 2.06% 1.05% 2.15% 2.15% 1.09% 2.39% 2.37% 1.21% 2.64% 2.60% 1.33% 0.18 0.48 0.87% 0.88% 0.42% 0.92% 0.94% 0.45% 0.96% 0.97% 0.47% 1.06% 1.06% 0.51% 1.16% 1.16% 0.55% 0.09 0.24 0.39% 0.40% 0.18% 0.41% 0.42% 0.19% 0.42% 0.43% 0.20% 0.46% 0.47% 0.21% 0.50% 0.51% 0.23% % O/S 3.77% 4.92% 10.84% 2.46% 3.34% 8.03% 1.84% 2.57% 6.55% 0.88% 1.32% 3.88% 0.41% 0.67% 2.26% O/S in Crusher feed 6.5% 4.6% 3.7% 2.0% 1.1% U/S in Crusher Feed 93.5% 95.4% 96.3% 98.0% 98.9% Note: SHG refers to Sembehun high-grade ore; SLG refers to Sembehun low-grade ore. 08 TABLE 5.10 Particle size distributions predicted for a range of blasting energy factors within limestone (LS) and granodiorite (GD) E Factor (kcal/st) 162.5 164.7 100 140 160 180 220 Material........ LS GD LS GD LS GD LS GD LS GD LS GD Inches cm 384 975.36 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 192.00 487.68 100.00% 100.00% 99.76% 99.90% 99.99% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 96.00 243.84 99.45% 99.83% 94.52% 97.40% 98.69% 99.51% 99.39% 99.80% 99.73% 99.92% 99.95% 99.99% 48.00 121.92 90.31% 95.89% 75.22% 85.55% 86.23% 93.29% 89.92% 95.48% 92.69% 96.98% 96.25% 98.66% 30.00 76.20 74.22% 86.33% 57.21% 71.57% 68.85% 81.83% 73.66% 85.56% 77.84% 88.56% 84.51% 92.88% 24.00 60.96 64.91% 79.61% 48.85% 64.13% 59.61% 74.61% 64.35% 78.74% 68.64% 82.23% 75.97% 87.67% 12.00 30.48 37.49% 54.73% 27.54% 41.92% 33.92% 50.11% 37.10% 53.88% 40.20% 57.41% 46.15% 63.75% 6.00 15.24 19.01% 32.63% 14.34% 25.02% 17.26% 29.73% 18.81% 32.08% 20.39% 34.40% 23.57% 38.86% 3.00 7.62 9.02% 17.87% 7.17% 14.15% 8.30% 16.39% 8.94% 17.58% 9.61% 18.80% 11.01% 21.23% 1.50 3.81 4.15% 9.34% 3.51% 7.77% 3.88% 8.68% 4.12% 9.21% 4.38% 9.77% 4.94% 10.92% 0.75 1.90 1.88% 4.76% 1.70% 4.19% 1.79% 4.49% 1.87% 4.71% 1.96% 4.94% 2.17% 5.44% 0.38 0.95 0.85% 2.40% 0.82% 2.24% 0.82% 2.30% 0.84% 2.38% 0.87% 2.47% 0.95% 2.68% 0.18 0.48 0.39% 1.22% 0.40% 1.21% 0.38% 1.19% 0.39% 1.21% 0.39% 1.24% 0.42% 1.32% 0.09 0.24 0.17% 0.61% 0.19% 0.64% 0.17% 0.60% 0.17% 0.61% 0.17% 0.62% 0.18% 0.64% Determination of Oversise in waste blasts % U/S 97.16% 98.85% 89.69% 94.44% 95.58% 97.96% 97.02% 98.72% 97.97% 99.18% 99.02% 99.66% % O/S 2.84% 1.15% 10.31% 5.56% 4.42% 2.04% 2.98% 1.28% 2.03% 0.82% 0.98% 0.34% 81 TABLE 5.10 (Continued) E. Factor (kcal/st) 250 280 300 350 400 Material - LS GD LS GD LS GD LS GD LS GD Inches cm 384 975.36 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 192.00 487.68 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 96.00 243.84 99.99% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% 48.00 121.92 97.78% 99.29% 98.70% 99.62% 99.10% 99.75% 99.65% 99.92% 99.87% 99.97% 30.00 76.20 88.28% 95.03% 91.20% 96.55% 92.76% 97.30% 95.60% 98.55% 97.38% 99.22% 24.00 60.96 80.46% 90.66% 84.19% 92.94% 86.32% 94.15% 90.54% 96.37% 93.54% 97.75% 12.00 30.48 50.35% 67.93% 54.31% 71.66% 56.82% 73.91% 62.61% 78.82% 67.75% 82.84% 6.00 15.24 25.94% 42.05% 28.30% 45.10% 29.85% 47.05% 33.66% 51.65% 37.34% 55.89% 3.00 7.62 12.09% 23.03% 13.17% 24.81% 13.90% 25.98% 15.73% 28.84% 17.56% 31.61% 1.50 3.81 5.37% 11.80% 5.82% 12.68% 6.12% 13.27% 6.89% 14.73% 7.67% 16.18% 0.75 1.90 2.33% 5.83% 2.51% 6.23% 2.62% 6.50% 2.92% 7.17% 3.23% 7.84% 0.38 0.95 1.01% 2.84% 1.07% 3.01% 1.12% 3.13% 1.23% 3.42% 1.35% 3.72% 0.18 0.48 0.44% 1.39% 0.46% 1.46% 0.48% 1.51% 0.52% 1.64% 0.57% 1.77% 0.09 0.24 0.19% 0.67% 0.20% 0.70% 0.20% 0.72% 0.22% 0.77% 0.23% 0.82% De te rm in a tio n o f O vers ise in w a s te blasts % U/S 99.43% 99.82% 99.67% 99.90% 99.77% 99.94% 99.91% 99.98% 99.97% 99.99% % O/S 0.57% 0.18% 0.33% 0.10% 0.23% 0.06% 0.09% 0.02% 0.03% 0.01% 82 CHAPTER 6 ESTIMATION OF CRUSHER SIMULATION PARAMETERS 6.1 Overview In this chapter, the procedures that were used to generate the crushing simulation parameters are described. Due to the limitations discussed in Sections 4.4.3 and 4.4.4, no direct testing could have been done to generate those parameters. Therefore, indirect methods of estimation were used. 6.2 Estimation of crushing simulation parameters The crusher parameters which required estimation for use in this simulation work are listed in Table 6.1, each parameter in relation to the crusher to which it is relevant. The parameter that is common to all the crushers is the crusher work index. In addition, the cone crushers (Cones 1 and 2) require the classification and breakage functions to be estimated. As discussed in Section 4.3.2.1 (and in King 2012), previous work has provided viable ranges for these latter parameters, and these ranges were explored in this work. In order to be considered valid, the estimated parameters had to meet the following criteria: i. The use of the set of estimated parameters must lead to the prediction of a particle size distribution of simulated final product that is comparable to the particle size distribution actually measured at the crusher product stockpile. ii. For baseline operating feed size distributions, the simulated energy consumption at the crusher must be roughly identical to that observed under baseline operating conditions. Obtaining a fair representation of blast product size distribution on-site for validation purposes was a challenge. Kuz-Ram predictions are averages, and values estimated by photo-granulometry are often very localized and tend to depart significantly from shot averages. Consequently, a very rough approximation was made on the basis of degree of oversize produced by the blasts. The prediction of ore oversize in this work is a mean of about 21%, and a maximum of 26%. Observed oversize ranged from about 7% to about 20% in ore. The researcher's judgment is that, given the natural inhomogeneities in rocks, and the lack of resources to do detailed verification and validation of photo­granulometry with sieving of a whole muckpile, this is an acceptable difference. The simple and broad assumption is made, therefore, that the crusher feed particle size distribution produced by the contract blasting practice is roughly equivalent to that which is predicted by the revised Kuz-Ram model in this research. 6.2.1 Preliminaries for parameter estimation The following preliminaries were carried out, leading to the parameter estimation process itself. 84 i. In MODSIM simulation package, the crushing circuit was built (see Figure 6.1), with features including a jaw crusher, two cone crushers, screens, and feed and product stockpiles. ii. Characteristics of the circuit were specified, including crusher gap dimensions, open and closed side settings, screen perforation sizes, dimensions of all screen surface areas, screen inclinations, and circuit paths between crushers, screens, and crushers. Details of the circuit characteristics are provided in Appendix I (crushing circuit parameters). iii. The feed characteristics were specified. These characteristics included the ore type (Bom ore, Sembehun low-grade ore, and Sembehun high-grade ore), density, and particle size distribution. The base case particle size distribution specified was a modified form of that predicted by the Kuz-Ram model for the blast pattern established by the contractor. The modification was done to account for the contribution of secondary breakage of all oversize (>30 inches) ore. The particle size distribution of the secondary-broken ore was assumed to be identical to the size distribution of the blast-generate sub-30-in material. This method of size reconstitution was used for all the crusher feeds produced by the various energy factor blasts (Tables 6.2a, b, c). iv. Key process features were specified. These features included the head feed rates and the feed blending proportions. Blending was in the ratio: Bom/Sembehun high-grade/Sembehun low-grade (1:1:1) v. A preliminary and arbitrary crusher work index value of 30 kWh/t was assumed. 85 6.2.2 Crusher and screen settings and characteristics An important aspect of the specifications that were made in the simulation of the crushing system was the set of physical characteristics and settings of the crushers and screens in the system. To be representative of the operating situation at the mine, the data (dimensions and settings) of the equipment at the mine were obtained and used as input, as required, at the model parameter specification stage of the simulation. The data specified in this research have been presented in Tables 6.3a (settings and features of the jaw crusher), 6.3b (settings and features of the cone crushers), 6.3c (settings and features for Screen 1), and 6.3d (settings and features for Screen 2). 6.2.3 The crusher breakage and classification functions i. These two functions were estimated for only the cone crushers. ii. Initially, the crusher breakage and classification functions were specified in MODSIM to match average values of the recommended ranges of setting for both the breakage and classification functions. These ranges are mentioned in Section 4.4.2.I. iii. A simulation was then run, and the simulated product particle size distributions overlain on a plot of the actual mill feed (or crusher run) particle size distribution. Details of the sampling and size analysis procedure for mill feed are given in Appendix A. After each run, the departure from the reference plot formed the basis of adjustment of parameters. All the parameters were gradually adjusted in suitable directions, until an approximate overlap was achieved (see Figure 6.2). The settings at which this approximate overlap occurred were chosen as the 86 87 circuit's parameter settings for the rest of the simulation. These settings are presented in Table 6.4. 6.2.4 The crusher work index i. The crusher work index was estimated using the operating work index method described in Section 4.4.4, using the equation: All terms are as described in Equation 4.11. ii. For the reconstituted base case feed (simulated) and crushing product (also simulated), the 80% passing sizes F80 and P80 were determined. The 80% passing feed and product sizes for each of the three crushers were determined. iii. Values of crusher power draw at the time of the crusher product sampling were obtained from the mine power team. iv. Setting ( - ^ - ) = k, and using average crusher power draw (Pc) and feed \VP80 VF80/ tonnes of fresh feed rate (Ff), the operating work index Wi(o) was computed as shown in the table. v. Assuming motor efficiencies of 80% at each crusher motor, an estimate of true work index, Wi, was made by de-rating the operating work index (Wi(o)). However, the operating work index was the value eventually used in all subsequent simulations, as no provision lies within MODSIM to account for motor efficiency in the estimation of power draw. A weighted average operating work index of 20.86 kWh/t is calculated (prorated by mass flow through the plant), and a "true" work index estimate of 16.69 kwh/t is made. This value is consistent with various published values of typical copper ores or in related rocks such as dolomite in skarn deposits (from 1.8 to 40 kWh/t - and averaging 12 to 20 kWh/t) (Bergstrom 1985; Nematollahi 1994; Tavares and Carvalho 2007). All values of input parameters leading to this estimate, as well as the estimate of the crusher work index, are shown in Table 6.5. vi. The variation of crusher work index in the different crushers for the blended ore is in line with Magdalinovic's observation (Section 4.4.4) which indicates that the work index is material and crusher specific. 6.2.5 Verification of crushing simulation parameters In Table 6.5, note that the power draw for each crusher is the same as that provided by the power supply staff at W.U.S. Copper. This equality of predicted and actual values of power draw meets one of the criteria for parameter verification, as specified in i and ii of Section 6.2. The other validation is provided by the approximate overlap of actual and simulated product particle size distributions, as shown in Figure 6.2 88 29 Jaw Crusher Screen 1 200.02 100 155 0 21 18 241.16 100 148 0 241.16 100 10.3 0 114.16 100 4.25 0 Fresh Feed to Jaw Crusher 200.02 100 491 0 1 + 163.66 100 13.5 0 163.66 100 7.02 0 85.86 100 4.43 0 19 200.02 100 4.33 0 } Screen 2 Legend 20 t/h % Sol P80 (mm) L/min Crusher Final Product [Mill Feed; FIGURE. 6.1 Flowsheet of the crushing circuit, showing mass flow. This mass flow is based on jaw crusher feed size estimates from the blend of fragmentation profiles from contract blasts 89 Cumulative fraction passing FIGURE. 6.2 Parameter verification plot of simulated and actual product particle size distributions. The test crush simulation product is overlaid on the measured crusher product (mill feed) particle size profile. 06 91 TABLE 6.1 The set of parameters whose estimation was required for the simulations Crusher Model Parameter to estimate Jaw The Empirical Model for Jaw and Gyratory Crushers (EJMC) The crusher work index (kWh/t) Cone 1 The Standard Cone Crusher Model (CRSH) Classification proportionality constants, a 1 and a2 The cumulative breakage function, Bij The crusher work index Cone 2 The Short-Head Cone Crusher Model (SHHD) Classification proportionality constants, a 1 and a2 The cumulative breakage function, Bij The crusher work index (kWh/t) TABLE 6.2a Crusher feed, reconstituted for oversize (100 to 160 kcal/st) 129 142 155 100 140 160 mm Inches cm Bum SHG SLG Bum SHG SLG Bum SHG SLG Bum SHG SLG 762 30 00 76 20 100 0 0 % 100 0 0 % 100 0 0 % 100 0 0 % 100 0 0 % 100 0 0 % 00010100 0 0 % 0001 0 100 0 0 % 0001 0 100 0 0 % 610 24 00 60 96 90 0 9 % 90 14% 87 2 3 % 88 3 6 % 88 19% 85 2 9 % 90 4 7 % 90 0 4 % 86 61% 9 1 5 5 % 9 1 0 3 % 87 4 4 % 305 12 00 30 48 56 9 8 % 57 3 2 % 8994 54 0 9 % 54 15% 47 7 3 % 57 7 0 % 57 14% 49 10% 59 8 5 % 59 0 3 % 50 3 0 % 152 6 00 15 24 3 1 2 5 % 3171% 25 16% 29 6 9 % 30 0 9 % 24 5 9 % 3 1 6 9 % 3 1 6 0 % 24 7 7 % 33 0 9 % 32 7 9 % 25 31% 76 3 00 7 £2 15 8 5 % 16 2 4 % 1187% 15 3 5 % 15 8 2 % 12 14% 16 0 4 % 16 2 0 % 11.7 8 % 16 6 8 % 16 .71% 1192% 38 150 3 81 7 7 3 % 8 0 0 % 5 4 3 % 7 7 0 % 8 0 8 % 5 8 7 % 7 7 9 % 7 9 9 % 5 4 5 % 8 0 2 % 8 16% 5 4 4 % 19 0 75 190 3 6 9 % 3 8 6 % 2 4 5 % 3 8 0 % 4 0 6 % 2 81% 3 7 0 % 3 8 6 % 2 4 8 % 3 7 6 % 3 8 9 % 2 4 4 % 10 0 38 0 95 1 7 5 % 1 8 5 % 110% 1 8 6 % 2 0 3 % 1 3 4 % 1 7 5 % 1 8 5 % 113% 1 7 5 % 1 8 4 % 1 0 9 % 5 0 18 0 48 0 8 4 % 0 8 9 % 0 5 0 % 0 9 2 % 1 0 2 % 0 6 4 % 0 8 3 % 0 8 9 % 0 5 2 % 0 8 2 % 0 8 8 % 0 4 9 % 2 0 09 0 24 0 3 9 % 0 4 2 % 0 2 2 % 0 4 5 % 0 51% 0 31% 0 3 9 % 0 4 3 % 0 2 3 % 0 3 8 % 0 41% 0 2 2 % Note: SHG refers to Sembehun high-grade ore; SLG refers to Sembehun low-grade ore 92 TABLE 6.2b Crusher feed, reconstituted for oversize (180 to 280 kcal/st) 180 220 250 280 Inches cm Bum SHG SLG Bum SHG SLG Bum SHG SLG Bum SHG SLG 30 00 76 20 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 1 0 0 00% 24 00 60 96 92 58% 92 00% 88 32% 94 43% 93 78% 90 11% 95 60% 94 94% 91 40% 96 57% 95 94% 92 61% 12 00 30 48 62 11% 6 1 04% 51 68% 66 70% 65 23% 5 4 83% 70 07% 68 36% 5 7 39% 73 29% 71 40% 60 02% 6 00 15 24 34 66% 3 4 15% 26 03% 38 08% 3 7 19% 2 7 85% 40 79% 39 64% 29 45% 43 55% 42 16% 31 18% 3 00 7 62 17 43% 17 35% 12 17% 19 19% 18 89% 12 91% 20 64% 20 19% 13 61% 22 17% 21 57% 14 41% 1 50 3 81 8 33% 8 40% 5 49% 9 09% 9 05% 5 74% 9 74% 9 63% 6 00% 10 44% 10 26% 6 31% 0 75 1 90 3 87% 3 96% 2 43% 4 17% 4 21% 2 49% 4 43% 4 44% 2 58% 4 73% 4 70% 2 69% 0 38 0 95 1 78% 1 85% 1 07% 1 89% 1 94% 1 08% 1 99% 2 02% 1 10% 2 11% 2 13% 1 14% 0 18 0 48 0 83% 0 87% 0 48% 0 %6 8 0 %09 0 47% 0 90% 0 93% 0 48% 0 95% 0 97% 0 49% 0 09 0 24 0 38% 0 41% 0 21% 0 39% 0 41% 0 20% 0 40% 0 42% 0 20% 0 42% 0 43% 0 21% Note: SHG refers to Sembehun high-grade ore; SLG refers to Sembehun low-grade ore 93 TABLE 6.2c Crusher feed, reconstituted for oversize (300 to 400 kcal/st) 300 350 400 inches cm Bum SHG SLG B um SHG SLG Bum SHG SLG 3 0 . 00 76 20 100 00% 100 00% 1 0 0 . 00% 100 00% 1 0 0 . 00% 100 00% 100 00% 100 00% 1 0 0 . 00% 2 4 . 00 60 96 97 12% 9 6 52% 93 . 36% 98 18% 9 7 . 68% 95 02% 98 89% 98 50% 9 6 36% 1 2 . 00 30 48 75 32% 73 34% 6 1 . 80% 79 94% 7 7 . 85% 66 19% 83 87% 8 1 . 80% 70 39% 6 . 00 15 24 45 39% 43 85% 32 . 39% 49 92% 48 . 08% 35 55% 54 26% 52 18% 3 8 . 82% 3 . 00 7 62 23 22% 22 52% 14. 98% 25 89% 2 4 . 98% 16 52% 28 58% 2 7 . 47% 1 8 . 17% 1. 50 3 81 10 93% 10 70% 6. 54% 12 19% 1 1 . 86% 7. 18% 13 50% 13 07% 7. 87% 0. 75 1 90 4 93% 4. 89% 2. 78% 5. 47% 5. 38% 3. 02% 6 04% 5. 91% 3. 29% 0. 38 0 95 2 19% 2. 20% 1. 17% 2. 41% 2. 41% 1. 26% 2 65% 2. 62% 1. 36% 0. 18 0 48 0 98% 1. 00% 0. 50% 1. 07% 1. 08% 0. 53% 1 16% 1. 17% 0. 57% 0. 09 0 24 0 43% 0. 44% 0. 21% 0. 47% 0. 48% 0. 22% 0 50% 0. 51% 0. 23% Note: SHG refers to Sembehun high-grade ore; SLG refers to Sembehun low-grade ore 94 TABLE 6.3a Jaw Crusher Settings and features 95 Parameter Value Gap (m) 0.1778 rmax 1.251 Exponent, m 0.843 Gape (mm) 1117.6 mm x 787.4 mm (44 in. x 31 in.) Installed power (kW) 112 Source: Processing staff at W.U.S. Copper TABLE 6.3b Settings and features of cone crushers Setting Cone 1 Cone 2 Open-Side Set (OSS) (meters) 127 mm (5 in.) 44.45 mm (1.75 in.) Closed-Side Set (CSS) (meters) 12.7 mm (0.5 in.) 6.35 mm (0.25 in.) Installed power (kW) 298 298 Source: Processing staff at W.U.S. Copper 96 TABLE 6.3c Settings and features for Screen 1 Feature/Setting Value Number of decks of screen 3 Deck 1 No. of screen panels in parallel 5 Size of screen panels in parallel 31.75 mm Modsim screen model used SCRN Crusher receiving screen oversize Cone 1 Deck 2 No. of screen panels in parallel 5 Mesh size of screen panels in parallel 4 screens: 9.525 mm; 1 screen: 28.575 mm Modsim screen model used SCRN Crusher receiving screen oversize Cone 1 (from 4 screens); Cone 2 (from one screen) Deck 3 No. of screen panels in parallel 5 Size of screen panels in parallel 6.35 mm Modsim Screen model used SCRN Crusher receiving screen oversize Cone 2 Source: Processing staff at W.U.S. Copper 97 TABLE 6.3d Settings and features for Screen 2 Feature/Setting Value Number of decks of screen 3 Deck 1 No. of screen panels in parallel 5 Size of screen panels in parallel 15.88 mm Modsim screen model used SCRN Crusher receiving screen oversize Cone 1 Deck 2 No. of screen panels in parallel 5 Mesh size of screen panels in parallel 12.70 mm Modsim screen model used SCRN Crusher receiving screen oversize Cone 1 Deck 3 No. of screen panels in parallel 5 Size of screen panels in parallel 6.35 mm Modsim Screen model used SCRN Crusher receiving screen oversize Cone 2 Source: Processing staff at W.U.S. Copper TABLE 6.4 The values inferred for the crushing simulation parameters Crusher Parameter(s) Value Cone 1 Classification proportionality constants, a 1 and a 2 0 .5 ; 1.85 The cumulative breakage function, Bij 0 .6 Cone 2 Classification proportionality constants, a 1 and a 2 0 .5 ; 1.85 The cumulative breakage function, B ij 0 .6 TA B L E 6.5 The values of work index inferred for the crushing circuit Crusher F so (Hm) P 80 ( Hm) k 10 k Feed, tph Op Kilowatts kWh/t Op. Work Index (Wi(o)) W i Jaw 490,640 155,130 0.00111 0.01111 200.02 81 0.4050 36.44 29.15 Cone 1 148,090 10,300 0.00725 0.07255 241.2 101 0.4187 5.77 4.62 Cone 2 13,500 7,020 0.00333 0.03329 163.7 131 0.8002 24.04 19.23 Weighted average W i = 20.86 16.69 98 CHAPTER 7 SIMULATION OF THE CRUSHING OPERATION 7.1 Overview Simulations were carried out to assess the influence of the blast-generated feed particle size distributions on crushing outcomes. This simulation was done using MODSIM. All simulations were performed on streams of material hypothetically mined from three sources: Bom, Sembehun high-grade and Sembehun low-grade ore domains. These ores were blended in the ratio 1:1:1. All materials in each blend were hypothetically shot with the same specific energy. Each processed stream in this work was uniquely identified by the energy factor with which that material was shot. Hence, Bom ore that was shot with 100 kcal/st was blended with Sembehun high-grade ore and Sembehun low-grade ore, each of which was shot with 100 kcal/st. This blend produced Stream 100 kcal/st. 7.2 Simulation setup The modeled/simulated crushing circuit configuration was the same as that used for the parameter estimation exercise described in all of Section 6.2. The circuit included one jaw crusher, two cone crushers (Cones 1 and 2), and 2 banks of screens, as shown in Figures 1.1 and 6.1. The settings within the crusher circuit (including screens) are outlined in Tables 6.3a 6.3b, 6.3c, and 6.3d, with further details provided in Appendix I. The model parameters are outlined in Tables 6.4 and 6.5. The main variable in each cycle of simulation was the particle size distribution of the feed, dictated and identified by the blasting energy used to generate the particle size distributions. An important aspect of the crushing circuit is the feed particle size limit imposed by the dimensions of the jaw crusher's throat. The maximum crushable particle size is 0.76 meters (30 inches). Any size larger than this must be set aside and secondary-broken, using a rock breaker. Usually, this re-break is done either at the crusher or at the mining pit, and at an extra cost beyond the basic rates for blast fragmentation. The extra cost is borne by the contractor, after an allowed maximum of 5% oversize.