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Piston press test procedures for predicting energy-size reduction of high pressure grinding rolls Davaanyam, Zorigtkhuu 2015

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Piston Press Test Procedures for PredictingEnergy–Size Reduction of High Pressure GrindingRollsbyZORIGTKHUU DAVAANYAMB.Sc., Colorado School of Mines, 2001M.Eng., Dong-A University, 2005A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENT FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Mining Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)July 2015© Zorigtkhuu Davaanyam, 2015ABSTRACTHigh Pressure Grinding Rolls (HPGR) have been used for over 20 years, however the technol-ogy has not received wide industry acceptance despite reports of substantial energy advantages.One barrier is that full and fair consideration cannot be given to HPGR-based comminutioncircuits for early-stage mining projects, because industry standard tests require large samplesizes for evaluation of the technology.The main objective of the research was to develop methodologies, requiring small samplequantities, to predict the energy–size reduction performance of HPGRs. A key outcome is thedevelopment of three piston press testing procedures that require significantly less sample thanstandard HPGR evaluation methods.One method, referred to as the direct calibration methodology, involves calibrating resultsof piston press tests against pilot-scale HPGR tests. This methodology was developed primarilyfor situations where HPGR test data is only available for a composite sample and the energyrequirements of individual geometallurgical units within a deposit are to be determined.To address the case where HPGR test results are not available, a second method was devel-oped which relies only on piston press testing and empirical equations that were determinedfrom a database of pilot-scale HPGR results.The simulation-based methodology was also developed to be able to assess the impactof changes in HPGR operation or circuit configuration on comminution performance. Anexisting energy–breakage model was adopted and modified for application to particle-bediicomminution. The three methodologies were compared by applying them to samples froma copper-gold deposit in central British Columbia.Through utilization of these methodologies, the energy–size reduction performance of theHPGR technology can be predicted with small sample requirements which can be applied to abroad range of ore types and provide a stronger statistical basis for the process design.During development of the methodologies, significant research outcomes resulted. Con-trolled piston press and HPGR pilot tests on the same samples confirmed that normalizedproduct PSDs of the respective equipment can be regarded as equivalent. Furthermore, datafrom particle-bed comminution tests was used to determine master curves describing breakageappearance functions for the compression mode of breakage.iiiPREFACEI was responsible for designing the experimental program, conducting test work, and devel-oping the piston test methodologies under the supervision of Prof. Bern Klein. Also, I wasresponsible for running the hydraulic press and HPGR, data analysis, developing relationshipsbetween piston press data and pilot scale HPGR data, developing multiple linear regressionmodels, and running simulations on an Excel spreadsheet.Stefan Nadolski and Amit Kumar assisted with the pilot-scale HPGR testing. Summer co-op students—Aaron Wright, Bhanu Venkatesh, Prabhat Singh, Enkhbold Tsagaankhuu, KunalMathenkar, Fred Zhou, and Tugsbuyan Tsedenbaljir—assisted me with labor intensive taskssuch as crushing, screening of the test feeds and determination of particle size distributions.Preliminary results of this research were published in the following paper:Davaanyam, Z., Klein, B., Nadolski, S., Kumar, A. (2013). A new bench scale test for de-termining energy requirement of an HPGR. In Materials Science and TechnologyConference and Exhibition 2013 (MS&T ’13), Montreal, Quebec, Canada (Vol. 3,pp. 1917–1925). Association for Iron and Steel Technology.An updated results was presented at the 47th Annual Canadian Mineral Processors Conferencein January 2015.Davaanyam, Z., Klein, B., Nadolski, S., Kumar, A. (2015). Predicting the energy requirementsof an High Pressure Grinding Roll with piston press test. In The 47th AnnualCanadian Mineral Processors Conference, Ottawa, Ontario, CanadaivTABLE OF CONTENTSABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTABLE OF CONTENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vLIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xLIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiLIST OF SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiiiDEDICATION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiv1 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Thesis Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 LITERATURE REVIEW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1 High Pressure Grinding Roll . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.1.1 Overview of HPGR technology . . . . . . . . . . . . . . . . . . . . . 92.1.2 History of HPGR application . . . . . . . . . . . . . . . . . . . . . . 102.1.3 HPGR operating parameters . . . . . . . . . . . . . . . . . . . . . . . 122.1.4 HPGR-based comminution circuit configurations in hard-rock mining 152.1.5 Simulation model of HPGR . . . . . . . . . . . . . . . . . . . . . . . 182.1.6 Advantages of HPGR . . . . . . . . . . . . . . . . . . . . . . . . . . 20v2.1.7 Shortcomings of HPGR . . . . . . . . . . . . . . . . . . . . . . . . . 232.1.8 Comparison of energy efficiency of HPGR and SAG mill . . . . . . . 242.2 Research Studies on Particle Bed Comminution . . . . . . . . . . . . . . . . 272.2.1 Geometric constraints in a piston-die arrangement . . . . . . . . . . . 272.2.2 Self-similar particle size distribution . . . . . . . . . . . . . . . . . . 292.2.3 The phenomenon of energy saturation . . . . . . . . . . . . . . . . . 292.2.4 Influence of moisture on energy consumption . . . . . . . . . . . . . 312.2.5 Pressure distribution between rolls . . . . . . . . . . . . . . . . . . . 322.3 Comminution Theories and Tests . . . . . . . . . . . . . . . . . . . . . . . . 342.3.1 Comminution theories . . . . . . . . . . . . . . . . . . . . . . . . . . 342.3.2 Bond ball mill grindability test . . . . . . . . . . . . . . . . . . . . . 372.3.3 JK Drop Weight test . . . . . . . . . . . . . . . . . . . . . . . . . . 382.3.4 SAG Mill Comminution test . . . . . . . . . . . . . . . . . . . . . . 422.3.5 Static pressure test . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432.3.6 Energy–size reduction models of particle bed comminution . . . . . . 432.4 Summary of Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 473 EXPERIMENTAL PROGRAM OVERVIEW . . . . . . . . . . . . . . . . . . . . 513.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.2 Sample Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.3 Pilot-scale HPGR Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.3.1 Description of the equipment . . . . . . . . . . . . . . . . . . . . . . 543.3.2 HPGR test procedure . . . . . . . . . . . . . . . . . . . . . . . . . . 553.3.3 Design implications of the HPGR test results . . . . . . . . . . . . . . 593.3.4 HPGR test repeatability . . . . . . . . . . . . . . . . . . . . . . . . . 593.4 Piston Press Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603.4.1 Overall criteria for the piston press testing . . . . . . . . . . . . . . . 603.4.2 Piston press test procedure . . . . . . . . . . . . . . . . . . . . . . . 633.4.3 Statistical analysis of the piston press tests . . . . . . . . . . . . . . . 664 RESULTS OF HPGR TESTING AND EMPIRICAL MODELS . . . . . . . . . . 754.1 Summary of HPGR Test Results . . . . . . . . . . . . . . . . . . . . . . . . . 754.2 Effect of Specific Pressing Force on Specific Energy . . . . . . . . . . . . . . 774.3 Effect of Feed Coarseness on Size Reduction . . . . . . . . . . . . . . . . . 774.4 Normalization of Product PSD . . . . . . . . . . . . . . . . . . . . . . . . . 794.5 Development of Regression Models of Net Specific Energy . . . . . . . . . . 85vi4.5.1 Statistical analysis of the HPGR database . . . . . . . . . . . . . . . . 854.5.2 Regression models of net specific energy consumption . . . . . . . . . 924.5.3 Cross-validation of the linear regression models . . . . . . . . . . . . 1124.6 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175 DIRECT CALIBRATION METHODOLOGY . . . . . . . . . . . . . . . . . . . 1195.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1195.2 Conducting HPGR Tests (Step 1) . . . . . . . . . . . . . . . . . . . . . . . . 1205.3 Conducting Piston Press Tests (Step 2) . . . . . . . . . . . . . . . . . . . . . 1215.4 Calibration between Ppiston and FSP (Step 3) . . . . . . . . . . . . . . . . . . 1235.5 Calibration between Reduction Ratios (Step 4) . . . . . . . . . . . . . . . . . 1275.6 Comparison of Normalized PSD Curves (Step 5) . . . . . . . . . . . . . . . . 1335.7 Scale-up of Results (Step 6) . . . . . . . . . . . . . . . . . . . . . . . . . . . 1345.8 Summary of the Direct Calibration Methodology . . . . . . . . . . . . . . . . 1356 DATABASE-CALIBRATED METHODOLOGY . . . . . . . . . . . . . . . . . . 1376.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1376.2 Calculation of Piston Pressure (Step 1) . . . . . . . . . . . . . . . . . . . . . 1386.3 Conducting Piston Press Tests (Step 2) . . . . . . . . . . . . . . . . . . . . . 1426.4 Scaling to HPGR Reduction Ratio (Step 3) . . . . . . . . . . . . . . . . . . . 1436.5 Prediction of Energy–Size Reduction Relationship (Step 4) . . . . . . . . . . 1466.6 Summary of the Database-Calibrated Methodology . . . . . . . . . . . . . . . 1517 SIMULATION-BASED METHODOLOGY . . . . . . . . . . . . . . . . . . . . . 1537.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1537.2 Piston Press Tests on Narrowly Sized Particles (Step 1) . . . . . . . . . . . . 1547.3 Defining Relationship between ESP and t10 (Step 2) . . . . . . . . . . . . . . 1577.3.1 Compression breakage of narrowly sized particles . . . . . . . . . . . 1577.3.2 Quantification of the effect of fine particles on compression breakage . 1657.4 Defining Relationship between t10 and tn (Step 3) . . . . . . . . . . . . . . . 1667.5 Simulation of Energy Input versus Size Reduction (Step 4) . . . . . . . . . . 1697.6 Summary of Simulation Methodology . . . . . . . . . . . . . . . . . . . . . 1758 COMPARISON OF HPGR ENERGY PREDICTION METHODOLOGIES . . . . 1788.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1788.2 Application of the Direct Calibration Methodology . . . . . . . . . . . . . . 180vii8.2.1 Calibration between HPGR and piston press tests . . . . . . . . . . . 1808.2.2 Piston press tests on geometallurgical units . . . . . . . . . . . . . . . 1838.3 Application of the Database-Calibrated Methodology . . . . . . . . . . . . . 1888.3.1 Calculation of piston pressure using empirical calibration equation . . 1888.3.2 Reduction ratio scale-up . . . . . . . . . . . . . . . . . . . . . . . . . 1898.4 Application of Simulation-based Methodology . . . . . . . . . . . . . . . . . 1918.4.1 Determination of t10–Energy relationship . . . . . . . . . . . . . . . . 1918.4.2 Determination of relationship between t10 and tn . . . . . . . . . . . . 1938.4.3 Simulation of energy–size reduction . . . . . . . . . . . . . . . . . . 1948.5 Discussion on the Comparison of HPGR Energy Prediction Methodologies . . 2039 CONCLUSIONS AND RECOMMENDATIONS . . . . . . . . . . . . . . . . . . 2069.1 Main Outcomes of the Research . . . . . . . . . . . . . . . . . . . . . . . . . 2069.2 Limitations of the Methodologies . . . . . . . . . . . . . . . . . . . . . . . . 2089.3 Recommendations for Future Research . . . . . . . . . . . . . . . . . . . . . 20910 CLAIMS OF ORIGINAL CONTRIBUTIONS . . . . . . . . . . . . . . . . . . . . 211REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213Appendix A HPGR TEST DATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220A.1 Copper-Molybenum (P) Ore . . . . . . . . . . . . . . . . . . . . . . . . . . . 221A.2 Gold (C) Ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226A.3 Gold (B) Ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233A.4 Nickel-Copper Ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234Appendix B PISTON PRESS TEST DATA . . . . . . . . . . . . . . . . . . . . . . . 244B.1 Piston Press Tests on -12.5 mm Feed . . . . . . . . . . . . . . . . . . . . . . 245B.1.1 Copper-molybdenum (P) ore . . . . . . . . . . . . . . . . . . . . . . 245B.1.2 Gold (C) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246B.1.3 Gold (B) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247B.1.4 Nickel-copper ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . 248B.1.5 Copper-molybdenum (H) ore . . . . . . . . . . . . . . . . . . . . . . 249B.1.6 Tungsten ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250B.1.7 Dolomite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251B.1.8 Copper-gold-silver ore . . . . . . . . . . . . . . . . . . . . . . . . . . 252B.1.9 Kimberlite ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253viiiB.1.10 Copper-molybdenum (C) ore . . . . . . . . . . . . . . . . . . . . . . 254B.1.11 Copper (M) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255B.1.12 Copper (E) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256B.1.13 Taconite ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257B.1.14 Palladium ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258B.1.15 Copper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 259B.2 Piston Press Tests on Geometallurgical Units of a Copper-Gold Ore . . . . . . 260B.2.1 Geometallurgical unit 1 . . . . . . . . . . . . . . . . . . . . . . . . . 260B.2.2 Geometallurgical unit 2 . . . . . . . . . . . . . . . . . . . . . . . . . 261B.2.3 Geometallurgical unit 3 . . . . . . . . . . . . . . . . . . . . . . . . . 262B.2.4 Geometallurgical unit 4 . . . . . . . . . . . . . . . . . . . . . . . . . 263B.2.5 Geometallurgical unit 5 . . . . . . . . . . . . . . . . . . . . . . . . . 264B.2.6 Geometallurgical unit 6 . . . . . . . . . . . . . . . . . . . . . . . . . 265B.2.7 Geometallurgical unit 7 . . . . . . . . . . . . . . . . . . . . . . . . . 266B.2.8 Geometallurgical unit 8 . . . . . . . . . . . . . . . . . . . . . . . . . 267B.2.9 Geometallurgical unit 9 . . . . . . . . . . . . . . . . . . . . . . . . . 268B.2.10 Geometallurgical unit 10 . . . . . . . . . . . . . . . . . . . . . . . . 269B.2.11 Geometallurgical unit 11 . . . . . . . . . . . . . . . . . . . . . . . . 270B.2.12 Geometallurgical unit 12 . . . . . . . . . . . . . . . . . . . . . . . . 271B.2.13 Geometallurgical unit 13 . . . . . . . . . . . . . . . . . . . . . . . . 272B.2.14 Geometallurgical unit 14 . . . . . . . . . . . . . . . . . . . . . . . . 273Appendix C A WORKED EXAMPLE OF SIMULATION . . . . . . . . . . . . . . 274ixLIST OF TABLES2.1 List of parameters required to use the Morrell/Tondo model . . . . . . . . . 202.2 Direct specific energy comparison between SABC and HPGR circuits . . . . 252.3 Operating cost comparison between SABC and HPGR circuits . . . . . . . . 262.4 Summary of piston-die arrangements used . . . . . . . . . . . . . . . . . . 282.5 Size intervals and nominal specific energy input levels in a JK DWT . . . . 392.6 Standard appearance function data used in AG/SAG model of JKSimMetsimualtion software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423.1 List of ore types used in the research project . . . . . . . . . . . . . . . . . . 543.2 Summary result of 4 repeat HPGR tests . . . . . . . . . . . . . . . . . . . . 603.3 Variation in PSD of feed subsamples split before moisture adjustment . . . . 673.4 Variation in PSD of feed subsamples split after moisture adjustment . . . . . 693.5 Results of multiple piston press tests on a geometallurgical unit . . . . . . . 703.6 An example of confidence deviation and prediction intervals . . . . . . . . . 723.7 PSDs of 10 replicates of piston press tests on copper-gold ore . . . . . . . . 733.8 Summary results of experimental errors in the piston press testing . . . . . . 744.1 Summary of pilot-scale HPGR test work . . . . . . . . . . . . . . . . . . . . 764.2 Descriptive statistics of HPGR database operating parameter and feedconditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 864.3 Summary results of stepwise regression on five parameters and their two-wayinteractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 944.4 Summary results of the simplified regression model that considered fiveparameters and their two-way interactions . . . . . . . . . . . . . . . . . . 954.5 Summary results of regression on standardized variables . . . . . . . . . . . 964.6 Summary results of stepwise regression on eight parameters and theirtwo-way interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104x4.7 Summary results of the simplified regression model that considered eightparameters and their two-way interactions . . . . . . . . . . . . . . . . . . . 1054.8 Standardized beta coefficients of the seven-variable model of the net specificenergy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1064.9 Cross-validation results for the three variable model . . . . . . . . . . . . . 1134.10 Cross-validation results for the seven variable regression model . . . . . . . 1154.11 Relative errors and error sums of squares of 30 cross-validations for the sevenvariable regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1164.12 Comparison of the net specific energy model statistics . . . . . . . . . . . . 1185.1 Example of piston press test parameters and results . . . . . . . . . . . . . . 1235.2 Slopes and intercepts for defining calibration between piston pressure andspecific pressing force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1265.3 Reduction ratios achieved in piston press and HPGR tests on Cu-Au-Ag ore 1305.4 Slopes and intercepts of the ore-specific calibration lines for scaling-upreduction ratios of piston press tests . . . . . . . . . . . . . . . . . . . . . . 1326.1 Summary table of HPGR test variables used in the development of anempirical calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1396.2 Summary of the empirical model for calculating the required piston pressurethat delivers equivalent net specific energy into the sample for a given specificpressing force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1416.3 Summary of the empirical model for scaling the reduction ratio achieved inthe piston press test to the HPGR result . . . . . . . . . . . . . . . . . . . . 1457.1 Summary of size classes and nominal specific energy levels used in the pistonpress tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1557.2 tn sizes for different size classes . . . . . . . . . . . . . . . . . . . . . . . . 1577.3 t10–ESP models are compared for a tungsten ore . . . . . . . . . . . . . . . 1597.4 List of fitted parameters and coefficient of determination for the relationshipbetween specific energy and t10 . . . . . . . . . . . . . . . . . . . . . . . . 1637.5 Comparison of the fitted constants for the five ore types and the fittedconstants of the master curve . . . . . . . . . . . . . . . . . . . . . . . . . 1697.6 Variations in the test parameters of the simulated HPGR tests . . . . . . . . 1707.7 Simulation results with varying definition of fines . . . . . . . . . . . . . . 173xi8.1 Summary of operating and feed parameters and results of HPGR tests on theCentral BC copper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1798.2 Summary of the piston press tests on 14 geometallurgical units . . . . . . . 1848.3 Summary of the scale-up results of the piston press tests . . . . . . . . . . . 1858.4 Input variable, calculated piston pressures and the results of the piston presstests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1898.5 Circuit specific energies for producing -4 mm product . . . . . . . . . . . . 1918.6 Results of piston press tests on size classes for the copper-gold ore . . . . . 1928.7 βi coefficients for defining tn–t10 relationships for the copper-gold ore . . . 1938.8 HPGR test matrix for the copper-gold ore and the resulting specific energy . 1958.9 Comparison of measured and the simulated results and their relative errors . 1968.10 Comparison of the error in specific energy prediction using the threemethodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2048.11 Overall comparison of the methodologies . . . . . . . . . . . . . . . . . . . 2058.12 Applicability of the methodologies throughout the stages of a mine project . 205A.1 Summary of HPGR tests on copper-molybdenum (P) ore . . . . . . . . . . . 221A.2 Summary of HPGR tests on gold (C) ore . . . . . . . . . . . . . . . . . . . 226A.3 Summary of HPGR tests on gold (B) ore . . . . . . . . . . . . . . . . . . . 233A.4 Summary of HPGR tests on nickel-copper ore . . . . . . . . . . . . . . . . . 234C.1 Feed particle size distribution . . . . . . . . . . . . . . . . . . . . . . . . . 276C.2 Calculated t10 for the size classes in the +16 mm fraction . . . . . . . . . . . 277C.3 βi coefficients used to define tn–t10 relationships for the copper-gold ore . . 277C.4 Full PSDs for each size classes in the +16 mm fraction . . . . . . . . . . . . 278C.5 Feed PSD to the grinding stage . . . . . . . . . . . . . . . . . . . . . . . . 279C.6 Calculated t10 for each size class in the feed to the grinding stage . . . . . . 281C.7 Measured and predicted product PSDs . . . . . . . . . . . . . . . . . . . . 282xiiLIST OF FIGURES1.1 A forecast of the global energy consumption . . . . . . . . . . . . . . . . . 21.2 World net electricity generation by energy source . . . . . . . . . . . . . . . 32.1 Illustration of the main components of HPGR . . . . . . . . . . . . . . . . . 102.2 Schematic presentation of HPGR feed preparation in reverse-closed circuit atthe Cerro Verde operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Schematic presentation of HPGR feed preparation in regular closed circuit atthe Boddington operation . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.4 Schematic structure of the Morrell/Tondo model of size-reduction in HPGR . 192.5 Breakage fraction of 2.83x3.36 mm limestone diminishes in the presence ofvarious sizes and quantity of fines . . . . . . . . . . . . . . . . . . . . . . . 302.6 Illustration of the pressure profile within the particle bed . . . . . . . . . . . 332.7 An example of a t10 vs. Ecs relationship . . . . . . . . . . . . . . . . . . . . 402.8 Relationship between tn and t10 for single particle impact breakage . . . . . 412.9 Energy–size reduction relationship graphs . . . . . . . . . . . . . . . . . . 453.1 Overview of the experimental program . . . . . . . . . . . . . . . . . . . . 533.2 Köppern pilot-scale HPGR at UBC . . . . . . . . . . . . . . . . . . . . . . 553.3 An example of machine data for an HPGR test . . . . . . . . . . . . . . . . 563.4 HPGR products are split into centre and edge products through the splitter box 573.5 Illustration of piston-die arrangement . . . . . . . . . . . . . . . . . . . . . 633.6 Strain curve of the entire piston-die setup . . . . . . . . . . . . . . . . . . . 643.7 An example of force displacement curve before and after the correction forthe strain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653.8 Illustration of numerical integration of force-displacement curves . . . . . . 663.9 Results of piston press tests on a geometallurgical unit . . . . . . . . . . . . 71xiii4.1 Linear relationship between net specific energy and specific pressing forcefor the tests on -32 mm feed . . . . . . . . . . . . . . . . . . . . . . . . . . 774.2 Comparison of reduction ratios achieved with 12.5 mm and 32 mm top sizefeed for Au (C) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 784.3 Comparison of reduction ratios achieved with 12.5 mm and 32 mm top sizefeed for Au (B) ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 794.4 A comparison of a) regular and b) normalized PSDs of Cu-Mo (P) ore at FSPranging from 2 N/mm2 to 5 N/mm2 . . . . . . . . . . . . . . . . . . . . . . 804.5 Modelling of cumulative percent passing as function of normalized particlesize using Eq. 2.4 is shown for HPGR tests on Cu-Mo (P) ore . . . . . . . . 814.6 A comparison of regular and normalized PSDs of Ni-Cu ore . . . . . . . . . 824.7 A comparison of normalized PSDs of products from HPGR tests on differentfeed top sizes of Au (C) ore; showing match of fitted curves regardless offeed top size and tested pressure . . . . . . . . . . . . . . . . . . . . . . . . 834.8 A comparison of regular and normalized PSDs of products from HPGR testson different feed size distribution for the Au (B) ore . . . . . . . . . . . . . 844.9 Specific energy versus specific pressing force for the 157 HPGR tests on 22ore types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 874.10 Specific energy versus specific pressing force graph for three levels of feedmoisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 884.11 Specific energy versus specific pressing force graph for three levels of feedcoarseness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 894.12 Trellis graph illustrating the interaction effect of feed moisture and F80 . . . . 904.13 Reduction ratio achieved as function of feed size, grouped into three levels ofspecific energy input . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 914.14 Measured versus predicted net specific energies for three variable regressionmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 974.15 Residuals versus predicted net specific energy for the three variableregression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 984.16 Relative error versus measured net specific energy for the three variableregression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.17 Residuals versus specific pressing force for the three variable regression model 1004.18 Residuals versus feed F80 for the three variable regression model . . . . . . 1014.19 Residuals versus feed moisture for the three variable regression model . . . 1024.20 Residuals versus feed bulk density for the three variable regression model . . 103xiv4.21 Measured versus predicted net specific energies for seven variable regressionmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1074.22 Residuals versus predicted net specific energy for the seven variableregression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1084.23 Relative error versus measured net specific energy for the seven variableregression model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1094.24 Residuals versus FSP, F80, moisture, and bulk density plots for the sevenvariable regression model . . . . . . . . . . . . . . . . . . . . . . . . . . . 1104.25 Residuals versus m, Wpi, and P1mm plots for the seven variable regressionmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115.1 Comparison of using regular and reverse-closed circuits for feed preparationof piston press test on Ni-Cu ore . . . . . . . . . . . . . . . . . . . . . . . . 1225.2 Illustration of calibration between specific pressing force and piston pressure,such that both give the same net specific energy to the sample . . . . . . . . 1245.3 Specific energy prediction using ore-specific calibration . . . . . . . . . . . 1275.4 Piston press test produces product comparable to the centre product of HPGRwhen both tests are carried out on -12.5 mm feed . . . . . . . . . . . . . . . 1285.5 Piston press test produces product comparable to the centre product of HPGRwhen both tests are carried out on -12.5 mm feed . . . . . . . . . . . . . . . 1295.6 (A) Fitting reduction ratio achieved in piston press tests to Eq. 2.30 anddetermining reduction ratios at the same ESP as the HPGR tests; (B)Calibration of reduction ratios of piston press tests against the reductionratios achieved in HPGR tests . . . . . . . . . . . . . . . . . . . . . . . . . 1305.7 Fitting reduction ratio achieved in piston press tests to a line and determiningreduction ratios at the same ESP as the HPGR tests; (B) Calibration ofreduction ratios of piston press tests against the reduction ratios achieved inHPGR tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1315.8 Comparison of the HPGR reduction ratios with scaled reduction ratios of thepiston press tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1335.9 Comparison of normalized PSDs of products from piston tests on -12.5 mmfeed and HPGR tests on -32 mm and -12.5 mm feeds . . . . . . . . . . . . . 1345.10 Block diagram of the direct calibration methodology . . . . . . . . . . . . . 1366.1 Direct correlation between Ppiston and FSP; regression line and its 95%confidence interval are shown . . . . . . . . . . . . . . . . . . . . . . . . . 140xv6.2 The required pressure versus the modelled pressure to input same specificenergy to the sample as in HPGR operation . . . . . . . . . . . . . . . . . . 1426.3 Specific energy prediction using the empirical calibration equation . . . . . 1436.4 Direct correlation of reduction ratios achieved in the HPGR and the pistonpress tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1446.5 Modelled reduction ratio of HPGR with the empirical model (Eq. 6.2) . . . 1466.6 Comparison of normalized product PSDs of the HPGR tests and the pistonpress tests on Cu-Mo (P) ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1476.7 Comparison of normalized product PSDs of the HPGR tests and the pistonpress tests on Ni-Cu ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1486.8 Comparison of normalized product PSDs of the HPGR tests and the pistonpress tests on a tungsten ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1496.9 Comparison of normalized product PSDs of the HPGR tests and the pistonpress tests on a taconite ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1496.10 Comparison of normalized product PSDs of the HPGR and the piston presstests on the Cu-Mo (H) ore . . . . . . . . . . . . . . . . . . . . . . . . . . 1506.11 Comparison of normalized product PSDs of the HPGR tests and the pistonpress tests on the Cu-Au-Ag ore . . . . . . . . . . . . . . . . . . . . . . . . 1516.12 Block diagram of the database-calibrated methodology . . . . . . . . . . . . 1527.1 Illustration of determination of t10 from particle size distributions of pistonpress tests on -12.5+11.2 mm size class . . . . . . . . . . . . . . . . . . . . 1567.2 t10 modelled as function of specific energy . . . . . . . . . . . . . . . . . . 1597.3 t10 modelled as function of specific energy and particle size . . . . . . . . . 1607.4 t10 modelled as function of specific energy and square root of particle size . 1617.5 t10 modelled by Eq. 7.3 , which allows the exponent (n) of particle size to beore-specific . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1627.6 Specific energy and t10 relationship of the Cu-Mo (P) ore . . . . . . . . . . 1637.7 Specific energy and t10 relationship of the Au (C) ore . . . . . . . . . . . . . 1647.8 Specific energy and t10 relationship of the Cu-Mo (H) ore . . . . . . . . . . 1657.9 Modelling of t10 as function of ESP and percentage of fines added to-12.5+11.2 mm particles; . . . . . . . . . . . . . . . . . . . . . . . . . . . 1667.10 Scatter plot showing relationship between tn and t10 along with model fittedlines–each vertical line of t10 enables reconstruction of a particle sizedistribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167xvi7.11 Master curve fitted to the five tested ores . . . . . . . . . . . . . . . . . . . 1687.12 Schematic of the simulation model . . . . . . . . . . . . . . . . . . . . . . 1727.13 Simulation results of 36 HPGR tests by defining fines as -1.4 mm in the feedof the respective tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1747.14 Residuals versus predicted particle sizes for simulation of 36 HPGR tests . . 1747.15 Relative % error versus measured passing sizes for simulation results of 36HPGR tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1757.16 Block diagram of the simulation methodology . . . . . . . . . . . . . . . . . 1768.1 HPGR specific energy versus specific pressing force for the copper-goldcomposite ore sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1808.2 Piston press specific energy versus piston pressure for the copper-goldcomposite ore sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1818.3 Specific energy versus reduction ratios achieved in the HPGR and the pistonpress tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1828.4 Comparison of normalized product PSDs from the HPGR and piston presstests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1838.5 Prediction of net specific energy consumption for each geometallurgical unitat three different specific pressing forces . . . . . . . . . . . . . . . . . . . 1878.6 Prediction of the circuit specific energy for each geometallurgical unit,assuming a -4 mm product . . . . . . . . . . . . . . . . . . . . . . . . . . . 1878.7 Comparison of measured and predicted HPGR product PSDs for thecomposite sample at 3 N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . 1898.8 Comparison of measured and predicted HPGR product PSDs for thecomposite sample at 4 N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . 1908.9 Comparison of measured and predicted HPGR product PSDs for thecomposite sample at 5 N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . 1908.10 Specific energy and t10 relationship for the copper-gold ore and the fittedcurve using Eq. 7.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1938.11 t10–tn relationship of the copper-gold ore and the fitted curves using Eq. 7.5through 7.10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1948.12 Comparison of simulated and measured product PSDs for the HPGR test runat 3N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1978.13 Comparison of simulated and measured product PSDs for the HPGR test runat 4 N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197xvii8.14 Comparison of simulated and measured product PSDs for the HPGR test runat 5 N/mm2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1988.15 Comparison of simulated and measured product PSDs for the HPGR test runat roll speed of 0.6m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1998.16 Comparison of simulated and measured product PSDs for the HPGR test runat roll speed of 0.9m/s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1998.17 Comparison of simulated and measured product PSDs for the HPGR test runon feed with 0.9% moisture . . . . . . . . . . . . . . . . . . . . . . . . . . 2008.18 Comparison of simulated and measured product PSDs for the HPGR test runon feed with 4.5% moisture . . . . . . . . . . . . . . . . . . . . . . . . . . 2018.19 Comparison of simulated and measured product PSDs for the HPGR test runon 25 mm top size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2028.20 Comparison of simulated and measured product PSDs for the HPGR test runon 19 mm top size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202A.1 Feed and product PSDs of test No. Cu-Mo (P) 1 . . . . . . . . . . . . . . . . 222A.2 Feed and product PSDs of Test No. Cu-Mo (P) 2 . . . . . . . . . . . . . . . 223A.3 Feed and product PSDs of test No. Cu-Mo (P) 3 . . . . . . . . . . . . . . . . 224A.4 Feed and product PSDs of test No. Cu-Mo (P) 4 . . . . . . . . . . . . . . . . 225A.5 Feed and product PSDs of test No. Au (C) 1 . . . . . . . . . . . . . . . . . . 227A.6 Feed and product PSDs of test No. Au (C) 2 . . . . . . . . . . . . . . . . . . 228A.7 Feed and product PSDs of test No. Au (C) 3 . . . . . . . . . . . . . . . . . . 229A.8 Feed and product PSDs of test No. Au (C) 4 . . . . . . . . . . . . . . . . . . 230A.9 Feed and product PSDs of test No. Au (C) 5 . . . . . . . . . . . . . . . . . . 231A.10 Feed and product PSDs of test No. Au (C) 6 . . . . . . . . . . . . . . . . . . 232A.11 Feed and product PSDs of test No. Au (B) 1 . . . . . . . . . . . . . . . . . 235A.12 Feed and product PSDs of test No. Au (B) 2 . . . . . . . . . . . . . . . . . . 236A.13 Feed and product PSDs of test No. Au (B) 3 . . . . . . . . . . . . . . . . . . 237A.14 Feed and product PSDs of test No. Au (B) 4 . . . . . . . . . . . . . . . . . . 238A.15 Feed and product PSDs of test No. Ni-Cu 1 . . . . . . . . . . . . . . . . . . 239A.16 Feed and product PSDs of test No. Ni-Cu 2 . . . . . . . . . . . . . . . . . . 240A.17 Feed and product PSDs of test No. Ni-Cu 3 . . . . . . . . . . . . . . . . . . 241A.18 Feed and product PSDs of test No. Ni-Cu 4 . . . . . . . . . . . . . . . . . . 242A.19 Feed and product PSDs of test No. Ni-Cu 5 . . . . . . . . . . . . . . . . . . 243B.1 Specific energy versus piston pressure plot for a copper-molydenum (P) ore . 245xviiiB.2 Specific energy versus piston pressure plot for a gold (C) ore . . . . . . . . . 246B.3 Specific energy versus piston pressure plot for a gold (B) ore . . . . . . . . . 247B.4 Specific energy versus piston pressure plot for a Ni-Cu ore . . . . . . . . . . 248B.5 Specific energy versus piston pressure plot for a copper-molybdenum (H) ore 249B.6 Specific energy versus piston pressure plot for a tungsten ore . . . . . . . . . 250B.7 Specific energy versus piston pressure plot for a dolomite . . . . . . . . . . . 251B.8 Specific energy versus piston pressure plot for a copper-gold-silver ore . . . 252B.9 Specific energy versus piston pressure plot for a kimberlite ore . . . . . . . . 253B.10 Specific energy versus piston pressure plot for a copper-molybdenum (C) ore 254B.11 Specific energy versus piston pressure plot for a copper (M) ore . . . . . . . 255B.12 Specific energy versus piston pressure plot for a copper (E) ore . . . . . . . . 256B.13 Specific energy versus piston pressure plot for a taconite ore . . . . . . . . . 257B.14 Specific energy versus piston pressure plot for a palladium ore . . . . . . . . 258B.15 Specific energy versus piston pressure plot for a copper-gold ore . . . . . . . 259B.16 Specific energy versus piston pressure plot for geometallurgical unit 1 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260B.17 Specific energy versus piston pressure plot for geometallurgical unit 2 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261B.18 Specific energy versus piston pressure plot for geometallurgical unit 3 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262B.19 Specific energy versus piston pressure plot for geometallurgical unit 4 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263B.20 Specific energy versus piston pressure plot for geometallurgical unit 5 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264B.21 Specific energy versus piston pressure plot for geometallurgical unit 6 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265B.22 Specific energy versus piston pressure plot for geometallurgical unit 7 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266B.23 Specific energy versus piston pressure plot for geometallurgical unit 8 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267B.24 Specific energy versus piston pressure plot for geometallurgical unit 9 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268B.25 Specific energy versus piston pressure plot for geometallurgical unit 10 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269xixB.26 Specific energy versus piston pressure plot for geometallurgical unit 11 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270B.27 Specific energy versus piston pressure plot for geometallurgical unit 12 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271B.28 Specific energy versus piston pressure plot for geometallurgical unit 13 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272B.29 Specific energy versus piston pressure plot for geometallurgical unit 14 of acopper-gold ore . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273xxLIST OF SYMBOLSA Impact breakage parameter which indicates maximum possible t10 [%]b Impact breakage parameter which indicates ramp up rate of t10 as specific energyincreases [t/kWh/t]βsplit HPGR simulation model parameter for energy split between pre-crushing stageand grinding stagec A constant parameter in the HPGR simulation modelD Roll diameter [mm]DWi Drop weight index obtained from SMC test [kWh/m3]Ecs Specific comminution energy of impact breakage [J/kg]Emin Threshold energy [J/kg]ESP Net specific energy consumption of HPGR test [kWh/t]F80 80% passing aperture size of feed by weight [mm]fmat Material breakage property [kg J−1m−1]f ∗mat Material breakage property [t kWh−1 mm−n]FSP Specific pressing force of HPGR test [N/mm2]Ftotal Total hydraulic force of HPGR test [N]HPi High pressure index obtained from Static Pressure test [kWh/t]L Roll width [mm]m˙ M-dot or Specific throughput constant [t s m−3h−1]xxiM Fitted parameter representing maximum attainable t10 [%]Mia Work index obtained from SMC test for AG/SAG operation [kWh/m3]Mic Work index obtained from SMC test for conventional crushing operation [kWh/m3]Mih Work index obtained from SMC test for HPGR operation [kWh/m3]P80 80% passing aperture size of product by weight [mm]Pidle Idle motor power draw of HPGR [kW]Ptotal Total motor power draw during HPGR test [kW]Q HPGR test throughput [t/h]ta Abrasion parameter obtained from tumbling test [%]t10 Percentage passing 1/10th of original particle size after breakage [%]υ Roll peripheral speed [m/s]Wi Bond ball mill work index [kWh/t]w Moisture content [%]xc HPGR simulation model parameter for classifying feed particles according to theirsizexxiiACKNOWLEDGEMENTSOver the last five years, many people have helped me in many ways along my journey towardsthe completion of this research.First, I would like to express my greatest gratitude to my supervisor Prof. Bern Klein forproviding guidance, support, and advice throughout my study. I thank my committee membersProf. Maria Holuszko, Prof. Rob Hall, and Prof. Davide Elmo for providing advice, criticism,and feedback from the research proposal through the completion of the thesis.The financial support from NSERC and the Canadian Mining Industry Research Organiza-tion (CAMIRO) and its member companies are much appreciated. I thank Dr. Andrew Bamberfor the valuable advice on conducting research and the introduction to the consulting world.Stefan Nadolski and Jeff Drozdiak were my mentors of HPGR technology and I have agreat appreciation for their knowledge, experience, and friendship. I thank Pius Lo and AaronHope for their technical assistance with the equipment in the Coal and Mineral ProcessingLaboratory and for making my life easier. I thank Juan Anes for the opportunity to apply andvalidate the methodologies in practice.I thank fellow graduate students Chengtie Wang, Amit Kumar, Tong Yang, and Hans YuHou for their friendship and mutual learning experience at UBC. I also thank the summer co-opstudents who helped me with the most of the labor intensive parts of performing HPGR andpiston press experiments.I thank Mendee Jargalsaikhan and Dr. Aaron Gunson and their families for welcoming myfamily to Vancouver and making the experience of adjustment to the new environment a verypleasant one.Last but not least, I thank my wife, Mart, and sons, Tod and Sod, for their love and laughterat home. Without their presence, I would not have been able to complete this journey.xxiiiDEDICATIONTo my parents with love and respectxxivChapter 1INTRODUCTIONThis chapter introduces the background of the research problem and states the research ob-jectives. The last section provides an outline of the thesis and describes how the chapters areorganized.1.1 BackgroundThe High Pressure Grinding Roll (HPGR) is a relatively new comminution technology that hasbeen shown to be more energy-efficient compared to tumbling mills, such as semi-autogenousgrinding (SAG) and ball mills. Typically, HPGR-based comminution circuits are 10–40%more energy-efficient than equivalent SAG-based circuits (Saramak et al., 2010). One couldargue that for all future hard rock mining operations, energy efficiency and reduction of energyusage will be the main criteria for the selection of a comminution circuit. The reasons for thisargument include the following facts and predictions:• Energy demand and cost are predicted to rise in the future.• Comminution is an energy-intensive and inefficient process.1• Governments have started to introduce carbon tax schemes to discourage the use of fossilfuels and to reduce greenhouse gas emissions.• Rich and easily-liberated ores or economically viable ores are being depleted; if futuremining operations treat the current unviable ores, they will have to grind greater tonnageto finer liberation sizes in order to recover the metal in concentrate.• Expectations of civil society demand that mining operations promote sustainable devel-opment and reduce their environmental footprint in order to maintain their public imageand obtain social license to operate.The U.S. Energy Information Administration (U.S. EIA) forecasts that the global energy con-sumption will continue to grow over the coming years, as shown in Figure 1.1, especially asdeveloping countries, who are currently not members of the Organization for Economic Co-operation and Development (OECD), continue to modernize (U.S. EIA, 2011).01002003004005006007008009001990 1995 2000 2005 2010 2015 2020 2025 2030 2035Global energy consumption [quadrillion Btu]OECD Rest of world China and IndiaHistoric dataForecastFigure 1.1: A forecast of the global energy consumption(data from U.S. EIA, 2011)2Simple economic principles suggest that the predicted increase in energy demand will driveits cost higher, since the supply of natural resources for energy generation is limited. Thisexpected increase in cost of energy will exert greater pressure on future mining operations toreduce their energy consumption.Regardless of energy cost, the source of the energy generation itself is a major concern.Figure 1.2 shows that currently, 40% of world net electricity is generated by coal. The U.S.EIA (2013) predicts that coal will continue to be the predominant fuel for electricity generationuntil 2040, although the share of coal-fired electricity is predicted to drop slightly to 36%.The environmental concern doubles as an economic issue when the governments implementpolicies to reduce greenhouse gas emissions. An example would be the carbon tax introducedin British Columbia, which increased from $10 per tonne of CO2 in 2008 to $30 per tonne ofCO2 in 2014 (Beaty et al. 2014).0102030402010 2015 2020 2025 2030 2035 2040Electricity generation by source[trillion kWh]LiquidsNonhydropowerrenewablesHydropowerNuclearNatural  gasCoalForecastFigure 1.2: World net electricity generation by energy source(data from U.S. EIA, 2013)Hard rock mining operations are becoming increasingly conscious of their energy con-sumption for the aforementioned economic and environmental reasons. The actions of Barrick3Gold Corp., Teck Resources Ltd., and Rio Tinto PLC who invested in large-scale wind-farmprojects to reduce their energy costs and environmental footprint is an evidence of this energyconsciousness. For example, Barrick Gold Corp. invested $70m in Chile’s Punta Coloradowind operation and Rio Tinto invested $31m in wind farm energy production at their DiavikDiamond operation (Bouw, 2011).It is well known that comminution is the most energy-intensive component of mineralprocessing. On average, comminution energy accounts for 55% of total energy consumption inmetal mining operations (U.S. Department of Energy, 2007) and 66-80% of the total electricalenergy consumption for mineral processing (Abouzeid and Fuerstenau, 2009, Claffin et al.,2009). In cost terms, power represents around 44% of the total operating cost in a typicalmineral processing operation (Claffin et al., 2009). Energy expended on comminution takesup a large percentage of the total energy consumption of mining operations because traditionalcomminution equipment, such as tumbling mills, are inefficient. In terms of the amount ofenergy required to generate new fracture surface area, comminution efficiency for tumblingmills is in the range of 1-2% (Tromans, 2008).Therefore, it is natural for mining operations to look for improvements in comminutionefficiency to reduce their total energy consumption. The practical improvements are especiallycrucial for mines processing low-grade, high-tonnage deposits.Numerous trade-off studies compared the operating and capital costs of HPGR-based cir-cuits against those of SAG-based circuits for various sizes of projects (Valery and Jankovic,2002; Anguelov et al., 2008; Daniel et al., 2010; Ghaffari et al., 2013). The trade-off studiesreported energy savings in the range of 11-32%, which indicates that the HPGR technologyis more energy efficient for the grinding duty of preparing feed for ball mills, comparedto traditional SAG mills. However, the uptake of HPGR technology in hard rock miningapplications has been slow. The Canadian Mining Industry Research Organization (CAMIRO)4has identified the lack of industry-accepted, small-scale tests for the selection and sizing of anHPGR as one of major reasons for the slow uptake of HPGR (Bamber et al., 2009).Currently, machine selection and sizing is done by manufacturers on pilot-scale HPGR(0.7–1.0 m roll diameter) units, and the procedures and methodologies are proprietary to eachmanufacturer. Polysius, one of the HPGR manufacturers offers laboratory scale HPGR units(0.25–0.30 m roll diameter). However, 1) laboratory scale HPGR units have not replaced pilotHPGR testing, and 2) the majority of the HPGR manufacturers do not offer laboratory scaleunit for testing. Those two facts indicate that the scale-up from laboratory unit is not wellaccepted by manufacturers and pilot testing is the current industry practice. Pilot-scale HPGRunits have a capacity of 25–35 t/h, requiring large amounts of sample (1–10 tonnes dependingon the level of study) for a typical test program, making it labor-intensive, costly, and time-consuming. Another concern is that the results of test work from one manufacturer may ormay not be acceptable, or accessible, to other manufacturers.In comparison, for SAG milling, a 6’×2’ pilot-scale SAG mill has a 1 t/h capacity andscoping level selection and sizing of SAG mills are often done through simulation based on theresults of bench-scale tests that require samples as small as 100 kg.There is clearly a need for a small-scale industry-accepted method for the selection andsizing of an HPGR, that is manufacturer-independent. A test that reliably determines energy–size reduction relationship using a small sample of ore would allow comparison of the HPGRwith other technologies, and should help to promote the widespread usage of energy-efficientHPGRs in the hard-rock mining industry.1.2 Thesis ObjectivesThe goal of this thesis is to develop methodologies to predict the energy–size reduction perfor-mance of the HPGR technology through small-scale piston press testing. The ability to predictHPGR performance with a small quantity of sample will match the industry accepted tests for5SAG circuits, facilitating more testing at the early stages of projects, and ultimately leading tothe expansion of HPGR usage, especially in hard rock mining applications.The development of small-scale tests for predicting energy requirements of an HPGR will,• contribute to the knowledge and understanding of HPGR technology itself,• provide the preliminary selection and sizing methodology of HPGRs for early stageprojects that cannot supply a large quantity of sample for testing,• significantly reduce the amount of sample required for testing, and in so doing, lower thecost and labor intensity of the test work,• reduce the mining industry’s reliance on manufacturers for testing,• facilitate geometallurgical mapping of orebody in existing HPGR operations in a cost-effective manner, and• provide a means of simulating the energy–size reduction performance of the HPGR withthe results of piston press tests alone.A small-scale piston press test and its associated procedures will require a much smalleramount of sample than pilot-scale testing. The ability to use smaller test samples will in turnwill facilitate early consideration of the HPGR technology for many early stage projects, whichhave only limited quantities of drill core sample available. Piston press tests will ultimatelysupport the selection of the HPGR technology for the start of new hard rock mining projects.An independent, standardized, public domain, small-scale test and associated procedure willalso promote knowledge and understanding of the potential of HPGR technology compared toother technologies such as SAG milling.61.3 Thesis OutlineThis thesis consists of the following chapters:Chapter 1 describes the background and objectives.Chapter 2 presents the literature review. Section 2.1 introduces the HPGR technology itself,along with its distinct characteristics. Section 2.2 reviews research studies on interparticlecomminution in packed particle beds. Section 2.3 considers comminution theories, tests, andmodels relevant to the HPGR technology. Section 2.4 summarizes and concludes the chapteron the literature review.Chapter 3 introduces the overall experimental program, describes the samples used, liststhe procedures for the HPGR testing and the piston press testing. In addition repeatability andstatistical analysis of experimental errors of both tests are discussed.Chapter 4 summarizes the results of 19 HPGR tests carried out within the scope of thisresearch and presents the statistical analysis on the database of HPGR test results. This chapterprovides details of the development of two regression models for predicting specific energyconsumption of HPGR, with regard to the operating and the feed parameters.Chapter 5 presents the direct calibration methodology, which is developed primarily forsituations where HPGR test data is only available for a composite sample, and the energy–sizereduction performance of the HPGR is needed for individual geometallurgical units.Chapter 6 presents the database-calibrated methodology, which is similar to the direct cali-bration methodology, except that it does not require HPGR test data, and instead, an empiricalequation is used to calculate the appropriate pressure for conducting piston press tests. Inaddition, the reduction ratio achieved in the piston press test is scaled-up to that of HPGRusing an empirical equation.Chapter 7 presents the simulation-based methodology, which is developed as a means touse piston press test results for the simulation of energy–size reduction performance of theHPGR.7Chapter 8 compares the methodologies through an application to a copper-gold mine projectin central British Columbia, which has selected a HPGR-based comminution circuit.Chapter 9 draws conclusions based on the outcomes of the research, and provides recom-mendations for future research.Chapter 10 provides the list of original contributions of the research.8Chapter 2LITERATURE REVIEW2.1 High Pressure Grinding RollThis section introduces the HPGR technology. The main components of the HPGR, related ter-minologies, and operating parameters are defined. Also the advantages and the disadvantagesof the technology are discussed.2.1.1 Overview of HPGR technologyThe concept of the HPGR technology was first introduced in 1977, as the result of a fundamen-tal study on the efficiency of interparticle comminution by Prof. Schönert (Klymowsky et al.,2006). In the literature, various authors have given the HPGR several alternative names, suchas High Pressure Roller Mill (Lubjuhn et al., 1994), High-Compression Roll Mill (Schönert,1988), High-Pressure Roll Crusher (Daniel, 2007), and Roll Press (Klymowsky and Liu, 1997).The HPGR comminutes a bed of particles by interparticle breakage between its counter-rotating cylindrical rolls, one of which is mounted on a fixed bearing, while the other ismounted on a movable bearing. The moving roll (also called floating roll) is allowed to slidelaterally when the choke-fed feed material creates a back-pressure to push the rolls apart and9expands the gap between the rolls. The back-pressure from the feed material drawn into the gapis counter-balanced by the pressure from hydraulic cylinders pushing on the bearing housingof the moving roll. Figure 2.1 illustrates the main components of the HPGR.Figure 2.1: Illustration of the main components of HPGRThe roll diameter ranges from 200 mm for the lab-scale test unit to 2800 mm for the largestindustrial unit. The diameter to length aspect ratio of rolls varies with manufacturers: highaspect ratio D>L for ThyssenKrupp Polysius, square aspect ratio D=L for KHD HumboldtWedag (Weir), and low aspect ratio D<L for Köppern (Morley, 2006).There are different types of roll surface profiles: smooth, studded, and hexagonal-tiled. Thestudded and tiled roll surfaces promote the formation of an autogenous grinding layer and thusprotect and prolong the life of roll surfaces (Morley, 2006).2.1.2 History of HPGR applicationThe first commercial installation of the HPGR was in the cement industry in 1985 and was usedfor grinding cement clinker at the Dykerhoff Lengerich cement plant in Wiesbaden, Germany10(McIvor, 1997). Daniel (2007) estimated that there were around 400 units installed for high-tonnage cement clinker grinding in 2007.The next HPGR application was in the niche market of diamond ore comminution at variousdiamond-mining operations (e.g., Argyle, Diavik, Premier, Kimberley, Jwaneng, Venetia andEkati). The HPGR technology had the ability to preferentially break host rocks and liberatelarger diamond crystals without breaking them (Morley, 2006).The HPGR technology was then adopted in the iron ore industry, following the first com-mercial scale installation for coarse iron ore processing at the Cleveland Cliffs Empire Mine, in1997 (Maxton et al., 2006). Recently, the HPGR has become widely used and well-establishedin iron ore-processing operations (e.g. CMH-Los Colorados, CVRD, Kudermukh) as a replace-ment for tertiary and quaternary crushing stages, prior to pelletizing and briquetting.The first full plant test run of an HPGR for a hard competent ore was in 1995 at the CyprusSierrita copper operation. Due to the hardness and abrasiveness of the ore, liner maintenanceresulted in considerable downtime, and as a result, the availability averaged only 60% duringthe first year (Thompsen, 1997). Eventually, the unit was decommissioned because the wearprotection and studded liner technology at the time could not handle the abrasive ore.The latest success of the HPGR technology has been in hard-rock metal mining applica-tions. The first successful trial of an HPGR was in 2003 at the Lone Tree gold ore-processingoperation. Another successful trial followed in 2004 at the Potgietersrust platinum mine (Patzeltet al., 2006). The first full commercial plant installation of an HPGR for copper ore processingwas commissioned in 2006 at Cerro Verde (Vanderbeek et al., 2006).The next installations of HPGR in hard-rock mining were PT Freeport Indonesia’s Grasbergcopper-gold operation in 2007 (Banini et al., 2011), and Newmont’s Boddington gold operationin 2009 (Hart et al., 2011).Despite having substantial energy advantage as compared to SAG milling, the adaptationof HPGR technology has been slow. As of 2011, the HPGR technology accounted for only1125% of total installed-power for new Chilean projects, which included 11 greenfield and 7brownfield projects (Rosas et al., 2012).2.1.3 HPGR operating parametersThere are a number of HPGR operating parameters that are determined from testing. These aredescribed as follows:Specific pressing force is defined as the total force from the hydraulic piston, divided by theprojected area of the rollers.FSP =FtotalDL(2.1)whereFSP — specific pressing force [N/mm2]Ftotal — total applied force [N]D — roll diameter [mm]L — roll width [mm]The specific pressing force is the most important operating parameter, because it has influ-ence on the specific energy consumption, the size reduction achieved, the operating gap, andthe machine throughput.Net specific energy consumption is defined as net energy input per tonne of collected testproduct. It is measured by subtracting the idle power draw before testing from the totalpower draw during testing with feed material, and then dividing the difference by thethroughput rate of fresh feed during the stable test period. Thus, net specific energyconsumption is the net power draw per throughput rate.ESP =Ptotal −PidleQ(2.2)12whereESP — net specific energy consumption [kWh/t]Pidle — idle motor power draw measured without feed material [kW]Ptotal — total motor power draw measured with feed material [kW]Q — throughput rate [t/h]Following are a few general observations about the net specific energy consumption:• Net specific energy consumption increases linearly with an increase in specific pressingforce over the typical pressing force range that is applied (1–6 N/mm2). A higher specificpressing force causes formation of a narrower gap, and it is frequently observed thatproduct flakes are warmer when operated at higher pressing forces, which is a sign ofenergy being wasted as heat.• A narrow operating gap corresponds to a higher net specific energy consumption, sincea higher power draw is required to drive material through a narrower gap. Also, lessvolume of material passes through the narrow gap per revolution, and rolls have to makemore revolutions for the given product volume when the operating gap is narrow.• A higher feed moisture results in a narrower gap and a higher net specific energy con-sumption for a given specific pressing force.Specific throughput constant (m˙ or m-dot) is the machine throughput rate per roll diameter,per roll length, and per roll peripheral speed (Eq. 2.3). The specific throughput constant isused for scaling up from pilot to industrial scale units, and for predicting the throughputof HPGRs with larger and wider rolls. For a specific feed, the m-dot value representsthe throughput of an HPGR with a roll dimension of 1 m in diameter, 1 m in length, andoperated at 1 m/s peripheral speed.m˙ =QDLυ(2.3)13wherem˙ — specific throughput constant [ts/m3h]Q — throughput rate [t/h]D — roll diameter [m]L — roll width [m]υ — roll peripheral speed [m/s]Operating gap is the gap that forms between the rolls as a result of feed material pushing tworolls apart. Instantaneous measurement of the operating gap fluctuates somewhat duringthe operation because the floating roll dynamically responds to the back-pressure fromthe feed that is balanced against the hydraulic pressure. Therefore, the operating gap isrecorded by a programmable logic controller (PLC) and the average is calculated.Higher specific pressing forces result in higher net specific energy inputs and higher sizereduction ratios, but narrower operating gaps and lower specific throughputs. Thus, in anHPGR operation, specific pressing force is one of the two main operational control parameters,the other being the roll peripheral speed.Morley (2006) summarized the relationships between m-dot and operating variables asfollows.• m-dot increases with ore hardness, since harder ores create wider operating gaps;• m-dot decreases with increasing specific pressure, since higher pressure leads to nar-rower gaps;• m-dot increases with roll texture such that it is higher for profiled surfaces than smoothsurfaces, and higher with the studded surfaces; and this relationship is explained byincreased kinetic friction between the roll surface and ore, and improved nipping of orebetween the roll surfaces;14• m-dot can increase slightly with an increase in feed top size;• m-dot decreases significantly as feed-bottom size is increased; this is explained by theincreased void space in truncated feeds, which results in a lower back pressure on therolls, and thus a reduced operating gap;• m-dot decreases with increasing moisture; this is explained by, 1) water taking flakevolume in place of solids; 2) high moisture content resulting in excessive slippage andwashing out the autogenous layer of feed on the studded rolls, and 3) as previously stated,moist materials form narrower gaps;• m-dot is directly related to operating gap; the ratio of operating gap to roll diameter isnormally in the range of 0.010 to 0.028.2.1.4 HPGR-based comminution circuit configurations in hard-rockminingHPGRs can be considered for both existing and new comminution circuits utilizing con-ventional SAB or SABC circuits. Currently, HPGRs are utilized in comminution circuitsto perform the following three duties that traditionally have been the role of shorthead conecrushers:1. Tertiary crushing2. Quaternary crushing3. Pebble crushingThe most pertinent HPGR-based comminution circuit that competes with currently dominantSAG mill-based alternatives is an HPGR operating in tertiary crushing duty. There are a fewHPGRs performing quaternary crushing duty, as this option is a possibility only for existing15conventional three-stage crushing circuits to send finer crushed feed to ball mills and increasethe ball mill circuit throughput. Likewise, a few HPGRs are installed in a pebble-crushingduty because pebble crushers handle only a small percentage of fresh feed, and thus it is a lowtonnage application.Feed for HPGRs installed in tertiary crushing is prepared using secondary cone crushersoperating either in regular closed circuit, or in reverse-closed circuit. With respect to thedevelopment of piston press tests for sizing, which is the objective of this thesis, it is importantto prepare the feed to the piston press tests in a similar manner as the feeds are prepared for theHPGR. Therefore, examples of the two types of feed preparation circuits are given below.Cerro Verde is a 120,000 tpd copper-molybdenum primary sulphide ore-mining and con-centration operation. It is the first and considered the most prominent installation of the HPGRtechnology in a hard-rock mining operation. At Cerro Verde, the HPGR circuit is fed by thesecondary crushing circuit product, prepared in a reverse-closed circuit as shown in Figure 2.2(Koski et al., 2011).16Dry screenSecondary crusher HPGRWet screenFeed to ball millCoarse ore stockpile(o/s) (u/s)(o/s)(u/s)Figure 2.2: Schematic presentation of HPGR feed preparation in reverse-closed circuit at theCerro Verde operationBoddington is a 105,000 tpd gold operation. At Boddington, the HPGR circuit is fed by thesecondary crushing circuit product prepared in a regular closed circuit as shown in Figure 2.3(Hart et al., 2011).17Dry screenSecondary crusherHPGRWet screenFeed to ball millCoarse ore stockpile(o/s)(u/s)(o/s) (u/s)Figure 2.3: Schematic presentation of HPGR feed preparation in regular closed circuit at theBoddington operationIn hard-rock mining applications, HPGRs are operated in closed circuit with wet screening,and the HPGR circuit product becomes the feed for the ball mill circuit. The majority of HPGRproducts are in the form of flakes, which are lumps of crushed ore. Wet screening helps to breakthe flakes, which improves the screening efficiency and limits the dust generation. The slurryfrom screen undersize is further classified in hydrocyclones and the underflow is recycled tothe ball mills.2.1.5 Simulation model of HPGRMorrell et al. (1997) introduced the first size reduction model for the HPGR that includes threeindependent breakage mechanisms. The model is based on three assumptions:181. Particles larger than a critical size are directly broken by the roll surface in the pre-crushing zone. The pre-crushed products are combined with the particles smaller thanthe critical size, and all particles enter the bed compression region;2. Particles passing at the centre and edge of the rolls experience different breakages. Theedge material experiences breakage that is similar to breakage in a conventional rollcrusher, referred to as the edge effect zone;3. The breakage condition at the centre of the rolls occurs in a compressed bed of particlesand it is therefore called the compression zone.Figure 2.4 illustrates the structure of the Morrell et al. (1997) model of HPGR size-reduction.The HPGR breaks particles predominantly in anautogenous way, unlike other comminution devices suchas ball and rod mills. The grinding force is transferredfrom one particle to the next, with only a small propor-tion of the particles coming into direct contact with therolls.Scho¨nert (1988, 1991) also mentions that even thoughthe inter-particle process in less efficient than single par-ticle stressing, he found that when a bed of particles iscompressed and comminuted, the result is that the mate-rial is comminuted more efficiently than in a ball mill.Scho¨nert concluded that the main reason for this is thefact that the controlled transport and stressing featuredin HPGR results in a high proportion of available en-ergy being used solely for the purpose of stressing thematerial. In conventional mills, the material transportand stressing inside the active volumes of the mill be-tween the balls occurs randomly. This often allows par-ticles to move out of position resulting in unproductivecollisions between grinding media and the liner wallwithin the mill. This mode of energy input is inherentlywasteful because of the hit-and-miss nature of theprocess.3. Model structure and theoryThe Morrell/Tondo/Shi model consists of three parts,namely a model for the prediction of product size distri-bution, a throughput model, and a power consumptioncomponent. The throughput model component uses astandard plug flow model version that has been usedextensively by the manufacturers and researchers. Thepower consumption is based on the throughput andthe specific comminution energy (Ecs) input.3.1. Modelling particle size distributionModelling the product size distribution also com-prises three separately defined processes that are eachmodelled and then combined to produce a final result.The size reduction model relies on the assumptionthat the three breakage mechanisms occur independ-ently within the HPGR (Morrell et al., 1997). Thesesub processes or zones within the crusher are definedas(i) the pre-crusher zone,(ii) the edge effect zone and(iii) the compression zone.The zones are described conceptually in Fig. 2.3.1.1. The ‘‘pre-crusher’’ zoneIf particles are bigger than a certain critical size (xc),they will be broken directly by the roll faces as would oc-cur in a conventional rolls crusher. The product of thispre-comminution process then passes into a regionwhere a bed under compression has formed. Thus theinterface between the compression and pre-crusherzones is defined by the critical gap (xc), and is expressedas:xc ¼ 0:5 ðDþ xgÞ  ðDþ xgÞ2 4qgDxgqc 0:5( ); ð1Þwhere D is the roll diameter (m); xg is the working gap(m); qg is the flake density (t/m3); and qc is the bulk‘‘compacted’’ density (t/m3).3.1.2. The ‘‘edge effect’’ zoneBreakage at the edge of the rolls is different to that atthe centre and conforms more to that experienced in aconventional rolls crusher. This so-called ‘‘edge effect’’is what defines the proportion of relatively coarse parti-cles usually seen in HPGR products. Its existence hasbeen explained by the pressure gradient across the widthof the roll and the zero confinement of the ore at theedges of the rolls where cheek-plates are sometimes pro-vided (Watson and Brooks, 1994).The model assumes a step-change in pressure profileat the rolls edge where material is comminuted in singleparticle mode similar to the pre-crusher zone. No com-pressed bed breakage is assumed to take place in thiszone, whereas in reality a gradual change in pressure islikely to be encountered.The interface which defines the boundary between thecompression zone and the edge effect zone is representedmathematically by a fraction of the original feed mate-rial which undergoes the single particle comminution.This fraction is represented by the following equation(2) (Morrell et al., 1997).f ¼ cxgL; ð2ÞPre-crusherEdge effect crusherCompressive bedbreakagecrusherSplitterProduct from the HPGRFeed to HPGRCombinerFig. 2. The current Morrell/Tondo model structure representedconceptually (Morrell et al., 1997).M.J. Daniel, S. Morrell / Minerals Engineering 17 (2004) 1149–1161 1151Figure 2.4: Schematic structure of the Morrell/Tondo model of siz -r duction in HPGR(Source: Morrell et al., 1997)Daniel and Morrell (2004) verified the validity of the Morrell/Tondo model and concludedthat the pre-crushing and the edge effect zones of the model are not dominant, but contribute tothe overall accuracy of predic ion of product size distr bution. Laborato y-scale or pilot-scaleHPGR test data is required to calibrate the model. Table 2.1 lists the parameters required touse the Morrell/Tondo model. Of the listed parameters, 12 are known/fixed and 4 determinedby calibration against laboratory-scale HPGR test data.19Table 2.1: List of parameters required to use the Morrell/Tondo modelSymbol Name Descriptionxc Critical gap Calculated throughlaboratory-scale HPGR test dataγ Split factor Obtained through model fitting tolaboratory-scale HPGR test datat10p, t10e, t10h Breakage index forpre-crushing, edge effect andcompression zonesObtained through model fitting tolaboratory-scale HPGR test dataK p(hpgr), K p(edge) Power coefficient forcompression and edge zonesObtained through model fitting tolaboratory-scale HPGR test dataK1p, K2p, K3p Pre-crusher model parametersfor classification functionK1p and K2p are determined byrunning laboratory roll crusher;K3 = 2.3K1e, K2e, K3e Edge crusher modelparameters for definingclassification functionK1e and K2e are determined byrunning laboratory roll crusher;K3 = 2.3K1h, K2h, K3h Compression zone modelparameters for classificationfunctionK1h = 0, K2h is equal tooperating gap scaled-up fromlaboratory-scale HPGR test data;K3 = 2.32.1.6 Advantages of HPGRThere are several reported advantages of the HPGR as follows:• Higher energy efficiency than SAG mills,• Induces microcracks and preferential liberation,• Better throughput stability, and• Does not require grinding media.As more industrial experience is gained the technology is expected improve in the future.20— Energy efficiencyAccording to Fuerstenau et al. (1991), the highest energy utilization, measured by the surfacearea produced per unit energy expended, in comminution of brittle solids is achieved by slowcompression of a single particle. The next most efficient breakage method is by slow compres-sion of a bed of particles . The most important advantage of the HPGR technology is that itutilizes particle bed compression method of comminution, and is widely known for its greaterenergy efficiency, relative to SAG milling.Schönert (1988) cited his original research on compressing limestone and cement clinkerparticles under 25-300 MPa pressure and deagglomerating afterwards by ball or impact mill.The final results indicated that combination of both compression and deagglomeration stepsconsumed about one half of the energy consumed in a ball mill. Thus, the HPGR requires upto 50% less energy than traditional tumbling media ball mills, even accounting for the energyconsumed by the deagglomeration step.— Microcracking and Preferential liberationIn HPGR comminution of diamond and sulphide ores, two phenomena have been observed;1) liberation occurs preferentially along the natural grain boundaries, and 2) microcracks areinduced in coarse fragments. Preferential breakage and microcrack formation can be advanta-geous for downstream processes. In the case of the HPGR-product-fed ball mills, weakenedmaterials required 16-20% less specific energy compared to a tertiary cone crushed product(Patzelt et al., 2006). This energy benefit is due to two factors, 1) finer product, and 2) weakerfragments. The latter has been reported to be in the range of 5-10%, depending on ore type andHPGR operating conditions. Amelunxen et al. (2011) reports that at the Cerro Verde operation,the Bond ball mill work index on HPGR product is 7% lower than the values obtained ondiamond drill core samples. For gold heap leaching, HPGR-treated ores show 5-25% increasedextraction due to the presence of microcracks and preferential liberation along grain boundary21(Baum et al., 1997). Preferential liberation of larger and therefore more valuable diamondswithout breaking them was the key to HPGR technology’s success in the diamond industry(Daniel and Morley, 2010).— Throughput stabilityThe HPGR technology is noticeably less susceptible to ore hardness and primary crusherproduct size variation in comparison to SAG mills. Amelunxen et al. (2011) suggests thata significant cost penalty be applied to SABC circuits when relative economics are evaluatedthrough HPGR trade-off studies. The HPGR-based circuits are much less susceptible to vari-ability in ore hardness. The HPGR is also relatively compact in design and has a low footprintper capacity.— No grinding media requiredAnother advantage of the HPGR is that unlike tumbling media mills, no steel-grinding mediais required. Radziszewski (2002) stated that the comminution process cost is roughly splitinto two halves between energy and steel (media and liner). Not using steel media results insignificant cost savings.Musa and Morrison (2009) proposed considering indirect energy consumption in their newmethods of sustainable assessment of comminution efficiency. That means the energy notused for steel media production could be considered in the overall energy-savings and carbonfootprint reduction.Since the HPGR is a relatively new technology, more improvements and optimizationpotential resulting from recent experiences/installations can be expected in the near future,compared to SAG milling that has already gone through decades of experience and develop-ment.222.1.7 Shortcomings of HPGRAlthough the HPGR has several advantages, there are number of shortcomings including:• Processing soft and clay-rich ores,• Additional cost of dust control and complex upstream provisions,• Wear life of roll liners,• Lack of experienced operating personnel.— Soft and clay-rich oreSoft and clay-rich materials that do not create an adequate back-pressure to push the rolls apartand therefore are not amenable to the HPGR technology. The throughput suffers dramaticallysince the operating gap between the rolls is narrower. However, there are ways to mitigate thisshortcoming, including using an AG mill as a scrubber to remove soft and clay-rich materialahead of the HPGR (Rosario et al., 2011).— Cost of dust control and complex upstream provisionsThe HPGR is a dry grinding technology, and excessive moisture causes the throughput toreduce. Thus, dust creation is significant in comparison with wet grinding. Upstream pro-visions for dry material-handling add significant complexity to the plant design and layout,when compared to SAG milling (Danilkewich and Hunter, 2006). Plant layout complexityalso significantly increases capital expenditures of small to medium-size projects with shortoperating life spans. Even for the Cerro Verde operation, which has a long operating life (30+years) and large tonnage (120 ktpd), the HPGR circuit capital cost was 23.5% more than theSABC alternative (Vanderbeek et al., 2006).23— Roll liner wearEarly roll liner designs were unable to handle abrasive feeds, resulting in reduced availability,since highly-abrasive materials wear roll liners quickly. Recent advances in roll liner design ismaking liner wear shortcoming less relevant. Although few in number, HPGR installations athard-rock mining operations have started to report improved availability and roll wear life.Koski et al. (2011) reported that HPGR units operating at Cerro Verde are reaching 97%availability, and that roll wear life is exceeding 6500 hours. Hart et al. (2011) reported that theavailability of HPGRs at Newmont’s Boddington gold operation is approximately 88%, and theroll wear life ranged from 4400 to 5700 hours. Banini et al. (2011) reported a roller tire life ofbetween 18535 and 23320 hours at the PT Freeport Indonesia copper-gold operation. The longwear life at Freeport is due to the ore softness and the role of the HPGR that treats finer feedin a quaternary crushing application. Despite these improvements in wear over recent years,more evidence of availability and reliability data will be needed for the HPGR technology tobe recognized as a viable alternative to SAG milling.— Lack of experienced operating personnelThere are more experienced operating personnel available for the SAG milling technologycompared to the relatively new HPGR technology. The lack of experienced operating personnelcan be another significant barrier to the widespread usage of HPGR technology, especially indeveloping countries.2.1.8 Comparison of energy efficiency of HPGR and SAG millvon Michaelis (2009) claims that energy savings of 10–20% can be expected when installingHPGR vs. SAG mill. Table 2.2 lists the results of trade-off studies where the direct energysavings of HPGR circuit were reported. The energy savings range from 11–32% and theaverage is 21.8%.24Table 2.2: Direct specific energy comparison between SABC and HPGR circuitsProject name Units SABC HPGR Energy Referencesavings [%]Boddington Gold kWh/t 23.10 18.00 22.1 Parker et al. (2001)Los Broncos Copper kWh/t 16.21 13.02 19.7 Oestreicher and Spollen (2006)Cerro Verde Copper kWh/t 20.10 15.90 20.9 Vanderbeek et al. (2006)Ruby Creek Moly $/t 4.53 3.83 15.5 Anguelov et al. (2008)Copper Gold project in Russia $/t 0.78 0.53 32.1 Anguelov et al. (2008)Courageous Lake Gold $/t 3.59 2.47 31.2 Anguelov et al. (2008)Morrison Copper/Gold/Moly $/t 0.63 0.56 11.1 Anguelov et al. (2008)Mine A kWh/t 19.90 16.90 15.1 Daniel et al. (2010)Mine B kWh/t 14.80 12.30 16.9 Daniel et al. (2010)Mine C kWh/t 11.10 8.90 19.8 Daniel et al. (2010)Case A kWh/t 14.73 11.03 25.1 Rosario (2011)Case B kWh/t 15.73 10.73 30.2 Rosario (2011)Ajax Copper/Gold $/t 0.60 0.47 21.7 Ghaffari et al. (2013)Case H (160 µm grind) kWh/t 18.76 13.23 29.5 Wang (2013)Case H (75 µm grind) kWh/t 22.28 18.74 15.9 Wang (2013)Energy saving and reduced media consumption translate into lower operating costs. Thereported overall operating costs are compared in Table 2.3 suggesting HPGR-based comminu-tion circuits offer significant cost savings, ranging from 14 to almost 30% for the operationslisted.25Table 2.3: Operating cost comparison between SABC and HPGR circuitsProject nameSABC HPGR Cost savingsReference[US$/t] [US$/t] [%]Boddington Gold 4.18* 2.95* 29.4 Parker et al. (2001)Los Broncos Copper 1.85 1.48 20.0 Oestreicher and Spollen (2006)Cerro Verde Copper 1.685 1.326 21.3 Vanderbeek et al. (2006)Ruby Creek Moly 5.30 4.56 14.0 Anguelov et al. (2008)Copper Gold project in Russia 2.24 1.63 27.2 Anguelov et al. (2008)Courageous Lake Gold 4.98 3.62 27.3 Anguelov et al. (2008)Morrison Copper/Gold/Moly 2.66 2.03 23.7 Anguelov et al. (2008)Mine A 2.86 2.20 23.1 Daniel et al. (2010)Mine B 2.46 1.88 23.6 Daniel et al. (2010)Mine C 2.17 1.63 24.9 Daniel et al. (2010)Ajax Copper/Gold 2.48 1.92 22.6 Ghaffari et al. (2013)* Australian dollarNovel comminution circuits that utilize HPGR technology in combination with a stirredmedia mill, have potential to provide even more energy savings than is achievable with theHPGR-ball mill circuit. Valery and Jankovic (2002) reported that incorporating high intensityblasting, HPGR and Verti mill technologies in a novel comminution circuit could provide46.6% energy savings compared to an existing SABC circuit. Drozdiak (2011) reported that atwo-stage HPGR and IsaMill circuit offers 9.2% energy reduction over HPGR-ball mill circuit.Similarly, Wang (2013) reported that the specific energy consumption of 14.36 kWh/t for thetwo-stage HPGR and IsaMill circuit was 35.5% less than SABC circuit and 23.4% less thanHPGR-ball mill circuit. Thus even bigger energy savings could be realized in the near futureby incorporating HPGR in innovative circuits.262.2 Research Studies on Particle Bed ComminutionParticle breakage in the HPGR is due to slow compression of a bed of particles. Manyresearchers have studied various aspects of particle bed comminution by pressing samples in apiston-die arrangement.The aspects of particle bed comminution that have been studied are as follows:• Influence of particle bed configuration,• Effect of presence of fines in the feed, and• Liberation enhancement.This section summarizes the results of research studies on particle bed comminution.2.2.1 Geometric constraints in a piston-die arrangementSchönert (1996) was the first to study the influence of particle bed configuration on comminu-tion, and defined an ideal particle bed in a piston-die as having the following four characteris-tics: (1) homogeneous structure of the bed, (2) homogeneous compaction of the bed, (3) knownvolume or mass of the compressed particles, and (4) wall effects are negligible with respect tothe overall size-reduction effect. Schönert (1995, 1996) claimed that in his experience, thewall effects are minimized by ensuring the height of the particle bed is larger than six times themaximum particle size, and smaller than one-third of the diameter of the piston-die cylinder.The majority of the researchers adhere to Schönert’s ideal particle bed criteria, and havemade deliberate efforts to minimize the wall effect by insuring that the ratio of die diameter tomaximum particle size was at least 18. Table 2.4 summarizes the particle bed configurationsfor piston-die arrangements of researchers who studied particle bed comminution.27Table 2.4: Summary of piston-die arrangements usedTop Piston die Sample mass Applied Energysize diameter (initial particle Pressure input Reference[mm] [mm] bed height) [MPa] [kWh/t]4 100 <320g (4-45mm) 150 <2.25 Schönert (1996)3.35 30-65 50-95g (18mm) 250 <2.5 Fuerstenau et al. (1996)4 25 20-24g 100-200 <4.0 Apling and Bwalya (1997)4 15-49 <100g 130 <10 Hawkins (2007)1.25 35 (≈10mm) 500 N/A Mütze and Husemann (2008)19 100 ≈1600g 55 N/A Bulled and Husain (2008)3.35 60 95g 26.5-283 0.18-2.22 Hosten and Cimilli (2009)3 80 100g 300 N/A Vizcarra et al. (2010)12 50-200 ≈207g (18mm) 63-252 0.18-2.25 Kalala et al. (2011)4 100 ≈500g 185 N/A Nadolski (2012)As listed in Table 2.4, the die diameter, particle top size, applied pressure, and measuredenergy inputs varied among the researchers. The majority maintained the ratio of die diameterto maximum particle size at over 18. The notable exceptions are Kalala et al. (2011) and Bulledand Husain (2008) who tested lower ratios.Kalala et al. (2011) showed that there was not a major difference between compressing -12 mm top size ore in 50 mm, 75 mm or 100 mm diameter die, as long as the maximum pressureapplied to the particle bed was the same. The important observation from the study was thatthe ratio of initial bed thickness to feed top size should be maintained at 1.5. In the study,the initial bed thickness was maintained at 18 mm for the feed top size of 12 mm. Bulled andHusain (2008) also noticed that having different initial depths of ore in the cylinder affectedresults even though the maximum pressure was kept constant while pressing -19 mm particlesin 75 mm and 100 mm diameter dies.282.2.2 Self-similar particle size distributionFuerstenau et al. (1991) reported that grinding dolomite, limestone, and quartz in a laboratory-scale HPGR produced product size distributions that were self-similar, which means the parti-cle size distributions could be normalized to a dimensionless size by dividing by their respectivemedian sizes. The importance of having a self-similar particle size distribution is that themedian size becomes a consistent measure of the degree of fineness of the product.Other researchers (Lim et al., 1996; Liu and Schönert, 1996) also found that an HPGR’sproduct size distribution can be normalized. In addition, the relationship between the reductionratio and the specific energy expended was found to be reasonably linear, regardless of specificenergy input, roll speed, feed size distribution or moisture content.Lim et al. (1996) proposed the following empirical equation to describe the cumulativeweight percent passing for the HPGR’s product as a function of dimensionless size:F( xX50)= 100(1− exp(−A( xX50) (m( xX50 )+n)))(2.4)where A, m, and n are fitted parameters and x/X50 is the dimensionless size normalized bydividing by the median particle size of the product.2.2.3 The phenomenon of energy saturationSchönert (1988) found that both ‘fines’ generation and specific energy input increase with spe-cific pressing force. However, the ‘fines’ generation reached a plateau while the specific energyinput continued to increase. Therefore, the ‘fines’ generation slows down while specific energyincreases as specific pressing force increases. The finding is an indication that increasing thespecific pressing force above a limit results in a decrease in net ’fines’ generation per energyinput. Even with considerable additional energy input only small additional comminutionresults, which is referred to as the ‘retardation phenomena,’ the ‘energy saturation point,’ and/or29the ‘breakage limit’ (Fuerstenau et al., 1996; Hawkins, 2007). The phenomenon of energysaturation is characteristic of particle-bed comminution, where diminishing size reduction isobserved with increasing energy input.The pressing force limit results from the formation of ineffective, isostatic-like compressionof larger particles by surrounding smaller particles (Fuerstenau et al., 2004). The isostatic-like compression of particles occurs in stages for each size class as particle size fractionsstabilize and cease breaking in a consecutive manner from the top size downward. The granularcomposition of the particle-bed dictates the maximum degree of size reduction possible throughthis self-regulating mechanism (Gutsche and Fuerstenau, 1999).Gutsche and Fuerstenau (1999) found that when admixtures of coarse and fine particlesare compressed, the smaller the size and the greater the amount of the fine particles, themore rapidly the breakage probability of the coarse particles decreases. Figure 2.5 shows thatthe breakage probability of -3.36+2.83 mm (6x8 mesh) limestone diminishes with increaseingamounts of fine particles.( )O. Gutsche, D.W. FuerstenaurPowder Technology 105 1999 113–118 115from the compaction of the particle bed and the associatedgranulometric stabilization has been coined retardation byFuerstenau et al. Fig. 3 illustrates the retardation of grind-ing kinetics of coarse particles in the presence of fineparticles. The breakage fraction of the coarse 6=8 meshconstituent is plotted as a function of the fraction of finesin the feed. The breakage fraction, that is the ratio of themass of broken particles to the total mass of the feed, is amodified fracture probability for irregular shaped particles.The general trend is that the breakage fraction decreaseswith the amount of fines in the feed. The energy persurface area, or the exerted stress, is lower in embeddedcoarse particles that have a large number of force transmit-ting neighbors. Thus, the stabilization of coarse particlesby fines is the result of the distribut on of the force flux onthe surface of coarse particles. Embedded coarse particlesexperience increasingly an even distribution of stress ontheir surface, which eventually becomes isostatic. Thestabilization of the coarse size is a function of the size ofthe fine component. The smaller the ‘‘fine’’ component,the more rapid the decrease. The size effect disappearstowards small fractions of fines in the feed, wh n the finematerial mostly fills the voids between coarse particles andtransmits only a small share of the total energy.The retardation of grinding kinetics of coarse particlesis accompanied by an acceleration of grinding kinetics offine particl s. Fig. 4 hows the breakage fraction of 16=30mesh limestone particles comminuted in the presence of20% coarse 6=8 mesh particles as a function of bedpressure. The probability of fracture of 16=30 meshlimestone particles increases by about 10% when commin-uted in the presence of coarse 6=8 mesh limestoneparticles. The fines in the admixture have only a fewcontact points that transmit force and thus xperiencemuch higher local stresses. As a consequence, their break-age fraction increases in the presence of coarse particles. AFig. 3. Breakage probability for 6=8 mesh limestone comminuted in thepresence of fines. This graph illustrates the retardation of breakagekinetics of 6=8 mesh limestone particles by fine particles.Fig. 4. Breakage probability for 16=30 mesh limestone comminuted inthe presence of 6=8 mesh coarse particles. This graph illustrates theacceleration of breakage kinetics of 16=30 mesh limestone particles bycoarse particles.network of particles with a certain void volume is requiredfor fine particles to be nipped by larger particles. Fig. 5 .shows the fraction solids 1y« as a function of bedpressure for the comminution of 8=10 mesh quartzite.The steep increase at low pressure P indicates the fillingof the initial void volume. The load carrying solids per unitdie area increases when fragments begin to transmit force.As a result, the local stress or energy per surface areadecreases, the apparent strength of the particle network or .resistance of the bed to compaction D 1y« rD P in-creases and the slope of the compaction curve decreases.The size of particles that can still break at a given pressureand solids fraction is related to the particle network withits pore size distribution. Further size reduction of intactFig. 5. Compaction curve for 8=10 mesh quartzite. The steep increase ofthe fraction solids at low pressures illustrates that initially fragments fillvoids without carrying load. The point when fragments transmit the loadis characterized by change in slope and increase in resistance to com-paction.Figure 2.5: Breakage fraction of 2.83x3.36 mm limestone diminishes in the presence ofvarious sizes and quantity of fines(Source: Gutsche and Fuerstenau, 1999)30The decrease in breakage fraction of coarse particles explains the phenomenon of energysaturation. In other words, as compression energy increases, the coarse particles break intofiner particles and thus increase the fraction of fine particles and reducing of the breakageprobability of the remaining unbroken coarse particles.2.2.4 Influence of moisture on energy consumptionIt is well-known that excessive moisture increases the HPGR net specific energy consumption.Pilot-scale HPGR testing performed on Cerro Verdo copper-molybdenum ore showed thatincreasing the feed moisture from 2% to 4% reduced the specific throughput by 5%, andincreased the specific energy by 20% (Vanderbeek et al., 2006). From test work conductedat the NBK Institute of Mining, it is also observed that increasing the moisture content ofcopper-nickel sulphide ore from 1% to 5% increases specific energy by 29.4% and decreasesm-dot by 10.2% (Köppern Machinery Australia, 2010).As the feed moisture increases, the operating gap between rolls becomes narrower (Köp-pern Machinery Australia, 2010; Schönert, 1988). However, the narrower operating gap doesnot necessarily result in finer product size distribution, which is logically expected from anarrower gap.Fuerstenau and Abouzeid (2007) reported that at a lower specific energy input (0.7 kWh/t),the percentage of fine particles produced was lower in moist feed as compared to dry feed. Theresult was explained by free movement of the finer particles when water is present that acts asa lubricant. For moist versus dry feed, at a high specific energy input (1.8 kWh/t), the productPSD is finer at the coarse end, and nearly identical at the fine end. The result is explained bywater lubrication that rearranges particles and thereby quickly compacts, and coarser particlesare broken at a higher rate.An argument could be made that the strong influence of moisture on HPGR performance isexplained by one or combination of the following factors:31• Moisture increases slippage between the particles and the roll surface. Thus, increasedenergy is required to pass material through the operating gap;• Internal friction increases with moisture (moisture adds cohesiveness). Thus, more en-ergy is required to draw feed into the roll gaps;• Moisture renders material more compactable resulting in a narrower operating gap. Ahigher power draw is required to push material through a narrow gap than a wide gap.In addition, a narrow gap allows a smaller volume of material to pass per revolution thusrequiring a greater number of revolutions for a given volume of feed.2.2.5 Pressure distribution between rollsFigure 2.6 shows the pressure profile between the rolls of the HPGR. As illustrated in theschematic, hydraulic cylinders apply force to the rolls and create the pressure profile in theparticle bed. As material enters the rolls, it is compressed and enters the compaction zonewhere pressure increases to a maximum and the material is nipped. As material moves pastthe point where rolls are closest to each other, the pressure then sharply decreases as productflakes exit the compression zone.32hD/2 D/2F Fδ–grip angle; α–nip angle; h–compaction zone heightFigure 2.6: Illustration of the pressure profile within the particle bed(Source: FLS, 1990)If the pressure profile is approximated by a triangle, the maximum pressure can be esti-mated as twice the average pressure given by Eq. 2.9.h =D2sinα (2.5)FSP =FDL(2.6)Pavg. =FhL(2.7)Substituting h and F,Pavg. =2FDL sinα=2FSPsinα(2.8)Pmax = 2Pavg. =4FSPsinα(2.9)The nipping angle normally ranges between 7 and 9°, hence the denominator of Eq. 2.9 willbe between 0.12 and 0.16. If the pressure profile is assumed to be consistent across the lengthof the roll, the maximum pressure experienced within the operating gap would be in the order33of 25–33 times that of the specific pressing force.The fact that the edge product of the HPGRis coarser than the centre product is evidence that the pressure is lower towards the roll edges.The maximum pressure at the centre is expected to be more than 25–33 times higher than theapplied specific pressing force.In an early publication, Schönert (1988) suggested that the maximum pressure can beestimated by multiplying the specific pressing force by 50. In a later publication, Schönert(1995) measured the pressure distribution directly and confirmed that the maximum pressureis in the order of 30–40 times that of the specific pressing force. In other words, a specificpressing force of 1 N/mm2 (equal to 1 MPa) would create a maximum pressure of 30–40 MPain the gap, at the centre of the roll.2.3 Comminution Theories and TestsThis section reviews comminution theories and laboratory-scale comminution tests that arerelevant to the development of small-scale tests for the HPGR comminution technology.There are as several small-scale comminution tests for characterizing ores, many of whichare for specific types of comminution equipment. SGS Mineral Services (2009) lists 17 testsdesigned to characterize ores and minerals by their crushability and grindability. The mostrelevant tests for evaluating the HPGR technology are discussed in this section. In addition,the application of test results to the modelling of the energy–size reduction relationship isreviewed.2.3.1 Comminution theoriesThere are several well-known theories describing the relationship between comminution en-ergy and particle size reduction. Although the feed and the product of comminution have adistribution of particle sizes, the particle sizes are usually expressed by a single size index. A34common size index is the weight percentage passing through a given sieve opening size. Thepercentages typically used are 50, 80, or 95%.For all theories, the incremental energy required to achieve an incremental change in parti-cle size is a function of particle size itself. In addition, as particle size decreases more energyis required to achieve the same order of size reduction. Thus the differential form of energyexpenditure is an inverse function of particle size as shown in the following equations (King,2001).dEdx= −K1xn(2.10)dE =−Kxndx (2.11)E =x2ˆx1−K x−n dx (2.12)The general equation forms relating specific energy required to reduce feed particle size,x1, to product particle size, x2, are as follows,E =−K ln x +C n = 1 (2.13)E1−2 =K (ln x1− ln x2) (2.14)E =Kn−1x (1−n) +C n , 1 (2.15)E1−2 =Kn−1(x (1−n)2 − x(1−n)1)(2.16)where K is a constant related to the properties of the ore and n varies depending on the proposedtheory.In Kick’s theory, n = 1 and the integrated form is as shown in Eq. 2.17. A physicalinterpretation of the equation is that the energy consumed is proportional to the reduction ratio35of the particle sizes.E1−2 = K ln(x1x2)(2.17)In Rittinger’s theory, n = 2 and substituting 2 to Eq. 2.16 results in the integrated formpresented as Eq. 2.18. Its physical interpretation is that the energy consumed is proportional tothe new surface area created per unit volume.E1−2 = K(1x2−1x1)(2.18)Kick’s theory found supporting evidence in coarse crushing applications, while Rittinger’stheory found supporting evidence in fine grinding applications, but neither of these theorieswere satisfactory for both coarse and fine comminution applications (Napier-Munn et al.,1996). Based on his experimental work, Bond (1952) presented “The third theory of com-minution”, where n takes an intermediate value of 1.5. Substituting n = 1.5 in Eq. 2.16 resultsin the following integrated form:E1−2 = 2K *,1x1/22−1x1/21+-(2.19)After a review of a wide range of industrial devices, Hukki (1961) found that no singlevalue of n adequately covered the full spectrum of comminution stages, from primary crushingto fine grinding, and suggested that the particle size exponent 1− n in Eq. 2.16 is a function ofparticle size.Based on Hukki’s suggestion, Morrell (2004a) proposed an alternative energy–size reduc-tion relationship given by Eq. 2.20. A linear function was suggested for the exponential term1− n as given in Eq. 2.21 (Morrell, 2006).E1−2 = MiK(x f (x2)2 − xf (x1)1)(2.20)36f (xi) = −(0.295+xi106)(2.21)where W is specific energy in kWh/t, K is a constant chosen to balance the units of theequation, and Mi is an index related to the breakage property of the ore and measured in kWh/t.The next sections describe tests that are used to predict the specific energy required for agiven size reduction.2.3.2 Bond ball mill grindability testEq. 2.19 becomes Bond’s work input equation, when x1 is the 80% passing size of the feed, x2is the 80% passing size of the product, and the constant term is replaced with work index Wi.W = Wi(10√P80−10√F80)(2.22)Bond (1961) developed a laboratory test procedure for determining Wi. The Bond ball millgrindability test is carried out in a standardized ball mill with internal dimensions of 0.305 min diameter and 0.305 m in length. The standard Bond ball mill has no lifters and is rotated at70 rpm with a 20.125 kg charge that consists of 285 steel balls ranging from 15.8–38.1 mm indiameter (Austin et al., 1984).The feed sample for the Bond test is prepared by crushing in stages down to 100% passing3.35 mm, and a 700 cc sample is ground in the mill for 100 rotations for the first cycle. Aftereach cycle, the ground sample is screened, and the net grams of undersize product produced permill revolution is determined. The undersize product mass from the previous cycle is replacedby the same mass of fresh feed, and the number of revolutions for the next cycle is calculatedto achieve a 250% circulating load. The test is considered complete once the the circulatingload stabilizes at 250%; usually, it takes about 7 cycles to reach that equilibrium. The Bond37ball mill work index, Wi, is calculated using the following equation.Wi =44.5P0.231 ·Gpr0.82 ·(10√P80− 10√F80) ·1.1 (2.23)where P1 is closing screen, Gpr or grams per revolution is average net grams of undersizeproduct per mill revolution from the last three cycles, and the particle sizes are in microns. TheBond ball mill work index, Wi, has the units of kWh/t.The Bond ball mill grindability test is a classic example of a locked-cycle test, and is awidely accepted test in the mineral processing industry that characterizes ores by their grind-ability. The test provides ore characterization information related specifically to ball milling,so the true ore characteristic is interrelated with the comminution equipment—in this case, theball mill operating at a 250% circulating load.2.3.3 JK Drop Weight testThe JK Drop Weight test is an ore characterization test that aspires to separate the ore charac-teristics from those of the comminution equipment (Napier-Munn et al., 1996). The JK DropWeight test determines impact and abrasion breakage parameters of the ore and requires about100 kg of a representative sample.In order to determine the impact breakage parameters, the five narrow-size classes listedin Table 2.5 are obtained from the ore sample and each size class is subjected to three levelsof specific energy input. In each size class and specific energy input level combination, 20–30rocks are broken by dropping a known mass from a pre-calculated height to achieve the targetspecific energy input levels. The drop masses range from 2 kg to 50 kg.38Table 2.5: Size intervals and nominal specific energy input levels in a JK DWT(Source: Napier-Munn et al., 1996)Size class Size Interval Specific Comminution Energy [kWh/t]1 -63+53 mm 0.10 0.25 0.402 -45+37.5 mm 0.10 0.25 1.003 -31.5+26.5 mm 0.25 1.00 2.504 -22.4+19 mm 0.25 1.00 2.505 -16+13.2 mm 0.25 1.00 2.50All broken products from each combination are combined and the particle size distributionis determined by dry sieving. From each particle size distribution, the t10 breakage indexis determined, which is defined as the cumulative percentage finer than 1/10th of the originalgeometric mean particle size.The relationship between t10 and specific comminution energy, Ecs, is modelled by Eq. 2.24(Napier-Munn et al., 1996).t10 = A(1− exp (−b · Ecs))(2.24)where A and b are ore specific impact breakage parameters found through non-linearregression. An example of fitting A and b parameters to t10 vs. Ecs data is shown in Figure2.7. The multiplication of parameters A · b is the slope of the fitted curve at the origin. Thesteeper the fitted curve, the higher the value of b and the softer the ore because a relatively highbreakage index of t10 could be attained with a low specific comminution energy.39,.. Chapter 4: Rock Testing- Determining the Material-Specific Breakage Function The amount of breakage, or breakage index, t 10, is related to the specific comminution energy as follows: tw =A [1 - e(-b. Ecs)] (4.22) where t 10 is the percent passing 1/10th of the initial mean particle size, Ecs is the specific comminution energy (kWh/t), and A and b are the ore impact breakage parameters. Graphically this relationship is shown in Figure 4.12 for a primary gold bearing ore. Table 4.6: Example of JKMRC ore impact breakage test results, -31.5+26.5 mm SAG FEED SIZE: -31.5 +26.5mm HT:1 SIZE(rrm) 22.400 16.000 11.200 8.000 5.600 4.000 2.800 2.000 -2.000 WI'(gms) 14.870 49.060 229.240 136.240 93.810 52.470 44.300 29.280 129.000 WI'% 1.911 6.304 29.455 17.505 12.054 6.742 5.692 3.762 16.575 CtMJI.ATIVE % PASSIN; Y/n CU1% PASS 98.089 91.786 62.331 44.825 32.771 26.030 20.337 16.575 .000 INITIAL WEIGH!' ( gms) FINAL WEIGHI'(gms) JNPUl' ENERGY (kg-an) JNPUl' ENERGY (kwh/tonne) INITIAL PARTICLE SIZE (rrm) NJo1BER OF PARTICLES TESI'ED : (Y =INITIAL PARTICLE SIZE(rrm) & n = 10,2,4,25,50 and 75) "tor t/10"= 20.790 "t/2" = 85.177 "t/4" = 41.119 "t/25" = 11.768 "t/50"= 7.546 "t/75"= 5.795 t10 {%) A = 49.1 __ _so 778.8000 778.270 619.433 .433 28.890 20 Figure 4.12: Effect of specific comminution energy on the breakage index, t10 82 Figure 2.7: An example of a t10 vs. Ecs relationship(Source: Napier-Munn et al., 1996)Shi and Kojovic (2007) proposed the following alternative form to replace equation 2.24 sothat the effect of particle size is incorporated.t10 = M(1− exp(− fmat · x · k (Ecs −Emin)))(2.25)whereM is a fitted parameter equivalent to A and represents the maximum attainable t10 [%],fmat is a fitted parameter representing a material breakage property [kg J−1 m−1],x is particle size [m],k is the number of successive impacts,Ecs is the mass-specific impact energy [J kg−1],Emin is the threshold energy below which breakage does not occur [J kg−1].The abrasion breakage parameter, ta, is found by tumbling 3 kg of -55+38 mm particles for10 minutes in a laboratory mill similar to the Bond ball mill, except the mill is fitted with 4 mmby 6 mm lifter bars and is operated without a ball charge. First, the t10 value from the tumbling40test is determined. The abrasion parameter is defined as ta = t10/10. A, b, and ta are keyinput variables for describing ore specific breakage in the AG/SAG models of the JKSimMetsimulation package.Similar to the definition of t10, tn is the cumulative percentage finer than 1/nth of the originalgeometric mean particle size after the breakage. For impact breakage, there seems to be ageneral relationship between t10 and the other tn values, as shown in Figure 2.8 for a widevariety of sample types.Figure 2.8: Relationship between tn and t10 for single particle impact breakage(Source: Morrison and Morrell, 1997)When the t10 for a given energy input is known, the whole size distribution can be deter-mined by calculating the other tn values using the following equation (King, 2001).tn = 1− (1− t10)(10−1n−1)α(2.26)41where α is an ore specific parameter.JKSimMet uses a cubic spline interpolation/extrapolation approach to derive the wholeparticle size distribution, knowing the key tn points at t10 values of 10, 20, and 30% (Napier-Munn et al., 1996). Table 2.6 shows an example of the key tn points for AG/SAG model ofJKSimMet simulation software.Table 2.6: Standard appearance function data used in AG/SAG model of JKSimMetsimualtion softwaret10 t75 t50 t25 t4 t210 2.33 3.06 4.98 23.33 50.5320 6.89 9.41 15.62 61.58 92.4930 10.32 14.71 25.88 82.86 96.47(Source: Napier-Munn et al., 1996)2.3.4 SAG Mill Comminution testThe SAG Mill Comminution (SMC) test was originally developed to use quartered drill coresamples and is an abbreviated version of the JK Drop Weight test (SGS Mineral Services,2009). Instead of completing drop weight tests on five size classes, the SMC test requires onlyone size class, which can be either -31.5+26.5 mm, -22.4+19 mm, or -16+13.2 mm. The SMCtest is faster because it reduces the number of drop weight tests to 5 (1 size class at 5 energylevels) compared to 15 (5 size classes at 3 energy levels each) in the full JK Drop Weight test(Morrell, 2004b).Using a proprietary methodology, the SMC test generates the Drop Weight Index (DWi)having the units of kWh/m3, which is directly related to the A and b parameters of the JK DropWeight test. In addition, the SMC test provides comminution parameters Mic, Mih, and Mia.These material work indices are used in power-based calculations which can be expressed asfollows:Wi = Mi4(x f (x2)2 − xf (x1)1)(2.27)42where Mi takes value of Mic for conventional crushing, Mih for HPGR crushing, and Miafor AG/SAG grinding, where f (xi) is the same as in Eq. 2.21 (Morrell, 2010).2.3.5 Static pressure testThe static pressure test (SPT) involves pressing 1.6 kg of -19+3.35 mm size sample in a 100 mmdie at 55 MPa pressure for the first cycle and -19 mm fresh feed at subsequent cycles (Bulledand Husain, 2008). It is a locked-cycle test, so the product from each cycle is screened at3.35 mm, and replaced with fresh feed. The feed to the first cycle is truncated at 3.35 mmand the replacement fresh feeds in the subsequent cycles are not truncated. Reaching fasterstabilization was the reason for the inconsistent feed for the first cycle. Cycles are continueduntil the amount of -3.35 mm product stabilizes. The high pressure index (HPi) for the ore isfound using Eq. 2.28 .HPi =Eavg.√1P80−√1F80(2.28)where the average specific energy of the last three cycle, Eavg., and HPi have units ofkWh/t, P80 is the 80% passing size of the product from the final cycle, F80 is the 80% passingsize of the whole feed without truncation. The specific energy inputs are determined bynumerically integrating the force displacement curve recorded during the test. Bulled andHusain reported that the HPi exponentially increases with test pressure due to the phenomenonof energy saturation (Bulled et al., 2008).2.3.6 Energy–size reduction models of particle bed comminutionIn the literature, the specific energy and size reduction relationship of particle bed comminutionare modelled in various ways. The models could be classified into three different types:• linear,• power, and43• variations of Eq. 2.16.Linear model of energy–size reduction relationshipAfter studying the particle bed comminution of quartz with and without steel balls in theparticle bed, Schönert (1996) concluded that the energy absorption was the dominating factorfor the size reduction in particle beds. In other words, the stress distribution in the bedshowed only a minor influence. Although the stress distribution had minor significance onsize reduction, the stress distribution itself was strongly influenced by the friction between thepiston and the wall. The pressure in the centre was reported to be higher than the pressure nearthe wall.Studies of comminution in bench-scale high-compression roller mills and comminution inpiston-die arrangements both showed that Eq. 2.29 is valid. In other words, the relationshipbetween the reduction ratio from median feed size to median product size (F50/P50), andspecific grinding energy (E) is linear (Fuerstenau and Kapur, 1995; Fuerstenau et al., 1996).F50P50= j (F50) · E + c (2.29)where j (F50) is the slope of reduction ratio versus energy curve and is a function of medianfeed size, and c is the intercept of the line with the F50/P50 axis. In theory, c is equal to1 because when the specific energy input is zero, the median size of the feed is unchangedor F50 = P50. The relationship was confirmed from roller mill tests with up to 3.5 kWh/t ofspecific grinding energy for dolomite, quartz, hematite and limestone. Figure 2.9 shows thelinear relationship observed during piston press testing of eight different materials, and changesin the slope of the line with size. The figure shows that size is a very significant variable.44D.W. Fuerstenau et al./lnt. J. Miner. Process. 44-45 (1996) 521-537 531 Fig. 7. Energy-reduction ratio plots for eight solids. comminution in these modes on a uniform and consistent basis. The two grindabilities for the eight materials are plotted in Fig. 10. The data lie approximately on a straight line witlh a slope of 0.46. In other words, on average energy utilization in the 14 ., ., ., , , ., , . 13 4.75 X6.68 mm 12 g:; Y 2 3 z 7 53 5 P 5 43 2 1 0 2 4 6 3 10 12 14 16 %'=~cE-w, J/g Fig. 8. Energy-reduction ratio plots for six size fractions of limestone. (a) Reduction rati variation by sample typeD.W. Fuerstenau et al./lnt. J. Miner. Process. 44-45 (1996) 521-537 531 Fig. 7. Energy-reduction ratio plots for eight solids. comminution in these modes on a uniform and consistent basis. The two grindabilities for the eight materials are plotted in Fig. 10. The data lie approximately on a straight line witlh a slope of 0.46. In other words, on average energy utilization in the 14 ., ., ., , , ., , . 13 4.75 X6.68 mm 12 g:; Y 2 3 z 7 53 5 P 5 43 2 1 0 2 4 6 3 10 12 14 16 %'=~cE-w, J/g Fig. 8. Energy-reduction ratio plots for six size fractions of limestone. (b) Reduction ratio variation by sample sizeFigure 2.9: Energy–size reduction relationship graphs(Source: Fuerstenau et al., 1996)More recently Kalala et al. (2011) found that the linear relationship between the energyand reduction ratio was only valid up to 2 kWh/t for gold and iron ores.Power model of energy–size reduction relationshipNorgate and Weller (1994) proposed a power law relationship between reduction ratio andspecific grinding energy. They observed that above 4 kWh/t, the relationship became non-linear for zinc and gold ore samples that had been previously tested. This power relationshipis expressed by the following equation:X50 fX50p= kEb +1 (2.30)where k and b are ore and size specific model parameters.45Variation of Eq. 2.16There are a few models in the form of Eq. 2.16 that is reproduced below for convenience.E1−2 =Kn−1(x (1−n)2 − x(1−n)1)(2.16 revisited)As noted, Bulled et al. (2008) developed the Static Pressure Test (SPT) to determine awork index for high pressure grinding rolls. The SPT is a small-scale, locked cycle test thatinvolves pressing crushed drill core samples in a piston-die arrangement, and recording thespecific energy for the compression breakage achieved. The measurements are then calibratedagainst a lab-scale HPGR unit. The energy required to crush samples from F80 to P80 is givenby:E = 10HPi *.,√1P80−√1F80+/-(2.31)where E is specific energy input (kWh/t), HPi is high-pressure grinding index (kWh/t),and P80 and F80 are the 80% passing aperture size of product and feed in microns respectively.Klymowsky and Liu (1997) proposed a model that is another variation of Eq. 2.16 (Eq. 2.32).First, the model is based on Rittinger’s comminution theory, instead of Bond’s. Second,the authors believed that it is better to have an index for open circuit grinding, rather thanlocked-cycle closed circuit grinding. Third, the 50% passing size (i.e., P50) is considered morecharacteristic of HPGR product than the P80 used by Bulled et al. (2008). The proposed modelhas the following form:E = E∗(XpX∗p)α(2.32)where E∗is the specific energy consumption that is needed to crush the feed particle size toa product with a 50% passing size X∗p, and α was -1 for samples that the authors tested—twocoal, four kimberlite, two copper and three iron ore samples.46Morrell (2009) proposed another variation of Eq. 2.16, where the (1-n) term is a functionof the particle size.Wh = ShK3Mih4(x f (x2)2 − xf (x1)1)(2.33)Sh = 35 (x1 · x2)−0.2 (2.34)where K3 is equal to 1 for closed circuit operation and 1.19 for open circuit operation, x1and x2 are the 80% passing particle size of the circuit feed and product respectively, expressedin microns, and Mih is the HPGR ore work index, which is a function of the DWi determined bythe SMC test. Sh is the coarse ore hardness parameter which makes allowance for the decreasein ore hardness that becomes significant in relatively coarse crushing applications and it isfound to improve predictive accuracy (SMC Testing, 2015). Morrell (2009) claimed that theequation predicts specific energies of typical HPGRs operating with a specific pressing forcesin the range of 2.5–3.5 N/mm2.Factors that have an influence on specific energy consumption include the feed materialhardness, size distribution and moisture, roll surface profile, and roll speed.2.4 Summary of Literature ReviewThe HPGR is an energy-efficient comminution technology that is replacing conventional crush-ers and coarse grinding tumbling mills in comminution circuits. One of the major reasons forthe slow adaptation is that there is no industry-accepted small-scale test for the sizing andselection of an HPGR. The only published small-scale test procedures are the SMC test andthe SPT. Both of the tests are proprietary and have numerous shortcomings, as outlined below.Shortcomings of the SMC test are as follows,• the breakage mechanism is not particle bed compression; since it was originally designedfor AG/SAG mills, the SMC test employs impact breakage;47• the Drop Weight test is performed on one set of narrowly sized particles at five energylevels, which effectively results in only five data points to fit two parameters; if theselected size class is not representative of full HPGR feed, the effect of particle size canbe missed.• the M ih index from the test is only suitable for power-based calculations and does notallow model-based simulations;• the calculations do not account for the full size distribution of the feed or the feedconditions—the HPGR performance is known to be greatly influenced by feed truncationand moisture.Shortcomings of the SPT are as follows,• although the breakage mechanism of this test is particle bed compression, the chosenmaximum pressure is very low. The maximum pressure of 55 MPa was consideredadequate as the flake density at that pressure was similar to densities observed in manyHPGR tests. However, the maximum pressure of the test should be chosen on the basisof attaining specific energy input levels similar to those observed in HPGR tests;• due to large sample requirement the number of lock-cycle pilot-scale HPGR tests arelimited; thus the choice of calibrating locked-cycle HPGR test data against locked-cyclepiston press test data would severely limit the calibration test database and the growth ofthe lock-cycle test database can be assumed to be slow;• the procedure on how to convert the SPT test results to bench-scale HPGR results is notpublished; also no conversion from bench scale HPGR to full scale;• particle bed height has a major influence on the comminution effect. 1.6 kg sample in a100 mm die results in a particle bed height of over 80 mm, which is significantly higherthan observed in pilot-scale HPGR tests;48• the geometric constraint was arbitrarily selected, as the feed preparation for SAG PowerIndex (SPI) test was directly adapted and may not be suitable for HPGR ore characteri-zation;• the feed to the test is truncated at 3.35 mm. The HPGR performance is known to begreatly influenced by feed truncation;• the HPi index is only suitable for ranking and indexing the ore variability and can beused only for power-based calculations, and does not allow model-based simulations;• the force-displacement curve is not corrected for the strain of the entire setup;• a lab-scale HPGR is used for calibration of SPT; however, pilot-scale HPGR tests aremore reliable for scaling up to industrial scale HPGR.The development of a new small-scale test should have the following objectives:1. Employ the appropriate breakage mechanism, which is interparticle breakage under slowcompression of a bed of particles;2. Design the test for the sole purpose of sizing and selecting an HPGR, so that the ge-ometric constraints, feed preparation procedure, and maximum pressure achievable arerelevant and meaningful;3. Select an open cycle test procedure to increase the number of available HPGR testresults for direct calibration, and improving the statistical significance and validity ofthe correlation;4. Take into account the full size distribution and conditions of the feed;5. Provide full product size distribution for a given specific energy input;6. Generate information for both power-based calculations and model-based simulations.49There is a need for a small-scale test that can provide energy–size reduction informationobtained, which is considered more reliable than lab-scale HPGR testing for the purposes ofscaling up to industrial scale. Size reduction, specific energy consumption, and full productparticle size distribution information for corresponding specific pressing force are obtainedfrom pilot-scale HPGR testing. The developed piston press test should be able to provide thesame information using a significantly smaller sample.50Chapter 3EXPERIMENTAL PROGRAM OVERVIEW3.1 IntroductionThe experimental program consisted of performing both pilot-scale HPGR tests and pistonpress tests on samples from a range of ore types. For pilot-scale HPGR testing, the standardprocedure used by the manufacturer for sizing and selection was followed. The piston presstesting involved pressing samples in the piston-die arrangement, and then obtaining energy–size reduction information. The piston press testing methodologies are used to predict theenergy–size reduction performance of the HPGR. Three different methodologies of performingpiston press tests and analyzing the results were developed.1. The database-calibrated methodology uses two regression equations. The first equationrelates the specific pressing force to piston pressure and the second equation definesrelationship between reduction ratio achieved in the piston press and the HPGR. Thismethodology requires no HPGR calibration testing thus the sample requirement is low.2. The direct calibration methodology is used in cases where data from 2–3 HPGR pilottests are available for a composite ore sample from which results could be used tocalibrate a model against piston press results. The model can then be used to predict51the HPGR energy–size reduction relationship from piston press tests on samples repre-senting ore variability such as different geometallurgical units.3. The simulation-based methodology is used to simulate HPGR operation or various circuitconfigurations for a range of operating conditions. Piston press tests are performed onnarrow-size fractions and a modified version of an existing model is adopted to modelthe energy–breakage relationship.This chapter describes the sample requirements, equipment used and test procedures fol-lowed. It also describes the design criteria and justifications for the geometry used in thefabrication of the piston-die apparatus.In total, 19 HPGR tests were conducted on 4 different ore types within the scope of thisresearch. Subsamples from each ore type were collected for the piston press tests. In addition,the thesis used results and feed subsamples from HPGR testing on 11 different ore typesfor which 92 tests were conducted within the scope of other research and commercial testprograms. All 15 ore types were used for piston press tests and the results were calibratedagainst the 45 HPGR test results that evaluated the effect of specific pressing force. Piston presstests on narrowly-sized particles were performed to simulate the 36 HPGR tests conducted on5 ore types. There were data from an additional 46 HPGR tests on 7 ore types, from whichsubsamples were not available, but were included in the development of the regression modelfor net specific energy, ESP. Figure 3.1 shows an overview of the experimental program.52HPGR TEST DATABASE19 HPGR tests on 4 ore typesFeed subsamples available92 data sets on 11 ore typesFeed subsample available46 data sets only used for linear regressionPISTON PRESS TEST DATABASECalibration Tests45 data sets from HPGR pressure tests on 15 ore types Two empirical models of specific energy via multiple linear regressionSimulation Tests36 data sets from various HPGR tests on 5 ore types Procedure per ore type 4 piston press tests Calibrate FSP to Ppiston Calibrate size reductions achieved Confirm normalized curves Piston press tests on other geometallugical units Scale up to pilot-scale resultsProcedure per ore type 15 piston press tests on 5 mono-size classes at 3 energy levels Determine parameters of the breakage function (ESP vs. t10) Reconstitute product size distribution based on tn-family of curvesFigure 3.1: Overview of the experimental program3.2 Sample DescriptionSamples were provided from four different mining operations. The samples weighed between1 and 1.5 tonnes (i.e. 4–6 drums). A total of 19 HPGR pilot scale tests were completed onthe ore samples. As noted, samples representing 11 different ore types were used for pistonpress testing for which HPGR test results were available. All 15 ore types were used for thedirect calibration methodology and five of these ore types were also used for the simulation-based methodology. Table 3.1 shows number of available HPGR test data for each ore type andnumber of piston press tests conducted for each methodology on the ore types.53Table 3.1: List of ore types used in the research projectOre Number of Number of piston press teststype HPGR tests Calibration Simulation1 Cu-Mo (P) 4 4 152 Au (C) 6 4 153 Ni-Cu 5 44 Au (B) 4 45 Cu-Mo (H) 7 4 156 W 10 3 247 Cu-Au (A) 9 4 158 Dolomite 3 49 Cu-Au-Ag 13 410 Kimberlite 12 411 Cu-Mo (C) 6 412 Cu (M) 6 413 Cu (E) 6 414 Taconite 7 415 Pd 13 4Total 111 59 693.3 Pilot-scale HPGR Testing3.3.1 Description of the equipmentPilot-scale tests were performed using a Köppern HPGR with a 750 mm diameter and 220 mmwide roll as shown in Figure 3.2.The hydraulic unit of the machine is capable of applying a specific pressing force of upto 8 N/mm2. The HPGR is equipped with variable frequency drive (VFD) and data logging54to record power draw, operating pressure, and operating gap. The throughput capacity of themachine is 25–35 t/h, depending on material and specific pressing force setting.Figure 3.2: Köppern pilot-scale HPGR at UBC3.3.2 HPGR test procedureThe standard test procedure for sizing and selection as specified by Köppern was followed. Foreach test, a drum of material (250–300 kg) is required. When multiple tests are conducted onan ore, all samples are crushed in stages to −32 mm and homogenized using a rotating splitterand split into individual drums.A “conceptual level study” requires four drums of sample, with each tested at differentspecific pressing forces. The specific pressing force is set between 1 and 6 N/mm2. For “pre-feasibility level studies”, 13 drums of sample are required. Of the 13 tests:55• 4 tests are conducted to assess the effect of specific pressing force and the optimal specificpressing force for the ore is selected for the rest of the test program, which includes:• 2 tests to evaluate the effect of different roll speeds;• 2 tests to evaluate the effect of moisture;• 2 tests to evaluate the effect of top size;• 3 tests to simulate in closed circuit operation.During each test, the power draw, hydraulic pressure, and the operating gap are recordedas shown in Figure 3.3. A typical drum of material passes through the HPGR within 40–60seconds, and during the stable operation, centre and edge products are collected. As soon as thefeed material is released from the feed hopper, the power draw (blue line) spikes and hydraulicpressure (green line) destabilizes as the operating gap (red line) expands from the initial staticgap of 9 mm. Within 5 seconds the operation stabilizes and product sample is collected forabout 20 seconds.5101520253020304050607080Gap[mm]rdraw[kW]andPressure[bar]Samplingstart Samplingstop001028 32 36 40 44 48 52 56 60 64 68 72PoweTime[sec]Powerdraw Pressure GapFigure 3.3: An example of machine data for an HPGR test56Centre and edge products are collected from the product conveyor separately into threedrums using a splitter box. Figure 3.4 shows a photo and a diagram of the product splitter. Theposition of dividers are adjusted such that approximately 73% product mass is collected intothe centre product and the both edge products are equal.(a) Picture of HPGR product splitterEdgeProduct(~13.5%)Centre product(~73% by weight)EdgeProduct(~13.5%)HPGR product conveyor width44.5 cm55 cm(b) Diagram of HPGR product splitterFigure 3.4: HPGR products are split into centre and edge products through the splitter boxThe weight of sample collected and total sampling time are used to calculate the throughputrate.Q =Mt(3.1)where throughput rate, Q, is in t/h, M is mass of collected sample in tonnes, t is samplingtime in hours.The net power draw during the sample collection is divided by the throughput rate todetermine the net specific energy consumption (Eq. 2.2). Then the calculated throughputrate is divided by roll diameter, roll length, and roll speed to determine the specific throughputconstant (Eq. 2.3).57During the feed homogenization with the use of a rotary splitter, two sets of representativesamples (~15 kg) are collected. One representative sample is used to determine the feed particlesize distribution and the other is used for piston press tests. Also, 10–15 kg samples aretaken from the collected centre and edge products to determine their respective particle sizedistributions. During each test, 12–20 pieces of flake are collected from the product conveyorand the collected flakes are used for determining flake density using the Archimedes’s principle.Prior to submersion in water, the flake samples are coated with wax to prevent them from fallingapart or getting wet during submersion. The density of each flake is calculated using Eq. 3.2.ρ f lake =m f lake((m f lake −msub)/ρwater −(mwax −m f lake)/ρwax) (3.2)whereρ f lake is density of flake [g/cc];m f lake is mass of flake [g];mwax is mass of flake with wax [g];msub is mass of flake with wax under water [g];ρwax is density of wax, 0.91 g/cc.The results obtained from each single pass test include:• net specific energy consumption,• specific throughput constant (m-dot),• particle size distribution of feed, centre and edge products, and• flake density measurement on unbroken flakes collected during the test.583.3.3 Design implications of the HPGR test resultsThe optimal specific pressing force is used in sizing the HPGR bearings. A higher optimalspecific pressing force would require a higher quality bearings at a greater cost. The specificenergy consumption is used for sizing the HPGR motors and planetary gearboxes. The higherthe specific energy consumption at the optimal pressing force, the larger the motor power thatwould be required (Klein et al., 2014).The specific throughput (m-dot) is used for sizing the HPGR rolls and also for specifyingthe required motor speed range in rpm. The operating gap determines the acceptable feed topsize because ideally the feed top size should not exceed the expected operating gap to minimizebreaking of rocks directly with the roll surface, which affects the wear life of the rolls (Kleinet al., 2014).The knowledge of the centre and edge product PSDs are used for process flowsheet develop-ment and evaluation. Based on the product PSDs, decisions regarding the circuit configurationand the transfer sizes to downstream grinding equipment are made.3.3.4 HPGR test repeatabilityDue to the large sample requirements for HPGR tests, it is prohibitive to conduct repeat testingfor each research project and thus no repeat HPGR tests were performed within the scope of thisresearch. However, Nadolski (2012) conducted four repeat tests on the same Köppern HPGRused in this research and attempted to quantify repeatability of HPGR tests. Table 3.2 showsthe results of 4 repeat HPGR tests. The most pertinent parameters to this research are specificpressing force (FSP) with relative standard error of 0.10% and net specific energy (ESP) withrelative standard error of 0.58%. The results show very good precision for pilot-scale HPGRtesting. As the standard test procedure specified by Köppern is followed, a similar level ofvariability can be assumed for this research.59Table 3.2: Summary result of 4 repeat HPGR testsFeed sampling Recorded parameters Calculated parametersF80 F50 F20 Gap FSP Power Speed ESP Q m-dot[mm] [mm] [mm] [mm] [N/mm2] [kW] [m/s] [kWh/t] [t/h] [ts/hm3]Mean 21.57 13.82 3.04 22.09 3.95 66.97 0.75 1.54 38.03 306.94Standarderror 0.21 0.32 0.34 0.067 0.004 0.498 0.007 0.009 0.456 5.926Relativestandarderror0.9% 2.3% 11.2% 0.30% 0.10% 0.74% 0.93% 0.58% 1.20% 1.93%Standarddeviation 0.55 0.91 0.96 0.13 0.01 1.00 0.01 0.02 0.91 11.85Range 1.54 2.56 2.63 0.32 0.02 2.03 0.03 0.04 1.91 24.18Number ofdata points 8 8 8 4 4 4 4 4 4 4CI (95%) 0.46 0.76 0.80 0.21 0.01 1.59 0.02 0.03 1.45 18.86(Source: Nadolski, 2012)3.4 Piston Press Testing3.4.1 Overall criteria for the piston press testingSample requirementsThe goal of the research was to develop tests that could determine design parameters usingsmall sample sizes. Limiting the sample requirement to no more than 10 kg per ore type allowsthe HPGR technology to be considered in the early stages of flowsheet development and isparticularly important for greenfield projects when it is difficult to collect large samples. Suchtests would also allow assessment of ore variability using samples from drill programs.Sample preparationThe samples for the piston press tests are prepared using conventional crushing and screeningprocedures so that the samples would have “natural” particle size distributions.60Selection of piston-die geometryBased on the literature review, the following conclusions were drawn concerning the design ofthe piston-die apparatus;1. Subsection 2.2.1 discussed the ideal particle bed geometry was defined by Schönert. Themajority of researchers adhered to this geometry in their research. However, the HPGRproduces edge product that is coarser than the centre product. Therefore, adhering to theideal particle bed geometry may no be sufficient for the design of a piston press apparatusfor calibrating to HPGR tests. Rather, the geometric constraints of the piston press testapparatus should resemble those observed in the HPGR such that:(a) the compressed particle bed height is similar to the operating gap observed in theHPGR,(b) the ratio of die diameter to top particle size is similar to the ratio of the roll widthto the feed top size for the HPGR.2. Feed top size should be as large as possible for a meaningful representation of actual feedto an HPGR and the hydraulic press should be capable of providing net specific energiescomparable to those obtained from the pilot HPGR.The MTS hydraulic press for rock mechanics tests was used in this research and the maximumpressing force was 1,400 kN . In order to induce a piston pressure in the range of 200 to250 MPa, which is the estimated maximum pressure observed at the roll centre during theHPGR testing, the required die diameter ranges from 94.4 mm to 84.4 mm, respectively. Thediameter was calculated as follows:Area =ForcePressure=1,400,000N250N/mm2= 5,600mm261Diameter =√4 · Areapi=√4 ·5,600mm2pi= 84.4mmThe HPGR unit used for pilot-scale testing has a 220 mm wide roll and the feed top size is32 mm. The geometric constraint is that the roll length to particle top size for the pilot unit is220/32, or the roll length is 6.875 times the particle top size.Dividing die diameter by feed top size would create the similar geometric constraint for thepiston press. If the die diameter is 84.4 mm, the feed top size can be 12.3 mm (84.4/6.875).If the die diameter is 94.4 mm the feed top size can be 13.7 mm. The closest standard screensaperture in that range are 12.5 mm and 13.2 mm. Therefore, a feed top size of 12.5 mm wasselected with the possibility of reaching higher pressures up to 240 MPa with an 86 mm diediameter.Sample size per testThe sample mass selected for piston press testing was based on the minimum mass requirementas outlined in the ASTM standard D6913-04 for determining particle size distribution of soilsby sieve analysis. According to the standard, for a particle top size of 12.5 mm, the minimumsample mass of 344 g is necessary for a material with a specific gravity of 2.8 g/cc. Anotherconsideration was that the height of the compressed particle bed should be similar to theoperating gap observed in pilot HPGR testing, which ranges from 15 to 25 mm. Consideringthe variation in bulk density across different ore types, a constant volume of sample should betested. The minimum volume of 202 cc was calculated by dividing the minimum sample massof 344 g by the average bulk density of 1.7 g/cc. A volume of 240 cc was selected as the samplesize per test as it is slightly greater than the minimum sample volume required and it is also thevolume of a standard measuring cup.623.4.2 Piston press test procedureThe piston press testing was selected to study the energy–size reduction relationships for thefollowing reasons;• both the HPGR and the piston press have the same breakage mechanism, which isinterparticle breakage under slow compression of a bed of particles;• the net energy input to the sample can be accurately recorded and measured;• a large number of particles are tested, which is important for statistical significance.The selected piston-die arrangement is illustrated in Figure 3.5. The die has an internal diame-ter of 86 mm and height of 60 mm. The apparatus was designed with a removable plate in thebottom, which facilitates easy removal of the pressed sample for sieving. The displacement ofthe piston is measured from the top of the die as shown in Figure 3.5.Piston at seating load of 2.5 kN0 mm60 mmPiston at end force of 65-1390kNDie86 mmDisplacementFigure 3.5: Illustration of piston-die arrangementFigure 3.6 shows the force-displacement curve for the empty piston-die apparatus. Whendetermining force-displacement curves for test samples, the empty force-displacement resultsare subtracted to correct for measurement response. The empty apparatus includes the piston,the removable bottom, and the spacers placed underneath the piston-die arrangement.6302004006008001000120014000.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4Force [kN]Displacement [mm]Figure 3.6: Strain curve of the entire piston-die setupFor each piston press test, a 240 mL sample is placed in the die and pressed with thepiston while the force and displacement are recorded every 0.25 seconds. A typical force-displacement curve that can be obtained from a piston press test is shown in Figure 3.7.64100012001400UncorrectedCorrected400600800Force[kN]020015 19 23 27 31 35 39Displacement [mm]Figure 3.7: An example of force displacement curve before and after the correction for thestrainThe total energy input to the sample is equal to the area under the strain-corrected force-displacement curve. The formula of the trapezoid area is used in the numerical integrationof the corrected force-displacement curve to calculate the total energy, and is then dividedby the sample mass to determine the specific energy input. Figure 3.8 illustrates the use ofthe trapezoidal rule for numerical integration. Since there are four force and displacementreadings per second, the displacements between readings are of the order of ~0.01 millimeters.In addition, the force ramp-up is time-controlled at 200 kN/min. Thus, the force increaseslinearly between readings, which allows accurate calculation of energy absorbed and justifiesthe use of the trapezoidal rule.65d1 d2 d3 d4 d5F1F2F3F4F5TrapezoidArea=½ ( a+b ) hh = d i – d i-1a = F i-1b = F ihabFigure 3.8: Illustration of numerical integration of force-displacement curvesThe results from each piston press test include:• Specific energy input corresponding to the applied piston pressure;• Feed and product particle size distributions;• Compressed particle bed density;• Thickness of particle bed.3.4.3 Statistical analysis of the piston press testsExperimental errors of the piston press test were quantified in the following areas:• Variation in feed subsampling;• Variation in specific energy measurement;• Variation in product PSD determination.The summary results of statistical analysis is presented at the end of this section.66Variation in feed subsamplingIn order to estimate variation in obtaining subsamples from feed, repeat samples (~500 g) werecollected and compared for statistical analysis. Two sets of eight subsamples were taken byriffling from dry and 2.5% moist feeds of a copper-gold ore. The moist sample was oven driedbefore determining PSDs.Table 3.3 lists PSDs of the eight dry subsamples. The coefficient of variation of d80 andd50 were 2.82% and 8.32%, respectively. The mean of d80 was 9.97±0.24 mm (95% C.I., n=8)and the mean of d50 was 6.71±0.46 mm (95% C.I., n=8).Table 3.3: Variation in PSD of feed subsamples split before moisture adjustmentSubsample 1 2 3 4 5 6 7 8Particlesize [mm]Cumulative percentage passing [%]12.5 100 100 100 100 100 100 100 10011.2 90.3 90.7 90.0 92.5 95.5 89.5 93.0 93.48 54.7 54.2 58.1 62.5 67.3 63.7 62.7 61.75.6 35.4 35.4 40.1 39.7 48.7 43.5 42.6 42.14 25.4 25.0 26.9 25.9 36.4 32.7 29.3 31.02.8 19.6 18.4 20.3 20.2 28.4 26.1 23.1 24.52 15.8 15.2 16.5 16.4 23.2 21.3 19.0 20.31.4 13.6 12.7 13.3 14.0 19.5 18.1 15.4 16.81 11.5 10.7 11.1 11.7 16.4 15.5 12.9 14.10.71 9.7 9.1 9.3 9.9 13.7 13.0 10.8 11.80.5 8.3 7.7 7.9 8.4 11.6 11.0 9.1 10.00.355 7.1 6.5 6.6 7.2 9.8 9.4 7.8 8.50.25 6.0 5.5 5.5 6.1 8.3 8.0 6.6 7.20.125 3.9 3.6 3.6 4.1 5.6 5.3 4.4 4.8d80 10.27 10.26 10.20 9.87 9.44 10.03 9.83 9.85d50 7.41 7.46 6.92 6.69 5.77 6.37 6.49 6.5767Table 3.4 lists PSDs of the eight subsamples taken after moisture adjustment to 2.5%. Thecoefficient of variation of d80 and d50 were 1.78% and 4.67%, respectively. The mean of d80was 10.05±0.15 mm (95% C.I., n=8) and the mean of d50 was 6.78±0.26 mm (95% C.I., n=8).The variation in the subsamples split after the moisture adjustment was much lower thandry subsamples. Therefore, piston press test feeds were subsampled after the moisture wasadjusted to match the moisture content in the HPGR tests in order to reduce the variationin subsamples. Overall results show an acceptable level of reproducibility when the feed issampled after moisture adjustment.68Table 3.4: Variation in PSD of feed subsamples split after moisture adjustmentSubsample 1 2 3 4 5 6 7 8Particlesize [mm]Cumulative percentage passing [%]12.5 100 100 100 100 100 100 100 10011.2 91.2 90.8 91.9 92.3 90.3 91.7 88.5 92.98 59.8 56.4 60.8 63.2 57.2 64.3 58.9 62.15.6 40.9 38.5 39.1 43.6 37.7 43.6 39.6 42.84 28.9 27.7 28.4 32.6 26.8 32.5 28.8 32.02.8 23.1 21.6 22.4 26.1 20.9 26.4 23.0 26.22 19.4 18.0 18.7 21.7 17.3 22.5 19.2 21.91.4 15.6 14.9 15.4 17.4 14.1 18.7 15.2 17.81 13.2 12.6 13.0 14.7 12.0 16.0 12.8 15.20.71 11.2 10.7 10.9 12.5 10.2 13.6 10.9 12.80.5 9.5 9.2 9.3 10.6 8.7 11.6 9.3 11.00.355 8.1 7.8 7.9 9.0 7.5 9.9 8.0 9.30.25 6.9 6.6 6.7 7.7 6.5 8.4 6.8 7.90.18 5.8 5.5 5.7 6.4 5.4 7.0 5.7 6.50.125 4.6 4.4 4.5 5.0 4.3 5.6 4.4 5.10.09 3.7 3.5 3.6 3.9 3.5 4.3 3.5 4.1d80 10.05 10.20 9.97 9.85 10.20 9.83 10.28 9.86d50 6.75 7.14 6.81 6.38 7.11 6.35 6.89 6.49Variation in specific energy measurementRepeat piston press tests were conducted to assess reproducibility of piston press tests. Twentypiston press tests were performed on a copper-gold ore. Table 3.5 lists the results of thepiston press tests. Ideally, volume controlled sampling should yield the same mass for eachsubsample. However, the coefficient of variation (standard deviation divided by the mean) ofmass was 3.15%.69Table 3.5: Results of multiple piston press tests on a geometallurgical unitTest Force Pressure Mass Sp. Energy 95% C.I. Coeff. of# [kN] [MPa] [g] [kWh/t] for repeats Variation1 400 68.8 306.2 0.960.97±0.088 5.73%2 400 68.8 339.8 0.903 399 68.8 343.5 1.034 400 68.8 350.2 0.985 678 117 323.2 1.306 843 145 324.1 1.711.65±0.043 3.63%7 843 145 314.2 1.768 843 145 325.8 1.689 844 145 326.6 1.6810 843 145 323.1 1.6311 843 145 323.8 1.6312 843 145 323.9 1.5913 843 145 323.5 1.5814 843 145 323.9 1.6315 843 145 323.7 1.5716 983 169 323.6 1.8417 1388 239 333.5 2.602.62±0.048 1.16%18 1388 239 311.4 2.6119 1388 239 317.9 2.6220 1388 239 323.8 2.66The relationship between piston pressure and specific energy can be defined by a slope0.0098±0.00026 and an intercept 0.244±0.041 (95% C.I., n=20). The sum of squared error,SSE, is calculated as 0.073. The residual standard error (SE) of the regression is 0.0636 kWh/ton 18 degrees of freedom.Figure 3.9 shows the scatter plot of specific energy input versus piston pressure. The bluefitted line represents the estimated mean specific energy for a given piston pressure. The dashed70orange lines represent the 95% confidence interval for the estimated mean specific energy for agiven piston pressure and the red lines represent the 95% prediction interval for a single valueof specific energy for a given piston pressure.0.00.51.01.52.02.53.00 50 100 150 200 250 300Specific energy input [kWh/t]Piston pressure [MPa]Fitted lineData95% confidence interval95% prediction intervalFigure 3.9: Results of piston press tests on a geometallurgical unitThe precision of both intervals vary slightly with piston pressure and the precision is lowestat the piston pressure that is equal to the mean of the tested pressures. The estimated meanspecific energy, confidence and prediction deviation for three pressures are shown in Table 3.6.Overall results show that piston press testing has more variability than pilot HPGR testing.71Table 3.6: An example of confidence deviation and prediction intervalsPressure Estimated mean ESP Confidence Prediction Coefficient[MPa] [kWh/t] [kWh/t] [kWh/t] of variation50 0.73 ±0.062 ±0.15 3.99%150 1.71 ±0.030 ±0.14 0.83%250 2.69 ±0.063 ±0.15 1.11%Variation in product PSDsTen piston press tests were performed on the copper-gold ore at the same piston pressure of145 MPa. PSDs of the 10 piston press test products are listed in Table 3.7. The coefficient ofvariation of d80 and d50 are 3.94% and 4.44%, respectively. The mean of d80 is 5.78±0.16 mm(95% C.I., n=10) and the mean of d50 is 1.49±0.05 mm (95% C.I., n=10). The results showthat experimental error in product PSDs is low.72Table 3.7: PSDs of 10 replicates of piston press tests on copper-gold oreSubsample 1 2 3 4 5 6 7 8 9 10Particlesize [mm]Cumulative percentage passing [%]12.5 100 100 100 100 100 100 100 100 100 10011.2 99.6 99.2 98.4 99.4 100.0 99.6 99.5 98.3 97.9 99.48 88.4 89.9 90.7 88.7 90.8 91.3 89.0 88.4 90.5 90.25.6 78.9 78.1 79.1 79.2 80.3 77.7 77.7 79.4 81.5 79.84 70.5 69.3 69.6 70.4 71.5 69.6 68.9 70.2 72.6 71.22.8 63.9 62.4 62.8 63.1 64.6 62.8 62.4 62.8 65.4 64.12 57.7 56.4 56.8 57.1 58.6 56.3 56.8 56.1 59.4 58.11.4 50.2 47.7 48.6 48.8 49.7 48.2 48.3 47.7 50.2 48.51 44.4 42.5 42.8 43.3 44.6 42.8 42.8 42.3 44.6 42.90.71 38.3 37.3 37.5 37.6 39.0 37.0 37.3 37.0 39.0 37.40.5 33.3 32.5 32.6 32.9 34.2 32.0 32.4 32.3 33.9 32.40.355 29.1 28.3 28.4 28.6 30.0 27.9 28.0 28.4 29.6 28.20.25 25.5 24.9 24.9 25.1 26.4 24.4 24.4 24.9 25.9 24.70.18 22.3 21.8 21.8 22.0 23.2 21.3 21.2 21.9 22.7 21.50.125 19.3 18.9 18.8 19.0 20.2 18.4 18.1 18.9 19.6 18.5d80 5.87 5.99 5.78 5.79 5.54 6.01 6.08 5.77 5.34 5.64d50 1.39 1.56 1.50 1.48 1.42 1.54 1.52 1.57 1.39 1.49Summary of statistical analysis of piston press testsVariation in feed subsampling, specific energy measurement, and product PSDs determinationare the main sources of experimental errors. Table 3.8 shows the summary results of statisticalanalysis of experimental errors in the piston press testing. Although the relative standard errorof specific energy measurement is 1.97 times higher in the piston press test as compared to theHPGR testing, measurement errors are well within acceptable level for a small-scale test.73Table 3.8: Summary results of experimental errors in the piston press testingF80 F50 ESP P80 P50[mm] [mm] [kWh/t] [mm] [mm]No. data points 8 8 10 10 10Mean 10.03 6.74 1.65 5.78 1.49Standard deviation 0.179 0.310 0.060 0.228 0.066Standard error 0.063 0.110 0.019 0.072 0.021Relative standard error 0.63% 1.63% 1.15% 1.25% 1.40%Coefficient of variation 1.79% 4.60% 3.63% 3.94% 4.44%95% Confidence interval 0.150 0.259 0.043 0.163 0.04774Chapter 4RESULTS OF HPGR TESTING ANDEMPIRICAL MODELSThis chapter presents the results of the pilot-scale HPGR tests carried out within the scopeof the research. The results show that specific energy has a linear relationship with specificpressing force, and that the size reduction achieved is highly dependent on the coarsenessof the feed. In addition, two specific energy models are presented, which are based on thestatistical analysis of the HPGR results database.4.1 Summary of HPGR Test ResultsIn total, 19 pilot-scale HPGR tests were completed as part of this research:• four tests on SAG mill pebble crusher feed from a copper-molybdenum ore concentratorlocated in British Columbia, coded as Cu-Mo (P),• five tests on SAG mill pebble crusher feed from a nickel-copper ore concentrator locatedin Ontario, coded as Ni-Cu,• six tests on gold ore from a project located in Quebec, coded as Au (C), and• four tests on gold ore from a grind-leach-CIP operation located in Ontario, coded asAu (B).75Normally, the feed top size for a pilot-scale HPGR pressure test is −32 mm. However, two ofthe ore types were also tested at a top size of −12.5 mm, in order to directly compare resultsof the HPGR and the piston press tests on the same top size feed (Section 4.3). The HPGRtest results are summarized in Table 4.1 and the detailed individual test results are included inAppendix A.Table 4.1: Summary of pilot-scale HPGR test workTest Ore FSP ESP m− dot H2O ρbulk F80 P80No. type [N/mm2] [kWh/t] [ts/hm3] [%] [g/cc] [mm] [mm]1 Au (C) 4.00 2.60 182 1.48 1.60 27.44 7.752 Au (C) 2.99 2.16 196 1.48 1.60 27.44 8.713 Au (C) 1.96 1.47 201 1.48 1.60 27.44 11.164 Au (C) 4.01 2.01 216 2.06 1.69 9.83 4.895 Au (C) 3.03 1.59 218 2.06 1.69 9.83 5.656 Au (C) 1.83 1.11 226 2.06 1.69 9.83 5.767 Au (B) 3.99 2.25 215 1.70 1.64 21.66 7.308 Au (B) 1.95 1.18 242 1.70 1.64 21.66 5.009 Au (B) 3.92 1.94 232 2.02 1.69 8.85 9.3310 Au (B) 1.97 1.06 246 2.02 1.69 8.85 5.7311 Cu-Mo (P) 4.98 2.35 200 1.48 1.55 20.47 5.5212 Cu-Mo (P) 3.95 1.98 196 1.48 1.55 20.47 6.3013 Cu-Mo (P) 2.98 1.57 200 1.48 1.55 20.47 7.1414 Cu-Mo (P) 2.01 1.15 210 1.48 1.55 20.47 8.7815 Ni-Cu 4.98 2.53 191 2.39 2.08 23.67 8.0216 Ni-Cu 3.94 2.04 207 2.39 2.08 23.67 8.0517 Ni-Cu 2.98 1.61 210 2.39 2.08 23.67 9.3318 Ni-Cu 2.01 1.24 212 2.39 2.08 23.67 9.5019 Ni-Cu 2.99 1.48 217 0.35 1.91 23.67 11.28764.2 Effect of Specific Pressing Force on Specific EnergyFigure 4.1 shows the relationship between specific pressing force and net specific energyconsumption for the four ore types tested. The linear relationship is typical in the range ofspecific pressing force from 2 to 5 N/mm2.R² = 0.986R² = 1 R² = 0.997R² = 0.9980.00.51.01.52.02.53.03.50 1 2 3 4 5 6Net specific energy [kWh/t]Specific pressing force [N/mm2]Au (C)Au (B)Ni-CuCu-Mo (P)Figure 4.1: Linear relationship between net specific energy and specific pressing force for thetests on -32 mm feed4.3 Effect of Feed Coarseness on Size ReductionFigure 4.2 compares the reduction ratios of different feed top sizes for gold ore (C), whileFigure 4.3 compares reduction ratios for gold ore (B). For both ore types, the reduction ratioachieved with a 12.5 mm top size feed is much lower than that achieved with a 32 mm top sizefeed. The following are the reasons for the decrease in reduction ratio for finer feed:77• The −32 mm feed contains particles that are larger than the operating gap. Therefore,the coarse fractions are broken with certainty as they pass through the gap, whereas nofractions of −12.5 mm feed are broken with such certainty.• Coarser particles have a higher number of flaws or micro-cracks and mineral grainboundaries that can lead to fracture when compared to smaller particles.• The -12.5 mm feed has a higher proportions of fine particles, which leads to an isostatic-like state relatively quickly, compared to the -32 mm feed. Therefore, fine fractions(<1 mm) in the feed approach the behavior of powder, and the probability of breakingfine particles by compression decreases.• Smaller particles are inherently more difficult to break due to the reduced contact area.123456780.5 1.0 1.5 2.0 2.5 3.0Reduction ratio (F50/P50)Specific energy [kWh/t]Ore: Au (C)-32mm feed-12.5mm feedFigure 4.2: Comparison of reduction ratios achieved with 12.5 mm and 32 mm top size feedfor Au (C) ore78123456780.5 1.0 1.5 2.0 2.5 3.0Reduction ratio (F50/P50)Specific energy [kWh/t]Ore: Au (B)-32mm feed-12.5mm feedFigure 4.3: Comparison of reduction ratios achieved with 12.5 mm and 32 mm top size feedfor Au (B) ore4.4 Normalization of Product PSDAs described in section 2.2.2, the combined particle size distributions (PSD) of HPGR productsare often self-similar and normalized by dividing by their median size (Fuerstenau et al., 1991).Figure 4.4 compares the regular and normalized PSDs of products from HPGR tests on the Cu-Mo (P) ore. Four tests were conducted at four different pressing forces (FSP). As expected,the 5 N/mm2 test produced the finest product, while the 2 N/mm2 test produced the coarsestproduct (Figure 4.4a). However, once the product PSDs are normalized by dividing by theirmedian size, the curves overlap as shown in Figure 4.4b.7901020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Particle size [mm]a) Regular PSD2N/mm² 3N/mm² 4N/mm²5N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]b) Normalized PSD2N/mm² 3N/mm² 4N/mm²5N/mm² Fit curveFigure 4.4: A comparison of a) regular and b) normalized PSDs of Cu-Mo (P) ore at FSPranging from 2 N/mm2 to 5 N/mm2Eq. 2.4, which was discussed in the literature review (Section 2.2.2), was used to convertthe normalized data points into a functional form. The fitted curve describes the cumulativepercentage passing versus normalized particle size, which fits the normalized data very well asshown in Figure 4.5.F( xX50)= 100(1− exp(−A( xX50) (m( xX50 )+n)))(2.4 revisited)80020406080100020406080100Modelled cum.  passing   [%]Measured cum. passing [%]R2= 0.992N/mm²3N/mm²4N/mm²5N/mm²1:1 lineFigure 4.5: Modelling of cumulative percent passing as function of normalized particle sizeusing Eq. 2.4 is shown for HPGR tests on Cu-Mo (P) oreFigure 4.6 makes the same comparison of the measured and the normalized PSDs forproducts from HPGR tests on the Ni-Cu ore to demonstrate that the normalization of productPSDs applies to a variety of ore types. The functional fitted curved is the gray line in Figure4.6b and it demonstrates a good fit to the normalized data points.8101020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Particle size [mm]a) Regular PSD2N/mm² 3N/mm² 4N/mm²5N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]b) Normalized PSD2N/mm² 3N/mm² 4N/mm²5N/mm² Fit curveFigure 4.6: A comparison of regular and normalized PSDs of Ni-Cu oreFigure 4.7 compares the normalized PSDs of products from HPGR tests using samples withdifferent feed top sizes. Plots (a) and (c) are the product PSDs from HPGR tests on -32 mmand -12.5 mm feeds of Au (C) ore. Plots (b) and (d) are normalized PSDs of the products, andthey are compared in plot (e). Regardless of the two very different feed size distributions andthe three different test pressures, the six products all have the same normalized product particlesize distribution, as shown in plot (f). A similar comparison is shown in Figure 4.8 for anothergold ore.The self-similar characteristic of HPGR products seems to apply regardless of ore type,test pressure, or feed top size. This unique self-similar characteristic will be utilized in theprocedure of scaling up from piston press results to HPGR results in order to predict the productPSD.8201020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Particle size [mm](a) Regular PSD -32mm2N/mm² 3N/mm²4N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](b) Normalized PSD -32mm2N/mm² 3N/mm²4N/mm² Fit curve01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Particle size [mm](c) Regular PSD -12.5mm2N/mm² 3N/mm²4N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](d) Normalized PSD -12.5mm2N/mm² 3N/mm²4N/mm² Fit curve01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm](e) Comparison of normalized PSD-32mm -12.5mm01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](f) Comparison of fitted curves-32mm -12.5mmFigure 4.7: A comparison of normalized PSDs of products from HPGR tests on different feedtop sizes of Au (C) ore; showing match of fitted curves regardless of feed top sizeand tested pressure8301020304050607080901000.01 0.1 1 10 100Cum.percentpassing[%]Particle size [mm](a) Product PSD -32mm2N/mm² 4N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](b) Normalized PSD -32mm2N/mm² 4N/mm² Fit curve01020304050607080901000.01 0.1 1 10 100Cum.percentpassing[%]Particle size [mm](c) Product PSD -12.5mm2N/mm² 4N/mm² Feed01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](d) Normalized PSD -12.5mm2N/mm² 4N/mm² Fit curve01020304050607080901000.01 0.1 1 10 100Cum.percentpassing[%]Normalized particle size [mm/mm](e) Comparison of normalized PSD-32mm -12.5mm01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm](f) Comparison of fitted curves-32mm -12.5mmFigure 4.8: A comparison of regular and normalized PSDs of products from HPGR tests ondifferent feed size distribution for the Au (B) ore844.5 Development of Regression Models of Net SpecificEnergyThis section presents the statistical analysis of the HPGR test results. The objective ofthe analysis was to obtain multiple linear regression models for the HPGR net specific energy,using operating and feed parameters as input variables. R Language for Statistical Computing(R Core Team, 2013) was used for the statistical analysis and regression modelling.4.5.1 Statistical analysis of the HPGR databaseIn total, 157 HPGR tests were performed on 22 ore types. The results from these tests formedthe database. The database included 111 HPGR tests conducted on 15 ore types as describedin section 3.2, from which representative samples were available for piston press testing. Inaddition, the database included the results of 46 HPGR tests, for which samples were notavailable for piston press testing.The summary of HPGR operating parameters and feed conditions, including the mean andstandard deviation values, are tabulated in Table 4.2. The table shows that operating parametersand feed conditions in the database vary extensively, making it well suited to the developmentof a model applicable to a wide variety of feed types and operating conditions.85Table 4.2: Descriptive statistics of HPGR database operating parameter and feed conditionsStatistic Unit Mean St. Dev. Min MaxSpeed m/s 0.74 0.09 0.46 1.01Operating gap mm 18.55 2.77 7.40 25.62Specific pressing force N/mm2 3.59 0.98 0.94 5.96Net specific energy kWh/t 1.88 0.51 0.53 3.53m-dot ts/hm3 224.3 33.3 102.1 330.0Moisture % 2.84 1.69 0.00 10.00Bulk density g/cc 1.77 0.26 1.28 2.20F80 mm 17.44 6.61 1.84 27.44F50 mm 10.41 4.93 0.95 20.21Figure 4.9 shows a scatter plot of the net specific energy versus specific pressing force forthe 157 HPGR tests on 22 ore types along with regression line with coefficient of determinationof R2 = 0.52. Clear outliers in the plot represent HPGR tests conducted at a specific pressingforce of 2.5 N/mm2 on a kimberlite ore with an extremely high moisture content of 8%.86y = 0.54 + 0.37 x;   R2 = 0.520.51.01.52.02.53.03.54.00.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5Specific pressing force (N mm2)Specific energy (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.9: Specific energy versus specific pressing force for the 157 HPGR tests on 22 oretypesA linear regression model with a coefficient of determination of 0.52 cannot be considereda good model fit. Therefore, other feed and operating parameters were considered in additionto specific pressing force. Figure 4.10 shows the scatter plot with the data categorized intoranges of moisture levels. It shows that when the moisture is high, the regression line has asteeper slope, suggesting that moisture affects the energy consumption.870.51.01.52.02.53.03.51.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Specific pressing force (N mm2)Specific energy (kWh/t)Moisture < 2% 2−5% > 5%Figure 4.10: Specific energy versus specific pressing force graph for three levels of feedmoistureThe effect of feed coarseness in terms of F80 is shown in Figure 4.11, suggesting an increasein coarseness leads to an increased energy consumption. It is interesting that the regressionline of medium size feed (10–20 mm) indicates similar specific energy as fine feed (<10 mm)at low pressure, and transitions to yield a similar specific energy for the coarse feed (>20 mm)at a higher pressing force.880.51.01.52.02.53.03.51.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Specific pressing force (N mm2)Specific energy (kWh/t)Coarseness < 10mm 10−20mm > 20mmFigure 4.11: Specific energy versus specific pressing force graph for three levels of feedcoarsenessA trellis graph lays out smaller charts in a grid with consistent scales. Each small chartrepresents an item in a category and allows graphical analysis of complex, multi-variable datasets such as the HPGR test database.Figure 4.12 shows trellis graphs grouped by moisture content and F80. When the datapoints are grouped by both moisture and F80, the coefficients of determination are higher thanthe previous 0.52 value.It is clear that the effect of FSP on ESP depends on the levels of moisture (4.10), F80 (4.11),and combination of them (4.12). When the effect of one predictor variable on the responsevariable depends on the level of the other predictor variable it is highly likely there is aninteraction between predictor variables. Therefore, all interactions of variables were consideredin the selection of the linear regression model.89< 10mm 10-20mm > 20mmR2 = 0.29R2 = 0.73R2 = 0.81R2 = 0.82R2 = 0.58R2 = 0.9R2 = 0.61R2 = 0.78R2 = 0.280.51.01.52.02.53.03.50.51.01.52.02.53.03.50.51.01.52.02.53.03.5< 2%2-5%> 5%1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6Specific pressing force (N mm2)Specific energy (kWh/t)Figure 4.12: Trellis graph illustrating the interaction effect of feed moisture and F8090Figure 4.13 shows a scatter plot of size reduction ratio achieved in the HPGR tests as afunction of coarseness of feed. As the feed becomes coarser, a higher size reduction ratio isachieved. The result is explained as follows:• when large particles are present, a greater proportion of the particles are broken withcertainty;• larger particles have more flaws (micro-cracks and mineral grainboundaries) than smallerparticles and therefore require less energy to break;• coarser feed has less fines that can inhibit breakage.The data are grouped by specific energy input and as expected a higher specific energy inputresults in higher reduction ratio.0246810120 5 10 15 20 25 30F80 (mm)Reduction ratio (F50/P50)Sp.Energy < 1.25kWh/t 1.25-2.25kWh/t > 2.25kWh/tFigure 4.13: Reduction ratio achieved as function of feed size, grouped into three levels ofspecific energy input914.5.2 Regression models of net specific energy consumptionThe following describes the eight feed and operating parameters that were considered as pre-dictor variables for the regression model of the net specific energy consumption, ESP.1. Specific pressing force, FSP in units of N/mm2, is considered because it is an importantHPGR operating parameters that influences size reduction.2. Roll peripheral speed, ν in units of m/s, is considered because it is the operating param-eter that controls the instantaneous throughput of HPGRs.3. 80% passing size of HPGR feed, F80 in units mm, is considered because it represents thecoarseness of the feed.4. HPGR feed moisture, w in units of %, is considered because it influences the packingcharacteristics of the feed and the operating gap formation.5. HPGR feed bulk density,ρbulk in units g/cc, is considered because HPGR throughputis a volume of material passing through the operating gap and mass of the volume isdependent on the bulk density.6. Piston press work index, W pi = ESP/(10/√P80 − 10/√F80) in kWh/t, is consideredbecause it represents grindability/hardness of the tested ore in compression bed breakage.Wpi is determined from piston press tests where size reduction from feed size of F80 inmicrons to product size of P80 in microns is achieved by specific energy input of ESP.Wpi is determined as the average of 4–8 piston press tests.7. Percentage passing -1 mm material in HPGR feed, P1mm in units of %, is consideredbecause it represents the amount of fines in the feed. The amount of fines influences thecharacteristic of feed packing and compression bed breakage.8. The slope of HPGR feed PSD in log-log space, m, is considered because it represents theshape of feed particle size distribution.92The first five parameters were available for 157 sets of HPGR test data and all eight parameterswere available for 90 tests. Therefore, two models were considered; 1) based on five predictorsand their 10 possible cross-product pairs, and 2) based on eight predictors and their 28 possiblecross-product pairs.A regression model from consideration of five parameters and their two-wayinteractionsStepwise regression was run in R statistical programming software. One of the preferredmethods for model selection is Akaike Information Criterion (AIC) which is expressed by thefollowing equation (Schwartz, 2011).AICregression = n× log(SSEn)+2K (4.1)where, SSE is the error sum of squares, n is the number of data points, and K is the number ofterms in the model and K=p+1, where p is number of predictors.AIC balances the improvement of fit against number of predictor variables. As morepredictor variables are added to the model, a better fit to data can be achieved i.e. higherR2. However, the standard errors of coefficient estimates become larger as more predictorvariables are used in the model. In the stepwise regression routine, AIC are evaluated for eachaddition or elimination of variables to the specific energy regression model, which starts out asESP ∼ f (FSP). A parameter addition or elimination takes place only if the action reduces thecurrent AIC. A parameter addition or elimination that results in the largest reduction of AICtakes precedence. The stepwise regression ends when neither addition nor elimination of anypredictor variable lowers AIC of the current model.The stepwise regression that considered five parameters and their two-way interactionsresulted in a model with seven variables. The stepwise regression model has a residual standard93error (SE) of 0.209 kWh/t on 149 degrees of freedom, and a R2 of 0.839 and an adjusted R2 of0.831. The F-statistic for the model is 111 (p < 2 ·10−16) on 7 and 149 degrees of freedom.Coefficient estimates are listed in Table 4.3 along with the their standard errors, t-value,and p-values. The t-value are t-test statistics for the hypothesis that the true values of thecoefficients are equal to zero, i.e. null hypothesis is H0 : βi = 0 and the alternative hypothesisis H1 : βi , 0. The p-values are probabilities of achieving t-values as large or larger if the nullhypothesis were true while controlling all other variables.Table 4.3: Summary results of stepwise regression on five parameters and their two-wayinteractionsVariable Coefficient estimate Standard error t-value Pr(>t)Constant 1.31 2.56E-01 5.1 1.00E-06FSP 3.71E-01 3.70E-02 10.04 < 2E-16F80 -2.59E-04 6.41E-03 -0.04 9.68E-01w -2.48E-01 9.27E-02 -2.68 8.20E-03ρbulk -6.61E-01 1.55E-01 -4.27 3.50E-05F80 ·w 9.70E-03 1.72E-03 5.66 7.70E-08FSP ·w 1.60E-02 9.63E-03 1.66 9.93E-02w · ρbulk 9.73E-02 6.01E-02 1.62 1.07E-01Residuals:Min 1st quartile Median 3rd quartile Max-0.46 -0.14 -0.01 0.10 0.69The model after stepwise regression was further simplified by eliminating insignificantvariables one at a time until all the variables were significant at a 0.05 significance level. Table4.4 summarizes the results of the simplified regression model. The simplified model has aresidual standard error (SE) of 0.213 kWh/t on 153 degrees of freedom, and a R2 of 0.828 andan adjusted R2 of 0.825.94Table 4.4: Summary results of the simplified regression model that considered fiveparameters and their two-way interactionsVariable Coefficient estimate Standard error t-value Pr(>t)Constant 0.693 1.28E-01 5.4 2.60E-07FSP 0.437 1.80E-02 24.4 < 2E-16ρbulk -0.452 6.86E-02 -6.6 6.70E-10F80 ·w 0.00875 5.40E-04 16.2 < 2E-16Residuals:Min 1st quartile Median 3rd quartile Max-0.54 -0.15 -0.03 0.12 0.68The simplified regression model is presented as Eq. 4.2.ESP = 0.693+0.437 ·FSP +0.00875 ·F80 ·w−0.452 · ρbulk (4.2)whereESP is net specific energy consumption in kWh/t,FSP is in N/mm2,F80 is 80% passing size of feed in mmw is moisture content in %,ρbulk is bulk density in g/cc.In order to compare the relative importance of the variables, all predictor variables werestandardized to z-scores and the standardized beta coefficient were determined by running theregression model on the standardized variables. The beta coefficients are listed in Table 4.5.The most important predictor variable is the specific pressing force because an increase ofone standard deviation in FSP is associated with an increase of 0.841 standard deviation in thenet specific energy consumption if the other two variables are held constant. The next mostimportant predictor variable is the product of the F80 and moisture (interaction effect), where95a change of one standard deviation in the interaction results in an increase of 0.558 standarddeviation in ESP. The bulk density has a minor negative effect. An increase of one standarddeviation in bulk density is associated with a decrease of 0.227 standard deviation in ESP.Table 4.5: Summary results of regression on standardized variablesVariable Coefficient estimate Standard error t-value Pr(>t) RankConstant -2.21E-17 3.34E-02 0 1FSP 0.841 0.0345 24.4 < 2E-16 1ρbulk -0.227 0.0344 -6.6 6.70E-10 3F80 ·w 0.558 0.0344 16.2 < 2E-16 2Residuals:Min 1st quartile Median 3rd quartile Max-1.06 -0.30 -0.06 0.23 1.35The measured specific energy is plotted against the predicted specific energy, using thethree variable linear regression model (Eq. 4.2) in Figure 4.14. The majority of the data occuralong the parity line with gradient 1.96R2 =0.8280.00.51.01.52.02.53.03.54.00.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Predicted specific energy (kWh/t)Measured specific energy (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.14: Measured versus predicted net specific energies for three variable regressionmodelThe residuals versus fitted plot is shown in Figure 4.15. The majority of the residuals(measured-predicted) are within ±0.5 (red lines) so in absolute terms the model predictionsare generally within ±0.5 kWh/t. However, some points are above 0.5 (under predicted) andrelatively few fall below -0.5 (over predicted).97-0.75-0.50-0.250.000.250.500.750.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Predicted specific energy (kWh/t)Residuals (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.15: Residuals versus predicted net specific energy for the three variable regressionmodelFigure 4.16 shows the relative errors of the model predictions and the majority of the dataare within the 25% (red lines) limits. Therefore in relative terms, the model predictions aregood within ±25%. The average magnitude of the relative error is 9.25% with a standarddeviation of 7.36%.98-50-40-30-20-10010203040500.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0Measured specific energy (kWh/t)Relative error (%)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.16: Relative error versus measured net specific energy for the three variableregression modelIn Figure 4.17, the residuals are plotted against the specific pressing force. The plot showsthat the three variable model does not have a bias based on the specific pressing force.99-0.75-0.50-0.250.000.250.500.750.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5Specific pressing force (N mm2)Residuals (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.17: Residuals versus specific pressing force for the three variable regression modelA similar plot, where the residuals are plotted against the feed F80 is shown in Figure 4.18where there is a slight bias that the residuals increase with increase in feed F80.100-0.75-0.50-0.250.000.250.500.750 5 10 15 20 25 30Feed F80 (mm)Residuals (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.18: Residuals versus feed F80 for the three variable regression modelThe residuals versus feed moisture plot is shown in Figure 4.19, where there is a slight biasthat the residuals are decreasing with increase in feed moisture as the blue fitted trendline isnot completely horizontal.101-0.75-0.50-0.250.000.250.500.750 2 4 6 8 10Moisture (%)Residuals (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.19: Residuals versus feed moisture for the three variable regression modelThe residuals versus feed bulk density plot is shown in Figure 4.20, where there is no biasin the residuals with respect to feed bulk density.102-0.75-0.50-0.250.000.250.500.751.0 1.5 2.0 2.5Bulk density (g/cc)Residuals (kWh/t)AgAu (B)Au (C)Au (I)Au (L)Cu-Au-AgCu-Au (A)Cu-Au (C)Cu-Au (E)Cu-Au (M)Cu-Au (R)Cu-Mo (H)Cu-Mo (P)DolomiteGranodioriteHematiteKimberliteLimestoneNiPdTaconiteWFigure 4.20: Residuals versus feed bulk density for the three variable regression modelA regression model from consideration of eight parameters and their two-wayinteractionsAnother stepwise regression that considered all eight parameters and their two-way interac-tions was run with AIC as the criteria for predictor additions or eliminations. Table 4.6 showsthe results of the stepwise regression. The resulting model has a residual SE of 0.133 kWh/t on76 degrees of freedom, and a R2 of 0.91 and an adjusted R2 of 0.894. The F-statistic for themodel is 58.9 (p < 2 ·10−16) on 13 and 76 degrees of freedom.103Table 4.6: Summary results of stepwise regression on eight parameters and their two-wayinteractionsVariable Coefficient estimate Standard error t-value Pr(>t)Constant 4.14 1.14 3.61 5.40E-04FSP 0.511 0.166 3.08 2.85E-03F80 0.0161 0.0049 3.28 1.58E-03ρbulk -2.96 0.64 -4.59 1.70E-05w -0.191 0.234 -0.81 4.18E-01W pi 0.0338 0.0135 2.51 1.40E-02P1mm -0.0208 0.0047 -4.46 2.80E-05m -3.80 1.32 -2.87 5.30E-03ρbulk ·w 0.221 0.116 1.91 6.05E-02FSP ·w 0.0980 0.0300 3.26 1.65E-03w ·m -0.609 0.171 -3.55 6.60E-04ρbulk ·m 3.80 0.78 4.85 6.40E-06Wpi ·m -0.0617 0.0210 -2.94 4.34E-03FSP · ρbulk -0.167 0.104 -1.6 1.14E-01Residuals:Min 1st quartile Median 3rd quartile Max-0.262 -0.091 -0.0081 0.091 0.327The model was further simplified until all the predictor variables in the remaining modelwere statistically significant at a 0.05 significance level. A variable was included in the modelif the analysis of variance (ANOVA) indicated it was significant and also if the inclusion ofthe variable increased the adjusted R2. The resulting simplified model has seven predictorvariables as shown in Table 4.7. The model has residual standard error of 0.153 kWh/t on 82degrees of freedom, and a R2 of 0.871 and an adjusted R2 of 0.86. The F-statistic for the modelis 78.8 (p < 2 ·10−16) on 7 and 82 degrees of freedom.104Table 4.7: Summary results of the simplified regression model that considered eightparameters and their two-way interactionsVariable Coefficient estimate Standard error t-value Pr(>t)Constant 1.76 0.24 7.39 1.13E-10FSP 0.178 0.036 4.88 5.10E-06F80 0.0123 0.0050 2.48 1.52E-02ρbulk -0.380 0.099 -3.85 2.34E-04W pi -0.00642 0.00186 -3.45 8.85E-04P1mm -0.0232 0.0049 -4.71 1.02E-05FSP ·w 0.103 0.014 7.58 4.65E-11w ·m -0.355 0.065 -5.45 5.21E-07Residuals:Min 1st quartile Median 3rd quartile Max-0.310 -0.086 -0.027 0.079 0.480Standardized beta coefficients were determined through regression on z-scores of the sevenpredictor variables. Table 4.8 shows that the interaction of specific pressing force and moisturehad the highest influence on the net specific energy as one standard deviation change in theinteraction would result in 1.07 standard deviation change in the net specific energy. Thepiston press work index has the least influence among the seven variables.105Table 4.8: Standardized beta coefficients of the seven-variable model of the net specificenergyVariable Coefficient estimate Standard error t-value Pr(>t) RankConstant 1.5E-16 4.0E-02 0 1FSP 0.385 0.0788 4.88 5.10E-06 4F80 0.177 0.0714 2.48 1.52E-02 6ρbulk -0.194 0.0504 -3.85 2.34E-04 5W pi -0.158 0.0457 -3.45 8.85E-04 7P1mm -0.506 0.107 -4.71 1.02E-05 3FSP ·w 1.068 0.141 7.58 4.65E-11 1w ·m -0.534 0.0979 -5.45 5.21E-07 2Residuals:Min 1st quartile Median 3rd quartile Max-0.758 -0.210 -0.066 0.194 1.18The seven variable model is expressed asESP = c0 + c1 ·FSP + c2 ·F80 + c3 · ρbulk + c4 ·Wpi + c5 · P1mm + c6 ·FSP ·w+ c7 ·w ·m (4.3)whereESP is net specific energy consumption in kWh/t,FSP is in N/mm2,F80 is 80% passing size of feed in mm,w is moisture content in %,ρbulk is bulk density in g/cc,W pi is operating work index from piston press test in kWh/t,P1mm is percentage of -1 mm material in the feed in %,m is slope of feed PSD in log-log space,ci are coefficients listed in Table 4.7.106Figure 4.21 compares the measured net specific energy against the predicted net specificenergy using the seven-variable regression model (Eq. 4.3).R2 =0.8710.00.51.01.52.02.53.03.50.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Predicted specific energy (kWh/t)Measured specific energy (kWh/t)Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteWFigure 4.21: Measured versus predicted net specific energies for seven variable regressionmodelThe residuals versus fitted plot for the model is shown in Figure 4.22. The majority ofthe residuals are within ±0.25 (red lines), so in absolute terms the model predictions are goodwithin ±0.25 kWh/t. However some points are above 0.25 (under predicted) and only one pointwas below -0.25 (over predicted).107-0.50-0.250.000.250.500.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Predicted specific energy (kWh/t)Residuals (kWh/t)Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteWFigure 4.22: Residuals versus predicted net specific energy for the seven variable regressionmodelRelative errors of the seven-variable regression model is shown in Figure 4.23 where ma-jority of data points are within red lines of ±15%. The average magnitude of the relative erroris 6.01% with a standard deviation of 4.92%.108-30-20-1001020300.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5Measured specific energy (kWh/t)Relative error (%)Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteWFigure 4.23: Relative error versus measured net specific energy for the seven variableregression modelFigures 4.24 and 4.25 shows plots of the residuals versus input parameters for the seven-variable model. The model has a slight bias toward the feed moisture and no apparent biastoward the other parameters.109-0.50-0.250.000.250.501.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5Specific pressing force (N mm2)Residuals (kWh/t)-0.50-0.250.000.250.500 5 10 15 20 25 30Feed F80 (mm)-0.50-0.250.000.250.500 1 2 3 4 5 6Moisture (%)Residuals (kWh/t)-0.50-0.250.000.250.501.50 1.75 2.00 2.25 2.50Bulk density (g/cc)Figure 4.24: Residuals versus FSP, F80, moisture, and bulk density plots for the sevenvariable regression model110-0.50-0.250.000.250.500.25 0.75 1.25Slope (log(% passing)/log(Size))Residuals (kWh/t)Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteW-0.50-0.250.000.250.5025 30 35 40 45 50 55Piston press work index (kWh/t)Residuals (kWh/t)-0.50-0.250.000.250.500 5 10 15 20 25 30 35 40 45Percentage passing 1mm in feed (%)Residuals (kWh/t)Figure 4.25: Residuals versus m, Wpi, and P1mm plots for the seven variable regression model1114.5.3 Cross-validation of the linear regression modelsCross-validation of the three variable regression modelIn order to evaluate the regression models, they were applied to results of HPGR tests that werenot considered as part of the data set to create the model. Since all tests were used to calibratethe model, the approach used was to randomly split the data into two subsets, for training andfor testing. Fitting a model to the training set and evaluating the resulting model with usingthe testing set is called holdout cross validation. The three-variable regression model was fittedto 79 training data sets that were randomly selected. The resulting model was evaluated usingthe remaining 78 test data sets. Table 4.9 shows results of 30 repeat runs of holdout crossvalidation. The average R2 value of 0.826 is very close to to the value of 0.828 found throughfitting all 157 data sets. In addition, the average values of the coefficients found throughfitting the 79 data sets to the three variable regression model are in close agreement with thecoefficients found through fitting the 157 data sets. The average relative errors obtained byevaluating the resulting models using the testing sets can be an estimate of out-of-sample errorsince the testing sets are not used in the model training. The true mean of average relative errorfor out-of-sample is estimated to be 9.44±0.27 (95% C.I., n=29).112Table 4.9: Cross-validation results for the three variable modelRun Coefficients R2 SE Avg. rel. error % SSE# c0 FSP ρbulk F80 ·w Testing Training Test Train1 0.432 0.492 -0.382 0.00749 0.871 0.205 9.8 8.9 4.66 3.142 0.927 0.400 -0.467 0.00745 0.708 0.218 10.5 9.1 3.83 3.563 0.742 0.435 -0.475 0.00927 0.844 0.228 9.2 10.0 3.18 3.894 0.643 0.437 -0.429 0.00892 0.813 0.203 9.6 8.9 3.86 3.085 0.565 0.467 -0.410 0.00776 0.809 0.233 9.1 9.5 3.20 4.086 0.527 0.480 -0.465 0.00997 0.846 0.226 10.0 9.5 3.61 3.827 0.656 0.424 -0.413 0.00950 0.831 0.216 10.8 8.7 3.66 3.498 0.581 0.433 -0.372 0.00899 0.814 0.224 9.7 9.8 3.34 3.789 0.640 0.467 -0.448 0.00783 0.754 0.225 8.9 9.8 3.50 3.7910 0.689 0.449 -0.477 0.00887 0.840 0.214 9.1 9.2 3.50 3.4511 0.830 0.432 -0.524 0.00898 0.859 0.201 9.7 8.8 3.97 3.0212 0.748 0.467 -0.525 0.00788 0.818 0.205 9.4 8.5 4.14 3.1413 0.941 0.420 -0.566 0.00901 0.799 0.232 7.9 10.7 3.11 4.0214 0.584 0.440 -0.409 0.00929 0.860 0.202 10.4 8.4 3.95 3.0515 0.771 0.435 -0.491 0.00884 0.835 0.210 9.3 9.2 3.63 3.3116 0.757 0.477 -0.586 0.00978 0.878 0.193 10.0 8.9 4.58 2.8017 0.599 0.458 -0.457 0.00939 0.834 0.224 9.3 9.4 3.28 3.7618 0.561 0.433 -0.347 0.00789 0.804 0.230 8.4 10.5 3.17 3.9619 0.788 0.448 -0.520 0.00807 0.847 0.209 8.8 9.0 3.86 3.2820 0.645 0.448 -0.452 0.00864 0.858 0.192 9.9 8.3 4.20 2.7821 0.808 0.406 -0.423 0.00727 0.807 0.208 9.3 9.4 4.14 3.2522 0.774 0.418 -0.442 0.00766 0.812 0.219 8.9 9.3 3.64 3.5923 0.782 0.456 -0.541 0.00926 0.791 0.242 8.9 10.0 2.73 4.4024 0.687 0.456 -0.491 0.00887 0.841 0.214 8.9 9.4 3.55 3.4325 0.627 0.391 -0.317 0.00864 0.802 0.221 11.0 8.7 3.70 3.6526 0.599 0.429 -0.381 0.00868 0.832 0.224 9.1 9.7 3.22 3.7627 0.770 0.444 -0.507 0.00850 0.819 0.221 8.6 9.5 3.34 3.6528 1.064 0.408 -0.610 0.00882 0.829 0.218 8.5 10.2 3.82 3.5529 0.737 0.437 -0.506 0.00964 0.880 0.208 9.9 8.6 3.85 3.2430 0.891 0.441 -0.591 0.00890 0.849 0.191 10.4 7.5 4.50 2.74Max 1.064 0.492 -0.317 0.00997 0.880 0.242 11.0 10.7 4.66 4.40Min 0.432 0.391 -0.610 0.00727 0.708 0.191 7.9 7.5 2.73 2.74Avg. 0.712 0.441 -0.467 0.00867 0.826 0.215 9.4 9.2 3.69 3.48SD 0.137 0.024 0.073 0.00074 0.036 0.013 0.73 0.68 0.46 0.41113Crosss-validation of the seven-variable regression modelHoldout cross-validation was performed by randomly splitting the 90 data sets into 45 data setsfor training and 45 data sets for testing. For each run of a cross-validation, the seven-variableregression model was fitted to a training set and the resulting model was evaluated using atesting set.Table 4.10 shows results of 30 repeat runs from cross-validation. Depending on Theaverage R2 value of 0.879 is very close to the value of 0.871 found through fitting all 90data sets. Also the average value of the coefficients found through fitting 45 data to the sevenvariable regression model are in close agreement with the coefficients found through fitting all90 data.Table 4.11 compares the average magnitude of the relative errors and SSE between trainingand testing sets for the 30 repeat runs of cross-validation. The true mean of average relativeerror for out-of-sample is estimated to be 7.35±0.3 (95% C.I., n=29).114Table 4.10: Cross-validation results for the seven variable regression modelRun Coefficients R2 SE# c0 FSP F80 ρbulk Wpi P1mm FSP ·w w ·m1 1.65 0.224 0.0123 -0.448 -0.00674 -0.0200 0.105 -0.328 0.878 0.1582 1.88 0.179 0.0178 -0.534 -0.00422 -0.0184 0.104 -0.398 0.819 0.1823 1.87 0.153 0.0159 -0.440 -0.00660 -0.0250 0.116 -0.378 0.852 0.1724 1.42 0.209 0.0179 -0.212 -0.00920 -0.0191 0.088 -0.344 0.898 0.1295 1.67 0.168 0.0197 -0.361 -0.00787 -0.0200 0.115 -0.418 0.852 0.1696 1.55 0.235 0.0053 -0.314 -0.00552 -0.0179 0.063 -0.188 0.861 0.1287 1.64 0.183 0.0132 -0.371 -0.00517 -0.0280 0.111 -0.361 0.875 0.1568 1.15 0.295 0.0214 -0.392 -0.00382 -0.0098 0.050 -0.192 0.895 0.1459 1.53 0.196 0.0186 -0.369 -0.00524 -0.0181 0.095 -0.355 0.808 0.17610 1.47 0.193 0.0147 -0.345 -0.00207 -0.0217 0.109 -0.417 0.881 0.15311 1.94 0.172 0.0193 -0.640 -0.00199 -0.0227 0.125 -0.454 0.867 0.17412 0.86 0.299 0.0315 -0.406 -0.00607 -0.0078 0.062 -0.152 0.902 0.15413 1.68 0.214 0.0167 -0.488 -0.00681 -0.0193 0.096 -0.285 0.906 0.14614 1.64 0.184 0.0149 -0.351 -0.00961 -0.0161 0.079 -0.192 0.927 0.12615 1.45 0.274 0.0048 -0.300 -0.00488 -0.0192 0.055 -0.168 0.911 0.12716 1.80 0.141 0.0029 -0.216 -0.00611 -0.0340 0.115 -0.376 0.920 0.14117 1.83 0.154 0.0153 -0.452 -0.00497 -0.0273 0.119 -0.388 0.884 0.16518 1.94 0.137 0.0083 -0.368 -0.00534 -0.0291 0.120 -0.418 0.845 0.17819 1.75 0.143 0.0038 -0.247 -0.00576 -0.0261 0.114 -0.398 0.878 0.14520 2.25 0.100 0.0125 -0.562 -0.00542 -0.0286 0.144 -0.492 0.881 0.15021 1.95 0.131 0.0092 -0.407 -0.00476 -0.0268 0.119 -0.402 0.883 0.16822 1.49 0.211 0.0212 -0.426 -0.00330 -0.0192 0.098 -0.380 0.798 0.19023 2.02 0.241 0.0164 -0.659 -0.00653 -0.0163 0.079 -0.279 0.877 0.14024 1.69 0.238 0.0119 -0.488 -0.00412 -0.0190 0.081 -0.283 0.919 0.13525 1.79 0.215 0.0068 -0.393 -0.00572 -0.0230 0.084 -0.289 0.921 0.12326 1.81 0.219 0.0146 -0.449 -0.00923 -0.0258 0.104 -0.351 0.855 0.15127 1.65 0.219 0.0161 -0.323 -0.00986 -0.0195 0.079 -0.284 0.932 0.11828 2.06 0.195 0.0108 -0.423 -0.00948 -0.0212 0.085 -0.336 0.875 0.14329 1.43 0.303 0.0233 -0.465 -0.01043 -0.0094 0.065 -0.225 0.908 0.14430 1.75 0.123 0.0119 -0.207 -0.00875 -0.0248 0.126 -0.463 0.871 0.163Max 2.25 0.303 0.0315 -0.207 -0.00199 -0.0078 0.144 -0.152 0.932 0.190Min 0.86 0.100 0.0029 -0.659 -0.01043 -0.0340 0.050 -0.492 0.798 0.118Avg. 1.69 0.198 0.0143 -0.402 -0.00619 -0.0211 0.097 -0.333 0.879 0.152SD 0.28 0.052 0.0063 0.112 0.00226 0.0059 0.024 0.092 0.034 0.019115Table 4.11: Relative errors and error sums of squares of 30 cross-validations for the sevenvariable regression modelRun Relative error % SSE# Testing set Training set Testing set Training set1 7.77 5.99 1.31 0.932 6.11 7.11 0.87 1.233 6.76 6.58 0.96 1.104 8.40 4.88 1.60 0.625 7.55 5.90 1.07 1.056 6.75 5.17 1.91 0.617 6.96 6.00 1.18 0.908 7.51 5.84 1.82 0.779 6.21 6.76 0.88 1.1510 8.40 5.85 1.46 0.8711 7.58 7.73 1.30 1.1212 7.71 6.18 1.65 0.8813 7.06 5.68 1.23 0.7914 8.38 5.13 1.82 0.5915 7.54 4.85 1.91 0.6016 6.71 5.39 1.37 0.7317 7.27 6.03 1.07 1.0018 6.32 6.26 0.82 1.1819 6.61 5.74 1.50 0.7720 8.60 5.36 1.49 0.8421 6.85 5.70 0.98 1.0522 6.52 7.58 0.86 1.3423 7.81 5.67 1.60 0.7324 6.37 5.48 1.45 0.6725 6.50 4.92 1.55 0.5626 8.75 5.55 1.49 0.8427 8.79 4.36 1.79 0.5128 7.51 5.88 1.58 0.7629 8.05 6.10 1.73 0.7730 7.21 6.27 1.26 0.98Max 8.79 7.73 1.91 1.34Min 6.11 4.36 0.82 0.51Avg. 7.35 5.86 1.38 0.86SD 0.80 0.76 0.33 0.221164.6 DiscussionThe net specific energy consumption of the HPGR increases linearly with the specific pressingforce. The feed top size and particle size distribution significantly affect the reduction ratioachieved. It was shown that the reduction ratios of tests on feeds with top sizes of 32 mmand 12.5 mm were significantly different. A feed with finer particle size distribution results ina lower reduction ratio. Since piston press tests are performed on samples with a finer feedparticle size distributions and smaller top sizes than used in pilot HPGR testing the decreasedreduction ratio needs to be considered. On the other hand, normalized product PSDs matchregardless of feed top sizes or specific pressing force.The database contains a sufficiently large number of experimental observations to drawgeneralizations and to develop linear regression models. The database also included the HPGRtest results on a variety of ore types and test conditions.Two linear regression models were developed for net specific energy; 1) the three-variablemodel (Eq. 4.2) and 2) the seven-variable model (Eq. 4.3). In addition, the selected regressionmodels were cross-validated by fitting the models to one-half of the observations and thenverifying the predictive capability of the model by evaluating it on the other half of the ob-servations in the database. The seven-variable model has a higher R2 of 0.871 compared tothe three-variable model with a R2 of 0.828. Also the seven-variable model has lower averagerelative error compared the three-variable model. However, the three variable model is basedon a much larger database and is simpler to use. Table 4.12 shows summary of the regressionmodels of net specific energy.117Table 4.12: Comparison of the net specific energy model statisticsRegression models: Three variable Seven variableR2 0.828 0.871Residual SE (kWh/t) 0.213 0.153Approximate 95% predictioninterval±0.42(tα=0.025 d. f .=153 ·0.213) ±0.31(tα=0.025 d. f .=82 ·0.153)The true mean of averagerelative error forout-of-sample (%)9.44±0.27 7.35±0.30Observations in the database 157 90The development of these linear regression models are useful for predicting the net specificenergy in HPGR operation in the absence of samples for pilot-scale tests. The estimated netspecific energy from the models can also be used as an input for simulation of HPGR circuits.118Chapter 5DIRECT CALIBRATION METHODOLOGY5.1 IntroductionFor early stage projects, large samples for HPGR pilot testing are difficult and expensive toobtain. In addition, many deposits will contain individual geometallurgical or lithologicalunits. In these cases, pilot-scale testing of each unit is not practical. Composite samplesrepresenting a blend of all geometallurgical units may be used for pilot-scale HPGR tests,however the results may not cover the range of responses in the deposit, potentially resultingin an underdesigned circuit.This chapter describes a testing methodology that allows prediction of HPGR performancefrom piston press tests.The direct calibration methodology involves performing both HPGR and piston press testson the same composite sample, and then calibrating the results of the piston press tests againstHPGR tests. Piston press testing can then be conducted on samples representing differentrock types and the responses are entered into the calibrated model to predict the energy-sizereduction parameters. The direct calibration methodology involves the following six steps:1191. Conduct pilot-scale HPGR tests on the composite feed over a range of specfic pressingforces,2. Conduct piston press tests on the same composite feed sample over a range of pistonpressures,3. Calibrate piston press pressure against specific pressing force,4. Calibrate size reduction achieved in piston press tests against size reduction achieved inHPGR tests,5. Compare normalized product size distributions from piston press and HPGR tests, and6. Perform piston press tests on other geometallurgical units and use calibration models topredict HPGR performance.Each step is discussed in detail in the following sections. The main outputs for each sampleinclude the net specific energy, specific pressing force, and product particle size distribution.5.2 Conducting HPGR Tests (Step 1)The objective of conducting HPGR pilot tests on a composite sample at various specific press-ing force is to determine:• the relationship between net specific energy consumption and specific pressing force,• the product particle size distributions at different specific pressing forces,• the relationship between net specific energy consumption and the achieved reductionratio (F50/P50).It is demonstrated in section 4.2 that the net specific energy of the HPGR increases linearlywith specific pressing force over the range of specific pressing forces typically used in HPGR120operations. It is therefore possible to define the relationship between net specific energyconsumption and specific pressing force with only two HPGR pilot tests. However, 3 to 4HPGR tests are recommended to reliably define the relationship. Figure 5.2 shows the specificenergy consumption versus the specific pressing force (red squares). The relationship is definedby the slope and the y-intercept of the fitted line at zero specific pressing force.5.3 Conducting Piston Press Tests (Step 2)Two representative subsamples (10–15 kg) of the composite are collected during the homoge-nization of the feed. Samples are obtained using a rotary riffle splitter to ensure that they arerepresentative. One subsample is used for determining the feed PSD and the other is usedfor piston press testing. To prepare the sample for piston press testing, the representativesubsample is crushed from -32 mm to -12.5 mm using a reverse-closed circuit procedure. Thereasons for this procedure are:1. The feed to an industrial scale HPGR is often prepared by crushing and screening in areverse-closed circuit.2. As shown in Figure 5.1, crushing and screening in reverse-closed circuit produced moretop size particles (-12.5+8 mm) than crushing in regular closed circuit, and having moretop size particles reduces sampling variation in number of top size pariticles in eachsubsamples. For the Ni-Cu ore reverse-closed circuit produced F80 of 10.31 mm whereasregular closed circuit produced F80 of 8.98 mm.1210 10 20 30 40  50 60  70  80  90 100 0.01 0.1 1 10 100 Cumulative percent passing [%] Particle size [mm]  Regular closed circuit  Reverse closed circuit  Figure 5.1: Comparison of using regular and reverse-closed circuits for feed preparation ofpiston press test on Ni-Cu oreThe moisture of the crushed sample for piston press tests is adjusted to match the moisturecontent in the HPGR tests. After moisture adjustment, subsamples for individual piston presstests are taken. As discussed in section 3.4.3, sampling after moisture adjustment reduced thevariation between subsamples, which could be attributed to reduced segregation of coarse andfine particles.In order to compare compaction and size reduction of ores with different bulk densities,the sample volume is held constant for each piston press test. A 240 mL cup is filled withsample until it is full and any excess material is scraped off the top with a straight edge. Carewas taken to keep the mass differences between samples minimal by gauging the mass ofindividual samples against the pre-calculated mass of a 240 mL sample based on the bulkdensity. The bulk density was determined by shaking a 1 L sample for 10 min in a similarmanner to determining the 700 mL sample mass for the Bond ball mill grindability test. Themass of the 240 mL sample is recorded before placing it in the die. Each 240 mL sample is122pressed to a pre-determined pressure and the specific energy input is calculated by numericalintegration of the force-displacement curve.The pressed test product is removed from the die by removing the bottom plate. The productis wet sieved using a 325 mesh screen to thoroughly de-agglomerate the product particles andthen the sample is dried over night. The dried samples are sieved on a Haver & Boecker sieveshaker for 15 min to determine the particle size distribution.5.4 Calibration between Ppiston and FSP (Step 3)In order to relate the results of piston press tests to those from HPGR testing, the piston presspressure needs to be calibrated against the specific pressing force. This is achieved by pressinga minimum of four sets of 240 mL subsamples at different pressures.In subsection 3.4.3, the errors in the piston press testing were discussed. The relative stan-dard error in specific energy measurement was found to be 1.15% and coefficient of variationwas found to be 3.63%. The relationship between piston press pressure and specific energy canbe defined reasonably well by using results of four piston press tests. An example of the testparameters and results is shown in Table 5.1.Table 5.1: Example of piston press test parameters and resultsTest No.Force Pressure Energy F50 P50 Reduction[kN] [MPa] [kWh/t] [mm] [mm] ratioT121 400 69 0.914.691.85 2.54T122 600 103 1.25 1.67 2.80T123 900 155 1.67 1.36 3.44T124 1390 239 2.47 1.13 4.16123y = 0.009x + 0.291 y = 0.441x + 0.251 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 50 100 150 200 250 300 350 HPGR specific pressing force [N/mm2] Net specific energy  [ kWh/t] Piston Pressure [MPa] Piston pressure Specific pressing force Figure 5.2: Illustration of calibration between specific pressing force and piston pressure,such that both give the same net specific energy to the sampleFigure 5.2 shows the fitted regression lines for specific energy versus the piston presspressure (blue line) and HPGR specific pressing force (red line). The regression equationsare used to calculate the piston press pressure required to deliver the same net specific energyto the sample for a given specific pressing force. For example, an HPGR test performed at aspecific pressing force of 4 N/mm2 and a piston press test performed at a pressure of 190 MPaboth result in a specific energy input of 2.0 kWh/t, as illustrated by the green line in Figure 5.2.The generic formula relating piston press pressure, Ppiston, to HPGR specific pressing force,FSP, is derived in equations 5.1–5.4.124ESP (kW h/t) = m1 · Ppiston (MPa) + b1 (5.1)ESP (kW h/t) = m2 ·FSP (N/mm2) + b2 (5.2)m1 · Ppiston (MPa) + b1 = m2 ·FSP (N/mm2) + b2 (5.3)Ppiston =m2m1·FSP +b2− b1m1(5.4)The calibration of piston pressure against specific pressing force can be defined by theslope (m2/m1) and the y-intercept, which is equal to (b2− b1) /m1. The direct calibrationmethodology was applied to 15 ore types and the ore-specific calibration equations for pistonpress pressure against specific pressing forces were determined. The calibration slopes andintercepts for each ore type are shown in Table 5.2.125Table 5.2: Slopes and intercepts for defining calibration between piston pressure and specificpressing forceNo. Ore type Slope Intercept1 Dolomite 53.9 4.42 Cu-Mo (H) 93.0 -56.83 Cu-Mo (P) 48.6 22.24 Cu-Au-Ag 59.3 -7.05 Ni-Cu 50.7 30.66 Au (B) 70.3 9.57 Au (C) 70.0 31.38 W 70.9 -17.49 Cu-Au (A) 48.4 -4.210 Kimberlite 61.8 33.711 Cu-Mo (C) 58.7 -19.012 Cu (M) 48.2 56.713 Cu (E) 41.9 38.214 Pd 62.8 -86.315 Taconite 45.0 -15.9Figure 5.3 compares the net specific energy for HPGR tests to those predicted from pistonpress tests using ore specific calibration equations. The pressures are calculated using theslopes and the intercepts for the ore specific calibration between piston pressure and specificpressing force. All predictions lie within the ±10% envelope.1260.51.01.52.02.53.00.5 1.0 1.5 2.0 2.5 3.0Specific energy of piston press tests at calibrated pressures  [kWh/t]Net specific energy of HPGR tests [kWh/t]R2 = 0.98(±10% envelope)DolomiteCu-Mo (H)Cu-Mo (P)Cu-Au-AgNi-CuAu (B)Au (C)WCu-AuKimberliteCu-Mo (C)Cu-Au (M)Cu-Au (E)PdTaconiteFigure 5.3: Specific energy prediction using ore-specific calibration5.5 Calibration between Reduction Ratios (Step 4)The reduction ratio achieved in the HPGR test needs to be calibrated against the ratio achievedin the piston press test, for the following reasons:• As was demonstrated in section 4.3, the reduction ratio decreases with feed top size.Therefore, the reduction ratio achieved in the piston press test on -12.5 mm feed will belower than the reduction ratio achieved in HPGR tests on -32 mm feed;• When the same -12.5 mm feed is used in both piston press tests and HPGR tests, theparticle size distribution of the piston press product is similar to that of the centre productof the HPGR test. Figures 5.4 and 5.5 show that the piston product size is comparable tothat of the center product or the scaled product of the HPGR. The scaled product PSD isexpected from an industrial scale HPGR, where the full product consists of 90% centre127and 10% edge. The pilot-scale HPGR used in this program produces around 73% centreand 27% edge product.• The feed moisture reduces the operating gap, and thus, extruding material through anarrower gap requires higher power draw and significantly increases specific energyconsumption while not necessarily achieving a higher reduction ratio. Such a significantenergy increase is not observed in the piston press testing. Therefore, it is important toinclude the effect of moisture in the scale-up model of the reduction ratio.01234560.5 1.0 1.5 2.0 2.5P50 [mm]Specific energy input [kWh/t]Ore: Au (C)CentreEdgeScaledPistonFigure 5.4: Piston press test produces product comparable to the centre product of HPGRwhen both tests are carried out on -12.5 mm feed12801234560.5 1.0 1.5 2.0 2.5P50 [mm]Specific energy input [kWh/t]Ore: Au (B)CentreEdgeScaledPistonFigure 5.5: Piston press test produces product comparable to the centre product of HPGRwhen both tests are carried out on -12.5 mm feedReduction ratios achieved in the HPGR test and the piston press test can be directly cal-ibrated on the basis of specific energy. The ore-specific calibration of reduction ratio can beused for other ore types within the same deposit.In order to determine reduction ratios of piston press test at the same net specific energy asHPGR tests, the reduction ratio achieved in piston press tests are modelled by a simple line. Ifscatter plot of F50/P50 versus ESP has a curvature, Eq. 2.30 is used instead of a line.F50P50= k · Eb +1 (2.30 revisited)For example, four piston press tests on -12.5 mm feed and four pilot HPGR tests on -32 mmfeed were performed on the Cu-Au-Ag ore. The net specific energy and the reduction ratiosachieved in the tests are shown in Table 5.3.129Table 5.3: Reduction ratios achieved in piston press and HPGR tests on Cu-Au-Ag orePiston tests HPGR tests Piston reduction ratio at the same ESPESP F50/P50 ESP F50/P50 F50/P500.62 3.50 1.55 7.53 5.980.95 4.44 1.74 8.33 6.451.39 5.34 1.99 10.28 7.052.13 7.60 2.61 12.06 8.46The reduction ratios from piston press tests on the Cu-Au-Ag ore were modelled usingEq. 2.30. Figure 5.6 (A) shows the fitted model by a gray line. The reduction ratios of pistonpress test at the same net specific energy as HPGR are calculated using the fitted model and areshown by hollow red line. Then the model calculated reduction ratios of piston press tests areplotted against the reduction ratios of HPGR test as shown in Figure 5.6 (B). The regressionline through the blue squares becomes the reduction ratio calibration equation for the ore.024681012140.0 0.5 1.0 1.5 2.0 2.5 3.0Reduction ratio F50/P50Net specific energy input [kWh/t](A)HPGR F50/P50 Piston F50/P50 @ same EspPiston F50/P50 Fitted line to piston datay = 1.85x - 3.37R² = 0.96024681012144 6 8 10HPGR  F50/P50Piston F50/P50 @ same Esp(B)Figure 5.6: (A) Fitting reduction ratio achieved in piston press tests to Eq. 2.30 anddetermining reduction ratios at the same ESP as the HPGR tests; (B) Calibrationof reduction ratios of piston press tests against the reduction ratios achieved inHPGR tests130The following is an example of where the scatter plot of piston press reduction ratio versusspecific energy is best modelled by a line. Four piston press tests were conducted on the Ni-Cu ore. Figure 5.7 (A) shows that the piston press reduction ratio versus specific energy ismodelled by a line. The piston press reduction ratios at the same net specific energy as HPGRwere calculated using the fitted line. The hollow red circles are the calculated piston pressreduction ratios. Figure 5.7 (B) shows the calibration of piston press reduction ratios againstthe reduction ratios of HPGR.012345670.0 0.5 1.0 1.5 2.0 2.5 3.0Reduction ratio F50/P50Net specific energy input [kWh/t](A)HPGR F50/P50 Piston F50/P50 @ same EspPiston F50/P50 Fitted line to piston datay = 1.31x - 0.56R² = 0.96012345670 2 4 6 8HPGR  F50/P50Piston F50/P50 @ same Esp(B)Figure 5.7: Fitting reduction ratio achieved in piston press tests to a line and determiningreduction ratios at the same ESP as the HPGR tests; (B) Calibration of reductionratios of piston press tests against the reduction ratios achieved in HPGR testsTable 5.4 shows the slopes and intercepts of the ore-specific calibration lines for scalingreduction ratios of piston press tests to that of HPGR tests.131Table 5.4: Slopes and intercepts of the ore-specific calibration lines for scaling-up reductionratios of piston press testsOre type Slope Intercept R2Au (C) 1.54 -2.23 0.998Au (B) 1.93 -1.15 1.00Cu-Au-Ag 1.85 -3.37 0.96Ni-Cu 1.31 -0.56 0.96W 2.54 -4.24 0.888Cu-Mo (P) 1.61 -1.40 0.993Cu-Au 1.43 -0.33 0.987Cu-Mo (H) 0.67 1.09 0.988Kimberlite 1.47 -2.75 0.994Pd 1.21 -0.91 0.904Taconite 1.46 -0.81 0.952Cu-Au (M) 1.01 -0.95 0.623Cu-Au (E) 1.41 -2.91 0.785Dolomite 0.29 3.76 0.531Figure 5.8 compares reduction ratios achieved from HPGR tests to the scaled reductionratios from piston press tests, using the ore-specific calibration equations. The plot shows thatthe predicted reduction ratios fit the HPGR reduction ratios well.132024681012140 2 4 6 8 10 12 14Scaled-up reductionratio of piston pressReduction ratio of HPGRR2 = 0.98Au (C)Au (B)Cu-Mo (P)Cu-Au-AgNiWCu-AuKimberliteCu-Mo (H)PdTaconiteCu-Au (M)Cu-Au (E)Dolomite1:1 lineFigure 5.8: Comparison of the HPGR reduction ratios with scaled reduction ratios of thepiston press tests5.6 Comparison of Normalized PSD Curves (Step 5)To scale the product particle size distribution from the piston press test to the HPGR results, thenormalized product PSDs need to match. Figure 5.9 shows the normalized PSDs of productsfrom piston press tests on -12.5 mm samples and from HPGR tests on -32 mm and -12.5 mmfeeds (gold (C) and gold (B) ores). The normalized product PSDs and the fitted curves matchwell. The results confirm that the normalized product curves for product from piston presstesting can be used to predict the actual HPGR product particle size distributions.13301020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized product PSDs of Au (C) ore-32mm HPGR -12.5mm HPGR-12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Au (C) ore-32mm HPGR -12.5mm HPGR-12.5mm Piston01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized product PSDs of Au (B) ore-32mm HPGR -12.5mm HPGR-12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Au (B) ore-32mm HPGR -12.5mm HPGR-12.5mm PistonFigure 5.9: Comparison of normalized PSDs of products from piston tests on -12.5 mm feedand HPGR tests on -32 mm and -12.5 mm feeds5.7 Scale-up of Results (Step 6)Once the calibration model between the specific pressing force and piston pressure (Step 3) isobtained for the composite sample of an ore body, the piston press pressures can be calculatedfor each desired specific pressing force, using Eq. 5.4. Piston press tests can then be conducted134at the calculated piston pressure on various geometallurgical units within the deposit. Thereduction ratio obtained from the piston press test is scaled to the HPGR reduction ratio, usingthe calibration of reduction ratios (Step 4). Then, the full product size distribution is obtainedand reconstituted using the normalized product PSDs from the piston press test (Step 5).5.8 Summary of the Direct Calibration MethodologyThe direct calibration methodology has the following six steps:1. Conduct HPGR pilot-scale tests on a composite feed sample,2. Perform multiple piston press tests on subsamples of the composite feed that was usedin the HPGR tests,3. Calibrate the net specific energy against piston pressure Ppiston and specific pressingforce FSP, to derive an equation for Ppiston required to deliver the same ESP for a givenFSP.4. Calibrate the reduction ratios achieved in piston press tests against reduction ratios achievedin HPGR tests,5. Compare the normalized PSDs of products from HPGR tests and piston press tests,6. Perform piston press tests on various geometallurgical units and scale-up the piston presstest results to that of the HPGR test results.Figure 5.10 shows the block model of the direct calibration methodology.135Composite sample(~1 tonne)3 HPGR tests Piston press testsPressure calibrationReduction ratio calibrationDrill core samples for block modelsPiston press test at desired pressuresEnergy-size reduction relationship predictionFigure 5.10: Block diagram of the direct calibration methodologyThe direct calibration methodology requires about 1 tonne of composite sample represent-ing the main geometallurgical units. The sample is used to conduct three pilot-scale HPGRtests and piston press tests at range of pressures. Once the calibrated models are generated,the models can used to predict the energy–size reduction information for other ore types fromthe deposit. Approximately 5–10 kg of drill core sample from each geometallurgical unit isrequired for piston press tests. This testing approach allows the prediction of specific energiesand product PSDs for HPGR’s for a range of ore types using small samples. The results assistwith the equipment sizing and selection and can be used for geometallurgical mapping of thedeposit.136Chapter 6DATABASE-CALIBRATEDMETHODOLOGY6.1 IntroductionIn Chapter 5, HPGR and piston press tests were conducted on 15 ore types and the directcalibration methodology was applied to enable the use of piston press for the prediction of netspecific energy and PSDs for the HPGR. The application of the direct calibration methodologygenerated 45 pairs of specific pressing force and piston pressure data sets. Those data forma database used in the development of an empirical model to predict the HPGR performancefrom piston press test results, without the need for pilot-scale HPGR testing. The ability topredict HPGR performance using only piston press tests can be useful for projects as follows:• Early stage projects where there is insufficient sample for pilot-scale HPGR tests;• Projects for which there is an interest to assess HPGR-based comminution circuits atthe scoping level stage without committing a large quantity of sample for HPGR pilottesting;• Projects that do not have sufficient budget to cover the high cost of collecting large sam-ples and conducting the pilot-scale HPGR test work but there is an interest in evaluatingthe HPGR technology.137The database-calibrated methodology is a natural extension of the direct-calibration methodol-ogy and the procedure is the same except that it does not require HPGR testing for calibration.In other words, the main difference is that instead of performing calibration HPGR testing andobtaining ore specific calibrations, piston press tests are calibrated using the database generatedon ore samples where both piston press and HPGR testing has been conducted.The database-calibrated methodology has the following four steps:1. Calculate the piston pressure (Ppiston) equivalent to the desired specific pressing forceusing the database and multiple linear regression equation. This is the keystep that relatesPpiston to FSP without conducting pilot-scale HPGR tests to determine the ESP vs. FSPrelation.2. Perform the piston press tests at the calculated piston pressures and obtain specific energyand product size distributions on test products.3. Use piston press test results to predict the HPGR results, using the linear regressionequations for the particle size reduction ratio.4. Predict energy–size reduction performance of the HPGR.The development of the empirical model for determining the appropriate piston pressure andthe steps to determining specific energy are described in detail in the next sections.6.2 Calculation of Piston Pressure (Step 1)To develop the empirical model that relates HPGR specific pressing force to piston pressure,a database was created from 15 different ore types. Table 6.1 summarizes the feed propertiesand operating parameters of the HPGR tests.138Table 6.1: Summary table of HPGR test variables used in the development of an empiricalcalibrationUnits Mean Std. Dev. Min MaxFSP [N/mm2] 3.47 1.02 1.47 5.00ESP [kWh/t] 1.82 0.48 0.73 2.61Moisture [%] 2.38 0.55 1.48 3.30ρbulk [g/cc] 1.84 0.22 1.55 2.20F80 [mm] 21.95 2.93 16.68 27.44F50 [mm] 13.87 3.81 5.20 20.21Figure 6.1 shows the scatter plot of Ppiston versus FSP, along with the regression line fittedto the data. The coefficient of determination is only 0.61, which was not considered suitable.Therefore, an empirical model for Ppiston was considered with more variables than only theFSP. Both HPGR and piston press test feed variables were considered as the predictors for thedevelopment of the empirical model for calculating the required Ppiston to deliver equivalentnet specific energy into the sample for a given specific pressing force. The considered variableswere:• Specific pressing force (FSP).• Feed moisture (w) and bulk density(ρbulk), which greatly influence the net specificenergy in the HPGR tests, but their influence on specific energy in the piston press test isless pronounced.• Feed coarseness to the HPGR tests(FHPGR50)and piston press tests(FPiston50)and theirratio(FHPGR50 /FPiston50). It is important to account for the difference in feed particle size.• Percentage passing 1 mm in the feeds to both the HPGR(PHPGR1mm)and the piston press(PPiston1mm)tests.• Piston press work index(Wpi)and slope of HPGR feed PSD in log-log space (m).1390501001502002503003504000 1 2 3 4 5 6 7Piston Pressure [MPa]Specific Pressing Force [N/mm2]R2 = 0.61 95% CIDolomiteCu-Mo (H)Cu-Mo (P)Cu-Au-AgNiAu (B)Au (C)WCu-AuKimberliteCu-Mo (C)Cu (M)Cu (E)TaconitePdFigure 6.1: Direct correlation between Ppiston and FSP; regression line and its 95%confidence interval are shownTable 6.2 shows the statistically significant variables that were included in the empiricalmodel for calculating the required piston pressure that delivers equivalent net specific energy tothe sample. Only the constant term was not statistically significant with p-value well over 0.05criteria. The empirical piston pressure model has a residual standard error (SE) of 25.6 MPa on38 degrees of freedom and an adjusted R2 of 0.863. The F-statistic for the piston pressuremodel is 39.8 (p = 6.48 · 10−15) on 6 and 38 degrees of freedom. The approximate 95%confidence interval is ±8.4 MPa and the 95% prediction interval is ±51.9 MPa.140Table 6.2: Summary of the empirical model for calculating the required piston pressure thatdelivers equivalent net specific energy into the sample for a given specific pressingforceVariable Coefficient estimate Standard error t-value Pr(>t)Constant 5.53 58.9 0.09 0.93FSP 53.3 3.8 14.07 < 2e-16w 24.3 9.4 2.58 0.014ρbulk -86.2 25.8 -3.35 1.85E-03FHPGR50 13.1 2.4 5.53 2.55E-06FHPGR50 /FPiston50 -44.4 12.2 -3.64 8.00E-04PPiston1mm 2.98 0.6 4.76 2.81E-05Residuals:Min 1st quartile Median 3rd quartile Max-47.3 -13.4 -4.4 10.6 71.8When ore-specific Ppiston vs FSP relationship is unknown due to lack of pilot-scale HPGRtest results, the required piston pressure for a given specific pressing force can be calculated byEq. 6.1.Ppiston = 5.53+53.3FSP +24.3w−86.2ρbulk + (6.1)+13.1FHPGR50 −44.4FHPGR50 /FPiston50 +2.98PPiston1mmwherePpiston is the estimation of required piston pressure in MPa to deliver equivalent net specificenergy for a given specific pressing force;FSP is the given specific pressing force in N/mm2;w is the feed moisture content in %;ρbulk is the feed bulk density in g/cc;F50 is 50% passing sizes of feed in mm;141PPiston1mm is percentage passing 1 mm in feed to piston press test.Figure 6.2 compares the required piston pressure, which is determined from ore-specificcalibration equation to deliver same net specific energy as a given specific pressing force,with the predicted pressures using Eq. 6.1. The coefficient of determination for the empiricalmodel is 0.863, which means the model explains 86.3% of variance in the data. The averagemagnitude of relative error is 9.06% with standard deviation of 8.55%.R2 =0.8630501001502002503003500 50 100 150 200 250 300 350Model predicted pressure [MPa]Required piston pressure [MPa] Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteWFigure 6.2: The required pressure versus the modelled pressure to input same specific energyto the sample as in HPGR operation6.3 Conducting Piston Press Tests (Step 2)The second step of the database-calibrated methodology is to perform the piston press testsat the pressures calculated by using the empirical model (Eq. 6.1). Figure 6.3 comparesthe measured net specific energies of HPGR tests with net specific energies of piston presstests at calculated pressures using the empirical model. The lack of ore-specific calibration142between Ppiston and FSP results in greater scatter than when pilot scale calibration is conducted.However, the net specific energy predictions lie within ±25% of the measured value. Theresidual standard deviation is 0.186 kWh/t.0.00.51.01.52.02.53.00.0 0.5 1.0 1.5 2.0 2.5 3.0Specific energy of piston press testsat calculated pressure [kWh/t]Measured net specific energy of HPGR tests [kWh/t]R 2 = 0.85225% envelopeCu-Au (A)DolomiteAu (C)Au (B)Cu-Mo (P)Cu-Au-AgPdTaconiteCu-Au (E)Cu-Au (M)KimberliteWNi-CuCu-Mo (H)Figure 6.3: Specific energy prediction using the empirical calibration equation6.4 Scaling to HPGR Reduction Ratio (Step 3)The reduction ratio achieved in the piston press has to be scaled to the HPGR results. Figure6.4 shows the scatter plot of reduction ratios achieved in the HPGR and the piston press testsalong with the regression line with coefficient of determination of 0.635.143024681012140 2 4 6 8 10F50/P50 HPGRF50/P50 Piston pressR2 = 0.635 Au (C)Au (B)Cu-Mo (P)Cu-Au-AgNi-CuWCu-AuKimberliteCu-Mo (H)PdTaconiteCu-Au (M)Cu-Au (E)DolomiteCu-Mo (C)Figure 6.4: Direct correlation of reduction ratios achieved in the HPGR and the piston presstestsIncluding other feed parameters in the empirical model for scaling the reduction ratioachieved with the piston press test to the HPGR result was expected to reduce the variation.The following feed parameters were considered as predictor variables for the empirical modelof scaling reduction ratio.• Reduction ratio achieved in piston press test(RRpiston);• Feed moisture (w) and bulk density(ρbulk);• 50% passing size of HPGR feed(FHPGR50)and piston press feed(FPiston50)and their ratio(FHPGR50 /FPiston50);• Percentage passing 1 mm in the feeds to both the HPGR(PHPGR1mm)and the piston press(PPiston1mm)tests;• Piston press work index(Wpi)and slope of HPGR feed in log-log space (m).144Table 6.3 shows the statistically significant variables that were included in the empirical modelfor scaling the reduction ratio achieved with the piston press to the HPGR results. The em-pirical reduction ratio scaling model has a residual standard error (SE) of 0.94 on 40 degreesof freedom, and a R2 of 0.828 and an adjusted R2 of 0.811. The F-statistic for the empiricalreduction ratio scaling model is 48.1 (p = 9.22 · 10−15) on 4 and 40 degrees of freedom. Theapproximate 95% confidence interval is ±0.3 and the 95% prediction interval is ±1.9.Table 6.3: Summary of the empirical model for scaling the reduction ratio achieved in thepiston press test to the HPGR resultVariable Coefficient estimate Standard error t-value Pr(>t)Constant 1.86 1.25 1.49 0.143RRpiston 1.41 0.11 12.42 2.60E-15w -1.02 0.32 -3.20 0.00269FHPGR50 -0.41 0.08 -4.97 1.29E-05FHPGR50 /FPiston50 2.31 0.39 5.86 7.47E-07Residuals:Min 1st quartile Median 3rd quartile Max-2.22 -0.76 0.23 0.55 1.75The best fit empirical model for predicting the reduction ratio of HPGR is Eq. 6.2.RRHPGR = 1.86+1.41RRpiston +2.31FHPGR50 /FPiston50 −0.41FHPGR50 −1.02w (6.2)whereRRHPGR is the estimated reduction ratio in the HPGR;RRpiston is the reduction ratio achieved in piston press test;F50 are 50% passing sizes of feeds in mm;w is moisture content in %.145Figure 6.5 compares measured HPGR reduction ratio with the modelled reduction ratioobtained from the Eq. 6.2. The average magnitude of relative error is 12.6% with standarddeviation of 7.9%.R2 =0.828024681012140 2 4 6 8 10 12 14Predicted HPGR reduction ratio (F50/P50)Measured HPGR reduction ratio (F50/P50)Au (B)Au (C)Cu-Au-AgCu-Au (A)Cu-Au (E)Cu-Au (M)Cu-Mo (H)Cu-Mo (P)DolomiteKimberliteNi-CuPdTaconiteWFigure 6.5: Modelled reduction ratio of HPGR with the empirical model (Eq. 6.2)6.5 Prediction of Energy–Size Reduction Relationship(Step 4)Once the specific energy is determined in piston press testing (Step 2) and the expectedHPGR reduction ratio is estimated (Step 3), the normalized piston press product size distribu-tion can be fitted using Eq. 2.4.F( xX50)= 100(1− exp(−A( xX50) (m( xX50 )+n)))(2.4 revisited)146Then the normalized PSD can be converted to the predicted product PSD for the HPGR. Thenormalized PSDs of the HPGR test and the piston press test can be assumed to match if thefollowing are true:• The feeds to HPGR tests and piston press tests are products from a cone crusher;• The feed is not manipulated—scalped or truncated;• The normalized PSDs of products are a result of comparable specific energy input.The assumption that normalized curves for products of the HPGR tests and piston presstests match is supported by the following comparisons of normalized plots and fitted curves fora variety of ore types. Figure 6.6 compares the normalized product PSDs of HPGR and pistonpress tests for the copper-molybdenum (P) ore. The plots show that fitted curves match verywell.01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized  particle  size  [mm/mm]Normalized product PSDs of Cu‐Mo (P) ore‐32mm  HP GR ‐12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized  particle  size  [mm/mm]Fitted curves of Cu‐Mo (P) ore‐32mm  HP GR ‐12.5mm PistonFigure 6.6: Comparison of normalized product PSDs of the HPGR tests and the piston presstests on Cu-Mo (P) oreFigure 6.7 compares the normalized product PSDs of the HPGR and piston press tests for anickel-copper ore. The fitted curves match the normalized product PSDs match very well with147a small discrepancy in the higher percentage passing sizes. This discrepancy is believed to bedue to the HPGR breaking coarse particles larger than the operating gap with certainty whereas piston press does not eliminate any particles with certainty.01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized product PSDs of Ni-Cu ore-32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Ni-Cu ore-32mm HPGR -12.5mm PistonFigure 6.7: Comparison of normalized product PSDs of the HPGR tests and the piston presstests on Ni-Cu oreFigure 6.8 compares normalized product PSDs of HPGR tests and piston tests for a tungstenore. As in Figure 6.7, the normalized PSD of HPGR is showing higher cumulative percentagepassing at larger particle sizes, but the overall agreement is very good.14801020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized PSDs of tungsten ore -32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of tungsten ore -32mm HPGR -12.5mm PistonFigure 6.8: Comparison of normalized product PSDs of the HPGR tests and the piston presstests on a tungsten oreFigure 6.9 compares the normalized product PSDs for a taconite ore and again the normal-ized curves match extremely well.01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized PSDs of taconite -32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of taconite -32mm HPGR -12.5mm PistonFigure 6.9: Comparison of normalized product PSDs of the HPGR tests and the piston presstests on a taconite ore149Figure 6.10 compares the normalized PSDs of the HPGR and piston tests for a copper-molybdenum (H) ore. Occasionally, the normalized PSD of the HPGR and piston tests do notmatch well, especially in the coarse sizes. However, it is assumed that the normalized PSDsobtained from piston press test is the same as from the HPGR test.Assuming the match between the normalized curves can be a major disadvantage andsource of error for the database-calibrated methodology compared to the direct calibrationmethodology where the assumption is confirmed before proceeding.01020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized PSD of Cu-Mo (H) ore -32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Cu-Mo (H) ore -32mm HPGR -12.5mm PistonFigure 6.10: Comparison of normalized product PSDs of the HPGR and the piston press testson the Cu-Mo (H) oreFigure 6.11 compares the normalized PSDs of the HPGR and piston press test productsfor a copper-gold-silver ore. The fitted curves show a small discrepancy in the low range ofcumulative percentage passing. This could be caused by differences in wet and dry screeningefficiency. The piston press products are wet sieved first while the HPGR products are not.15001020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized PSD of Cu-Au-Ag ore-32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Cu-Au-Ag ore-32mm HPGR -12.5mm PistonFigure 6.11: Comparison of normalized product PSDs of the HPGR tests and the piston presstests on the Cu-Au-Ag oreOverall, the discrepancies in the normalized PSDs are small. The results show that thepiston press test data can be used with a reasonable level of confidence to predict the HPGRproduct PSDs.6.6 Summary of the Database-Calibrated MethodologyThe database-calibrated methodology has the following four steps:1. Calculate the piston pressure that corresponds to the desired specific pressing force withthe use of the empirical model (Eq. 6.1);2. Perform the piston press tests at the calculated pressures;3. Scale the reduction ratios achieved in piston press tests to HPGR operation with the useof the empirical model (Eq. 6.2);1514. Predict the energy–size reduction performance of HPGR, assuming normalized PSDs arethe same.Figure 6.12 shows the block diagram of the database-calibrated methodology.Drill core sample s( 5- 10 kg )Piston press testson - 12.5mm materialRegression equation for piston pressureEnergy - si ze reduction relationship Piston press result s Specific energy Reduction ratioRegression equation for scaling of reduction ratioFigure 6.12: Block diagram of the database-calibrated methodologyThe database-calibrated methodology has the advantage over the direct calibration method-ology in that it does not require large sample for pilot-scale HPGR testing. Instead a regressionequation is used to estimate the piston pressure corresponding to the desired specific pressingforce. Another regression equation is used to scale the size reduction ratio achieved in thepiston press test to the HPGR test.As the database of direct calibration tests grows to include a wider array of ore types,the regression equations will be applicable to more ore types and will become even morestatistically reliable. The procedure can also evolve by grouping the database, for exampleby ore types such as porphyry or massive sulphides to improve the accuracy of this approach.152Chapter 7SIMULATION-BASED METHODOLOGY7.1 IntroductionThe direct calibration and the database-calibrated methodologies are empirical in that theyrequire either direct calibration to pilot-scale HPGR tests or calibration to a database usingfitted empirical equations. The methodologies are limited in that they cannot be used forsimulation of the HPGR size reduction process.The simulation-based methodology that was developed and is presented in this chapter issemi-empirical in that it characterizes the ore by its energy–breakage relationship at differentparticle sizes. It then uses the ore characteristics information to simulate the energy–sizereduction performance for the HPGR.The simulation-based methodology involves piston press testing on multiple classes ofnarrowly sized particles at multiple energy levels in each size class. Five to eight size classes ofparticles are prepared for each ore type, and each class is pressed at three energy levels. Testingmultiple size classes of particles at three energy levels is analogous to the JK Drop Weight test.The difference is the breakage mechanism, which is particle bed compression instead of singleparticle impact breakage. In addition, the breakage function is modified to incorporate theeffect of particle size. The simulation-based methodology involves the following four steps:1531. Prepare five to eight classes of narrowly sized particles and then conduct piston presstests on each size class at three energy levels. The specific energy input for each test is de-termined from numerical integration of force-displacement curves and the tn-parametersare determined from the particle size distribution of each test.2. Calibrate the relationship between the specific energy and t10 using the appropriate modelform.3. Calibrate the relationship between t10 and other tn parameters using the appropriatemodel form.4. Simulate the energy–size reduction of the ore using an Excel or similar spreadsheet, andmodels developed in steps 2 and 3.These four steps are explained in detail in the following sections.7.2 Piston Press Tests on Narrowly Sized Particles (Step 1)Table 7.1 lists the size classes and nominal specific energy inputs used in this study. Each oretype had at least five of the size classes. The multiple size classes are tested in order to captureparticle size effect on the energy–breakage characteristics of the tested ores. Testing on sizeclasses as wide range as possible provides possibility of capture particle size effect properly.154Table 7.1: Summary of size classes and nominal specific energy levels used in the pistonpress testsSize Size Geometric mean Nominal specific energyclass intervals particle size levels [kWh/t]1 -12.5+11.2 mm 11.8 mm 0.25 1.25 3.002 -11.2+9.5 mm 10.3 mm 0.25 1.25 3.003 -9.5+8.0 mm 8.7 mm 0.25 1.25 3.004 -8.0+6.3 mm 7.1 mm 0.25 1.25 3.005 -6.3+5.6 mm 5.9 mm 0.25 1.25 3.006 -5.6+4.0 mm 4.7 mm 0.25 1.25 3.007 -4.0+2.8 mm 3.3 mm 0.25 1.25 3.008 -2.8+2.0 mm 2.4 mm 0.25 1.25 3.00The same piston-die arrangement and 240 mL volume of sample was used for performingpiston press tests on the size classes as described in subsection 3.4.2. The specific energy inputfor each test is calculated from numerical integration of the force-displacement curve. Fromeach particle size distribution, the t10 was determined. The t10 was defined in subsection 2.3.3as the cumulative percentage finer than 1/10th of the original geometric mean particle size. Inother words, the t10 represents a breakage index or more correctly a size distribution “fineness”index. A higher t10 represents a finer product from a higher specific energy input. Figure 7.1illustrates the determination of t10 from three tests on the -12.5+11.2 mm size class. In thefigure, the geometric mean size is 11.8 mm and t10 is the cumulative percent passing 1.18 mm.15541.725.58.001020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Particle size [mm]-12.5 +11.2 mm2.97 kWh/t1.32 kWh/t0.23 kWh/tFigure 7.1: Illustration of determination of t10 from particle size distributions of piston presstests on -12.5+11.2 mm size classIn a similar manner, other tn values can be determined from the particle size distributionsby finding the cumulative percent passing corresponding to tn-sizes, which are 1/nth of theoriginal geometric mean particle size. Table 7.2 lists tn sizes for different size classes. t0-sizerepresents the aperture size of the upper sieve of the size class and the t0 value is always 100%as all particles in a size class pass through the upper sieve size.156Table 7.2: tn sizes for different size classesSize classes [mm]tn sizes -12.5+11.2 -11.2+9.5 -9.5+8.0 -8.0+6.7t0-size 12.5 11.2 9.5 8.0t1.2-size 9.86 8.60 7.26 6.10t2-size 5.92 5.16 4.36 3.66t4-size 2.96 2.58 2.18 1.83t10-size 1.18 1.03 0.87 0.73t25-size 0.47 0.41 0.35 0.29t50-size 0.24 0.21 0.17 0.15t75-size 0.16 0.14 0.12 0.107.3 Defining Relationship between ESP and t10 (Step 2)7.3.1 Compression breakage of narrowly sized particlesFour model equations were considered for the breakage function to model the relationshipbetween specific energy input and t10 for compression breakage of a bed of narrowly sizedparticles.Two of the models,• Eq. 2.24 t10 = A(1− exp (−b · Ecs))and• Eq. 2.25 t10 = M(1− exp(− fmat · x · k (Ecs −Emin)))were described in theliterature review (Shi and Kojovic, 2007).In practice, k is equal to 1 and Emin is usually taken to be zero (Napier-Munn, 2014). SoEq. 2.25 effectively takes form of Eq. 7.1.t10 = M(1− exp(− fmat · x · Esp))(7.1)157The third model is a modified version of equation 7.1 and incorporates the effect of particlesize as its square root and is shown in Eq. 7.2. Preliminary results of this research werepublish using Eq. 7.2 as it gave better fit than Eq. 7.1 (Davaanyam et al., 2013, 2015). Alsorepresenting particle size effect as the square root of the particle size gave better fit in singleparticle compression tests (Nadolski et al., 2014).t10 = M(1− exp(− f ∗mat · x0.5 · Esp))(7.2)whereM is a fitted parameter representing the maximum attainable value of t10 [%];f ∗mat is a fitted parameter representing material breakage property [t/kWh·mm−0.5].The fourth model was discovered during external review process of this dissertation andis a more general form of Eq. 7.2 and allows the exponent 0.5 to vary and be ore-specific asshown in Eq. 7.3 (Shi et al., 2015).t10 = M(1− exp(− f ∗mat · xn · Esp))(7.3)whereM is a fitted parameter representing the maximum attainable value of t10 [%];f ∗mat is a fitted parameter representing material breakage property [t/kWh·mm−n];n is an exponent for the initial particle size and is ore specific.The four models were compared using data from testing on a tungsten ore. Table 7.3summarizes the goodness of fit of the considered models and shows that Eq. 7.3 has the highestR2 value, the lowest sum of squared error and the lowest residual standard error. Also theuncertainty of prediction of t10 by Eq. 7.3 is about ±3.84%, which is the lowest.158Table 7.3: t10–ESP models are compared for a tungsten oreModel Eq. # Equation form R2 SSE SE 95% CI1 2.24 t10 = A(1− exp (−b · Ecs))0.875 406 4.30 8.912 7.1 t10 = M(1− exp(− fmat · x · Ecs))0.958 161 2.70 5.613 7.2 t10 = M(1− exp(− f ∗mat · x0.5 · Esp))0.980 85 1.97 4.084 7.3 t10 = M(1− exp(− f ∗mat · xn · Esp))0.984 72 1.85 3.84Figure 7.2 shows the poor fit of Eq. 2.24 for the tungsten ore. It is necessary to model t10as a function of not only specific energy, but also particle size, which is absent from Eq. 2.24.0510152025303540450 1 2 3 4t 10[%]Sp.Energy [kWh/t]Tungsten oreR2 = 0.875Fit line-12.5+11.210.328.727.105.944.733.352.37Figure 7.2: t10 modelled as function of specific energyFigure 7.3 shows the model fit that incorporates particle size and specific energy for thetungsten ore according to Eq. 7.1. The plot is a significant improvement over Eq. 2.24, butthere is some scatter.1590510152025303540450 10 20 30 40t 10[%]Esp·Size [kWh/t∙mm]Tungsten oreR2 = 0.958Fit line-12.5+11.2-11.2+9.5-9.5+8.0-8.0+6.3-6.3+5.6-5.6+4.0-4.0+2.8-2.8+2.0Figure 7.3: t10 modelled as function of specific energy and particle sizeFigure 7.4 shows the model fit incorporating the square root of the particle size for the sametungsten ore based on Eq. 7.2, which shows a good fit with a high coefficient of determinationof 0.98.1600510152025303540450 1 2 3 4 5 6 7 8 9 10 11t 10[%]Sp. Energy· x0.5 [kWh/t·mm0.5]Tungsten oreR2 = 0.98Fit line-12.5+11.2-11.2+9.5-9.5+8.0-8.0+6.3-6.3+5.6-5.6+4.0-4.0+2.8-2.8+2.0Figure 7.4: t10 modelled as function of specific energy and square root of particle sizeFigure 7.5 shows the model fit of allowing the exponent n in Eq. 7.3 to be ore-specificand for the tungsten ore n was 0.628. Eq. 7.3 has three fitted parameters while the other threemodels have two fitted parameters. The fitting of an extra parameter is justified when it resultsin the lowest residual standard error. In instances where there are only few data points, theloss of one degree of freedom could result in Eq. 7.2 to have lower residual standard error thanEq. 7.3 as the standard error has the degrees of freedom term(SE =√SSE/df).1610510152025303540450 3 6 9 12 15t 10[%]Sp.Energy·xn [kWh/t∙mmn]Tungsten oreR2 = 0.984Fit line-12.5+11.2-11.2+9.5-9.5+8.0-8.0+6.3-6.3+5.6-5.6+4.0-4.0+2.8-2.8+2.0Figure 7.5: t10 modelled by Eq. 7.3 , which allows the exponent (n) of particle size to beore-specificEquation 7.3 has been fitted to five different ore types and the fitted parameters are listed inTable 7.4. The parameter M represents the maximum value of t10 achievable for the ore, f ∗matrepresents how fast t10 approaches the maximum, and n represents the severity of particle sizeeffect. If an ore has a higher value of n, that means the breakage of the ore varies highly withparticle size. If an ore has a lower value of n, the breakage of the ore does not vary as muchwith particle size. Although very unlikely n=0 would mean that there is no particle size effect,i.e. ore breakage does not vary with particle size. For a given particle size, the product M · f ∗matis indicative of the softness of the ore. A higher value of M · f ∗mat indicates a softer ore at thesame particle size. In general, M · f ∗mat · xn can be used as competence indicator for the testedore at a particle size x. The coefficient of determination ranges from 0.976 to 0.998 indicatingan excellent fit over the range of ore types tested.162Table 7.4: List of fitted parameters and coefficient of determination for the relationshipbetween specific energy and t10Ore type M f ∗mat n M · f∗mat R2 SSE SE 95% CIW 43.1 0.171 0.628 7.39 0.980 71.8 1.85 3.84Cu-Mo (P) 55.4 0.290 0.395 16.06 0.998 5.7 0.69 1.51Au (C) 43.1 0.229 0.422 9.85 0.986 24.7 1.44 3.13Cu-Mo (H) 48.5 0.128 0.655 6.18 0.993 27.9 1.53 3.32Cu-Au 45.0 0.166 0.574 7.48 0.976 58.1 2.20 4.79Figure 7.6 shows the relationship between specific energy and t10 for the copper-molybdenum(P) ore and the fit to equation 7.3. The model describes the data very well for all particle sizeclasses.0 10 20 30 40 50 60 0 2 4 6 8 10 t 10 [%] Sp. Energy·xn [kWh/t·mmn] Cu-Mo (P) R2=0.999 Fitted line -12.5+11.2 -11.2+9.5 -9.5+8.0 -8.0+6.7 -6.7+5.6 Figure 7.6: Specific energy and t10 relationship of the Cu-Mo (P) ore163Figure 7.7 shows the relationship between specific energy and t10 for the gold (C) ore andthe model fit curve. It demonstrates that the model describes the relationship very well eventhough the lowest particle size tested is smaller than for the copper-molybdenum (P) ore.0 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 t 10 [%]  Sp. Energy· xn  [kWh/t·mmn] Au (C) R2 = 0.986 -12.5+11.2 -9.5+8.0 -6.7+5.6 -4.75+4.0 -2.8+2.0 Fitted line Figure 7.7: Specific energy and t10 relationship of the Au (C) oreFigure 7.8 shows the relationship between specific energy and t10 for the copper-molybdenum(H) ore. The model describes the relationship well except with minimal scatter at low energytests.1640 5 10 15 20 25 30 35 40 45 0 2 4 6 8 10 12 14 16 18 t 10 [%]  Sp. Energy· xn  [kWh/t·mmn] Cu-Mo (H) R2 = 0.993 -12.5+11.2 -11.2+9.5 -9.5+8.0 -8.0+6.3 -6.3+5.6 Fitted line Figure 7.8: Specific energy and t10 relationship of the Cu-Mo (H) ore7.3.2 Quantification of the effect of fine particles on compressionbreakageAs discussed in subsection 2.2.3, the gradual increase in the fraction of small particles(fines) decreases the breakage probability of coarse particles and eventually leads to the phe-nomenon of energy saturation. Since fine particles are absent in the piston press tests onnarrowly sized particles, there is an issue with determining the relationship between specificenergy and t10.To quantify the effect of the presence of fines on comminution, additional piston press testswere performed on narrowly sized particles in the presence of fines. The weight fraction offines (-0.5 mm) was varied from 0% to 75% in the -12.5+11.2 mm tests. It was found that thesame value of M , f ∗mat , and n that were obtained for coarse narrowly sized particles could stillbe used to describe the t10–ESP relationship for admixtures of coarse and fines after a simple165subtraction of the initial amount of fines from parameter M . In effect, the t10–ESP relationshipis defined by Eq. 7.4.t10 =(M − c · P f ines) (1− exp(− f ∗mat · xn · ESP))(7.4)where c is a fitted constant for percentage of fines in the feed, P f ines.Figure 7.9 compares the measured t10 and predicted t10 modelled by Eq. 7.4. The goodnessof fit is excellent for a range of fines fraction from 0% to 75%.0510152025303540450 5 10 15 20 25 30 35 40 45Modelled t 10 [%]Measured t10 [%]R2 = 0.9771:1 line75% fines50% fines25% fines0% finesFigure 7.9: Modelling of t10 as function of ESP and percentage of fines added to-12.5+11.2 mm particles;7.4 Defining Relationship between t10 and tn (Step 3)Figure 7.10 shows a scatter plot of tn and t10 values for the tungsten ore, along with the fittedlines. Once the tn versus t10 relationship is determined, the particle size distributions can bereconstructed with the knowledge of the calculated t10 value and the original geometric mean166size, i.e., each vertical line corresponds to a t10 value and thereby represents a particle sizedistribution.01020304050607080901000 5 10 15 20 25 30 35 40 45t n[%]t10  [%]t10 and tn relationship  of tungsten  oret1.2t2t4t25t75Figure 7.10: Scatter plot showing relationship between tn and t10 along with model fittedlines–each vertical line of t10 enables reconstruction of a particle sizedistributionThe relationship between t10 and tn are modelled using the following functions. A “plateaucurve” of the form y = ax/(b+ x) was found to give the better fit than exponential form y =a(1− exp(−bx) for t1.2, t2, and t4, while simple linear forms gave the best fit for t25, t50, andt75.t1.2 =β1 · t10(β2 + t10) (7.5)t2 =β3 · t10(β4 + t10) (7.6)t4 =β5 · t10(β6 + t10) (7.7)t25 = β7 · t10 (7.8)167t50 = β8 · t10 (7.9)t75 = β9 · t10 (7.10)where β1 to β9 are fitted constants.It is not surprising that a master curve can represent the relationship between tn and t10 fora variety of ore types since particle bed breakage produces self-similar PSDs. All five testedores display similar relationships between tn and t10. Figure 7.11 shows master curves fitted toall of the tested ores. The plots shows that the fitted curves represents all ore types reasonablywell.t1.2t2t4t25t7501020304050607080901000 10 20 30 40 50 60t n[%]t10 [%]Au (C)Cu-AuCu-Mo (H)Cu-Mo (P)WFigure 7.11: Master curve fitted to the five tested oresA consequence of the ability to represent the tn versus t10 relationship with a set of mastercurves is that size analysis can be conducted using only two screens that encompass the t10size eliminating the need to determine ore-specific tn versus t10 relationships and simplifying168the laboratory testing procedure. Table 7.5 lists the fitted constants describing the tn versus t10relationships.Table 7.5: Comparison of the fitted constants for the five ore types and the fitted constants ofthe master curvet1.2 t2 t4 t25 t50 t75β1 β2 β3 β4 β5 β6 β7 β8 β9Au (C) 103.9 5.4 115.7 20.5 195.3 88.7 0.60 0.43 0.32Cu-Au 107.1 5.7 123.4 23.2 152.4 65.5 0.59 0.37 0.25Cu-Mo (H) 105.1 5.7 121.2 23.8 183.0 84.3 0.57 0.31 0.19Cu-Mo (P) 103.4 5.6 117.9 24.5 170.8 83.6 0.66 0.42 0.30W 104.8 5.6 114.5 21.1 151.3 67.3 0.63 0.42 0.35Mean 104.8 5.6 118.5 22.6 170.6 77.9 0.61 0.39 0.28Std. dev. 1.4 0.1 3.7 1.7 19.1 10.7 0.03 0.05 0.0695% CI 1.8 0.2 4.6 2.2 23.8 13.3 0.04 0.06 0.08Master curve 104.7 5.5 116.3 21.7 155.6 68.8 0.62 0.40 0.307.5 Simulation of Energy Input versus Size Reduction(Step 4)Once the relationships between specific energy input and breakage index t10 (Step 2), andtn versus t10 (Step 3) are defined, the energy–size reduction performance can be simulatedby reconstituting the product particle size distributions for any given specific energy input.If a given set of feed and operating parameters are known, the specific energy input can beestimated through the use of one of the regression models (Eq. 4.2 or 4.3).A total of 36 pilot-scale HPGR tests performed on the five ore types were simulated.Table 7.6 shows that the test parameters of the simulated HPGR tests varied significantly. Forexample, the specific energy consumption ranged from 1.11 to 2.60 kWh/t and the F80 rangedbetween 4.43 mm and 27.44 mm. It is important to include a wide variety of test parameters inthe calibration of the simulation model for it to be applicable to wide variety of data sets. If169there is a need to simulate the HPGR performance for coarse feed that is out of the range of thesimulation, then the fitted parameters may not be applicable.Table 7.6: Variations in the test parameters of the simulated HPGR testsTest parameter Unit Mean Std. Dev. Min MaxOperating gap mm 19.42 1.91 15.72 23.45Sp. pressing force N/mm2 3.46 0.71 1.83 4.99Specific energy kWh/t 1.83 0.37 1.11 2.60F80 mm 18.76 6.94 4.43 27.44F50 mm 12.32 5.55 1.95 20.21The simulation can be run using spreadsheet software such as Excel. Simulation can beused:1. To predict the product particle size distribution by expending a specified amount ofenergy on material with a know size distribution, and2. To predict the specific energy required to generate a desired product particle size distri-bution from material with a knows size distribution.Figure 7.12 shows the schematic of the model for simulating the feed particle breakage in theHPGR. The simulation model makes the following assumptions.1. Similar to the Morrell/Tondo model discussed in subsection 2.1.5, feed particles are splitinto two fractions, according to a critical size, xc. However, the coarser particles inthe feed are assumed to break within a particle bed, and not by single particle impactbreakage. The breakage in the pre-crushing stage is modelled by Eq. 7.3 because theeffect of fine particles will be minimal.2. The product of the pre-crushing stage is combined with the finer particles and furtherbreakage is by grinding. In other words, the coarser fraction of the feed break via170both pre-crushing and grinding stages, while the finer fraction only break via grinding.The breakage in the grinding stage is modelled by Eq. 7.4 because when the particlebed is fully compacted the effect of fine particles on interparticle breakage needs to beconsidered.3. The total available energy is distributed between the pre-crushing and the grinding stages.The energy to the pre-crushing stage is assumed to be a function of the fraction of coarserparticles in the feed such thatEcrush = βsplit · fcoarse · EtotalEcrushSP = βsplit · ESPFor example, if a specific energy input of 1.5 kWh/t is being simulated and assuming thatthe coarse fraction represents 40% of the mass and βsplit is 0.157, the specific energyavailable for the pre-crushing stage would be 0.157 · 0.4 · 1.5/0.4 = 0.236 kWh/t andthe specific energy available for the grinding stage would be (1.5−0.157 ·0.4 ·1.5) /1 =1.41 kWh/t. The method used to estimate xc and βsplit is described below.171Coarser fraction Finer fractionPre - cru sh ingComb inerH P GR  feedE grinding = E total -  E pre- crushingE pre- crushingGrindingH P GR  productFigure 7.12: Schematic of the simulation modelIn order to calibrate the simulation model, the results of 36 HPGR tests were simultaneouslyfitted. Particle size below which is considered fines (P f ines in Eq. 7.4) in the feed to thegrinding stage was varied from 0.355 mm to 2.0 mm. The pre-crushing critical size (xc),the multiplication constant (c) for percentage of fines, and energy split(βsplit)were fittedso that the sum of squared residuals between the measured and the predicted product PSDs isminimized. In effect, the simulation model has three fitted parameters (xc, c, and βsplit). Thefitted parameters do not need to be fitted to individual ore types.Table 7.7 presents simulation results with varying particle sizes considered for fines. Defin-ing fines as the -1.4 mm fraction in the feed to the grinding stage resulted in optimal orminimum sum of squared error (SSE) for prediction of the P50 and the P80.172Table 7.7: Simulation results with varying definition of finesDefinition Fitted parameters P50 P80of fines c xc βsplit SSE R2 SE SSE R2 SE-2.0 mm 0.85 16.0 0.145 4.78 0.742 0.381 7.76 0.904 0.485-1.4 mm 1.08 16.0 0.157 4.61 0.743 0.374 7.76 0.905 0.485-1.0 mm 1.34 15.4 0.153 4.56 0.735 0.372 7.89 0.904 0.489-0.71 mm 1.65 14.4 0.140 4.61 0.719 0.374 7.84 0.905 0.487-0.50 mm 1.99 14.1 0.133 4.68 0.709 0.377 8.26 0.903 0.500-0.355 mm 2.35 14.0 0.122 4.74 0.702 0.379 8.55 0.903 0.509Figure 7.13 shows the predicted P50 and P80 from the simulation with the fines definedas particles finer than 1.4 mm. A worked example that shows numerical steps involved in thesimulations is presented in Appendix C.The standard error for the P50 and the P80 are 0.374 mm and 0.485 mm respectively on 33degrees of freedom. Figure 7.14 shows a scatter plot of the residuals versus predicted P50 andP80 particle sizes. The majority of residuals are within red lines indicating ±1 mm. Figure 7.15shows a scatter plot of relative percentage errors for the prediction versus the measured P50and P80. The mean of the relative percentage error for P80 is 5.5% and for P50 is 10.3%. Thefigures show that the simulation-based methodology can provide reasonably good predictionsof product particle size distribution based on the results of piston press tests on narrowly sizedparticles.1730246810120 2 4 6 8 10 12Predicted particle size [mm]Measured particle size [mm]P80P501:1 lineFigure 7.13: Simulation results of 36 HPGR tests by defining fines as -1.4 mm in the feed ofthe respective tests-1.5-1.0-0.50.00.51.01.50 2 4 6 8 10 12Residuals [mm]Predicted passing size [mm]P80P50Figure 7.14: Residuals versus predicted particle sizes for simulation of 36 HPGR tests1740510152025300 2 4 6 8 10 12Relative % error [%]Measured passing size [mm]P80P50Avg. % error for P80Avg. % error for P50Figure 7.15: Relative % error versus measured passing sizes for simulation results of 36HPGR tests7.6 Summary of Simulation MethodologyThe simulation methodology involves four steps:1. Perform piston press tests on narrowly sized particles;2. Define the ESP–t10 relationship for the ore by determining values of M , f ∗mat and n.3. Define the t10–tn relationship for the ore by determining values of βi or using the valuesfor the master curve for faster laboratory turnaround;4. Simulation of the energy–size reduction performance of the HPGR.Since the set of master curves can be used to define the relationships between tn and t10, thethird step could be considered optional.When HPGR test data is available it is possible to fine tune the simulation model for aspecific ore type. In other words, if the three fitted parameters (βsplit , xc, c) are allowed to175vary, they can be adjusted to improve the prediction model. However, HPGR test data is notrequired for the simulation as the following fitted parameters can be used.• -1.4 mm defines the size below which particles are considered to be fines (P f ines);• 1.08 as the multiplying constant c in equation 7.4;• 16 mm is the pre-crushing critical size (xc);• 0.157 as energy split constant(βsplit).The overall block diagram for the simulation methodology is shown in Figure 7.16.Drill core sample s( 5- 10 k g )Piston  pres s  test son 5 size clas ses at 3 energy levels eachDefine Models1. Energ y — t102. t10 — tn Energ y - s ize reduction simulationReconstitute product size distribution at E spU se regression eq uation to predict specific energy ( E sp )Figure 7.16: Block diagram of the simulation methodologyThe simulation-based methodology was applied successfully to five types of ore. Thepredictions are reasonably good despite the following:• sample requirement is only 10 kg;176• the simulated ore types had a range of feed compositions and operating variables;• the use of the master curves for the breakage appearance function.The simulation-based methodology is a tool that enables simulation of the effects of feed andoperating variables through the use of the empirical specific energy models (Eq. 4.2 or 4.3).During development of the simulation-based methodology, the following significant researchoutcomes were achieved.• An existing model that describes the degree of impact breakage of single particles wasmodified to simulate compression breakage in a particle-bed. It was found that applyingan ore-specific exponent to the particle size provides the best fit for particle-bed com-minution. Also the modified model accounts for interactions between coarse and fineparticles in the feed.• It was found that M values are much lower in particle bed compression breakage inpiston press test than single particle impact breakage in a Drop Weight test.• Master curves that describe the appearance function for compression breakage in particle-bed was presented. It is found that the particle-bed compression breakage has signifi-cantly lower t2 and t4 values compared to the single particle impact breakage.177Chapter 8COMPARISON OF HPGR ENERGYPREDICTION METHODOLOGIES8.1 IntroductionThree methodologies were developed to predict the HPGR performance using data from pistonpress testing. The methods are referred to as the Direct Calibration Methodology (Chapter5), the Database-calibrated Methodology (Chapter 6), and the Simulation-based Methodology(Chapter 7). To demonstrate the applicability and the differences between the methodologies,they were applied to a copper-gold mine project in central British Columbia and results werecompared. A composite sample representing 14 geometallurgical units from the copper-golddeposit was collected and nine pilot-scale HPGR tests were performed on the composite sam-ple. Table 8.1 lists the operating and feed parameters, and the main results of the nine HPGRtests.Based on the results of the pilot-scale HPGR test work, an HPGR-based comminutioncircuit was designed for the project. In order to assess the ore variability among the geometal-lurgical units, the direct calibration methodology was used. This approach allowed testing ofeach ore type with a minimum amount of sample resulting in significant cost savings as largesamples were not needed for pilot testing.178Table 8.1: Summary of operating and feed parameters and results of HPGR tests on theCentral BC copper-gold oreTest Operating parameters Feed parameters ResultsNo. TypeFSP ν H2O ρbulk F50 ESP m-dot[N/mm2] [m/s] [%] [g/cc] [mm] [kWh/t] [ts/hm3]1 Pressure 3.02 0.73 2.50 1.70 12.99 1.58 229.42 Pressure 3.99 0.75 2.50 1.70 12.99 2.01 224.73 Pressure 4.99 0.74 2.50 1.70 12.99 2.45 221.34 Speed 3.96 0.60 2.50 1.70 12.99 1.93 229.95 Speed 3.94 0.92 2.50 1.70 12.99 1.96 220.96 Moisture 3.97 0.75 0.90 1.70 12.99 1.72 245.57 Moisture 3.95 0.77 4.50 1.70 12.99 2.08 220.18 Top size 3.97 0.75 2.50 1.75 10.72 1.92 224.79 Top size 3.97 0.76 2.50 1.69 9.87 1.78 229.6Changes in feed and operating parameters are emphasized by bold fontThe results of the HPGR tests on the composite sample were directly calibrated against thepiston press test. Two equations were obtained as result of the direct calibration.1. By relating HPGR specific pressing force to piston press pressure, an equation was de-rived for calculating piston press test pressures required to deliver the equivalent specificenergy at the target specific pressing forces.2. By relating reduction ratios achieved in HPGR and piston press tests, an equation wasderived for scaling piston press reduction ratio to HPGR.Piston press tests were performed on 14 geometallurgical units at pressures calculated usingthe calibration equation and the energy requirements of each unit were determined. Alsopiston press tests results were evaluated at pressures calculated using Eq. 6.1 in order to assessthe accuracy of the database-calibrated methodology, when compared against the HPGR test179results. The simulation-based methodology was also applied and the results were comparedwith the HPGR results.8.2 Application of the Direct Calibration Methodology8.2.1 Calibration between HPGR and piston press testsThree pilot-scale HPGR tests were performed to evaluate the effect of specific pressing forceon the specific energy consumption. Figure 8.1 shows a linear relationship between specificenergy and specific pressing force. Four piston press tests were performed on a subsample ofthe composite feed sample used in the HPGR tests. Figure 8.2 shows the linear relationshipbetween specific energy input and piston pressure.y   =  0.4407x  +  0.25130.00.51.01.52.02.53.02.0 3.0 4.0 5.0 6.0Specific energy [kWh/t]Specific pressing  force [N/mm 2]Figure 8.1: HPGR specific energy versus specific pressing force for the copper-goldcomposite ore sample180y = 0.0091x + 0.29070.00.51.01.52.02.53.00 50 100 150 200 250 300Specific energy input [kWh/t]Piston Pressure [MPa]Figure 8.2: Piston press specific energy versus piston pressure for the copper-gold compositeore sampleThe relationship between specific pressing force and piston pressure was obtained by equat-ing the fitted equations as shown in Eq. 8.1, which simplifies to Eq. 8.2. Eq. 8.2 can be usedto determine the piston press pressure that corresponds to the equivalent specific energy at thetarget specific pressing force.0.0091Ppiston +0.2907 = 0.4407FSP +0.2513 (8.1)Ppiston = 48.43FSP −4.33 (8.2)Figure 8.3 shows the relationship between the specific energy and the reduction ratio forthe HPGR and piston press tests. The reduction ratio achieved with the piston press test and theHPGR tests were then related by equating the two fitted equations as shown in Eq. 8.3, which181simplifies to Eq. 8.4.0.6444RRHPGR−1.1897 = 0.9236RRPiston−1.4128 (8.3)RRHPGR = 1.43RRPiston−0.35 (8.4)y = 0.6444x - 1.1897R² = 0.9871y = 0.9236x - 1.4128R² = 0.98770.00.51.01.52.02.53.02.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0Specific energy [kWh/t]Reduction ratio F50/P50 [mm/mm]HPGRPistonFigure 8.3: Specific energy versus reduction ratios achieved in the HPGR and the pistonpress testsFigure 8.4 compares the normalized product PSDs from the HPGR tests and the piston presstests for the composite sample. Since the fitted curves match well, the piston press normalizedcurves combined with the reduction ratio (Eq. 8.4) can be used to predict the HPGR productPSDs.18201020304050607080901000.01 0.1 1 10 100Cum. percent passing [%]Normalized particle size [mm/mm]Normalized product PSDs of Cu-Au ore-32mm HPGR -12.5mm Piston01020304050607080901000.01 0.1 1 10 100Normalized particle size [mm/mm]Fitted curves of Cu-Au ore-32mm HPGR -12.5mm PistonFigure 8.4: Comparison of normalized product PSDs from the HPGR and piston press tests8.2.2 Piston press tests on geometallurgical unitsIndustrial scale HPGRs operate at specific pressing force in the range of 2.5–3.5 N/mm2.Eq. 8.2 was used to determine piston pressures corresponding to specific pressing forces of2.5, 3.0 and 3.5 N/mm2, which were found to be 117, 145 and 169 MPa, respectively. Table8.2 summarizes the piston press test results for the 14 different geometallurgical units. Thetable shows that the specific energy consumption at 3.5 N/mm2 can range from 1.48 kWh/tto 1.90 kWh/t, which means the energy consumption can vary by as much 28.4% between ge-ometallurgical units. Such information can be important to mine planning as it can significantlyaffect process operations. The piston press test can provide such information faster and in amore cost effective manner compared to conducting HPGR tests.183Table 8.2: Summary of the piston press tests on 14 geometallurgical unitsGeo F50 Specific energy [kWh/t] Reduction ratio F50/P50Unit [mm] 2.5N/mm2 3.0N/mm2 3.5N/mm2 2.5N/mm2 3.0N/mm2 3.5N/mm21 7.40 1.33 1.55 1.78 3.55 4.14 4.972 6.67 1.42 1.65 1.88 3.33 3.79 4.083 7.50 1.34 1.55 1.76 4.33 5.03 5.764 6.86 1.14 1.31 1.48 3.60 3.81 4.055 7.24 1.11 1.31 1.50 3.32 3.84 4.576 7.20 1.22 1.43 1.64 4.00 4.35 4.777 7.57 1.31 1.52 1.74 3.75 4.09 4.388 7.86 1.17 1.35 1.53 3.50 3.79 4.139 7.65 1.40 1.63 1.85 3.63 3.97 4.3710 7.85 1.38 1.63 1.87 4.14 4.50 4.8511 7.58 1.39 1.63 1.86 4.46 4.91 5.3312 7.12 1.20 1.39 1.58 3.29 3.46 3.6013 7.69 1.27 1.48 1.70 3.28 3.45 3.6214 7.60 1.42 1.66 1.90 3.68 3.97 4.30Mean 7.41 1.29 1.51 1.72 3.71 4.08 4.48Min 6.67 1.11 1.31 1.48 3.28 3.45 3.60Max 7.86 1.42 1.66 1.90 4.46 5.03 5.76Std. Dev. 0.36 0.11 0.13 0.15 0.39 0.48 0.61Coef. Var. 4.79 8.26 8.51 8.73 10.48 11.66 13.66Table 8.3 summarizes the scaled-up piston press test results. The net specific energyobtained from pilot HPGR testing are divided by screening efficiency, drivetrain inefficiency,and percentage of screen undersize in the product to estimate the circuit specific energy andsize the electrical motor (Nadolski, 2014;Klein et al., 2014). The circuit specific energy iscalculated using Eq. 8.5, assuming:• a closed circuit operation with a F50 of 13 mm,• a closing screen size of 4 mm with a screening efficiency of 90%, and184• an efficiency factor of 0.95 to account for the drivetrain inefficiencies.EcircuitSP =ESPεscreen ·0.95 · P4mm(8.5)whereEcircuitSP is the specific energy of closed circuit operationESP is the specific energy of open circuit operationεscreen is the assumed screening efficiency equal 0.9P4mm is the percentage of -4 mm material in the productTable 8.3: Summary of the scale-up results of the piston press testsGeo Scaled-up reduction ratio Circuit specific energy for -4mm productUnit 2.5N/mm2 3.0N/mm2 3.5N/mm2 2.5N/mm2 3.0N/mm2 3.5N/mm21 4.73 5.58 6.76 2.57 2.77 2.902 4.41 5.06 5.48 2.85 3.09 3.383 5.84 6.84 7.89 2.34 2.51 2.684 4.81 5.10 5.44 2.20 2.44 2.675 4.39 5.15 6.19 2.24 2.42 2.546 5.37 5.87 6.47 2.22 2.49 2.727 5.01 5.50 5.92 2.47 2.74 3.018 4.66 5.07 5.55 2.29 2.53 2.749 4.84 5.32 5.89 2.67 2.97 3.2210 5.57 6.09 6.59 2.47 2.78 3.0811 6.02 6.67 7.27 2.39 2.67 2.9412 4.36 4.60 4.79 2.42 2.73 3.0313 4.34 4.59 4.83 2.57 2.92 3.2514 4.91 5.32 5.80 2.70 3.03 3.33Mean 4.95 5.48 6.06 2.46 2.72 2.96Std. Dev. 0.56 0.68 0.88 0.20 0.22 0.27Coef. Var. 11.22 12.40 14.45 8.02 8.15 9.03185Figure 8.5 shows the net specific energy requirements for the 14 geometallurgical units,whilst Figure 8.6 shows the calculated circuit specific energy to produce a -4 mm product.1860.00.51.01.52.02.53.03.5Unit1Unit2Unit3Unit4Unit5Unit6Unit7Unit8Unit9Unit10Unit11Unit12Unit13Unit14Net specific energy [kWh/t]2.5N/mm² 3.0N/mm² 3.5N/mm²Figure 8.5: Prediction of net specific energy consumption for each geometallurgical unit atthree different specific pressing forces0.00.51.01.52.02.53.03.5Unit1Unit2Unit3Unit4Unit5Unit6Unit7Unit8Unit9Unit10Unit11Unit12Unit13Unit14Circuit specific energy [kWh/t]2.5N/mm² 3.0N/mm² 3.5N/mm²Figure 8.6: Prediction of the circuit specific energy for each geometallurgical unit, assuminga -4 mm product187With application of the direct calibration methodology, energy requirements for each ge-ometallurgical unit were determined at three specific pressing forces, with a minimal samplerequirement. The geometallurgical units 2, 7, 9, 10, 12, 13, and 14 were identified as havinghigh circuit specific energy requirements i.e. above 3 kWh/t.The results of this study could be used to inform additional pilot test programs. Forexample, based on the results, a decision could be made to verify results obtained from pistonpress testing for selected samples such as those requiring high circuit specific energies.8.3 Application of the Database-Calibrated MethodologyAs noted, the effect of specific pressing force was assessed by conducting three HPGR pilottests at 3 N/mm2, 4 N/mm2 and 5 N/mm2. When HPGR test data is available for calibration,the direct calibration methodology is preferred to the database-calibrated methodology. How-ever, for the purpose of comparison, the database-calibrated methodology was evaluated bydetermining specific energies at the piston pressures calculated using the empirical equation(Eq. 6.1) and then comparing them with the measured specific energies of HPGR test results.8.3.1 Calculation of piston pressure using empirical calibration equationEq. 6.1 was used to calculate the piston pressure that correspond to the tested specific pressingforces. Table 8.4 lists feed parameters and the results of the piston press tests at the calculatedpressures. The piston press predicted energies were between 5.27% and 6.98% greater than theHPGR test results. The prediction is reasonable considering the small sample requirement, lowcost, and short time expended on the piston press tests compared to HPGR tests. According toScott and Johnston (2002), an order of magnitute estimate requires ±30-35% probable accuracyand preliminary feasibility estimate requires ±20-25% probable accuracy. According to Halbeand Smolik (2002), a prefeasibility study has accuracy of ±30%. Therefore, the database-188calibrated methodology is well suited for for scoping and prefeasibility level studies whichaim for ±25% accuracy.Table 8.4: Input variable, calculated piston pressures and the results of the piston press testsFSP MeasuredESPw ρbulk FHPGR50 FPiston50 Ppiston1mm CalculatedPpistonPredictedESPError[N/mm2] [kWh/t] [%] [g/cc] [mm] [mm] [%] [MPa] [kWh/t] [%]3 1.58 2.5 1.70 12.99 4.69 7.79 151 1.66 5.274 2.01 2.5 1.70 12.99 4.69 7.79 203 2.13 6.025 2.45 2.5 1.70 12.99 4.69 7.79 256 2.62 6.988.3.2 Reduction ratio scale-upEq. 6.2 was used to convert the size reduction achieved in the piston press test to the ratios thatwould be produced by the HPGR. The normalized product curve from the piston press test isthen used to predict the HPGR product PSD. Figures 8.7, 8.8 and 8.9 compare the measuredand predicted PSDs.01020304050607080901000.01 0.1 1 10 100Cumulative percent passing [%]Particle size [mm]3 N/mm2Measured product3N/mm²Predicted product3N/mm²Figure 8.7: Comparison of measured and predicted HPGR product PSDs for the compositesample at 3 N/mm218901020304050607080901000.01 0.1 1 10 100Cumulative percent passing [%]Particle size [mm]4 N/mm2Measured product4N/mm²Predicted product4N/mm²Figure 8.8: Comparison of measured and predicted HPGR product PSDs for the compositesample at 4 N/mm201020304050607080901000.01 0.1 1 10 100Cumulative percent passing [%]Particle size [mm]5 N/mm2Measured product5N/mm²Predicted product5N/mm²Figure 8.9: Comparison of measured and predicted HPGR product PSDs for the compositesample at 5 N/mm2190The predicted product PSDs were finer than the measured PSDs from HPGR tests. Thefact that the predicted products were finer is expected since the specific energy inputs werehigher, as shown in Table 8.4. Therefore, the piston press test predicted a higher specificenergy requirement, but it also predicted a finer product.Table 8.5 summarizes the results from the HPGR and the database-calibrated methodology.Measured specific energies, percentage passing 4 mm in the product, and circuit specific energyfor producing 4 mm product are shown.The error for the specific energy ranges from 5.27 to 6.98%, whereas the error in thepercentage passing -4 mm is between 5.58 and 7.58%. The errors in circuit specific energyfor producing -4 mm material ranges from 0.31 to 2.15%. This shows that if piston presstests conducted at pressures calculated using Eq. 5.4 predicts higher specific energy but alsofiner product then errors tend to negate each other to some degree. Thus predictions of circuitspecific energy have less error than predictions of specific energy and product PSDs.Table 8.5: Circuit specific energies for producing -4 mm productHPGR test results Database-calibrated pistonpress resultsErrorsFSP ESP -4 mm EcircuiSP ESP -4 mm EcircuitSP ESP -4 mm EcircuitSP[N/mm2] [kWh/t] [%] [kWh/t] [kWh/t] [%] [kWh/t] [%] [%] [%]3.02 1.58 58.19 2.71 1.66 62.60 2.66 5.27 7.58 2.153.99 2.01 63.20 3.18 2.13 66.73 3.20 6.02 5.58 0.424.99 2.45 66.19 3.70 2.62 70.59 3.71 6.98 6.65 0.318.4 Application of Simulation-based Methodology8.4.1 Determination of t10–Energy relationshipFive classes of narrowly sized particles were prepared from a subsample of the composite feedsample of the copper-gold ore. Piston press tests were performed at three different energy191levels on each size class. The PSDs of the 15 piston test products were determined using wetand dry sieving. Table 8.6 summarizes the results of piston press tests.Table 8.6: Results of piston press tests on size classes for the copper-gold oreSize Geometric t10-size Specific Measuredclass mean size energy t10-parameter[mm] [mm] [mm] [kWh/t] [%]-12.5+11.2 11.8 1.18 3.34 41.9211.8 1.18 1.40 25.5511.8 1.18 0.31 9.03-11.2+9.5 10.3 1.03 3.33 43.8410.3 1.03 1.38 25.9410.3 1.03 0.31 8.90-9.5+8.0 8.7 0.87 3.26 34.668.7 0.87 1.32 23.248.7 0.87 0.29 6.91-8.0+6.7 7.3 0.73 3.15 35.307.3 0.73 1.31 24.487.3 0.73 0.31 8.28-6.7+5.6 5.9 0.59 3.16 32.175.9 0.59 1.27 21.335.9 0.59 0.31 7.65Figure 8.10 shows the relationship between specific energy and t10, along with the fittedcurve using Eq. 7.3. Parameters M , f ∗mat and n were determined as 45.0, 0.166 and 0.574,respectively.1920510152025303540450 2 4 6 8 10 12 14t 10[%]Sp. Energy· xn [kWh/t·mmn]Cu-AuR2 = 0.976-12.5+11.2-11.2+9.5-9.5+8.0-8.0+6.7-6.7+5.6Fit lineFigure 8.10: Specific energy and t10 relationship for the copper-gold ore and the fitted curveusing Eq. 7.38.4.2 Determination of relationship between t10 and tnRelationships between t10 and other tn are defined by fitting equations 7.5 through 7.10. Theβi coefficients are shown in Table 4.8.Table 8.7: βi coefficients for defining tn–t10 relationships for the copper-gold oret1.2 t2 t4 t25 t50 t75β1 β2 β3 β4 β5 β6 β7 β8 β9107.1 5.7 123.4 23.2 152.4 65.5 0.59 0.36 0.23Figure 8.11 shows a scatter plot of the tn–t10 relationships for the copper-gold ore and thefitted curves. The fitted curves describe the experimental data well, especially for t2 and t4.19301020304050607080901000 5 10 15 20 25 30 35 40 45t n[%]t10 [%]t₁.₂t₂t₄t₂₅t₅₀t₇₅Figure 8.11: t10–tn relationship of the copper-gold ore and the fitted curves using Eq. 7.5through 7.108.4.3 Simulation of energy–size reductionNine pilot-scale HPGR tests were performed on the copper-gold ore:• 3 tests evaluated the effect of specific pressing force;• 2 tests evaluated the effect of roll speed;• 2 tests evaluated the effect of moisture;• 2 tests evaluated the effect of feed top size.Table 8.8 summarizes the matrix of test parameters in the HPGR tests on the composite sampleof the copper-gold ore.194Table 8.8: HPGR test matrix for the copper-gold ore and the resulting specific energyTest Sp. energy Sp. pressing force Roll speed Moisture Top size# [kWh/t] [N/mm2] [m/s] [%] [mm]1 1.58 30.75 2.5 322 2.01 43 2.45 54 1.9340.602.5 325 1.96 0.906 1.724 0.750.9327 2.08 4.58 1.924 0.75 2.5259 1.78 19The energy–size reduction performance of the HPGR for the copper-gold ore was simulatedusing an Excel spreadsheet. The numerical steps involved in the simulation of 3 N/mm2 test isincluded in Appendix C as a worked example.Section 7.5 described the simulation model and the best simulation parameters (Table 7.7)were determined as xc=16 mm, βsplit=0.157, and c=1.08. First, the HPGR feed is classified tocoarse (+16 mm) and fine (-16 mm) fractions. The specific energy of the pre-crushing stage isEcrushSP = βsplit · ESP. The t10 for each size class after pre-crushing was calculated according toEq. 7.3, which took the following form once the fitted values of 45.0, 0.166 and 0.574 weresubstituted for M , f ∗mat and n, respectively.t10 = 45 ·(1− exp(−0.166 · x0.574 · EcrushSP))(8.6)The product of pre-crushing is combined with the -16 mm fraction and are subjected tothe grinding stage. The specific energy is a balance of energy expended on the crushingstage EgrindSP = ESP(1− βsplit · P+16mm). The t10 for each size class after the grinding stage195is calculated according to Eq. 7.4, which took the following form.t10 = (45−1.08 · P1.4mm)(1− exp(−0.166 · x0.575 · EgrindSP))(8.7)where P1.4mm is the cumulative percentage passing 1.4 mm in the feed to grinding stage, xis the geometric mean particle size of the size class.The calculated t10 was used to create the progeny particle size distribution for each sizeclass of the feed sample at the given specific energy. The final simulated product PSD is thesum of the progenies of all the size classes broken at their respective t10 levels.Table 8.9 compares the measured and the simulated P80 and P−4mm. The error in P80 rangesfrom 1.41 to 8.33%, whereas the error in P−4mm is between 0.13 and 3.47%.Table 8.9: Comparison of measured and the simulated results and their relative errorsTest Parameter Sp. energy Measured Simulated Error %# Change [kWh/t] P80 -4 mm P80 -4 mm P80 -4 mm1 FSP=3 N/mm2 1.58 7.79 58.2 7.55 60.0 3.09 3.172 FSP=4 N/mm2 2.01 6.83 63.2 7.00 63.6 2.42 0.553 FSP=5 N/mm2 2.45 6.29 66.2 6.58 66.0 4.68 0.274 ν=0.6 m/s 1.93 6.99 62.8 7.09 63.0 1.41 0.395 ν=0.9 m/s 1.96 6.77 63.1 7.05 63.2 4.23 0.136 w=0.9% 1.72 7.55 59.9 7.35 61.3 2.61 2.297 w=4.5% 2.08 6.58 64.7 6.93 64.0 5.38 1.198 F100=25 mm 1.92 7.07 62.6 6.65 64.8 5.92 3.479 F100=19 mm 1.78 5.96 66.4 6.46 64.7 8.33 2.49Figures 8.12 to 8.14 compare the simulated and measured PSDs for the HPGR test runs on-32 mm composite feed at specific pressing forces of 3, 4, and 5 N/mm2. For all three specificpressing force tests, the largest difference occurs around the 0.2–3 mm range, where simulationpredictions are finer.19601020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]FSP=3N/mm2FeedMeasuredProductSimulatedProductFigure 8.12: Comparison of simulated and measured product PSDs for the HPGR test run at3N/mm201020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]FSP=4N/mm2FeedMeasuredProductSimulatedProductFigure 8.13: Comparison of simulated and measured product PSDs for the HPGR test run at4 N/mm219701020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]FSP=5N/mm2FeedMeasuredProductSimulatedProductFigure 8.14: Comparison of simulated and measured product PSDs for the HPGR test run at5 N/mm2Figures 8.15 and 8.16 compare the simulated and measured PSDs for the HPGR tests runat roll speeds of 0.6 and 0.9 m/s. The figures suggest the simulation model reasonably predictsfor both the low and the high roll speed results. However, the bias around 0.2–3 mm is clearlyvisible.19801020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]Speed=0.6m/sFeedMeasuredProductSimulatedProductFigure 8.15: Comparison of simulated and measured product PSDs for the HPGR test run atroll speed of 0.6m/s01020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]Speed=0.9m/sFeedMeasuredProductSimulatedProductFigure 8.16: Comparison of simulated and measured product PSDs for the HPGR test run atroll speed of 0.9m/s199Figures 8.17 and 8.18 compare the simulated and measured PSDs for the HPGR tests runon feeds with 0.9% and 4.5% moisture. The higher moisture feed required 20.8% more specificenergy than the lower moisture feed. The simulation model can make reasonable predictionsfor tests on both low and high moisture feed. However, there is a clear bias below the 0.3 mmrange.01020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]Moisture=0.9%FeedMeasuredProductSimulatedProductFigure 8.17: Comparison of simulated and measured product PSDs for the HPGR test run onfeed with 0.9% moisture20001020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]Moisture=4.5%FeedMeasuredProductSimulatedProductFigure 8.18: Comparison of simulated and measured product PSDs for the HPGR test run onfeed with 4.5% moistureFigures 8.19 and 8.20 compare the simulated and measured PSDs for the HPGR tests runon feeds with top sizes of 25 mm and 19 mm. The finer top size feed has significantly lessparticles that report to the pre-crushing stage. The figures suggest the simulation model canaccommodate changes in feed top size and provide reasonable predictions.20101020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]F100=25mmFeedMeasuredProductSimulatedProductFigure 8.19: Comparison of simulated and measured product PSDs for the HPGR test run on25 mm top size01020304050607080901000.01 0.1 1 10 100Cum. percentage passing [%]Particle size [mm]F100=19mmFeedMeasuredProductSimulatedProductFigure 8.20: Comparison of simulated and measured product PSDs for the HPGR test run on19 mm top size202The application of the simulation-based methodology to the composite sample from thecopper-gold deposit shows that the simulated product PSDs are in close agreement with themeasured product PSDs from HPGR tests. The HPGR tests assessed variations in specificpressing force, roll speed, feed moisture and feed top size.One of the advantages of the simulation methodology is that it can simulate closed-circuitoperation at a variety of operating parameters and closing screen sizes. Performing closed-circuit pilot-scaled HPGR tests is labor-intensive and expensive. Once the closing screen size ischosen, the test data does not readily transfer to other closing screen sizes. With the simulation-based methodology, simulating closed circuit operation with different closing screen sizes issimply a matter of entering a new screen aperture into the spreadsheet.8.5 Discussion on the Comparison of HPGR EnergyPrediction MethodologiesThe direct calibration methodology was applied to the case study (Section 8.2) where itwas demonstrated that the methodology is an effective tool for assessing the effect of operatingparameters for a range of geometallurgical units within the deposit. If pilot-scale HPGRtests were conducted on all 14 geometallurgical units individually, the time and the cost ofsample acquisition by drilling and HPGR pilot testing would have been prohibitive. Thegeometallurgical units with high circuit specific energies were successfully identified. Suchresults can be used as the basis for planning followup pilot testing, and for design and operatingpurposes.The database-calibrated methodology was demonstrated in Section 8.3. For the case study,conducting piston press tests at calculated pressures resulted in a higher specific energy pre-diction with an error up to 6.98%. At the same time, the predicted product PSDs were finerand contained more -4 mm material with an error up to 7.58%. The errors of predicting higher203energy and finer product cancel each other to some degree such that results for the circuitspecific energy were lower. Considering that the scoping level studies are conducted at ±25%accuracy, the database-calibrated methodology can be a useful tool for studies in early stageprojects.The simulation methodology allows estimation of the energy-size reduction performanceof the HPGR under a variety of operating and feed conditions. The simulated product PSDsclosely approximate measured product PSDs for the HPGR over a range of operating parame-ters such as feed top size and feed moisture.Table 8.10 compares the relative percentage errors for specific energy prediction of thethree methodologies. As expected, the direct calibration methodology has the smallest error,and the other two methodologies have comparable levels of error.Table 8.10: Comparison of the error in specific energy prediction using the threemethodologiesFSPMeasured Direct calibration Error Database-calibrated Error Simulation-based ErrorESP Predicted ESP Predicted ESP Predicted ESP[N/mm2] [kWh/t] [kWh/t] [%] [kWh/t] [%] [kWh/t] [%]3 1.58 1.58 0.11 1.66 5.11 1.41 10.54 2.01 2.01 0.19 2.13 5.88 1.87 7.35 2.45 2.45 0.03 2.62 6.92 2.26 7.7Table 8.11 shows an overall comparison of the three methodologies in terms of sample size,pilot-scale HPGR test requirement, and accuracy. Table 8.12 lists the applicability of themethodologies to mining projects at different stages of development.204Table 8.11: Overall comparison of the methodologiesMethodologySample size Pilot tests Accuracy Other Benefits[kg] required [%]Directcalibration1 tonne forHPGR5–10 kg forpiston pressper testYes ±10% Fast lab turnaround once the directcalibration is established;Can be applied to a range ofgeometallurgical units.Database-calibrated5–10 kg perore typeNo ±25% Fast lab turnaround, orevariability,cost effectiveSimulation 10 kg per oretypeNo / Yes ±25% Energy–size reductionrelationship can be simulatedusing spreadsheet to includeclosed circuit operation,Can be fine tuned for the ore withHPGR testTable 8.12: Applicability of the methodologies throughout the stages of a mine projectStages Direct calibration Database-calibrated Simulation-basedScoping level study Yes Yes YesPre-feasibility level study Yes No YesFeasibility level study Yes No YesDesign Yes No YesOperation No No Yes205Chapter 9CONCLUSIONS ANDRECOMMENDATIONS9.1 Main Outcomes of the ResearchThe main outcomes of the research are the following:1. The development of the piston press testing methodologies for predicting the HPGRenergy–size reduction performance. Three methodologies were developed, each havingtheir respective advantages and disadvantages.The direct calibration methodology has the advantage of high accuracy (±10%) and thatit can be applied to determine the HPGR performance for a range of geometallurgicalunits, using piston press tests once a calibrated model has been developed. The disad-vantage is that it requires some HPGR test data for the calibration.The database-calibrated methodology overcomes the requirement of HPGR calibrationand can provide scoping-level HPGR sizing information with minimal sample require-ments. The disadvantage is that it has greater levels of error (±25%).The simulation methodology provides the possibility of simulating the energy–size re-duction performance using an Excel spreadsheet. The main advantage of the simulationmethodology is that it does not require HPGR test data, although it can be fine-tuned with206HPGR test data. The other advantages are that the simulation-based methodology canbe used to evaluate the effects of a range of operating parameters, including close-circuitevaluation.2. The development of two regression models (Eq. 4.2 and 4.3) that relate HPGR feedconditions and operating variables to specific energy consumption. The regression mod-els were based on the database from a large set of HPGR test results. Also within thedatabase-calibrated methodology, regression models were developed for calculating ap-propriate pressure to perform piston press tests, and for relating the particle size reductionratio achieved in piston press tests to that of HPGR tests.3. It was known that particle bed comminution products can be normalized. The researchprovides further proof that the normalized product PSDs from piston press and HPGRtests match very closely. The approach was shown to be applicable to products from awide range of energy input levels and top sizes, and to products from both piston pressand HPGR tests. This unique characteristic of particle bed comminution was exploitedin the direct calibration and the database-calibrated methodologies to predict full particlesize distributions for HPGR tests.4. The results from tests on five ore types, used to validate the simulation-based methodol-ogy, show that there is a set of master curves for products from particle bed comminution,which can be used to estimate the full product PSDs from the knowledge of breakage in-dex t10. With the use of the set of master curves, the laboratory workload and turnaroundtime for the simulation-based methodology can be improved significantly. As few as twosieves that straddle the t10 particle size are needed to use the master curves to predictPSDs.5. An existing energy–breakage model for single particle impact breakage was modifiedand adopted to model the relationship between t10 and specific energy in compression207breakage of particle-beds. The modified model (Eq. 7.3) applies an ore-specific expo-nent to the initial particle size and accounts for the presence of fines in the feed. Theinteraction between coarse and fine particles and the feed particle size distribution is ofparamount importance in particle-bed comminution in the HPGR.6. Application and validation of the methodologies is as important as their development.The methodologies were applied different ore types and validated on a copper-goldmining project in central British Columbia.7. The ability to simulate the energy–size reduction performance of the HPGR using anExcel spreadsheet requiring only piston press test results, has two important implica-tions. Firstly, it is easily accessible and it avoids the need for specialized software, andsecondly, it is possible to evaluate different circuit configurations, such as changing thetransfer screening cut-point. The ability to evaluate different circuit configurations issomething that is difficult to replicate in pilot-scale HPGR tests, due to the high samplerequirements, high costs, and considerable time to complete such test work.8. A total of 19 sets of HPGR test results on four different ore types are presented and madeavailable to the public domain as a consequence of this work.9.2 Limitations of the MethodologiesEach methodology is based on a set of assumptions and each have limitations. The logic behindthe assumptions and the limitations must be understood before applying the methodologies.The application of the direct calibration methodology makes the explicit assumption thatthe composite feed size distribution to the HPGR test is derived from the product of a cone-crushing operation, either in regular closed circuit or reverse-closed circuit screening. If thecomposite feed sample used for the HPGR test is manipulated in some way, the assumptionis that other geometallurgical units would also be prepared using the same process. It is208important to confirm the match between normalized product size distributions of HPGR testproducts and piston press test products. If the normalized product size distributions of pistonand HPGR tests do not match reasonably well, the predictions will not be satisfactory. In thiscase the simulation-based methodology is recommended because it does not require matchingof normalized product PSDs.The database-calibrated methodology assumes that the feed to the HPGR test is a cone-crusher product, precluding its application if the feed size distribution has been produced usingother procedures. The two regression equations for calculating piston press pressure and scale-up of reduction ratios does not apply to manipulated, truncated or scalped feeds.The simulation-based methodology can be applied to closed-circuit HPGR operations andcan accommodate all types of feed. However, the screening cut point has to be realistic andpractical. The fact that the HPGR produces compacted flake has to be remembered and anappropriate screening efficiency has to be used. Otherwise, the computer simulation will falselyassume that screening can be performed at any specified screen mesh size with 100% efficiency.9.3 Recommendations for Future ResearchFollowing the development of the methodologies, the next step is to apply and validate them inindustrial applications. The following aspects of the methodologies need to be specified.The hydraulic pressure transducer in the MTS piston press used to measure the force had acombined error of hysteresis and non-linearity of ±2.5 kN or 0.30% of the full scale 1650 kN.There are commercially available force transducers that have a combined error of 0.20% of thefull capacity in the range of 1500–2500 kN. For industrial applications an acceptable level ofcombined error in the measurement of force should be established.The fabrication of the piston and the die needs to be specified in order to eliminate anyvariation across different laboratories. Areas to be developed further include:209• Assess need for greater precision in force measurements,• Re-assess piston and die geometry,• Evaluate steel designation for construction with respect to hardness and clearance speci-fications,Flake screening efficiency is an important operating variable, and an accompanying fit-for-purpose test should be developed to avoid making assumptions regarding screening efficiencywhen a closed-circuit operation is simulated.Currently the database-calibrated methodology uses regression equations that do not takegeology and lithology into account. It is possible to separate the database according to orebodygeology and develop separate regression equations. For instance, there could be two separateregression equations for porphyry and massive sulphides.The methodologies predict the full product particles size distribution, whereas pilot-scaleHPGR test products are collected separately as centre and edge products. Some operationsrecycle edge product and avoid screening. The methodologies cannot be used for comminutioncircuits that require knowledge of edge and centre products separately. Simulation capabilityto predict centre and edge PSDs separately is another desirable feature, since there are circuitsthat treat them separately.The development of the methodologies are based on and calibrated to pilot-scale HPGR. Itis important to validate the methodologies against an industrial scale HPGR in the future. Itwould also be worthwhile comparing these new methodologies with the existing HPGR modelsin the JKSimMet simulation package.210Chapter 10CLAIMS OF ORIGINAL CONTRIBUTIONSThe original contributions from the research undertaken for this dissertation are listed below.The three main contributions of the research are:1. A methodology was developed to size HPGR’s using results of piston press test by cali-brating on ore specific model using pilot scale testing. This methodology, called DirectCalibration, predicts the energy input versus size reduction relationship and predictsproduct particle size distribution with relative error of ±10% for the ore samples usedin the thesis study.2. A methodology was developed to size HPGR’s using results of piston press tests bycalibrating a model to a database of pilot scale HPGR data. This methodology, calledDatabase Calibrated, predicts the energy input versus size reduction relationship andproduct particle size distribution with a relative error of ±25% for the ore samples usedin the thesis study.3. A methodology was developed to size HPGR’s using results of piston press tests thatrelies on an ore-specific breakage index model to simulate the effect of bed breakageon a given feed. In this methodology, called Simulation-based, the model can also be211used to simulate HPGR operation over a range of operating circuit configurations andoperating conditions.To support the development of the three methodologies, the following original contributionswere made:4. A piston press apparatus was designed that can be used in standard hydraulic pressequipment such as the MTS. Procedures for experimental testing of samples and datacollection were also developed.5. Two empirical equations (Eq. 4.2 and 4.3) were developed through multiple linear regres-sion for estimating the net specific energy of the HPGR from knowledge of the operatingand feed parameters.6. The self-similarity of PSDs from piston press test was exploited to predict full particlesize distributions for HPGR test after reduction ratio achieved in piston press was scaledusing Eq. 6.2.7. An existing energy–breakage model for single particle impact breakage was modifiedand adopted to model energy–breakage relationship in compression breakage of particlebeds. The modified model incorporates the particle size effect and accounts for presenceof fines. The size effect exponent ranged from 0.395 to 0.655 for the tested ores.8. A set of master curves is presented for compression breakage of particle beds. The setof curves (Eq. 7.5–7.10 and Table 7.5) can be used to estimate the full size distributionfrom the knowledge of t10.212REFERENCESAbouzeid, A. M. and Fuerstenau, D. W. (2009). Grinding of mineral mixtures in high-pressuregrinding rolls. International Journal of Mineral Processing, 93(1):59–65.Amelunxen, P., Mular, M., Vanderbeek, J., Hill, L., and Herrera, E. (2011). The Effects of OreVariability on HPGR Trade-off Economics. Vancouver, BC, Canada.Anguelov, R., Ghaffari, H., and Alexander, J. (2008). 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MASc, The University of British Columbia,Vancouver, BC, Canada.219Appendix AHPGR TEST DATA220A.1 Copper-Molybenum (P) OreTable A.1: Summary of HPGR tests on copper-molybdenum (P) oreRoller Diameter ( D ) [m] 0.750Roller Width ( W) [m] 0.220Symbol UnitQ [m/s ] 0.75 0.75 0.75 0.75n [rpm] 19.10 19.10 19.10 19.10Static Gap X 0 [mm] 9.0 9.0 9.0 9.0Hydraulic Pressure P [bar] 103 82.1 61.5 41.0Pressing Force F [kN] 825.0 660.0 495.0 330.0Specific Pressing Force F SP [N/mm2] 5.0 4.0 3.0 2.0Test Time t [s] 20.00 20.20 20.60 19.79Average Actual Speed: ZAV [m/s ] 0.75 0.77 0.75 0.76Standard Deviation VZ 0.07 0.20 0.06 0.06Actual Roller gap (average) X gAV [mm] 17.68 18.09 18.30 20.01Standard Deviation VX 0.47 0.50 0.43 0.73Actual Hydraulic Pressure (average) PAV [bar] 101.8 80.9 61.0 41.1Standard Deviation 0.76 1.08 1.07 2.08Actual Pressing Force (average) F AV [kN] 819 650 491 330Actual Specific Pressure (average) F SPAV [N/mm2] 4.98 3.95 2.98 2.01Id le Power Draw Pi [kW ] 9.78 9.44 9.50 9.45Power Draw P [kW ] 68.05 58.48 48.49 39.43Total Specific Energy Consumption E S P [kW h/t] 2.75 2.36 1.95 1.51Net Specific Energy Consumption E SP net [kWh/t] 2.35 1.98 1.57 1.15Press throughput W [t/h] 24.78 24.81 24.86 26.17Specific Throughput Constant m dot [ts/hm3] 200 196 200 210Average Flake Density UF [t/m3] 2.17 2.19 2.18 2.17Standard Deviation 0.05 0.07 0.03 0.03F lake Thickness Average X F [mm] 21.50 22.17 20.69 22.82Standard Deviation 1.68 2.20 1.64 1.48Feed Moisture [%] 1.5% 1.5% 1.5% 1.5%Proctor Density (wet) [t/m3] 1.92 1.92 1.92 1.92Proctor Density (solids) [t/m3] 1.89 1.89 1.89 1.89Particle Size DistributionFeed: 100% Passing Size F100 [mm] 32 32 32 32Feed: 80% Passing Size F 80 [mm] 20.47 20.47 20.47 20.47Feed: 50% Passing Size F 80 [mm] 15.31 15.31 15.31 15.31Centre: 80% Passing Size P 80 [mm] 4.18 4.85 5.90 7.68Centre: 50% Passing Size P 50 [mm] 0.95 1.23 1.54 2.22Edge: 80% Passing Size P 80 [mm] 9.16 9.70 10.08 11.48Edge: 50% Passing Size P 50 [mm] 3.40 3.71 4.46 5.34Combined 90% Center & 10% Edge: 80% Passing Size P 80 [mm] 4.77 5.35 6.50 8.19Combined 90% Center & 10% Edge: 50% Passing Size P 50 [mm] 1.08 1.33 1.72 2.43Reduction Ratio F80/P80 (Scaled Product) 4.29 3.82 3.15 2.50Reduction Ratio F50/P50 (Scaled Product) 14.17 11.53 8.93 6.304 mm % Passing (Scaled Product) [%] 76.8% 73.8% 69.1% 61.1%1 mm % Passing (Scaled Product) [%] 48.8% 44.2% 39.9% 34.1%Mass BalanceTotal Feed Material M F [kg] 261 262 261 263Total Centre Product M C [kg] 100.4 97.4 99.8 102.1Centre Product % of Centre & Edge Material MCE% [%] 73.2% 70.1% 70.3% 71.0%Total Edge Product M E [kg] 36.8 41.5 42.2 41.8Edge Product % of Centre & Edge Material M E F% [%] 26.8% 29.9% 29.7% 29.0%Edge Product % of Centre Product M E C% [%] 37% 43% 42% 41%Total Waste Product MW [kg] 123 119 115 116Waste Product % of Total Feed MWF% [%] 47.0% 45.2% 44.0% 44.0%Total Recovered Product MP [kg] 260 257 257 260Mass Reconciliation (+ "gain; - "loss") MPF% [%] 0.4% 1.9% 1.6% 1.3%Cu-Mo (P) 3 Cu-Mo (P) 4Process Set PointsSpeedPress ConstantsData Description Material dataProcess DataTest Number: Cu-Mo (P) 1 Cu-Mo (P) 2221Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 119.3 99.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 420.7 95.3 100.0-25  +19 19 0 100.0 16.4 99.9 100.0 2358.2 75.0 100.0-19  16 16 16.5 99.9 90.9 99.1 99.6 2430.4 54.1 99.8-16  +12.5 12.5 172.6 98.5 623.0 93.6 97.2 2383.2 33.5 98.0-12.5  +8 8 819.5 91.8 2085.0 75.3 87.4 1822.8 17.8 90.1-8  +5.6 5.6 747.8 85.7 1349.0 63.5 79.7 494.1 13.5 83.5-5.6  +4 4 793.9 79.3 1037.9 54.4 72.6 370.4 10.4 76.8-4  +2.8 2.8 944.3 71.6 999.8 45.6 64.6 217.4 8.5 69.0-2.8  +2 2 888.4 64.4 724.5 39.2 57.6 149.4 7.2 61.8-2  +1.4 1.4 878.1 57.2 717.3 32.9 50.7 119.8 6.2 54.8-1.4  +1 1 751.6 51.1 539.2 28.2 45.0 89.0 5.4 48.8-1  +0.71 0.71 803.6 44.6 440.4 24.3 39.1 73.0 4.8 42.5-0.71  +0.5 0.5 782.5 38.2 424.7 20.6 33.5 60.1 4.2 36.4-0.5  +0.355 0.355 680.9 32.7 349.1 17.5 28.6 61.5 3.7 31.1-0.355  +0.25 0.25 662.4 27.3 330.9 14.6 23.9 48.2 3.3 26.0-0.25  +0.18 0.18 619.1 22.2 302.6 12.0 19.5 52.6 2.8 21.2-0.18  +0.125 0.125 716.7 16.4 337.4 9.0 14.4 53.7 2.4 15.7-0.125  +0.09 0.09 402.1 13.1 222.6 7.1 11.5 27.3 2.1 12.5-0.09  +0.063 0.063 540.4 8.7 246.6 4.9 7.7 38.3 1.8 8.4-0.063  +0.045 0.045 274.6 6.5 126.8 3.8 5.8 10.3 1.7 6.2-0.045 -0.045 799.7 432.1 200.0Total mass 12294.7 11396.32 11599.8Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.1: Feed and product PSDs of test No. Cu-Mo (P) 1222Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 119.3 99.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 420.7 95.3 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 2358.2 75.0 100.0-19  16 16 7.18 99.9 143.7 98.7 99.6 2430.4 54.1 99.8-16  +12.5 12.5 215.64 98.0 630.2 92.8 96.4 2383.2 33.5 97.4-12.5  +8 8 809.6 90.5 2202.4 72.2 85.0 1822.8 17.8 88.7-8  +5.6 5.6 773.6 83.4 1213.8 60.9 76.7 494.1 13.5 81.1-5.6  +4 4 784.1 76.2 949.3 52.1 69.0 370.4 10.4 73.8-4  +2.8 2.8 884.4 68.0 920.1 43.5 60.7 217.4 8.5 65.6-2.8  +2 2 840.9 60.3 669.5 37.2 53.4 149.4 7.2 58.0-2  +1.4 1.4 788.7 53.0 649.1 31.2 46.5 119.8 6.2 50.9-1.4  +1 1 757.7 46.1 459.7 26.9 40.3 89.0 5.4 44.2-1  +0.71 0.71 657.1 40.0 427.4 22.9 34.9 73.0 4.8 38.3-0.71  +0.5 0.5 611.3 34.4 350.5 19.6 30.0 60.1 4.2 32.9-0.5  +0.355 0.355 540.0 29.4 302.8 16.8 25.7 61.5 3.7 28.2-0.355  +0.25 0.25 548.3 24.4 301.9 14.0 21.3 48.2 3.3 23.4-0.25  +0.18 0.18 477.6 20.0 266.2 11.5 17.5 52.6 2.8 19.2-0.18  +0.125 0.125 552.2 14.9 309.1 8.6 13.0 53.7 2.4 14.3-0.125  +0.09 0.09 433.8 10.9 234.9 6.4 9.6 27.3 2.1 10.5-0.09  +0.063 0.063 390.6 7.3 223.3 4.3 6.4 38.3 1.8 7.0-0.063  +0.045 0.045 275.5 4.8 119.5 3.2 4.3 10.3 1.7 4.6-0.045 -0.045 522.6 345.0 200.0Total mass 10870.8 10718.43 11599.8FeedEdgeCentre01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.2: Feed and product PSDs of Test No. Cu-Mo (P) 2223Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 119.3 99.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 420.7 95.3 100.0-25  +19 19 0 100.0 9.4 99.9 100.0 2358.2 75.0 100.0-19  16 16 59.4 99.5 147.9 98.5 99.2 2430.4 54.1 99.4-16  +12.5 12.5 281.66 97.0 772.3 91.4 95.4 2383.2 33.5 96.5-12.5  +8 8 1134.8 87.1 2285.0 70.2 82.1 1822.8 17.8 85.4-8  +5.6 5.6 938.1 79.0 1500.4 56.3 72.2 494.1 13.5 76.7-5.6  +4 4 861.8 71.5 961.5 47.4 64.3 370.4 10.4 69.1-4  +2.8 2.8 956.2 63.1 873.5 39.3 56.1 217.4 8.5 60.7-2.8  +2 2 850.7 55.7 650.3 33.3 49.1 149.4 7.2 53.5-2  +1.4 1.4 863.8 48.2 584.8 27.9 42.2 119.8 6.2 46.2-1.4  +1 1 742.0 41.7 452.0 23.7 36.4 89.0 5.4 39.9-1  +0.71 0.71 667.1 35.9 382.3 20.2 31.2 73.0 4.8 34.3-0.71  +0.5 0.5 590.4 30.8 327.7 17.1 26.7 60.1 4.2 29.4-0.5  +0.355 0.355 546.7 26.0 276.7 14.6 22.6 61.5 3.7 24.9-0.355  +0.25 0.25 525.0 21.4 262.5 12.2 18.7 48.2 3.3 20.5-0.25  +0.18 0.18 434.6 17.6 252.4 9.8 15.3 52.6 2.8 16.9-0.18  +0.125 0.125 485.3 13.4 283.5 7.2 11.6 53.7 2.4 12.8-0.125  +0.09 0.09 357.3 10.3 206.9 5.3 8.8 27.3 2.1 9.8-0.09  +0.063 0.063 318.4 7.5 205.2 3.4 6.3 38.3 1.8 7.1-0.063  +0.045 0.045 205.0 5.7 81.6 2.6 4.8 10.3 1.7 5.4-0.045 -0.045 658.0 283.1 200.0Total mass 11476.2 10798.88 11599.8Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.3: Feed and product PSDs of test No. Cu-Mo (P) 3224Full PSD Feed Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 119.3 99.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 420.7 95.3 100.0-25  +19 19 33.92 99.7 44.0 99.6 99.7 2358.2 75.0 99.7-19  16 16 184.54 98.2 336.7 96.3 97.6 2430.4 54.1 98.0-16  +12.5 12.5 532.3 93.8 1157.2 85.1 91.3 2383.2 33.5 92.9-12.5  +8 8 1504.2 81.3 2319.7 62.6 75.9 1822.8 17.8 79.4-8  +5.6 5.6 1151.4 71.7 1155.7 51.4 65.8 494.1 13.5 69.7-5.6  +4 4 1039.2 63.1 873.1 42.9 57.3 370.4 10.4 61.1-4  +2.8 2.8 950.2 55.2 771.9 35.4 49.5 217.4 8.5 53.3-2.8  +2 2 865.1 48.1 576.2 29.9 42.8 149.4 7.2 46.2-2  +1.4 1.4 832.5 41.2 533.3 24.7 36.4 119.8 6.2 39.5-1.4  +1 1 681.6 35.5 352.5 21.3 31.4 89.0 5.4 34.1-1  +0.71 0.71 581.9 30.7 315.7 18.2 27.1 73.0 4.8 29.4-0.71  +0.5 0.5 538.5 26.2 259.2 15.7 23.2 60.1 4.2 25.2-0.5  +0.355 0.355 495.7 22.1 212.8 13.6 19.6 61.5 3.7 21.2-0.355  +0.25 0.25 429.8 18.5 201.1 11.7 16.5 48.2 3.3 17.8-0.25  +0.18 0.18 363.2 15.5 191.9 9.8 13.9 52.6 2.8 14.9-0.18  +0.125 0.125 415.7 12.1 235.9 7.5 10.8 53.7 2.4 11.6-0.125  +0.09 0.09 281.0 9.7 178.1 5.8 8.6 27.3 2.1 9.3-0.09  +0.063 0.063 266.3 7.5 313.5 2.8 6.1 38.3 1.8 7.1-0.063  +0.045 0.045 196.5 5.9 68.4 2.1 4.8 10.3 1.7 5.5-0.045 -0.045 710.8 217.7 200.0Total mass 12054.3 10314.49 11599.8Centre Edge01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.4: Feed and product PSDs of test No. Cu-Mo (P) 4225A.2 Gold (C) OreTable A.2: Summary of HPGR tests on gold (C) oreRoller diameter (D) [m] 0.750Roller width (W ) [ m] 0.220Symbol UnitQ [ m/ s] 0.750 0.750 0.750 0.750 0.750 0.750n [rpm] 19.10 19.10 19.10 19.10 19.10 19.10Static gap X 0 [ mm] 9.0 9.0 9.0 9.0 9.0 9.0Hydraulic pressure P [ bar] 82 62 41 82 62 41Pressing force F [ k N] 660.0 495.0 330.0 660.0 495.0 330.0Specific pressing force F SP [N/mm 2 ] 4.00 3. 00 2. 00 4. 00 3. 00 2. 00Test time t [s] 15.28 12.83 16.37 15.93 17.10 16.73Average actual speed ZAV [ m/ s] 0.83 0.77 0.80 0.80 0.80 0.81Standard deviation VZ 0.40 0.20 0.28 0.33 0.32 0.32Actual roller gap (average) X gAV [mm] 18.24 18. 72 20. 53 20. 20 20. 65 22. 25Standard deviation VX 0.48 0.52 0.73 0.31 0.36 0.26Actual hydraulic pressure (average) PAV [bar] 81.9 61. 3 40. 1 82. 1 62. 0 37. 4Standard deviation 0.47 1.95 0.73 0.38 0.40 0.84Actual pressing force (average) F AV [ k N] 659 493 323 660 499 301Actual specific pressure (average) F SPAV [N/mm 2 ] 4.00 2. 99 1. 96 4. 01 3. 03 1. 83I d le power draw Pi [k W ] 10.96 10.62 10.39 9.87 9.66 9.74Power draw P [ k W ] 75.72 64.12 48.95 67.32 55.53 43.16Total specific energy consumption E S P [ k W h/t] 3.04 2.59 1.86 2.36 1.93 1.43Net Specific energy consumption E SP net [kWh/t] 2.60 2. 16 1. 47 2. 01 1. 59 1. 11Press throughput W [t/h] 24. 88 24. 79 26. 31 28. 52 28. 79 30. 09Specific throughput constant m dot [ts/hm 3 ] 182 196 201 216 218 226Average flake density UF [t/m 3 ] 2.34 2. 37 2. 39 2. 31 2. 29 2. 28Standard deviation 0.04 0.07 0.02 0.05 0.01 0.02F lake thickness average X F [mm] 20.27 20. 44 21. 08 21. 78 23. 25 23. 95Standard deviation 1.49 2.47 1.64 2.42 1.44 1.66Feed moisture [%] 1.48 1.48 1.48 2.06 2.06 2.06Feed bulk density [t/m 3 ] 1.60 1.60 1.60 1.69 1.69 1.69Feed Proctor density (solids) [t/m 3 ] 2.01 2.01 2.01 2.08 2.08 2.08Particle size distributionFeed: 100% passing size P 100 [ mm] 32 32 32 12.5 12.5 12.5Feed: 80% passing size P 80 [ mm] 27.44 27.44 27.44 9.83 9.83 9.83Feed: 50% passing size P 50 [ mm] 20.21 20.21 20.21 6.27 6.27 6.27Centre: 80% passing size P 80 [ mm] 6.46 7.45 10.14 3.81 4.70 4.63Centre: 50% passing size P 50 [ mm] 2.21 2.65 4.01 1.21 1.72 1.71Edge: 80% passing size P 80 [ mm] 10.54 11.45 13.34 7.31 7.71 8.29Edge: 50% passing size P 50 [ mm] 4.96 5.91 7.27 3.67 4.13 4.82Scale-up: 80% passing size P 80 [ mm] 7.21 8.22 10.67 4.40 5.14 5.25Scale-up: 50% passing size P 50 [ mm] 2.49 2.98 4.43 1.42 1.96 1.99Reduction ratio F80/P80 3.80 3.34 2.57 2.24 1.91 1.87Reduction ratio F50/P50 8.11 6.77 4.57 4.43 3.20 3.15Mass balanceTotal feed material M F [ k g] 295.1 281.8 283.8 270.5 293.6 293.7Total centre product M C [ k g] 98.1 86.4 99.3 100.2 97.4 111Total edge product M E [ k g] 45.7 39.7 46.5 44.7 45.3 49.8Edge product % of centre & edge material M E F % [%] 31.8% 31.5% 31.9% 30.8% 31.7% 31.0%Total waste product MW [ k g] 142.5 150.1 132.2 118.3 137.0 127.1Waste product % of total feed MWF% [%] 48.3% 53.3% 46.6% 43.7% 46.7% 43.3%Total recovered product MP [ k g] 286 276 278 263 280 288Mass reconciliation (+ "gain; - "loss") MPF% [%] -3.0% -2.0% -2.0% -2.7% -4.7% -2.0%Material dataProcess dataAu (C) 3 Au (C) 4 Au (C) 5 Au (C) 6Process set pointsSpeedPress constantsData Description Test number: Au (C) 1 Au (C) 2226Centre Edge Full PSD Feed Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 2462.9 69.3 100.0-25  +19 19 25 99.7 59.3 99.3 99.6 1942.8 45.1 99.7-19  16 16 72.3 98.9 229.9 96.5 98.2 889.4 34.0 98.7-16  +12.5 12.5 173.8 97.0 553.9 89.8 94.7 750.7 24.7 96.3-12.5  +8 8 985.6 86.1 1865.4 67.3 80.1 913.2 13.3 84.2-8  +5.6 5.6 863.7 76.6 1094.6 54.0 69.4 362.2 8.8 74.3-5.6  +4 4 960.1 66.0 839.3 43.9 59.0 191.8 6.4 63.8-4  +2.8 2.8 885.8 56.2 670.6 35.8 49.7 127.2 4.8 54.2-2.8  +2 2 767.0 47.8 554.8 29.1 41.8 72.9 3.9 45.9-2  +1.4 1.4 615.8 41.0 379.7 24.5 35.7 49.8 3.3 39.3-1.4  +1 1 556.0 34.8 315.6 20.7 30.3 34.9 2.9 33.4-1  +0.71 0.71 405.9 30.4 232.4 17.9 26.4 23.1 2.6 29.1-0.71  +0.5 0.5 405.1 25.9 207.2 15.4 22.6 26.8 2.2 24.8-0.5  +0.355 0.355 253.7 23.1 143.9 13.6 20.1 18.0 2.0 22.1-0.355  +0.25 0.25 256.0 20.3 139.5 12.0 17.6 16.4 1.8 19.4-0.25  +0.18 0.18 202.6 18.0 109.5 10.6 15.7 13.5 1.6 17.3-0.18  +0.125 0.125 208.1 15.7 110.7 9.3 13.7 15.2 1.5 15.1-0.125  +0.09 0.09 165.8 13.9 86.6 8.3 12.1 11.3 1.3 13.3-0.09  +0.063 0.063 166.3 12.1 97.4 7.1 10.5 15.9 1.1 11.6-0.063  +0.045 0.045 134.3 10.6 78.0 6.1 9.2 11.9 1.0 10.1-0.045 -0.045 959.7 508.0 78.0Total mass 9062.6 8276.3 8027.9P 80 6.46 10.54 7.97 27.44 6.97P 50 2.21 4.96 2.83 20.21 2.4001020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.5: Feed and product PSDs of test No. Au (C) 1227Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 2462.9 69.3 100.0-25  +19 19 22.1 99.8 42.9 99.6 99.7 1942.8 45.1 99.8-19  16 16 93.5 98.9 416.2 95.3 97.8 889.4 34.0 98.6-16  +12.5 12.5 357.3 95.6 923.2 85.8 92.6 750.7 24.7 94.7-12.5  +8 8 1428 82.5 2436.5 60.9 75.7 913.2 13.3 80.3-8  +5.6 5.6 1176.9 71.7 1218.4 48.4 64.3 362.2 8.8 69.3-5.6  +4 4 1149.0 61.1 927.9 38.9 54.1 191.8 6.4 58.9-4  +2.8 2.8 1026.3 51.7 742.7 31.3 45.2 127.2 4.8 49.6-2.8  +2 2 975.3 42.7 610.4 25.0 37.1 72.9 3.9 40.9-2  +1.4 1.4 648.1 36.7 440.4 20.5 31.6 49.8 3.3 35.1-1.4  +1 1 624.3 31.0 274.9 17.7 26.8 34.9 2.9 29.6-1  +0.71 0.71 434.2 27.0 193.2 15.7 23.4 23.1 2.6 25.8-0.71  +0.5 0.5 479.3 22.6 249.9 13.2 19.6 26.8 2.2 21.6-0.5  +0.355 0.355 288.3 19.9 155.9 11.6 17.3 18.0 2.0 19.1-0.355  +0.25 0.25 272.2 17.4 129.1 10.2 15.1 16.4 1.8 16.7-0.25  +0.18 0.18 215.8 15.4 102.8 9.2 13.5 13.5 1.6 14.8-0.18  +0.125 0.125 206.7 13.5 122.8 7.9 11.8 15.2 1.5 13.0-0.125  +0.09 0.09 173.8 11.9 82.2 7.1 10.4 11.3 1.3 11.4-0.09  +0.063 0.063 181.2 10.2 104.5 6.0 8.9 15.9 1.1 9.8-0.063  +0.045 0.045 151.5 8.8 77.2 5.2 7.7 11.9 1.0 8.5-0.045 -0.045 961.3 509.9 78.0Total mass 10865.1 9761 8027.9P 80 7.45 11.45 9.15 27.44 7.93P 50 2.65 5.91 3.44 20.21 2.85FeedEdgeCentre01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.6: Feed and product PSDs of test No. Au (C) 2228Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 2462.9 69.3 100.0-25  +19 19 131 99.0 214.3 97.6 98.5 1942.8 45.1 98.8-19  16 16 364.1 96.1 678.9 90.0 94.2 889.4 34.0 95.5-16  +12.5 12.5 778.4 90.0 1180.3 76.8 85.8 750.7 24.7 88.6-12.5  +8 8 2407.9 71.0 2076.1 53.6 65.4 913.2 13.3 69.2-8  +5.6 5.6 1372.2 60.2 1072.2 41.6 54.3 362.2 8.8 58.3-5.6  +4 4 1301.4 49.9 799.5 32.7 44.4 191.8 6.4 48.2-4  +2.8 2.8 1107.4 41.2 606.3 25.9 36.3 127.2 4.8 39.6-2.8  +2 2 934.3 33.8 442.0 21.0 29.7 72.9 3.9 32.5-2  +1.4 1.4 756.0 27.8 368.0 16.9 24.3 49.8 3.3 26.8-1.4  +1 1 557.9 23.5 206.2 14.6 20.6 34.9 2.9 22.6-1  +0.71 0.71 445.6 19.9 155.9 12.8 17.7 23.1 2.6 19.2-0.71  +0.5 0.5 384.5 16.9 189.3 10.7 14.9 26.8 2.2 16.3-0.5  +0.355 0.355 247.1 15.0 114.7 9.4 13.2 18.0 2.0 14.4-0.355  +0.25 0.25 235.7 13.1 106.0 8.2 11.6 16.4 1.8 12.6-0.25  +0.18 0.18 181.9 11.7 97.2 7.2 10.2 13.5 1.6 11.2-0.18  +0.125 0.125 188.7 10.2 82.4 6.2 8.9 15.2 1.5 9.8-0.125  +0.09 0.09 145.6 9.0 103.8 5.1 7.8 11.3 1.3 8.6-0.09  +0.063 0.063 150.9 7.8 73.7 4.3 6.7 15.9 1.1 7.5-0.063  +0.045 0.045 132.8 6.8 42.4 3.8 5.8 11.9 1.0 6.5-0.045 -0.045 862.2 338.2 78.0Total mass 12685.6 8947.4 8027.9P 80 10.14 13.34 11.22 27.44 10.49P 50 4.01 7.27 4.91 20.21 4.29FeedEdgeCentre01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.7: Feed and product PSDs of test No. Au (C) 3229Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 0 100.0 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 0 100.0 100.0-19  16 16 0 100.0 0.0 100.0 100.0 0 100.0 100.0-16  +12.5 12.5 0 100.0 0.0 100.0 100.0 55.8 99.4 100.0-12.5  +8 8 137.4 97.6 1604.5 85.1 93.8 2944.0 66.7 96.4-8  +5.6 5.6 347.3 91.7 1909.4 67.3 84.2 2080.6 43.5 89.2-5.6  +4 4 584.9 81.7 1555.0 52.8 72.8 1318.1 28.9 78.8-4  +2.8 2.8 612.8 71.1 1097.3 42.6 62.3 704.3 21.1 68.3-2.8  +2 2 493.7 62.7 842.9 34.8 54.1 462.1 15.9 59.9-2  +1.4 1.4 527.9 53.6 734.8 28.0 45.7 313.0 12.4 51.1-1.4  +1 1 437.5 46.1 465.8 23.6 39.2 193.9 10.3 43.9-1  +0.71 0.71 347.3 40.2 338.8 20.5 34.1 106.8 9.1 38.2-0.71  +0.5 0.5 357.9 34.0 333.3 17.4 28.9 136.2 7.6 32.4-0.5  +0.355 0.355 221.8 30.2 219.0 15.3 25.6 80.7 6.7 28.7-0.355  +0.25 0.25 221.9 26.4 197.4 13.5 22.4 68.8 5.9 25.1-0.25  +0.18 0.18 168.9 23.5 158.0 12.0 20.0 53.1 5.3 22.4-0.18  +0.125 0.125 182.3 20.4 162.8 10.5 17.3 60.7 4.7 19.4-0.125  +0.09 0.09 128.3 18.2 130.1 9.3 15.4 66.6 3.9 17.3-0.09  +0.063 0.063 153.2 15.6 134.6 8.0 13.2 54.9 3.3 14.8-0.063  +0.045 0.045 109.3 13.7 113.6 7.0 11.6 38.7 2.9 13.0-0.045 -0.045 798.0 750.7 258.4Total mass 5830.4 10747.99 8996.7Linear 80 3.81 7.31 5.02 9.83 4.19Linear 50 1.21 3.67 1.71 6.27 1.34Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.8: Feed and product PSDs of test No. Au (C) 4230Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 0 100.0 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 0 100.0 100.0-19  16 16 0 100.0 0.0 100.0 100.0 0 100.0 100.0-16  +12.5 12.5 0 100.0 6.9 99.9 100.0 55.8 99.4 100.0-12.5  +8 8 170.1 96.5 1031.1 82.3 92.0 2944.0 66.7 95.1-8  +5.6 5.6 433.8 87.5 1113.3 63.3 79.8 2080.6 43.5 85.1-5.6  +4 4 638.7 74.2 848.1 48.8 66.2 1318.1 28.9 71.7-4  +2.8 2.8 528.1 63.3 607.7 38.5 55.4 704.3 21.1 60.8-2.8  +2 2 450.2 54.0 426.3 31.2 46.7 462.1 15.9 51.7-2  +1.4 1.4 410.5 45.5 383.0 24.7 38.9 313.0 12.4 43.4-1.4  +1 1 278.5 39.7 209.8 21.1 33.8 193.9 10.3 37.8-1  +0.71 0.71 268.2 34.1 161.1 18.3 29.1 106.8 9.1 32.5-0.71  +0.5 0.5 256.1 28.8 178.3 15.3 24.5 136.2 7.6 27.5-0.5  +0.355 0.355 159.9 25.5 106.4 13.5 21.7 80.7 6.7 24.3-0.355  +0.25 0.25 163.5 22.1 98.5 11.8 18.8 68.8 5.9 21.1-0.25  +0.18 0.18 124.6 19.5 90.3 10.3 16.6 53.1 5.3 18.6-0.18  +0.125 0.125 117.3 17.1 77.4 8.9 14.5 60.7 4.7 16.3-0.125  +0.09 0.09 121.5 14.6 89.6 7.4 12.3 66.6 3.9 13.9-0.09  +0.063 0.063 102.2 12.5 83.8 6.0 10.4 54.9 3.3 11.8-0.063  +0.045 0.045 83.5 10.7 51.2 5.1 8.9 38.7 2.9 10.2-0.045 -0.045 517.5 298.9 258.4Total mass 4824.24 5861.7 8996.7P 80 4.70 7.71 5.64 9.83 4.99P 50 1.72 4.13 2.30 6.27 1.88Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.9: Feed and product PSDs of test No. Au (C) 5231Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 0 100.0 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 0 100.0 100.0-19  16 16 0 100.0 0.0 100.0 100.0 0 100.0 100.0-16  +12.5 12.5 0 100.0 10.8 99.8 99.9 55.8 99.4 100.0-12.5  +8 8 299 95.8 1176.5 78.7 90.5 2944.0 66.7 94.1-8  +5.6 5.6 618.6 87.2 1182.6 57.4 77.9 2080.6 43.5 84.2-5.6  +4 4 844.3 75.3 845.4 42.2 65.1 1318.1 28.9 72.0-4  +2.8 2.8 795.5 64.2 533.9 32.6 54.4 704.3 21.1 61.0-2.8  +2 2 692.7 54.5 391.3 25.6 45.5 462.1 15.9 51.6-2  +1.4 1.4 674.3 45.1 298.2 20.2 37.4 313.0 12.4 42.6-1.4  +1 1 459.4 38.6 169.4 17.1 32.0 193.9 10.3 36.5-1  +0.71 0.71 372.6 33.4 111.9 15.1 27.8 106.8 9.1 31.6-0.71  +0.5 0.5 407.2 27.7 144.0 12.5 23.0 136.2 7.6 26.2-0.5  +0.355 0.355 249.2 24.2 84.6 11.0 20.1 80.7 6.7 22.9-0.355  +0.25 0.25 233.6 21.0 74.4 9.7 17.5 68.8 5.9 19.8-0.25  +0.18 0.18 180.1 18.4 62.8 8.6 15.4 53.1 5.3 17.5-0.18  +0.125 0.125 184.6 15.9 66.3 7.4 13.2 60.7 4.7 15.0-0.125  +0.09 0.09 138.1 13.9 56.4 6.4 11.6 66.6 3.9 13.2-0.09  +0.063 0.063 134.7 12.0 62.5 5.2 9.9 54.9 3.3 11.4-0.063  +0.045 0.045 103.3 10.6 31.5 4.7 8.8 38.7 2.9 10.0-0.045 -0.045 756.8 259.3 258.4Total mass 7144 5561.8 8996.7P 80 4.63 8.29 5.99 9.83 5.05P 50 1.71 4.82 2.40 6.27 1.89Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.10: Feed and product PSDs of test No. Au (C) 6232A.3 Gold (B) OreTable A.3: Summary of HPGR tests on gold (B) oreRoller diameter (D) [m] 0.750Roller width (W ) [ m] 0.220Symbol UnitQ [ m/ s] 0.750 0.750 0.750 0.750n [rpm] 19.10 19.10 19.10 19.10Static gap X 0 [ mm] 9.0 9.0 9.0 9.0Hydraulic pressure P [ bar] 82 82 41 41Pressing force F [ k N] 660.0 660.0 330.0 330.0Specific pressing force F SP [N/mm 2 ] 4.00 4. 00 2. 00 2. 00Test time t [s] 15.81 13.55 18.09 16.90Average actual speed ZAV [ m/ s] 0.81 0.78 0.79 0.78Standard deviation VZ 0.35 0.23 0.27 0.23Actual roller gap (average) X gAV [mm] 20.40 20. 97 23. 17 22. 35Standard deviation VX 0.44 0.24 0.70 0.41Actual hydraulic pressure (average) P AV [bar] 81.6 80. 3 39. 8 40. 4Standard deviation 0.51 0.44 0.37 0.44Actual pressing force (average) F AV [ k N] 656 646 320 325Actual specific pressure (average) F SPAV [N/mm 2 ] 3.99 3. 92 1. 95 1. 97I d le power draw Pi [k W ] 9.66 12.07 10.72 10.25Power draw P [ k W ] 74.17 70.14 48.18 43.65Total specific energy consumption E S P [ k W h/t] 2.58 2.35 1.52 1.39Net Specific energy consumption E SP net [kWh/t] 2.25 1. 94 1. 18 1. 06Press throughput W [t/h] 28. 72 29. 88 31. 65 31. 45Specific throughput constant m dot [ts/hm 3 ] 215 232 242 246Average flake density UF [t/m 3 ] 2.28 2. 29 2. 31 2. 29Standard deviation 0.02 0.01 0.03 0.01F lake thickness average X F [mm] 25.76 22. 91 25. 58 22. 91Standard deviation 1.19 2.35 2.75 2.35Feed moisture [%] 1.70 2.02 1.70 2.02Feed bulk density [t/m 3 ] 1.64 1.69 1.64 1.69Feed Proctor density (solids) [t/m 3 ] 2.15 2.16 2.15 2.16Particle size distributionFeed: 100% passing size P 100 [ mm] 32 12.5 32 12.5Feed: 80% passing size P 80 [ mm] 21.66 8.85 21.66 8.85Feed: 50% passing size P 50 [ mm] 11.54 4.75 11.54 4.75Centre: 80% passing size P 80 [ mm] 5.81 4.14 7.62 4.57Centre: 50% passing size P 50 [ mm] 1.86 1.38 2.37 1.46Edge: 80% passing size P 80 [ mm] 10.36 6.79 12.95 8.39Edge: 50% passing size P 50 [ mm] 3.91 2.77 5.87 4.19Scale-up: 80% passing size P 80 [ mm] 6.61 4.55 8.63 5.16Scale-up: 50% passing size P 50 [ mm] 2.07 1.53 2.70 1.72% Passing 4mm of scaled product [%] 66.41 76.25 59.39 72.05Reduction ratio F80/P80 3.28 1.95 2.51 1.72Reduction ratio F50/P50 5.59 3.11 4.28 2.76Mass balanceTotal feed material M F [ k g] 278 271.8 284.1 269.8Total centre product M C [ k g] 103.9 152.5 108.7 112.4Total edge product M E [ k g] 50.5 73.1 51.3 49.4Edge product % of centre & edge material M E F % [%] 32.7% 32.4% 32.1% 30.5%Total waste product MW [ k g] 114.7 39.5 120.0 102.3Waste product % of total feed MWF% [%] 41.3% 14.5% 42.2% 37.9%Total recovered product MP [ k g] 269 265 280 264Mass reconciliation (+ "gain; - "loss") MPF% [%] -3.2% -2.5% -1.4% -2.1%Material dataAu (B) 3 Au (B) 4Process set pointsSpeedProcess dataPress constantsData Description Test number: Au (B) 1 Au (B) 2233A.4 Nickel-Copper OreTable A.4: Summary of HPGR tests on nickel-copper oreRoller Diameter ( D ) [ m] 0.750Roller Width ( W) [ m] 0.220Symbol UnitQ [ m/ s] 0.75 0.75 0.75 0.75 0.75n [rpm] 19.10 19.10 19.10 19.10 19.10Static Gap X 0 [ mm] 9.0 9.0 9.0 9.0 9.0Hydraulic Pressure P [ bar] 103 82.1 61.5 62 41.0Pressing Force F [ k N] 825.0 660.0 495.0 495.0 330.0Specific Pressing Force F SP [N/mm 2 ] 5.0 4. 0 3. 0 3. 0 2. 0Test Time t [s] 20.20 20.80 20.80 18.19 19.61Average Actual Speed: ZAV [ m/ s] 0.77 0.76 0.76 0.77 0.76Standard Deviation VZ 0.22 0.11 0.10 0.19 0.13Actual Roller gap (average) X gAV [mm] 16.88 17. 86 18. 31 19. 34 16. 47Standard Deviation VX 0.51 0.59 0.46 0.77 0.44Actual Hydraulic Pressure (average) PAV [bar] 101.8 80. 6 61. 0 61. 2 41. 1Standard Deviation 0.82 1.20 1.00 0.76 0.85Actual Pressing Force (average) F AV [ k N] 819 649 491 492 331Actual Specific Pressure (average) F SPAV [N/mm 2 ] 4.98 3. 94 2. 98 2. 99 2. 01I d le Power Draw Pi [k W ] 10.04 9.84 9.75 10.18 8.60Power Draw P [ k W ] 71.37 62.46 51.85 50.98 41.69Total Specific Energy Consumption E S P [ k W h/t] 2.94 2.42 1.98 1.85 1.57Net Specific Energy Consumption E SP net [kWh/t] 2.53 2. 04 1. 61 1. 48 1. 24Press throughput W [t/h] 24.23 25.83 26.22 27.50 26.62Specific Throughput Constant m dot [ts/hm 3 ] 191 207 210 217 212Average Flake Density UF [t/m 3 ] 2.56 2. 55 2. 53 2. 52 2. 54Standard Deviation 0.06 0.08 0.05 0.09 0.12F lake Thickness Average X F [mm] 21.47 22. 29 21. 50 21. 71 19. 66Standard Deviation 2.56 1.70 2.01 1.70 3.79Feed Moisture [%] 2.4% 2. 4% 2. 4% 0. 4% 2. 4%Feed Bulk Density (dry) [t/m 3 ] 2.08 2.08 2.08 1.91 2.08Particle Size DistributionFeed: 100% Passing Size F100 [ mm] 32 32 32 32 32Feed: 80% Passing Size F 80 [ mm] 23.67 23.67 23.67 23.67 23.67Feed: 50% Passing Size F 80 [ mm] 16.90 16.90 16.90 16.90 16.90Centre: 80% Passing Size P 80 [ mm] 6.32 7.13 8.37 8.42 10.05Centre: 50% Passing Size P 50 [ mm] 2.08 2.31 2.95 2.73 4.01Edge: 80% Passing Size P 80 [ mm] 9.51 10.19 11.46 11.81 13.80Edge: 50% Passing Size P 50 [ mm] 3.89 4.63 5.93 6.19 7.86Combined 90% Center & 10% Edge: 80% Passing Size P 80 [ mm] 6.72 7.50 8.84 8.96 10.45Combined 90% Center & 10% Edge: 50% Passing Size P 50 [ mm] 2.22 2.47 3.18 3.00 4.31Reduction Ratio F80/P80 (Scaled Product) 3.52 3.15 2.68 2.64 2.26Reduction Ratio F50/P50 (Scaled Product) 7.61 6.84 5.31 5.64 3.92Mass BalanceTotal Feed Material M F [ k g] 279 270 283 256 288Total Centre Product M C [ k g] 91.0 104.0 104.5 94.5 97.5Centre Product % of Centre & Edge Material MCE% [%] 66.9% 69.7% 69.0% 68.0% 67.2%Total Edge Product M E [ k g] 45.0 45.2 47.0 44.5 47.5Edge Product % of Centre & Edge Material M E F % [%] 33.1% 30.3% 31.0% 32.0% 32.8%Edge Product % of Centre Product M E C % [%] 127.0 110.5 122.5 110.0 134.0Total Waste Product MW [ k g] 127 111 123 110 134Waste Product % of Total Feed MWF% [%] 45.6% 41.0% 43.3% 43.0% 45.6%Total Recovered Product MP [ k g] 263 260 274 249 279Mass Reconciliation (+ "gain; - "loss") MPF% [%] -5.6% -3.6% -3.2% -2.7% -3.1%Ni-Cu 3 Ni-Cu 4 Ni-Cu 5Material DataProcess Set PointsSpeedProcess DataTest Number:PressConstantsData Description Ni-Cu 1 Ni-Cu 2234Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 1208.6 89.1 100.0-25  +19 19 21.4 99.8 124.0 99.0 99.6 1814.7 72.8 99.7-19  16 16 51.2 99.4 335.0 96.4 98.4 1074.5 63.1 99.1-16  +12.5 12.5 320.1 96.8 971.6 88.8 94.2 1091.4 53.2 96.0-12.5  +8 8 1147.2 87.6 2376.3 70.2 81.9 1692.7 38.0 85.8-8  +5.6 5.6 1024.7 79.3 1308.6 60.0 73.0 822.6 30.6 77.4-5.6  +4 4 1247.4 69.2 1205.8 50.6 63.1 611.1 25.1 67.3-4  +2.8 2.8 1113.6 60.2 995.5 42.8 54.5 476.8 20.8 58.5-2.8  +2 2 1064.0 51.6 834.7 36.3 46.6 385.6 17.3 50.1-2  +1.4 1.4 881.7 44.5 676.3 31.0 40.1 292.4 14.7 43.1-1.4  +1 1 771.4 38.3 532.4 26.8 34.5 210.3 12.8 37.1-1  +0.71 0.71 571.9 33.6 429.8 23.5 30.3 161.4 11.3 32.6-0.71  +0.5 0.5 483.8 29.7 326.9 20.9 26.9 140.7 10.1 28.9-0.5  +0.355 0.355 357.3 26.8 244.6 19.0 24.3 96.9 9.2 26.1-0.355  +0.25 0.25 331.8 24.2 224.7 17.3 21.9 87.0 8.4 23.5-0.25  +0.18 0.18 270.3 22.0 182.4 15.8 20.0 79.1 7.7 21.4-0.18  +0.125 0.125 328.9 19.3 234.9 14.0 17.6 103.5 6.8 18.8-0.125  +0.09 0.09 277.3 17.1 204.6 12.4 15.6 92.6 5.9 16.6-0.09  +0.063 0.063 350.1 14.3 347.1 9.7 12.8 125.9 4.8 13.8-0.063  +0.045 0.045 344.4 11.5 184.6 8.2 10.4 109.4 3.8 11.2-0.045 -0.045 1420.6 1053.6 422.2Total mass 12379.1 12793.4 11099.4P 80 5.81 10.36 7.49 21.66 6.35P 50 1.86 3.91 2.34 11.54 1.99Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.11: Feed and product PSDs of test No. Au (B) 1235Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 0 100.0 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 0 100.0 100.0-19  16 16 0 100.0 0.0 100.0 100.0 0 100.0 100.0-16  +12.5 12.5 0 100.0 9.4 99.9 100.0 54.6 99.3 100.0-12.5  +8 8 380.1 96.1 1059.1 87.1 93.2 1956.9 75.5 95.2-8  +5.6 5.6 641.5 89.6 1163.3 73.1 84.3 1485.9 57.4 88.0-5.6  +4 4 1044.1 79.0 1044.3 60.4 73.0 1138.7 43.5 77.2-4  +2.8 2.8 1016.6 68.7 839.5 50.3 62.8 759.7 34.3 66.9-2.8  +2 2 938.2 59.2 650.9 42.5 53.8 558.3 27.5 57.5-2  +1.4 1.4 871.4 50.4 545.8 35.9 45.7 407.7 22.5 48.9-1.4  +1 1 676.1 43.5 439.1 30.6 39.3 274.5 19.1 42.2-1  +0.71 0.71 504.6 38.4 320.6 26.7 34.6 212.3 16.6 37.2-0.71  +0.5 0.5 444.7 33.9 275.2 23.4 30.5 169.5 14.5 32.8-0.5  +0.355 0.355 280.2 31.0 169.4 21.3 27.9 114.8 13.1 30.1-0.355  +0.25 0.25 287.3 28.1 173.2 19.2 25.2 97.7 11.9 27.2-0.25  +0.18 0.18 239.3 25.7 138.2 17.6 23.1 85.0 10.9 24.9-0.18  +0.125 0.125 287.8 22.8 167.1 15.5 20.4 104.8 9.6 22.1-0.125  +0.09 0.09 242.6 20.3 145.3 13.8 18.2 110.3 8.2 19.7-0.09  +0.063 0.063 333.2 16.9 194.4 11.4 15.2 118.5 6.8 16.4-0.063  +0.045 0.045 310.6 13.8 194.8 9.1 12.3 111.9 5.4 13.3-0.045 -0.045 1359.0 752.8 446.4Total mass 9857.3 8282.4 8207.5P 80 4.14 6.79 4.99 8.85 4.42P 50 1.38 2.77 1.72 4.75 1.48Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.12: Feed and product PSDs of test No. Au (B) 2236Full PSD Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 21.3 99.8 99.9 1208.6 89.1 100.0-25  +19 19 116.2 98.9 297.0 96.7 98.2 1814.7 72.8 98.7-19  16 16 159.3 97.4 777.5 88.5 94.6 1074.5 63.1 96.6-16  +12.5 12.5 471.7 93.1 935.2 78.7 88.5 1091.4 53.2 91.6-12.5  +8 8 1252.4 81.4 1776.4 60.2 74.6 1692.7 38.0 79.3-8  +5.6 5.6 975.9 72.4 1091.6 48.7 64.8 822.6 30.6 70.0-5.6  +4 4 1031.8 62.8 815.8 40.2 55.5 611.1 25.1 60.5-4  +2.8 2.8 931.5 54.1 682.6 33.1 47.4 476.8 20.8 52.0-2.8  +2 2 831.8 46.4 519.5 27.6 40.4 385.6 17.3 44.5-2  +1.4 1.4 728.0 39.6 462.2 22.8 34.2 292.4 14.7 38.0-1.4  +1 1 439.6 35.6 282.5 19.8 30.5 210.3 12.8 34.0-1  +0.71 0.71 468.6 31.2 229.3 17.4 26.8 161.4 11.3 29.8-0.71  +0.5 0.5 408.8 27.4 199.3 15.3 23.5 140.7 10.1 26.2-0.5  +0.355 0.355 264.5 24.9 125.7 14.0 21.4 96.9 9.2 23.9-0.355  +0.25 0.25 261.5 22.5 121.8 12.8 19.4 87.0 8.4 21.5-0.25  +0.18 0.18 222.2 20.5 102.4 11.7 17.6 79.1 7.7 19.6-0.18  +0.125 0.125 260.8 18.0 130.3 10.3 15.6 103.5 6.8 17.3-0.125  +0.09 0.09 239.6 15.8 124.9 9.0 13.6 92.6 5.9 15.1-0.09  +0.063 0.063 303.4 13.0 153.7 7.4 11.2 125.9 4.8 12.4-0.063  +0.045 0.045 240.3 10.8 146.4 5.9 9.2 109.4 3.8 10.3-0.045 -0.045 1157.9 561.4 422.2Total mass 10765.8 9556.8 11099.4P 50 2.37 5.87 3.19 11.54 2.58P 80 7.62 12.95 9.75 21.66 8.26Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.13: Feed and product PSDs of test No. Au (B) 3237Scaled 90/10Sieve range(mm)Nominalsize,(mm)Retained(g)Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%Retained(g)Cum. Passing%Cum. Passing%-35.5 +32 32 0 100.0 0.0 100.0 100.0 0 100.0 100.0-32  +25 25 0 100.0 0.0 100.0 100.0 0 100.0 100.0-25  +19 19 0 100.0 0.0 100.0 100.0 0 100.0 100.0-19  16 16 0 100.0 0.0 100.0 100.0 0 100.0 100.0-16  +12.5 12.5 0 100.0 12.1 99.9 100.0 54.6 99.3 100.0-12.5  +8 8 238.7 95.7 1933.6 78.1 90.3 1956.9 75.5 93.9-8  +5.6 5.6 478.3 87.0 1532.6 60.8 79.0 1485.9 57.4 84.3-5.6  +4 4 591.4 76.2 1090.1 48.6 67.8 1138.7 43.5 73.4-4  +2.8 2.8 574.5 65.8 848.5 39.0 57.6 759.7 34.3 63.1-2.8  +2 2 454.5 57.5 618.6 32.0 49.7 558.3 27.5 54.9-2  +1.4 1.4 457.9 49.2 479.9 26.6 42.3 407.7 22.5 46.9-1.4  +1 1 401.6 41.9 330.1 22.9 36.1 274.5 19.1 40.0-1  +0.71 0.71 298.2 36.4 267.6 19.9 31.4 212.3 16.6 34.8-0.71  +0.5 0.5 246.9 31.9 203.4 17.6 27.6 169.5 14.5 30.5-0.5  +0.355 0.355 157.8 29.1 138.5 16.1 25.1 114.8 13.1 27.8-0.355  +0.25 0.25 162.2 26.1 125.0 14.6 22.6 97.7 11.9 25.0-0.25  +0.18 0.18 125.9 23.8 101.2 13.5 20.7 85.0 10.9 22.8-0.18  +0.125 0.125 151.9 21.1 123.0 12.1 18.3 104.8 9.6 20.2-0.125  +0.09 0.09 135.3 18.6 126.2 10.7 16.2 110.3 8.2 17.8-0.09  +0.063 0.063 169.1 15.5 152.0 9.0 13.5 118.5 6.8 14.9-0.063  +0.045 0.045 174.7 12.3 150.5 7.3 10.8 111.9 5.4 11.8-0.045 -0.045 678.8 647.9 446.4Total mass 5497.7 8880.8 8207.5P 80 4.57 8.39 5.82 8.85 4.96P 50 1.46 4.19 2.03 4.75 1.63Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.14: Feed and product PSDs of test No. Au (B) 4238Full PSD Scaled 90/10Sieve range(mm)N ominalsiz e,(mm)Retained(g )Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%-35.5 +32 3 2 0 100.0 0 . 0 100.0 100.0 52.01 99.7 100.0-32  +25 2 5 0 100.0 0 . 0 100.0 100.0 3064.9 84.8 100.0-25  +19 1 9 0 100.0 0 . 0 100.0 100.0 4434.9 63.2 100.0-19  16 1 6 6 3 . 2 99.4 1 7 0 . 4 98.5 99.1 3868.5 44.3 99.3-16  +12.5 1 2 . 5 2 5 8 . 7 97.1 5 0 7 . 8 94.0 96.0 3702 26.3 96.7-12.5  +8 8 1 1 6 7 . 6 86.4 2 3 7 1 . 3 72.9 81.9 2 8 6 3 . 3 12.3 85.0-8  +5.6 5 . 6 9 9 3 . 6 77.3 1 3 9 5 . 4 60.6 71.7 8 6 5 . 3 8.1 75.6-5.6  +4 4 1 1 1 1 . 8 67.1 1 1 0 5 . 6 50.8 61.7 4 2 1 . 1 6.0 65.5-4  +2.8 2 . 8 1 0 9 3 . 3 57.1 9 4 8 . 5 42.3 52.2 2 6 4 . 1 4.7 55.6-2.8  +2 2 8 6 0 . 5 49.2 7 4 9 . 6 35.7 44.7 1 4 5 . 8 4.0 47.9-2  +1.4 1 . 4 7 8 3 . 8 42.0 6 3 9 . 9 30.0 38.1 1 2 0 . 1 3.4 40.8-1.4  +1 1 6 1 2 . 7 36.4 4 6 3 . 3 25.9 32.9 8 2 . 4 3.0 35.4-1  +0.71 0 . 7 1 5 2 9 . 9 31.6 3 7 5 . 4 22.6 28.6 6 4 . 8 2.7 30.7-0.71  +0.5 0 . 5 4 3 0 . 0 27.6 3 0 7 . 5 19.8 25.1 4 8 . 9 2.5 26.9-0.5  +0.355 0 . 3 5 5 3 6 1 . 5 24.3 2 6 7 . 1 17.5 22.1 4 2 . 9 2.3 23.6-0.355  +0.25 0 . 2 5 3 6 1 . 5 21.0 2 4 3 . 9 15.3 19.1 4 1 . 8 2.1 20.5-0.25  +0.18 0 . 1 8 3 6 3 . 8 17.7 2 2 3 . 4 13.3 16.2 4 3 . 8 1.9 17.3-0.18  +0.125 0 . 1 2 5 5 9 2 . 1 12.3 3 6 2 . 2 10.1 11.6 8 4 . 8 1.4 12.1-0.125  +0.09 0 . 0 9 3 4 3 . 2 9.1 2 6 5 . 4 7.8 8.7 9 7 . 2 1.0 9.0-0.09  +0.063 0 . 0 6 3 4 3 9 . 2 5.1 3 6 0 . 7 4.6 4.9 7 2 . 7 0.6 5.1-0.063  +0.045 0 . 0 4 5 2 9 0 . 6 2.5 1 8 2 . 1 2.9 2.6 1 6 . 6 0.5 2.5-0.045 - 0 . 0 4 5 2 6 7 . 7 3 3 1 . 6 1 0 9 . 3T otal mass 1 0 9 2 4 . 7 1 1 2 7 1 . 1 2 0 5 0 7 . 2d 80 6.32 9.51 7.55 23.67 6.72d 50 2.08 3.89 2.56 16.90 2.22Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.15: Feed and product PSDs of test No. Ni-Cu 1239Full PSD Scaled 90/10Sieve range(mm)N ominalsiz e,(mm)Retained(g )Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%-35.5 +32 3 2 0 100.0 0 . 0 100.0 100.0 52.01 99.7 100.0-32  +25 2 5 0 100.0 0 . 0 100.0 100.0 3064.9 84.8 100.0-25  +19 1 9 9 . 9 99.9 6 6 . 0 99.4 99.8 4434.9 63.2 99.9-19  16 1 6 6 3 . 9 99.4 1 4 6 . 5 98.1 99.0 3868.5 44.3 99.3-16  +12.5 1 2 . 5 4 1 0 . 1 96.1 7 0 7 . 3 91.9 94.8 3702 26.3 95.7-12.5  +8 8 1 5 6 4 . 9 83.5 2 6 0 5 . 4 68.8 79.1 2 8 6 3 . 3 12.3 82.1-8  +5.6 5 . 6 1 2 1 0 . 0 73.8 1 4 2 4 . 6 56.2 68.5 8 6 5 . 3 8.1 72.1-5.6  +4 4 1 1 5 5 . 1 64.5 1 1 5 2 . 3 46.0 58.9 4 2 1 . 1 6.0 62.7-4  +2.8 2 . 8 1 2 0 1 . 9 54.9 8 9 6 . 6 38.1 49.8 2 6 4 . 1 4.7 53.2-2.8  +2 2 9 9 7 . 4 46.9 6 6 4 . 9 32.2 42.4 1 4 5 . 8 4.0 45.4-2  +1.4 1 . 4 8 5 3 . 5 40.0 5 6 2 . 5 27.2 36.1 1 2 0 . 1 3.4 38.7-1.4  +1 1 6 6 4 . 7 34.7 4 0 6 . 9 23.6 31.3 8 2 . 4 3.0 33.6-1  +0.71 0 . 7 1 5 7 2 . 3 30.1 3 1 9 . 0 20.8 27.3 6 4 . 8 2.7 29.1-0.71  +0.5 0 . 5 4 3 2 . 3 26.6 2 5 0 . 0 18.6 24.2 4 8 . 9 2.5 25.8-0.5  +0.355 0 . 3 5 5 3 9 5 . 0 23.4 2 0 6 . 0 16.7 21.4 4 2 . 9 2.3 22.8-0.355  +0.25 0 . 2 5 3 8 7 . 1 20.3 1 9 6 . 2 15.0 18.7 4 1 . 8 2.1 19.8-0.25  +0.18 0 . 1 8 4 8 1 . 0 16.4 1 9 3 . 2 13.3 15.5 4 3 . 8 1.9 16.1-0.18  +0.125 0 . 1 2 5 5 7 5 . 5 11.8 2 6 3 . 3 11.0 11.6 8 4 . 8 1.4 11.7-0.125  +0.09 0 . 0 9 4 5 2 . 8 8.2 2 2 8 . 1 8.9 8.4 9 7 . 2 1.0 8.3-0.09  +0.063 0 . 0 6 3 5 3 1 . 8 3.9 4 7 9 . 8 4.7 4.2 7 2 . 7 0.6 4.0-0.063  +0.045 0 . 0 4 5 2 1 8 . 4 2.2 1 1 3 . 9 3.7 2.6 1 6 . 6 0.5 2.3-0.045 - 0 . 0 4 5 2 6 8 . 9 4 1 6 . 1 1 0 9 . 3T otal mass 1 2 4 4 6 . 5 1 1 2 9 8 . 6 2 0 5 0 7 . 2d 80 7.13 10.19 8.26 23.67 7.50d 50 2.31 4.63 2.83 16.90 2.47Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.16: Feed and product PSDs of test No. Ni-Cu 2240Full PSD Scaled 90/10Sieve range(mm)N ominalsiz e,(mm)Retained(g )Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%-35.5 +32 3 2 0 100.0 0 . 0 100.0 100.0 52.01 99.7 100.0-32  +25 2 5 0 100.0 0 . 0 100.0 100.0 3064.9 84.8 100.0-25  +19 1 9 2 1 99.8 5 6 . 5 99.5 99.7 4434.9 63.2 99.8-19  16 1 6 1 6 4 . 3 98.4 3 4 1 . 8 96.4 97.8 3868.5 44.3 98.2-16  +12.5 1 2 . 5 4 5 1 . 8 94.5 1 1 7 5 . 5 85.9 91.8 3702 26.3 93.7-12.5  +8 8 1 8 4 0 . 3 78.7 2 8 4 1 . 7 60.4 73.0 2 8 6 3 . 3 12.3 76.9-8  +5.6 5 . 6 1 2 6 1 . 9 67.9 1 3 5 2 . 7 48.3 61.8 8 6 5 . 3 8.1 65.9-5.6  +4 4 1 1 6 1 . 9 57.9 1 0 2 7 . 1 39.1 52.1 4 2 1 . 1 6.0 56.0-4  +2.8 2 . 8 1 0 4 8 . 8 48.9 7 9 6 . 0 32.0 43.6 2 6 4 . 1 4.7 47.2-2.8  +2 2 8 8 9 . 2 41.2 6 1 6 . 5 26.5 36.7 1 4 5 . 8 4.0 39.8-2  +1.4 1 . 4 7 3 7 . 4 34.9 4 6 0 . 9 22.3 31.0 1 2 0 . 1 3.4 33.6-1.4  +1 1 5 8 9 . 1 29.8 3 1 8 . 4 19.5 26.6 8 2 . 4 3.0 28.8-1  +0.71 0 . 7 1 4 7 6 . 1 25.7 2 5 9 . 4 17.2 23.1 6 4 . 8 2.7 24.9-0.71  +0.5 0 . 5 3 9 5 . 0 22.3 2 1 5 . 3 15.2 20.1 4 8 . 9 2.5 21.6-0.5  +0.355 0 . 3 5 5 3 0 7 . 9 19.7 1 7 8 . 5 13.6 17.8 4 2 . 9 2.3 19.1-0.355  +0.25 0 . 2 5 3 0 0 . 7 17.1 1 6 7 . 1 12.1 15.6 4 1 . 8 2.1 16.6-0.25  +0.18 0 . 1 8 2 8 6 . 1 14.7 1 6 2 . 5 10.7 13.4 4 3 . 8 1.9 14.3-0.18  +0.125 0 . 1 2 5 4 0 0 . 5 11.2 2 5 4 . 7 8.4 10.3 8 4 . 8 1.4 10.9-0.125  +0.09 0 . 0 9 3 2 0 . 9 8.5 1 9 0 . 3 6.7 7.9 9 7 . 2 1.0 8.3-0.09  +0.063 0 . 0 6 3 4 5 1 . 9 4.6 2 5 6 . 0 4.4 4.5 7 2 . 7 0.6 4.6-0.063  +0.045 0 . 0 4 5 1 7 3 . 5 3.1 1 0 2 . 5 3.5 3.2 1 6 . 6 0.5 3.1-0.045 - 0 . 0 4 5 3 5 9 . 2 3 8 9 . 3 1 0 9 . 3T otal mass 1 1 6 3 7 . 5 1 1 1 6 2 . 7 2 0 5 0 7 . 2d 80 8.37 11.46 9.66 23.67 8.84d 50 2.95 5.93 3.71 16.90 3.18Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.17: Feed and product PSDs of test No. Ni-Cu 3241Full PSD Scaled 90/10Sieve range(mm)N ominalsiz e,(mm)Retained(g )Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%-35.5 +32 3 2 0 100.0 0 . 0 100.0 100.0 52.01 99.7 100.0-32  +25 2 5 0 100.0 0 . 0 100.0 100.0 3064.9 84.8 100.0-25  +19 1 9 1 0 4 . 3 99.2 1 1 5 . 5 99.0 99.1 4434.9 63.2 99.1-19  16 1 6 2 2 8 97.3 3 6 9 . 9 95.6 96.8 3868.5 44.3 97.1-16  +12.5 1 2 . 5 4 7 8 . 7 93.4 1 2 9 4 . 8 83.9 90.4 3702 26.3 92.5-12.5  +8 8 1 8 2 5 78.6 2 7 8 8 . 0 58.6 72.2 2 8 6 3 . 3 12.3 76.6-8  +5.6 5 . 6 1 2 1 7 . 7 68.8 1 2 5 4 . 7 47.2 61.9 8 6 5 . 3 8.1 66.6-5.6  +4 4 1 1 7 3 . 9 59.2 9 9 6 . 6 38.2 52.5 4 2 1 . 1 6.0 57.1-4  +2.8 2 . 8 1 0 6 6 . 8 50.6 8 3 2 . 5 30.6 44.2 2 6 4 . 1 4.7 48.6-2.8  +2 2 8 8 0 . 1 43.5 6 1 2 . 3 25.1 37.6 1 4 5 . 8 4.0 41.6-2  +1.4 1 . 4 7 6 1 . 9 37.3 5 4 4 . 7 20.1 31.8 1 2 0 . 1 3.4 35.6-1.4  +1 1 6 3 2 . 3 32.2 3 6 1 . 8 16.9 27.3 8 2 . 4 3.0 30.6-1  +0.71 0 . 7 1 5 3 8 . 6 27.8 2 9 3 . 1 14.2 23.4 6 4 . 8 2.7 26.4-0.71  +0.5 0 . 5 4 0 0 . 0 24.5 2 1 8 . 5 12.2 20.6 4 8 . 9 2.5 23.3-0.5  +0.355 0 . 3 5 5 3 5 0 . 9 21.7 1 7 1 . 9 10.7 18.2 4 2 . 9 2.3 20.6-0.355  +0.25 0 . 2 5 3 3 7 . 9 19.0 1 4 8 . 7 9.3 15.9 4 1 . 8 2.1 18.0-0.25  +0.18 0 . 1 8 3 0 3 . 1 16.5 1 3 1 . 3 8.1 13.8 4 3 . 8 1.9 15.7-0.18  +0.125 0 . 1 2 5 3 7 9 . 1 13.4 1 4 8 . 8 6.8 11.3 8 4 . 8 1.4 12.8-0.125  +0.09 0 . 0 9 3 3 9 . 4 10.7 1 5 2 . 1 5.4 9.0 9 7 . 2 1.0 10.2-0.09  +0.063 0 . 0 6 3 3 8 4 . 1 7.6 1 5 9 . 2 4.0 6.4 7 2 . 7 0.6 7.2-0.063  +0.045 0 . 0 4 5 2 4 2 . 9 5.6 7 3 . 2 3.3 4.9 1 6 . 6 0.5 5.4-0.045 - 0 . 0 4 5 6 9 0 . 9 3 6 3 . 5 1 0 9 . 3T otal mass 1 2 3 3 5 . 6 1 1 0 3 1 . 1 2 0 5 0 7 . 2d 80 8.42 11.81 9.93 23.67 8.96d 50 2.73 6.19 3.64 16.90 3.00Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.18: Feed and product PSDs of test No. Ni-Cu 4242Full PSD Scaled 90/10Sieve range(mm)N ominalsiz e,(mm)Retained(g )Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%Retained(g )Cum. Passing%Cum. Passing%-35.5 +32 3 2 0 100.0 0 . 0 100.0 100.0 52.01 99.7 100.0-32  +25 2 5 0 100.0 0 . 0 100.0 100.0 3064.9 84.8 100.0-25  +19 1 9 3 1 99.7 2 3 5 . 6 98.1 99.2 4434.9 63.2 99.6-19  16 1 6 2 6 2 . 6 97.6 8 7 0 . 6 91.0 95.4 3868.5 44.3 96.9-16  +12.5 1 2 . 5 7 4 9 . 4 91.5 2 1 3 4 . 5 73.5 85.6 3702 26.3 89.7-12.5  +8 8 2 6 0 2 . 3 70.4 2 8 0 6 . 3 50.6 63.9 2 8 6 3 . 3 12.3 68.4-8  +5.6 5 . 6 1 3 0 7 . 7 59.7 1 2 8 9 . 1 40.1 53.3 8 6 5 . 3 8.1 57.8-5.6  +4 4 1 1 9 9 . 5 50.0 1 0 1 4 . 5 31.8 44.0 4 2 1 . 1 6.0 48.1-4  +2.8 2 . 8 1 0 8 5 . 8 41.1 7 1 9 . 7 25.9 36.1 2 6 4 . 1 4.7 39.6-2.8  +2 2 7 8 6 . 2 34.7 5 4 0 . 6 21.5 30.4 1 4 5 . 8 4.0 33.4-2  +1.4 1 . 4 6 7 3 . 6 29.3 4 4 2 . 3 17.9 25.5 1 2 0 . 1 3.4 28.1-1.4  +1 1 4 9 9 . 2 25.2 3 0 4 . 4 15.4 22.0 8 2 . 4 3.0 24.2-1  +0.71 0 . 7 1 4 3 3 . 4 21.7 2 6 0 . 0 13.3 18.9 6 4 . 8 2.7 20.8-0.71  +0.5 0 . 5 3 2 1 . 6 19.1 1 9 1 . 8 11.7 16.6 4 8 . 9 2.5 18.3-0.5  +0.355 0 . 3 5 5 2 6 9 . 6 16.9 1 5 8 . 5 10.4 14.7 4 2 . 9 2.3 16.2-0.355  +0.25 0 . 2 5 2 5 9 . 1 14.8 1 4 4 . 6 9.2 12.9 4 1 . 8 2.1 14.2-0.25  +0.18 0 . 1 8 2 4 0 . 2 12.8 1 4 9 . 8 8.0 11.2 4 3 . 8 1.9 12.3-0.18  +0.125 0 . 1 2 5 3 5 7 . 3 9.9 2 4 6 . 8 6.0 8.6 8 4 . 8 1.4 9.5-0.125  +0.09 0 . 0 9 2 7 1 . 9 7.7 1 7 5 . 0 4.6 6.7 9 7 . 2 1.0 7.4-0.09  +0.063 0 . 0 6 3 3 6 9 . 7 4.7 2 0 2 . 7 2.9 4.1 7 2 . 7 0.6 4.5-0.063  +0.045 0 . 0 4 5 1 4 4 . 7 3.5 8 8 . 0 2.2 3.1 1 6 . 6 0.5 3.4-0.045 - 0 . 0 4 5 4 3 0 . 1 2 6 7 . 8 1 0 9 . 3T otal mass 1 2 2 9 4 . 9 1 2 2 4 2 . 6 2 0 5 0 7 . 2d 80 10.05 13.80 11.34 23.67 10.45d 50 4.01 7.86 5.03 16.90 4.31Centre Edge Feed01020304050607080901000.01 0.1 1 10 100Cum. percent passing, %Particle size, mmCentreEdgeFull PSDFeedFigure A.19: Feed and product PSDs of test No. Ni-Cu 5243Appendix BPISTON PRESS TEST DATA244B.1 Piston Press Tests on -12.5 mm FeedB.1.1 Copper-molybdenum (P) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1389 239.1 2.182 900 154.9 1.433 600 103.3 1.004 400 68.9 0.78567891011121314151617181920Summary statisticsn 4R2 0.997Intercept 0.170 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0083 50 0.59 ± 0.148 kWh/t ± 0.22 kWh/tSSE 0.003 150 1.42 ± 0.085 kWh/t ± 0.19 kWh/tMSE 0.00155 250 2.25 ± 0.166 kWh/t ± 0.24 kWh/tRMSE 0.0394Cu-Mo (P) -12.5 mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.1: Specific energy versus piston pressure plot for a copper-molydenum (P) ore245B.1.2 Gold (C) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1388 239.0 2.082 900 154.9 1.373 600 103.2 0.984 400 68.8 0.72567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.162 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0080 50 0.56 ± 0.087 kWh/t ± 0.13 kWh/tSSE 0.001 150 1.36 ± 0.051 kWh/t ± 0.11 kWh/tMSE 0.00054 250 2.15 ± 0.099 kWh/t ± 0.14 kWh/tRMSE 0.0233Au (C) -12.5 mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.2: Specific energy versus piston pressure plot for a gold (C) ore246B.1.3 Gold (B) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.8 0.632 600 103.2 0.803 900 154.9 1.264 1389 239.1 1.895 400 68.8 0.646 899 154.7 1.197 1387 238.8 1.87891011121314151617181920Summary statisticsn 7R2 0.995Intercept 0.092 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0074 50 0.46 ± 0.073 kWh/t ± 0.13 kWh/tSSE 0.009 150 1.21 ± 0.042 kWh/t ± 0.12 kWh/tMSE 0.00183 250 1.95 ± 0.076 kWh/t ± 0.13 kWh/tRMSE 0.0428Au (B)Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.3: Specific energy versus piston pressure plot for a gold (B) ore247B.1.4 Nickel-copper oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.9 0.732 600 103.3 0.993 900 154.9 1.384 1389 239.1 1.88567891011121314151617181920Summary statisticsn 4R2 0.996Intercept 0.291 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0068 50 0.63 ± 0.144 kWh/t ± 0.22 kWh/tSSE 0.003 150 1.30 ± 0.083 kWh/t ± 0.18 kWh/tMSE 0.00147 250 1.98 ± 0.162 kWh/t ± 0.23 kWh/tRMSE 0.0383Ni-Cu -12.5 mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.4: Specific energy versus piston pressure plot for a Ni-Cu ore248B.1.5 Copper-molybdenum (H) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1389 239.1 2.142 900 154.9 1.443 600 103.3 1.014 400 68.8 0.68567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.117 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0085 50 0.54 ± 0.067 kWh/t ± 0.10 kWh/tSSE 0.001 150 1.39 ± 0.039 kWh/t ± 0.09 kWh/tMSE 0.00032 250 2.24 ± 0.076 kWh/t ± 0.11 kWh/tRMSE 0.0180Cu-Mo (H) -12.5 mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.5: Specific energy versus piston pressure plot for a copper-molybdenum (H) ore249B.1.6 Tungsten oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1389 239.1 1.952 900 154.9 1.273 600 103.2 0.904567891011121314151617181920Summary statisticsn 3R2 0.999Intercept 0.085 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0078 50 0.47 ± 0.396 kWh/t ± 0.50 kWh/tSSE 0.001 150 1.25 ± 0.179 kWh/t ± 0.35 kWh/tMSE 0.00055 250 2.03 ± 0.311 kWh/t ± 0.43 kWh/tRMSE 0.0235Tungsten -12.5 mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.6: Specific energy versus piston pressure plot for a tungsten ore250B.1.7 DolomiteTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.9 0.382 503 86.5 0.483 900 154.9 0.924 1388 239.0 1.63567891011121314151617181920Summary statisticsn 4R2 0.995Intercept -0.153 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0073 50 0.21 ± 0.180 kWh/t ± 0.28 kWh/tSSE 0.005 150 0.95 ± 0.111 kWh/t ± 0.25 kWh/tMSE 0.00259 250 1.68 ± 0.215 kWh/t ± 0.31 kWh/tRMSE 0.0509DolomiteConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.7: Specific energy versus piston pressure plot for a dolomite251B.1.8 Copper-gold-silver oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.9 0.622 600 103.3 0.953 900 154.9 1.394 1388 238.9 2.13567891011121314151617181920Summary statisticsn 4R2 1.000Intercept 0.020 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0089 50 0.46 ± 0.061 kWh/t ± 0.09 kWh/tSSE 0.001 150 1.35 ± 0.035 kWh/t ± 0.08 kWh/tMSE 0.00026 250 2.23 ± 0.069 kWh/t ± 0.10 kWh/tRMSE 0.0163Cu-Au-AgConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.8: Specific energy versus piston pressure plot for a copper-gold-silver ore252B.1.9 Kimberlite oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1389 239.0 2.272 1064 183.1 1.323 819 141.0 1.034 589 101.4 0.79567891011121314151617181920Summary statisticsn 4R2 0.932Intercept -0.410 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0106 50 0.12 ± 1.106 kWh/t ± 1.42 kWh/tSSE 0.086 150 1.18 ± 0.467 kWh/t ± 1.00 kWh/tMSE 0.04277 250 2.24 ± 0.856 kWh/t ± 1.23 kWh/tRMSE 0.2068KimberliteConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.9: Specific energy versus piston pressure plot for a kimberlite ore253B.1.10 Copper-molybdenum (C) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1388 238.9 1.842 1364 234.8 1.863 924 159.0 1.304 759 130.7 1.07567891011121314151617181920Summary statisticsn 4R2 0.997Intercept 0.139 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0072 50 0.50 ± 0.192 kWh/t ± 0.23 kWh/tSSE 0.002 150 1.22 ± 0.080 kWh/t ± 0.15 kWh/tMSE 0.00080 250 1.95 ± 0.098 kWh/t ± 0.16 kWh/tRMSE 0.0282Cu-Mo (C)Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.10: Specific energy versus piston pressure plot for a copper-molybdenum (C) ore254B.1.11 Copper (M) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1388 238.9 2.122 899 154.7 1.383 600 103.3 1.004 399 68.8 0.77567891011121314151617181920Summary statisticsn 4R2 0.997Intercept 0.193 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0080 50 0.59 ± 0.152 kWh/t ± 0.23 kWh/tSSE 0.003 150 1.39 ± 0.088 kWh/t ± 0.20 kWh/tMSE 0.00164 250 2.18 ± 0.172 kWh/t ± 0.24 kWh/tRMSE 0.0405Cu (M)Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.11: Specific energy versus piston pressure plot for a copper (M) ore255B.1.12 Copper (E) oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1388 238.9 2.222 899 154.8 1.553 599 103.1 1.074 400 68.9 0.82567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.235 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0083 50 0.65 ± 0.105 kWh/t ± 0.16 kWh/tSSE 0.002 150 1.48 ± 0.061 kWh/t ± 0.14 kWh/tMSE 0.00079 250 2.32 ± 0.119 kWh/t ± 0.17 kWh/tRMSE 0.0281Cu (E)Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.12: Specific energy versus piston pressure plot for a copper (E) ore256B.1.13 Taconite oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.8 0.872 599 103.1 1.153 899 154.8 1.544 1388 238.9 2.24567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.313 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0080 50 0.71 ± 0.064 kWh/t ± 0.10 kWh/tSSE 0.001 150 1.52 ± 0.037 kWh/t ± 0.08 kWh/tMSE 0.00029 250 2.32 ± 0.072 kWh/t ± 0.10 kWh/tRMSE 0.0171Taconite oreConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.13: Specific energy versus piston pressure plot for a taconite ore257B.1.14 Palladium oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 1388 238.9 2.372 899 154.7 1.673 600 103.2 1.294 400 68.8 0.99567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.439 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0081 50 0.84 ± 0.070 kWh/t ± 0.11 kWh/tSSE 0.001 150 1.65 ± 0.040 kWh/t ± 0.09 kWh/tMSE 0.00035 250 2.46 ± 0.079 kWh/t ± 0.11 kWh/tRMSE 0.0187Pd oreConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.14: Specific energy versus piston pressure plot for a palladium ore258B.1.15 Copper-gold oreTest#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.8 0.912 599 103.2 1.253 899 154.8 1.674 1387 238.8 2.47567891011121314151617181920Summary statisticsn 4R2 0.999Intercept 0.291 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0091 50 0.75 ± 0.100 kWh/t ± 0.15 kWh/tSSE 0.001 150 1.66 ± 0.058 kWh/t ± 0.13 kWh/tMSE 0.00071 250 2.56 ± 0.113 kWh/t ± 0.16 kWh/tRMSE 0.0267Cu-Au (A) -12.5mmConfidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.15: Specific energy versus piston pressure plot for a copper-gold ore259B.2 Piston Press Tests on Geometallurgical Units of aCopper-Gold OreB.2.1 Geometallurgical unit 1Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 678 116.8 1.342 678 116.8 1.303 678 116.8 1.314 678 116.8 1.415 678 116.7 1.316 678 116.8 1.287 843 145.1 1.488 843 145.1 1.659 843 145.2 1.5610 844 145.2 1.6711 843 145.2 1.6412 843 145.2 1.5413 843 145.2 1.6114 843 145.1 1.5915 983 169.2 1.9016 983 169.2 1.7617 983 169.3 1.8518 983 169.3 1.8119 983 169.3 1.8320 983 169.2 1.8321 983 169.3 1.8022 983 169.3 1.75n 22R2 0.938Intercept 0.236 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0093 50 0.70 ± 0.110 kWh/t ± 0.15 kWh/tSSE 0.054 150 1.64 ± 0.024 kWh/t ± 0.11 kWh/tMSE 0.00272 250 2.57 ± 0.118 kWh/t ± 0.16 kWh/tRMSE 0.0521Cu-Au geometallurgical unit 1Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.16: Specific energy versus piston pressure plot for geometallurgical unit 1 of acopper-gold ore260B.2.2 Geometallurgical unit 2Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 643 110.7 1.352 643 110.7 1.283 643 110.8 1.334 679 116.8 1.345 678 116.7 1.356 678 116.7 1.387 678 116.8 1.398 678 116.7 1.519 678 116.7 1.5710 678 116.7 1.5611 678 116.7 1.5812 844 145.2 1.6813 843 145.2 1.6314 843 145.1 1.7015 843 145.1 1.6016 843 145.1 1.6217 843 145.1 1.7918 983 169.3 1.8819 983 169.2 1.8320 984 169.3 1.8321 983 169.2 1.8322 983 169.3 2.0523 1388 238.9 2.66n 23R2 0.916Intercept 0.323 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0094 50 0.79 ± 0.116 kWh/t ± 0.21 kWh/tSSE 0.154 150 1.73 ± 0.039 kWh/t ± 0.18 kWh/tMSE 0.00732 250 2.68 ± 0.140 kWh/t ± 0.23 kWh/tRMSE 0.0855Cu-Au geometallurgical unit 2Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.17: Specific energy versus piston pressure plot for geometallurgical unit 2 of acopper-gold ore261B.2.3 Geometallurgical unit 3Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 678 116.7 1.282 678 116.8 1.383 679 116.8 1.374 679 116.8 1.355 678 116.7 1.426 678 116.8 1.297 843 145.2 1.598 843 145.2 1.599 843 145.1 1.5410 843 145.1 1.5611 843 145.1 1.5712 983 169.3 1.7613 983 169.3 1.7414 983 169.2 1.7715 983 169.3 1.7716 983 169.3 1.7417 1263 217.5 2.3418 421 72.5 1.031920212223n 18R2 0.967Intercept 0.341 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0086 50 0.77 ± 0.082 kWh/t ± 0.14 kWh/tSSE 0.046 150 1.63 ± 0.028 kWh/t ± 0.12 kWh/tMSE 0.00287 250 2.48 ± 0.095 kWh/t ± 0.15 kWh/tRMSE 0.0536Cu-Au geometallurgical unit 3Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.18: Specific energy versus piston pressure plot for geometallurgical unit 3 of acopper-gold ore262B.2.4 Geometallurgical unit 4Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 421 72.5 0.712 678 116.8 1.153 678 116.8 1.144 678 116.7 1.195 679 116.8 1.196 679 116.8 1.167 678 116.7 1.108 843 145.1 1.339 843 145.1 1.3310 843 145.2 1.3711 843 145.2 1.3512 843 145.1 1.3613 983 169.2 1.5414 983 169.2 1.6015 983 169.3 1.5716 983 169.3 1.5317 983 169.2 1.5018 1264 217.5 1.681920212223n 18R2 0.931Intercept 0.336 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0069 50 0.68 ± 0.098 kWh/t ± 0.17 kWh/tSSE 0.064 150 1.37 ± 0.033 kWh/t ± 0.14 kWh/tMSE 0.00402 250 2.07 ± 0.112 kWh/t ± 0.17 kWh/tRMSE 0.0634Cu-Au geometallurgical unit 4Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.19: Specific energy versus piston pressure plot for geometallurgical unit 4 of acopper-gold ore263B.2.5 Geometallurgical unit 5Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 678 116.7 1.122 678 116.8 1.173 678 116.7 1.094 678 116.8 1.155 678 116.8 1.126 678 116.7 1.087 843 145.1 1.328 843 145.1 1.319 843 145.1 1.3310 843 145.2 1.3111 843 145.1 1.3412 983 169.2 1.5013 983 169.2 1.5714 983 169.2 1.5715 983 169.2 1.5516 983 169.3 1.5217181920212223n 16R2 0.974Intercept 0.183 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0080 50 0.58 ± 0.070 kWh/t ± 0.10 kWh/tSSE 0.013 150 1.38 ± 0.017 kWh/t ± 0.07 kWh/tMSE 0.00091 250 2.17 ± 0.082 kWh/t ± 0.10 kWh/tRMSE 0.0302Cu-Au geometallurgical unit 5Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.20: Specific energy versus piston pressure plot for geometallurgical unit 5 of acopper-gold ore264B.2.6 Geometallurgical unit 6Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 537 92.4 1.082 538 92.5 1.093 537 92.4 1.024 537 92.5 1.075 538 92.5 1.066 843 145.2 1.467 843 145.1 1.478 843 145.1 1.459 844 145.2 1.4710 843 145.2 1.4811 843 145.1 1.3712 1388 238.9 2.4013 1388 239.0 2.2814 1388 239.0 2.2515 1387 238.8 2.2516 1388 238.9 2.2717 399 68.7 0.7918 982 169.1 1.5319 679 116.8 1.2020212223n 19R2 0.987Intercept 0.233 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0085 50 0.66 ± 0.059 kWh/t ± 0.14 kWh/tSSE 0.062 150 1.51 ± 0.029 kWh/t ± 0.13 kWh/tMSE 0.00363 250 2.36 ± 0.057 kWh/t ± 0.14 kWh/tRMSE 0.0603Cu-Au geometallurgical unit 6Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.21: Specific energy versus piston pressure plot for geometallurgical unit 6 of acopper-gold ore265B.2.7 Geometallurgical unit 7Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 679 116.8 1.362 678 116.8 1.293 679 116.8 1.244 678 116.7 1.305 678 116.8 1.246 678 116.7 1.277 678 116.8 1.258 678 116.8 1.329 399 68.7 0.9010 400 68.8 0.9811 400 68.8 0.9412 399 68.8 0.9513 1388 239.0 2.4214 1388 239.0 2.4815 1388 238.9 2.4116 1388 238.9 2.3517 843 145.1 1.5018 983 169.2 1.711920212223n 18R2 0.990Intercept 0.286 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0088 50 0.72 ± 0.050 kWh/t ± 0.13 kWh/tSSE 0.052 150 1.60 ± 0.029 kWh/t ± 0.12 kWh/tMSE 0.00323 250 2.48 ± 0.060 kWh/t ± 0.13 kWh/tRMSE 0.0568Cu-Au geometallurgical unit 7Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.22: Specific energy versus piston pressure plot for geometallurgical unit 7 of acopper-gold ore266B.2.8 Geometallurgical unit 8Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.8 0.792 400 68.8 0.823 400 68.9 0.814 400 68.8 0.845 400 68.8 0.806 843 145.2 1.377 843 145.2 1.378 843 145.1 1.349 843 145.2 1.5210 843 145.1 1.3711 843 145.2 1.3912 1388 238.9 2.0713 1388 238.9 2.1114 1388 238.9 2.0815 1388 239.0 2.0916 678 116.8 1.1917 983 169.3 1.49181920212223n 17R2 0.992Intercept 0.302 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0075 50 0.68 ± 0.040 kWh/t ± 0.10 kWh/tSSE 0.028 150 1.42 ± 0.022 kWh/t ± 0.09 kWh/tMSE 0.00184 250 2.17 ± 0.044 kWh/t ± 0.10 kWh/tRMSE 0.0429Cu-Au geometallurgical unit 8Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.23: Specific energy versus piston pressure plot for geometallurgical unit 8 of acopper-gold ore267B.2.9 Geometallurgical unit 9Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 399 68.7 0.922 400 68.8 0.903 399 68.7 0.964 400 68.8 0.925 843 145.1 1.676 843 145.1 1.587 843 145.2 1.628 843 145.1 1.649 843 145.2 1.6810 843 145.1 1.7011 844 145.2 1.7212 843 145.2 1.7113 843 145.2 1.7614 844 145.2 1.6315 1388 238.9 2.5716 1388 238.9 2.5117 1388 238.9 2.5018 1388 239.0 2.5519 678 116.8 1.4420 983 169.2 1.92212223n 20R2 0.993Intercept 0.299 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0094 50 0.77 ± 0.044 kWh/t ± 0.10 kWh/tSSE 0.037 150 1.71 ± 0.021 kWh/t ± 0.10 kWh/tMSE 0.00204 250 2.65 ± 0.045 kWh/t ± 0.11 kWh/tRMSE 0.0452Cu-Au geometallurgical unit 9Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.24: Specific energy versus piston pressure plot for geometallurgical unit 9 of acopper-gold ore268B.2.10 Geometallurgical unit 10Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.8 0.922 399 68.8 0.903 400 68.8 0.954 400 68.8 0.955 678 117 1.476 678 117 1.267 843 145 1.668 843 145 1.699 843 145 1.7110 843 145 1.6511 843 145 1.7612 843 145 1.5413 983 169 1.9214 983 169 1.7015 1388 239 2.5916 1388 239 2.6517 1388 239 2.7118 1388 239 2.571920Summary statisticsn 18R2 0.982Intercept 0.220 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0100 50 0.72 ± 0.082 kWh/t ± 0.19 kWh/tSSE 0.111 150 1.72 ± 0.042 kWh/t ± 0.18 kWh/tMSE 0.00694 250 2.71 ± 0.084 kWh/t ± 0.20 kWh/tRMSE 0.0833Cu-Au geometallurgical unit 10Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.25: Specific energy versus piston pressure plot for geometallurgical unit 10 of acopper-gold ore269B.2.11 Geometallurgical unit 11Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 69 0.962 400 69 0.903 399 69 1.034 400 69 0.985 678 117 1.306 843 145 1.717 843 145 1.768 843 145 1.689 844 145 1.6810 843 145 1.6311 843 145 1.6312 843 145 1.5913 843 145 1.5814 843 145 1.6315 843 145 1.5716 983 169 1.8417 1388 239 2.6018 1388 239 2.6119 1388 239 2.6220 1388 239 2.66Summary statisticsn 20R2 0.987Intercept 0.244 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0098 50 0.73 ± 0.062 kWh/t ± 0.15 kWh/tSSE 0.073 150 1.71 ± 0.030 kWh/t ± 0.14 kWh/tMSE 0.00404 250 2.69 ± 0.063 kWh/t ± 0.15 kWh/tRMSE 0.063695% Pred.inter.Confidence and Prediction IntervalsCu-Au geometallurgical unit 110.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.26: Specific energy versus piston pressure plot for geometallurgical unit 11 of acopper-gold ore270B.2.12 Geometallurgical unit 12Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 399 68.7 0.792 399 68.7 0.793 400 68.8 0.794 399 68.7 0.795 400 68.8 0.946 843 145.2 1.307 843 145.2 1.368 843 145.2 1.379 843 145.2 1.3810 843 145.2 1.5211 983 169.3 1.7412 1388 239.0 2.1613 1387 238.9 2.1414 1388 239.0 2.2015 1388 238.9 2.0916 678 116.7 1.2817181920Summary statisticsn 16R2 0.980Intercept 0.285 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0078 50 0.68 ± 0.072 kWh/t ± 0.18 kWh/tSSE 0.080 150 1.46 ± 0.041 kWh/t ± 0.17 kWh/tMSE 0.00574 250 2.24 ± 0.078 kWh/t ± 0.18 kWh/tRMSE 0.0758Cu-Au geometallurgical unit 12Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Data 95% confidence interval 95% prediction interval Figure B.27: Specific energy versus piston pressure plot for geometallurgical unit 12 of acopper-gold ore271B.2.13 Geometallurgical unit 13Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 400 68.9 0.902 400 68.8 0.883 400 68.8 0.864 400 68.8 0.875 679 116.8 1.206 843 145.2 1.517 843 145.2 1.538 843 145.1 1.489 843 145.2 1.5110 843 145.1 1.5011 983 169.3 1.6612 1388 239.0 2.3913 1388 239.0 2.3714 1388 238.9 2.4115 1388 238.9 2.331617181920212223n 15R2 0.995Intercept 0.238 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0088 50 0.68 ± 0.045 kWh/t ± 0.10 kWh/tSSE 0.024 150 1.56 ± 0.024 kWh/t ± 0.10 kWh/tMSE 0.00184 250 2.45 ± 0.045 kWh/t ± 0.10 kWh/tRMSE 0.0429Cu-Au geometallurgical unit 13Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.28: Specific energy versus piston pressure plot for geometallurgical unit 13 of acopper-gold ore272B.2.14 Geometallurgical unit 14Test#Force [kN]Pressure[MPa]Sp. Energy[kWh/t]1 399 68.7 0.922 399 68.7 0.953 399 68.7 0.954 399 68.8 0.965 678 116.8 1.456 843 145.2 1.707 843 145.2 1.698 843 145.2 1.639 843 145.2 1.7110 843 145.2 1.7111 983 169.2 1.9612 1388 239.0 2.6313 1388 239.0 2.5814 1388 239.0 2.6715 1388 239.0 2.681617181920212223n 15R2 0.998Intercept 0.256 Pressure [MPa] Mean 95% Conf.inter.Slope 0.0100 50 0.75 ± 0.034 kWh/t ± 0.08 kWh/tSSE 0.014 150 1.75 ± 0.018 kWh/t ± 0.07 kWh/tMSE 0.00107 250 2.75 ± 0.034 kWh/t ± 0.08 kWh/tRMSE 0.0327Cu-Au geometallurgical unit 14Confidence and Prediction Intervals95% Pred.inter.0.0 0.5 1.0 1.5 2.0 2.5 3.0 0 50 100 150 200 250 300 Specific energy [kWh/t] Piston pressure [MPa] Fitted line Series1 95% confidence interval 95% prediction interval Figure B.29: Specific energy versus piston pressure plot for geometallurgical unit 14 of acopper-gold ore273Appendix CA WORKED EXAMPLE OF SIMULATION274The numerical steps involved in the simulation-based methodology are presented by simu-lating energy–size reduction of an HPGR test run at 3 N/mm2 on the copper-gold ore discussedin Section 8.4.The following are the numerical steps involved in simulation-based methodology.1. Conduct piston press tests on narrowly sized particles and determine the parameters M ,f ∗mat and n in Eq. 7.3. In subsection 8.4.1, M , f∗mat and n were determined for the copper-gold ore as 45.0, 0.166 and 0.574, respectively.2. Decide on the ESP of interest to simulate. It can be estimated using empirical models(Eq. 4.2 or Eq. 4.3). For this worked example, ESP of interest is 1.58 kWh/t as shown inTable 8.8 for the HPGR test run at 3 N/mm2.3. In section 7.5, the HPGR simulation model parameter xc was determined as 16 mm.Therefore, the HPGR feed is classified into coarse (+16 mm) and fine (-16 mm) fractions.Table C.1 shows the feed PSD for the copper-gold ore.275Table C.1: Feed particle size distributionSieve size Geometric Screen weight Retained Cumulative passing[mm] mean size [mm] [g] [%] Size [mm] [%]-38.1 +32 34.92 0.0 0.00 38.1 100-32 +25 28.28 606.8 6.05 32 100-25 +19 21.79 1961.3 19.57 25 93.95-19 +16 17.44 1256.6 12.54 19 74.37-16 +12.5 14.14 1379.9 13.77 16 61.84-12.5 +8 10.00 2056.8 20.52 12.5 48.07-8 +5.6 6.69 943.1 9.41 8 27.54-5.6 +4 4.73 499.1 4.98 5.6 18.13-4 +2.8 3.35 337.0 3.36 4 13.15-2.8 +2 2.37 221.8 2.21 2.8 9.79-2 +1.4 1.67 119.6 1.19 2 7.58-1.4 +1 1.18 131.6 1.31 1.4 6.38-1 +0.71 0.84 76.1 0.76 1 5.07-0.71 +0.5 0.60 77.5 0.77 0.71 4.31-0.5 +0.355 0.42 60.0 0.60 0.5 3.54-0.355 +0.25 0.30 51.5 0.51 0.355 2.94-0.25 +0.18 0.21 39.5 0.39 0.25 2.42-0.18 +0.125 0.15 38.2 0.38 0.18 2.03-0.125 +0.09 0.11 27.5 0.27 0.125 1.65-0.09 +0.063 0.08 35.3 0.35 0.09 1.37-0.063 +0.045 0.05 17.7 0.18 0.063 1.02-0.045 84.7 0.85 0.045 0.85Total 10021.64. In section 7.5, the HPGR simulation model parameter βsplit was determined as 0.157.The +16 mm fraction goes through pre-crushing stage and the specific energy for the276stage is calculated by the following equation.EcrushSP = βsplit · ESPEcrushSP = 0.157 ·1.58 = 0.248kW h/tt10 for each size class in the +16 mm fraction is calculated using Eq. 7.3 is shown inTable C.2.t10 = M(1− exp(− f ∗mat · xn · Esp))(7.3 revisited)t10 = 45 ·(1− exp(−0.166 · x0.574 ·0.248))Table C.2: Calculated t10 for the size classes in the +16 mm fractionSieves Geometric mean size, x [mm] t10-sizes [mm] Calculated t10-value [%]-32 +25 28.28 2.83 11.01-25 +19 21.79 2.18 9.66-19 +16 17.44 1.74 8.625. In subsection 8.4.2, the tn–t10 relationships were defined using equations 7.5 through7.10 with βi coefficients shown in Table C.3.Table C.3: βi coefficients used to define tn–t10 relationships for the copper-gold oret1.2 t2 t4 t25 t50 t75β1 β2 β3 β4 β5 β6 β7 β8 β9107.1 5.7 123.4 23.2 152.4 65.5 0.59 0.36 0.23277For example, t1.2 for -32+25 mm size class would be calculated using the followingequation.t1.2 =β1 · t10(β2 + t10) (7.5 revisited)t1.2 =107.1 ·11.01(5.7+11.01)= 70.64Table C.4 shows the full particle size distribution for each size classes in the +16 mmfraction. Full PSDs can be estimated by substituting the calculated t10 in equations 7.5through 7.10.Table C.4: Full PSDs for each size classes in the +16 mm fractionx=28.28 mm x=21.79 mm x=17.44 mm6.05 wt. % 19.57 wt. % 12.54 wt. %Size Cum. % passing Size Cum. % passing Size Cum. % passingt0 32.00 100 25.00 100 19.00 100t1.2 23.57 70.64 18.16 67.43 14.53 64.54t2 14.14 39.73 10.90 36.29 8.72 33.44t4 7.07 21.93 5.45 19.58 4.36 17.72t10 2.83 11.01 2.18 9.66 1.74 8.62t25 1.13 6.55 0.87 5.74 0.70 5.12t50 0.57 4.09 0.44 3.59 0.35 3.20t75 0.38 2.78 0.29 2.44 0.23 2.17When the three cumulative PSDs for each size class are combined according to theirweight percentages they form the product PSD of the pre-crushing stage.6. The product of the pre-crushing stage is combined with the -16 mm fraction and be-comes the feed to the grinding stage as shown in Table C.5. For example, the cumula-tive percentage passing -5.6 mm of the feed to the grinding stage can be calculated as38.16%·20.45+61.84%·29.32=25.94%.278Table C.5: Feed PSD to the grinding stageProduct of pre-crushing -16 mm fraction Feed to grinding stage38.16 wt. % 61.84 wt. % 100 wt. %Size [mm] Cum. % passing Cum. % passing Cum. % passing32 100.00 100 100.0025 96.13 100 98.5219 78.31 100 91.7216 62.13 100 85.5512.5 45.41 77.73 65.408 28.04 44.54 38.245.6 20.45 29.32 25.944 15.42 21.27 19.042.8 11.70 15.83 14.252 9.21 12.25 11.091.4 7.36 10.32 9.191 6.11 8.20 7.400.71 4.98 6.97 6.210.5 3.91 5.72 5.030.355 2.99 4.75 4.080.25 2.13 3.92 3.240.18 1.54 3.28 2.620.125 1.07 2.67 2.060.09 0.77 2.22 1.670.063 0.54 1.65 1.230.045 0.38 1.37 0.992797. The specific energy for the grinding stage is the balance of energy expended in thecrushing stage and is calculated using the following equation.EgrindSP = ESP(1− βsplit · P+16mm)1.58 · (1−0.157 ·38.16%) = 1.49 kW h/tt10 for each size class is calculated using Eq. 7.4. The HPGR simulation model parameterc was determined as 1.08 in section 7.5. The percentage of -1.4 mm in the feed togrinding stage is P−1.4mm=9.19%, then t10 is calculated as follows. Table C.6 showsthe calculated t10 for each size classes in the feed to the grinding stage.t10 =(M − c · P f ines) (1− exp(− f ∗mat · xn · ESP))(7.4 revisited)t10 = (45−1.08 ·9.19)(1− exp(−0.166 · x0.575 ·1.49))280Table C.6: Calculated t10 for each size class in the feed to the grinding stageSieves Geometric meansize, x [mm]t10-sizes [mm] Calculatedt10-value [%]-32 +25 28.3 2.828 28.55-25 +19 21.8 2.179 26.83-19 +16 17.4 1.744 25.26-16 +12.5 14.1 1.414 23.74-12.5 +8 10.0 1.000 21.18-8 +5.6 6.69 0.669 18.26-5.6 +4 4.73 0.473 15.87-4 +2.8 3.35 0.335 13.67-2.8 +2 2.37 0.237 11.67-2 +1.4 1.67 0.167 9.90-1.4 +1 1.18 0.118 8.35-1 +0.71 0.84 0.084 7.03-0.71 +0.5 0.60 0.060 5.88-0.5 +0.355 0.42 0.042 4.89-0.355 +0.25 0.30 0.030 4.06-0.25 +0.18 0.21 0.021 3.38-0.18 +0.125 0.15 0.015 2.80-0.125 +0.09 0.11 0.011 2.31-0.09 +0.063 0.08 0.008 1.91-0.063 +0.045 0.05 0.005 1.578. Similar to the step 5, full particle size distributions for each size class is estimated usingthe the tn–t10 relationships. When the PSDs for each size class are combined accordingto the weight percentages, the final result is the product PSD of the grinding stage. Theproduct PSD of the grinding stage is the final result of simulation. Table C.7 shows thecomparison of the measured and the simulation predicted product PSDs. The standarderror is 1.40% and the 95% confidence interval for predictions are ±2.93%.281Table C.7: Measured and predicted product PSDsParticle Cumulative % passing Error ErrorSize [mm] Measured Predicted (Measured-Predicted) Squared32 100.0 100.0 0.0 0.0025 100.0 99.9 0.1 0.0219 99.7 99.0 0.7 0.4316 98.0 97.8 0.2 0.0412.5 94.3 93.9 0.3 0.118 81.0 82.2 -1.2 1.375.6 69.6 70.6 -1.0 1.064 58.2 60.0 -1.8 3.412.8 47.9 50.0 -2.1 4.532 39.3 41.7 -2.4 5.771.4 31.8 34.5 -2.8 7.641 27.0 28.7 -1.7 2.980.71 22.1 23.8 -1.7 2.890.5 18.3 19.6 -1.2 1.480.355 15.2 16.0 -0.8 0.590.25 12.5 12.7 -0.3 0.070.18 10.3 10.1 0.2 0.030.125 8.4 7.7 0.7 0.500.09 6.9 5.9 0.9 0.890.063 5.1 4.4 0.7 0.530.045 4.2 3.3 0.9 0.78Sum of squared error (SSE) 35.1Standard error (SE) 1.4095% prediction interval 2.93282

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