Geometallurgical estimation of comminution indices for porphyry copper deposit applying mineralogical approach

Geometallurgical estimation of

comminution indices for porphyry copper deposit applying mineralogical approach

Aitik Mine, New Boliden

Danish Bilal

Natural Resources Engineering, master's level (120 credits) 2017

Luleå University of Technology

Department of Civil, Environmental and Natural Resources Engineering

Preface

This is the final report of my master thesis “Geometallurgical estimation of comminution indices for porphyry copper deposit applying mineralogical approach” at Luleå University of Technology. The presentation of this work has been done on 19^th June 2017 at Luleå University of Technology. This work is a part of PREP project (Primary resource efficiency by enhanced prediction). All members of PREP and Aitik Boliden are gratefully acknowledged for their support during this work. EMERALD (Erasmus Mundus Master Program) is thanked for scholarship and support.

This work would not have been possible without support and help of

• Prof. Pertti Lamberg (LTU), supervisor

• Prof. Jan Rosenkranz (LTU), examiner

• Cecilia Lund (LTU) (LTU) Associate Senior Lecturer, co-supervisor

• Pierre-Henri Koch (LTU) PhD, co-supervisor

• Viktor Lishchuk (LTU) PhD, co-supervisor

My family is thanked for their full support during whole master program.

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List of abbreviation

BWi: Bond ball mill work index EMC: Element to mineral conversion GCT: Geometallurgical comminution test MLA: Mineral liberation analysis

MSE: Mean square error PCA: Root men square error PLI: Point load index

PLT: Point load strength test

PREP: Primary resource efficiency by enhanced prediction PSD: Particle size distribution

RMSE: Root mean square error RWi: Bond rod mill work index SDP: Senior design project SPI: Sag power index

UCS: Uniaxial compressive strength

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1 INTRODUCTION ...7

2 LITERATURE REVIEW ...8

2.1 AITIK MINE ... 8

2.5 GEOLOGY OF AITIK DEPOSIT ... 8

2.2 COMMINUTION ... 11

2.3 COMMON COMMINUTION INDICES ... 13

2.4 EXISTING COMMINUTION TEST METHODS ... 14

2.5 GEOMETALLURGICAL COMMINUTION TEST (GCT) ... 18

2.6 CORRELATIONS BETWEEN COMMINUTION TEST METHODS ... 20

2.7 ESTIMATION OF COMMINUTION INDICES BASED ON MINERALOGY, CHEMICAL ASSAYS, LITHOLOGY AND ALTERATION ... 24

2.8 PRINCIPLE COMPONENT ANALYSIS ... 27

2.9 ELEMENT TO MINERAL CONVERSION ... 28

3 METHODS ... 29

3.1 SAMPLES ... 29

3.2 GCT SAMPLE PREPARATION ... 34

3.3 SAMPLING ERROR ... 36

3.4 SAMPLE COLLECTION FROM AITIK REGRINDING CIRCUIT (PROCESS SAMPLES) ... 37

3.5 ELEMENT TO MINERAL CONVERSION ... 39

2.10 MINERAL LIBERATION ANALYSIS ... 43

2.11 MULTIPLE LINEAR REGRESSION FOR PREDICTION OF BOND WORK INDEX ... 43

4 RESULTS AND DISCUSSIONS ... 48

4.1 PARTICLE SIZE DISTRIBUTION ... 48

4.2 BOND BALL MILL WOK INDEX ... 49

4.3 ELEMENT TO MINERAL CONVERSION ... 50

4.4 REGRINDING CIRCUIT AITIK (PEBBLE MILL) ... 52

4.5 AUTOMATED MINERALOGY RESULTS OF REGRINDING CIRCUIT ... 53

4.6 CLASSIFICATION OF SAMPLES ... 59

5 CONCLUSIONS ... 64

6 REFERENCES ... 67

7 APPENDICES ... 69

4.7 APPENDIX A... 69

4.8 APPENDIX B ... 79

4.9 APPENDIX C ... 80

4.10 APPENDIX D:ELEMENT TO MINERAL CONVERSION DATA: ... 83

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List of figures

Figure 1 (A) Bedrock in horizontal view at 2300 m level, (B) Bedrock in vertical section at profile Y4500. Local

coordinate system in meters.(Sammelin et al. 2011) ... 9

Figure 2: Plan view of the Aitik deposit (100 m level) with the spatial occurrence of mineralization styles outlined schematically ... 10

Figure 3: typical interlocking of valuable mineral in gangue mineral; regular (a), vein (b), frame(c), and occlusion (d) (Kelly 1982) ... 11

Figure 4: Optical range of particle size for separation (Drzymala 2007) ... 11

Figure 5: The shattering process (King 2012) ... 12

Figure 6: Fracture by cleavage (King 2012) ... 13

Figure 7: Attrition and chipping (King 2012) ... 13

Figure 8: Frequency Distribution of Axb ((Mcken and Williams 2005) ... 17

Figure 9: Correlations to Bond Work Index: (A) Effect of modulus of elasticity of the different studied materials on Bond work index, (B) Effect of compressive strength of the different studied materials on Bond work index, (C) Effect of abrasion of the different S ... 21

Figure 10: Correlation between Bwi and Friability ... 22

Figure 11: Correlation between Measured Bond work index and calculated bond work index using Hardgrove grindability ... 22

Figure 12 The relationship between (a) grindability index G, (b) work index Wi and friability valueS20, where G is the average value net grams of undersize produced per mill revolution in last three cycles of standard bond test ... 23

Figure 13 Correlation between bond work index and Axb parameter in various lithologies and alterations ... 23

Figure 14 correlation between BWi and Axb parameter ... 24

Figure 15 Correlation of predicted and calculated BWi in two classes (Keeney and Walters 2011) ... 25

Figure 16 A- Measured VS estimated BWI, B and C, Correlation between where mica and SPI in two different lithologies (Hunt et al. 2013) ... 26

Figure 17 Correlation between measured and calculated Axb and BWI (Keeney et al. 2011) ... 26

Figure 18 PCA scatter plot of samples ... 27

Figure 19 PCA plot of samples and direction of abundance of mineralogy ... 28

Figure 20 Core pictures of Sample 14 and sample 15: Fine grain Diorite ... 30

Figure 21 Core pictures of Sample (10, 12 and 13) Coarse grain diorite ... 31

Figure 22 Core pictures of sample 1 and 1A, Pegmatite ... 31

Figure 23 Core pictures of sample (3, 4 and 6), High Ccp, Py Feldspar biotite rich, ... 32

Figure 24 Core pictures of Sample 16, 17 and 18 ... 33

Figure 25 Pictures of sample 8(Muscovite Schist) and sample 2(barren) ... 33

Figure 26 Core pictures of sample 7A, 7B and 9 ... 34

Figure 27 Sample preparation flowsheet ... 35

Figure 28 Aitik concentration circuit, regrinding circuit is indicated in a rectangle (HSC Chemistry) ... 37

Figure 29 Aitik's regrinding circuit ... 38

Figure 30 (A) Microscopic picture of Polished section of Rougher concentrate (106-150 micron), (B) Hydrocyclone Overflow (106-150 micron), (C) Hydrocyclone Underflow (106-150), (D) Mill product (75 to 106 microns) ... 39

Figure 31 Comparison of modal minerology for SDP samples (quartz, actinolite, orthoclase, chalcopyrite, pyrrhotite/pyrite and albite) ... 41

Figure 32 Comparison of modal mineralogy of barite Molybdenite and other minerals (biotite, annite, muscovite, chlorite, epidote, andradite, calcite, anhydrite, magnetite and scapolite) ... 42

Figure 33 Prediction of BWi on basis of modal mineralogy ... 45

Figure 34 MLR results in main ore zone samples ... 46

Figure 35 MLR results for diorite samples ... 47

Figure 36 Particle size distribution at different grinding times ... 48

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Figure 37 Standard deviation based on two repeats at different grinding times ... 49

Figure 38 BWi along with twice standard deviation (4, 8, 11, 14, 16 and 18 comes from SDP) ... 50

Figure 39 Modal Mineralogy of Aitik mine samples calculated by EMC ... 51

Figure 40 Particle size distribution of Aitik regrinding circuit ... 53

Figure 41 Modal mineralogy of rougher concentrate ... 54

Figure 42 Modal mineralogy of mill product ... 54

Figure 43 Modal mineralogy of hydrocyclone underflow ... 55

Figure 44 Modal mineralogy of hydrocyclone overflow ... 55

Figure 45 Mode of occurrence of chalcopyrite in rougher concentrate ... 56

Figure 46 Mode of occurrence of chalcopyrite in Mill product ... 56

Figure 47 Liberation graphs of chalcopyrite in Hydrocyclone overflow ... 57

Figure 48 Liberation data of chalcopyrite in hydrocyclone underflow ... 58

Figure 49 particles in fraction 0-75µm ... 59

Figure 50 Cumulative variability of factors ... 61

Figure 51 Contribution of different properties to the first two factors. ... 61

Figure 52 Contribution of different properties to the first two factors along with the samples ... 62

Figure 53 Clustering of samples in PCA ... 63

Figure 54 Particle Size distribution at different grinding times ... 69

Figure 55 Standard deviation based on two repeats at different grinding times ... 69

Figure 56 Particle Size distribution at different grinding times ... 70

Figure 57 Standard deviation based on two repeats at different grinding times ... 70

Figure 58 Particle Size distribution at different grinding times ... 71

Figure 59 Standard deviation based on two repeats at different grinding times ... 71

Figure 60 Standard deviation based on two repeats at different grinding times ... 72

Figure 61 Particle Size distribution at different grinding times ... 72

Figure 62 Standard deviation based on two repeats at different grinding times ... 73

Figure 63 Particle Size distribution at different grinding times ... 73

Figure 64 Standard deviation based on two repeats at different grinding times ... 74

Figure 65 Particle Size distribution at different grinding times ... 74

Figure 66 Standard deviation based on two repeats at different grinding times ... 75

Figure 67 Particle Size distribution at different grinding times ... 75

Figure 68 Particle Size distribution at different grinding times ... 76

Figure 69 Standard deviation based on two repeats at different grinding times ... 76

Figure 70 Standard deviation based on two repeats at different grinding times ... 77

Figure 71 Particle Size distribution at different grinding times ... 77

Figure 72 Standard deviation based on two repeats at different grinding times ... 78

Figure 73 Particle Size distribution at different grinding times ... 78

Figure 74 Standard deviation based on two repeats at different grinding times ... 79

Figure 75 Particle Size distribution at different grinding times ... 79

Figure 76 EMC for remaining Minerals ... 80

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List of tables

Table 1: Resources and reserves of Aitik Mine on 2016-12-31 modified from (Boliden 2016) ... 8

Table 2: Summary of characteristics for the mineralization styles ... 10

Table 3: Common Bond Ball Work Index values for different types of rocks ... 14

Table 4: Common Bond Rod Work Index values for different types of rocks ... 14

Table 5: common values of Axb and ta of different rocks. ... 16

Table 6: Common fracture test methods having potential for geometallurgical tests. -(1) Simplicity, (2) repeatability, (3) sample preparation, (4) time exposure and cost, (5) sample amount, (6) parameters can be used in modelling and simulation, (7) can be extended to mineral liberation (Mwanga et al. 2015) ... 19

Table 7: Parameters for downscaling the bond mill test (Mwanga et al. 2015)... 20

Table 8: Description of Aitik mine samples ... 30

Table 9: List of masses of samples at different stage of sample preparation ... 36

Table 10 Parameters of Gy sampling Error calculations ... 36

Table 11 Gy sampling error ... 37

Table 12: List of minerals in Aitik (SEM results) ... 40

Table 13: Details of minerals and elements used in different rounds in EMC ... 40

Table 14: Grouping of minerals ... 43

Table 15: Pearson correlation coefficients with BWi ... 44

Table 16 Skewness and kurtosis for all samples ... 44

Table 17: Model fitting results ... 44

Table 18: Results of linear regression ... 45

Table 19 skewness and kurtosis in main ore zone samples ... 46

Table 20 Goodness of the fit in main ore zone samples ... 46

Table 21 skewness and kurtosis values in diorite samples ... 47

Table 22 Goodness of fit in diorite samples ... 47

Table 23: Bond ball mill work Index (sample ID 4, 8, 11, 14, 16 and 18 comes from SDP) ... 49

Table 24: EMC modal minerology of Aitik Mine samples ... 51

Table 25 Average Standard deviation calculated by Monte carlo Simulation in HSC software ... 52

Table 26: Classification of samples based on BWi values ... 59

Table 27: Correlation matrix (Pearson (n)): ... 60

Table 28: Groups based on PCA ... 63

Table 29 SAG/AG mill comminution test methods (Verret et al. 2011) ... 66

Table 30: ALS elemental grades ... 81

Table 31 Uncertainty of ALS elemental grades calculation ... 82

Table 32 Chemical assays part 1 from SDP samples ... 83

Table 33 chemical assays Part 2 from SDP samples ... 84

Table 34 Modal minerology of samples from SDP calculated by SEM ... 85

Table 35 Modal Minerology of SDP samples calculated by EMC ... 86

Table 36 Residues from EMC of SDP samples (Part 1) ... 86

Table 37 Residues from EMC of SDP samples (Part 2) ... 87

Table 38 Residues of Aitik mine samples after EMC ... 88

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Abstract:

Geometallurgy is a tool which combines knowledge of geology and mineral processing to develop a spatial based model for mineral processing. Mineral processing performance could be derived with a help of so called geometallurgical tests. Geometallurgical tests are small-scale lab tests which aim at measurements of metallurgical response of the samples. Informational about response of ore in comminution circuit can be obtained with a help of geometallurgical comminution test (GCT). Classification of ore body into different geometallurgical domains based of comminution behavior, leads to a better management and design of comminutions circuits.

This work presents results of geometallurgical comminution tests of Aitik samples and classification of samples into different classes depending on their comminution properties (BWi …). The samples are further classified into different groups based on modal mineralogy using principle component analysis (PCA). Experimental work includes sample preparation for GCT, chemical assays, geometallurgical comminution test, mineralogical characterization including mineralogy, modal mineralogy, mineral liberation, element to mineral conversion and sampling of Aitik’s regrinding circuit for liberation analysis.

EMC helped to make a recipe for conversion of elemental assays into modal mineralogy. BWi results revealed that the main ore zone has lower grindability as compared to foot wall and diorites. Multiple linear regression gave models for prediction of BWI in whole deposit, ore zone and diorites separately.

PCA classified samples into hanging wall, footwall, main ore zone and diorites. Liberation analysis of Aitik regrinding circuit showed that the mill feed already has liberated chalcopyrite and most of the pyrite is recirculated in hydrocyclone underflow to the mill.

Keywords: Geometallurgy, Grindability, liberation analysis, Aitik mine, porphyry ore

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1 Introduction

Geometallurgy is a tool that combines knowledge of geology and mineral processing to develop a spatial based model for mineral processing. Geometallurgical tests are small scale lab tests which aim at measuring of metallurgical response (Lamberg 2011). Performance and throughput of a comminution circuit depends on comminution property of the ore. Mapping of comminution properties within ore body, provide room for better management and prediction of comminution circuit (Alruiz et al. 2009).

The objectives and research questions of this thesis are as follows:

1. Measurement of grindability indices for Aitik ore using geometallurgical comminution test method.

2. Establishing Element-to-Mineral conversion routine for porphyry copper ore.

3. Estimation of bond work index using modal mineralogy.

4. Mineralogical characterization of samples.

5. Liberation Analysis of Aitik regrinding circuit.

Measurement of grindability indices for Aitik ore using geometallurgical comminution test method:

Comminution is the most energy consuming process in mineral processing and accounts for 75%

beneficiation energy (States et al. 2004). Grinding consumes 90% of total comminution energy, crushing consume 5-7% and blasting consume 3-5% (Alvarado et al. 1998). Since mineral processing properties within ore body may vary significantly, which effect efficiency and throughout of the plant. Alruiz et al (2009) developed a geometallurgical model for grinding circuit of Collahuasi porphyry copper mine, where plant throughput significantly varies between the geometallurgical domains. Mapping the variability of comminution properties within the ore body, leads to a better modelling, optimization and management of comminution circuit.

In geometallurgy, large number of comminution tests are required and conventional comminution test methods require more than 10 kg of material and are uneconomical and time consuming especially when large number of tests are required. Geometallurgical comminution test (GCT) is a method simplified from standard bond method and it requires small amount of sample (220g) and less time than a standard procedure for measuring bond work index (Mwanga et al. 2015). GCT will be used for measurement of bond work index of Aitik ore samples.

Establishing Element-to-Mineral conversion routine for porphyry copper ore: Measurement of chemical assays is cheaper and time efficient as compared to automated mineralogy (MLA, QEMSCAN) so elemental assays can be used to calculate modal minerology of the samples (Whiten 2007). Element to mineral conversion becomes more complex when there are multiple minerals containing common elements like Si, S, Fe, Na, Mg etc. HSC chemistry software will be used to calculate modal mineralogy for Aitik samples using chemical assays.

Estimation of bond work index using modal mineralogy: There is a possibility of having a good correlation between comminution properties and geological properties of the sample that could be used for prediction of comminution behavior of the sample (Keeney and Walters 2011). Prediction of comminution properties by geological description and physical properties, will enhance precision in cost estimates and throughput rates (Harbort et al. 2013). The possibility of BWi being function of modal mineralogy will be studied. Multiple linear regression will be used to model BWi using multiple linear regression.

Mineralogical characterization of samples: Mineralogical characterization helps to classify the samples into different classes. In this study, the Aitik samples will be classified using principle component analysis (PCA) based on modal mineralogy.

Liberation Analysis of Aitik regrinding circuit: Aitik has installed a regrinding pebble mill for rougher concentrate. Investigation of regrinding circuit of Aitik will help to know effectiveness of the circuit and

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degree of improvement in the processing. Samples from regrinding pebble mill will be collected and automated mineralogy will be used to study the liberation.

2 Literature review 2.1 Aitik mine

The Aitik mine is situated 60 km north of the Arctic Circle, and 15 km southeast of Gällivare in northernmost. The Aitik open pit has production of 36 million tonnes of ore in 2015 (Boliden 2014).

Boliden started the survey in 1930 for exploration of Aitik ore body. In 1968 the production of Aitik mine was started with the production rate of 2 million tonnes per year (Zweifel 1976). Aitik have production of 36 million tonnes of ore in 2015. Since this high production and large quantity of remaining reserves shows the potential for further investigations and improvements in the processing.

The distribution of mineral resources and reserves in Aitik are shown in Table 1.

Table 1: Resources and reserves of Aitik Mine on 2016-12-31 modified from (Boliden 2016)

Quantity in million tonnes Au Ag Cu

Year 2016 2015 g/t g/t %

Proven Reserve 823 850 0.15 1.2 0.23

Probable Reserve 371 377 0.14 1.2 0.23

2.5 Geology of Aitik deposit

Geology of Aitik deposit is important for this study because, geology effects comminution properties of the ore. Many authors, who studied effect of alteration, lithology and type of ore deposit on comminution properties of ore e.g. Bond published a list of bond ball mill indices for different lithologies and alterations (Bond 1949; Bond 1961). List of bond work indices of different commodity types was published by (Levin 1989) containing 248 tests. Pilot plant test has been conducted by (Bachman et al. 1970) for autogenous mill grinding energy requirements for different lithologies and alterations of Kennecott ore. Harbort et al.

(2013) in porphyry copper deposit found a trend in term of mineralization regarding to harness and competency e.g. Hypogene > supergene, skarn > oxide ≥ leached cap.

2.2.1 General geology

Porphyry deposits are formed by complex interactions and overprinting of many processes, where copper bearing sulphides exist in a network of stockwork veinlets controlled by fractures and in adjacent altered rocks as disseminated grains. Mineralization and alteration are related to the magma reservoirs, intermediate to silicic in composition. Potassic alteration (K-feldspar) is overlapped or surrounded by the zones of phyllic-argillic and marginal propylitic alterations (USGS, 2008). Porphyry copper deposits are famous for large volume along with low Cu grades. In porphyry deposits, primary minerals are structurally controlled and are related to the porphyritic intrusions. The Aitik Cu-Au-Ag deposit is hosted by strongly altered and deformed 1.9 Ga old Svecofennian volcanoclastic rocks. Mining area is divided into different types, depending on copper grades (footwall zone, hanging wall zone and structural boundaries), as shown in Figure 1. The footwall zone and ore zone are separated by fault zone. The rocks along the fault zones are highly altered to the K-feldspar and epidote. Footwall is mainly formed by the feldspar, biotite, amphibole gneiss and porphyritic quartz monzodiorite containing less than 0.26 % of Cu. The ore zone contains garnet bearing biotite and muscovite schist, gneiss towards hanging wall. The biotite schist is gneiss towards footwall. While hanging wall mainly contains un-mineralized feldspar biotite amphibole gneiss, separated by ore zone by mean of thrust.

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Pegmatite dykes are found in hanging wall and ore zone in both cross cutting the foliation and along strike.

The main ore minerals are chalcopyrite and pyrite with chalcocite, molybdenite, bornite, pyrrhotite and magnetite as minor minerals, occurring as disseminated and veinlets. Metals are unevenly distributed in the ore body. Same low economic mineralization is present in footwall rocks.

Stockwork veining occurs in south eastern part of the open pit containing chalcopyrite and pyrite, near contact between ore zone and footwall. Pegmatite dykes in the ore zone contain chalcopyrite, pyrite and molybdenite. Sparse sulfide minerals occur in epidote altered rock and K-feldspar at the contact between the ore zone and footwall, also in small restricted areas of fine grained massive tourmaline.

Figure 1 (A) Bedrock in horizontal view at 2300 m level, (B) Bedrock in vertical section at profile Y4500. Local coordinate system in meters.(Sammelin et al. 2011)

2.2.2 Ore genesis

Aitik Cu-Au-Ag deposit is a metamorphosed and deformed porphyry copper deposit related to 1.9 Ga quartz monzodiorite with 160 Ma of post modifications having overprinting of mineralization event of IOCG-type. The IOCG-mineralization event occurred about 100 Ma later. Extensive deformation and redistribution of metals in Aitik occurred. The Aitik deposit has mixed origin having major part of copper ore originating from porphyry copper system and second minor part, originating from an overprinting of IOCG-type.

Copper mineralization is associated with potassic alteration, occurs throughout the altered intrusion in disseminated form. Which is an indication of early stage mineralization. The copper pattern is zoned in the intrusions, same zoning reported in porphyry copper deposits (lower grade inner parts and higher grade outer part). Furthermore, the stockwork system is developed in apex of the intrusion, which is the typical feature of young porphyry systems. Yngström et al (1986) suggested that the origin of the origin of the ore is magmatic. The study of fluid inclusions showed medium and low salinity NaCl ± CaCl2± MgCl2- fluid inclusions in samples <1.8 Ga, reflecting the continuously hydrothermal processes until 1.73 Ga.

(Wanhainen 2005).

2.2.3 Mineralization

The mineralization of Aitik Cu-Ag-Au deposit is mainly disseminated and veinlets. Ore minerals are chalcopyrite, pyrite and pyrrhotite and lesser amount of magnetite, molybdenite and bornite. Depending on geological features and Cu and Au grades, four types (A, B, C and D) of mineralization styles are recognized by Wanhainen et al(2003) within ore body, shown in figure 2. Summary of Characteristics of mineralisation styles is shown in Table 2.

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Table 2: Summary of characteristics for the mineralization styles

Mineralization style A (characterized in Table 2, and shown in Figure 2) has relatively high grade of copper and gold, found in cores from 100-500 m level.

Figure 2: Plan view of the Aitik deposit (100 m level) with the spatial occurrence of mineralization styles outlined schematically

Mineralization style B (characterized in Table 2, and shown in Figure 2) has copper and gold grades below the average values, found in drill cores from 200-600m levels. Mineralization style c (characterized in Table 2, and shown in Figure 2) is found in drill cores from 200-600 m level. Garnet bearing biotite and schist are found at level of 100 and 200m, like mineralization style a but with foliation of various intensities. Mineralization style d (characterized in Table 2, and shown in Figure 2) is represented in drill cores at the 200, 400, 500 and 600m levels. The rock type is garnet bearing biotite schist.

2.2.4 Alterations

There are multiple main phases of alterations in Aitik. A pre-metamorphic potassic alteration comprises the replacement of amphibile by biotite and K-feldspar, which is preserved in quartz monzodiorite. Second phase of alteration is retrograde conditions with minerals like calcite, epidote, chlorite, sericite, and biotite. Biotisations and sericitization is dominate in ore zone while chlorotozation and sericitization is dominant in footwall and hanging wall rocks. The next main phase of alteration is hydrotherma in origin in which quartz, allanite, , apatite, muscovite, tourmaline, actinilite, scapolite, garnet, magnetite, amphibole, K-feldspar and epidote occur in all rock types togther with pyrite and cahalcopyrite.Another alteration phase has minerals characteristics of amphibolite facies high metamorphic conditions, like garnet and amphibole and garnet (Wanhainen 2005). Alterations within orebody may effect comminution properties e.g harbort et al. (2013) found following trend in porphry copper deposit in term of alteration regarding to hardness and competancy e.g. propylytic > potassic ≥ phyllic > argillic.

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2.2 Comminution

Comminution is the process of particle size reduction under application of forces. There are two purposes of comminution process, liberation of ore minerals from gangue minerals and making suitable particle size for downstream separation process (Drzymala 2007). The typical interlocking of ore minerals with gangue particle is shown in Figure 3. The optimal range of size of particles for different unit operations is shown in Figure 4.

Figure 3: typical interlocking of valuable mineral in gangue mineral; regular (a), vein (b), frame(c), and occlusion (d) (Kelly 1982)

Figure 4: Optical range of particle size for separation (Drzymala 2007) (* low intensity (LI), ** high intensity (HI), *** high gradient magnetic field (HG))

Materials are primarily fractured by applying compressive stress rapidly by impact. Fractures are caused by the high shear stress at the surface of particle. The former leads to cleavage and shattering while latter

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to attrition and wear. All materials have their own ability to resist the propagation of fractures till a certain level of stresses. (King 2012)

2.2.1 Patterns of fractures when single particle breaks

Brittle materials are fractured when placed under sufficient stress. There are several patterns of fracture when a single particle breaks. The fracturing pattern depends on level of stresses and physical properties of the particle (pre-existing fractures, cracks, cleavage etc.). The product particles vary from smaller to bigger in size depending on fracturing pattern. The common fracture mechanisms are shatter, cleavage, attrition and chipping.

2.2.1.1 Shatter

This mechanism of fracture is caused by the rapid application of compressive stress. This process is unselective and multiple product sizes are formed. This is a multiple fracturing process in which parent particles are fractured, followed by successive fracturing of daughter particles, shown in Figure 5. This multiple fracturing process takes place very quickly in micro time scale. The size distribution of progeny population forms for modelling of breakage functions. Hence shattering is the common mode of fracturing in autogenous, rod and ball mills (King 2012).

Figure 5: The shattering process (King 2012)

2.2.1.2 Cleavage

When a particle breaks along preferred surfaces, cleavage occurs. Fracture propagates along those preferred surfaces. In cleavage, parent particle breaks down in larger particle reflects the grain size of the material. Usually there is no further fracturing of the daughter particles. These daughter particles are produced along with very small particles, produced at the point of stress application. The particle size distribution is usually bimodal, having one distribution of population of coarse daughter particles and other is the population of fines produced at point of application of stress (King 2012). This is shown on Figure 6.

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Figure 6: Fracture by cleavage (King 2012)

2.2.1.3 Attrition and chipping

Attrition and chipping occur when the stress is not enough to break the particle. This phenomenon is common in SAG mill where the large particles act as media. Parent articles hardly changes the size while a number of small particles are generated, called birth process, shown in Figure 7. Since there is no corresponding death process because the parent particles hardly change their size (just move to the lower particle size class). The size distribution is bimodal having two peaks. The peak of residual parent particles is narrow and far from the distinct peak of progeny particles at small size. Two peaks are well separated by the size range of zero particles, shown in Figure 7 (King 2012).

Figure 7: Attrition and chipping (King 2012)

2.3 Common comminution indices

There indices are derived from grindability tests, are used in simulation and designing of the grinding circuits. Most commonly used grindability indices are; bond ball mill work index, bond rod mill work index, macpherson autogenous work index and sag power index

14 2.4.1 Bond ball mill work index (BWi)

The bond ball Mill Work Index provides a measure of energy required to grind a mineral in a ball mill. It is expressed as kWh needed to grind one tonne of mineral. Bond ball mill work index is calculated using the standard procedure derived by Bond (1961). The BWi is used to design new grinding circuits. BWi also used in the simulation and optimization of existing comminution circuits. Bond ball mill work index is normally distributed with an average of 14.6 and a median of 14.8 kWh/t (Mcken and Williams 2005). The common BWi values are shown in Table 3.

Table 3: Common Bond Ball Work Index values for different types of rocks

Property Soft Medium Hard Very Hard

Bond WI (kWh/t) 7 – 9 9 - 14 14 – 20 >20

2.4.2 Bond rod mill work index (RWi):

The bond Rod mill work index provides measure of energy used by rod mill. RWi indicates the resistance of the material to crushing and grinding (Rod et al. 1961). RWi also used along with the other Bond tests (BWI and CWI) for SAG mill design using semi-empirical relationship (Barratt et al. 1996).

The average and median of RWi are both 14.8 kWh/t (MacPherson Consultants (ARMC) database). The average is same as BWi but the median is different. The reason is the variation in hardness with size of feed of both tests (13 mm for RWI and 3.35 mm for BWI) (Mcken and Williams 2005). The common RWi values are given Table 4.

Table 4: Common Bond Rod Work Index values for different types of rocks

Property Soft Medium Hard Very Hard

Bond WI (kWh/t) 7– 9 9 - 14 14– 20 >20

2.4.3 MacPherson autogenous work index:

MacPherson is a small-scale AG/SAG steady state mill test. MacPherson autogenous work index is calculated by the procedure of MacPherson autogenous grindability test, derived by MacPherson and Turner (1978). After completion of whole procedure, mill power draw, particle size distribution and throughput is used to compute the specific energy input and Macpherson autogenous work index(AWi).

Around 750 tests of 250 different deposits of World show that 90% of AWi values are in range 3 and 7 KWh/t (Mcken and Williams 2005).

2.4.4 SAG power index (SPI)

SPI was first developed by John Starkey (Starkey and Dobby 1996). SPI is expressed in time in minutes which is required to reduce an ore sample from a P80 of 12.7mm to P80 of 1.7mm. Higher SPI values indicates harder the ore (Mcken and Williams 2005). The SPI is transformed in KWh/t and then it is used by MinnovEX for production forecast and circuit design using CEET software (Dobby et al. 2001).

2.4 Existing comminution test methods

To find most easy and economic comminution test method, the existing comminution methods are studied in context of Geometallurgy. These methods are divided into three major groups

• rock mechanical tests

• particle brakeage tests

• bench scale grindability tests.

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Each group is sub-divided into further methods (Mwanga et al. 2015).

2.4.1 Rock mechanical tests

Rock mechanical tests are used to measure rock strength using drill core samples. In these methods, stress is applied on the sample under specific conditions and the maximum stress and strain is noted by device before sample fails. These methods include uniaxial compressive test, point load test, Brazilian test, tri- axial compressive test and hardness test. These tests have same breakage mechanism under stress.

2.4.1.1. Uniaxial compressive strength tests (UCS)

UCS is widely used in rock engineering (Cargill and Shakoor 1990). Drill core piece having length to diameter ratio of 2-2.5 (ASTM standards), is used (Ergün and Tuncay 2009). Sample is placed between two perpendicular plates and stress is applied through one movable plate until the sample is failed/broken.

The Applied stress is uniformly increasing. The displacement in the sample is measured to compute elasticity of the sample. This is unconfined uniaxial compressive test, for tri-axial compressive strength test, the core is enveloped in a membrane/oil which provide pressure in the radial direction, with increasing the axial load the pressure of oil in radial direction also increase until the specimen fails. The sample could be prepared by Both American Society for Testing and Materials (ASTM) and the International Society for Rock Mechanics (ISRM). Sample preparation for UCS contains; drilling of drill core from bulk sample using diamond drill core, cutting the core perpendicular to the axial direction having L/D ration according to the standards used, grinding and polishing of cross section of drill core and finally drying the core before testing (Cargill and Shakoor 1990).

2.4.1.2. Point load strength test (PLT)

A single point load strength index is obtained by sample in shape of core or bulk. This index correlates to the uniaxial compressive strength. In PLT, load is applied between tips of two cones, in form of point load.

The maximum load applied and equivalent core diameter De(50mm) is used to find the Point load strength index (𝐼𝑠₅₀), as shown in equation (1).

𝐼𝑠₅₀= ^𝑃

𝐷_𝑒²

(1) 𝐼𝑠₅₀ is the point load strength index [Psi], P is the maximum point load applied [lbf], De is the equivalent diameter [in]. Point load index is further used to calculate the uniaxial compressive strength UCS [Psi]

using a linear conversion factor K (having value of 16 – 24, [unitless]) (Rusnak and Mark 2000), shown in equation (2).

𝑈𝐶𝑆 = 𝐾 × 𝐼𝑠₅₀

(2) 2.4.1.3. Brazilian test

Brazilian test is indirect measure of tensile strength of brittle materials. Compressive stress is applied along the diameter of the core between two plates, which induce the tensile load on the sample. The indirect tensile strength is calculated based on the assumption that the failure occurs at maximum tensile stress at the center of the disc. The formula for indirect tensile strength measurement is given in equation (3).

𝜎_𝑡 = 2 ∙ 𝑃

𝜋 ∙ 𝐷 ∙ 𝑡 (3)

16

𝜎_𝑡 is the tensile strength [𝑀𝑃𝑎], P is the applied compressive load at failure [N], D is the diameter of the core [mm], t is the thickness of the specimen measured from the centers of the sample[mm] (Li and Wong 2013).

2.4.2 Particle breakage tests 2.4.2.1 Simple drop weight tests

In drop weight test, a certain weight is lifted and dropped on the sample. The broken simple is analyzed in term of particle size distribution to study the breakage behavior. Different impact levels are tested by varying the potential energy PE of the drop weight 𝑀_𝑑𝑤 .Potential energy is dependent on the drop weight 𝑀_𝑑𝑤 and drop weight height𝐻_𝑑𝑤, as shown in equation (4).

𝑃𝐸 = 𝑀_𝑑𝑤× 𝑔 × 𝐻_𝑑𝑤 (4)

PE is the potential energy [joules], 𝑀_𝑑𝑤 is the mass of the drop weight [Kg], G is the gravitational acceleration [9.8 𝑚/𝑠²] and 𝐻_𝑑𝑤 is height of the drop weight [m].

The JKTech drop-weight test is developed in Julius Kruttschnitt Mineral Research Center (JKTech 1992).

This test is divided into three parts. First part is the measurement of resistance to the impact of coarse particles, within the range of 63-13.2 mm (Five fractions). The second part is the evaluation of resistance to abrasion breakage, within the range of 53 to 37.5mm. Final part is the measurement of the density of 20 particles, its average and its dispersion.

This test generates breakage pattern of ore under a range of impact and abrasion conditions, which is reduced to three parameters: A, b (dimensionless, impact) and ta (abrasion), shown in Table 5. Axb parameter is the slope of the t10 vs Espec curve. A is the significant for higher energy levels whereas b is significant for lower energy levels. A is the maximum value of t10 achieved. A and b are dependent to each other therefore one value of Axb is indicated as hardness of ore in term of impact breakage (JKTech 1992).

These parameters are used in JKSimMet modeling and simulation package to predict the response of ore in comminution processes e.g. AG/SAG mill, ball mill and HPGR (Mcken and Williams 2005). The fragments from all tests are collected and analyzed for particle size distribution. Which are normalized to t values (percent weight of fragments that passes 1/t of its original size) showing the size reduction. The percentage passing 1/n of the starting particle size can be related to the comminution energy by the equation given in equation (5).

𝑡𝑛= 𝐴 ∙ (1 − 𝑒^{−𝑏∙𝐸𝑐𝑠})

(5) Ecs is the specific energy in kWh/t and A and b are ore-specific parameters. t10 is reduced to twovariables A and B along with Ecs using equation (5), by least squares fitting to drop weight test data.

Table 5: common values of Axb and ta of different rocks.

Property Very Hard Hard Mod. Hard Medium Mod. Soft Soft Very Soft

A×b < 30 30-38 38-43 43-56 56-67 67-127 >127

ta < 0.24 0.24-0.35 0.35-0.41 0.41-0.54 0.54-0.65 0.65-1.38 >1.38

A and b are determined by fitting the experimental data with different specific energies. Axb describes the hardness of the ore. A higher value of Axb represents soft material and vice versa. The frequency

17

distribution of Axb from JKTech coming from great number of test over the years, given in Figure 8 (Mcken and Williams 2005).

Figure 8: Frequency Distribution of Axb ((Mcken and Williams 2005)

2.4.2.2 Instrumental drop weight test

Drop weight test is further modified by adding different instrument for measurements during the test.

One of the instrumental drop weight test device is “Ultra-fast load cell device (UFLC)” developed by university of Utah (Weichert and Herbst 1986). It contains a laser and a photo diode, as well as a strain gauge to calculate actual load applied to the sample instead of the potential energy of the drop weight.

(Tavares 1999).

2.4.2.3 Twin pendulum test

A single particle is mounted between two pendulum hammers and the hammers are released from certain heights unless the particle is broken. One of the instrument is bond twin pendulum tester which works on the same principle. The sample preparation is easy and consist on the crushing and sieving between two close size ranges e.g. Sahoo et al. (2004) used three particle sizes (9.5-11.2mm, 11.2-13.2 mm and 13.2- 16mm) of two types of coal. Crusher work index, defined by the bond is given in equation (6) (Narayanan 1985).

𝐶𝑊_𝑖 =53.5 ∙ 𝐶_𝐵

𝜌𝑝 (6)

𝐶𝑊_𝑖 is the crushing work index [KWh/t], 𝐶𝑏 =^{117∙(1−𝜃)}

𝑑_𝑝 , is the impact energy per particle thickness 𝑑_𝑝 [j/mm] and 𝜌𝑝 is the particle density [𝑔 𝑐𝑚⁄ ³] and θ in [degree].

18 2.4.2.4 Split hopkinson pressure bar test

Split hopkinson pressure bar apparatus consists of two bars, incident bar and transmitted bar. The sample (single particle) is placed between two steel bars. A gas gun is used as a stress loading system. The deformation wave travel through the steel bars and sample, recorded by the strain gauges. Cylindrical specimens are used mostly for the test (Kaiser et al. 1998).

2.4.2.5 Rotary single impact tester

The principle of rotary single impact tester is the collision of single particle with impact surface. For collision, either sample is accelerated against static plate or advancing sample in rotor-stator impact system. The particles are fed in the rotor and make impact to the perpendicular saw tooth profile of the stator by centrifugal force. This test is based on the single collision of particle against static perpendicular surface, while in a mill a particle faces multiple collisions between other particles, grinding bodies and mill surface but relatively with low velocity. This method has ability to test more samples as compared to other methods. The results from the rotary breakage tester are used for the energy-size reduction profile, further used in process design (Schönert and Marktscheffel 1986).

2.4.3 Bench scale grindability tests 2.4.3.1 Bond ball mill Test

Bond test is used to measure the grindability of the sample at the lab scale, using a bond ball mill. It consists on dry locked cycle, until the circulation load reaches to 250% (Bond 1952, Bond 1961 and Bond 1949). This is often possible after 7-10 cycles. After each cycle, fines are replaced by the equal amount of fresh feed. The standard bond ball mill has same length and diameter of 305mm. The bulk material is below 3.35mm having volume of 0.7x 10⁻³ 𝑚³ . For single test, around 10 kg of sample is required (Magdalinovic 1989).

The bond ball mill work index 𝐵𝑊𝑖 [kWh/t] is defined in equation (7).

𝐵𝑊_𝑖 = 1.1 ∙ 44.5

𝑃^0.23∙ 𝐺^0.82∙ (10

√𝑃− 1

√𝐹) (7)

Pc is screen aperture [µm], G is the mass of product per mill revolution [g], P and F are 80% passing size [µ] of Product and feed respectively [wt.%].

The relation between grinding work index W[kWh/t] and particle size during the grinding is given in equation (8) (Bond, 1952).

𝑊 = 𝐵𝑊_𝑖∙ ( 10

√𝑃80

− 10

√𝐹80

) (8)

Bond Work index is mostly used to represent the behavior of ore in grinding circuit; energy consumption during the comminution. Bond work index is repeatable all over the world and used most of the years for designing the comminution circuits.

2.5 Geometallurgical comminution test (GCT)

A comparison was made by Mwanga et al.(2015) between comminution tests having potential for geometallurgy, shown in Table 6.

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Table 6: Common fracture test methods having potential for geometallurgical tests. -(1) Simplicity, (2) repeatability, (3) sample preparation, (4) time exposure and cost, (5) sample amount, (6) parameters can be used in modelling and simulation, (7) can be extended to mineral liberation (Mwanga et al. 2015)

Fracture Test Method Suitable Criteria for Geometallurgical test (-=adverse, 0=acceptable, +=advantage)

1 2 3 4 5 6 7

Unconfined compressive strength test + 0 - 0 + - -

Point load test + 0 0 0 + - -

Brazilian test + 0 - 0 + - -

Drop weight test 0 0 - - - + 0

Ultra Fast load cell test - 0 0 0 - + 0

Twin pendulum test - - 0 0 0 + 0

Split Hopkinson test - 0 - - - 0 0

Rotary breakage test - + 0 0 0 + 0

Bond ball mill test 0 + 0 - - + +

Bond rod mill test 0 + 0 - - + +

Single pass test e.g. Morgan mill + + 0 0 - + +

Unconfined compressive strength test has a shortcoming of intense work in sample preparation (drilling, cutting, grinding, polishing core according to the standards). While parameters calculated by UCS cannot be used directly in modelling and simulation (Rusnak and Mark 2000). Whereas UCS test cannot be extended to the liberation study. Point load test doesn’t fulfill the criteria of using of parameters in modelling and simulation directly and extension of product to liberation analysis. Brazilian test has same shortcoming as point load test with additional shortcoming of intense sample preparation. Drop weight test has shortcoming of sample preparation, time exposure, cost and sample amount. Ultrafast load cell test has shortcoming of simplicity and sample amount. Twin pendulum test has shortcoming of simplicity and repeatability. Split Hopkinson bar test has many shortcomings for having potential for geometallurgical tests. Bond ball and rod mill test have negative points in term of time exposure, cost and sample amount. Mergan mill is a simplified test with single pass but still it has one shortcoming of Size of sample. This comparison shows that none of the test fulfills all the required criteria required for geometallurgical tests.

Considering Bond test as basic method, a new procedure (GCT) is developed for comminution test having potential to fulfill all criteria of geometallurgical tests. GCT provides the estimation of BWi, particle size distribution at different grinding energies and time along with the possibility that the mill product could be used for liberation analysis (Mwanga et al. 2015).

This method is derived by considering the same mechanisms of standard bond test. Because of down- scaling, parameters are changed and different correction factors are used to obtain same phenomena inside the mill. Scale factor for geometrical relationship between two mills is 1.63 (square root of ratio of the diameter of bond mill to small ball mill). To get the same fracture effects between two mills, a dimensionless factor λimpact(β) called Froude number is sued, shown in equation (9).

𝜆𝑖𝑚𝑝𝑐𝑡(𝛽) =𝜈𝑖𝑚𝑝(𝛽)𝐿

√𝑔 × 𝐷𝐿

÷𝜈𝑖𝑚𝑝(𝛽)𝑆

√𝑔 × 𝐷𝑠 (9)

𝜆𝑖𝑚𝑝𝑐𝑡(𝛽) is a dimensionless factor for impact velocity between two mills, 𝜈𝑖𝑚𝑝(𝛽)𝐿 is impact velocity [m/s] of bond mill at any thrown angle β, 𝜈𝑖𝑚𝑝(𝛽)𝑆 is impact velocity [m/s] of the small mill

20

at any throw angle β, g is the gravity constant [m/s²], 𝐷_𝐿 is the diameter of large mill (Standard bond mill) [m] and 𝐷𝑠 is the diameter of small mill [m].

The bond energy equation for calculation of BWi is given in equation (10).

𝐵𝑊𝐼 = 𝐸

𝐾 × 𝐸𝑓1 × 𝐸𝑓2 × 𝐸𝑓3 × 𝐸𝑓4 × 10 × ( 1

√𝑃80− 1

√𝐹80) (10)

BWI is bond work index (estimated ) [kWh/t], E is measured specific energy in the small mill [kWh/t], P80 is the product 80% passing size (µm), F80 is the mill feed 80% passing size (µm), k is the scale factor defined by square root of the ratio of the diameter of bond mill to small ball mill equal (1.63), Ef1 is correction factor for dry grinding, Ef2 is the correction factor efficient diameter (usually 1.842 is taken), Ef3 is the ball mill efficiency factor (0.835), Ef4 is the efficiency factor for fineness (0.95).

The parameters used for downscaling bond mills are given in Table 7:

Table 7: Parameters for downscaling the bond mill test (Mwanga et al. 2015)

Parameters Conditions for

downscaling

Standard Bond

Ball Mill Small ball mill

Mill dimension 1 Diameter (mm) To be changed 305 115

2 Length (nm) To be changed 305 132

Ball Charge

3 Percentage mill volume filling by ball

charge (%) Fixed 19 19

4 Average ball size (mm) Fixed 27 27

5 Ball charge (Kg) Scaled by filling (3) 21.9 1.33

Sample

6 Sample to ball ratio (w/w) Fixed 0.16 0.16

7 Sample size (Kg) Scaled by ratio (6) 3.4 0.220

8 Sample particle size distribution (mm) Fixed <3.35 <3.35

Operational conditions

9 Speed, vs critical (%) Fixed 91 91

10 Grinding time (minutes) To be changed 10.5 17.0

11 No. of revolution/ minute To be changed 70 114

12 Test type To be changed Locked Cycle Single pass

13 Mill product sizing Fixed Standard sieve

series

Standard sieve series

Finally, it is obvious that GCT is the easiest, less time consuming (required small amount of sample) comminution test methods which can be used for the study of grindability of the ore. Bond work index is calculated by GCT.

2.6 Correlations between comminution test methods

Correlation between comminution test methods may helpful for prediction of comminution indices, suing available indices.

2.6.1 Correlation between bond work index and mechanical properties

Standard method of bond work index is time consuming and require a significant mass of sample. Many people tried to find correlation between BWi and mechanical properties of rocks. Haffez (2012) compared different mechanical properties of some Saudi ores (bauxite, kaolinite, granodiorite, magnetite, granite, feldspar and quartz) to bond work index. He concluded that the bond work index is positively correlated

21

with modulus of elasticity (𝑅²= 0.90), shown in Figure 9A. Compressive strength (UCS) is also positively correlated with Bond work index (𝑅²= 0.81), shown in Figure 9B. Abrasion is negatively correlated to the Bond work index (𝑅²= 0.80), shown in Figure 9C. Correlation between bond work index and hardness value was positively correlated (𝑅²= 0.75), shown in figure 9D.

Figure 9: Correlations to Bond Work Index: (A) Effect of modulus of elasticity of the different studied materials on Bond work index, (B) Effect of compressive strength of the different studied materials on Bond work index, (C) Effect of abrasion of the different S

2.6.2 Correlation between BWi, friability and grindability index G

Swain and Rao (2009) compared bond work index and friability (tendency of a material to break by duress or contact e.g. by rubbing). They found a good correlation between BWi and friability, shown in Figure 10.

The R square value was 0.93, showing good correlation. One can predict value of bond work index with small error using this correlation for same ore type.

22

Figure 10: Correlation between Bwi and Friability .

Swain and Rao (2009) were also calculated the bond work index using Hardgrove grindability index (measurement of grindability of coal, [unitless]), Shown in Figure 11. The R² value was 0.99, showing very strong correlation between measured and calculated bond work index.

Figure 11: Correlation between Measured Bond work index and calculated bond work index using Hardgrove grindability

Ozkahraman (2005) found a good correlation among Bond work index, friability and grindability index G, shown in Figure 12. A correlation coefficient of 0.99 is found between grindability index G and friability value. A correlation coefficient of 0.97 is found between bond work index and friability values.

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Figure 12 The relationship between (a) grindability index G, (b) work index Wi and friability valueS20, where G is the average value net grams of undersize produced per mill revolution in last three cycles of standard bond test

2.6.3 Correlation between bond work Index and Axb parameter of drop weight test

Harbort et al. (2013) found a correlation between bond work index and Axb parameter in different lithologies, shown in Figure 13.

Figure 13 Correlation between bond work index and Axb parameter in various lithologies and alterations

T.J. Napier-Munn in his book; Mineral Comminution Circuits also tries to compare bond work index and Axb parameter and found a correlation, shown in Figure 14.

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Figure 14 correlation between BWi and Axb parameter

The aim of correlations is to study the opportunity for prediction of other parameters using available parameters. These correlations are associated to specific deposits. E.g. Figure 13 and figure 14 have slightly different correlation model because of different deposits.

2.7 Estimation of comminution indices based on mineralogy, chemical assays, lithology and alteration

Comminution test methods require time, equipment and specific sample. Many people put their efforts in estimation of comminution indices from data which is available on mine site or which can be obtainable easily and cheaply. These authors used multiple linear regression to generate models, having chemical assays, modal mineralogy, lithology and alteration as input parameters.

Keeney and Walters (2011) made models for prediction of bond work index in two different classes, hematite-pyrite and feldspar class. They also used multiple regression to generate models. The model prediction relative errors were 7.4 and 2.1% respectively to the class. Results are shown in Figure 15, showing good correlations to the actual BWi values. They used fluorite, hematite, pyrite, specific gravity, sulphide, hardness and chlorite as independent variables for prediction of BWi. Models are shown in equation (11Error! Reference source not found.) and (12). These models are just an example for prediction of BWi and are only valid for a specific deposit.

Model for hematite-Pyrite class:

Bond Workindex [KWh/t]= −66.65 + 1.24 × Fluorite(%)^0.61− 0.27 × Hematite(%) − 1.49 × Pyrite(%) + 19.23 × SG + 8.39 × (Pyrite(%)/Sulphide(%))^0.84+ 0.72 × QHard^1.22+ 0.72 × (Chlorite(%)/Sulphide(%))^1.31

(11) R2=0.84, Model prediction relative error =7.4%

Model for Feldspar class:

Bond work Index [KWh/t]= -104.4 -0.17×K-feldspar(%) -0.88×Quartz(%) -0.12×Siderite(%) - 0.47×Fluorite(%) -0.43×Sulphide(%) -0.54× (Sericite(%)/K-feldspar(%)) + 0.88×

(Sulphide(%)/Hematite(%)) +8.56×QHard

(12) R2=0.83, Model prediction relative error =2.1%

25

Figure 15 Correlation of predicted and calculated BWi in two classes (Keeney and Walters 2011)

Hunt et al. (2013) modelled comminution parameters using modal minerology, chemistry and drill core logging. They also used multiple linear regression for modelling. They modelled BWi, AXb and SPI. They found a good model with error of ±6% in calculation of BWi, Axb ±12% and SPI ±10-15%. They used Al2O3, Na2O, SiO2, K2O, TiO2, Zn, quartz, orthoclase, chlorite, lithology and alteration as independent variables in the model. The measured and estimated BWi values are shown in Figure 16A. The effect of lithologies on correlations was highlighted e.g. different correlation between SPI and white mica in different lithologies, shown in Figure 16B and Figure 16C.

26

Figure 16 A- Measured VS estimated BWI, B and C, Correlation between where mica and SPI in two different lithologies (Hunt et al. 2013)

Keeney et al. (2011) used multiple linear regression to model BWi and Axb using modal minerology, hardness and density information. They found average relative error of 3.2 and 4.7% for BWI and Axb respectively, plots between measured and predicted BWi and Axb are shown in Figure 17.

Figure 17 Correlation between measured and calculated Axb and BWI (Keeney et al. 2011)

A

B C

27

2.8 Principle component analysis

Principle component analysis is used to reduce the dimensions of the data. The larger number of variables are replaced by smaller numbers, called principle components. which are formed by linear combination of the original variables. The first principle component is calculated in the direction of maximum variability. The second principle component is always orthogonal to the first principle component, covering the second highest variability in the data set and so on. The original variables are converted into lower number of principle components and maximum variability in the dataset is covered (Jolliffe, 2002).

Keeney et al. (2011) used PCA (based on minerology) to classify samples (La Colosa porphyry Au deposit, Colombia) into different 7 classes. Where, first principle component was dominated by pyrite, chalcopyrite and feldspar while second component was distinctly dominated by magnetite and chlorite.

On PCA scatter plot the classes were made manually by considering the hardness, density and minerology of the samples. PCA scatter plot is shown in Figure 18.

Figure 18 PCA scatter plot of samples

Keeney and Walters (2011) also used PCA to classify 500 samples on basis of modal minerology and comminution indices (BWi and d Axb). The PCA scatter plot along with direction of increasing of mineralogical abundance, is shown in Figure 19.

28

Figure 19 PCA plot of samples and direction of abundance of mineralogy

Considering these examples, PCA seems a useful method for classification of Aitik samples into different classes

2.9 Element to mineral conversion

Element to mineral conversion is a traditional method in which mineral grades are calculated using elemental grades and chemical formula of minerals (% each element in the mineral). This method has simple mass balance equations of mineral grades, elemental grades and chemical composition of mineral.

This method is simple having limitation; number of minerals should not be greater than the analyzed components and chemical composition of minerals. Mathematically shown in equation (13).

A × x = b; [

a11 ⋯ a1n

⋮ ⋱ ⋮

an1 ⋯ ann

] × [ x₁

⋮ xn

] = [ b₁

⋮ b_n

] (13)

Where matrix A is the matrix of chemical composition of minerals, x is the matrix of unknown mass proportion of minerals and b is the vector of known chemical assays (elemental grades). This system of matrices can be solved using non-negative least square method. Electron probe micro-analysis (EPMA) is used to analyze the chemical composition of minerals, if we have right chemical composition of minerals we can improve EMC much more (Parian et al. 2015).

Geometallurgical comminution test (GCT) is as easy and quick method to calculate bond work index. GCT will be used for calculation of BWi, because of simplicity and availability of apparatus in the lab. Element