A Geometallurgical Forecast Model For Predicting Concentrate Quality in WLIMS
Process for Leveäniemi Ore
Kartikay Singh
Natural Resources Engineering, master's level (120 credits) 2017
Luleå University of Technology
Department of Civil, Environmental and Natural Resources Engineering
1
Abstract
Previous studies have suggested that Davis tube (DT) experiment can used to study wet low intensity magnetic separation (WLIMS) for magnetic iron ores. But DT process has never been used to map WLIMS process, specifically in a geometallurgical framework. This thesis work is a step towards fulfilling this gap by studying the Davis tube experiment performed on 13 different samples from Leveäniemi iron ore deposit. The methodology adapted to map WLIMS concentrate quality includes study and analysis of feed, DT and WLIMS. Analyses were made using experimental data, processing data using some analytical tools, some data-processing tools and post processing tools. For covering the geometallurgical aspect the analysis was done for both elements and minerals. The results from this study has reviled that DT can be used to predict WLIMS concentrate quality to an acceptable level of confidence. Furthermore, results show that a combination of DT and WLIMS information produce very accurate and highly reliable models for predicting and mapping WLIMS concentrate quality. This work serves as the first step towards studying an unexplored field pertaining to magnetic iron ore concentrate and has opened door to possible future work that could take this work a step further. Supplementing this study with more data from different sample is required not only to validate the model but also to make it better. A better modal mineralogy of the samples is needed to unlock the full potentials of mineralogical modelling approach used in this work.
2
Acknowledgement
This work could not have been possible without the help and guidance from a lot of people. Firstly, I would like to thank the entire EMERALD fraternity for providing me this opportunity to undertake this masters program. The education and knowledge embraced by the professors in these two year is immense and irreplaceable.
I would like to thank my supervisor Dr. Cecilia Lund for this project and her guidance through the course of this work. Also, I want to whole heartedly thank the PhD students in the MiMer department specially Viktor Lishchuk and PH Koch for answering all my small and big queries.
I would also like to pass my gratitude towards all my EMERALD colleagues doing their thesis at LTU, specially Efrain Cardenas, the discussions between us have solved many problem that arise in the progression of this work.
I would like to extend my humble gratitude toward our colleagues at LKAB, especially Mattias Gustafsson and Kari Niirranen for their support during the internship and also during lab work performed at LKAB facility.
Last but not the least I would like to thank my parents to be constantly present for supporting me in my work and for always telling me to keep pushing forward.
I would like to give special regards to my father, who always kept telling me to take it one day at a time. His golden words have acted as armor during my low moments.
Kartikay Singh July, 2017 Luleå, Sweden
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Table of content
... 1
ABSTRACT ... 1
ACKNOWLEDGEMENT ... 2
TABLE OF CONTENT ... 3
LIST OF FIGURES ... 5
LIST OF TABLES ... 6
LIST OF EQUATION ... 7
ABBREVIATIONS ... 7
1 INTRODUCTION ... 1
2 STATEMENT OF PROBLEM ... 1
3 OBJECTIVE, DELIVERABLES AND HYPOTHESIS ... 2
4 SCOPE AND LIMITATIONS ... 3
5 LITERATURE REVIEW ... 4
5.1 GEOMETALLURGY AND FORECAST MODEL ... 4
5.2 MAGNETIC SEPARATION ... 5
5.2.1 General overview and principle ... 5
5.2.2 Application and methods of magnetic separation ... 7
5.3 WLIMS(WET LOW INTENSITY MAGNETIC SEPARATION) ... 8
5.4 DAVIS TUBE ... 12
5.5 LEVEÄNIEM ORE ... 13
5.5.1 Deposit Geology ... 14
5.5.2 Case study: Leveäniemi Ore, LKAB... 16
5.6 ELEMENT TO MINERAL CONVERSION (EMC) ... 17
5.7 HENRY REINHARDT CHART ... 17
5.8 PRINCIPLE COMPONENT ANALYSIS (PCA) ... 18
5.9 MODELLING ... 19
5.9.1 Multiple linear regressions ... 20
5.9.2 Interpreting multiple linear regression ... 21
6 MATERIALS AND METHODS ... 22
6.1 AVAILABLE DATA ... 22
6.2 EXPERIMENTAL ... 23
6.2.1 Bulk Sampling ... 23
6.2.2 Davis tube (DT) ... 26
6.2.3 Wet low intensity magnetic separation (WLIMS) ... 29
6.2.4 Sampling Error ... 32
6.3 ANALYTICAL TOOLS ... 34
6.3.1 Optical Microscopy ... 34
6.3.2 Chemical Assays ... 34
6.3.3 Automated Mineralogy ... 34
6.4 PROCESSING TOOLS ... 34
6.4.1 Mass Balancing ... 34
6.4.2 Davis tube new stream creation ... 35
6.4.3 Element to mineral conversion (EMC) ... 36
6.4.4 Recoveries ... 36
6.5 POST – PROCESSING TOOLS ... 37
6.5.1 Grade – Recovery Curves ... 37
6.5.2 Selectivity Curves ... 37
6.5.3 Henry Reinhardt chart ... 37
6.6 MODELLING ... 37
4
7 RESULTS ... 38
7.1 GEOLOGICAL CHARACTERIZATION ... 38
7.2 ANALYTICAL ... 40
7.2.1 Microscopy ... 40
7.2.2 Automated Mineralogy ... 40
7.3 DATA PROCESSING ... 41
7.3.1 Mass Balance ... 41
7.3.2 Element to mineral conversion (EMC) ... 41
7.4 POST –PROCESSING ... 42
7.4.1 Modal mineralogy validation ... 42
7.4.2 Grade – recovery curves ... 45
7.4.3 Selectivity Curves ... 47
7.5 MODELLING ... 52
7.5.1 Data handling ... 52
7.5.2 Principle component analysis (PCA) ... 53
7.5.3 Traditional and proxy approach ... 55
7.5.4 Mineralogical Approach ... 63
8 DISCUSSIONS ... 71
8.1 MODAL MINERALOGY ... 71
8.2 GRADE – RECOVERY ANALYSIS ... 71
8.3 SELECTIVITY CURVES ANALYSIS FOR DT AND WLIMS ... 71
8.4 PRINCIPLE COMPONENT ANALYSIS (PCA) ... 72
8.5 FINAL SAMPLE GROUPING ... 72
8.6 MODELLING ... 73
8.6.1 Traditional and proxy approaches ... 73
8.6.2 Mineralogical approach ... 76
9 CONCLUSIONS ... 79
10 FUTURE WORK ... 80
REFERENCES... 1
APPENDIXES ... 3
APPENDIX 1.WLIMSCHEMICAL ASSAY AND EXPERIMENTAL MASSES... 3
APPENDIX 2.MICROSCOPIC SAMPLE DESCRIPTION ... 6
APPENDIX 3.WLIMSMASS BALANCE ... 12
APPENDIX 4.DTMASS BALANCE ... 13
APPENDIX 5.CLOSEST RESEMBLING DT AND WLIMSFE-GRADE-RECOVERY ... 16
APPENDIX 6.ELEMENTAL GRADE-RECOVERY QUALITY CLASSIFICATION BASED ON FE ... 17
APPENDIX 7.CLOSEST RESEMBLING DT AND WLIMSFE-OXIDES GRADE-RECOVERY ... 19
APPENDIX 8.MINERAL GRADE-RECOVERY QUALITY CLASSIFICATION BASES ON FE-OXIDES ... 20
APPENDIX 9.ELEMENTAL CORRELATIONS ... 21
APPENDIX 10.MINERAL CORRELATIONS ... 25
5
List of figures
FIGURE 1 STATEMENT OF PROBLEM... 1
FIGURE 2 SCHEMATIC WORK FLOW FOR THE THESIS ... 2
FIGURE 3 MODELLING APPROACHES... 3
FIGURE 4 GEOMETALLURGICAL CONCEPT (LUND, 2013) ... 4
FIGURE 5 FORCES ACTING ON A PARTICLE DURING MAGNETIC SEPARATION PROCESS (METSO, 2015)6 FIGURE 6 ELEMENTS OF A MAGNETIC SEPARATION PROCESS (OBERTEUFFER, 1974) ... 7
FIGURE 7 MAGNETIC SEPARATION METHODS (METSO, 2015) ... 8
FIGURE 8 MAGNETIZATION VERSUS APPLIED MAGNETIC FIELD STRENGTH FOR A FERROMAGNETIC MINERAL (LIKE MAGNETITE) (WILLS & NAPIER-MUNN, 2016) ... 8
FIGURE 9 A TYPICAL DRUM SEPARATOR (WILLS & NAPIER-MUNN, 2016) ... 9
FIGURE 10 TYPES OF WLIMS. A. CONCURRENT (CC) WLIMS. B. COUNTER ROTATION (CR) WLIMS. C. COUNTER CURRENT (CTC) WLIMS. D. COUNTER ROTATION FROTH WLIMS. E. DENSE MEDIA RECOVER (DM) WLIMS (METSO, 2015) ... 11
FIGURE 11 A DAVIS TUBE (NIIRANEN, 2017; OBERTEUFFER, 1974) ... 12
FIGURE 12 A 3D MODEL OF THE DAVIS TUBE ELECTROMAGNET (MURARIU & SVOBODA, 2003) ... 13
FIGURE 13. THE LEVEÄNIEMI MINE (BREMER, 2010) ... 14
FIGURE 14 GEOLOGICAL MAP OF LEVEÄNIEMI ORE: 1. MAGNETITE ORE, 2. CALCITE-RICH MAGNETITE ORE, 3. HEMATITE-ALTERED ORE 4. ORE BRECCIA 5. LEPTITE 6. SERICITE SCHIST 7. METABASITE 8. LINA GRANITE 9. SKARN (BREMER, 2010) ... 15
FIGURE 15 MINING BLOCK CONTAINING MINERAL PROCESSING PARAMETERS AS THAT OF THE DRILL CORE FOR THE LEVEÄNIEMI OPEN PIT (FAGERBERG & ORNSTEIN, 1962; NIIRANEN, 2015)17 FIGURE 16. SIMPLIFIED HENRY REINHARDT CHARTS (NIIRANEN, 2017) ... 18
FIGURE 17 PRINCIPLE COMPONENT ANALYSIS (PCA) (MODIFIED FROM: SMITH, 2002) ... 19
FIGURE 18 METHODOLOGY FOR MATHEMATICAL MODELLING (MODIFIED FROM: CARSON & COBELLI, 2001) ... 20
FIGURE 19 JAW CRUSHER (LEFT) AND ROTARY SPLITTER (RIGHT) IN MIMER LAB ... 25
FIGURE 20 BULK SAMPLE HANDLING PROCEDURE ... 25
FIGURE 21 GCT GRINDING MACHINE (LEFT) AND DAVIS TUBE (RIGHT). ... 26
FIGURE 22 DT SAMPLE PREPARATION PROCEDURE ... 27
FIGURE 23 DAVIS TUBE EXPERIMENT SETUP ... 28
FIGURE 24 DAVIS TUBE FLOWSHEET ... 29
FIGURE 25 WLIMS SAMPLE PREPARATION PROCEDURE ... 30
FIGURE 26 I. WLIMS EXPERIMENTAL SETUP. II. WLIMS FLOWSHEET ... 31
FIGURE 27 SAMPLING ERROR CALCULATION FLOWSHEET ... 32
FIGURE 28 MINERALOGICAL VALIDATION - EMC VS SEM CORRELATIONS ... 44
FIGURE 29 GRADE-RECOVERY CURVE FOR FE ... 46
FIGURE 30 GRADE-RECOVERY CURVES FOR FE-OXIDES ... 47
FIGURE 31 SELECTIVITY CURVE - DT ELEMENTAL ... 48
FIGURE 32 SELECTIVITY CURVE - DT MINERAL ... 49
FIGURE 33 SELECTIVITY CURVE – WLIMS ELEMENTS ... 51
FIGURE 34 SELECTIVITY CURVE – WLIMS MINERALS ... 52
FIGURE 35 HISTOGRAM FOR FE% BEFORE (LEFT) AND AFTER (RIGHT) NORMALIZATION ... 53
FIGURE 36 HISTOGRAM FOR FE-OXIDE% BEFORE (LEFT) AND AFTER (RIGHT) NORMALIZATION ... 53
FIGURE 37 PCA ON ELEMENTAL DATASET ... 54
FIGURE 38 PCA ON MINERAL DATASET ... 55
FIGURE 39 MODEL FOR DC FROM FEED GRADE - ELEMENTAL ... 57
FIGURE 40 MODEL FOR WC FROM FEED - ELEMENTAL ... 59
FIGURE 41 MODEL FOR WC FROM DT - ELEMENTAL ... 60
FIGURE 42 MODEL FOR WC FROM DT AND FEED - ELEMENTAL ... 62
FIGURE 43 MODEL FOR DC FROM FEED - MINERALS ... 65
FIGURE 44 MODEL FOR WC FROM FEED - MINERALS ... 67
FIGURE 45 MODEL FOR WC FROM DT - MINERALS ... 68
FIGURE 46 MODEL FOR WC FROM DT AND FEED – MINERALS ... 70
FIGURE 47 FE GRADE RESULTS IN WLIMS CONCENTRATE FOR DIFFERENT MODELLING APPROACHES WITH SEPARATED ORES ... 74
FIGURE 48 TRADITIONAL + PROXY APPROACH FOR ELEMENTS AND FE-RECOVERY ... 75
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FIGURE 49 FE-OXIDES GRADE IN WLIMS FROM MINERALOGICAL APPROACH MODELLING ... 77
FIGURE 50 MINERALOGICAL APPROACH MODELLING USING FEED AND DT MINERAL DATA ... 78
List of Tables
TABLE 1 MINERALS AND THEIR MAGNETIC SUSCEPTIBILITY (HUNT, MOSKOWITZ, & BANERJEE, 1995; METSO, 2015; ROBERTSSON, 1992) ... 6TABLE 2 GENERAL PROPERTIES OF MAIN TYPES OF WLIMS (METSO, 2015) ... 10
TABLE 3 FEATURE OF LEVEÄNIEMI ORE (BREMER, 2010; LUND, 2013; MARTINSSON ET AL., 2016; NIIRANEN, 2015). ... 16
TABLE 4 P-VALUE DEPICTING STRENGTH OF EVIDENCE (BRYMAN & CRAMER, 1990; FIELD, 2005; HOOPER & YAU, 1986; HOWELL, 1992) ... 22
TABLE 5 AVAILABLE DATA ... 22
TABLE 6 GEOLOGICAL CHARACTERIZATION OF SAMPLES ... 24
TABLE 7 WLIMS P80 ... 30
TABLE 8 SAMPLING ERROR (RELATIVE STANDARD DEVIATION, %) ... 33
TABLE 9 GEOLOGICAL SAMPLE GROUPING (GROUP 1) ... 39
TABLE 10 SAMPLE GROUPING ON ORE TYPE (GROUP 2) ... 39
TABLE 11 MINERAL GROUPING BASED ON MICROSCOPY (GROUP 3) ... 40
TABLE 12 SEM FEED DATA MINERAL GROUPING ... 41
TABLE 13 EMC RECIPE ... 42
TABLE 14 RMSD VALUES FOR EMC VS QEMSCAN ... 44
TABLE 15 DATA FOR DIFFERENT APPROACHES ... 52
TABLE 16 INPUT PARAMETER FOR MODELLING USING TRADITIONAL APPROACH (ELEMENTAL INFORMATION) ... 56
TABLE 17 MODELLING OUTPUTS FOR DT CONCENTRATE FROM FEED. ... 58
TABLE 18 MODELLING OUTPUTS FOR WLIMS CONCENTRATE (WC) FROM FEED ... 59
TABLE 19 MODELLING OUTPUTS FOR WLIMS CONCENTRATE (WC) FROM DT-CONCENTRATE (DC) .... 61
TABLE 20 MODELLING OUTPUTS FOR WLIMS CONCENTRATE (WC) FROM DT-CONCENTRATE (DC) AND FEET GRADES ... 63
TABLE 21 INPUT PARAMETERS FOR MINERALOGICAL APPROACH ... 64
TABLE 22 MINERALOGICAL APPROACH MODELLING OUTPUTS FOR DC FROM FEED ... 66
TABLE 23 MINERALOGICAL APPROACH MODELLING OUTPUTS FOR WC FROM FEED ... 67
TABLE 24 MINERALOGICAL APPROACH MODELLING OUTPUTS FOR WC FROM DT ... 69
TABLE 25 MINERALOGICAL APPROACH MODELLING OUTPUTS FOR WC FROM FEED AND DT ... 70
TABLE 26 FINAL SAMPLE GROUPING ... 73
TABLE 27 MODELLING STATISTICS FOR FE GRADE IN WLIMS CONCENTRATE ... 74
TABLE 28 MODELLING STATISTICS FOR ELEMENT OF INTEREST IN WLIMS CONCENTRATE ... 76
TABLE 29 MODELLING STATISTICS FOR FE-OXIDES GRADE IN WC ... 77
TABLE 30 MODELLING STATISTICS FOR MINERALOGICAL APPROACH ... 79
7
List of Equation
EQUATION 1 MAGNETIC FORCE ON A PARTICLE ... 6
EQUATION 2 MAGNETIC SUSCEPTIBILITY ... 6
EQUATION 3 FORCE INDEX CALCULATION ... 13
EQUATION 4 EMC FOR MODAL MINERALOGY CALCULATION ... 17
EQUATION 5 EMC RESIDUAL CALCULATION ... 17
EQUATION 6 MULTIPLE LINEAR REGRESSION ... 20
EQUATION 7 DT GENERATED PRODUCT (C12) GRADE CALCULATION ... 35
EQUATION 8 DT GENERATED PRODUCT (C23) GRADE CALCULATION ... 35
EQUATION 9 DT GENERATED PRODUCT (C123) GRADE CALCULATION ... 35
EQUATION 10 FORMULA FOR CALCULATING CONTENT (G) ... 36
EQUATION 11 FORMULA FOR CALCULATING RECOVERY ... 36
EQUATION 12 NATURAL LOG CALCULATION FOR NEGATIVELY SKEWED DISTRIBUTION ... 38
EQUATION 13 NATURAL LOG CALCULATION FOR POSITIVELY SKEWED DISTRIBUTION... 38
EQUATION 14 RMSD FOR EMC VS QEMSCAN ... 43
Abbreviations
WLIMS Wet low intensity magnetic separation
DT Davis tube
WC Wet low intensity magnetic separation concentrate DC Davis tube cumulative concentrate (C123)
Auto – SEM Automated mineralogy from scanning electron microscope LKAB Luossavaara-Kiirunavaara AB
GDB Geological database
EMC Element to mineral conversion PCA Principle component analysis
C1 Davis tube concentrate at current intensity of 0.1 A C2 Davis tube concentrate at current intensity of 0.2 A C3 Davis tube concentrate at current intensity of 0.5 A
C12 Davis tube cumulative concentrate of C1 and C2 (C1+C2) C23 Davis tube cumulative concentrate of C2 and C3 (C2+C3)
C123 Davis tube cumulative concentrate of C1, C2 and C3 (C1+C2+C3) (DC) GCT Geometallurgical Comminution Testing
H0 Null hypothesis
H1 Alternate hypothesis
P80/D80 Diameter of 80% of particles SEM Scanning electron microscope RMSD/E Root mean square deviation/error
BWI Bond work index
PSD Particle size distribution
1
1 Introduction
LKAB (Luossavaara-Kiirunavaara AB) has both underground mines and open pit mines that extracts and mines Norrbotten's iron ore to get different products for the global steel market.. Leveäniemi is one of the open pit mine in Svappavaara, the process of mining is benching and beneficiation is by Wet Low Intensity Magnetic separation (WLIMS) after comminution of the ore (LKAB, 2016).
Moreover, there are different orebodies within Leveäniemi, thus it is obvious that the ore coming from these orebodies would also differ from one another. Therefore, it becomes important to adjust production parameters to the variability in the ore being delivered to the processing plant in order to constantly produce sellable products within the penalty limits. For the same purpose the traditional approach of ore characterization which involves only the evaluation of grades is not sufficient.
Thus, a Geometallurgical approach which involves different parameters such as geology, grade, recovery and metallurgical performances is to be employed. Geometallurgy could be defined as a cross-disciplinary approach that connects geology, metallurgy and mineral processing aiming to build a 3D spatial predictive model (Lund & Lamberg, 2014). Lund & Lamberg (2014), Viktor Lishchuk, Koch, Lund, & Lamberg, (2015). Viktor Lishchuk, (2016) defines three types of approaches towards Geometallurgy. The first approach is traditional approach which is based on elemental grade. The second approach is a geometallurgical test approach in which the geometallurgical model is based on the measured the metallurgical responses from small scale laboratory tests such as Davis tube and GeM comminution index test. The third approach is a mineralogical approach; here the predictive model is completed based on mineralogy. Parameters such as modal mineralogy, mineral textures, mineral association, mineral grain sizes and liberation information is used as inputs to the model. In this thesis work all the three approaches would be used to effectively solve the problem which would be introduced in section 2.
2 Statement of problem
The statement of problem for this work is to “find and map concentrate quality of WLIMS separation process”. The mapping of concentrate quality includes the grade and recovery of iron/iron bearing minerals and grade of different gangue elements/minerals. Figure 1 shows the statement of problem for this work with the approaches used to solve the problem.
Figure 1 Statement of problem
In order to tackle the problem of mapping concentrate quality different geometallurgical approaches are employed as shown in Figure 1. The approach includes geological examination, geometallurgical
2 tests (DT) and different analytical techniques. All the information attained from the used approaches is used to create different geometallurgical models which are thereafter studied and compared with each other in order to come to some conclusions about each of the approaches.
3 Objective, deliverables and hypothesis
The main objective of this thesis work is to forecast quality of the magnetite concentrate in the magnetic separation process (WLIMS) with emphasise on Si, V, Ti and P content for the ore which comes from Leveaniemi deposit.
Second objective of this thesis work is to deliver predictive modelling results and raw data in such a format that it can be integrated into the geometallurgical framework at LTU. The geometallurgical framework at LTU makes use of a geological database (GDB) which is known to primarily comprises of elemental grades from the drill cores collected at mine site (Lishchuk & Koch, 2017). The elemental grades in GDB represents feed grade thus the modelling done in this thesis work would makes use of elemental grades of feed.
Literature such as Schulz, (1964), Steiner & Boehm (2000) and Niiranen (2015) have demonstrated that Davis Tube (DT) could be regarded as a most reliable instrument and process in assessing the performance of wet low intensity magnetic separation (WLIMS). Thus the hypothesis for the thesis work could be put forward in a statement as “Davis tube experiments give a realistic view of wet low intensity magnetic separation (WLIMS) and could be used to predict WLIMS concentrate quality to a high degree of confidence.”
Figure 2 Schematic work flow for the thesis
In order to prove the hypothesis and attaining the objectives of this work, a laboratory scale DT and WLIMS test was performed on all the samples. The results were compared to find connections, correlations and pattern between GDB (feed grades), DT and WLIMS. Moreover, Parian, (2015)
• Develop a predictive concentrate quality forcast model for leveäniemi ore.
• Deliver data and model in a format which is propagatable and can be integrated into the Geometallurgical framework at LTU.
Project objectives
• Geology – 13 bulk samples representing the different ore bodies of the deposit.
• Microscopy – 52 polished sections for different size fraction of feed.
• Auto-SEM data for all feed samples in different size fraction.
Ore Characterization
• DT and WLIMS experiment.
• Mass pull and chemical assays for grade, recovery and selectivity analysis.
• Modal mineralogy from EMC and validation with Auto-SEM data.
Experimental and Methods
• Ore behaviour through the T and WLIMSprocess and similar ore body grouping from geology, microscopy, grade-recovery and principle component analysis (PCA).
• Prediction model from traditional , proxy and mineralogical approach.
Results
3 suggests that proper characterization of the feed is crucial for modelling concentrate quality. Thus, apart from DT results feed characteristic was also be taken into due consideration for forecasting WLIMS concentrate quality, covering the second objective of this work as shown the project objective headings of Figure 2. Figure 2 shows the schematic work flow of this thesis. Thus, at the end of this work it is possible to study and compare the generated predictive models from traditional approach (feed grades), proxy (DT grade) and mineralogical approaches (modal mineralogy). The Figure 3 shows the 4 different kind of modelling methods that were applied in order to attain the deliverables.
Figure 3 Modelling Approaches
Method 1 and the 4 uses feed grades (GDB) and falls under traditional approach (only feed elemental grade). Method 2 uses both feed grades and DT concentrate information as input to predict WLIMS concentrate quality thus method 2 falls under a combination of traditional and proxy approach.
Method 3 is purely a proxy approach as it uses just DT information to predict WLIMS concentrate quality. Instead of elemental information when mineral information is used in all the 4 methods then a mineralogical approach is employed to attain WLIMS concentrate quality (Viktor Lishchuk, 2016).
4 Scope and Limitations
As this thesis work is in accordance to the larger research project at LTU on Geometallurgy, thus the scope of this work remains under the geometallurgical framework at LTU. Particularly, the work fits into the mineral processing component of this framework. The generated models need to be in sync with the geological database (GDB) and would be later implemented in a block model. This work opens doors for new possibilities in mineral processing technique and process evaluation as never before WLIMS and DT experiments have been compared pertaining to magnetic iron ores.
The major limitation for this work is that there exists a large amount of data that needed to be handled and managed. Some works on the samples were already done and the information from previous work to be incorporated into the information from the new work done under this thesis. This generates some limitations in terms to data consistency and may leads to a situation of compromise in terms of data analysis.
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5 Literature review
5.1 Geometallurgy and forecast model
Mining in present day faces many new challenges and has become more complex over the past few decades. The deposits are getting more complex in terms of geology, mineralization, depleting grades, expensive mining and extraction, forcing for a more accurate and reliable planning of mine operations. Moreover, increasing ore variability and fluctuating commodity price poses a constant threat to the economics of a mine ( Lishchuk, 2016). With these increasing complexities it has become more necessary to evaluate the deposit and ore from a multi-disciplinary approach, such an approach is called “Geometallurgy”. The Figure 4 is modified from Lund (2013) and explain the geometallurgical concept in context to this thesis work. The blue outline defines the limit of this work.
Figure 4 Geometallurgical concept (Lund, 2013)
In Figure 4 the lower two levels are internal factors where ore and process parameters from the deposit influence the geometallurgical outcome. The ore characterization level defines the basic characterization of the different ore samples in terms of mineralogy, chemistry and textures. The second level from the bottom often includes a laboratory scale geometallurgical test work such as Davis tube for magnetic iron ores, but this stage may also include pilot plant tests. The third level from the bottom is an external factor as it does not directly comes from the ore deposit and it includes geostatistical modelling, sustainability and resource efficiency. The top three levels of the pyramid are highly dependent of financial fluctuations. The most important aspect of this geometallurgical concept is the additive and transferable nature of data or information from one level to another. As this concept involves the work of geologists, mineral processing engineers, metallurgist and economists it becomes essential to establish good communication between every personal involved in the whole value chain. Clear and effective communication is essential firstly to have similar definition for various terms involved at different levels and secondly to maintain a smooth and additive flow of information from one level to another.
A geometallurgical program is different from the traditional approaches as it does not rely only on geological information but also incorporates mineral processing, mineralogical, metallurgical and particle information (Lund, 2013). Geometallurgy also involves a comprehensive deposit characterisation that aims at integrating geology, mineralogy, mineral processing and metallurgy to build a spatially-based model for production management that quantitatively predicts:
1. Quality of concentrates and tailings,
5 2. Metallurgical performance, such as metallurgical recoveries and throughput,
3. Environmental impact such as fresh water usage for tons produced (Viktor Lishchuk et al., 2015).
For this thesis work a geometallurgical approach would be used to predict the quality of the concentrate of WLIMS separation process for leveäniemi iron ore using feed and DT information.
The development of a geometallurgical program normally goes through the 8 steps, according to Lund
& Lamberg (2014):
1. Collection of geological data;
2. An ore sampling program for metallurgical testing;
3. Laboratory testing of these samples;
4. Developing new ore-type definitions called geometallurgical domains;
5. Developing mathematical relationships for the estimation of important metallurgical parameters across the geological database;
6. Developing a metallurgical model of the process;
7. Plant simulation using the metallurgical process model and the distributed metallurgical parameters as the data set; and
8. Calibration of the models via benchmarking for existing operations.
There could be different types of geometallurgical programs depending on the type of data used for program development. There are basically three different approaches for linking the steps listed above as discussed in the paper by V Lishchuk, Lamberg, & Lund, (2015). The first is the traditional approach for which chemical assays serve a main source of information. This approach is good for high grade ore but is still not recommended as it would lead to a compromise on sustainability. The second approach is called “proxies approach” and relies on geometallurgical testing done on a large number of small samples that indirectly measures the metallurgical response. Generally, a correction factor has to be applied to the results to give estimate on the metallurgical results of plant. The second approach is known as the “mineralogical approach”, this approach requires proper quantitative mineral characterization of the ore, but also defining the process model based on minerals (Viktor Lishchuk et al., 2015; Lund, 2013).
For this work all the three approaches would be employed and studied to see which amongst the three approaches which is best suited to handle the statement of problem with the highest confidence level.
5.2 Magnetic separation
5.2.1 General overview and principle
Magnetic separation is mineral processing separation technique which is used to separate magnetic materials from those that are less magnetic or non-magnetic. Magnetic separation is the largest industrial use of magnetism, exclusive of motors and electric power generating devices (Oberteuffer, 1974). The basic principle magnetic separation is to pass the material through a magnetic field and the different components of the material will react differently depending on their magnetic susceptibility. The materials that react strongly to this magnetic field (strongly magnetic in nature) are known as ferromagnetic material and those that are less magnetic in nature are called paramagnetic material. The materials that are non-reactive to magnetic fields or very minutely reactive are known as diamagnetic materials (Parian, 2015; Svoboda, 2004). Three forces are required for particle separation mathematically, which are magnetic force (Fm), gravitational force (Fg) and a drag force (Fd) (Metso, 2015). The Figure 5 and Equation 1 is taken from (Metso, 2015) and shows that magnetic force which pulls the particle towards the magnet is directly proportional to intrinsic properties of the material as well as the applied magnetic field.
6
Figure 5 Forces acting on a particle during Magnetic separation process (Metso, 2015)
𝑭𝒎= 𝑽 ∗ 𝝌 ∗ 𝑯 ∗ 𝒈𝒓𝒂𝒅 𝑯 Equation 1 Magnetic force on a particle
Where,
V = Particle Volume (determined by process)
χ = Mass specific magnetic susceptibility (determined by material type)
H = Magnetic field (determined by magnet), mT (milliTesla) or kG (kiloGauss)
grad H = magnetic field gradient (determined by magnet system design)
Magnetic susceptibility (κ) of a natural or synthetic material is a dimensionless unit and determines the measure of the extent to which the material would be magnetized in presence of a small magnetic field. Mathematically, magnetic susceptibility is defined as the ratio of induced magnetization per unit volume (M) and applied magnetic field intensity (H). If the density (ρ) of the particle is known then magnetic susceptibility relative to sample mass (which is not a dimensionless unit) can be obtained from the ratio of κ to ρ given by the Equation 2 (Lascu, 2009).
𝝌 =𝜿
𝝆
Equation 2 Magnetic Susceptibility
The Table 1 represents the magnetic susceptibility (χ) of few of the common minerals measured in weak magnetic field, room temperature and one atmospheric pressure (Robertsson, 1992).
Table 1 Minerals and their magnetic susceptibility (Hunt, Moskowitz, & Banerjee, 1995; Metso, 2015;
Robertsson, 1992)
Mineral Magnetic susceptibility, χm (10-8 m3 kg-1)
Magnetite 20000-110000
Hematite 10-760
Apatite -2.64
Calcite -0.3 -1.4
Pyrite 1-100
Chalcopyrite 0.55-10
Chlorite 80-90
Quartz -0.5-0.6
7 5.2.2 Application and methods of magnetic separation
Conventionally, magnetic separation is used for two purposes, the purification of feeds with magnetic material and the concentration of magnetic materials. In the first case the desired product is the non- magnetic material. One such example is the removal of tramp iron from feed of ferrous ores which could create problems in further beneficiation stages as well as pose a danger of fire. Whereas, in the second case the most suitable example would be enrichment of a magnetite concentrate from Iron ore in mineral processing (Oberteuffer, 1974; Wills & Napier-Munn, 2016).
Magnetic separation in mineral processing can either be carried out in a dry or a wet (slurry) environment; either ways the basic elements of the process remains the same and can be seen in the Figure 6.
Figure 6 Elements of a magnetic separation process (Oberteuffer, 1974)
The feed in the Figure 6 is combination of magnetic and non-magnetic material. As material passes through a magnetic separation process, usually represented by a device that has varying magnetic field intensity, material gets separated into a magnetic fraction (mags or concentrate), a non-magnetic fraction (tails) and a mixture of the both (middlings). There are always some magnetics in tails during this process and the efficiency of this process could be measured from grade of magnetic material in the concentrate and magnetic material recovery. Recovery is the ratio of magnetic material in the concentrate to feed and grade is the fraction/percentage of magnetic particles in the concentrate (Oberteuffer, 1974).
The magnetic separation methods can be classified on the basis of a book on mineral processing published by Metso in 2015 which is illustrated in Figure 7.
8
Figure 7 Magnetic Separation Methods (Metso, 2015)
Wet low intensity magnetic separation (WLIMS) and Davis tube (DT) are the main magnetic separation methods used in this thesis work. Also, WLIMS is the main separation process used at LKAB for ore beneficiation. Thus, the next sections describe these techniques in details.
5.3 WLIMS (Wet low intensity magnetic separation)
Wet low intensity magnetic separation (WLIMS) method is used to separate ferromagnetic and some highly paramagnetic particles from non-magnetic particles, i.e. to concentrate ferromagnetic ores.
The basic principle is to feed the ore slurry to separators, which is separated into thick magnetic concentrate and water dilute tailings (Stener, 2015). At low magnetic field (≈ 0.3 T) in the magnetic drums the ferromagnetic minerals have high susceptibility initially due to exchange coupling and thus can be concentrated in low intensity (Figure 8). A point of saturated magnetization is reached as soon as all the exchanged coupled magnetic moment gets aligned with applied magnetic force. In Figure 8 the magnetic saturation point is at 300 kAm-1 (point 3 in Figure 8) and at this stage there is no increase in magnetization with the increase in applied magnetic field (Wills & Napier-Munn, 2016).
Figure 8 Magnetization versus applied magnetic field strength for a ferromagnetic mineral (like magnetite) (Wills &
Napier-Munn, 2016)
9 A WLIMS Separator could have one to four drums in a single separator unit and the design would vary depending on the concentration circuit. A WLIMS separator has three major physical components i.e. rotating drum, static magnet assembly and a tank as shown in Figure 9 but with different labelling. Although during the operation many parameters of machine setting and feed properties could be adjusted (Parker, 1977). WLIMS are available with several tank designs, several drum diameters, and several magnet assembly configurations. The Figure 9 shows the design of a typical drum type separator (Wills & Napier-Munn, 2016).
Figure 9 A typical drum separator (Wills & Napier-Munn, 2016)
The drums are semi-immersed in a tank through which the ore slurry passes. The drums usually have magnets as seen in the magnetic unit in the Figure 9. The alignment of the magnets inside the drum is in radial or axial pole configurations. The axial magnet assembly is used when concentrate quality is important and it normally consists of five to 12 magnetic blocks with alternating polarities. Some separators uses many small magnet blocks where their direction of magnetization changes in small steps to generate very even magnetic field (Svoboda, 2004; Wasmuth & Unkelbach, 1991) . There are different apparatus set ups available depending on the rotation of the drums, the number of drums and the spatial arrangement of the magnets within a drum separator. The configuration of WLIMS depend on the specific requirements of the application (Wills & Napier-Munn, 2016). The Table 2 and Figure 10 illustrate these different WLIMS types and separator tank arrangements with their features and components.
10
Table 2 General properties of main types of WLIMS (Metso, 2015)
Parameters Concurrent, CC (A)
Counter rotation, CR (B)
Countercurrent, CTC (C)
Counter rotation froth (D)
Dense media recovery, DM (E)
Design
Medium long magnetics pick up zone
Extra- long magnetics
pick up zone
Long magnetics pick up zone
Long magnetics
pick up zone
Very long magnetics pick up zone
Ore Handling
For low to high Fe grade feed
For low to high Fe
grade feed
For recovery cleaning or finishing stages, for low Fe grade
For improved
recovery from aerated (frothy) slurries, for low to
high Fe grade
feed
For low to high Fe grade feed
Tailing control
Tank bottom spigots for tailings flow
control
Manually adjustable weir for
tailings flow control
Fixed overflow weir for tailings flow control
Manually adjustable weir for
tailings flow control
Bottom spigots combined with effluent weir
overflow Particle
Size
Coarse, upto 8 mm
Coarse, upto 3-4
mm
Medium, upto 0.8 mm
Coarse, upto 8
mm
Coarse, upto 8 mm
Usage
Primary stages as cobber and
rougher in single or multistage stage units
Primary stages as
cobber and rougher in single
stage units
Installed as cleaner or finisher in multistage units
Installed after floatation
stage in single
stage units
Both primary and secondary stages in
single stage units
Operating Concurrent Counter
rotational Countercurrent Counter
rotational Concurrent
11
Figure 10 Types of WLIMS. A. Concurrent (CC) WLIMS. B. Counter Rotation (CR) WLIMS. C. Counter Current (CTC) WLIMS. D. Counter Rotation Froth WLIMS. E. Dense Media Recover (DM) WLIMS (Metso,
2015)
The operation and design of WLIMS separator could be explained by dividing the apparatus into sections as shown in Figure 10, E. First is the feed section where the purpose is to pass even feed (often attained by dilution) to the drum. Second is the pick-up zone where the all the forces (force balance) along with position in the feed flow determine whether a particle will attach to the magnetic floc or not. This is the zone where the feed interacts with the drums. Third section is the cleaning and dewatering section where cleaning of concentrate is done by moving the material along the drum surface towards concentrator discharge, the resulting rotational motion of the magnetic field agitates
12 the floc which enables concentrate cleaning. Also, in this section dewatering (removal of water) from the concentrate takes place by the action of gravity. The solids concentration of the concentrate is normally between 65 wt% and 75 wt% solids and the dewatering help in attaining solid concentration and also in cleansing of concentrate as gangue particle would be washed away. Fourth is the transport and cleaning zone which is only present in con-current type separators and have a similar function as cleaning and dewatering section except the dewatering function. The last section is scavenger section and here the pulp with low solid concentration is flowed close to drums in a direction opposite to rotation of the drum. The aim here is to recover magnetic material not directly brought to the concentrate in the pick-up zone, thus increasing recovery of magnetic material (Lawver & Hopstock, 1985; Stener, 2015).
5.4 Davis Tube
Davis tube is a laboratory instrument which is commonly used in the mineral processing industry to separate small samples of magnetic ores (usually magnetite) into strongly magnetic and weakly magnetic fractions. Davis tube was developed in 1921 and there has not been much change in its design. Davis tube is not well-designed to be used as a separator nor as an analytical instrument, but it is considered to be the industry standard equipment for assessing the separability of magnetite ore by low intensity magnetic separation (Murariu & Svoboda, 2003). The Figure 11 B, represents a Davis tube and it consists of an inclined tube (25 mm, diameter) through which few grams of sample (dry or slurry) is passed (Oberteuffer, 1974). The Figure 11 A, shows a real Davis tube experimental setup recently installed at MiMer lab at LTU.
Figure 11 A Davis Tube (Niiranen, 2017; Oberteuffer, 1974)
The tube is placed between the pole tips of an electromagnet. As the material is passed, strongly magnetic materials are held by the magnetic field and the weakly magnetic material is washed down the tube (Svoboda, 2004). Schulz, (1964) suggested that a magnetic induction of 0.4 T or greater between the magnet poles should be used. However, Steiner & Boehm, (2000) claimed that current practice is to conduct the Davis tube tests at a magnetic induction equal to that on the surface of the drum of the magnetic separator.
The information obtained from the Davis tube tests conducted according to the practice mentioned by Steiner & Boehm, (2000) may not be directly applicable to low-intensity drum magnetic separators (WLIMS) because of two reasons. Firstly, due to the fact that the efficiency of separation is not determined by the magnetic field strength rather by the product of the magnetic induction (B) and the field gradient (∇B), usually called the force index (FI) (Equation 3).
13
𝑭𝑰 = 𝑩 ∗ 𝜟𝑩
Equation 3 Force Index calculation
Secondly, for efficient recovery of magnetic materials the separator must be able to generaterequired force index at a sufficient distance from the surface of the drum. The standard operating gap or distance between drum and bottom of tank cannot be generalized as it would vary according to drum diameter from one design to another (Murariu & Svoboda, 2003).
Modelling of the distribution of the magnetic field and of the force index for a Davis tube electromagnet and for several types of drum magnetic separators was performed by Murariu &
Svoboda (2003). The purpose was to understand the applicability of the Davis tube tests to production-scale LIMS. The Figure 12 shows 3D distribution of the magnetic field in a typical Davis tube.
Figure 12 A 3D model of the Davis tube electromagnet (Murariu & Svoboda, 2003)
In the figure 12 it could be seen that the winding and pole arrangements are of conical shape. It is known from Svoboda (1987) that conical pole pieces/tips are better than cylindrical as they help in attaining higher efficiency and bring uniformity of magnetic flux. Additionally, better results in concentrating magnetic flux are attained if pole tips are built shorter and steeper. The results from the study by Murariu & Svoboda (2003) show that in the case of conventional ferrite drum separators, with the standard gap of 25mm between the drum and the tank, Davis tube tests should be conducted at a magnetic field strength of about 0.1 T. On the other hand, correct assessment of performance of a rare-earth drum can be obtained by operating a DT at about 0.3 T or higher, depending on the design of the magnetic system.
5.5 Leveäniem Ore
Once the theory behind the separation techniques used in this work is understood, it is necessary to understand the geology of the ore from which the samples have been taken. It also becomes important to look at any previous study done for the deposit.
14 5.5.1 Deposit Geology
LKAB (Luossavaara-Kiirunavaara AB) produces several iron ore products but the most important and significant product is pallets. As per LKAB website and published annual report, the company produced 26.9 Mt of iron ore products in 2016 and plans to expand the production by 5% till 2021 (LKAB, 2016). Currently LKAB operates two underground mines at Kiruna and Malmberget and has the open pit operation in Sappavarra one of which is Leveäniemi. The Figure 13 shows the location of the Leveäniemi mine.
Figure 13. The Leveäniemi Mine (Bremer, 2010)
Leveäniemi ore body is located at Latitude 67”38’N, Longitude 21”01’E in the province of northern Norrbotten, Sweden. After the investigation work in 1957-1963 the mine came into operation during 1964 till 1980’s as an open pit mine, but it was shut down thereafter due to economic reasons. LKAB recently reopened the mine in 2015 is presently extracting ore from also an open pit mine located approximately two kilometres southwest of the village of Svappavaara, which is located in Malmberget in the Gällivare area (Gustafsson, 2016; Niiranen, 2015).
The bedrock of North Norrbotten region of Sweden is superposed with 2.5-1-9 Ga Karelian and 1.9- 1.8 Ga Svecofennian rocks which are discordantly orientated. Felsic to mafic meta-volcanic and sedimentary rocks dominates the geology in the Leveäniemi area. The volcanic host rocks are trachyandesitic and have varying amounts of biotite, feldspar, amphiboles, quartz and plagioclase.
15 The texture of the rock varies between massive and foliated in correlation with the varying amount of biotite. The meta-volcanic rocks are overlaid by a 30 m thick layer of metaconglomerates, which are stratigraphically followed by a banded section of pyrite, pyrrhotite and chalcopyrite containing carbonated scapolites (Gustafsson, 2016).
Figure 14 Geological Map of Leveäniemi ore: 1. Magnetite ore, 2. Calcite-rich magnetite ore, 3. Hematite- altered ore 4. Ore breccia 5. Leptite 6. Sericite schist 7. Metabasite 8. Lina granite 9. Skarn (Bremer, 2010)
Leveäniemi lies in the leptite-synform of Svappavaara and occupies an approximately 1500 m long and 600 m wide area stretched in a north to south direction. The ore comprises of a series of small and large bodies which are often outstretched and irregular. These bodies form a trough-like structure dipping toward north with its legs striking north to south. The northern part of the ore is thin with a virtually vertical dip whereas the southern par dips 50˚ toward north/northeast. There exists several ore types with gradual transitions as shown in the Figure 15, these includes Magnetite ore, Calcite- rich magnetite ore, Hematite-altered ore, Ore breccia, Leptite, Sericite schist, Metabasite, Lina granite and Skarn. Apart from ore minerals there mostly exists apatite, calcite, tremolite-actinolite and biotite.
Total area of ore is 129 500 m2 including breccia corresponding to approximately 300 million tonnes of ore. Out of this magnetite ore (64 200 m2) is the main ore followed by hematite altered ore (25 500 m2) and later by calcite rich magnetite ore (4800 m2), the Fe content varies from 63.2% to 64.5% to 64% respectively. The depth of the ore is greatest in the central parts which go down to 500 m. Also, in the central part the major portion of the ore is situated, reaching up to 150 m in width (Bremer, 2010).
16 The is adopted from Bremer (2010); Lund (2013); Martinsson, Billström, Broman, Weihed, &
Wanhainen, (2016) and Niiranen (2015) and represents the characteristics of Leveäniemi ore body.
Table 3 Feature of Leveäniemi ore (Bremer, 2010; Lund, 2013; Martinsson et al., 2016; Niiranen, 2015).
Location
Ore Bodies with Grades (%Fe)
Ore type
Associated Rocks
Alteration minerals
Ore/gangue minerals
Element Association
Ore
Characteristics
Svappavaara
Magnetite (63.2%), Hematite- altered (64.5%), Calcite- rich magnetite (64%) and Ore Breccia (35.4%).
Apatite Iron Ore
Felsic-mafic volcanic rocks;
Intermediate volcanic rocks, arenitic sediments
Actinolite, Albite,Biotite, Sericite, Serpentine;
Epidote, Chlorite, Quartz.
Magnetite, Hematite (Apatite), Actinolite, Biotite, Calcite;
Hematite
(Chalcopyrite,Pyrite);
Chlorite (Quartz)
Iron
(Vanadium, Rare earth);
Iron
(Phosphorus, Copper, Gold, Thorium, Rare Earth)
Massive lens, Breccia infill;
5.5.2 Case study: Leveäniemi Ore, LKAB
A geometallurgical plan consists of a predictive model; it is noteworthy to mention a case study that explains how predictive models could be derived. The case study relevant to this thesis work is for the ore from Leveäniemi open pit mine done in 1962 by Fagerberg & Ornstein which is also mentioned in the doctoral work of Niiranen (2015). In this case study, a systematic macroscopic examination of drill cores was made in order to produce a rough preliminary forecast for the product outcome of beneficiation of the Leveäniemi iron ore deposit. The idea in this study was to create a 3D model for ore recovery for the process followed at the beneficiation plant in Svappavaara as a part of the feasibility study on the Leveäniemi deposit.
Each drill core was examined for mineralogy and texture properties and was initially prepared by an inventory protocol that included chemical assays, identification of data and section boundaries for the proposed mining pallets. Then a probable product outcome for a concentrator flow sheet was estimated and recorded keeping in mind the possible variations in ore texture and/or the relationship between different ore qualities in the horizontal or vertical direction as this could lead to the changing of the product outcome from year to year. Now, a mining block (10 x 10 x 10 m3) was placed around each drill hole per mining level which would have the mineral processing properties same as the respective core of the drill hole. Latter, the probable product outcome could have been easily calculated through summation of benches and profiles, block by block, and the variation in different parts of the ore body could easily be examined. From this model, it would have conceivably been possible to estimate the average recovery and to study its variation in different parts of the deposit.
But to build a predictive model for processing parameters clearly more objective and analytical data is required (Fagerberg & Ornstein, 1962; Niiranen, 2015). The Figure 15 represents a schematic picture of a mining block model.
17
Figure 15 Mining block containing mineral processing parameters as that of the drill core for the Leveäniemi open pit (Fagerberg & Ornstein, 1962; Niiranen, 2015)
5.6 Element to mineral conversion (EMC)
Elemental assay to mineral conversions is primarily converting elemental information of the sample to minerals and EMC relies on the fact that the total amount of each element in a material is equal to the sum of the amounts of element in each mineral (Gustafsson, 2016). In HSC 7.1 EMC is governed by the Equation 4.
𝐴 ∗ 𝑥 = 𝑏
Equation 4 EMC for modal mineralogy calculation
In Equation 4 “A” is the matrix which defines the weight faction of the element in the minerals and is a known identity. Matrix “x” is unknown and represents the weight fractions of the minerals in the sample and matrix “b” is the known weight fraction of elements in the sample (Lund, 2013).
The Equation 4 could be solved for matrix “x” by multiplying the inverse of matrix “A” with matrix
“b”. The values of matrix “x” is over or under determined because it is common that number of appearing minerals and analysed elements are not equal. Thus such a value of “x” needs to be attained such that the residual (R) is minimum. Matrix “R” is defined in the Equation 5.
𝑅 = [𝑏 − 𝐴. 𝑥]
Equation 5 EMC Residual calculation
Matrix “R” could be minimised by a combination of matrix solving techniques like Gaussian elimination, LU Decomposition and Singular Value Decomposition and multiple regression algorithms (Gustafsson, 2016; Whiten, 2008).
5.7 Henry Reinhardt chart
Henry Reinhardt charts or washability curves have been used in the coal industry for analyzing the ash content and measuring coal quality. Henry Reinhardt charts is basically a graphical representation of mineralogical or chemical information and separability of physical parameters. The sink-float analysis is a coal washing method where coal containing ash is washed in a liquid of density between
18 the density of clean coal and ash. In such a scenario the clean coal would sink and the ash would float.
Thus sink-float test estimates the coals amenability towards gravity concentration methods.
Washability curves are made from the sink-float data and could be used to obtain and interpret valuable information about the clean coal or coal quality that could be obtained from a given coal under ideal conditions (Govindarajan & Rao, 1994; Salama, 1998).
Conventionally, Henry Reinhardt charts are not commonly used in mineral processing but under the scope of this study washability curves would be built for DT experiment as it was found through literature that DT correlates closely with WLIMS (Chapter 3). The Henry-Reinhardt chart (washability curves) would be used to study the grade and content of different gangue material and magnetic material retaining and passing through the DT under different magnetic strengths. The Henry-Reinhardt chart also provides information on the best possible separation result and on intergrowth characteristics (liberation) at a given physical property which is different current intensities for this study (Niiranen, 2015).
The Figure 16 shows a simplified version of Henry Reinhardt charts with two types of basic intergrowth curves (curve A and B). Curve A represent good separation with the selected property and curve B represents poor separation with the selected property either because of low degree of liberation or no amenability to the separation property (Niiranen, 2017).
Figure 16. Simplified Henry Reinhardt charts (Niiranen, 2017)
For this study the property of separation with DT experiment was the magnetization of the particles which would be attained at different current intensities (0.1, 0.2 and 0.5). Thus by varying degree of magnetization through applying of external current can be used to split sets of particles into classes of given boundaries of magnetization (Niiranen, 2015; Steiner & Boehm, 2000a, 2000b).
5.8 Principle component analysis (PCA)
Principal component analysis (PCA) is a multivariate technique that analyzes a dataset in which the observations are described by several inter-correlated quantitative dependent variables. The goal of PCA is to extract the important information from the dataset to represent it as a set of new orthogonal variables called principal components. Additionally, PCA display the pattern of similarity of the observations and of the variables as points in maps (Williams, 2010). The Figure 17 is modified from the PCA explanation as describe in Smith (2002) and the Figure 17 explains PCA in context to this work.
19
Figure 17 Principle component analysis (PCA) (Modified from: Smith, 2002)
The Figure 17 A illustrate the dataset which has size wise information about 13 sample used in this study in terms of feed grades for different elements/minerals, DT grade and recovery for every element/mineral and WLIMS grade and recovery for every element/mineral. Since the dataset comprises so much information it becomes multi (N) dimensional. The Figure 17 B briefly describes the spread of the dataset in n-dimensions. PCA finds principle components orthogonal to each other that describe maximum variability in the dataset as shown in Figure 17 C. The Figure 17 D shows the final output of PCA which reduces the dimensions of the dataset without any loss of information and groups the similarly behaving samples together in a map (Smith, 2002).
5.9 Modelling
Modelling could be defined as a cognitive activity of representing a real-world object or phenomenon as a set of mathematical equations. Modelling can be done in various forms like graphs, computer programs, mathematical formula and etc. Particularly when mathematical equations and formulas are involved then the developed models are known as mathematical models (Dabbaghian, 2010). The Figure 18 is modified from Carson & Cobelli (2001) and depicts the principle of mathematical modelling which are phrased as questions about the intentions and purposes of mathematical modeling.
20
Figure 18 Methodology for mathematical modelling (Modified from: Carson & Cobelli, 2001)
In this thesis, work was done till model prediction and validation of the predicted model with arbitrary or new data was not done and model validation becomes the future scope of this work.
There are different ways to models a dataset but for this work multiple linear regressions was used and thus the theory of multiple linear regression is discussed in details.
5.9.1 Multiple linear regressions
Multiple linear regression is a type of regression technique in which the values of a dependent variable, ŷ is predicted using a set of explanatory variables, x1, x2, x3….xn. Thus the predicted value for ŷ can be given by Equation 6.
ŷ = 𝛽0+ 𝛽1𝑥1+ 𝛽2𝑥2+ ⋯ 𝛽𝑛𝑥𝑛
Equation 6 Multiple linear regression
Where, the explanatory variables vary from x1 to xn. β0 is a constant term and β1 to βn are regression coefficients for each of the explanatory variables (x1, x2, x3….xn).
In this thesis work, for example the dependent variable would be Fe-grade in WLIMS concentrate which would be a function of multiple explanatory variables like Fe-grade in feed, SiO2-grade in feed, Fe-grade in DT, etc.
The coefficient of regression β1 measures the effect of explanatory variable x1 keeping the other explanatory variables fixed and similar is applicable to other regression coefficients (Uriel, 2013).
In order to apply multiple linear regression to any dataset there are some assumptions that need to be considered and satisfied. These assumptions are taken from Howell (1992) and are listed in context to this thesis work with an explanation on how these assumptions were satisfied for this work.
