DOCTORA L T H E S I S

Development of a geometallurgical framework for iron ores - A mineralogical approach to

particle-based modeling

Mehdi Amiri Parian

Mehdi A

miri Parian D

evelopment of a geom

etallurgical framew

ork for iron ores - A m

ineralogical approach to particle-based modeling

Department of Civil, Environmental and Natural Resources EngineeringDivision of Minerals and Metallurgical Engineering

ISSN 1402-1544 ISBN 978-91-7583-860-1 (print)ISBN 978-91-7583-861-8 (pdf)

Luleå University of Technology 2017

Mineral Processing

Development of a geometallurgical framework for iron ores - A mineralogical approach to particle-based

modeling

Mehdi Amiri Parian

Doctoral Thesis in Mineral Processing

Division of Minerals and Metallurgical Engineering

Luleå University of Technology

SE-971 87 LULEÅ

Sweden

May 2017

Printed by Luleå University of Technology, Graphic Production 2017

ISSN 1402-1544 ISBN 978-91-7583-860-1 (print)ISBN 978-91-7583-861-8 (pdf)

Luleå 2017

www.ltu.se

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Abstract

The demands for efficient utilization of ore bodies and proper risk management in the mining industry have resulted in a new cross-disciplinary subject called geometallurgy. Geometallurgy connects geological, mineral processing and subsequent downstream processing information together to provide a comprehensive model to be used in production planning and management. A geometallurgical program is an industrial application of geometallurgy. Various approaches that are employed in geometallurgical programs include the traditional way, which uses chemical elements, the proxy method, which applies small-scale tests, and the mineralogical approach using mineralogy or the combination of those. The mineralogical approach provides the most comprehensive and versatile way to treat geometallurgical data. Therefore, it was selected as a basis for this study.

For the mineralogical approach, quantitative mineralogical information is needed for both the deposit and the process. The geological model must describe the minerals present, give their chemical composition, report their mass proportions (modal composition) in the ore body and describe the ore texture. The process model must be capable of using mineralogical information provided by the geological model to forecast the metallurgical performance of different geological volumes and periods. A literature survey showed that areas, where more development is needed for using the mineralogical approach, are: 1) quick and inexpensive techniques for reliable modal analysis of the ore samples; 2) ore textural characterization to forecast the liberation distribution of the ore when crushed and ground; 3) unit operation models based on particle properties (at mineral liberation level) and 4) a system capable of handling all this information and transferring it to production model. This study focuses on developing tools in these areas.

A number of methods for obtaining mineral grades were evaluated with a focus on geometallurgical applicability, precision, and trueness. A new technique developed called combined method uses both quantitative X-ray powder diffraction with Rietveld refinement and the Element-to-Mineral Conversion method. The method not only delivers the required turnover for geometallurgy but also overcomes the shortcomings if X-ray powder diffraction or Element-to-Mineral Conversion were used alone.

Characterization of ore texture before and after breakage provides valuable insights about the fracture pattern in comminution, the population of particles for specific ore texture and their relation to parent ore texture. In the context of the mineralogical approach to geometallurgy, predicting the particle population from ore texture is a critical step to establish an interface between geology and mineral processing. A new method called Association Indicator Matrix developed to assess breakage pattern of ore texture and analyze mineral association. The results of ore texture and particle analysis were used to generate particle population from ore texture by applying particle size distribution and breakage frequencies. The outcome matches well with experimental data specifically for magnetite ore texture.

In geometallurgy, process models can be classified based on at which level the ore is defined, i.e. the feed stream to the processing plant and each unit operation, and what information subsequent streams carry. The most comprehensive level of mineral processing models is the particle-based one which includes practically all necessary information on streams for modeling unit operations. Within this study, a particle-based unit operation model was built for wet low-intensity magnetic separation,

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and existing size classification and grinding models were evaluated to be used at particle level. A property-based model of magnetic beneficiation plant was created based on one of the LKAB operating plants at mineral and particle level, and the results were compared. Two different feeds to the plant were used. The results revealed that at the particle level, the process model is more sensitive to changes in feed property than any other levels. Particle level is more capable for process optimization for different geometallurgical domains.

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Preface

The thesis presented here describes building and developing the mineralogical path to be used for geometallurgical modeling. The research based at Division of Minerals and Metallurgical Engineering, Luleå University of Technology and was carried out during 2012-2017. The work was funded by the Hjalmar Lundbohm Research Centre (HLRC).

I appreciate all helps from LKAB personal specifically Kari Niiranen, Andreas Fredriksson, Therese Lindberg, Mikko Kauppinen, and Axel Ståhlström. I am grateful to sample preparation crew at LKAB Kiruna namely Catrin Huuva, Ulrik Kalla, Emmeli Falk, Tomas Salmi and Peter Alanärä-Lassi (summer worker), for their positive attitude and their accurate work.

I kindly thank my colleagues Abdul Mwanga, Cecilia Lund, Jan Stener, Anders Sand, Bertil Pålsson, Pierre-Henri Koch, Tommy Karlkvist, and Lindsay Ohlin for the fruitful discussions.

Finally, I would like to thank my wife, daughter and my parents for their support, encouragement, and patience.

Mehdi Amiri Parian

Luleå, April 2017

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List of papers and tools

The thesis is based on the following papers:

I) Mehdi Parian, Pertti Lamberg, Robert Möckel, & Jan Rosenkranz, Analysis of mineral grades for geometallurgy: Combined element-to-mineral conversion and quantitative X-ray diffraction, Minerals Engineering, Volume 82, 15 October 2015, Pages 25-35, ISSN 0892-6875.

II) Mehdi Parian, Pertti Lamberg, & Jan Rosenkranz, Developing a particle-based process model for unit operations of mineral processing – WLIMS, International Journal of Mineral Processing, Volume 154, 10 September 2016, Pages 53-65, ISSN 0301-7516.

III) Mehdi Parian, Abdul Mwanga, Pertti Lamberg, & Jan Rosenkranz, Ore texture breakage characterization and fragmentation into multiphase particles. Manuscript submitted to Advanced Powder Technology Journal.

IV) Mehdi Parian, Pertti Lamberg, & Jan Rosenkranz, Process simulation in mineralogy-based geometallurgy of iron ores. Manuscript submitted to Minerals Engineering Journal.

The list of papers not included in this thesis:

1. Mwanga, A., Parian, M., Lamberg, P., & Rosenkranz, J., Comminution modeling using mineralogical properties of iron ores. Manuscript submitted to Minerals Engineering Journal.

2. Parian, M. &Lamberg, P., 2016, Reconciling modal mineralogy and chemical compositions of a sample, In: Bulletin of The Geological Society of Finland: Special Volume, 181- p.

3. Lamberg, P., Parian, M., & Lund, C., 2015, Using Mineral rather than Elemental Grades in Mineral Resource Estimate: Motivation and Techniques, In: Proceedings of the 13th SGA Biennial Meeting on Mineral Resources in a Sustainable World – Nancy, France.

4. Parian, M., Lamberg, P., & Rosenkranz, J., 2014, Using modal composition instead of elemental grades in mineral resource estimate – high quality modal analysis by combining X-ray powder diffraction and X-ray fluorescence, In: Preprints of Process Mineralogy Conference 2014 – Cape Town, South Africa.

5. Parian, M. & Lamberg, P., 2013, Combining chemical analysis (XRF) and quantitative X-ray powder diffraction (Rietveld) in modal analysis of iron ores for geometallurgical purposes in Northern Sweden, in Proceedings of the 12th SGA Biennial Meeting – Uppsala, Sweden.

6. Lamberg, P., Parian M., Mwanga A., & Rosenkranz, J., 2013, Mineralogical mass balancing of industrial circuits by combining XRF and XRD analyses, In: Proceedings of Minerals Engineering Conference – Luleå, Sweden.

7. Lamberg, P., Rosenkranz, J., Wanhainen, C., Lund, C., Minz, F., Mwanga, A., & Parian, M., 2013, Building a Geometallurgical Model in Iron Ores using a Mineralogical Approach with Liberation Data, In: Proceedings of the second AusIMM International Geometallurgy Conference – Brisbane, Australia.

Tools developed:

A. MATLAB code: Element-to-Mineral Conversion and combined method for large datasets; used in paper I.

B. Stand-alone software: Grain Classifier; IncaMineral classification software to post-process data of IncaMineral system (C++); used in paper I and paper II.

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C. MATLAB code: Image analysis for ore texture and polished sections - liberation and association analysis (MATLAB); used in paper III.

D. MATLAB code: Predicting particle population from ore texture by defining particle size distribution and breakage frequencies; used in paper III and paper IV.

E. MATLAB code & Stand-alone software: Export particle population in liberation form (From IncaMineral database or particle generation) to be used in HSC Chemistry software; used in paper II, III and IV.

My role in the papers included in the thesis:

I) The first author performed the sampling, sample preparation, modal quantification by different techniques as well as the development of the combined method to its final form. The paper was written by the first author and the other authors acted as supervisors and corrected the manuscript at different stages.

II) The sampling during the plant survey was done by LKAB personnel who also assisted in sample preparation. The process mineralogical analysis including preparing epoxy samples, automated mineralogy analysis, mass balancing and model development was conducted by the first author. The paper was written by the first author while the other authors acted as supervisors and corrected the manuscript at different stages.

III) The concept of developing the “Association Indicator Matrix” and forecasting particle population including fine sieving, epoxy sample preparations, optical microscopy and Auto-SEM analysis were done solely by the first author. Crushing and sieving of the ore texture samples was done by Abdul Mwanga. The paper was written by the first author and the other authors acted as supervisors and corrected the manuscript at different stages.

IV) Flowsheet drawing, set up of process models, calibrating model parameters as well as the simulations at different levels were done solely by the first author. The paper was written by the first author while the other authors acted as supervisors and corrected the manuscript at different stages.

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Table of Contents

Abstract ................................................................................................................................................... iii

Preface ...................................................................................................................................................... v

List of papers and tools ........................................................................................................................... vii

Table of Contents ..................................................................................................................................... ix

Chapter 1 - Introduction .......................................................................................................................... 1

Geometallurgical program and its approaches ........................................................................ 1 1.1

Scope of the present work ....................................................................................................... 2 1.2

Thesis Overview ....................................................................................................................... 3 1.3

Chapter 2 - Literature Survey ................................................................................................................... 5

Introduction ............................................................................................................................. 5 2.1

Geometallurgy of iron ores ...................................................................................................... 6 2.2

Ore characterization in geometallurgy .................................................................................... 8 2.3

2.3.1 Methods for obtaining mineralogical information ........................................................... 9

2.3.2 Ore texture characterization .......................................................................................... 12

2.3.3 Physical and metallurgical properties of ore .................................................................. 13

Process models for simulation of magnetite ore beneficiation plants ................................... 13 2.4

2.4.1 Magnetic separation models ......................................................................................... 16

2.4.2 Size classification models ............................................................................................... 18

2.4.3 Comminution models .................................................................................................... 22

2.4.4 Flotation models ............................................................................................................ 24

2.4.5 Summary of the process unit models for particle-based simulation ............................. 25

Chapter 3 - Experimental and methodology .......................................................................................... 27

Sample sets and sample preparation ..................................................................................... 27 3.1

3.1.1 Sample set for modal analysis study .............................................................................. 27

3.1.2 Sample set for ore textural study ................................................................................... 28

3.1.3 Sample set for model development and simulation framework .................................... 29

Analytical methods and approaches ...................................................................................... 30 3.2

3.2.1 Modal analysis ............................................................................................................... 30

3.2.2 Ore textural analysis ...................................................................................................... 35

3.2.3 Model development and simulation framework ........................................................... 38

Chapter 4 - Developing a quick and inexpensive technique for reliable modal analysis ........................ 41

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Introduction ........................................................................................................................... 41 4.1

Analysis of mineral grades in the iron ore samples ................................................................ 41 4.2

Developing a grade-based error model ................................................................................. 43 4.3

4.3.1 Precision of the analyses ................................................................................................ 43

4.3.2 Closeness of the analyses .............................................................................................. 44

Discussion on results of combined method and application of grade-based error model .... 46 4.4

Chapter 5 - Ore texture characterization and relation to mineral liberation ......................................... 49

Introduction ........................................................................................................................... 49 5.1

Association Indicator for ore texture ..................................................................................... 49 5.2

Association Indicator for particles ......................................................................................... 50 5.3

Ore texture and breakage characterization ........................................................................... 51 5.4

5.4.1 Particle size distribution after breakage ........................................................................ 51

5.4.2 Distribution of particle types after breakage ................................................................. 52

5.4.3 Association Indicator distribution for locked particles ................................................... 53

Forecasting particle population from ore texture .................................................................. 56 5.5

5.5.1 Assigning breakage frequency ....................................................................................... 57

5.5.2 Adjusting liberation to match modal mineralogy ........................................................... 58

5.5.3 Comparing liberation of iron oxide minerals ................................................................. 59

Discussion on ore texture characterization ........................................................................... 60 5.6

Chapter 6 - Developing a particle-based process model for unit operations of mineral processing ..... 63

Introduction ........................................................................................................................... 63 6.1

Quality of data and measurements ....................................................................................... 63 6.2

Mass balancing and data reconciliation ................................................................................. 64 6.3

Developing a process model for WLIMS ................................................................................ 66 6.4

6.4.1 Physical explanations for observations .......................................................................... 67

6.4.2 Semi-empirical model of WLIMS .................................................................................... 70

Verification of the model ....................................................................................................... 71 6.5

6.5.1 Verification based on bulk and sized level ..................................................................... 71

6.5.2 Verification based on mineral liberation level ............................................................... 72

Discussion on developing WLIMS process model .................................................................. 73 6.6

6.6.1 The effect of mineral nature, grain size, and shape ....................................................... 74

6.6.2 The effect of feed quality ............................................................................................... 74

6.6.3 The effect of stereological bias ...................................................................................... 75

Chapter 7 - Demonstrating the process plant simulation based on particles ........................................ 77

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Plant circuit ............................................................................................................................ 77 7.1

Process units .......................................................................................................................... 77 7.2

Plant feeds ............................................................................................................................. 78 7.3

Simulation for Ore A .............................................................................................................. 79 7.4

Simulation for Ore B .............................................................................................................. 79 7.5

Discussion on results of simulations ...................................................................................... 80 7.6

Chapter 8 - Conclusions and recommendations .................................................................................... 81

References ............................................................................................................................................. 85

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Chapter 1 - Introduction

Geometallurgical program and its approaches 1.1

Variation in feed quality of a plant has been a challenge for mineral processing operations. A prior understanding of the characteristics of the feed over the lifespan of the mining operation is the solution to successful circuit design, optimization, and troubleshooting. Also, demands for effective utilization of ore bodies and proper risk management in the mining industry have engendered an interest in geometallurgy. Several definitions have been proposed in the literature for geometallurgy (David, 2013; Dunham and Vann, 2007; Kittler et al., 2011; Lamberg, 2011). In this study, the following definition is used:

Geometallurgy is a cross-disciplinary subject that connects geological, mineral processing and subsequent downstream processing information together to provide a comprehensive and quantitative 3D model on the variability of the ore to be used for an efficient production planning and management.

Several key points that a geometallurgy study must possess are a cross-disciplinary approach, a focus on spatial variations in the ore body, a model to connect deposit information to the process and a final aim to be used in practice. A critical issue is to establish quantitative interfaces between the disciplines (i.e. geology and mineral processing) in a way that data content and structures are matching and ore characterization includes proper parameters which can be transferred along the process chain.

A geometallurgical program is an industrial application of geometallurgy. It provides a way to map the variation within the ore body, to handle the data and to forecast metallurgical performance at spatial and time level. The program also comprises a process to handle complex geological information and transfers them into geometallurgical domains to be used in process optimization, production planning, and business decision making. The program is an instrument which should evolve and change during the lifespan of a mine to ensure that geometallurgical domains address the variation properly in metallurgical performance.

Various approaches exist to establish a geometallurgical program (Kittler et al., 2011; Lishchuk, 2016). These include the conventional way, the proxy method, the mineralogical approach or a combination of these. The conventional approach heavily focuses on chemical assays and often neglects quantitative mineralogy. In the proxy approach, the main attempt is on finding correlations between the chemical composition of the ore and metallurgical performance in small-scale laboratory tests. Thus, tests provide a proxy to important ore properties relevant to processing. The most comprehensive of these is the mineralogical approach where all components of the geometallurgical model are based on quantitative mineralogical information or mineralogical attributes. This means that the geological model can provide details on the mineralogy of an ore deposit at spatial level and mineral processing model can deal with ore textural and mineralogical information received from the geological model. Generally speaking, the mineralogical approach is known to be the most thorough option (e.g. Lamberg 2011; Bonnici et al. 2008). This is natural since minerals define the value of the deposit, the method of extraction, economic risk valuation, and the concentration method (Hoal et al., 2013). However, many geometallurgical programs are not benefiting from the full potential of mineralogy due to the high cost of quantitative mineralogy and the large number of samples required.

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In principal, the process and the product requirements define which characteristics of an ore body are essential. Therefore, critical properties to be obtained for assigning geometallurgical domains can be selected first based on the processing circuit (David, 2007). For example, grindability and crusher work index are valid parameters for comminution circuits and mineral recovery and impurity levels in case of concentration circuit. Usually, the next step is to find a relation between geological dataset (chemical composition data) and results from metallurgical testing. This type of approach is towards a proxy approach to geometallurgy. The difficulty rises when the variation in the ore body is high or unknown, meaning that a significant number of samples need to be collected for the variability (metallurgical) tests in order to map the ore. In this case, the solution is often to carry out the tests on blends or the selected number of samples but in both cases the risk of missing information on variability increases.

A mineralogy-based geometallurgical model employs quantitative mineralogical information, both on the deposit and in the process. The geological model must describe the minerals present, give their chemical composition, report their mass proportions (modal composition) in the ore body and describe the ore texture. The process model must be capable of using mineralogical information provided by the geological model to forecast the metallurgical performance of different geological volumes, such as samples, ore blocks, geometallurgical domains or blends prepared for the plant feed for various periods from hourly and daily scale to weekly, monthly and annual production.

In a mineralogy-based approach to geometallurgy, the simulation environment must be capable of handling both size reduction and concentration circuit at the particle level. This means that comminution circuit model needs to provide particle size distribution, throughput and even more importantly, liberation information (i.e. particles). On the other hand, the concentration circuit model must operate at the same level (i.e. particle level), deliver liberation information for both tailing, and concentrate streams. This requires particle-based process models which have not been sufficiently developed.

Scope of the present work 1.2

This work focuses on building and developing a mineralogical path to be used within geometallurgical modeling. The mineralogical approach provides the most comprehensive and versatile way to treat geometallurgical data (Hoal et al., 2013). Therefore, it was selected as the basis for this study.

Lund (2013) studied the methods for mineralogical characterization of LKAB’s Malmberget iron ore to be used in geometallurgical modeling. According to this work, the areas where the mineralogical approach needs further development are:

1) Quick and inexpensive techniques for reliable modal analysis (i.e. analysis for mineral grades) of the ore.

2) Ore textural characterization for forecasting the liberation distribution of the ore when crushed and ground.

3) Unit operation models based on particle properties (at mineral liberation level). 4) A system capable of handling all this information and transferring it into a production model

(Figure 1).

These issues have been raised in several other studies (Dominy and Connor, 2016; Dunham and Vann, 2007; Walters and Kojovic, 2006). This study focuses on addressing the above areas with a particular

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reference to iron ore. Therefore, the objectives are defined as follows and some areas are knowingly left out of the scope:

• To develop a reliable modal analysis method for geometallurgy of iron ore. o The method should be fast, inexpensive, based on available techniques and be

applicable in mines. o Develop a generic method to estimate the error in modal analysis.

• To develop a procedure for forecasting particle liberation from ore texture. o The method should be drawn up for meso-scale of ore texture. o The breakage behavior of ore texture should be characterized.

• To develop a particle-based model for magnetic separation. o The method should be based on particle properties as received in mineral liberation

analysis. o The model should be verified with experimental data.

• To develop a geometallurgical simulation system to handle mineralogical data and predict the product based on that.

Geometallurgy is a wide research area and a study like this cannot cover all the parts. The following relevant topics were left outside of the scope of this study:

• Drill core scanning and related tools (macro-scale textural characterization and classification). • Block modeling and geostatistics of geometallurgy.

Geometallurgical program

Ore

1) Reliable modal analysis2) Ore texture quantification

Process Simulation Framework

3) Particle-based unit models and process model

4) Interface between ore and process

Figure 1. Schematic workflow for establishing a mineralogical path in a geometallurgical program.

Thesis Overview 1.3

The main areas of the study i.e. modal analysis, ore textural study, and process models are separate problems. Therefore, they are described and solved separately in the thesis. A brief description of chapters is as follows:

In Chapter 2, earlier works within the scope of the present study are reviewed. The literature survey is focused on ore characterization and process models that are of interest to the geometallurgy of iron ore. Ore characterization methods, with a focus on applicability to iron ore, are reviewed, and the drawbacks of each method are pointed out. Moreover, process models for magnetic separation, hydrocyclone classification, flotation and comminution are briefly reviewed.

In Chapter 3, selected sample sets for experiments and the methodology used to approach research the subject are described in detail. The subsequent chapters are dedicated to the areas that were previously mentioned in the scope of present work. At the end of each of these chapters, the outcomes are discussed.

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In Chapter 4, a new modal mineralogy method comprising a combination of Element-to-Mineral Conversion and X-ray diffraction is explained. Subsequently, a general error model applicable to modal analysis methods is introduced, and results of the various modal analysis methods are compared and discussed.

Chapter 5 describes ore textural studies on meso-scale and results that are obtained from investigating progeny particles of ore textures in size fractions. This includes changes in mineral associations, liberation, and exposed surface of minerals in particles and implication of any type of breakage.

Chapter 6 describes the approach to constructing a particle-based model by using plant survey liberation data around the primary magnetic separation stage. This kind of model can utilize liberation data and be coupled to any process model. This step is necessary towards establishing a simulation framework based on particle properties.

Chapter 7 demonstrates the application of the particle-based model in simulation and upgrading of existing unit models to work with particles. Also, possible extensions of a simulation framework for utilizing ore texture attributes and classifications are demonstrated.

Chapter 8 summarizes the result of this study and lists possible directions for future research.

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Chapter 2 - Literature Survey

Introduction 2.1

The basic ideas behind geometallurgy are simple and have been known for many years. However, geometallurgical approaches and applications have been improved by recent analytical and measurement innovations. Also, lessons have been learned from failures, and many researchers have acknowledged the multidisciplinary approach. The main aspects from several geometallurgical studies that researchers found important and critical are given in Table 1.

Table 1. Critical areas of geometallurgy and main aspects.

Critical area Main aspects References Sample selection and sampling

• Sample representativity. • Data quality, error analysis, and model

validation. • Small-scale tests. • Spatial variability in the deposit.

Ashley & Callow (2000); Liebezeit et al. (2011); Dominy et al. (2011); Dominy et al. (2016); Kittler et al. (2011)

New tools and shortcut tests for geometallurgy

• Application of a new or modified measurement technique.

• Small-scale and low-cost tests. • Ore textural classification and modeling. • Mineral quantification and mapping. • Multivariate analysis and modeling. • Geostatistical modeling of processing attributes.

Walters (2009); Hallewell (2009); Vatandoost et al. (2009); Keeney & Walters (2011)

Holistic and multidisciplinary approach

• Sustainability. • Geometallurgy application during the whole

cycle of a project. • Geometallurgical attributes and their additivity. • The proxy approach towards geometallurgy.

Dunham et al. (2011); Beniscelli (2011); Newton & Graham (2011); Dominy & Connor (2016); Dunham & Vann (2007)

Geometallurgy for circuit design, optimization, and simulation

• Shortcut tests for floatability and grindability. • Geostatistical distribution metallurgical

parameters. • Simulation to predict metallurgical performance

block by block. • Geometallurgy application in flotation circuit

design and optimization.

Bulled & McInnes (2005)

Systematical and traditional geometallurgical modeling

• Geostatistical distribution of assays. • Predictive equations based on assays. • Traditional approach toward geometallurgy.

Knight et al. (2011); Niiranen (2015); Liebezeit et al. (2016)

GeoMet model based on ore texture, particles, and simulation

• A geological model capable of delivering quantitative mineralogical data.

• Simulation of process at particle level.

Lamberg et al. (2013); Lund (2013)

Geometallurgical issues differ from one deposit to another. Therefore, no single template can be applied to all projects. There is no merit to applying the most comprehensive and expensive approach

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if a simpler and a more cost-effective approach can address the geometallurgical issues. However, objectives in geometallurgy are more or less the same regardless of commodity or ore type. The main purposes of geometallurgy are to quantify the ore regarding spatial variability, behavior in processing and economic value. This includes a creation of a base terminology and ore descriptions so that everyone in the project in different disciples can understand the terms (Ashley and Callow, 2000).

Geometallurgy of iron ores 2.2

Magnetite, hematite, and goethite are the most abundant and economic iron ore minerals. The cut-off grade for iron ore is around 25-30 % Fe and the iron ore products commonly have 55-65 % Fe. The products are usually in the form of lump, concentrate, pelletized or sintered fines. Marketable iron ore must satisfy required specifications of products (Table 2).

Table 2. Some physical and chemical composition requirements for Iron ore products.

Iron ore product Typical physical properties of concern* Typical chemical composition requirement for blast furnace *

Lump, Pellet, Sinter

Particle size, moisture level, tumble index (TI), abrasion index (AI), decrepitation index (DI), reduction degradation index (RDI), and reducibility index (RI)*

Fe > 63% P < 0.1% S < 0.2% Al2O3 < 3.5% SiO2 < 3%

Ti < 1% Mn < 2% Cr < 1% Ni < 0.5% As, Cu, Zn, Pb < 0.1%

* Description of indices and their application can be found in Clout & Manuel (2015) and LKAB (2014).

The iron ore products are further processed in a blast furnace. Only around 10% of the world’s iron ore is treated by direct reduction technology (Lu, 2015). The iron ore product used for direct reduction iron (DRI) process must have at least 67% Fe. Product quality in the case of iron ore normally means restrictions for certain impurities, the most serious being phosphorous, sulfur, silica and aluminum. Respectively, these impurities originate from apatite, sulfide minerals, and silicate minerals (such as quartz, feldspars, pyroxenes, amphiboles, and micas). Details on deleterious effects of the gangue and trace elements on downstream processes can be found e.g. in Clout & Manuel (2015). Also, certain physical properties of the product for transportation and downstream processes are necessary.

Iron ore beneficiation plants are high throughput operations, meaning that economy is often dictated by the capability of processing large production volumes at low costs per ton of final product. The quality of the product, the iron concentrate, varies widely from operation to another from the relatively low grade of direct shipping ores (>55 % Fe) to very high purity of iron pellets and other special products (>67 % Fe). The former ones are often hematite ores whereas the latter are mostly magnetite ore. Iron ore mines and their processing plants traditionally use chemical analysis in resource and reserve estimates, and in grade and product quality control.

As all iron ores are heterogeneous, maintaining reasonable recovery as well as having low impurity contents in the final product requires good knowledge of the ore body and a systematic way to manage the natural variability of the resource in production. This can be reached through employing a geometallurgical program. The most important parameters that are considered for a geometallurgical program that affect the production in iron ore operations are throughput, product quality, and recovery. Examples of such studies are briefly described below, and summaries are listed in Table 3.

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A geometallurgical model was built for the Hannukainen iron ore deposit to predict the concentrate quality and iron recovery (SRK Consulting (UK), 2014). An iron recovery function was established based on Davis Tube Recovery (DTR) tests done on geometallurgical samples and correlations drawn between the metallurgical response and the feed assay. The DTR is a conventional laboratory test for magnetite ore deposits. Many similar applications of DTR test have been reported in the literature (Farrell et al., 2011; Gerber et al., 2015; Leevers et al., 2005).

An empirical method has been developed to predict the SiO2 grade of the concentrate from Luossavaara-Kiirunavaara AB’s (LKAB) concentrator plants for the Kiruna iron ore deposit (Niiranen, 2006; Niiranen and Böhm, 2013, 2012; Niiranen and Fredriksson, 2012). The method requires lab-scale comminution and Davis Tube tests. Particle size distribution, energy consumption, chemical analysis of the samples tested are gathered in a database and used for determining correlations among desired parameters. The results are then used for predicting the silica content of the iron ore concentrates.

Geometallurgical studies on Nkout (Cameroon) and Putu (Liberia) iron ore deposits were conducted using QEMSCAN analysis and metallurgical tests (Anderson, 2014). A linear regression model was used to correlate iron head grade to iron oxide liberation, iron oxide content, and grade of some gangue minerals. Metallurgical tests included DTR test followed by wet high-intensity magnetic separation tests for the tailings from the DTR test. There is no indication that the information was used for developing a geometallurgical model.

A geometallurgical model has been applied to Carol Lake iron ore deposit to predict the variation in the milling plant energy consumption and throughput. This was achieved through routinely drill core sampling and hardness test conducting. The CEET (Comminution Economic Evaluation Tool, Kosick et al. (2001)) model was used to forecast mill energy consumption based on the hardness of each block. The results were reconciled with the latest mined ores and used to update the CEET model. A better understanding of the ore body, improved mine planning, consistency of ore hardness delivered to the plant, reduced downtime losses, and improved seasonal operation were considered as the remarks of the project (Bulled et al., 2009).

BHP Billiton West Australian Iron Ore conducts a geometallurgy program for its iron ore deposits in the Pilbara (Wright et al., 2013). Within its geometallurgical program a systematic approach is used as follows:

1. The drill holes are planned to capture variability in the deposits. 2. Various physical properties of products are measured on drill cores. 3. The data from previous steps are collected in a structured database. 4. Linear regression and correlation are developed and used for predicting geometallurgical

parameters (such as grade of Fe, SiO2, P, Al2O3, etc.). 5. Block estimation is done based on the algorithm developed in the previous step.

Future activities to improve the geometallurgical program were described as adding process specific variables and mineralogy.

Gomes et al. (2016) performed a geometallurgical study for the Pau Branco Mine. The geometallurgical model uses concentration factors of elements to predict the product quality of iron lumps. The overall gains after applying the geometallurgical model were described by an increase of

8

iron ore lump reserve, reduction of mine operational costs and overall positive impact on the net present value (NPV).

Lund et al. (2013) developed a preliminary geometallurgical model of LKAB’s Malmberget iron ore based on the mineralogical approach. In the preliminary geometallurgical model, each sample and block involves information on minerals present, their chemical composition, modal composition and ore textural type. Ore textural archetypes defined in the study were used to forecast particle types produced when the block is comminuted. The developed geological model of Malmberget was based on a mineralogical approach and was allowed to provide quantitative information including liberation distribution of the plant feed to the process.

At the Kings Valley mine, in Australia, product predictive models using multivariate regression analysis were developed within a geometallurgical study for channel iron deposit (CID) and detrital iron deposit (DID) ore types. The models were used to assess product quality as well as to estimate the processability of different material types. Additionally, a yield model of each ore type was proposed based on upgrading factors which considers feed and product grades. It was noted that further metallurgical test work is required to validate the regression models (Vatandoost et al., 2013).

Rio Tinto broadened the use of their standard classification scheme (i.e. using geological observations to predict metallurgical behavior) and applied the Material Type Classification Scheme (MTCS) to predict metallurgical behavior and product quality (Paine et al., 2016). Different case studies demonstrated the outcome of the applied technique for predicting changes in throughput, ore quality and recovery of various products.

Besides the cases listed above, limited information (e.g. company info pages, reports on limited work where the geometallurgical program is mentioned) is available on further deposits where a geometallurgical program has been developed. All this indicates that geometallurgy is gradually becoming a part of the product management within the ores in production. International standards, like JORC (The Australasian Institute of Mining and Metallurgy, 2012) and NI-43-101 (CSA, 2016) both mention variation or variability in ore to be covered in the feasibility studies, but do not explicitly define the term geometallurgy. However, it is becoming more and more common that geometallurgy is included as a separate item or chapter in deposit studies.

Table 3. Iron ore geometallurgical programs (published). √ = Considered.

Iron ore deposit Throughput Product quality

Recovery Reference

Kiruna (Sweden) √ √ - Niiranen (2015) Malmberget (Sweden) - √ √ Lund (2013) Hannukainen (Finland) - √ √ SRK Consulting (2014) Carol Lake (Canada) √ - - Bulled et al. (2009) Pilbara deposits (Australia) - √ - Wright et al. (2013) Kings deposit (Australia) - √ √ Vatandoost et al. (2013) Nkout & Putu (Cameron & Liberia) - √ √ Anderson (2014) Pau Branco Mine (Brazil) - √ - Gomes et al. (2016) Rio Tinto Iron Ore √ √ √ Paine et al. (2016)

Ore characterization in geometallurgy 2.3

The essential and most important part of a geometallurgical program is the ore characterization. The ore characterization includes mineralogical studies, measurement of physical properties, and

9

metallurgical test work of ore samples (drill core samples or composites). It reveals the behavior of ore in the process and provides criteria for process design and production management. Methods and techniques for ore characterization have been improved to offer faster, comprehensive and more accurate results. This includes novel mathematical algorithms and image processing techniques as well as instruments such as scanning electron microscopy and hyperspectral imaging.

Distinguished areas in ore characterization are known to be mineralogy and ore metallurgical attributes. In the following, the methods and techniques used in these areas are briefly reviewed.

2.3.1 Methods for obtaining mineralogical information Knowledge on the grades of valuable elements and their variation alone is not sufficient for geometallurgy. Firstly, the distribution of the valuable elements is complex in several ore types. For example, in nickel sulfide ores, it is important to know the distribution of nickel between non-sulfides and the different sulfide minerals (Newcombe, 2011). Similarly, in the process design and optimization for porphyry copper ore beneficiation, it is critical to know how much of the total copper is hosted by different sulfide and oxide minerals (Gregory et al., 2013). Secondly, the gangue minerals also play a crucial role in processing. For example in lateritic nickel ores, the gangue minerals have a direct effect on the acid consumption and permeability of the leaching heaps (David, 2008). In refractory and trace mineral ores, like gold and platinum group element ores, the gangue mineralogy defines the entire plant performance. Therefore, elemental grades are not necessarily the best attribute to use for the estimation of recovery and ultimate value. Besides, much of the sustainability and energy efficiency dimensions of geometallurgy are driven by mineralogy. Moreover, mineral grades are additive, which makes their geostatistical modeling relatively straightforward (Vann et al., 2011).

Different levels of mineralogical and chemical information (as summarized in Table 4) are routinely used for ore characterization in geometallurgical programs. They can be divided into the following types according to increasing complexity and details: (1) elemental composition, (2) qualitative mineralogy, (3) quantitative mineralogy, and (4) mineral textures (Jones, 1987; Lamberg et al., 2013). To gather this information into a geometallurgical program, the most cost- and time-efficient analysis methods should be selected. Examples of the methods used in mineralogical characterization are (2) identification of minerals by X-ray diffraction (XRD), (3) analysis of mineral grades by quantitative X-ray diffraction (Monecke et al., 2001), and (4) deriving mineral liberation information by automated mineralogy based on scanning electron microscopy (SEM) (Fandrich et al., 2007). When considering different methods for obtaining the mineralogical information, the trueness and precision of the information must be known. Only then, a selection of the most appropriate method can be made.

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Table 4. The level of information and analysis methods commonly used in geometallurgy.

Level Analysis result Commonly used analysis methods 1. Elemental composition

Chemical composition of samples X-ray fluorescence spectroscopy (XRF); Dissolution/Laser ablation + Atomic absorption spectroscopy (AAS) / Inductively coupled plasma optical emission spectrometry (ICP-OES) / Inductively coupled plasma mass spectrometry (ICP-MS)

2. Qualitative mineralogy

List of minerals present in samples, lithology

X-ray diffraction (XRD); Optical microscopy

3. Quantitative mineralogy

Bulk mineralogy, i.e. mass proportion of minerals in samples (modal composition)

Quantitative XRD; Element-to-Mineral Conversion (EMC); SEM-based automated mineralogy (MLA, QEMSCAN, IncaMineral, etc.); Optical image analysis; Hyperspectral imaging (SisuRock); X-Ray Computed Tomography (XCT); Mineral selective analysis methods (SATMAGAN, diagnostic leaching, etc.)

Chemical composition of minerals (as an extra measure to evaluate mineral grade against elemental grade)

Electron probe microanalysis (EPMA) with energy-dispersive spectrometer (EDS)/ Wavelength-dispersive spectrometer (WDS)

4. Ore texture Mineral grain sizes, grain shapes, associated minerals (rock samples), liberation distribution of minerals in samples (particulate samples)

SEM-based image analysis (MLA, QEMSCAN, TIMA, Mineralogic, IncaMineral, RoqSCAN); Optical image analysis; Electron backscatter diffraction (EBSD); Hyperspectral Imaging (SisuRock); X-Ray Computed Tomography (XCT)

In a mineralogical approach to geometallurgy, information of the mineral grades is required for the entire ore body (Lamberg, 2011). Thus, the number of samples to be analyzed for mapping the ore variation in a geometallurgical project is usually very large (>10 000; Richardson et al. 2004). When selecting a method, one must consider several factors such as the costs, required time, availability, reliability, trueness, and precision. Particularly the information on the precision of the method is frequently not available for the material to be studied.

Automated mineralogy Automated mineralogy based on scanning electron microscopy (SEM) and optical image analyses (OIA) from polished samples are the known techniques for mineral identification, estimating mineral grades, and liberation, and for ore textural study. SEM-based automated mineralogy is commonly regarded as the most reliable way of estimating mineral grades. However, the method requires careful and tedious sample preparation and the method itself is costly and time-consuming (Lastra and Petruk, 2014). On the other hand, OIA-based automated mineralogy has the lower cost and is less time demanding. CSIRO (Donskoi et al., 2013) reported an OIA-based automated mineralogy which has been used for iron ore characterization. In high-grade samples, the OIA system results were close to the SEM-based

11

automated mineralogy (QEMSCAN), but in lower grade samples and low resolutions, the OIA results drifted away from the true values (i.e. results from QEMSCAN and XRD).

Alternative methods such as quantitative XRD by Rietveld analysis (Mandile and Johnson, 1998) and the Element-to-Mineral Conversion (EMC) method (Herrmann and Berry, 2002; Lamberg et al., 1997; Lund et al., 2013; Paktunc, 1998; Whiten, 2007) allow for simpler and faster sample preparation and can even be non-destructive. Additionally, if the aim is the estimation of mineral grade, they may offer better value than automated mineralogical analysis system only if they can fulfill the requirements on trueness and precision.

Element-to-Mineral Conversion (EMC) The Element-to-Mineral Conversion, EMC, is a traditional and straightforward way to estimate mineral grades by simultaneously solving a set of mass balance equations formulated between chemical elements and minerals. The method is restricted to relatively simple mineralogy where the number of minerals is not larger than the number of analyzed components, and the chemical composition of the minerals (mineral matrix) is known. The set of equations in matrix form can be written in the following form:

× = × =

11 1 1 1

1

;n

n nn n n

a a x bA x b

a a x b

(1)

where

A : Matrix of chemical composition of minerals (known) b : Vector of analyzed chemical composition (known) x : Vector of mass proportion of minerals (unknown)

The unknown x can then be determined e.g. by using the non-negative least squares method (Lawson and Hanson, 1995). The EMC can be improved by using additional mineral selective analysis methods such as bromine-methanol leaching for nickel ores (Penttinen et al., 1977), copper phase analysis for copper ores (Lamberg et al., 1997) and Satmagan analysis for iron ores (Stradling, 1991).

The EMC should not be confused with normative mineralogy methods such as the CIPW Norm or the Cation Norm (Cross et al., 1902) which aims at allocating chemical compositions into minerals based on the order of mineral formation in rock. These techniques are frequently used in geochemistry and petrology for the classification of rocks. They suffer mainly from a preset mineral list with stoichiometric mineral compositions as well as from limitations when exotic minerals are present, which is common in ore deposit characterization. Additionally, they do not necessarily provide the mineral grades in weight percentages. Hence, they are not suitable for geometallurgical purposes.

Weighted least square method can be applied to improve bulk mineralogy estimation by the EMC. The method requires an initial guess and weight factors to find a solution. Usually, the initial guess is selected from results of another method such as quantitative XRD and weight factors are calculated from the standard deviation of the analysis result. A combination of the XRD Rietveld and EMC has been used by Berry et al. (2011). They applied a non-negative least square algorithm with weighted values to estimate mineral grades. Their combined method was partially successful in overcoming the limit of determination of the Rietveld analysis that was initially posed by the XRD measurement. However, using calculated weighting factors in the method not necessary gives the best solution.

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Quantitative x-ray diffraction Quantitative XRD methods include Known Addition, Absorption-Diffraction, Mineral Intensity Factors (MIFs) and Full-pattern-fitting (Kahle et al., 2002). The Rietveld method is a full-pattern-fitting method and is regarded as a standardless method (Rietveld, 1969). Moreover, sample preparation, measurement, and data analysis are considerably fast. Depending on the sample preparation, measurement conditions (X-ray source, data acquisition time) and crystallinity of the minerals, the detection limit can be as low as 0.5 weight percent. Demonstration of using the XRD Rietveld method for modal analysis exists in the literature (Gentili et al., 2015; König et al., 2012, 2011; König and Spicer, 2007; Paine et al., 2011; Santini, 2015).

Spectral logging and imaging Hyperspectral drill core logging and imaging technologies are a recognized method for mineralogical and ore type characterization. Reflectance spectroscopy, both in the visible and infrared wavelength range, is a fast and cost-effective technique to acquire quantitative mineralogy. Complementary information can be retrieved from Raman spectroscopy in addition to hyperspectral imaging when characterizing common iron oxide minerals and gangue minerals (Ramanaidou et al., 2015). Examples of application of such a technique in mineralogical studies can be found in the literature (Bonifazi et al., 2013; Konrad et al., 2015; Macrae et al., 2008; Ramanaidou and Wells, 2011; Yang et al., 2011).

2.3.2 Ore texture characterization Ore texture characterization concepts in geology focus on the geological aspects of the texture such as formation and genesis (Craig, 2001; Nyström and Henriquez, 1994). However, from a geometallurgical and process mineralogy point of view, ore texture characterization should be quantitative and provide quantitative information regarding progeny particles and their composition, i.e. on liberation distribution (Petruk, 1988). The effect of ore texture on beneficiation and other downstream processes is recognized and has been evaluated in mineral processing (Bonifazi et al., 1990; Donskoi et al., 2008; Gaspar, 1991). Qualitative or categorical geological classification is not sufficient for mineral processing. The mineralogical approach to geometallurgy requires information on ore textures to enable quantitative evaluation of mineral liberation distribution and the required crushing and grinding energies for mineral liberation. The terminology for describing mineral liberation used by various authors tends to be confusing; the following definitions are used here (see Figure 2):

Particle: A unity consisting of single or multiple grains and single or multiple phases (particles 1, 2 and 3).

Grain: A unit consisting of only one mineral that has a clear interfacial surface with other grains (A and B grains in particles 1 and 3).

Liberated particle: A particle consisting of only one phase (Particles 2 and 3). Degree of liberation: Mass proportion of mineral of interest as liberated particles in the

particulate material. Mineral liberation: a) An action where minerals are liberated (comminution).

b) A broad term which describes the mode of occurrence of mineral in particulate material.

Liberation distribution: Mass distribution of mineral of interest in a particle population.

The definition of what encompasses ore texture varies among geologists and metallurgists (Leigh, 2008). A comprehensive review of definitions for ore textures is given by Vink (1997) and Bonnici

13

(2012). The common definition for ore texture refers to volume, grain size, shape, spatial distribution and association of each mineral in the ore, thus in unfractured material. The other issue is in what scale textural information needs to be collected. The term microtexture is used for grain-scale features like mineral inclusions in another grain, mesotexture for hand specimen sizes, and macrotextures for scales larger than meso-scale (Richmond and Dimitrakopoulos, 2005). Ore texture is a generic term that refers to all scales.

1)BA

2)B

3)B B B

Figure 2. Composite and liberated particles.

Ore texture measurement is commonly performed on thin sections, polished slabs, or drill cores depending on the required scale and details for intact ore or particulate samples. Optical microscopy, scanning electron microscopy (SEM), hyperspectral imaging, and x-ray diffraction mapping are common methods to acquire spatial distribution of phases in the sample. The mineral map is generated, and parameters of interest are calculated. Image analysis tools are commonly used to measure and quantify ore textural attributes (Nguyen, 2013; Pérez-Barnuevo et al., 2012; Zhang and Subasinghe, 2012).

2.3.3 Physical and metallurgical properties of ore Ideally, all laboratory- and pilot-scale mineral processing tests can be used in a geometallurgical study. However, the large number of samples to be tested, the cost and time for conducting the tests, and being able to use small amounts of sample for the trials limit the selection of metallurgical tests for a geometallurgical study. This means that the tests must be suitable to be performed on drill core samples in large quantities in a relatively short time.

A geometallurgical model can benefit from measured physical properties of the ore while drilling or measured on drill cores. Despite the fact that many of the measured physical properties are not directly utilized in the geometallurgical program, they can still be used to establish a proxy relation to properties of interest. For example, a good prediction of ore hardness (crushability and grindability) has been reported by correlating drill core logging data against ore hardness (Hunt et al., 2013; Keeney and Nguyen, 2014; Nguyen et al., 2016; Vatandoost et al., 2009).

Many mineral processing properties of ores are collected based on systematic metallurgical tests that relate ore characteristics to process performance such as recovery, grade, throughput, energy consumption, particle size distribution and impurities (Kojovic et al., 2010; Lamberg et al., 2013). For example, a review of small-scale tests to characterize ore hardness, crushability, and grindability, can be found in Mwanga et al. (2015). Other frequently used tests for geometallurgy of magnetite ore include Davis Tube Recovery (DTR) test (Farrell et al., 2011; Leevers et al., 2005; McQuiston and Bechaud, 1968), Low-Intensity Magnetic Separation (LIMS) tests (Koenig and Broekman, 2011; Sundberg, 1998), floatability tests (Alexander and Collins, 2008; Franzidis, 2010). In addition, including the environmental impact of ore beneficiation has been acknowledged in recent geometallurgical studies (Becker et al., 2015; Opitz et al., 2016).

Process models for simulation of magnetite ore beneficiation plants 2.4

Minerals and particles are the fundamental elements in mineral processing operations and simulation. Both mineral and particle properties define the selection of a process and the process performance.

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However, the full potential of using particles in mineral processing simulation has not been accomplished yet. This has been partly due to lack of analyzing instruments to collect information at particle level as well as the lack of mass balancing techniques and data reconciliation methods capable of working at the mineral liberation level. Also, unit operation models which predict the behavior of individual (also multiphase) particles based on their properties are largely missing.

The development of automated mineralogy (Gu et al., 2014) has facilitated collecting particle level information. Additionally, data reconciliation and mass balancing techniques improved from the traditional approach of balancing solids and elements (Hodouin, 2010) to reconciling and adjusting particle populations (Lamberg and Vianna, 2007). These developments have built a foundation to take mineral processing unit models and simulation to a new level.

As to the level of details, mineral processing predictive models can be divided into three categories whether the smallest block in the simulation is an entire processing circuit (black box model), a section (e.g. comminution circuit) or a single unit (e.g. individual flotation cells). In geometallurgy, it is common to use models that predict the full process with simple equations. For example in Hannukainen iron ore deposit, the iron recovery into the iron concentrate is defined with a simple equation based on iron and sulfur head grade (Equation (2), SRK Consulting (2014)).

× −= × − × − × +0.06 ( 6)98.5 (1 ) ( 1.96 ( ) 1)FeFe

SR e Fe (2)

Models describing a section are also common especially when throughput or comminution energy usage is being forecasted (comminution circuit). Geometallurgical models going to unit operation level are rare. This is mainly due to the difficulty of obtaining quantitative results from geology to work at unit level as well as the lack of interface to connect geological data to the mineral processing unit.

Another way of classifying the models is based on the level of detaildness for describing the process streams. A stream has a flowrate of bulk mass, elements, minerals, and particles. A bulk stream can be considered as a set of sub-streams each representing a particle size class. The flow information that defines a stream, from lowest to the highest level of detailedness, are total solids, chemical elements, minerals, and particles. Obviously, the study goal determines the selection of the level and size information. For instance, sized solids (i.e. total solids flow of a narrow particle size class) are often used to model and simulate comminution circuits whereas bulk mineral information is common in froth flotation.

Other critical dimensions of a process model are what input parameters it takes, what the limitations are and how it was developed. Empirical models are solely based on observed data without using physical or chemical principals governing the system. Phenomenological (Semi-empirical) models are based on the data, but the theory of the process is to some extent used to correlate the equations and parameters in use. Finally, the fundamental models are solely based on physical and chemical properties and sub-processes in the system without the need of experimental data. Fundamental models that consider all involving elements in the process, have not yet found their place in mineral processing simulation. This is mainly due to a large number of sub- and micro-processes taking place even in simple mineral unit operations (e.g. pumping), the significant number of particles in the system and huge demand on computational resources.

The selection of a modeling level comes with certain restrictions (Table 5) that limit its usability when expanding it outside the scope where the model is created and calibrated. For instance, while a model at total solids flowrate level (i.e. tons per hour of total ore, concentrate, tailing, etc.) is enough for

15

equipment sizing in the basic engineering stage of an ore project, it cannot be used for estimating the performance of a separator unit. At the grindability type level, the material is divided into grindability types, e.g. hard and soft, and these types will behave differently in comminution circuit. Clearly, the feed stream that is defined only by grindability types cannot be adopted directly, for example, in a magnetic separation model, which at least requires elemental or mineral distribution information. At minerals by behavioral types (in bulk or by size) level, each mineral is divided into behavioral type classes for a certain processing phase. For example in flotation modeling, the floatability component approach divides each mineral into fast floating, slow floating and non-floating type class (Runge and Franzidis, 2003). Broadly speaking, these classes correlate to different liberation classes (Welsby et al., 2010). However, these behavioral type classes in various separation stages, e.g. magnetic separation, are not applicable since the classes are explicitly defined for a certain separation stage. At particle level (or mineral liberation level), the assumption is that similar particles (regarding the particle’s attributes such as composition and texture) behave similarly regardless of from which part of the ore they originate.

In a process or circuit simulation, the ideal situation is where all unit operation models work at the same level. If not, then transformation functions or models must be used where some of the required stream properties are generated based on existing information of the stream and additional information required by a model.

Table 5. Modeling levels and their limitations in minerals processing. The model is valid and can be extended outside the calibration point as long as the feed stream assumptions are met.

Level Feed stream assumptions Example of application

Bulk (B)

Solids (BS) Each particle will behave identically regardless of its size and composition

Solid splitter model, equipment scale-up, basic engineering

Element (BE) Mineralogy, particle size distribution, and liberation distribution are fixed

Recovery function model for elements

Mineral (BM) Particle size distribution and liberation distribution are unchanged

Mineral splitter model

Behavioral type (BB)

Particle size distribution is unchanged. Similar behavioral types will behave identically

Gravity separation model

Sized (S)

Solids (SS) Each particle of given size will behave identically

Comminution model, Size classification model, equipment scale-up

Grindability type (SG)

Each particle type of given size will behave identically

Comminution model

Element (SE) Mineralogy and liberation distribution are unchanged

Recovery function model in size classes

Mineral (SM) Liberation distribution is unchanged Mineral splitter model in size classes

Behavioral type (SB)

Similar behavioral types will behave identically in narrow size fraction

Flotation model (fast and slow floating materials in size classes), Gravity separation model in size classes

Particle (SP) Similar behavior of particles of same composition and size

Principally applicable to all unit models

This study focuses on geometallurgy of iron ore and flowsheet simulation. Process unit models to be studied are selected based on applicability at the particle level for iron ore beneficiation and flowsheet simulation. The task is to identify where appropriate models exist and where development is needed. A brief summary of the review outcomes is provided at the end of this chapter.

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2.4.1 Magnetic separation models Most of the unit operation models for mineral processing simulation are focused on design and operation of the unit with recommendations for improving their performance; this is true also for magnetic separators (Cui and Forssberg, 2003; Dobbins et al., 2009; Oberteuffer, 1974; Svoboda and Fujita, 2003). Models suitable for flowsheet simulation are quite a few, they are mostly empirical, and are rarely based on physical or chemical principles behind the process. In the following, various wet magnetic separator models are reviewed and compared against the modeling levels defined in Table 5.

In magnetite ore processing, the Davis Tube Recovery (DTR) test is traditionally used to develop recovery and grade models. Its development goes back to 1921, when a test previously performed manually was mechanized (Schulz, 1963). The model gives the concentrate quality and iron recovery based on iron grade in the feed. The approach has proved to be practical for judging the response of ore to magnetic separation. However, the model is valid (thus, can be extended outside the samples studied) if mineralogy, ore texture, and distribution of particle size and liberation in the feed remain unchanged. For example, a magnetite rich sample gives in the DTR test 97% recovery for iron, this value cannot be extended to ores where the main Fe mineral is hematite (mineralogy is different), where the grain size of magnetite is much finer (texture is different), similar comminution conditions give much coarser plant feed (particle size distribution) and the degree of liberation is much lower (liberation).

The empirical model of the wet high-intensity magnetic separator (WHIMS) by Dobby and Finch (1977) indicates that the recovery of particles into the magnetic concentrate is dependent on the magnetic susceptibility and size of particles. Experimental test work is required to determine the distribution of particle size and magnetic susceptibility in the feed. Their empirical model was defined as follows:

= + ×

10

50

log LM

MR C B

M

(3)

where:

MR : Recovery

50M : Machine parameter (magnetic cut point at which the recovery is 50%) B : Machine parameter C : Constant determined based on B and 50M

LM : An empirical parameter calculated from a formula that is related to mass fraction of magnetic material in the feed, and magnetic and hydrodynamic forces (King, 2012)

Davis and Lyman (1983) defined the feed stream using a binary system of magnetic and non-magnetic particles split into size classes and studied the effect of several operational variables like feed rate, drum speed, and magnetite/non-magnetite particle size distribution on an Eriez full-scale high gradient wet magnetic separator. A two-component model for the magnetic loss was described based on operational variables. The model lacks the ability to forecast the concentrate grade.

King and Schneider (1995) developed an empirical magnetic separator model that uses particle properties and therefore can forecast the behavior of each particle separately. In the model, the distribution of any given particle between the concentrate and tailing is a function of the volumetric

17

abundance of the magnetic phase in the particle. The following formula describes the fraction of particles that ends up in the tailings stream:

α α= + −( , ) ( ) (1 ( )) ( )v vt g d d d r g (4)

where

t : Recovery of particle in the tailing

vg : Volumetric abundance of the magnetic phase in the particle d : Particle size α( )d : Bypass fraction of particles based on size that reports directly to the tailing

( )vr g : Primary classification function based on volumetric grade of magnetic phase in the particle

The by-pass function (i.e. material that by-passes the magnetic separation and reports to the tailing) is modeled from experimental data using the reciprocal of a natural exponential function with two coefficients. The primary classification function is modeled by a Rosin-Rammler distribution function and is only a function of particle composition, or more exactly the volumetric grade of the magnetic phase in a particle. The model was implemented in the MODSIM simulation software. However, the size of a particle function was not considered in classification.

The magnetic separator model in the USIM PAC simulator is defined based on the recovery of minerals in size fractions also called as simple distribution or split model. The user defines recoveries to the magnetic concentrate for each mineral by particle size fraction based on experimental results. An application example was given in the context of designing an iron ore beneficiation plant in Kiruna where a statistical model for a wet low-intensity magnetic separator (WLIMS) was developed (Söderman et al., 1996). The authors simplified the model by assuming that recovery of magnetite per size class is not affected by minor changes in the head grade, feed rate or particle size distribution of the feed.

Rayner and Napier-Munn (2000) developed a model to predict the percentage loss of magnetic particles for a wet drum magnetic separator in a dense medium application. The model is represented by a flocculation rate and a residence time (Rayner and Napier-Munn, 2003a). The feed stream is described by the behavior type for magnetic particles and ferrosilicon as the dense medium. The size of the particles was not considered in the model.

A simplified approach called pseudo-liberation approach for simulating the effect of liberation in WLIMS was proposed by Ersayin (2004). The assumption behind the model was that increasing the grade of magnetite in the feed would result in decreasing the degree of liberation of gangue minerals. For a given ore and a plant, the pseudo-liberation model uses empirical data and cubic spline functions to generate a plant-operating surface as a magnetic separator model.

Metso reported a model for the LIMS that couples discrete element method (DEM), computational fluid dynamics (CFD) and finite element method (FEM; Murariu 2013). In the model, each particle is supposedly treated separately. But details on how the model predicts the behavior of particles in the unit operation are not given. According to Murariu (2013), the model can be used to study the effect of operational parameters and geometry of LIMS on the separation efficiency.

The models, as summarized in Table 6, can fairly predict the metallurgical performance of a magnetic separator unit. The majority of the models have been developed for optimization purposes with strict

18

adaption to the feed type. Moreover, the available models are not capable of making use of particle level information. The closest one to provide such a feature is the King and Schneider (1995) model. However, the model considers particle size only for calculating the bypass to the tailings. Thus, particles of similar composition behave identically regardless of their particle size.

Table 6. Magnetic separator models including model level (according to Table 5) and considered operational parameters.

Model Level Feed properties used in

model Input given by

user Output References

DTR function

BE, Empirical

Iron grade Empirical functions

Iron recovery Schulz (1963)

Dobby and Finch

SB, Empirical

Magnetic susceptibility and particle size

distribution of the feed

Machine and calibration parameters

Recovery in size class

Dobby and Finch (1977)

Davis and Lyman

BB, Empirical

Feed rate of magnetics (dry)

Drum speed, feed and

squeeze pan clearances

Magnetite loss, Concentrate

density

Davis and Lyman (1983)

USIM PAC SM, Empirical

Mineral composition of the feed by size

fractions

Recovery of minerals in size

fractions

Recovery and grade of

minerals in size fractions

Söderman et al. (1996)

King and Schneider

SP, Empirical

For each particle: magnetic volumetric grade, particle size

By-pass function

Recovery of particles

King and Schneider

(1995)

Rayner and Napier-Munn

BM, Phenomenological

Volumetric feed rate, gangue fraction, magnetic volume

susceptibility, magnetic density, the volume of

solids

Slurry viscosity in pickup zone

Magnetite loss in tailing

Rayner and Napier-Munn

(2003b)

Pseudo-liberation

SM, Empirical

Magnetite grade, particle size distribution

Calibration parameters

Magnetite recovery

Ersayin (2004)

Metso SP,

Fundamental Not specified Not specified Not specified

Murariu (2013)

2.4.2 Size classification models Screening or hydrodynamic classifiers generally are employed for particle size classification in mineral processing. In screening the separation of particles is affected by their sizes (as well as the size and the shape of the aperture in the screen) while hydrodynamic classifiers use the motion of particles. Hydrocyclone and spiral classifier fall into the second category. For hydrodynamic classifiers, the particle properties are fundamentally required to model classifiers while for screens, the size distribution of particles can be sufficient.

The schematic drawing of a typical hydrocyclone is shown in Figure 3. Several reviews of the hydrocyclone models and their applications are available in the literature (Barrientos and Concha, 1990; Chen et al., 2000; Frachon and Cilliers, 1999; Heiskanen, 1997; Kraipech et al., 2006; Svarovsky, 2000). In a context of flowsheet simulation in mineral processing, the number of suitable hydrocyclone models is limited. This is because solution from fundamental modeling of hydrocyclone is computationally intensive (Nageswararao et al., 2004). The remaining models are empirical or

19

phenomenological models that require experimental work to obtain material specific constants. Common models of these types are reviewed shortly in the following.

Feed

Overflow

Underflow

Inlet

Vortex Finder

Apex

Figure 3. Schematic view of a hydrocyclone.

Plitt’s hydrocyclone model (Flintoff et al., 1987; Plitt, 1976) is probably the most popular model used in the simulation of mineral processing circuits. The original Plitt’s model was revised by Flintoff et al. (1987) to have no dependency to feed size. Instead, the model uses factors for calibration to the feed data as follows:

ϕηρ

××= ×

−

0.46 0.6 1.21 0.5 0.063

50 10.71 0.38 0.45

39.71

1.6

c i oc k

su

D D D ed F

D h Q

(5)

× − + = × ×

0.15 1.5821

2 1.94s

scD hm F e

Q

(6)

ϕ××= ×

+

1.8 0.0055

3 0.37 0.94 0.28 2 2 0.87

1.88( )c i u o

Q eP F

D D h D D

(7)

ϕρ ×

× + = ×

3.31

0.24 0.54 2 2 0.36 0.0054

4 1.11 0.24

18.62 ( )up u o

o

c

Dh D D e

DS F

D P

(8)

The parameters in the equations are:

ϕ : Volumetric concentration of solids in the feed slurry (%)

S : The volumetric flow split, i.e. volumetric flowrate in underflow / Volumetric flowrate in overflow

1 2 3 4, , ,F F F F : Calibration factors ρs : Density of the solid phase (g/cm3)

uD : The Apex diameter (cm) ρp : Density of the cyclone feed slurry (g/cm3)

iD : The cyclone inlet diameter (cm) η : Viscosity of the carrier fluid (cP)

oD : The vortex finder diameter (cm) m : Sharpness of separation

cD : The cylindrical section diameter (cm) P : Cyclone inlet pressure (kPa) h : Free vortex height in cyclone (cm) 50cd : The corrected cut size Q : Volumetric flowrate of feed slurry (l/min) k : Hydrodynamic exponent

20

Lynch and Rao (1975) developed the first widely used empirical hydrocyclone model. The model uses the correlations between the geometry of the hydrocyclone and flowrates. The general form of the model is as follows: = − + + − +10 50 1 2 3 4 5 6log c o u i w fd F D F D F D F C F Q F (9)

= 0.73 0.86 0.427f o iQ F D D P (10)

= − +8 9 10

1uf

f f

DR F F F

W W

(11)

where the parameters are:

oD : The vortex finder diameter (cm) −1 10F : Calibration factors

uD : The Apex diameter (cm) fQ : Volumetric flowrate of feed slurry (l/min)

iD : The cyclone inlet diameter (cm) wC : Solids weight percent in feed

fW : Mass flowrate of water in feed (t/h) fR : Water reporting to underflow (%) Another empirical model for flowsheet simulation is of Nageswararao hydrocyclone model. In the development of the Nageswararao model, dimensionless variables were selected to predict the performance of industrial classifiers. In his model parameters defined in parenthesis, [ ] { }, , are used for scale factors, design variables, and operating variables, respectively (Nageswararao, 1995).

θρ

− =

0.500.67 0.45 0.20

1.90 0.101

o cic

c c c p

D LD PQ K D

D D D

(12)

θ λ

ρ

−− −

− =

0.220.52 0.47 0.40 0.20

0.65 0.20 0.93502

c o u cic

c c c c c p c

d D D LD PK D

D D D D D gD

(13)

θ λ

ρ

−− −

− =

0.531.19 2.40 0.50 0.22

0.00 0.24 0.273

o u cif c

c c c c p c

D D LD PR K D

D D D D gD

(14)

θ

ρ

−− −

− =

0.310.96 1.83 0.25 0.22

0.00 0.244

o u civ c

c c c c p c

D D LD PR K D

D D D D gD

(15)

where the parameters are:

cD : The cylindrical section diameter (cm) −1 4K : material specific constants dependent

oD : The vortex finder diameter (cm) θ : Full cone angle of cyclone (Rad)

uD : The Apex diameter (cm) P : Cyclone inlet pressure (kPa)

iD : The cyclone inlet diameter (cm) ρp : Density of the cyclone feed slurry (g/cm3)

cL : The length of the cylindrical section (cm) g : The acceleration due to gravity (cm/s2)

λ : is β β− 3(1 ) , β being the volumetric fraction of solids in the feed slurry

fR : Water reporting to underflow (%)

21

Asomah & Napier-Munn (1997) presented a model for inclined (not vertical) hydrocyclone. The model is similar to previous models, but it takes the angle of inclination and feed viscosity into the consideration. However, no data is available for the validation of the model in large-scale operations. The empirical model is formulated as follows:

α α−− − × − −

= −

2.940.46 0.95 1.3910.23 0.16 0.72180 18040

50 1 1oc c s e

o u

P Dd F D V R A e

D D

(16)

( )

α− − × − − −

= −

0.21 1.81 0.29 1.360.830.47 0.18 0.48 18040

2 1o cf c s e

o u c

P D LR F D V R A e

D D D

(17)

αρ ρµµ ρ

− −− − × − −

− =

1.05 0.16 2.180.85 0.090.15 0.11 0.43 180

3s po u sl

c ec c w s

D Dm F D R A e

D D

(18)

( ) ( )

α

ρ− − ×

−−

= −

0.46 1.110.44 1.542.00 1.48 0.25 180

4 1 cF c p s i o

c

LP F Q D V D D A e

D

(19)

where the parameters are:

cD : The cylindrical section diameter (cm) −1 4F : Calibration factors

oD : The vortex finder diameter (cm) 50cd : Corrected separation size (µm)

uD : The Apex diameter (cm) P : Cyclone inlet pressure (kPa)

iD : The cyclone inlet diameter (cm) ρp : Density of the cyclone feed slurry (kg/l)

cL : The length of the cylindrical section (cm) 40P : Size 40% feed material passing (cm) A : Cone angle of cyclone (degree) sV : Feed volume fraction of solids α : Cyclone inclination from vertical (degree) ρs : Density of the cyclone feed solid (kg/l)

eR : Reynolds number fR : Water reporting to underflow (%)

µsl : Slurry viscosity (cP) µw : Water (fluid) viscosity (cP) Svarovsky (1984) presented a hydrocyclone model based on a dimensional analysis which involved relationships between Stokes, Euler, and Reynolds number and defined as follows:

( )ρ ρ νµ

−=

×

250

50 18s l c

l c

dStk

D

(20)

ρν∆

=

2

2l c

PEu

(21)

ν ρµ

=Re c c l

l

D

(22)

ν

π×

= 2

4 fc

c

QD

(23)

where the parameters are:

50Stk : Stokes number for cut size 50d 50d : Cut size ρs : Solids density ν c : Characteristic velocity ρl : Liquid density cD : The internal diameter of a hydrocyclone

22

Eu : Euler number fQ : Liquid feed flowrate

µl : Liquid viscosity Re : Reynolds number ∆P : Static pressure drop However, Svarovsky’s model was developed with small cyclones and dilute slurries and has not been widely used in mineral processing (King, 2012).

An example of a hydrocyclone model that used for considering particles and ore texture is a study by Donskoi et al. (2005). He used revised Plitt’s hydrocyclone model (Flintoff et al., 1987) in USIM PAC simulation package and defined a various class of particles (density based) in size fractions as a separate phase. This data was used to predict recovery of minerals, total iron, and masses in the hydrocyclone underflow.

A common method of representing separation efficiency by size is by efficiency curve (Napier-Munn et al., 2005). It relates mass proportion of each particle size in the feed which reports to the particle size. None of the above-listed models can truly treat particles individually and give different behavior for particles being similar in size but different in composition (density).

2.4.3 Comminution models In iron ore beneficiation, the purpose of the comminution is mostly to liberate iron ore minerals from gangue minerals. Further comminution to finer than liberation is unnecessary unless there is a particle size requirement for the product such as fine magnetite concentrate for pelletizing process. Comminution equipment in the mineral industry are many and differ in design and application. It is not possible nor is the objective of this study to cover all crushing and grinding models. Emphasize is given on models which are capable of delivering stream properties for flowsheet simulation instead power consumption, operating conditions or optimization. This means size distribution and liberation models which can be applied for size reduction processes. Considering modeling levels given in Table 5, only sized level models are valid here.

In the most simplified case, particle size distribution of discharge stream can be modeled by fitting particle size distribution functions such as Rosin-Rammler, lognormal or logistic distribution (see King 2012) for the product. Based on the experimental work and observations the best distribution function can be selected to model particle size distribution of the discharge stream. The distribution functions as such cannot forecast how the size distribution will be if there are changes in grinding conditions, residence time or material properties (like feed particle size distribution, mineralogy, or ore texture). Some studies (Mwanga, 2016) have used an approach where P80 from Bond equation has been used to forecast the full particle size distribution by Rosin-Rammler equation by keeping the parameter describing the steepness of the cumulative distribution curve fixed. This kind of model can be described as a forecast of particle size distribution experimentally.

Population balance model (Austin et al., 1984) is versatile and has a wider range of forecasting capability than the one described above. Once the model is calibrated, it can forecast the product particle size distribution even if the particle size distribution of the feed changes. It is based on the mass balances by particle size comprising a selection function (S) and the breakage function (B). The equation in cumulative form is defined as follows:

∞∂ ∂=

∂ ∂∫( , ) ( , )

( ) ( , )x

M x t M y tS y B x y dy

t y

(24)

23

where:

( , )M x t : Cumulative mass of particles finer than size x ( )S y : The selection function which shows the mass fraction of size y which is going to be fragmented ( , )B x y : The cumulative breakage function which is the fraction of particles of size y which are

fragmented to give particles of size less than x

The equation (24) in discrete form changes to

−

=

= − +∑1

,1

( ) ( )i

ii i i j j j

j

dMS M t b S M t

dt

(25)

The most popular breakage function models are based on a mixture of two separate populations (Equation (26)). However, it can be even simplified as one population. A general and simplified representation of the selection function is in the form of equation (27).

( )

= + −

( , ) 1a b

x xB x y K K

y y

(26)

=( ) aS x Kx (27)

If one takes simplified forms of selection and breakage functions, the solution of equation (24) becomes well-known Rosin-Rammler distribution.

−=( , ) ( ,0)aAx tM x t M x e (28)

Size-mass balance models can relatively well predict particle size distribution of a mill product even if the particle size distribution of the feed changes. However, the model is not capable of predicting neither mineral grades by size nor liberation distribution.

In the concept of liberation modeling, various approaches are known. The first approach is to model liberation independently from size reduction modeling and assuming that liberation process is related to the texture of the ore and the target size (Gaudin, 1939; Wiegel and Li, 1967). Usually, the main parameters in this liberation model are the average grade of phases and the size ratio between particles and grains. This approach is also called texture modeling and is achieved by superimposing particles mesh over texture image. This approach further developed from simple textures to consider a variety of ore textures (Barbery, 1991) or transformation of textures to simple forms (Meloy and Gotoh, 1985). In this, the key parameters are the volumetric grade of the ore mineral and the interfacial surface area between phases which is related to the grain size.

The second approach was developed by extending the theory of liberation (Andrews and Mika, 1976; Wiegel, 1976). These authors have considered the problem of simultaneously accounting for liberation and breakage in a batch mill. Other approaches have been reported in the literature such as integration of liberation, size reduction and process modeling (Bax et al., 2016; Khalesi, 2010).

The first part of liberation model is how the ore texture is defined or is characterized to be used for developing predictive liberation models. The second part of liberation model is how the mineral distribution in particles is defined. This can be described by distribution functions without measurement or measured by images analysis techniques. A majority of liberation models are based on binary system (i.e. an ore mineral embedded in a gangue matrix), and they lack the capability of forecasting multiphase particles. A comprehensive review of liberation models and their development

24

in 80’s and before was given by Barbery and Leroux (1988). Another important part of liberation modeling is how actually fragmentation (breakage) occurs. As discussed earlier, a simple approach is to superimpose particle patterns over textures. A recent review of mineral liberation and liberation in comminution is given by Mariano et al. (2016).

Practical implementation of mineral liberation models in the mineral processing is rare. This is because the models are mainly for binary systems and taking models to the multiphase system is too complicated. Nevertheless, in simplified ore textures (binary system) the models have been tested and compared against experimental data (Barbery and Leroux, 1988; Choi et al., 1986; Finch and Petruk, 1984; Hsih and Wen, 1994; Leigh et al., 1996; Schneider et al., 1991).

In simulation software of mineral processing, MODSIM has implemented complete Andrews-Mika liberation modeling. HSC Chemistry since version 7.1 (Outotec, 2012) has included liberation model as built-in comminution models. Traditional comminution models describe the product particle size distribution and internally the software forecast the liberation distribution of the product if the liberation information on the feed stream is given (Lamberg and Lund, 2012). This is done by keeping the liberation distribution within the size fractions unchanged, and the changes are applied only to mass proportions of different size fractions. As the mineral grades between the particle size fractions may be different, the shift in mass proportions of the particle size fractions would change the mineral grades in bulk. Therefore, there is an extra reconciliation step to conserve the bulk mineral balance between the feed and product.

2.4.4 Flotation models It is known that kinetic model well describes the batch flotation results. In batch flotation modeling with its specific assumptions, such as perfect mixing, full particle suspension and capture efficiency, the rate of flotation is directly related to remaining floatable material in the cell (King, 2012). The flotation rate equation in differential form is:

− = ndC

kCdt

(29)

where n denotes the order of the equation. In the simplest form, the first order kinetic, the equation (29) becomes:

−= 0ktC C e (30)

By the assumption that a fraction of each mineral is non-floatable and considering the ultimate recovery (R∞) the form of the equation in terms of recovery of the mineral in batch flotation and perfect mixer (industrial single tank cell) becomes:

( )−∞= −1 ktR R e (31)

=

+1kt

Rkt

(32)

To find the constants, experimental data must be fitted with the equations. The extension of the first order kinetic model (Equation (31)) is the Klimpel model which has the rectangular rate distribution instead of uniform rate as the classic first order kinetic model (Dowling et al., 1985). The Klimpel (1980) kinetic model is defined as follows:

25

−

∞

−= −

11

kteR R

kt

(33)

The Klimpel model has been used for analysis of more than 300 flotation tests at WEMCO® and was found to fit experimental data reasonably well (Parekh and Miller, 1999).

Kelsall (1961) presented a kinetic based flotation model consisting slow and fast floating rate constant. Comparing to classic first order kinetic model, Kelsall’s model was considered to offer a better estimate. Later his model modified by Jowett (1974) to consider ultimate recovery as follows:

( )( ) ( )( )φ φ− −∞= − − + −1 1 1f sk t k tR R e e (34)

A comprehensive survey of flotation models can be found elsewhere (Dowling et al., 1985; Mavros and Matis, 1991; Runge and Franzidis, 2003; Wang et al., 2015). The other approaches of flotation modeling are the models considering environment effects. These models remark the relation between metallurgical performance and environment variables (Gorain et al., 1999; Mathe et al., 1998; Tabosa et al., 2016; Vera et al., 2002; Wang et al., 2016). Compared to other unit processing models, flotation models are more mature in reaching to particle level modeling (Lamberg and Vianna, 2007; Savassi, 2006; Welsby et al., 2010).

2.4.5 Summary of the process unit models for particle-based simulation In the concept of particle-based simulation, a minimum requirement for a unit model is the capability to work at particle size level and address relevant particle properties for the unit process. This means some of the existing unit operation models can still be used in particle-based simulations with some considerations. For example, even though Efficiency Curve or Plitt’s hydrocyclone model is not particle-based in nature, the particle population can be used to generate the bulk information needed to calculate the cut size of a hydrocyclone. Mineral liberation information would be required in some areas, including magnetic separation and flotation. Regarding this study, magnetic separation model is needed to perform simulations at liberation level. The applicability and limitation of existing unit operation models for the mineralogical approach are summarized in Table 7.

Table 7. Applicability of current unit models in particle-based simulation.

Area Model Considerations Magnetic separation King and Schneider (1995), Parian

et al. (2016) -

Comminution HSC Chemistry: combined fixed particle size distribution and liberation model

Assumes liberation in narrow size fractions remains unchanged

Particle size classifier Fixed particle size distribution The only size of particles is considered to affect separation

Hydrocyclone Efficiency curve/Efficiency curve by mineral

Does not take into account particle/mineral densities

Flotation HSC Chemistry, Lamberg & Vienna Kinetic constants for multiphase particles deviates from linear behavior

26

27

Chapter 3 - Experimental and methodology

Sample sets and sample preparation 3.1

Northern Sweden is known as a significant mining district in Europe with diverse styles of mineralization, including Fe oxide, Cu±Au and Au ores. In the area, more than 40 different iron ore deposits have been identified varying with respect to ore type, main ore minerals, and alteration features, etc. (Bergman et al., 2001).

One of the major companies that is active in mining and processing iron ore in Northern Sweden is LKAB. LKAB is operating in Kiruna, Malmberget and Svappavaara districts and has the world’s largest underground iron ore mines. The ore body of Kiruna is about four kilometers long and has a depth of two kilometers. The Malmberget mine consists of about 20 ore bodies and is mainly magnetite ore, but also hematite-bearing ore bodies exist. The recently opened Gruvberget mine in the Svappavaara ore field is operated as an open pit mine. Production from this mine together with the planned Leveäniemi and Mertainen mines close to Svappavaara account for about 25% of the company’s total output of iron ore in 2015.

In iron ores of Northern Sweden, from mineralogical and mineral processing point of view, the valuable iron-bearing minerals are magnetite and hematite, and the gangue minerals are apatite, amphiboles, feldspars, clinopyroxene and quartz. Garnet and calcite may be present in some of the deposits (Lund, 2013).

The sample selection for all experimental work for this study was done with collaboration with LKAB and the samples are from LKAB ore deposits and operations. The samples for each area of study are separate and vary mineralogically.

3.1.1 Sample set for modal analysis study For modal analysis study, a total of 20 ore and process samples from the different iron ore deposits of LKAB were collected. The iron grade in the samples varied between 21-63%. The ore samples were classified as semi-massive hematite ore and massive magnetite ore (Niiranen, 2006).

Sample preparation started with crushing and splitting of the samples (Figure 4). One subsample was taken for the preparation of resin mounts to be used for automated mineralogy. The remaining part was pulverized in a swing mill and again split into two. One subsample was used for X-ray fluorescence analysis, and the second one was further ground with a swing mill to produce a very fine powder with a P80 of 20 microns for filling the back-loading holders with an opening diameter of 26 mm for X-ray powder diffraction analysis.

28

Sample

Crushing

Splitting

PulverizingTo resin mounts

Splitting

To XRF To XRD

Figure 4. The schematic procedure of preparing samples for modal analysis.

In ore projects, normally 0.3-2.0 m long drill core sections are collected for chemical assays and mineralogical study. However, crushed drill core has a wide size particle distribution, which is a problem both in sample preparation and in measurement to analyze mineral grades. In the preparation of resin mounts, crushed samples tend to segregate, i.e. large and dense particles are enriched in the lower part of the resin. This leads to a bias in the analysis of particle size distribution, mineral grades and mineral distribution (Kwitko-Ribeiro, 2012). Therefore, a common procedure is to first size the samples into narrow size fractions, which is a measure used to minimize analysis error when the focus is on quantitative textural measurements, i.e. liberation, etc.

When assaying a large number of samples (>10000), sizing is not an option since it multiplies the number of samples to be analyzed. In an analysis of polished section, using unsized samples introduces segmentation and stereological errors. The stereological error is less significant than segmentation error and is more influential in the liberation analysis than bulk mineralogy analysis as shown by Lastra and Petruk (2014). To minimize the segregation, the samples were “double sectioned,” also known as vertical sectioning. This technique is commonly used in several mineralogical laboratories and has been validated to reduce the sample segregation significantly (Kwitko-Ribeiro, 2012). In double-sectioning samples were initially mold in resin and after hardening sawed into slices. The slices were after that arranged in another mold in a way that they show the sedimentation profile towards the side to be analyzed (Kwitko-Ribeiro, 2012).

3.1.2 Sample set for ore textural study Various AQ (core diameter 27 mm) and BQ drill cores (36.5 mm) of iron ore with variation in ore textures were selected for the ore textural study. The samples were cut along the core axis and were scanned by the flatbed scanner. Afterward, the drill cores were cut in intervals of two centimeters. Two pieces were used for preparing epoxy block; other pieces went through the crushing process. These pieces were crushed in laboratory jaw crusher with closed side setting opening of 3.35 mm. The crushing product was sieved, and subsamples of each size fraction were selected to make epoxy samples for particle measurements (Figure 5).

29

Drill core sample

Axial cut

Drill core scanning

Cut in pieces (20 mm)

Two pieces for ore textural study Crushing (-3.35 mm)

Sizing

Resin mounts for size fractions

Figure 5. The schematic procedure of preparing samples for ore textural study.

3.1.3 Sample set for model development and simulation framework Plant survey data was used for developing the WLIMS model and simulation framework of the process. The plant survey was done at one of the LKAB’s iron ore processing plants in Kiruna, Northern Sweden. While the plant was operating at steady state, selected streams in the plant were sampled during a two hours’ period. The sampling protocol at LKAB was followed. Incremental sampling was performed around the circuit during the sampling period. Samples were taken at 10-minute intervals and added to the same bucket after each sampling interval. The cutter width was at least three times the diameter of the largest particles in the stream to minimize the sampling error. Before sampling, a dummy sample was taken, and the sampler was emptied out before taking the proper sample.

Additionally, all the available information from the process control system was recorded during the sampling period. For two of the streams, sampling was repeated to find the standard deviation and ensure the quality of the sampling.

The survey samples were prepared according to the procedure shown in Figure 6. The sample preparation was started with weighting the samples in the wet and dry state (steps 2-4), followed by deagglomeration and splitting on a rotary splitter to produce subsamples for further sizing, ensuring there was 5 – 10kg per sample to assure sufficient coarser particles per sample (step 5). The pulp samples were dried at room temperature (3). The first split was stored for later usage (8), the second for bulk chemical analysis by X-ray fluorescence (XRF) (6) and the third for wet sieving (7) followed by drying. Sieving provided four particle size fractions: +125, -125+63, -63+38, -38 µm. Each size fraction from sieving (9) was split into two parts, one for an XRF analysis (11) and the other one for preparing resin mounts for optical and scanning electron microscopy.

30

1) Sampling 2) Sample weight

3) Drying sample4) Sample dry weight

5) Splitting

6) To bulk XRF analysis 7) Sieving 8) To storage

9) Splitting

10) To XRF analysis for size fractions

11) Resin mounts for size fractions

Figure 6. The schematic procedure of preparing survey samples for analysis.

Analytical methods and approaches 3.2

The analytical methods and approaches are structured separately, and each part is discussed in relation to the objective of the area.

3.2.1 Modal analysis Several types of iron ore samples were used to compare different methods of analyzing bulk mineralogy, i.e. mineral grades, to be applied in geometallurgy and process mineralogy. A new method called Combined EMC, and XRD (or shorter: Combined method) was developed in order to overcome some of the shortcomings in Element-to-Mineral Conversion and quantitative XRD by Rietveld analysis. Practically, the algorithm that was used for combined method can be applied for any other method of modal mineralogy to adjust the mineral grades to match closely with the chemical composition of given sample. Additionally, a model for describing precision and trueness in the analysis of mineral grades is presented. The model covers the whole grade range (0-100 wt%), is easy to use and informative.

Element-to-Mineral Conversion Based on the information available (elemental assays and chemical composition of minerals), mineral grades can be calculated by the non-negative least square method. However, here the system of linear equations is underdetermined by having twelve unknowns (mineral grades) and nine equations (reliable elemental assays and Satmagan). Therefore, mathematically this system of linear equations does not have a unique solution not even when the non-negativity constraint is added. Practically this means that mineral grades are calculated for nine phases and other phases, the solution gives zero grades.

Chemical analyses of the samples (Table 8) were done at chemical laboratory of LKAB using the company’s standardized methods. X-ray fluorescence spectrometry (MagiX FAST, PANalytical) was used for the eleven major and minor elements. Divalent iron was analyzed by the titrimetric method (ISO 9035:1989) and the mass proportion of magnetic material was measured with the Saturation

31

Magnetic Analyzer (Satmagan) model 135 (Stradling, 1991). A calibration of the Satmagan analysis was done to give similar results as with the titrimetric Fe2+ method; i.e. for a pure magnetite sample, the Satmagan value was 24.3%.

Table 8. Chemical analyses of samples as wt% by XRF and Satmagan (Sat.) method.

Sample Na Mg Al Si P K Ca Ti V Mn Fe Sat. (%)

1 0.16 0.72 0.68 2.5 0.21 0.26 0.8 0.318 0.138 0.039 64.7 21.6 2 0.00 0.52 0.17 1.1 0.17 0.04 0.4 0.042 0.049 0.085 68.5 14.5 3 0.00 0.52 0.06 0.1 0.07 0.00 0.1 0.024 0.052 0.093 70.9 17.1 4 0.00 0.50 0.17 0.8 0.37 0.03 0.8 0.078 0.050 0.070 66.2 6.5 5 0.00 0.51 0.05 0.0 0.03 0.00 0.1 0.018 0.052 0.093 71.2 17.2 6 0.00 0.16 0.12 3.6 0.40 0.03 2.6 0.018 0.026 0.101 62.8 3.1 7 0.00 0.28 0.14 4.9 0.76 0.02 4.6 0.024 0.022 0.101 56.0 0.3 8 0.00 0.13 0.10 4.1 0.35 0.01 3.7 0.024 0.025 0.101 59.1 0.5 9 0.00 0.52 0.22 7.0 1.73 0.05 7.3 0.030 0.020 0.132 46.3 0.7

10 0.00 0.23 0.12 4.6 0.48 0.02 4.2 0.024 0.025 0.108 57.3 0.5 11 0.00 0.27 0.13 5.1 0.80 0.03 4.9 0.024 0.025 0.116 55.4 0.6 12 0.04 1.30 0.46 4.8 0.10 0.26 1.2 0.246 0.192 0.050 59.0 21.1 13 0.01 0.95 0.18 2.9 0.45 0.05 1.3 0.192 0.192 0.053 63.0 21.5 14 0.36 1.50 1.17 6.6 1.17 0.10 5.1 0.078 0.071 0.084 47.9 16.2 15 0.26 2.07 0.95 6.7 0.97 0.31 3.5 0.120 0.082 0.053 49.3 16.6 16 0.75 2.82 3.72 19.7 0.24 0.69 2.7 0.186 0.017 0.039 21.3 7.3 17 0.05 2.32 2.48 12.3 0.02 1.54 1.2 0.168 0.039 0.085 39.6 12.0 18 0.37 1.34 1.05 4.8 0.66 0.52 3.0 0.360 0.088 0.093 56.6 18.1 19 0.01 0.17 0.11 0.5 0.06 0.07 0.8 0.126 0.110 0.070 70.0 23.9 20 0.30 0.69 0.71 3.3 0.41 0.34 1.7 0.240 0.097 0.077 62.3 20.1

* Margin of error (± 2δ) for XRF assays can be calculated by ±0.013 × √𝑥𝑥 where x is the elemental assay

X-ray powder diffraction The first trial of the X-ray powder diffraction analyses was done at Luleå University of Technology (LTU) using a PANalytical Empyrean X-ray diffractometer equipped with a copper tube, Pixel3D detector, and pyrolytic graphite monochromator. The 2θ range was from 5 to 75° with a step size of 0.02°. These conditions resulted in a total measurement time of 150 minutes for a single XRD scan. Mineral phases were identified using HighScore Plus Version 3 software package and the Crystallography Open Database (COD). In the Rietveld refinement background correction, scale factors, unit cells, preferred orientations, and profile variables were included.

X-ray diffraction and Rietveld refinement with a copper tube and monochromator on the iron ore samples led to underestimation of iron mineral phases (Parian and Lamberg, 2013). This was mainly due to microabsorption and also fluorescence radiation of the iron ore samples by copper tube (Villiers and Lu, 2015). Therefore, samples were reanalyzed at the Geological Survey of Finland (GTK) with PANalytical CubiX3 industrial XRD system equipped with Cobalt tube and X’Celerator detector. Phase identification and Rietveld refinement afterward were same as described previously.

Additionally, two of the samples were measured several times in Helmholtz-Institute for Resource Technology in Freiberg, Germany using PANalytical Empyrean, equipped with a Cobalt tube, monochromator, and Xe proportional counter detector. The step width and 2θ range were same as previous measurements. The Rietveld refinement of these data was done by BGMN (BGMN by

32

Bergmann et al., (1998)) and these data are used for estimating error for X-ray diffraction and Rietveld refinement.

Automated mineralogy A Merlin SEM - Zeiss Gemini (FESEM, Luleå University of Technology, Sweden) with Oxford Instrument EDS detector and IncaMineral software was used for automated mineralogy analyses. The IncaMineral system combines backscattered detector images with EDS information in the analysis of automated mineralogy (Liipo et al., 2012). Within the IncaMineral software, the raw analysis data is stored in a database, and mineral identification and quantification can be done either during analysis or retrospectively. To obtain a reliable estimate, the number of particles analyzed for the mineral quantification was at least 10,000. In this study, mineral identification was done based on back-scattered information and EDS analysis. Developed software at the Luleå University of Technology (by author) was used for post-processing the data i.e. mineral identification, reporting mineral grades and chemical composition of a sample.

To confirm IncaMineral results quality, two resin mount samples were analyzed at the geometallurgy laboratory, Technical University of Freiberg by Mineral Liberation Analyzer (MLA) system, which was equipped with FEI Quanta 650F and two Bruker Quantax X-Flash 5030 energy-dispersive X-ray spectrometers.

The automated mineralogy analysis provided a mineral list, which includes more than 15 phases. In some of the samples, even several types of one mineral were found, e.g. several amphiboles. For geometallurgy, this is not practical, and some simplification is necessary. The simplification is also required for comparing the methods. Therefore, the main phases in the samples were classified into groups of albite (Ab), actinolite (Act), apatite (Ap), biotite (Bt), diopside (Di), orthoclase (Or), quartz (Qtz), andradite (Adr), scapolite (Scp), calcite (Cal), magnetite (Mgt) and hematite (Hem). In the grouping of the minerals and the selection of group representer, the similar behavior of the minerals in the iron processing plant, the similarity in their chemical compositions, and abundance of the mineral in the group were considered to streamline application and evaluation of the methods. For example, a group of actinolite consists of various amphibole minerals such as tremolite, actinolite, and hornblende. The chemical compositions of the minerals (Table 9) were provided by LKAB and partly taken from a previous study from LKAB’s mine in Malmberget (Lund, 2013). Analysis of mineral chemistry, in those studies, was carried out at the Geological Survey of Finland (GTK) using a CAMECA SX100 electron microprobe equipped with five WDS. This information was also verified by automated mineralogy as the IncaMineral system provides the chemical composition of each analyzed grain and based on that an average composition of each phase can then be approximately calculated.

33

Table 9. The chemical composition of minerals (“the mineral matrix”) as wt%.

Mgt Hem Qtz Ap Cal Ab Bt Act Di Adr Scp Or

C % 0.00 0.00 0.00 0.00 12.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 O % 27.42 30.14 53.24 39.32 50.83 50.06 43.61 47.89 44.12 42.71 50.19 49.69 F % 0.00 0.00 0.00 3.72 0.00 0.00 0.00 0.00 0.11 0.00 0.00 0.00

Na % 0.00 0.00 0.00 0.00 0.00 5.11 0.02 0.02 0.00 0.00 7.35 0.11 Mg % 0.01 0.00 0.00 0.07 0.00 0.00 10.26 10.09 7.68 0.71 0.00 0.13 Al % 0.05 0.03 0.00 0.00 0.00 10.78 6.91 0.99 0.12 0.20 9.66 8.01 Si % 0.00 0.00 46.72 0.00 0.00 33.98 19.60 25.30 24.92 10.20 23.76 27.39 P % 0.00 0.00 0.00 16.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 Cl % 0.00 0.00 0.00 0.28 0.00 0.00 0.00 0.00 0.00 0.00 2.03 0.01 K % 0.00 0.00 0.01 0.00 0.00 0.00 6.55 0.11 0.00 0.00 0.41 14.39

Ca % 0.00 0.00 0.01 40.39 37.17 0.04 0.00 7.55 15.58 22.31 6.20 0.09 Ti % 0.05 0.20 0.00 0.00 0.00 0.01 2.24 0.01 0.00 0.15 0.00 0.00 V % 0.04 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Mn % 0.00 0.00 0.00 0.00 0.00 0.01 0.04 0.04 0.01 0.01 0.00 0.00 Fe % 72.43 69.56 0.02 0.16 0.00 0.01 10.77 8.00 7.46 23.71 0.40 0.17

Sat. % 24.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Combined method The combined EMC-XRD method originated to overcome limitations of EMC and XRD. It takes mineral grades by the Rietveld analysis as an initial estimate and changes mineral grades to minimize the following function:

= − ×( )f x b A x (35)

where

b : The vector of chemical composition of the sample A : The matrix of chemical compositions of minerals x : The vector of mineral grades, i.e. unknown to be solved

The absolute minimum of f(x) would be the results of simple Element-to-Mineral Conversion method by the methods described before (e.g. NNLS). However, finding a local minimum of f(x) close to the original Rietveld values was found to be a more appropriate solution, and therefore the Levenberg-Marquardt algorithm (Bates and Watts, 1988) was used in the combined method. Additionally, the algorithm can be applied to adjust mineral grades results from other methods to agree with the chemical composition of the sample.

Optimizing functions in MATLAB were used for an advanced combination of XRD and XRF data for solving the mineral grades. This is referred to as the combined EMC-XRD method.

Error analysis Trueness is defined as “the closeness of agreement between the expectation of a test result or measurement result and a true value” whereas precision is the repeatability (or reproducibility) of the measurement method. Accuracy means “closeness of agreement between a measured quantity value and a true quantity value of a measurand” (Reichenbächer and Einax, 2011). According to The International Vocabulary of Basic and General Terms in Metrology (VIM), accuracy is a qualitative concept and commonly regarded as a combination of trueness and precision. The trueness and

34

precision are normally expressed in terms of bias and standard deviation, respectively (Menditto et al., 2007). To validate a method result correctly, both terms must be considered.

Commonly standards or artificially mixed samples are used for evaluating the trueness. For the analysis of mineral grades, standards are not commonly available. As this study aims to assess different analysis methods of mineral grades for practical geometallurgy, the usage of a synthetic sample was avoided. Synthetic samples would not represent the original textures, complexity, and variation existing in natural specimens. Moreover, using synthetic samples would lead to underestimating the error in the analysis of ore samples in practice.

The alternative way to evaluate the trueness is to compare against a valid reference. However, the references such as XRF analysis for chemical analysis or SEM-based automated mineralogy for mineral grades cannot be regarded as true values. Therefore, when using these references for the estimation of the trueness, which is now unknown, instead of the term trueness the term closeness was selected to evaluate how close the results are compared to the references.

Here, the precision of the methods is addressed by the standard deviation. The estimate of the standard deviation is done by replicate samples and replicate analyses. Repeating only the measurement gives the repeatability and repeating the sample preparation and measurement gives the reproducibility. In this study, the standard deviation calculated for XRF and quantitative XRD by Rietveld analysis is a measure of reproducibility, while for automated mineralogy it is a measure of repeatability.

Based on bootstrapping technique Evans and Napier-Munn (2013) suggested that the standard deviation in an analysis of mineral grades is proportional to the square root of the total area of particles measured. Moreover, they conclude that the model reflects the relationship between standard deviation and number of particles measured. Similarly, the standard deviation of an estimated mineral grade can be calculated with the formula (Evans and Napier-Munn, 2013; Mann, 2010):

σ =

pqN

(36)

where

σ : The standard deviation p : The measured mineral grade q : is the value of −(1 )p N : The number of particles measured

Comparatively, the relationship between relative standard deviation and average mineral grade can be modeled as:

−= 0.5RSD ax (37)

where

RSD : The relative standard deviation a : Coefficient x : The grade of mineral of interest

35

The formula suggests that the relative standard deviation is proportional to the square root of the grade. This model was used in the following to estimate the (relative) standard deviation of the measurements for any mineral grade.

The measurement of the closeness is challenging. The paired t-test is often used for comparing two methods (e.g. Benvie et al., 2013). However, the t-test can be used to compare whether two methods give the same average value, but it does not provide an easy way for estimating the magnitude of the differences respect to a reference method. Nevertheless, the t-test was not completely rejected, and it was used to validate the comparison of methods in two ways; by comparing mineral grades and back-calculated elemental grades against references. The selected references for evaluating mineral grades and chemical composition analyses were SEM-based automated mineralogy and XRF analysis, respectively.

For the measuring of closeness, a Root-Mean-Square-Deviation (RMSD) was used besides the t-test (Hyndman and Koehler, 2006). Principally, RMSD aggregates the magnitude of deviations from the reference value into a single value. Mathematically, it is a concept similar to the standard deviation, but the term is used to describe an average deviation from the reference. This is used as the degree of closeness and is expressed as follows:

µ

=

−=∑ 2

1

( )n

ii

xRMSD

n

(38)

µ= ×100

RMSDRELATIVE RMSD

(39)

where

n : The number of measurements µ : The reference value

ix : The measured value µ : The average of the reference values

The Relative RMSD can be calculated for each mineral and element with different methods. The method showing smallest variation around the reference value (i.e. a lower RMSD) is regarded as the closest to the reference.

3.2.2 Ore textural analysis Routine analysis of ore textural samples is affected by required details, image resolution, time and cost of analysis. Optical and SEM-based automated mineralogy are the common methods of obtaining ore textural image. The image is usually treated by image processing tools to extract textural and mineralogical information.

Here, ore textural analysis was performed in optical and scanning electron microscopy. The aim was to analysis particulate and intact rock samples to generate the mineral map. Afterward, the mineral map was used for retrieving textural attributes and liberation. Therefore, for eight drill cores, mineral maps were created for intact ore and particulates samples after crushing. Crushed sample sieved and sized in 1.68-3.35 mm, 0.85-1.68 mm, 0.43-85 mm and 0.30-0.43 mm size fractions. Measurement of below 0.30 mm size fraction was skipped due to the high liberation of minerals in all samples.

36

Image acquisition Image acquisition of ore texture was performed by mosaic capturing of field images by automated stage optical microscopy (Zeiss Axio Imager) and SEM backscatter detector (AZtec - Zeiss Merlin). The whole image of the samples was made by stitching field images using built-in programs. Minerals relating to specific gray level in backscatter image were identified by EDS analysis of the phases at that gray level. This data was used later in assigning phases in mineral maps.

Image processing Image processing is a rapidly advancing area of retrieving information from images. The technique is used to classify objects in the image (such as grains, particles or phases) and retrieve a broad range of features. In an ore textural study, captured images are used for phase discrimination, calculation of object shape factors, mineral grades, and the association between phases. In this study, image processing sequences including phase discrimination, object separation, feature extractions were done by writing code in MATLAB. The code can analyze ore texture and particulate samples to give numeric ore textural features and liberation. The extension of the code can generate particle population from ore texture by defining breakage pattern and particle size distribution.

Phase separation Phase separation began by assigning multiple threshold values according to a range of gray levels corresponding to each phase. The image pixel values matching each threshold interval were assigned a new value representing a phase. In particulate samples, the epoxy region was assigned a zero value for simpler processing of objects during imaging processing.

Composition and liberation Obtaining a mineral map of ore texture or particulate sample facilitates the calculation of mineral grades and liberation. Commonly, the area of each phase (number of pixels occupied by the phase) in a particle or whole texture are calculated to obtain information on the composition of the particle. To convert this value to weight percentages, the density of the minerals is used as weight factors in the calculation of composition.

The other important factor that can be useful in characterizing breakage and also relevant in some aspect of mineral processing (such as flotation and leaching) is liberation by exposed surface area of particles. In each particle, this is calculated by normalizing measured shared boundary between phases and background (epoxy).

Mineral association Association of minerals can be estimated based on the proportion of minerals in the particles. However, this approach for the intact ore texture only gives mineral grades of texture. Therefore, an alternative method is to calculate the interfacial surface area between minerals in the intact ore texture or particle as an indication of association.

An image can be considered as a matrix of pixel values. An easy and straightforward way of estimating the association in the image is using co-occurrence matrix. A mineral map with n phases (n pixel values) will have n × n size co-occurrence matrix. Each cell of the matrix, C(i,j), is correspondence to the number of times that the cell i is situated with cell j in the defined offset. Here, for calculation of association, the co-occurrence matrix is the sum of cell values for 0-360° in intervals of 45° (Figure 7).

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315°

0°

45°90°135°

270°225°

180°

Figure 7. The schematic matrix of pixels showing different orientations for offsets.

For example, for a simple case with three-pixel values as below with one-pixel distance offset, the corresponding co-occurrence for different orientation is as Table 10.

1 2 3

Figure 8. An image matrix with three cell values.

Table 10. Table of co-occurrences, showing the abundance of co-occurrence cells in different orientations for Figure 8.

Co-occurrence 0° 45° 90° 135° 180° 225° 270° 315° Sum 1-1 2 1 3 0 2 1 3 0 12 1-2 2 3 3 3 2 1 4 4 22 1-3 3 1 0 1 1 3 1 3 13 2-1 2 1 4 4 2 3 3 3 22 2-2 4 1 2 1 4 1 2 1 16 2-3 2 4 2 1 2 1 1 1 14 3-1 1 3 1 3 3 1 0 1 13 3-2 2 1 1 1 2 4 2 1 14 3-3 2 1 4 2 2 1 4 2 18

Therefore, the co-occurrence matrix for Figure 8 is:

=

12 22 1322 16 1413 14 18

C

(40)

The co-occurrence matrix can be normalized to give an indication of association based on the abundance of a phase interfacial in the sample. This can be done by normalizing non-diagonal cells, row or column wise. This is called Association Indicator Matrix (AIM). For example, for above example, AIM is:

=

0 62.9 37.161.1 0 38.948.1 51.9 0

CAIM

(41)

The non-diagonal values are the association indicators. For the above example, phase one has 62.9% association with phase two and 37.1% with phase three. In the particles, the exposed surface of

38

particles may consider in the calculation. This can be done by including the background (epoxy) as another phase. This also makes the calculation of the surface exposure of minerals straightforward.

Limitations The optical image was planned to be used for discrimination of hematite and magnetite in the samples. Even though hematite and magnetite could be distinguished easily in the optical image, imperfect image stitching by built-in programs lead to incorrect registration of image objects (Figure 9). Additionally, uncorrected uneven illumination in the image fields presented another obstacle in the image processing of the data (Figure 10). These problems could have been fixed by correcting uneven illumination in the field images as well as aligning field images in a correct way. However, AZtec system for capturing backscatter images does not provide an easy way to access field images.

Figure 9. Imperfect image registration. Optical image (left), BSE image (middle), Blend of Optical and BSE images (right).

Figure 10. Uneven illumination effect in the stitched images (left side optical image, right side BSE image).

3.2.3 Model development and simulation framework

Wet Low-Intensity Magnetic Separator (WLIMS) model development Chemical analyses of the plant survey samples were done at the chemical laboratory of LKAB. The data was used as a quick sanity check to evaluate the quality of modal mineralogy by automated mineralogy. Epoxy samples on size fractions were prepared at the Kemi University of Applied Science. Scanning electron microscopy (SEM) and automated mineralogy analysis on epoxy samples were done by using a Merlin SEM (FESEM - Zeiss Gemini) with Oxford Instrument EDS detector at Luleå University of Technology, Sweden.

On average, more than 20,000 particles were measured in each size fraction, which sums up to around 300,000 particles in three streams around primary magnetic separator. Identifying of minerals, reporting of mineral grades and back-calculating of chemical compositions were done by post-

39

processing the raw data (software developed by author). The mineral list shown in Table 11 was used as the reference for the program and back-calculation of the chemical composition of samples. The chemical composition of minerals was taken from Lund et al. (2013) and verified by EDS analysis.

Mass balancing, data reconciliation, particle tracking, LIMS modeling were done using the modeling and simulation software HSC Chemistry 9 by Outotec and MATLAB by Mathworks.

Table 11. Average chemical composition of minerals (“the mineral matrix”) as wt% and their specific gravity (g/cm3).

Magnetite Quartz Apatite Biotite Albite Actinolite Calcite Titanite Ti-magnetite Anhydrite

Mgt Qtz Ap Bt Ab Act Cal Ttn Ttn-Mgt Anh

F % 0.00 0.00 3.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00

S % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 23.55

Na % 0.00 0.00 0.00 0.02 5.11 0.02 0.00 0.00 0.00 0.00

Mg % 0.01 0.00 0.07 10.26 0.00 10.09 0.00 0.00 1.94 0.00

Al % 0.05 0.00 0.00 6.91 10.78 0.99 0.00 0.00 2.60 0.00

Si % 0.00 46.72 0.00 19.60 33.98 25.30 0.00 14.32 0.02 0.00

P % 0.00 0.00 16.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00

K % 0.00 0.01 0.00 6.55 0.00 0.11 0.00 0.00 0.00 0.00

Ca % 0.00 0.01 40.39 0.00 0.04 7.55 37.17 20.44 0.00 29.43

Ti % 0.05 0.00 0.00 2.24 0.01 0.01 0.00 24.41 12.95 0.00

V % 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Mn % 0.00 0.00 0.00 0.04 0.01 0.04 0.00 0.00 0.71 0.00

Fe % 72.43 0.02 0.16 10.77 0.01 8.00 0.00 0.00 49.44 0.00

S.g.* 5.2 2.7 3.2 2.9 2.6 3.0 2.7 3.6 5.2 3.0 *Specific gravity

Simulation framework The flowsheet was drawn in HSC Chemistry 9.1 Sim module and is used to demonstrate different levels of modeling according to Table 5. The newly made particle-based WLIMS model was also adapted in HSC Chemistry 9.1 Sim to be used for the simulation.

40

41

Chapter 4 - Developing a quick and inexpensive technique for reliable modal analysis

Introduction 4.1

Reliable analysis of mineral grades is a crucial part of resource characterization, process mineralogy, and geometallurgy. It is a prerequisite for deportment analysis, mineralogical mass balancing and modeling and simulation of mineral processing circuits. Recently, automated mineralogy has become the major method for the analysis of mineral grades. In geometallurgy, however, the method is far too expensive and time demanding. When there is a need for assaying mineral grades in thousands of ore samples, sizing to narrow size fractions is necessary, and the total number of samples for the analysis becomes enormous. Therefore, an alternative method is needed for better value. In the following results from different modal analysis methods obtained and compared.

Analysis of mineral grades in the iron ore samples 4.2

In iron ores, it is essential to have a good estimate of the magnetite-hematite ratio since this ratio defines the concentration technique used and in Malmberget iron operations it determines the process line the ore is fed into (Alldén Öberg et al., 2008). Furthermore, in Kiruna iron operations the apatite grade is used to classify the iron ores (Niiranen and Böhm, 2012). The phosphorous content of the final concentrate is a quality criterion; for instance, in the Low Phosphorous Sinter Feed (MAF) the maximum acceptable grade is 0.025% P (LKAB, 2014).

From a geometallurgical point of view, magnetite, hematite, and apatite are the most significant minerals in the iron operations in Northern Sweden. The analytical results for these minerals by different methods are compared in Table 12. It should be noted for the magnetite grade by EMC, Satmagan analysis was used while this was not used in the combined method. Distinguishing magnetite and hematite in automated mineralogy is challenging and requires careful and precise setting (Figueroa et al., 2011). For apatite, the detection limit of XRD can be as low as one wt%. However, the combined method should allow overcoming this limit by considering XRF analysis.

Having a good estimate of the gangue silicate minerals in the ore is crucial considering that silica is one of the quality requirements for an iron concentrate. The main silicate minerals in the samples are albite, actinolite, and biotite. Iron-bearing garnet, i.e. andradite, is found with calcite in certain deposits (Frietsch, 1980). Accessory and trace silicate minerals include scapolite, diopside, orthoclase and quartz. The silicate minerals are normally not considered when classifying the ores of LKAB (Niiranen and Böhm, 2012). However, the silica content of the final product must be below certain values, e.g. for Low Phosphorous Sinter Feed (MAF), the limit is 0.80% SiO2 (LKAB, 2014). Adolfsson and Fredriksson (2011) observed that silica content in the concentrate does not directly correlate with the silica grade in the ore. This refers to that the silicate minerals do not all behave in the same way in iron ore processing. For example, biotite tends to be enriched in fine particle sizes (Westerstrand, 2013) where the separation efficiency in concentration is poor, while andradite can end up to concentrate if the magnetic separator is not properly tuned.

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Table 12. Analysis of mineral grades for the most significant minerals: magnetite, hematite, and apatite.

Sample Magnetite (wt%) Hematite (wt%) Apatite (wt%)

EMC XRD CMB EMC XRD CMB EMC XRD CMB AM

1 88.57 89.6 88.27 0.00 0.0 0.05 1.24 0.0 1.25 1.1 2 60.12 74.6 72.43 35.30 24.6 22.50 0.43 0.0 0.41 0.34 3 70.90 78.9 78.17 27.92 21.1 20.39 0.25 0.0 0.11 4 26.95 29.4 27.84 66.63 67.2 65.66 1.65 1.2 1.64 5 71.31 79.9 79.38 27.97 20.1 19.60 0.19 0.0 0.08 0.01 6 12.86 12.0 15.09 76.71 69.4 72.10 2.36 3.0 2.35

7 1.25 0.0 1.06 78.88 74.4 75.22 4.49 4.5 4.48 2.39 8 2.08 0.0 0.84 82.64 79.8 80.50 2.07 2.1 2.07

9 2.91 0.0 0.90 62.92 60.3 60.88 10.22 11.7 10.21 10.46

10 2.08 0.0 2.70 79.94 72.3 74.60 2.84 2.8 2.44 3.17 11 2.49 0.0 1.58 76.73 72.6 73.84 4.73 4.1 4.72

12 81.18 85.1 79.79 0.00 0.0 0.05 0.57 0.0 0.60 13 86.44 84.6 85.17 0.00 0.0 0.79 2.08 2.2 2.14 14 64.89 66.2 64.01 0.00 0.0 0.00 6.90 5.2 6.92 15 66.27 66.6 65.60 0.00 0.0 0.07 5.43 4.7 5.56 16 26.75 27.8 25.62 0.00 0.0 0.00 1.40 0.0 1.42 17 49.76 49.3 50.53 1.14 0.0 0.67 0.11 0.0 0.11 18 75.04 78.0 76.36 0.12 0.0 0.02 3.89 3.5 3.88 2.97 19 96.87 98.3 96.39 0.00 0.0 0.02 0.35 0.0 0.35 0.14 20 83.33 82.2 83.26 1.43 0.0 1.81 2.41 2.3 2.42

EMC: Element-to-Mineral Conversion, XRD: Quantitative XRD by Rietveld analysis, CMB: Combined EMC-XRD, AM: SEM-based automated mineralogy Considering iron ore processing, biotite, andradite and silicate minerals have significance. EMC underestimates the biotite and andradite grade (Table 13). This is due to the presence of many silicate minerals and the lack of enough assay variables to estimate them correctly. Comparing to automated mineralogy results, in some samples, the Rietveld analysis overestimated the biotite grade which could be due to preferred orientation and partly very low content resulting in high relative errors (Kleeberg et al., 2008). On the other hand, all methods gave more or less similar grades for other silicate mineral estimations, i.e. the sum of albite, actinolite, diopside, quartz and scapolite.

Table 13. Analysis of mineral grades for biotite, andradite and other silicates, which includes scapolite, diopside, orthoclase, and quartz.

Sample Biotite (wt%) Andradite (wt%) Other silicates (wt%)

EMC XRD CMB AM EMC XRD CMB AM EMC XRD CMB AM

1 4.32 1.4 4.75 1.63 0.00 0.0 0.18 0.08 5.27 9.0 5.08 7.04 2 1.14 0.8 1.72 0.16 0.00 0.0 0.08 0.04 3.49 0.0 2.75 0.19 3 1.07 0.0 0.35

0.00 0.0 0.07

0.16 0.0 0.60

4 1.39 1.7 2.05

0.00 0.0 0.00

2.24 0.5 1.78

5 0.86 0.0 0.29 0.09 0.00 0.0 0.04 0.02 0.00 0.0 0.46 0.02 6 0.00 0.0 0.00

0.00 7.1 6.81

8.40 7.3 6.76

7 0.00 0.0 0.00 0.72 0.00 12.1 11.58 17.08 11.81 8.0 8.89 10.49 8 0.00 0.0 0.00

0.00 10.3 10.30

9.42 6.1 6.82

9 0.00 0.0 0.92 0.92 0.00 13.3 12.31 15.04 17.34 13.2 13.58 12.98

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Sample Biotite (wt%) Andradite (wt%) Other silicates (wt%)

EMC XRD CMB AM EMC XRD CMB AM EMC XRD CMB AM

10 0.00 0.6 0.00 0.36 0.00 16.2 14.19 15.05 10.92 8.1 7.25 6.88 11 0.00 0.0 0.00

0.00 12.1 11.53

12.13 9.7 9.26

12 0.00 2.3 4.74

0.00 0.0 0.05

13.69 12.6 12.19

13 0.70 0.2 2.21

0.00 0.0 0.00

9.00 11.7 8.26

14 0.00 1.1 2.10

0.00 0.0 1.24

22.13 27.5 20.90

15 0.86 3.0 3.77

0.00 0.0 0.00

22.44 25.0 21.46

16 4.65 13.3 11.53

0.00 0.0 0.51

54.62 58.7 51.69

17 14.28 31.4 21.78

2.32 0.0 0.55

22.97 13.4 18.48

18 7.95 4.9 8.33 3.73 3.83 0.0 0.00 0.38 10.27 10.8 10.48 8.21

19 0.00 0.0 1.14 0.34 0.00 0.0 0.05 0.12 0.93 0.0 0.78 0.42

20 5.06 1.0 4.84 1.02 0.0 0.23 7.26 13.3 7.31 EMC: Element-to-mineral conversion, XRD: Quantitative XRD by Rietveld, CMB: Combined EMC-XRD, AM: SEM-based automated mineralogy

Developing a grade-based error model 4.3

4.3.1 Precision of the analyses Repeats and replicates were used for estimation of the standard deviation of the analyses. For establishing the error model for precision, the relative standard deviation against mineral grade was fitted with equation (37). In principle, the error model gives the coefficient of variation (i.e. relative standard deviation) for the mineral grade of interest (Figure 11). In general, a good fit between experimental data and model equation was achieved. Comparatively, the precision of the methods from the best to the worst are: 1) SEM-based automated mineralogy, 2) Element-to-Mineral Conversion, 3) quantitative XRD with Rietveld for simple mineralogy, 4) combined EMC-XRD, and 5) quantitative XRD with Rietveld for complex mineralogy. This means, for example, for an average ore sample with 70% magnetite (or hematite) the precision of the methods (i.e. uncertainty in 95% confidence level) vary from ±0.57 to ±3.68 wt%. This can be regarded as acceptable in geometallurgy. On the other hand, for average ore grade of 1 wt% such as apatite and biotite, the coefficient of variation is between 4 and 22% (standard deviation 0.04-0.22 wt%). The error is high for technical work like resource estimation or process mineralogy (Pitard, 1993) but the analysis quality is still good enough for geometallurgical purposes like domaining where acceptable error can be higher.

44

Figure 11.Relative standard deviation against mineral grades (CMB, AM, XRD). Curves for different methods derived from

replicates and repeats. For Element-to-Mineral Conversion (EMC) and combined method (CMB) curves were generated using Monte Carlo simulation. For calculating the relative standard deviation of combined method, relative standard deviation of

XRD with complex mineralogy was used. The dashed vertical line at 1% mineral grade shows the detection limit of XRD.

4.3.2 Closeness of the analyses For quality control, two resin mounts analyzed by IncaMineral were also analyzed by Mineral Liberation Analyzer (MLA). Comparing analyzed minerals by IncaMineral against MLA analysis (Table 14), mineral grades by IncaMineral are close to MLA mineral grades, which suggest that the two methods are giving similar results.

Table 14. Comparing mineral grades by IncaMineral (INCA) system and Mineral Liberation Analyser (MLA) system. For INCA 95% confidence interval is given.

Fe oxide (wt%) Apatite (wt%) Biotite (wt%) Andradite (wt%) Other silicates (wt%)

MLA INCA MLA INCA MLA INCA MLA INCA MLA INCA

A 89.90 89.83±0.68 1.12 1.01±0.07 1.74 1.51±0.09 0.00 0.07±0.02 6.38 6.82±0.19

B 77.53 77.68±0.63 3.62 3.33±0.13 1.95 1.43±0.09 0.00 0.06±0.02 16.32 17.14±0.30

Automated mineralogy analysis results were used as the reference values when comparing closeness of the methods. The paired t-test implies that XRD, combined EMC-XRD, and EMC do not give significantly different results compared to automated mineralogy (Table 15). On the other hand, relative RMSD shows that the difference between the automated mineralogy and EMC is relatively higher than that of the other methods (Figure 12 and Table 15). Relative RMSD reveals that XRD results for iron oxide are closest to automated mineralogy while paired t-test suggests XRD results are slightly positively biased.

100

101

102

0

10

20

30

40

50

60

70

Mineral grade (wt%)

Rel

ativ

e st

anda

rd d

evia

tion

(%)

EMC: y=5.23x-0.5

CMB: y=10.56x-0.5

XRD (Simple): y=8.97x-0.5

XRD (Complex): y=21.79x-0.5

AM: y=3.64x-0.5

45

Figure 12. Relative RMSD against mineral grades (EMC, XRD, CMB). Curves for different methods derived from fitting

calculated RMSD for experimental data.

Table 15. The closeness of analysis methods for mineral grades by paired t-test and RMSD against automated mineralogy as the reference.

t value RMSD

XRD CMB EMC XRD CMB EMC Fe oxides 2.82* 1.81 2.20 4.77 6.31 8.76 Apatite -0.07 -0.52 -0.31 1.80 1.56 1.54 Biotite 0.56 1.53 1.49 0.79 1.59 1.74

Andradite -1.38 -2.06 -2.21 1.74 2.12 9.64 Other silicate -0.16 0.63 2.20 1.63 1.61 2.41

t critical ±2.26 ±2.26 ±2.26 * Absolute value of t is greater than critical value indicating statistically significant difference in results between automated mineralogy and the method

The alternative way of evaluating closeness was by regarding XRF analysis as the reference value and comparing back-calculated chemical compositions of the samples against it. Paired t-test results suggest that combined EMC-XRD and EMC methods give significantly different mean values for the chemical composition (Table 16). However, relative RMSD indicates all the methods in terms of deviations from XRF assays are in the same range (Figure 13). In other words, the deviation from the true (i.e. reference) value in all the methods is about equal.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Mineral grade (wt%)

Rel

ativ

e R

MS

D (%

)

EMC: y=110x-0.5

XRD: y=56.48x-0.5

CMB: y=76.76x-0.5

46

Figure 13. Relative RMSD against elemental grades (AM, EMC, CMB, XRD). Curves for different methods derived from fitting

calculated RMSD for experimental data.

Table 16. The closeness of analysis methods for elemental grades by paired t-test and RMSD against XRF analysis as the reference.

Chemical Assays t value by paired t-test RMSD

XRD CMB EMC AM XRD CMB EMC AM Na 1.39 1.27 -0.36 2.85* 0.35 0.13 0.03 0.15 Mg -2.75* -2.07 -3.43* -1.06 0.36 0.14 0.15 0.37 Al 0.86 -0.34 2.17* 1.34 0.47 0.06 0.05 0.28 Si 2.40* 2.03 1.48 0.42 0.92 0.05 0.06 1.01 P -3.69* -5.52* -5.40* 0.40 0.14 0.06 0.05 0.29 K -0.06 4.35* -0.23 0.25 0.26 0.05 0.01 0.12

Ca -0.94 2.72* 1.77 0.81 0.60 0.02 0.02 1.05 Ti 0.78 1.75 -0.22 5.18* 0.18 0.13 0.12 0.19 V -2.19* -2.17* -2.03 -1.52 0.06 0.06 0.07 0.04

Mn -12.97* -12.80* -13.60* -8.97* 0.08 0.08 0.08 0.08 Fe -0.19 -1.17 2.57* -1.42 1.91 0.01 0.15 3.40

Satmagan 0.47 0.12 -2.67* 1.12 1.09 0.47 t critical ±2.09 ±2.09 ±2.09 ±2.26

* The absolute value of t is greater than the critical value indicating statistically significant difference between analyzed chemical composition (XRF) and back-calculated composition from the mineral composition.

Discussion on results of combined method and application of grade-based error 4.4model

Quantitative X-ray diffraction with Rietveld analysis has been proposed as a quick mineralogical method for geometallurgy. Challenges in the method are the detection limit and general doubts about its precision and trueness when there is complex mineralogy. Partially, these challenges can be overcome by proper sample preparation (Pederson et al., 2004). For iron ores, when there are significant variations in the grade of iron oxide, phyllosilicate, and minor phases in the samples, sample preparation needs to be adapted carefully for different grade ranges. Additionally, to obtain

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Elemental grade (%)

Rel

ativ

e R

MS

D (%

)

AM: y=26.03x-0.5

EMC: y=21.57x-0.5

CMB: y=24.74x-0.5

XRD: y=38.38x-0.5

47

best results from Rietveld refinement, the radiation source, the effective particle size to minimize micro-absorption, and the proper way of filling sample holder to minimize preferred orientation must be sensibly selected. When aiming for a practical solution in this study, not all these conditions were optimum.

A combined method using weighted values (Berry et al., 2011; Roine, 2009) provides an alternative to adjusting mineral grades to match the Rietveld analysis results and chemical assays, but its problem is how to define the weighting factors in order to get reliable results. Weighting factors can be set based on the uncertainties of the elemental and mineral grade, but still, this approach cannot overcome limitations such as XRD detection limit and high relative error in low mineral grades. The combined EMC-XRD method developed here does not use weighting factors but can still find the closest solution to match both the Rietveld analysis results and chemical assays. Knowing the error model, more constraints can be established for estimating mineral grades by combined method.

Any technique for the analysis of mineral grades in a geometallurgical program requires careful mineralogical study before the method is routinely applied. In combined method, the mineralogical study must provide information on the list of all possible minerals, their crystal structure, and their chemical composition. Additionally, to be able to apply the combined method, the minerals need to be grouped in a sensible way, i.e. groups consist of minerals with similarity in chemical composition as well as process behavior. Therefore, nature of the ore body and the process define the grouping of minerals, acceptable error, and eventually the method to be used.

However, combined method is not a universal solution for every situation. Principally, the algorithm for estimating mineral grades can take as many restrictive constraints as needed. Therefore, if several minor minerals are present in the sample but the information for calculating mineral grades is insufficient, the combined method requires additional constraints to converge to the optimal solution. In addition, the assumption used here is that the chemical composition of minerals is known and does not vary. Strictly speaking, this is not a realistic assumption, but it simplifies the complex situation for finding a bridge between elemental assays and mineral grades.

It is relatively rare to find error estimation for the analyses of mineral grades published in the literature and research reports. For quality control, the back-calculated chemical composition is often plotted against the analyzed ones (e.g. Berry et al., 2011; Hestnes and Sørensen, 2012). As these illustrations visualize the quality, they do not quantify how big the difference is. Paired t-test is used, but as was shown in the results, it fails in measuring how close the results are. In addition, it requires that standard deviations be equal and not dependent on the grade, which is an unrealistic assumption. Relative RMSD is an informative and efficient way of measuring the closeness. The calculation is similar to the standard deviation, which makes it straightforward and portable for several purposes like mass balancing and modeling.

The precision and degree of trueness of analysis for mineral grades are dependent on the abundance of a phase in a sample and the number of observations (counts) collected. In automated mineralogy, this depends on the number of particles and grains analyzed. In X-ray techniques (X-ray diffraction and X-ray fluorescence), the ratio of signal to noise, thus analysis time, plays the role. Here a simple equation was used to describe the standard deviation and the RMSD in the wide grade range where analysis conditions are the same as commonly used in process mineralogy. This approach is practical when individual standard deviations are needed for measurements. Examples of such problems are circuit mass balancing and Monte Carlo simulations.

48

The methods available for obtaining mineral grades either directly (such as quantitative XRD by Rietveld analysis and automated mineralogy) or indirectly (EMC and combined EMC-XRD) have different advantages and disadvantages. Table 17 summarizes the different methods and their applicability in geometallurgy. To be used for metallic ores, the detection limit must be lower than one wt%, which excludes XRD. In geometallurgical programs, the number of samples to be analyzed during developing a deposit model is high, several thousand in a year. Therefore, the requirements for sample preparation and analysis time and costs exclude the usage of automated mineralogy as a routine tool for the analysis of mineral grades in geometallurgy. Even though Element-to-Mineral Conversion has excellent repeatability, it suffers from poor trueness in most of the real geometallurgical cases. This is due to a larger number of unknowns (minerals) than known quantities (chemical elements assayed) which makes the system mathematically underdetermined. Hence, the combined method fulfills the requirements to be used in ore characterization and deposit modeling for geometallurgy.

The problem remaining is that with all methods the back-calculated chemical composition does not match perfectly with the chemical assays of the commodity elements. This makes adoption of mineral grades challenging as resource geologists and metallurgist have a long tradition to work with chemical assays, they find it difficult to take parallel mineralogical information that is not entirely consistent with chemical assays. Weighting can be a solution for that, but more work is needed to establish solid grounds for defining the weighting factors and controling that weighing does not cause the mineral grades to drift too far away from the true mineral composition. For a selection of the best possible option further information regarding practical considerations such as sample preparation, costs, detection limit, and the information that method offers are necessary (Table 17).

Table 17. Comparison of different methods for obtaining mineral grades.

Parameter XRD with Rietveld Automated Mineralogy EMC** Combined

Detection limit (wt%) 1 0.01 0.01 0.01 Sample preparation time (minutes)

45 480 0 45

Analysis time (minutes) 90 240 0 90 Cost (approximate, US$) 60 200 0 60 Experienced operator needed Yes Yes No Yes

Experienced mineralogist needed

Yes Yes Yes Yes

Precision* 9.0-21.8 3.6 5.2 10.6 Closeness (against XRF)* 38.4 32.5 21.6 24.7 Closeness (against AM)* 56.5 - 110.0 76.8

Additional information Crystalline structure of minerals

Textural information (liberation, association, grain size,

intergrowths, etc.) - -

**EMC method used here is a solution to the underdetermined situation. Closeness (against AM) is not representative of all EMC cases. *Closeness and precision are the “a” of the model (equation 3). It gives relative standard deviation directly for the grade. The smaller the value is, the better is the method.

49

Chapter 5 - Ore texture characterization and relation to mineral liberation

Introduction 5.1

Ore texture and particle composition information is a critical part of the mineralogical approach to geometallurgy. The ore texture and the progeny particles after a breakage in the comminution are the missing link between geology and mineral processing in the concept of geometallurgy. Mostly, ore texture is quantified in terms of descriptors (such as covariance function, proximity function and linear intercept length distribution (Zhang and Subasinghe, 2012). However, these descriptors are mostly developed for binary systems, and there is no extension for three-dimensional ore texture volume. In this study, ore textures and particles are quantified by association indicator to show the trend of ore texture breakage in crushing.

Association Indicator for ore texture 5.2

The analysis of eight drill cores of iron ore in terms of modal composition and association indicator shows variations in ore textures (Table 18). The average grain size of gangue phases was estimated by optical image microscopy while grain size of magnetite and iron oxide (magnetite and hematite) was measured by image processing technique.

The association between magnetite and apatite in magnetite samples is in order of F > E > D1 > G while the association between apatite and magnetite is F > E > G > D1. This shows that even though D1 has the highest apatite grade but the association between magnetite and apatite is less than E and F samples with high-grade magnetite. Consideration of both modal composition and Association Indicator gives insight about the assemblage of phase in the texture. Approximately in all samples, apatite is highly associated with magnetite and iron oxide phases regardless of apatite or magnetite grade. Also, considering grain size of phases, except in D1 sample that has roughly even grain size distribution, in the rest of the samples magnetite and hematite grains have the coarsest size among existing phases.

50

Table 18. Phases, mineral grades, Association Indicator Matrix of ore textures and average grain size (80% passing size).

Sample Phase Grades (wt%)

Association Indicator Matrix (%)

Average grain size (µm)

E

Biotite Amphibole

Apatite Magnetite

3.17 2.67 2.04

92.13

− − −

−

47.11 21.44 31.4534.64 24.43 40.9217.82 27.77 54.4120.87 36.86 42.28

400 600 400 881

F

Quartz Feldspar Apatite

Magnetite

0.17 1.10 1.35

97.38

− − −

−

38.31 17.32 44.3716.02 29.03 54.952.18 9.17 88.655.17 15.49 79.34

100 200 300 894

G

Quartz Feldspar Apatite

Magnetite

0.92 0.72 0.29

98.07

− − −

−

59.82 3.89 36.2851.18 6.86 41.9615.48 31.67 52.8536.87 48.68 13.45

200 300 300

1905

D1

Quartz Feldspar Biotite Apatite

Magnetite

5.52 12.88 10.27 7.24

64.09

− − −

− −

64.79 19.02 5.20 10.9847.62 34.98 4.13 13.2718.55 46.63 10.63 24.1914.08 15.22 29.25 41.4615.84 26.18 35.88 22.10

100 200 200 300 504

A2 Quartz Apatite

Hematite

2.18 1.87

95.96

− − −

43.04 56.9616.05 83.9520.10 79.90

200 300

1486

A1 Quartz Apatite

Iron oxide

4.23 3.86

91.90

− − −

20.62 79.3831.59 68.4164.35 35.65

300 500

1218

B2

Quartz Feldspar Apatite

Iron oxide

3.48 2.32 1.88

92.32

− − −

−

66.89 6.69 26.4352.62 7.93 39.4618.51 27.54 53.9527.45 52.18 20.38

400 400 600

1629

C1 Feldspar Apatite

Iron oxide

1.28 6.90

91.82

− − −

40.06 59.9419.13 80.8726.44 73.56

100 700

1192

Association Indicator for particles 5.3

The AIM can be used for characterizing breakage behavior of particles and estimating the association of minerals based on the interfacial perimeter in the particle. The Association Indicator for particles is a unique way of assessing particle population. AIM values for different types of particle (Figure 14) are listed in Table 19. For example, particles P1 and P2 have a similar composition. However, they have different AIM values. In the AIM of particles, surrounding area of particles (e.g. epoxy, free space) is considered as an additional phase. In this way, the exposed surface of particles is considered in the AIM. The first row of AIM shows liberation by exposed surface.

51

As many of the samples have high iron oxide grade and mineral liberation is expected to be very high in these, only four of the samples with a high amount of gangue phases namely E, D1, A1, and C1 were selected for further studies.

A B C

P1

P3P2

P3

Figure 14. Particles with different composition and interfacial perimeter.

Table 19. Comparison of Association Indicators for various types of particles according to Figure 14.

Type Composition AIM Type Composition AIM

P1 [ ]50 25 25

− − −

−

50 8 4260 40 012 44 4456 0 44

P2 [ ]50 25 25

− − −

−

50 25 2560 20 2050 33 1750 33 17

P3 [ ]65 10 25

− − −

−

67 0 3361 24 150 100 0

67 33 0

A [ ]100 0 0

− − −

−

100 0 0100 0 0

0 0 00 0 0

Ore texture and breakage characterization 5.4

Characterization of ore texture before and after breakage provides valuable insights about the fracture pattern in comminution, the population of particles for specific ore texture and their relation to parent ore texture. Characteristic of ore textures from simplest to more sophisticated way can be considered by analysis of particle size distribution after breakage, distribution of liberations and analysis of changes in associations. In the context of the mineralogical approach to geometallurgy, predicting the particle population from ore texture is a critical step to establish an interface between geology and mineral processing. This is also subject of interest in mineral processing for liberation analysis and comminution processes.

5.4.1 Particle size distribution after breakage Particle size distribution of comminuted ore textures in one stage crushing, and 100% less than 3.35 mm are demonstrated in Figure 15. The crushed samples approximately have similar particle size distribution.

Figure 15. Cumulative particle size distribution of particles after one stage crushing (left) and 100% crushing less than 3.35

mm (right).

10 -1 10 0 10 1 10 2

Upper size (mm)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

pass

ing

(%)

E

D1

A1

C1

10 -1 10 0 10 1 10 2

Upper size (mm)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

pass

ing

(%)

E

D1

A1

C1

52

Modeling of particle size distribution of the comminuted sample is a well-established area and not new. However, to compare the size distributions numerically and also enable generating the particle size distribution for further purposes, the particle size distributions were fitted with Rosin-Rammler distribution function as follows:

= × − − 63.2

( ) 100 1 expn

Df D

D

(42)

where

f(D): Cumulative weight percentage of particles passing size D D: The particle size D63.2: The particle size where the distribution value is 63.2% n: A factor describing the spread of the distribution

The parameter values of particle size distributions (Table 20) suggests that more or less all the ore textures have similar size distribution. In general, textures with finer grain size distributions have wider particle size distributions (lower n values) such as D1 and F samples. This data is used later for generating particle size distribution for forecasting particles.

Table 20. Parameters for Rosin-Rammler equation.

One stage crushing 100% less than 3.35 mm crushing D63.2 n D63.2 n

E 1.90 1.31 1.62 1.56 D1 3.32 0.90 1.16 1.06 A1 2.47 1.09 1.25 2.37 C1 2.48 1.08 1.38 1.47

5.4.2 Distribution of particle types after breakage The distribution of particle types in the samples shows that most of the samples have very high liberation even in the coarsest size fractions (Figure 16). Among the samples, D1 sample has the highest amount of locked particles. Iron oxide minerals are the major contributors to the liberated and locked particles.

53

Figure 16. Distribution of particles by liberated, binary and complex in weight percent in size fractions. Liberated particle

counted as >95 wt% of the phase of interest.

5.4.3 Association Indicator distribution for locked particles Distribution of particle Association Indicator has significance in defining the breakage behavior of particles. By comparing the Association Indicator in the intact sample and in crushed one conclusion on randomness versus degree of preference in breakage can be made. This value is an estimation how the breakage separates one phase from another compared to original ore texture.

Before analyzing the Association Indicator for different phases, it is important to understand how the breakage pattern affects the Association Indicator values. In simple cases as demonstrated in Table 21, when breakage is a phase-boundary fracture, phases reach a liberated state in coarse particle sizes. This means the interfacial area between phases disappears and consequently, Association Indicator values become zero. On the other hand, the association with the background (exposed surface) reaches to its maximum i.e. 100% Association Indicator value.

In a case of preferential breakage in one phase, Association Indicator value for the phase where breakage occurs decreases for non-liberated particle compared to original particle while Association Indicator value of the phase with no breakage remains same. In the case of boundary-region breakage, Association Indicator values for the phases decrease respect to parent particle while due to generating free surface Association Indicator values between phases and background increases. An indication of this type of fracture is observing a significant number of non-liberated particles in fine size fractions.

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100E

Biotite

Amphibole

Apatite

MagnetiteBinary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100D1

Quartz

Feldspar

Biotite

Apatite

MagnetiteBinary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100A1

Quartz

ApatiteIron oxide

Binary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100C1

Feldspar

ApatiteIron oxide

Binary

Complex

54

Table 21 A simple demonstration of the effect of breakage type on variation in AI values for particles. (A and B are phases and C is the background). DOL is the degree of liberation.

Parent particle0 Breakage Progeny particles1 AI change DOL A DOL B

BA

C

Phase-boundary

=

=

=

=

1

1

1

1

0

0

100

100

AB

BA

AC

BC

AI

AI

AI

AI

↓

↓

↑

↑

↑ ↑

Preferential in B

=

>

=

<

=

1 0

1 0

1 0

1 0

1( 100)

AB AB

BA BA

AC AC

BC BC

BC

AI AI

AI AI

AI AI

AI AI

AI

-

↑

-

↓

↑

- ↑

Boundary-region

<

<

>

>

1 0

1 0

1 0

1 0

AB AB

BA BA

AC AC

BC BC

AI AI

AI AI

AI AI

AI AI

↓

↓

↑

↑

- -

Looking at the distribution of Association Indicator values between phases, for example, magnetite and apatite in Figure 17, Association Indicator value for apatite-magnetite after breakage compared to ore texture has not been changed significantly, however for magnetite-apatite Association Indicator decreases in finer size fractions. These indicate that the breakage between magnetite and apatite (two major phases in D1 sample) is a combination of boundary-region and preferential in magnetite phase. The part that should not be neglected is the contribution of detachment breakage. Since the liberated particles are not considered in this graph, no conclusion can be made about this type of breakage. However, if the surface liberation of one phase increases dramatically simultaneously by decreasing particle size without leaving locked particles behind, that could be an indication of detachment process.

Figure 17. Distribution of Association Indicator values for magnetite and apatite in D1 sample.

10 -1 10 0 10 1 10 2

Magnetite-Apatite (%)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

frequ

ency

(%)

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

Ore texture AI

10 -1 10 0 10 1 10 2

Apatite-Magnetite (%)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

frequ

ency

(%)

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

Ore texture AI

55

To investigate changes of Association Indicator values for different phases, the term AI50 is introduced. The AI50 is the value of the Association Indicator for 50% of the population of locked particles (median value). AIM50 is the Association Indicator Matrix filled for AI50 values for each cell. AIM50 can be generated for each size class of locked particles and compared against AIM of the original ore texture. This can be used to evaluate breakage and trend of separation of two specific phases from each other.

The graphs (Figure 18-21) show the changes in AI50 values for different paired phases. AI50 for a phase and background (epoxy) demonstrates the abundance of a phase free surface in locked particles. The trend along with the liberation of the phase show the generation of free surface for the specific phase in size fractions.

Figure 18. Changes in AI50 from ore texture to size fractions for locked particles in E sample.

Figure 19. Changes in AI50 from ore texture to size fractions for locked particles in D1 sample.

Ore texture

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

20

40

60

80

100

AI

50

(%)

E

Background-Biotite

Background-Amphibole

Background-Apatite

Background-Magnetite

Ore texture

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

20

40

60

80

100

AI

50

(%)

E

Biotite-Background

Biotite-Amphibole

Biotite-Apatite

Biotite-Magnetite

Ore texture

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

20

40

60

80

100

AI

50

(%)

E

Amphibole-Background

Amphibole-Biotite

Amphibole-Apatite

Amphibole-Magnetite

Ore texture

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

20

40

60

80

100

AI

50

(%)

E

Apatite-Background

Apatite-Biotite

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Figure 20. Changes in AI50 from ore texture to size fractions for locked particles in A1 sample.

Figure 21. Changes in AI50 from ore texture to size fractions for locked particles in C1 sample.

A significant trend in all samples is the association between iron oxide minerals and gangue phases. The AI50 value in size fractions decreases from intact ore to particles while the iron oxide free surface in locked particles increases. This indicates that in these samples, the breakage takes place preferentially in iron oxide phase. Additionally, increased mass proportion of free iron oxide particles (thus liberation degree) is another reason to support preferential breakage.

Forecasting particle population from ore texture 5.5

Ore texture mapping and breakage behavior of ore are the critical steps for forecasting the particle population. Experimental work and analysis that has been done on the ore textures can be utilized for forecasting particle population. The particle size distribution modeled by Rosin-Rammler equation

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along with the degree of breakage either preferential in phase or random estimated by breakage characterization are the main parameters for forecasting liberation distribution.

Simple assumptions can be made to reduce the complexity of forecasting particle population. For example, rectangular particle shapes which selectively or randomly positioned over ore texture is used to generate particles. The size of particles is taken from modeled particle size distribution. Schematically, the approach that is applied here is shown in Figure 22.

Particle size, liberation and association

distribution analysis

Ore texture mineral map and association analysis

Breakage frequency definition

Particle generation

Particle population adjustment

Drill core

Corrected particle population

Drill core polishing and scanning

Crushing and sample preparation

Figure 22. The schematic view of forecasting particle population from ore texture.

5.5.1 Assigning breakage frequency To assign preferential breakage in a phase or entirely random breakage, breakage probability function was used for selecting pixels on the mineral map of ore texture. For example, if the breakage is known to be preferential in some specific phases, a probability function can be generated based on the degree of breakage to position random particles selectively over ore texture. To ensure that the particle has the surface exposure for that particular phase, the corner of the rectangle was selected for the anchor to position on the mineral map. For given ore texture D1, by random breakage and 100% preferential breakage in magnetite phase, the liberation distribution of magnetite in size fractions would be as Figure 23.

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Figure 23. Modeled liberation distribution of magnetite in size fractions for random breakage (left) and 100% preferential

breakage in magnetite (right).

From the degree of liberation and AIM values in size fractions, the degree of breakage can be roughly estimated as Table 22. For example, the degree of liberation of D1 sample is around 74% for magnetite and 4% for apatite in the fine fractions while AIM50 for these phases indicates that surface exposure of the phases in the locked particles is increasing in the fine fractions as well. This is suggesting that for the liberation of magnetite and apatite, preferential breakage in these phases is the main contributor. If we assume that the main breakages in the sample are either preferential in phases or random (no preferences in any way), it is safe to use the degree of liberations as a rough estimate to selectively position corner of rectangle particles over phases in mineral map. For the D1 sample, this would be 4% chance to place rectangular corner in apatite phase, 74% chance for magnetite phases and 21% chance to have no preferential positioning (random).

Table 22. The probability distribution for preferential breakage in a specific phase and random breakage established based on the degree of liberation.

Preferential Breakage E D1 A1 C1 Quartz - 0.1 1.3 - Feldspar - 0.1 - 0.5 Biotite 0.3 0.8 - - Amphibole 0.0 - - - Apatite 1.2 4.4 5.0 5.2 Iron oxide 88.1 73.5 83.3 83.2 Random 10.4 21.1 10.4 11.1

Applying preferential and random breakage over ore textures yields particle population. Approximately one million particles were generated for each sample.

5.5.2 Adjusting liberation to match modal mineralogy Generating particles by this method not necessary gives the same modal composition as the experimental work for some size fractions specifically for finer fractions. However, the liberation distribution is still close to the experimental liberation. The differences in modal composition and degree of liberation of some minerals could be due to the way that the particles are generated. In realistic breakage with classification stage, when particle breaks preferentially in one phase, non-liberated progeny particles are generated as well. This means that non-liberated particle still has a chance to break to fully liberated particles in finer size fractions, but this cannot be considered in the particle generation approach. In current particle generation, grade of the phase with highest preferential breakage increases in finer fractions. This specifically applies to the finest size fraction.

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Possible explanation is the resolution of the mineral map which in certain point particle size reaches to. This means that many fine particles are consisting of only a few pixels or even one pixel. This can be fixed by the approach that was introduced by Lamberg & Vianna (2007) to adjust the mass proportion of particles to match modal composition. This is not a perfect solution, but it solves the inconsistency between liberation distribution of particles and modal composition. The modal composition of selected samples from experimental and texture breakage with the adjusted composition are listed in Table 23-26. In general, similar composition reached for all samples only by adjusting the mass proportion of particles.

Table 23. The modal composition of E sample from experimental (Exp.) and forecasted particles after adjusting liberation (Adj.).

Fraction Biotite (wt%) Amphibole (wt%) Apatite (wt%) Magnetite (wt%) Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj.

>1680 1.64 1.57 1.51 1.52 0.90 1.42 95.95 95.49 850-1680 0.97 0.92 0.62 0.75 0.45 0.89 97.95 97.43 425-850 1.00 0.96 0.50 0.70 0.58 0.95 97.92 97.39 300-425 1.30 1.26 0.57 0.86 1.72 1.85 96.40 96.03

Table 24. The modal composition of D1 sample from experimental (Exp.) and forecasted particles after adjusting liberation (Adj.).

Fraction Quartz (wt%) Feldspar (wt%) Biotite (wt%) Apatite (wt%) Magnetite (wt%) Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj.

>1680 6.22 6.71 23.08 22.63 5.33 5.30 6.43 6.40 58.9 58.87 850-1680 3.63 4.08 13.02 12.49 5.64 5.65 9.38 9.38 68.3 68.29 425-850 1.50 1.51 2.07 2.58 7.15 6.94 5.76 5.77 83.5 83.30 300-425 1.50 1.76 2.78 3.22 7.28 6.96 6.03 5.87 82.4 82.19

Table 25. The modal composition of A1 sample from experimental (Exp.) and forecasted particles after adjusting liberation (Adj.).

Fraction Quartz (wt%) Apatite (wt%) Iron oxide (wt%) Exp. Adj. Exp. Adj. Exp. Adj.

>1680 6.67 6.46 3.90 4.42 89.43 89.12 850-1680 2.92 3.08 1.93 2.28 95.15 94.64 425-850 5.06 4.99 5.92 5.64 89.02 89.37 300-425 2.63 2.85 6.90 6.45 90.48 90.71

Table 26. The modal composition of C1 sample from experimental (Exp.) and forecasted particles after adjusting liberation (Adj.).

Fraction Feldspar (wt%) Apatite (wt%) Iron oxide (wt%) Exp. Adj. Exp. Adj. Exp. Adj.

>1680 1.52 1.49 3.26 3.76 95.22 94.75 850-1680 0.73 0.69 1.57 2.06 97.70 97.25 425-850 1.10 0.92 4.03 4.42 94.88 94.67 300-425 1.26 1.03 7.33 7.21 91.42 91.77

5.5.3 Comparing liberation of iron oxide minerals As the major phase in the samples is iron oxide mineral and its liberation is critical for mineral processing plant performance, the iron oxide liberation distribution comparison is made between experimental and forecasted particles. Generally speaking, in most of the samples, the trend of iron oxide liberation is predicted well (Figure 24). However, particle population of magnetite ore samples

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(E and D1) presents closer liberation distribution than those of iron oxide (both magnetite and hematite are present). In overall, this verifies that the primary ore texture is a major factor controlling the liberation distribution in crushing.

E

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Figure 24. Liberation distribution of iron oxide minerals from experimental (left) and forecasted particles (right).

Discussion on ore texture characterization 5.6

Image processing methods are widely used for ore texture and particle characterization, however, liberation by composition and exposed surface are still the dominated methods for liberation and

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particle characterization. One of the shortcomings of the existing methods for association and liberation distribution is the inability to compare the particle texture against the original ore texture numerically. Textural descriptors that are commonly used for particles (Pérez-Barnuevo et al., 2012) are to show the complexity of texture or identification, but they lack the capability to relate particles to the parent texture in a way that can be used for the breakage analysis and forecasting.

The Association Indicator Matrix (AIM) can be regarded as an extension of work by Lund et al. (2015) to account for a grade of mineral in the particle in the assessment of association. The suggested method could not consider phase boundaries or exposed surface. Therefore, the applicability of association index was limited especially when there were disseminated grains or inclusion in the particle. Current method accompanied by particle composition can store valuable information about the distribution of interfacial areas between phases and liberation distribution by composition and exposed surface.

The merits of Association Indicator over absolute value of interfacial area or common co-occurrence matrix are not only that it is less sensitive to scale, for example, due to fractal effect, but also values can be compared to different textures as well as particles and can be used as criteria for textural classification. The cell values in the AIM also give relevant information about how the phases are occurring in the ore texture. For example, if the AI value goes near 100%, it is an indication that one phase is mainly accompanied by another phase, for instance as inclusions.

The other potential strong point of AIM is the capability of evaluating the nature of breakage of given ore texture for further generation of full particle population. This was demonstrated by four drill core samples where liberation distribution of iron oxide minerals was compared. In general, results for magnetite samples were closer to experimental data. This could be because hematite and magnetite are lumped together in iron oxide samples, and same breakage frequency as magnetite was used for hematite.

The generated mineral map of ore texture from drill core mapping was used as an input for forecasting particles. The particle size distribution from crushing was used for generating various sizes of rectangles that were superimposed on the mineral map. For positioning the rectangles over the mineral map, breakage probability was used. The assumption was that the preferential breakage in the phase is the cause of the liberation of minerals and random breakage can yield both liberated and non-liberated particles. The obstacle in this approach is that grade of mineral with highest preferential in finer size fractions progressively increase. Therefore, liberation adjustment step was required to match modal composition in size fraction according to experimental.

The value of the developed method is that it links original texture and mineral liberation. The approach generates full particle population which can be used directly in particle-based process simulations.

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Chapter 6 - Developing a particle-based process model for unit operations of mineral processing

Introduction 6.1

Missing mineral liberation information and a lack of mass balancing techniques for multiphase particles has hindered the development of unit operation process models to be based on particle properties (Table 5). Particle level information provides an excellent opportunity to relate particle properties to physical sub-processes and to develop a model for forecasting the performance of any unit operation. In the development of the particle-based model, first, the quality of data and measurements are assessed then the techniques used for relating particle properties to the recovery of the instrument are described. The presentation of the model in mathematical form and verification of model by using industrial data is followed after.

Quality of data and measurements 6.2

The standard deviation for XRF and automated mineralogy measurements in repeated samples were calculated according to the developed error model. The standard deviation for XRF assays follows the equation

= ± ×0.007XRFSTD x (43)

where x is the elemental grade in wt%. Standard deviation for mineral grades measured by automated mineralogy follows the equation

= ± ×0.208AMSTD x (44)

where x is the mineral grade in wt%. Equation (44) was used for setting standard deviations during mass balancing the data for minerals.

To evaluate the quality of automated mineralogy, back-calculated chemical compositions were compared against chemical assays (Figure 25). Generally, good overall correlation was observed. However, minor elements such as vanadium (V), manganese (Mn) and potassium (K) show a weak correlation between chemical assays and back calculations. This could be due to either error in XRF analysis at low concentration or inaccuracy in the chemical composition of minerals (Table 11).

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Figure 25. Comparison of chemical composition between XRF assays against back-calculated from IncaMineral modal

measurements. Values on the graph are showing corresponding R2 value for each element.

Mass balancing and data reconciliation 6.3

Mass balancing and data reconciliation improve the reliability of measurements and can under certain circumstances even enable the estimation of unmeasured streams and variables. It is a requirement for estimating the metallurgical performance of the circuit (recovery calculations), for diagnosis of process bottlenecks, and for modeling the process. Well-established methods exist for mass balancing and data reconciliation of mineral processing data, and several software packages have been developed for performing these tasks (Hodouin, 2010).

Particle mass balancing also called particle tracking is the state-of-the-art technique as developed by Lamberg and Vianna (2007) for mineralogical mass balancing. It transfers the mass balancing concepts of conventional chemical assays to the mineral level and finally to the mineral liberation level. The method requires delicate considerations to provide consistent results and to overcome missing liberation data. The following steps need to be included when extending the mass balancing to the particle level (i.e. mineral liberation level):

1) Bulk mass balance by minerals 2) Sized mass balance by minerals 3) Particle mass balance (by so-called particle tracking)

In this study, as a first step, unsized data was used for mass balancing total solid and mineral flowrates in bulk. The result from the bulk mass balancing was then used as a constraint when mass balancing the minerals in size fractions. This stepwise procedure minimizes the error propagation and ensures that bulk and sized mass balances are consistent.

The adjustment of mineral grades in mass balancing for most of the minerals was minor as shown in Figure 27, where the parity line indicates no adjustment. Adjustment of anhydrate and titano-magnetite was relatively higher compared to others, and therefore information on these trace minerals is less reliable. This was mainly due to precipitation of anhydrate in tailing buckets and false identification of titano-magnetite during automated mineralogy. Titanium-bearing minerals such as titanite and rutile exist as the lamellae in magnetite grains (Lund, 2013), causing the identification of

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some of the magnetite grains falsely as titano-magnetite. To resolve this problem, titano-magnetite in each particle was lumped together with the magnetite, and the anhydrate phase was removed. Each particle composition was normalized after removing the anhydrate phase. Afterward, mass balancing was redone (Table 27).

Figure 26. Comparison of mineral grades between measured and balanced data. Values on the graph are showing

corresponding R2 value for each mineral.

Table 27. Bulk balanced values for WLIMS (mineral grades in wt%). For mineral abbreviations, see Table 11.

Streams Solids Mgt Qtz Ap Bt Ab Act Cal Ttn

Bal. t/h Bal. % Bal. % Bal. % Bal. % Bal. % Bal. % Bal. % Bal. %

Feed 454 83.8 0.83 3.16 3.50 2.85 3.86 1.76 0.28 Conc. 387 98.0 0.05 0.48 0.56 0.13 0.55 0.11 0.08 Tail. 68 2.20 5.25 18.48 20.33 18.34 22.76 11.21 1.44

The particle tracking technique (Lamberg and Vianna, 2007) aims at adjusting liberation data to match with mass balance results in bulk and size fractions. It is followed by the basic binning, which involves the classification of particles by size and composition into narrow liberation classes (bins). In principal, the number of bins can be as many as the possible combination of phases in particles and grade classes. Practically, in the basic binning stage the population of various particles in the stream defines how narrow the size classes should be and which combinations of phases in particles have to be considered. Population and mass distribution of particles in the studied samples showed that liberated and binary particles account for over 99% of the population (Table 28).

In some streams, some bins may have no or very few particles making the mass balancing result unreliable. In the following stage, the advanced binning, the bins with low numbers of particles are globally combined (i.e. in all the streams in a similar way) in order to reach a sound number of particles in each bin. In this work, the advanced binning was first done for the feed stream, and the minimum number of particles in each bin was set to 25. This equals to a maximum of 20% relative standard deviation for the mass proportion of the particle type (bin) in question. The other streams were binned in the same way by using the feed stream as a reference. In the final stage, the mass

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proportion of each bin (particle type) was adjusted to reach the mass balance in the whole circuit by keeping the total solids flowrate s as constraints. Additionally, the particle flowrate of each bin was balanced among feed, concentrate and tailing by considering a weighting factor calculated from the number of particles observed in each bin. In this study, the particle tracking resulted in the mass balancing of 702 different kinds of particles around the WLIMS. Once the particle types were mass-balanced in streams, it was possible to calculate the recovery of each particle type.

Table 28. Population and mass distribution of particles in streams.

Stream Particle Population (number of particles) Mass distribution (wt%)

Feed

Liberated 69,056 69.55 Binary 22,240 30.10

Ternary 280 0.32 Complex 27 0.06

Concentrate

Liberated 81,068 72.46 Binary 20,846 27.41

Ternary 210 0.14 Complex 15 0.00

Tailing

Liberated 81,277 67.46 Binary 20,755 30.70

Ternary 881 1.41 Complex 327 0.55

Figure 27. Parity chart showing measured particle type (bin) masses in the feed, concentrate and tailing streams after

advanced binning against mass-balanced particle types (bin) after the particle tracking.

Developing a process model for WLIMS 6.4

In the WLIMS, the rotating drum with the magnet is partially submerged into a slurry tank where it lifts out the magnetic particles. Based on the tank design and the feed slurry flow three types of setups can be distinguished: concurrent, counter-current and counter-rotation. Selection of the type of magnetic separator for treating an ore is governed by feed particle size, throughput, and concentrate grade and recovery (Stener, 2015).

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Based on the type of the magnetic separator, slurry tank, and magnetic arc, several different zones can be defined. For example, the counter-current magnetic separator can be divided into three zones. The pick-up zone is where the fresh slurry feed encounters the drum. The scavenger zone is a shallow zone close to the tailings outlet where the drum’s rotation is opposite to the slurry flow. The dewatering zone or cleaning zone is where the drum pushes the concentrate up to the discharge, and the concentrate water flows back to the tank (Figure 28).

Figure 28. The schematic view of counter-current WLIMS (modified after Stener (2015)).

When a ferromagnetic material is exposed to the magnetic field, magnetic ordering occurs based on an intrinsic property of the material which defines spontaneous magnetization (Svoboda, 2004). The other phenomenon happening is the growth of magnetic domains. Depending on the size of the particle and the strength of the magnetic field, the magnetic particle can consist of single or multiple magnetic domains. If the external field is strong enough or the particle is small enough (less than 0.1 µm) particle magnetization becomes homogenous; this is called magnetic saturation. Even when the saturated particle is outside of the magnetic field, the particle will not become completely demagnetized.

Magnetized particles in the slurry tend to gradually gather into groups and form flocs or aggregates. This is called magnetic flocculation. Before magnetic saturation is reached, the strength of the flocs increases with the growth in field strength and efficient permeability. The magnetic content of the particles, the fineness and as well as the nature of the non-magnetic material affect the effective permeability (Lantto, 1977). It is believed that the magnetic flocculation plays a crucial role in the recovery of fine magnetic particles.

6.4.1 Physical explanations for observations

Recovery of binary magnetite-bearing particles The major mass population of particles in the concentrate is formed by liberated and magnetite-rich binary particles, as expected. For modeling purposes, the aim is to find an equation for the recovery of particles into the magnetic concentrate when its composition and size is known. Therefore, in Figure 29 the recovery of particles is plotted against composition. Firstly, recovery is directly related to the magnetite content in the particle. For liberated magnetite particles, no matter the size, recovery is 100%. Secondly, it can be seen that the recovery of magnetite-bearing particles in coarse size fractions is higher than those in fine size fractions (Figure 29). This is mainly due to higher magnetic force on

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coarse magnetite particles and their important contribution to increasing the effective permeability of flocs. For example, in the case of apatite, particles with around 10% magnetite have a recovery of around 22% in the fine size fraction (<37 µm), but the same particles in coarse size fraction (>125 µm) have more than 70% recovery to the concentrate. Similar behavior can be seen with other binary particles with magnetite.

Figure 29. Recovery of different binary particles with magnetite, error bar shows two standard deviations. Error in recovery was calculated by Monte Carlo simulation. High errors in some particle bins are due to a low number of particles in the bin.

The arbitrary trend curve shows magnetite content in particle and recovery relationship.

Recovery of liberated gangue particles Liberation measurements revealed that there are liberated non-magnetic particles in the concentrate and the mass balancing confirms that there is a positive relation between the liberated gangue particle size and the recovery into the concentrate (Figure 30). For apatite, fully liberated particles contribute with around 30% of the total apatite in the concentrate. For other minerals, this value varies. Recovery of fully liberated gangue minerals in the concentrate can be artificial due to stereological bias, or true due to entrainment or entrapment.

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Figure 30. Recovery of liberated gangue particles in various sizes. Error bars show twice the standard deviation.

Stereological bias A stereological bias in two-dimensional particle image analysis means that particles that are regarded as liberated in sections can be composite particles in three dimensions. If this is the case, then the recovery should show a decrease by increasing particle size. Relatively speaking in a similar texture a fine-grained particle in coarse size fraction changes to the coarse-grained particle in fine size fraction, as depicted in Figure 31. This is analogous to that in fine textures the stereological bias is smaller (Leigh et al., 1996; Spencer and Sutherland, 2000). Therefore, stereological bias, as a possible reason for this observation can be excluded.

Figure 31. The stereological effect on recovery of particles in coarse and fine size fractions. With similar texture, stereological

bias is higher in small particles than in coarse ones.

Entrainment phenomena Entrainment means that particles are dragged into the concentrate with water. This effect is stronger for fine particles than for coarse ones (Neethling and Cilliers, 2009), i.e. opposite to the observation. Therefore, also this explanation is rejected.

Entrapment As discussed earlier, in a flocculation process magnetite particles attach to each other. During this process, liberated gangue minerals can be trapped between magnetic particles. The entrapment of non-magnetic particles has been previously reported as enclosures in the flocs (Lantto, 1977). In the dewatering step (Figure 28) when the drum pushes the flocs up towards the concentrate discharge, water inside the flocs drains back to the tank and takes some of the fine liberated gangue particles with (drainage). Madai (1998) has shown that for fine particles the drag force is stronger than its counter force, the magnetic force. Therefore, fine particles have a higher probability to escape from

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the flocs than coarser particles. On the other hand, the small porosity size in the flocs hinders the coarse gangue particles to be drained out from the flocs. Therefore, the coarse liberated gangue particles have higher chance to be trapped in the flocs and to end up in the concentrate (Figure 32).

Figure 32. The effect of drainage water in dewatering zone to wash out fine gangue particles. Gray particles are magnetic

particles, and bright ones are gangue particles. Drainage flow is shown by the straight arrow toward the bottom of the tank.

6.4.2 Semi-empirical model of WLIMS Even though observations show a clear correlation between the recovery of different particle types and the physical processes, it is not possible to develop a purely physical model. This is mainly due to numerous and complex sub-processes involved in the separation. Further, the data available from the plant survey describes only one operational point. Therefore, the model developed here is semi-empirical in nature and tries to reproduce recovery curves at mineral liberation level. Requirements to be formulated for such a model are that (i) it should be flexible to adapt to linear or curve shaped recoveries, (ii) should have a reasonably low number of parameters, and (iii) should reflect physical sub-processes in the system. At a later stage, the model can be further developed to consider operational variables.

A flexible and relatively simple way to model the recovery patterns of binary particles is to use the incomplete beta function Ix(a,b) (Abramowitz and Stegun, 1965). The incomplete beta function is defined as follows:

− −= −∫ 1 1( , ) (1 )

xa b

xa

I a b t t dt (45)

If for the sake of simplicity, the a parameter is fixed at 1, various curve shapes can be generated by changing only the b variable alone.

For the entrapment, the observation shown in Figure 30 suggests that the probability of entrapment increases by size and nature of gangue mineral. A simple linear relationship based on the particle size can be applied for each mineral as follows:

= +1 2ER E d E (46)

where RE is the recovery due to entrapment, d is the particle size, and E1 and E2 are the constants. This linear model is applied to predict the entrapment of different sizes of liberated gangue particles.

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To model the recovery of various magnetite binary particles in the WLIMS concentrate, the following function is used:

= (1, )x xR I b (47)

where x is the grade of magnetite in the particle and b is a spread value. Depending on the mineral type that is binary with magnetite, the b can vary from 0.01 to 30. Finer size fractions generally have smaller b value than coarser size fractions. The trend of increasing b values from fine size fractions to coarse size fractions shows the spread of recovery curves. Therefore, the spread value in equation (47) is dependent on the particle size, the susceptibility of non-magnetic portion of the particle, shape of the particle, and specific gravity of the particle. Finally, the recovery model by considering entrapment becomes as follows:

= + −(1 )x x ER R R R (48)

Fitting the equation (48) with the experimental points gives various b values for compositionally different binary particles in different size fractions. During the data fitting, each particle type recovery was assigned a weight factor calculated from the number of particles falling into the particle bin type. In addition, the highest and lowest b values at 95% confidence level were calculated for the particles in each size fraction. In general, a linear regression describes the increase of b values respect to the particles size. A similar approach was perused for calculating RE. The results of the regression models for b and RE are listed in Table 29.

Table 29. Linear regression models for b and RE. x in the function is the size of particle in microns.

Regression model Mgt-Qtz Mgt-Ap Mgt-Bt Mgt-Ab Mgt-Act Mgt-Cal Mgt-Ttn

b 0.0408x 0.1174x + 1 0.1190x + 1 0.0261x 0.1040x + 1 0.0057x 0.0180x RE 6E-06x 0.10x 0.11x 6E-03x 0.11x 8E-03x 3E-03x

The results indicate that binary pairs of magnetite with gangue can be divided into two groups. The first group is magnetite binary particles with apatite, biotite, and actinolite and the second group is magnetite binaries with quartz, albite, calcite and titanite. For each group an average regression model for b and RE can be selected and applied to the model as follows:

First group: = + × + − + × × ×(1,1 0.12 ) (1 (1,1 0.12 )) 0.11x xR I d I d d (49)

Second group: = ×(1.0.02 )xR I d (50)

where x is the magnetite grade of the particle and d is the particle size.

Verification of the model 6.5

To verify the developed model, the model was compared against observations at two levels. At the first level, the comparison was made against the bulk and sized mineral flowrates. At the second level, the comparison was made on liberation distribution in the concentrate.

6.5.1 Verification based on bulk and sized level Comparison of solid flowrates and mineral grades from observations and model indicates that the model forecasts well the solid and mineral flowrates (Table 30). However, in the finest size fraction, the differences between model and observation are higher than in the other size fractions and in bulk.

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This could be related to the unpredictable behavior of fine particles in the process. This can also be seen in the recovery of fine minerals in finest fraction (Figure 33).

Table 30. Solid and mineral flowrate s in bulk and sized fractions from model and observations.

Conc. Fraction Solid t/h Mgt % Qtz % Ap % Bt % Ab % Act % Cal % Ttn %

Obs.

Bulk 387 98.0 0.06 0.48 0.57 0.14 0.55 0.11 0.08 0-37 um 116.9 98.8 0.06 0.13 0.39 0.03 0.21 0.34 0.00 37-63 um 68.5 98.2 0.03 0.56 0.47 0.19 0.48 0.00 0.03 63-125 um 109.5 97.7 0.05 0.66 0.68 0.16 0.60 0.01 0.11 +125 um 91.7 97.1 0.09 0.67 0.73 0.19 0.99 0.02 0.18

Model

Bulk 385 98.0 0.06 0.47 0.51 0.07 0.50 0.05 0.09 0-37 um 115.5 98.0 0.01 0.19 0.31 0.02 0.20 0.03 0.02 37-63 um 68.5 98.6 0.04 0.49 0.39 0.04 0.37 0.03 0.07 63-125 um 109.4 98.0 0.05 0.59 0.55 0.05 0.50 0.04 0.11 +125 um 92.2 97.4 0.15 0.68 0.80 0.20 1.00 0.09 0.18

Figure 33. Recovery of minerals in size fraction from observations (left) and model (right).

6.5.2 Verification based on mineral liberation level Evaluation of the model at particle level was done first by comparing the liberation curves for magnetite particles in the concentrate; thus comparing measured concentrate against modeled concentrate from the feed stream and developed equations (45)-(50). As shown in Figure 34, the model well describes the liberation of magnetite particles. However, the mode of occurrence of minerals in particles is not well described for certain minerals (Table 31 and Table 32). The differences for quartz, albite, calcite, and titanite are higher than for the other minerals. This is arising from using simple linear regression model for b values in the model for this group of minerals. However, more observations of particles are required to form a better model.

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Figure 34. Liberation curve for magnetite particles from observations (left) and model (right) in concentrate stream.

Table 31. Mode of occurrence of minerals in the concentrate from observations. Each row describes the association of named mineral with the minerals stated on columns in percentages; each row sums up to 100%. Diagonal values give the mass proportion (wt%) of liberated particles.

OBS Mgt Qtz Ap Bt Ab Act Cal Ttn Mgt 98.14 0.10 0.55 0.52 0.07 0.35 0.07 0.12 Qtz 75.79 9.42 1.23 3.37 0.40 3.55 0.70 0.60 Ap 59.88 0.07 32.62 0.71 0.49 0.97 0.25 0.01 Bt 66.33 0.33 0.50 27.99 0.60 0.78 0.16 0.32 Ab 41.75 0.96 0.95 1.09 45.63 2.15 1.44 0.22 Act 54.10 0.43 0.67 0.86 0.82 36.52 0.22 0.18 Cal 49.72 0.79 1.29 3.40 1.22 0.71 40.62 0.27 Ttn 91.32 0.46 0.05 1.47 0.96 0.95 0.51 1.50

Table 32. Mode of occurrence of minerals in the concentrate based on the model and the feed. Diagonal values give the mass proportion (wt%) of liberated particles.

Model Mgt Qtz Ap Bt Ab Act Cal Ttn Mgt 97.93 0.10 0.59 0.53 0.11 0.39 0.10 0.12 Qtz 88.00 5.92 0.13 0.15 0.02 0.39 0.01 0.02 Ap 63.12 0.03 32.21 0.04 0.02 0.06 0.01 0.01 Bt 72.19 0.02 0.09 23.52 0.08 0.22 0.05 0.01 Ab 71.34 0.02 0.10 0.59 17.25 1.31 0.02 0.03 Act 61.43 0.05 0.06 0.13 0.12 33.19 0.03 0.01 Cal 88.90 0.05 0.12 0.21 0.11 0.34 7.84 0.11 Ttn 95.15 0.02 0.02 0.12 0.07 0.38 0.03 0.00

Discussion on developing WLIMS process model 6.6

The developed particle-based WLIMS model can forecast recovery and product quality of any new feed stream if the particle level information is available. Generally speaking, process simulators and unit operation models that operate at particle level are developing and becoming more common. In addition, simulation of a process where the model level is at particle level stays straightforward, i.e. input and output stream of the model can be directly used by any other unit model.

The developed model can be used in optimization for example by testing the effect of grinding fineness and detaching of flocs before sending the concentrate to the cleaning stage. From the curve shapes, coarser grinding gives higher recovery but lower grade compared to fine grinding. A detachment of the flocs could potentially decrease the entrapment. Further development is needed to relate the model parameters to the operational parameters or include certain sub-processes of

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magnetic separation if the model is intended to be used for process control or to investigate the effect of operational conditions.

Observations at particle level as well as physical theory imply that magnetic separation is a complex process that is controlled by both operational conditions and the feed stream properties. Studying and characterizing the feed stream at particle level provides insight into the performance of a magnetic separator that previously was not possible to reach accurately. The developed semi-empirical model of WLIMS describes the recovery of individual particles based on two mechanisms; recovery of particles due to magnetic volume and entrapment. This was achieved through applying the particle tracking technique. However, there are several other factors that need to be addressed.

6.6.1 The effect of mineral nature, grain size, and shape The relationship between particle size and recovery of fully liberated gangue particles can be explained by the entrapment phenomenon. As seen in Figure 30, there are slight differences between the gangue minerals, i.e. apatite, actinolite, and biotite show higher entrapment than the rest. In the case of apatite, fine magnetite inclusion (<1 µm) were observed in the apatite in the concentrate, which was not possible to detect under normal condition of automated mineralogy. On the other hand, apatite in the tailings seems not to have magnetite inclusion as those found in the concentrate. This also can be true for actinolite and biotite since such an observation has been reported previously (Niiranen, 2015). Detection of fine magnetite inclusion can be easily missed in the measurements and data processing of automated mineralogy, hence magnetic susceptibility measurement of present minerals and individual particles, if possible, would be needed to verify whether the liberated gangue particles end up to concentrate because of their magnetic susceptibility rather than entrapment. While higher susceptibility due to magnetite inclusion probably plays a major role, the effect of grain shape should not be neglected. Actinolite and biotite, can vary in shape and are often elongated that makes their release from flocs harder. In addition, angular particles have naturally stronger magnetic forces at the corners and edges.

The spread factor b in equation (47) is closely correlated to particle size, the susceptibility of a non-magnetic portion of the particle, shape of the particle, and specific gravity of the particle. The smaller the grain size is, the lower the magnetic force on the material becomes, resulting in weakening and shortening of the flocs (Lantto, 1977). On the other hand, coarse magnetic particles increase the strength of the flocs and the length of the chains, thus resulting in an increase of total recovery. The nature of gangue minerals, the magnetic susceptibility of grains, shape and total susceptibility of particles affect the flocs’ effective permeability. For particles with sharp corners, porosity in the flocs increases and the total effective permeability becomes smaller compared to when flocs are packed with rounded particles. The specific gravity of particles may have a high impact during the cleaning stage. Particles with lower specific gravity tend to follow drainage water more easily than others.

6.6.2 The effect of feed quality As seen in observations, the entrapped liberated gangue particles in the concentrate are one of the sources of impurities in the products. While the formation of the flocs is stronger in high-grade magnetite ore and is crucial for the recovery of fine particles, releasing gangue particles from these flocs is highly unlikely. Unless the flocs become demagnetized or detached, entrapped gangue particles inside the flocs find their way to the concentrate. A mechanical detachment of the flocs can be momentarily but may be enough to let gangue particles escape from the flocs.

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The studied ore is such a high grade and shows strong recovery not only in the first magnetic separation but also in the whole process. This raises the question whether liberation information is needed for the process simulation. However, in producing high-quality products, the recovery is not the main concern, but the impurities are. Thus the grade of gangue minerals in the concentrate is necessary. For a high-quality iron product, the requirements for certain impurities are tight and must be met (LKAB, 2014). For example, phosphorus and silicon contents of the product are the determinative criteria meaning that relatively high liberation is needed to reach a pure product. In some iron deposits, even sulfur exist mainly in the form of sulfides which is problematic. Especially when monoclinic (thus magnetic) pyrrhotite is present (Arvidson et al., 2013).

Conversely, in the processing of low-grade ore, the mineral liberation can cause a recovery issue as well. It is expected that the strength of formed flocs in the low-grade feed will be weaker and the loss of binary particles with magnetite and fine magnetite particles accordingly be higher.

6.6.3 The effect of stereological bias As it is known, two-dimensional measurement of liberation which inherently is defined in three dimensions is a biased estimate of the liberation. The liberation is always overestimated, and the magnitude of the overestimation depends on ore texture. The bias exists for liberation estimation. However, the bias affects the model parameters in less degree. In the calculation of modal parameters, instead of using the absolute value of liberation, the recovery was used. This means the overestimation of liberation presents itself in feed and concentrate which to some extent cancel each other as the recovery is calculated by dividing the particle flowrate in the concentrate by corresponding value in the feed. In this way, the model can take the uncorrected liberation data as well as corrected liberation data as an input and gives the same quality of the liberation.

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77

Chapter 7 - Demonstrating the process plant simulation based on particles

Plant circuit 7.1

A flowsheet used here consist of comminution and concentration circuits and is based on LKAB Kiruna concentration plant (Samskog et al., 1997; Söderman et al., 1996). A circuit is a general form of the process that LKAB uses in Kiruna for the beneficiation of magnetite ore. The feed to the plant is the product of crushing and cobbing plant. The beneficiation process consists of three major steps including comminution, magnetic separation and apatite flotation. The comminution circuits include autogenous grinding followed by the spiral classifier and pebble milling coupled with hydrocyclone (Figure 35).

Figure 35. Flowsheet of magnetite beneficiation plant for the demonstration of different levels of modeling and simulation.

Process units 7.2

The process unit models used in the simulation at different modeling levels are gathered in Table 33. The results from the mass balancing of the plant data were used for calibrating and defining the model parameter values of different models.

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Table 33. The models that are used in the simulation of flowsheet at different levels.

Unit Bulk model Mineral by size model Particle level model Autogenous Mill Perfect mixer (Fixed) PSD HSC comminution model

with decoupled size reduction and liberation models

Trommel Mineral splitter/mass splitter

Efficiency curve / Efficiency curve by mineral

Efficiency curve/efficiency curve by mineral

Mixer Perfect mixer Perfect mixer Perfect mixer Pebble Mill Perfect mixer (Fixed) PSD HSC comminution model

with decoupled size reduction and liberation models

WLIMS Mineral splitter Mineral by size splitter Developed WLIMS model (Parian et al. 2016)

Spiral classifier Mineral splitter Efficiency curve/efficiency curve by mineral

Efficiency curve/efficiency curve by mineral

Hydrocyclone Mineral splitter Efficiency curve/efficiency curve by mineral

Efficiency curve/efficiency curve by mineral

Flotation Flotation kinetics by mineral

Flotation kinetics by mineral by size

Particle-based kinetic flotation model

Plant feeds 7.3

Two different magnetite ores were selected to be used for simulation. The first ore is the actual feed to the plant during the survey (Ore A). The second ore is D1 drill core sample which was studied in ore texture characterization (Ore B). The procedure for forecasting particle population from D1 sample was described earlier in chapter 5. The two ores are texturally different thus have different mineral grades and liberation distribution (Table 34, Figure 36). The assumptions that are used here are that mineral compositions and particle size distribution after crushing for both ores are same.

The ore B was selected because it represents an ore which is significantly lower in the magnetite head grade and texture is much more fine-grained giving lower liberation degree at given particle size (Figure 36). Also, the Ore B would represent the plant feed in a case where cobbing is not used. In the ore B the degree of liberation is high in the size fractions lower than 75 microns. This is important to note because the final grinding size is fine. Thus, even the difference is significant in the degree of liberation; the final metallurgical result in simulations may not be significantly different in such a fine grinding.

Table 34. Modal composition of plant feed samples. Ab = albite, Act = actinolite, Ap = apatite, Bt = biotite, Cal = calcite, Mgt = magnetite, Qtz = quartz.

Ab (wt%) Act (wt%) Ap (wt%) Bt (wt%) Cal (wt%) Mgt (wt%) Qtz (wt%) Ttn (wt%) Ore A 3.01 3.43 2.48 3.50 0.91 85.57 0.96 0.14 Ore B 12.88 0.00 7.24 10.27 0.00 64.09 5.52 0.00

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Figure 36. Liberation curves of magnetite in the Ore A (left) and Ore B (right).

Simulation for Ore A 7.4

Mass balancing results were used for calibrating models in bulk mineral and mineral by size levels. For simulation at particle level, models described in Table 33 were used and adjusted to match experimental and mass balancing results. In overall, for Ore A, three levels of simulation give the same grade and recovery for all minerals for the final concentrate of the plant with the calibrated parameters. The effect of coarse grinding was investigated by increasing product particle size in grinding circuit (pebble mill and hydrocyclone). The simulation reveals that even in coarse product magnetite recovery and grade is still preserved.

Table 35. Results of the simulations for Ore A at different levels: composition of the magnetite concentrate (Grade wt%) and mineral recoveries. For mineral symbols, see Table 34.

Grinding Level Ab Act Ap Bt Cal Mgt Qtz Ttn

Fine (P80 = 38

µm)

Bulk Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Size Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Particle Recovery (%) 13.87 17.17 23.02 13.19 17.80 95.62 0.00 99.70 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.22 0.00 0.17

Coarse (P80 = 72

µm)

Bulk Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Size Recovery (%) 18.84 24.21 20.41 16.38 17.47 95.59 0.00 99.79 Grade (wt%) 0.67 0.98 0.60 0.68 0.19 96.71 0.00 0.17

Particle Recovery (%) 10.17 22.33 23.23 16.24 26.54 95.81 0.00 99.74 Grade (wt%) 0.36 0.91 0.68 0.67 0.29 96.92 0.00 0.17

Simulation for Ore B 7.5

For the simulation of Ore B, the calibrated parameters that were used at bulk mineral, mineral by size and particle levels for Ore A, were used. The results show that at bulk mineral and mineral by size levels, the mineral recoveries are similar as for the Ore A in fine grinding (Table 36). This is a property of models which define the behavior of minerals on unsized or size-based: regardless of the plant feed the mineral recoveries (and distribution in the full process) is similar, but the grades change. When the head grade lowers, the concentrate grade drops as well.

0 20 40 60 80 100

Magnetite (wt%) in particle

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

yiel

d (%

)0-38 µm

38-53 µm

53-75 µm

75-150 µm

150-300 µm

300-600 µm

600-1700 µm

1700-3350 µm

0 20 40 60 80 100

Magnetite (wt%) in particle

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

yiel

d (%

)

0-38 µm

38-53 µm

53-75 µm

75-150 µm

150-300 µm

300-600 µm

600-1700 µm

1700-3350 µm

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At the liberation level, the result is, however, different. Similar particles behave in the same way as in the base case, but because the mass proportion of particles (thus liberation distribution) is different in the plant feed for the Ore A and Ore B, the final result will differ for both grades and recoveries. The particle level simulation forecasts slightly lower grade and recovery for the Ore B as for the Ore A. Compared to bulk and mineral by size level, the particle level simulation forecast lower gangue recovery thus higher magnetite grade.

Table 36. Results of the simulations for Ore B at different levels for the ore B: composition of the magnetite concentrate (Grade wt%) and mineral recoveries. For mineral symbols, see Table 4.

Grinding Level Ab Act Ap Bt Cal Mgt Qtz Ttn

Fine (P80 = 38

µm)

Bulk Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Size Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Particle Recovery (%) 7.68 0.00 17.60 9.28 0.00 89.29 3.21 0.00 Grade (wt%) 3.13 0.00 2.02 0.90 0.00 93.58 0.37 0.00

Coarse (P80 = 72

µm)

Bulk Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Size Recovery (%) 19.80 0.00 18.85 19.66 0.00 95.58 0.00 0.00 Grade (wt%) 7.18 0.00 1.92 1.70 0.00 89.20 0.00 0.00

Particle Recovery (%) 6.79 0.00 15.22 13.89 0.00 89.62 7.26 0.00 Grade (wt%) 2.75 0.00 1.73 1.34 0.00 93.34 0.83 0.00

Discussion on results of simulations 7.6

Comparison of simulations for Ore A and Ore B demonstrates the difference between mineral and particle level modeling and simulation. In the Ore B, the results from the particle level simulation give more plausible result than the mineral and mineral by size level. This is due to the fact that the parameters were calibrated based on the liberation of particles instead of general calibration to the ore in bulk mineral and mineral by size level. At the particle level, the assumption is that similar particles behave in the same way whereas at the mineral level the assumption is that mineral behaves identically regardless of texture and particle composition. Although no verification and validation for results of Ore B were provided, the simulation results at particle level comparatively to other levels is more credible.

This simulation framework at particle level coupled with ore textural characterization enables the mineralogical approach of geometallurgy to be the most comprehensive approach and only one that can handle quantitative mineralogy in simulation routinely.

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Chapter 8 - Conclusions and recommendations

The main findings of the research study are divided into scientific and practical results. The major scientific results and novelties of this research are as follows:

1. A new Combined method for modal analysis. 2. A new magnetic separator model operating at particle and mineral liberation level. 3. A first published mass balancing an industrial-scale process at mineral liberation level

(multiphase particles). 4. Novel ore textural characterization method. 5. A new concept of utilizing ore texture and breakage information to forecast liberation

distribution. 6. Demonstration of a geometallurgical simulation framework for magnetite ore at particle level.

Moreover, the practical outcomes of the study that has been employed or has the potential for implementation in geometallurgy and mineral processing area are:

7. Generic error model developed for Element-to-Mineral Conversion, implemented in HSC Chemistry 9.

8. Combined method for reconciliation of modal mineralogy and the chemical composition. 9. Combined method for estimation of magnetite and hematite grades without using Satmagan

analysis. 10. Toolbox of automated mineralogy including

- Grain classifier; Automatic identification of minerals in IncaMineral database and exporting particles to HSC Chemistry 9.

- MATLAB code for generating mineral map from BSD and optical images, measuring mineral association, mineral liberation and exporting particles to HSC Chemistry 9.

- MATLAB code for forecasting particle population from mineral map of ore textures .

Conclusions from different parts of the study are drawn and summarized in below, and future directions and research lines are suggested.

Conclusions from the modal analysis study are:

• Three different methods for the analysis of mineral grades were compared firstly in terms of the closeness (cf. trueness) and precision but also with respect to their applicability in geometallurgy. A comprehensive evaluation was done including detection limit, sample preparation, analysis time, costs and additional information that they provide.

• A combined technique of quantitative X-ray diffraction and Element-to-Mineral Conversion has been developed and introduced to overcome the limitations of each of the techniques. Based on critical evaluation it is suggested to be suitable for geometallurgy for the analysis of mineral grades in bulk.

• In iron ores, the combined method gives an estimate on both magnetite and hematite grades and can replace tedious Satmagan and wet chemical Fe2+ analysis.

• A problem occurring with all modal analysis methods is that back-calculated chemical composition from mineral grades does not match perfectly with the elemental grades of commodities received from chemical assays. This can be partially solved by the combined

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method. However, this can be fully avoided for certain elements by weighting, but this requires further study for developing a sound technique for determining weighting factors.

The conclusion from ore texture characterization and predicting particle population are:

• To the best of my knowledge, the Association Indicator was introduced for the first time and used for characterization of ore texture and breakage.

• In the studied Kiruna iron ore samples, the analysis of the Association Indicator values reveals that the breakage is preferential in the iron oxide phase and specifically in magnetite.

• The full particle population was generated artificially based on applying breakage frequency and superimposing particles on ore texture mineral map. The mass proportion of generated particles was adjusted to match the known modal composition of the samples. The outcome showed promising results.

• The developed technique for forecasting particle population from intact ore texture is not ore specific and can be used for any commodity and ore texture.

Conclusions from the WLIMS model development are:

• Using particle-tracking technique, in this study for the first time, demonstrated that the behavior of magnetite-gangue composite particles in magnetic separation is not only dependent on the magnetite grade and particle size but also on nature of the gangue mineral. Particles containing gangue minerals such as biotite, actinolite, and apatite are showing similar behavior in WLIMS where others such as albite, quartz, and calcite are having different behavior respect to the first group. The origin of differences in behavior seems to be tiny magnetite inclusions in the first group of minerals.

• The entrapment phenomenon in magnetic separation was pointed out, and a simple regression model was used for modeling the degree of entrapment for different particles.

• Even though the developed model lacks operating parameters, it can be used for any WLIMS. Entrapment parameters and spread values for each mineral by size must be calibrated. When calibrated for certain operational conditions the parameter value do not require changing as the feed composition changes.

• Benefits of the developed model are that it is portable and does not need continuous calibration according to fluctuation in feed mineralogy, particle size distribution, and liberation characteristics. The developed model requires that the feed be characterized at mineral liberation level.

Conclusions from the process plant simulation are:

• The benefits of different levels of modeling in process simulation were shown. The particle level simulation showed plausible results when feed liberation varied.

• Within this study, it has been demonstrated that simulations at bulk and mineral levels with calibrated parameters to the ore feed are only valid for ores of similar texture and thus having similar liberation characteristics. However, calibrated parameters at particle levels are based on the composition of particles and are capable of giving estimates that are more reliable. In iron ore, the forecasts for the iron grade and recovery do not differ significantly, but for the impurity levels, the particle level simulation gives results that are more reliable.

• The particle level simulation enables optimization, thus finding optimal processing conditions, e.g. in grinding fineness, for different textural ore types and geometallurgical domains.

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• The particle population forecasting has a wide potential to be used in mineralogical approach to geometallurgy as the forecasting the liberation distribution from texture is a critical issue and step between geology and mineral processing. Forecasted particle population from a studied ore texture was used to demonstrate the potential of simulation at particle level.

Based on this work and scope of the geometallurgical approach using mineralogy, following tasks are proposed for future development:

- Integration of combined method to be used in the mineral resource estimates. - Development of texture model in meso-, macro-scale and possibly in three-dimensional space. - Extension and development of the method for forecasting particle population from ore

texture. - Proper validation of particle forecast and process simulation. - Development of particle-based process models for other unit operations important in iron ore

processing (grinding, size classification, flotation, gravimetric separation). - Development of the methods to evaluate the error in geometallurgical prediction. - Practices to define adequate accuracy for geometallurgical predictions. - Validation of developed low intensity magnetic separation model and further development to

introduce operational parameters. - Verification and validation of particle-based models for other ore deposits than iron ore. - Developing the simulation framework in general form to be applied for any ore deposit. - Applying forecasted particle population and simulation framework in the geometallurgical

program and comparing results against processed products.

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Paper I

Analysis of mineral grades for geometallurgy: Combinedelement-to-mineral conversion and quantitative X-ray diffraction

Mehdi Parian a,⇑, Pertti Lamberg a, Robert Möckel b, Jan Rosenkranz a

a Minerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Swedenb Helmholtz-Zentrum Dresden – Rossendorf, Helmholtz Institute Freiberg for Resource Technology, Halsbruecker Straße 34, 09599 Freiberg, Germany

a r t i c l e i n f o

Article history:Received 14 February 2015Revised 29 April 2015Accepted 30 April 2015Available online 11 June 2015

Keywords:GeometallurgyBulk mineralogyElement-to-mineral conversionCombined XRD and element-to-mineralPrecision and trueness

a b s t r a c t

Knowledge of the grade of valuable elements and its variation is not sufficient for geometallurgy.Minerals define not only the value of the deposit, but also the method of extraction and concentration.A number of methods for obtaining mineral grades were evaluated with a focus on geometallurgicalapplicability, precision and trueness. For a geometallurgical program, the number of samples to be ana-lyzed is large, therefore a method for obtaining mineral grades needs to be cost-efficient, relatively fast,and reliable. Automated mineralogy based on scanning electron microscopy is generally regarded as themost reliable method for analyzing mineral grades. However, the method is time demanding and expen-sive. Quantitative X-ray diffraction has a relatively high detection limit, 0.5%, while the method is notsuitable for some base and precious metal ores, it still provides significant details on gangue mineralgrades. The application of the element-to-mineral conversion has been limited to the simple mineralogybecause the number of elements analyzed limits the number of calculable mineral grades. This studyinvestigates a new method for the estimation of mineral grades applicable for geometallurgy by combin-ing both the element-to-mineral conversion method and quantitative X-ray diffraction with Rietveldrefinement. The proposed method not only delivers the required turnover for geometallurgy, but alsoovercomes the shortcomings if quantitative X-ray diffraction or element-to-mineral is used alone.

� 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Geometallurgy is a cross-disciplinary approach that connectsinformation from geology, mineral processing and subsequentdownstream processes into a model in order to describe variabilityin the ore deposit to be used in production planning and manage-ment (Dobby et al., 2004; Dunham and Vann, 2007; Jackson et al.,2011). Geometallurgy has gained attention in recent years and dif-ferent approaches are used for implementation. It is natural to usemineralogy to some extent as a link between geology and mineralprocessing (Hoal, 2008; Lamberg, 2011). This is intuitive since min-erals define the value of the deposit, the method of extraction, eco-nomic risk valuation and the concentration method (Hoal et al.,2013).

A geometallurgical program is an industrial application ofgeometallurgy. It provides a way to map the variation in the orebody, to handle the data and to give forecast on metallurgical per-formance on spatial level. The program also comprises a procedureto employ complex geological information and transfer them to

geometallurgical domains to be used in process improvement, pro-duction planning and business decision-making. The program is aninstrument, which should evolve and change to ensure thatgeometallurgical domains address properly the metallurgicalperformance.

Knowledge on the grades of valuable elements and their varia-tion alone is not sufficient for geometallurgy. Firstly, in several oretypes the distribution of the valuable elements is complex. Forexample in nickel sulfide ores, it is important to know the distribu-tion of nickel between non-sulfides and the different sulfide min-erals (Newcombe, 2011). Similarly, in the process design andoptimization for porphyry copper ores it is critical to know howmuch of copper is hosted in different sulfide and oxide minerals(Gregory et al., 2013). Secondly, the gangue minerals also play acrucial role in processing. For example in lateritic nickel ores, thegangue minerals have a direct effect on the acid consumptionand permeability of the heaps (David, 2008). In refractory and tracemineral ores, like gold and platinum group element ores, thegangue mineralogy defines the entire plant response. Therefore,elemental grades are not necessarily the best attribute to use forthe estimation of recovery and ultimate value. Much of the sustain-ability and energy efficiency dimensions of geometallurgy are

http://dx.doi.org/10.1016/j.mineng.2015.04.0230892-6875/� 2015 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: mehdi.parian@ltu.se (M. Parian).

Minerals Engineering 82 (2015) 25–35

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Minerals Engineering

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driven by mineralogy. Moreover, mineral grades are additive,which makes their geostatistical modeling relatively straightfor-ward (Vann et al., 2011).

Different levels of mineralogical and chemical information assummarized in Table 1 are routinely used for ore characterizationin geometallurgical programs. They can be divided into the follow-ing types with increasing complexity and details: (1) elementalcomposition, (2) qualitative mineralogy, (3) quantitative mineral-ogy, and (4) mineral textures (Jones, 1987; Lamberg et al., 2013).In addition, geometallurgical programs commonly use (5) geomet-allurgical and (6) metallurgical testing (Kojovic et al., 2010;Lamberg et al., 2013). To gather this information into a geometal-lurgical program, the most cost- and time-efficient analysis meth-ods should be selected. Examples of the methods used inmineralogical characterization are (2) identification of mineralsby X-ray diffraction (XRD), (3) analysis of mineral grades by quan-titative X-ray diffraction (Monecke et al., 2001), and (4) derivingmineral liberation information by automated mineralogy basedon scanning electron microscopy (SEM) (Fandrich et al., 2007).When considering different methods for obtaining the mineralog-ical information, the trueness and precision of the informationmust be known. Only then a selection of the most appropriatemethod can be done.

In a mineralogical approach of geometallurgy, information ofthe mineral grades is required for the entire ore body (Lamberg,2011). Thus, the number of samples to be analyzed for mappingthe ore variation in a geometallurgical project is normally large(>10,000; Richardson et al., 2004). When selecting a method, onemust consider several factors such as the costs, required time,availability, reliability, trueness and precision. Particularly theinformation on the precision of the method is frequently not avail-able for the material to be studied.

Mineral grades and textural information are commonly ana-lyzed in polished sections. Automated mineralogy based on scan-ning electron microscopy (SEM) and optical image analyses (OIA)are the known techniques. SEM-based automated mineralogy iscommonly regarded as the most reliable way of estimating mineralgrades. However, the method requires careful and tedious samplepreparation and the method itself is costly and time-consuming(Lastra and Petruk, 2014). On the other hand, OIA-based automatedmineralogy has the lower cost and is less time demanding. CSIRO(Donskoi et al., 2013) has developed an OIA-based automated min-eralogy which has been used for iron ore characterization. In highgrade samples, the OIA system results were close to the SEM-basedautomated mineralogy (QEMSCAN), but in lower grade samplesand low resolutions the OIA results were drifting away from truevalues (i.e. results from QEMSCAN and XRD).

Alternative methods such as quantitative XRD by Rietveld anal-ysis (Mandile and Johnson, 1998) and the element-to-mineral con-version method (Lamberg et al., 1997; Lund et al., 2013; Paktunc,1998; Whiten, 2007) require simpler and faster sample prepara-tion and can be non-destructive. Additionally, if the aim is the esti-mation of mineral grade, they may offer better value thanautomated mineralogical analysis system only if they can fulfillthe requirements on trueness and precision.

The element-to-mineral conversion method is a traditional andsimple way to estimate mineral grades by simultaneously solving aset of mass balance equations formulated between chemical ele-ments and minerals. The method is restricted to relatively simplemineralogy where the number of minerals is not larger than thenumber of analyzed components and the chemical compositionof the minerals (mineral matrix) is known. Mathematically thiscan be written in the following form:

A� x ¼ b;

a11 � � � a1n

..

. . .. ..

.

an1 � � � ann

2664

3775�

x1

..

.

xn

2664

3775 ¼

b1

..

.

bn

2664

3775 ð1Þ

where A is the matrix of the chemical composition of minerals, x isthe vector including the unknown mass proportion of minerals(bulk mineralogy) in the sample and b is the vector of analyzedchemical composition of the sample. The unknown x can then bedetermined e.g. using the nonnegative least squares method(Lawson and Hanson, 1995). The element-to-mineral conversioncan be improved by using additional mineral selective analysismethods such as bromine-methanol leaching for nickel ores(Penttinen et al., 1977), copper phase analysis for copper ores(Lamberg et al., 1997) and Satmagan analysis for iron ores(Stradling, 1991).

The element-to-mineral conversion should not be confusedwith normative mineralogy methods such as the CIPW Norm orthe Cation Norm (Cross et al., 1902) which aims at allocating chem-ical compositions into minerals based on the order of mineral for-mation in rock. These techniques are frequently used ingeochemistry and petrology for the classification of rocks. Theysuffer mainly from a preset mineral list with stoichiometric min-eral compositions as well as from limitations when exotic mineralsare present, which is common in ore deposit characterization.Hence, they are not suitable for geometallurgical purposes.

Quantitative XRD methods include Known Addition,Absorption-Diffraction, Mineral Intensity Factors (MIFs) andFull-pattern-fitting (Kahle et al., 2002). The Rietveld is afull-pattern-fitting method and is regarded as a standardlessmethod. Moreover, sample preparation, measurement and data

Table 1Level of information and analysis methods commonly used in process mineralogical studies and geometallurgy.

Level Analysis result Commonly used analysis methods

1. Elementalcomposition

Chemical composition of samples X-ray fluorescence spectroscopy (XRF); dissolution + Atomic absorptionspectroscopy (AAS)/Inductively coupled plasma optical emission spectrometry(ICP-OES)/Inductively coupled plasma mass spectrometry (ICP-MS)

2. Qualitativemineralogy

List of minerals present in samples, lithology X-ray diffraction (XRD); Optical microscopy

3. Quantitativemineralogy

Bulk mineralogy, i.e. mass proportion of minerals in samples(modal composition)

Quantitative XRD; Element-to-mineral conversion (EMC); SEM-basedautomated mineralogy (MLA, QEMSCAN, IncaMineral, etc.); Optical imageanalysis (OIA) (CSIRO Recognition3/Mineral3); Hyperspectral imaging(SisuRock)

Chemical composition of minerals (as an extra measure toevaluate mineral grade against elemental grade)

Electron probe micro-analysis (EPMA) with energy-dispersive spectrometer(EDS)/Wavelength-dispersive spectrometer (WDS)

4. Mineraltextures

Mineral grain sizes, grain shapes, associated minerals (rocksamples), liberation distribution of minerals in samples(particulate samples)

SEM-based image analysis (MLA, QEMSCAN, TIMA, Mineralogic, IncaMineral,RoqSCAN); Optical image analysis (CSIRO Recognition3/Mineral3); Electronbackscatter diffraction (EBSD); Hyperspectral Imaging (SisuRock)

26 M. Parian et al. / Minerals Engineering 82 (2015) 25–35

analysis are considerably fast. Depending on the sample prepara-tion, measurement conditions (X-ray source, data acquisition time)and crystallinity of the minerals, the detection limit can be as lowas 0.5 wt.%. Spicer et al. (2008) have shown that it is possible to getreliable analysis on mineral grades for heavy mineral sands by theRietveld method. Comparing with Mineral Liberation Analyzer(MLA) measurements, the Rietveld results were not significantlydifferent for rutile, zircon, ilmenite, and total iron oxides but sepa-rately for magnetite and hematite the difference was significantlyhigher (König and Spicer, 2007; Spicer et al., 2008). The differenceswere originated from the way that the two techniques detect mag-netite and hematite. MLA under normal analyzing condition can-not distinguish well between hematite and magnetite. Similarly,König et al. (2011) used the Rietveld analysis for phase quantifica-tion for sinter and slag from a steel plant.

Ramanaidou and Wells (2011) studied the utilization of hyper-spectral imaging for characterizing iron ores. The method is pro-posed for grade control in in-situ mapping and scanning of drillchips. The advantages of the method are that measurements arequick and samples of different volume can be processed. On theother hand, the method requires dry conditions for the imagingtarget (wall, drill core samples), and it fails in identifying certainphases such as sulphide minerals and magnetite.

To improve bulk mineralogy estimation, a combination of theRietveld and chemical analysis has been used by Berry et al.(2011). They applied a nonnegative least square algorithm withweighted values to estimate mineral grades. Their combinedmethod was partially successful in overcoming the limit of deter-mination of the Rietveld analysis which initially posed by XRDmeasurement.

This study uses several types of iron ore samples to comparedifferent methods of analyzing bulk mineralogy, i.e. mineralgrades, to be applied in geometallurgy and process mineralogy.In the comparison of the methods, solely their potential to estimatebulk mineral grades is considered. Additional information thatsome methods offer are considered in the final evaluation of themethods. The element-to-mineral conversions, quantitative XRDby Rietveld analysis and SEM-based automated mineralogy areused in this study. An additional method called Combined EMCand XRD (or shorter: combined method) is developed in order toovercome some of the shortcomings in element-to-mineral con-version and quantitative XRD by Rietveld analysis. Practically, thealgorithm that is used for combined method can be applied forany other method of modal mineralogy to adjust the mineralgrades to match closely with chemical composition of given sam-ple. In addition, this paper aims to develop a model for describingprecision and trueness in analysis of mineral grades. The modelshould cover the whole grade range (0–100 wt.%), be easy to useand be informative.

2. Statistical terminology

Trueness is defined as ‘‘the closeness of agreement between theexpectation of a test result or measurement result and a true value’’whereas precision is the repeatability (or reproducibility) of themeasurement method. Accuracy means ‘‘closeness of agreementbetween a measured quantity value and a true quantity value of ameasurand’’ (Reichenbächer and Einax, 2011). According to TheInternational Vocabulary of Basic and General Terms inMetrology (VIM), accuracy is a qualitative concept and commonlyregarded as a combination of trueness and precision.

The trueness of a measurement method is achievable when it ispossible to conceive a true value. However, in chemical and miner-alogical analysis it is quite common that the true value isunknown. This can be overcome by establishing a reference to

another measurement method or by preparing a synthetic stan-dard or reference sample (ISO 5725–4:1994). The trueness and pre-cision are normally expressed in terms of bias and standarddeviation, respectively (Menditto et al., 2007). To validate correctlya method result, both terms must be considered.

Commonly standards or artificially mixed samples are used forevaluating the trueness. For the analysis of mineral grades, stan-dards are not commonly available. As this study aims to evaluatedifferent analysis methods of mineral grades for practical geomet-allurgy, the usage of a synthetic sample was avoided. Syntheticsamples would not represent the original textures, complexityand variation existing in natural samples. Moreover, using syn-thetic samples would lead to underestimating the error in the anal-ysis of ore samples in practice.

The alternative way to evaluate the trueness is to compareagainst a valid reference. However, the references such as XRFanalysis for chemical analysis or SEM-based automated mineralogyfor mineral grades cannot be regarded as true values. Therefore,when using these references for the estimation of the trueness,which is now unknown, instead of the term trueness the termcloseness was selected to evaluate how close the results are com-pared to the references.

Here, the precision of the methods is addressed by the standarddeviation. The estimate of the standard deviation is done by repli-cate samples and replicate analyses. Repeating only the measure-ment gives the repeatability and repeating the samplepreparation and measurement gives the reproducibility. In thisstudy, the standard deviation calculated for XRF and quantitativeXRD by Rietveld analysis is a measure of reproducibility, whilefor automated mineralogy it is a measure of repeatability.

Based on boot strapping technique Evans and Napier-Munn(2013) suggested that the standard deviation in an analysis of min-eral grades is proportional to the square root of the total area ofparticles measured. Moreover, they conclude that the modelreflects the relationship between standard deviation and numberof particles measured. Similarly, the standard deviation of an esti-mated mineral grade can be calculated with the formula:

r ¼ffiffiffiffiffiffipqN

rð2Þ

where r is the standard deviation, p is the measured mineral grade,q is the value of (1�p) and N is the number of particles measured(Evans and Napier-Munn, 2013; Mann, 2010). Comparatively, therelationship between relative standard deviation and average min-eral grade can be modeled as:

RSD ¼ ax�0:5 ð3Þ

where x is the grade of mineral of interest, RSD is the relative stan-dard deviation, and a is a coefficient. The formula suggests that therelative standard deviation is proportional to the square root of thegrade. This model was used in the following to estimate the (rela-tive) standard deviation of the measurements for any mineralgrade.

The measurement of the closeness is more challenging. Thepaired t-test is often used for comparing two methods (e.g.Benvie et al., 2013). However, the t-test can be used to comparewhether two methods give the same average value but it doesnot provide an easy way for estimating magnitude of the differ-ences respect to a reference method. Nevertheless, the t-test wasnot completely rejected and it was used to validate the comparisonof methods in two ways; by comparing mineral grades andback-calculated elemental grades against references. The selectedreferences for evaluating mineral grades and chemical compositionanalyses were SEM-based automated mineralogy and XRF analysis,respectively.

M. Parian et al. / Minerals Engineering 82 (2015) 25–35 27

For the measuring of closeness, a Root-Mean-Square-Deviation(RMSD) was used besides the t-test (Hyndman and Koehler,2006). Principally, RMSD aggregates the magnitude of deviationsfrom the reference value into a single value. Mathematically, it isa concept similar to the standard deviation, but the term is usedto describe an average deviation from the reference. This is usedas the degree of closeness and is expressed as follows:

RMSD ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðl� xiÞ2

n

sð4Þ

Relative RMSD ¼ 100� RMSD�l

ð5Þ

where n is the number of measurements, l is the reference value, xi

is the measured value and �l is average of the reference values. TheRelative RMSD can be calculated for each mineral and element withdifferent methods. The method showing smallest variation aroundthe reference value (i.e. a lower RMSD) is regarded as the closestto the reference.

3. Materials and methods

3.1. Samples

Northern Sweden is a significant mining district in Europe andcharacterized by diverse styles of mineralization including Feoxide, Cu ± Au and Au ores. More than 40 different iron ore depos-its are known in the area and they all have a variation in characterbased on the ore type, main ore minerals and alteration featuresetc. (Bergman et al., 2001). The Fe content varies between 25–70% and the P content up to 5%. The main minerals are magnetiteand hematite, and the gangue minerals are apatite, amphibole,feldspars, clinopyroxene and quartz. Garnet and calcite are presentin some of the deposits. From textural point of view, there is a widevariation on grain size (100–1400 lm), shape and association ofthe main minerals. Different textures of iron oxides includehomogenous magnetite, magnetite intergrowths of ilmenite andrutile, oxidation assemblage of hematite and rutile (Lund, 2013).

A total of 20 ore and process samples from different iron oredeposits in Northern Sweden were collected for this study. The irongrade in the ore samples (drill cores) varied from 21.3% to 63.0% Feand the ore samples were classified as semi-massive hematite oreand massive magnetite ore (Niiranen, 2006).

The samples, for different analyses, went through multiple sam-ple preparation steps. From crushed samples, a part was taken for apreparation of resin mounts. The remaining part was pulverized inthe disc mill and split into two parts. The first part was used forX-ray fluorescence analysis, and the second was further groundwith a swing mill. The fine powder was used for filling theback-loading holders with an opening of 26 mm in diameter forX-ray diffraction analysis. The p80 of the powder was 20 lm.

3.2. Methods

3.2.1. Elemental assaysChemical analyses of the samples (Table 2) were done at chem-

ical laboratory of Luossavaara-Kiirunavaara AB (LKAB) using thecompany’s standardized methods. X-ray fluorescence spectrome-try (MagiX FAST, PANalytical) was used for the 11 major and minorelements. Divalent iron was analyzed by the titrimetric method(ISO 9035:1989) and the mass proportion of magnetic materialwas measured with the Saturation Magnetic Analyzer (Satmagan)model 135 (Stradling, 1991). A calibration of the Satmagan analysiswas done to give similar results as with the titrimetric Fe2+

method; i.e. for a pure magnetite sample, the Satmagan valuewas 24.3%.

3.2.2. Quantitative X-ray diffraction with Rietveld analysisThe first trial of the X-ray powder diffraction analyses were

done at Luleå University of Technology (LTU) using a PANalyticalEmpyrean X-ray diffractometer equipped with a copper tube,Pixel3D detector and pyrolytic graphite monochromator. The 2hrange was from 5� to 75� with a step size of 0.02�. These conditionsresulted in a total measurement time of 150 min for a single XRDscan. Mineral phases were identified using HighScore PlusVersion 3 software package and the Crystallography OpenDatabase (COD). In the Rietveld refinement, background correction,scale factors, unit cells, preferred orientations, and profile variableswere included.

X-ray diffraction and Rietveld refinement with a copper tubeand monochromator on the iron ore samples led to underestima-tion of iron mineral phases (Parian and Lamberg, 2013). This wasmainly due to microabsorption (Pederson et al., 2004) and also flu-orescence radiation of the iron ore samples by copper tube.Therefore, samples were reanalyzed at the Geological Survey ofFinland (GTK) with PANalytical CubiX3 industrial XRD systemequipped with Cobalt tube and X’Celerator detector. Phase identi-fication and Rietveld refinement afterwards was same as describedpreviously.

Additionally, two of the samples were measured several timesin Helmholtz-Institute for Resource Technology in Freiberg usingPANalytical Empyrean, equipped with a Cobalt tube, monochroma-tor and Xe proportional counter detector. The step width and 2hrange was same as previous measurements. The Rietveld refine-ment on these data was done by BGMN (BGMN by Bergmannet al., (1998)) and these data are used for estimating error forX-ray diffraction and Rietveld refinement.

3.2.3. Automated mineralogyAutomated mineralogy is commonly regarded as the most reli-

able method for the analysis of mineral grades. However, its capa-bilities are beyond reporting only mineral grades. It providestextural properties such as grain size and shape, mineral associa-tions and mineral liberation numerically.

In ore projects, normally 0.3–2.0 m long drill core sections arecollected for chemical assays and mineralogical study. However,crushed drill core has a wide size particle distribution, which is aproblem in the analysis of mineral grades both in sample prepara-tion and in measurement. In the preparation of resin mounts,crushed samples tend to segregate, i.e. large and dense particlesare enriched in the lower part of the resin. This leads to a bias inparticle size distribution as well as in the analysis of mineralgrades (Kwitko-ribeiro, 2012). Therefore, the common procedureis to first size the samples into narrow size fractions, which is ameasure used to minimize analysis error when the focus is onquantitative textural measurements, i.e. liberation etc.

When assaying a large number of samples (>10,000), sizing isnot an option since it multiplies the number of samples to be ana-lyzed. In analysis of polished sections, using unsized samples intro-duces segmentation and stereological errors. The stereologicalerror is less significant than segmentation error and is more influ-ential in the liberation analysis than bulk mineralogy analysis asshown by Lastra and Petruk (2014). To minimize the segregation,the samples were ‘‘double sectioned’’ also known as vertical sec-tioning. This technique is commonly used in several mineralogicallaboratories and has been validated to reduce the sample segrega-tion significantly (Kwitko-ribeiro, 2012). In double-sectioning sam-ples were first mold in resin and after hardening sawed into slices.The slices were thereafter arranged in another mold in a way that

28 M. Parian et al. / Minerals Engineering 82 (2015) 25–35

they show the sedimentation profile towards the side to be ana-lyzed (Kwitko-ribeiro, 2012).

A Merlin SEM – Zeiss Gemini (FESEM, Luleå University ofTechnology, Sweden) with Oxford Instrument EDS detector andIncaMineral software was used for automated mineralogy analy-ses. The IncaMineral system combines backscattered detectorimages with EDS information in the analysis of automated miner-alogy (Liipo et al., 2012). Within the IncaMineral software, the rawanalysis data is stored in a database and mineral identification andquantification can be done either during analysis or retrospec-tively. To obtain a reliable estimate, the number of particles ana-lyzed for the mineral quantification was at least 10,000. In thisstudy, mineral identification was done based on back-scatteredinformation and EDS analysis. Developed software at Luleå univer-sity of Technology (by first author) was used for post-processingthe data i.e. mineral identification, reporting mineral grades andchemical composition of a sample.

To confirm IncaMineral results quality, two resin mount sam-ples were analyzed at the geometallurgy laboratory, TechnicalUniversity of Freiberg by Mineral Liberation Analyzer (MLA) sys-tem, which was equipped with FEI Quanta 650F and two BrukerQuantax X-Flash 5030 energy-dispersive X-ray spectrometers.

The automated mineralogy analysis provided a mineral list,which includes more than 15 phases. In some of the samples, evenseveral types of one mineral were found, e.g. several amphiboles.For geometallurgy, this is not practical and some simplification isnecessary. The simplification is also required for comparing themethods. Therefore, the main phases in the samples were classifiedinto groups of albite (Ab), actinolite (Act), apatite (Ap), biotite (Bt),diopside (Di), orthoclase (Or), quartz (Qtz), andradite (Adr), scapo-lite (Scp), calcite (Cal), magnetite (Mgt) and hematite (Hem). In thegrouping of the minerals and the selection of group representer,the similar behavior of the minerals in the iron processing plant,similarity in their chemical compositions, and abundance of themineral in the group were considered to streamline applicationand evaluation of the methods. For example, group of actinoliteconsists of various amphibole minerals such as tremolite, actinoliteand hornblende. The chemical compositions of the minerals(Table 3) was provided by LKAB and partly taken from a previousstudy from LKAB’s mine in Malmberget (Lund, 2013). Analysis ofmineral chemistry, in those studies, was carried out at theGeological Survey of Finland (GTK) using a CAMECA SX100 electronmicroprobe equipped with five WDS. This information was also

verified by automated mineralogy as the IncaMineral system pro-vides the chemical composition of each analyzed grain and basedon that an average composition of each phase can then be approx-imately calculated.

3.2.4. Element-to-mineral conversion (EMC) and combined methodusing EMC and XRD Rietveld analysis

EMC method is the fastest and the most practical method ofobtaining mineral grades when the existing minerals and theirchemical compositions are known. Principally, the EMC methodsolves a system of linear equations where mineral grades are theunknown variables. In cases where the linear system is not deter-mined, the least-square method can be applied to find an approx-imate solution. Negative solutions are not acceptable for mineralgrades, thus a nonnegative method is used. Several numericalmethods exist for solving the system of equations withnon-negativity constraints. These include the nonnegativeleast-square algorithm (NNLS) (Lawson and Hanson, 1995), theBarzilai-Borwein gradient projection algorithm, the interior pointNewton algorithm, the projected gradient algorithm, and thesequential coordinate-wise algorithm (Cichocki et al., 2009).

Based on the information available (elemental assays andchemical composition of minerals), mineral grades can be calcu-lated by the nonnegative least-square method. However, here thesystem of linear equations is underdetermined by having 12unknowns (mineral grades) and 9 equations (reliable elementalassays and Satmagan). Therefore, mathematically this system oflinear equations does not have a unique solution not even whennon-negativity constraint is added. Practically this means thatmineral grades are calculated for nine phases and for other phases,the solution gives zero grades.

The calculation of mineral grades with the EMC method can bedone sequentially, i.e. system of equations can be divided into twoor more set of equations, and each set forms a calculation round ofits own. The rounds are solved sequentially and the residual chem-ical composition of the round will be used in the following round.EMC with rounds enables to have a better control on importantelements and to reach a solution where the back-calculated chem-ical composition matches perfectly with assays for selected ele-ments. For example in iron ores, silicates are calculated first withnon-negative least squares solution and finally iron and titaniumoxides are calculated from residual iron and titanium (Lundet al., 2013). This gives zero iron residual whereas elements in

Table 2Chemical analyses of samples as wt.% by XRFa and Satmagan (Sat.) method.

Sample Na Mg Al Si P K Ca Ti V Mn Fe Sat. (%)

1 0.16 0.72 0.68 2.5 0.21 0.26 0.8 0.318 0.138 0.039 64.7 21.62 0.00 0.52 0.17 1.1 0.17 0.04 0.4 0.042 0.049 0.085 68.5 14.53 0.00 0.52 0.06 0.1 0.07 0.00 0.1 0.024 0.052 0.093 70.9 17.14 0.00 0.50 0.17 0.8 0.37 0.03 0.8 0.078 0.050 0.070 66.2 6.55 0.00 0.51 0.05 0.0 0.03 0.00 0.1 0.018 0.052 0.093 71.2 17.26 0.00 0.16 0.12 3.6 0.40 0.03 2.6 0.018 0.026 0.101 62.8 3.17 0.00 0.28 0.14 4.9 0.76 0.02 4.6 0.024 0.022 0.101 56.0 0.38 0.00 0.13 0.10 4.1 0.35 0.01 3.7 0.024 0.025 0.101 59.1 0.59 0.00 0.52 0.22 7.0 1.73 0.05 7.3 0.030 0.020 0.132 46.3 0.7

10 0.00 0.23 0.12 4.6 0.48 0.02 4.2 0.024 0.025 0.108 57.3 0.511 0.00 0.27 0.13 5.1 0.80 0.03 4.9 0.024 0.025 0.116 55.4 0.612 0.04 1.30 0.46 4.8 0.10 0.26 1.2 0.246 0.192 0.050 59.0 21.113 0.01 0.95 0.18 2.9 0.45 0.05 1.3 0.192 0.192 0.053 63.0 21.514 0.36 1.50 1.17 6.6 1.17 0.10 5.1 0.078 0.071 0.084 47.9 16.215 0.26 2.07 0.95 6.7 0.97 0.31 3.5 0.120 0.082 0.053 49.3 16.616 0.75 2.82 3.72 19.7 0.24 0.69 2.7 0.186 0.017 0.039 21.3 7.317 0.05 2.32 2.48 12.3 0.02 1.54 1.2 0.168 0.039 0.085 39.6 12.018 0.37 1.34 1.05 4.8 0.66 0.52 3.0 0.360 0.088 0.093 56.6 18.119 0.01 0.17 0.11 0.5 0.06 0.07 0.8 0.126 0.110 0.070 70.0 23.920 0.30 0.69 0.71 3.3 0.41 0.34 1.7 0.240 0.097 0.077 62.3 20.1

a Margin of error (±2d) for XRF assays can be calculated by �0:013�ffiffiffixp

where x is the elemental assay.

M. Parian et al. / Minerals Engineering 82 (2015) 25–35 29

several silicate minerals, like aluminum, magnesium and silica,may show non-zero residual. Therefore, the balance for iron, whichis important element here, is good whereas for elements being lesscritical the balance is acceptable.

Generally, the combined EMC–XRD method originated to over-come limitations of EMC and XRD. It takes mineral grades by theRietveld analysis as an initial estimate and changes mineral gradesto minimize the following function:

f ðxÞ ¼ jb� A� xj ð6Þ

where b is the vector of chemical composition of the sample, A is thematrix of chemical compositions of minerals, and x is the vector ofmineral grades, i.e. unknown to be solved. The absolute minimumof f(x) would be the results of simple element-to-mineral conver-sion method by the methods described above (e.g. NNLS).However, finding a local minimum of f(x) close to the originalRietveld values was found to be more appropriate solution andtherefore the Levenberg–Marquardt algorithm (Bates and Watts,1988) was used in the combined method. Additionally, the algo-rithm can be applied to adjust mineral grades results from othermethods to agree with chemical composition of the sample.

Optimizing functions in MATLAB were used for advanced com-bination of XRD and XRF data for solving the mineral grades. This isreferred to as the combined EMC–XRD method.

4. Results

4.1. Analysis of mineral grades in the samples

It is essential to have a good estimate of the magnetite hematiteratio in iron ores since this ratio defines the process line the ore isfed into (Alldén Öberg et al., 2008). Furthermore, the apatite gradeis used to classify the iron ores in Kiruna ore deposit (Niiranen andBöhm, 2012). The phosphorous content of the final concentrate is aquality criterion; for instance in the Low Phosphorous Sinter Feed(MAF) the maximum acceptable grade is 0.025% P (LKAB, 2014).

From a geometallurgical point of view, magnetite, hematite andapatite are the most important minerals. The analytical results forthese minerals by different methods are compared in Table 4. Itshould be noted for the magnetite grade by EMC, Satmagan analy-sis was used while this was not used in the combined method.Distinguishing magnetite and hematite in automated mineralogyis challenging and requires careful and precise setting (Figueroaet al., 2011). For apatite, the detection limit of XRD can be as lowas 1 wt.%. However, the combined method should allow overcom-ing this limit by taking XRF analysis into account.

Having a good estimate of the gangue silicate minerals in theore is crucial considering that silica is one of the quality require-ments for an iron concentrate. The main silicate minerals in thesamples are albite, actinolite and biotite. Iron bearing garnet i.e.andradite is found with calcite in samples (Frietsch, 1980).Occurring minor silicates include scapolite, diopside, orthoclaseand quartz. The silicate minerals are generally not consideredwhen classifying the ores of LKAB (Niiranen and Böhm, 2012).However, the silica content of the final product must be below cer-tain values, e.g. for Low Phosphorous Sinter Feed (MAF) the limit is0.80% SiO2 (LKAB, 2014). Adolfsson and Fredriksson (2011)observed that silica content in the concentrate does not directlycorrelate with the silica grade in the ore. This refers to that the sil-icate minerals do not all behave in the same way in iron ore pro-cessing. For example biotite tends to be enriched in fine particlesizes (Westerstrand, 2013) where the separation efficiency in con-centration is poor, while andradite can end up to concentrate ifmagnetic separator was not properly tuned.

Considering iron ore processing, biotite, andradite and silicateminerals have significance. Estimation of the biotite and andraditegrade by EMC is underestimated and therefore wrong (Table 5).This is due to the presence of many silicate minerals and the lackof enough assay variables to estimate them correctly. Comparingto automated mineralogy results, in some samples, the Rietveldanalysis overestimated the biotite grade which could be due topreferred orientation and partly very low content resulting in highrelative errors (Kleeberg et al., 2008). On the other hand, all meth-ods gave more or less similar grades for other silicate mineral esti-mations, i.e. the sum of albite, actinolite, diopside, quartz andscapolite.

4.2. Precision of the analyses

Repeats and replicates were used for estimation of the standarddeviation of the analyses. For establishing the error model for pre-cision, the relative standard deviation against mineral grade wasfitted with Eq. (3). In principle, the error model gives the coefficientof variation (i.e. relative standard deviation) for the mineral gradeof interest (Fig. 1). Generally a good fit between experimental dataand model equation was achieved. Comparatively, the precision ofthe methods from the best to the worst are: (1) SEM-based auto-mated mineralogy, (2) element-to-mineral conversion, (3) quanti-tative XRD with Rietveld for simple mineralogy, (4) combinedEMC–XRD, and (5) quantitative XRD with Rietveld for complexmineralogy. This means, for example, for an average ore samplewith 70% magnetite (or hematite) the precision of the methods(i.e. uncertainty in 95% confidence level) vary from ±0.57 to

Table 3Chemical composition of minerals (‘‘the mineral matrix’’) as wt.%.

Mgt Hem Qtz Ap Cal Ab Bt Act Di Adr Scp Or

C% 0.00 0.00 0.00 0.00 12.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00O% 27.42 30.14 53.24 39.32 50.83 50.06 43.61 47.89 44.12 42.71 50.19 49.69F% 0.00 0.00 0.00 3.72 0.00 0.00 0.00 0.00 0.11 0.00 0.00 0.00Na% 0.00 0.00 0.00 0.00 0.00 5.11 0.02 0.02 0.00 0.00 7.35 0.11Mg% 0.01 0.00 0.00 0.07 0.00 0.00 10.26 10.09 7.68 0.71 0.00 0.13Al% 0.05 0.03 0.00 0.00 0.00 10.78 6.91 0.99 0.12 0.20 9.66 8.01Si% 0.00 0.00 46.72 0.00 0.00 33.98 19.60 25.30 24.92 10.20 23.76 27.39P% 0.00 0.00 0.00 16.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01Cl% 0.00 0.00 0.00 0.28 0.00 0.00 0.00 0.00 0.00 0.00 2.03 0.01K% 0.00 0.00 0.01 0.00 0.00 0.00 6.55 0.11 0.00 0.00 0.41 14.39Ca% 0.00 0.00 0.01 40.39 37.17 0.04 0.00 7.55 15.58 22.31 6.20 0.09Ti% 0.05 0.20 0.00 0.00 0.00 0.01 2.24 0.01 0.00 0.15 0.00 0.00V% 0.04 0.07 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Mn% 0.00 0.00 0.00 0.00 0.00 0.01 0.04 0.04 0.01 0.01 0.00 0.00Fe% 72.43 69.56 0.02 0.16 0.00 0.01 10.77 8.00 7.46 23.71 0.40 0.17Sat.% 24.12 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

30 M. Parian et al. / Minerals Engineering 82 (2015) 25–35

±3.68 wt.%. This can be regarded as acceptable in geometallurgy.On the other hand, for average ore grade of 1 wt.% such as apatiteand biotite the coefficient of variation is between 4% and 22%(standard deviation 0.04–0.22 wt.%). The error is high for techni-cal work like resource estimation or process mineralogy (Pitard,1993) but the analysis quality is still good enough for geometallur-gical purposes like domaining where acceptable error can behigher.

4.3. Closeness of the analyses

For quality control, two resin mounts analyzed by IncaMineralwere also analyzed by Mineral Liberation Analyzer (MLA).Comparing analyzed minerals by IncaMineral against MLA analysis(Table 6), mineral grades by IncaMineral are close to MLA mineralgrades, which suggest that the two methods are giving similarresults.

Automated mineralogy analysis results were used as the refer-ence values when comparing closeness of the methods. The pairedt-test implies that generally XRD, combined EMC–XRD and EMC donot give significantly different results compared to automatedmineralogy (Table 7). Meanwhile, relative RMSD shows that thedifference between the automated mineralogy and EMC is rela-tively higher than that of the other methods (Fig. 2 and Table 7).Relative RMSD reveals that XRD results for iron oxide is closestto automated mineralogy while paired t-test suggests XRD resultsare slightly positively biased.

The alternative way of evaluating closeness was by regardingXRF analysis as the reference value and comparingback-calculated chemical compositions of the samples against it.Paired t-test results suggest that combined EMC–XRD and EMCmethods give significantly different mean values for the chemicalcomposition (Table 8). However, relative RMSD indicates all themethods in terms of deviations from XRF assays are in the same

Table 4Analysis of mineral grades for the most important minerals: magnetite, hematite and apatite.

Sample Magnetite (wt.%) Hematite (wt.%) Apatite (wt.%)

EMC XRD CMB EMC XRD CMB EMC XRD CMB AM

1 88.57 89.6 88.27 0.00 0.0 0.05 1.24 0.0 1.25 1.12 60.12 74.6 72.43 35.30 24.6 22.50 0.43 0.0 0.41 0.343 70.90 78.9 78.17 27.92 21.1 20.39 0.25 0.0 0.114 26.95 29.4 27.84 66.63 67.2 65.66 1.65 1.2 1.645 71.31 79.9 79.38 27.97 20.1 19.60 0.19 0.0 0.08 0.016 12.86 12.0 15.09 76.71 69.4 72.10 2.36 3.0 2.357 1.25 0.0 1.06 78.88 74.4 75.22 4.49 4.5 4.48 2.398 2.08 0.0 0.84 82.64 79.8 80.50 2.07 2.1 2.079 2.91 0.0 0.90 62.92 60.3 60.88 10.22 11.7 10.21 10.46

10 2.08 0.0 2.70 79.94 72.3 74.60 2.84 2.8 2.44 3.1711 2.49 0.0 1.58 76.73 72.6 73.84 4.73 4.1 4.7212 81.18 85.1 79.79 0.00 0.0 0.05 0.57 0.0 0.6013 86.44 84.6 85.17 0.00 0.0 0.79 2.08 2.2 2.1414 64.89 66.2 64.01 0.00 0.0 0.00 6.90 5.2 6.9215 66.27 66.6 65.60 0.00 0.0 0.07 5.43 4.7 5.5616 26.75 27.8 25.62 0.00 0.0 0.00 1.40 0.0 1.4217 49.76 49.3 50.53 1.14 0.0 0.67 0.11 0.0 0.1118 75.04 78.0 76.36 0.12 0.0 0.02 3.89 3.5 3.88 2.9719 96.87 98.3 96.39 0.00 0.0 0.02 0.35 0.0 0.35 0.1420 83.33 82.2 83.26 1.43 0.0 1.81 2.41 2.3 2.42

EMC: Element-to-mineral conversion, XRD: Quantitative XRD by Rietveld analysis, CMB: Combined EMC–XRD, AM: SEM-based automated mineralogy.

Table 5Analysis of mineral grades for biotite, andradite and other silicates, which includes scapolite, diopside, orthoclase, and quartz.

Sample Biotite (wt.%) Andradite (wt.%) Other silicates (wt.%)

EMC XRD CMB AM EMC XRD CMB AM EMC XRD CMB AM

1 4.32 1.4 4.75 1.63 0.00 0.0 0.18 0.08 5.27 9.0 5.08 7.042 1.14 0.8 1.72 0.16 0.00 0.0 0.08 0.04 3.49 0.0 2.75 0.193 1.07 0.0 0.35 0.00 0.0 0.07 0.16 0.0 0.604 1.39 1.7 2.05 0.00 0.0 0.00 2.24 0.5 1.785 0.86 0.0 0.29 0.09 0.00 0.0 0.04 0.02 0.00 0.0 0.46 0.026 0.00 0.0 0.00 0.00 7.1 6.81 8.40 7.3 6.767 0.00 0.0 0.00 0.72 0.00 12.1 11.58 17.08 11.81 8.0 8.89 10.498 0.00 0.0 0.00 0.00 10.3 10.30 9.42 6.1 6.829 0.00 0.0 0.92 0.92 0.00 13.3 12.31 15.04 17.34 13.2 13.58 12.98

10 0.00 0.6 0.00 0.36 0.00 16.2 14.19 15.05 10.92 8.1 7.25 6.8811 0.00 0.0 0.00 0.00 12.1 11.53 12.13 9.7 9.2612 0.00 2.3 4.74 0.00 0.0 0.05 13.69 12.6 12.1913 0.70 0.2 2.21 0.00 0.0 0.00 9.00 11.7 8.2614 0.00 1.1 2.10 0.00 0.0 1.24 22.13 27.5 20.9015 0.86 3.0 3.77 0.00 0.0 0.00 22.44 25.0 21.4616 4.65 13.3 11.53 0.00 0.0 0.51 54.62 58.7 51.6917 14.28 31.4 21.78 2.32 0.0 0.55 22.97 13.4 18.4818 7.95 4.9 8.33 3.73 3.83 0.0 0.00 0.38 10.27 10.8 10.48 8.2119 0.00 0.0 1.14 0.34 0.00 0.0 0.05 0.12 0.93 0.0 0.78 0.4220 5.06 1.0 4.84 1.02 0.0 0.23 7.26 13.3 7.31

EMC: Element-to-mineral conversion, XRD: Quantitative XRD by Rietveld, CMB: Combined EMC–XRD, AM: SEM-based automated mineralogy.

M. Parian et al. / Minerals Engineering 82 (2015) 25–35 31

range (Fig. 3). In other words, the deviation from the true (i.e. ref-erence) value in all the methods is about equal.

5. Discussion

Reliable analysis of mineral grades is a crucial part of resourcecharacterization, process mineralogy, and geometallurgy. It is aprerequisite for deportment analysis, mineralogical mass balanc-ing and modeling and simulation of mineral processing circuits.Recently automated mineralogy has become the major methodfor the analysis of mineral grades. In geometallurgy the method,however, is far too expensive and time demanding. When thereis a need for assaying mineral grades in thousands of ore samples,sizing to narrow size fractions is needed and the total number ofsamples for the analysis becomes very big. Therefore, an alterna-tive method is needed for better value.

Quantitative X-ray diffraction with Rietveld analysis has beenproposed as a quick mineralogical method for geometallurgy.Challenges in the method are the detection limit and generaldoubts about its precision and trueness when there is complexmineralogy. Partially, these challenges can be overcome by propersample preparation (Pederson et al., 2004). For iron ores, whenthere are large variations in the grade of iron oxide, phyllosilicate,and minor phases in the samples, sample preparation needs to beadapted carefully for different grade ranges. Additionally, to obtainbest results from Rietveld refinement, the radiation source, theeffective particle size to minimize micro-absorption, and theproper way of filling sample holder to minimize preferred orienta-tion must be sensibly selected. When aiming for practical solutionin this study not all these conditions were optimum.

Instead of using quantitative X-ray diffraction for getting exactmineral grades, the method has been used for classifying purposes,such as geometallurgical domaining and ore block grading (Paine

et al., 2011). This may work in high grade ores like iron, aluminumand industrial minerals. However, in the case of precious and mostof the base metal ores the detection limit creates limitation, whichrestrict that the classification is capable to work only with mainminerals, which may not be the most relevant for geometallurgicalpurposes like domaining.

A combined method using weighted values (Berry et al., 2011;Roine, 2009) provides an alternative to adjust mineral grades tomatch the Rietveld analysis results and chemical assays, but itsproblem is how to define the weighting factors in order to get reli-able results. Weighting factors can be set based on the uncertain-ties of the elemental and mineral grade, but still this approachcannot overcome limitations such as XRD detection limit and higherror in low mineral grades. Combined EMC–XRD method devel-oped here, does not use weighting factors but can still find the clos-est solution to match both the Rietveld analysis results andchemical assays. Knowing the error model, more constraints canbe established for estimating mineral grades by combined method.

Any technique for the analysis of mineral grades in a geometal-lurgical program requires careful mineralogical study before themethod is routinely applied. In combined method, the mineralog-ical study must provide information on the list of all possible min-erals, their crystal structure, and their chemical composition.Additionally, to be able to apply the combined method, the miner-als need to be grouped in a sensible way, i.e. groups consist of min-erals with similarity in chemical composition as well as processbehavior. Therefore, nature of the ore body and the process definethe grouping of minerals, acceptable error, and eventually themethod to be used.

However, combined method is not a universal solution for everysituation as it is. Principally, the algorithm for estimating mineralgrades can take as many restrictive constraints as needed.Therefore, if several minor minerals are present in the samplebut the information for calculating mineral grades is insufficient,the combined method requires additional constraints to convergeto the optimal solution. In addition, the assumption used here isthat the chemical composition of minerals is known and does notvary. Strictly speaking, this is not a realistic assumption, but it sim-plifies the complex situation for finding a bridge between elemen-tal assays and mineral grades.

It is relatively rare to find error estimation for the analyses ofmineral grades published in the literature and research reports.For quality control, back-calculated chemical composition is oftenplotted against the analyzed ones (e.g. Berry et al., 2011; Hestnesand Sørensen, 2012). As these illustrations visualize the quality,they do not quantify how big the difference really is. Paired t-testis used but as was shown in the results, it fails in measuring howclose the results are. In addition, it requires that standard devia-tions are equal and not dependent on the grade, which is unrealis-tic assumption. Relative RMSD is an informative and effective wayof measuring the closeness. The calculation is similar to the stan-dard deviation, which makes it straightforward and portable forseveral purposes like mass balancing and modeling.

The precision and degree of trueness of an analysis for mineralgrades are dependent on the abundance of a phase in a sample andthe number of observations collected. In automated mineralogy,this depends on the number of particles and grains analyzed. In

100101 102

0

10

20

30

40

50

60

70

Mineral grade (wt%)

Rel

ativ

e st

anda

rd d

evia

tion

(%) EMC: y=5.23x -0.5

CMB: y=10.56x -0.5

XRD (Simple): y=8.97x-0.5

XRD (Complex): y=21.79x-0.5

AM: y=3.64x -0.5

Fig. 1. Relative standard deviation against mineral grades (CMB, AM, XRD). Curvesfor different methods derived from replicates and repeats. For Element-to-mineralconversion (EMC) and combined method (CMB) curves are generated using MonteCarlo simulation. For calculating relative standard deviation of combined method,relative standard deviation of XRD with complex mineralogy is used. The dashedvertical line at 1% mineral grade shows the detection limit of XRD.

Table 6Comparing mineral grades by IncaMineral (INCA) system and Mineral Liberation Analyser (MLA) system. For INCA 95% confidence interval is given.

Fe oxide Apatite Biotite Andradite Other silicates

MLA INCA MLA INCA MLA INCA MLA INCA MLA INCA

a 89.90 89.83 ± 0.68 1.12 1.01 ± 0.07 1.74 1.51 ± 0.09 0.00 0.07 ± 0.02 6.38 6.82 ± 0.19b 77.53 77.68 ± 0.63 3.62 3.33 ± 0.13 1.95 1.43 ± 0.09 0.00 0.06 ± 0.02 16.32 17.14 ± 0.30

32 M. Parian et al. / Minerals Engineering 82 (2015) 25–35

X-ray techniques (X-ray diffraction and X-ray fluorescence), theratio of signal to noise, thus analysis time, plays the role. Here asimple equation was used to describe the standard deviation andthe RMSD in the wide grade range where analysis conditions arethe same as commonly used in process mineralogy. This approachis practical when individual standard deviations are needed for

measurements. Examples of such problems are circuit mass bal-ancing and Monte Carlo simulations.

The methods available for obtaining mineral grades eitherdirectly (such as quantitative XRD by Rietveld analysis and auto-mated mineralogy) or indirectly (EMC and combined EMC–XRD)have different advantages and disadvantages. Table 9 summarizesthe different methods and their applicability in geometallurgy. Tobe used for metallic ores, the detection limit must be lower than1 wt.%, which excludes XRD. In geometallurgical programs, thenumber of samples to be analyzed during developing a depositmodel is high, several thousand in a year. Therefore, the require-ments on sample preparation and analysis time and costs excludethe usage of automated mineralogy as a routine tool for the analy-sis of mineral grades in geometallurgy. Even thoughelement-to-mineral conversion has good repeatability, it suffersfrom poor trueness in most of the real geometallurgical cases.This is due to a larger number of unknowns (minerals) than knownquantities (chemical elements assayed) which makes the systemmathematically underdetermined. Hence, the combined methodfulfills the requirements to be used in ore characterization anddeposit modeling for geometallurgy.

Table 7Closeness of analysis methods for mineral grades by paired t-test and RMSD againstautomated mineralogy as the reference.

t Value RMSD

XRD CMB EMC XRD CMB EMC

Fe oxides 2.82a 1.81 2.20 4.77 6.31 8.76Apatite �0.07 �0.52 �0.31 1.80 1.56 1.54Biotite 0.56 1.53 1.49 0.79 1.59 1.74Andradite �1.38 �2.06 �2.21 1.74 2.12 9.64Other silicate �0.16 0.63 2.20 1.63 1.61 2.41

t critical ±2.26 ±2.26 ±2.26

a Absolute value of t is greater than critical value indicating statistically signifi-cant difference in results between automated mineralogy and the method.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Mineral grade (wt%)

Rel

ativ

e R

MS

D (

%)

EMC: y=110x -0.5

XRD: y=56.48x-0.5

CMB: y=76.76x -0.5

Fig. 2. Relative RMSD against mineral grades (EMC, XRD, CMB). Curves for differentmethods derived from fitting calculated RMSD for experimental data with Eq. (3).Relative RMSD values are calculated by Eqs. (4) and (5).

Table 8Closeness of analysis methods for elemental grades by paired t-test and RMSD against XRF analysis as the reference.

Chemical assays t Value by paired t-test RMSD

XRD CMB EMC AM XRD CMB EMC AM

Na 1.39 1.27 �0.36 2.85a 0.35 0.13 0.03 0.15Mg �2.75a �2.07 �3.43a �1.06 0.36 0.14 0.15 0.37Al 0.86 �0.34 2.17a 1.34 0.47 0.06 0.05 0.28Si 2.40a 2.03 1.48 0.42 0.92 0.05 0.06 1.01P �3.69a �5.52a �5.40a 0.40 0.14 0.06 0.05 0.29K �0.06 4.35a �0.23 0.25 0.26 0.05 0.01 0.12Ca �0.94 2.72a 1.77 0.81 0.60 0.02 0.02 1.05Ti 0.78 1.75 �0.22 5.18a 0.18 0.13 0.12 0.19V �2.19a �2.17a �2.03 �1.52 0.06 0.06 0.07 0.04Mn �12.97a �12.80a �13.60a �8.97a 0.08 0.08 0.08 0.08Fe �0.19 �1.17 2.57a �1.42 1.91 0.01 0.15 3.40Satmagan 0.47 0.12 �2.67a 1.12 1.09 0.47

t Critical ±2.09 ±2.09 ±2.09 ±2.26

a Absolute value of t is greater than critical value indicating statistically significant difference between analyzed chemical composition (XRF) and back calculatedcomposition from the mineral composition.

0 10 20 30 40 50 60 70 80 90 1000

10

20

30

40

50

60

70

80

90

100

Elemental grade (%)

Rel

ativ

e R

MS

D (

%)

AM: y=26.03x -0.5

EMC: y=21.57x -0.5

CMB: y=24.74x -0.5

XRD: y=38.38x-0.5

Fig. 3. Relative RMSD against elemental grades (AM, EMC, CMB, XRD). Curves fordifferent methods derived from fitting calculated RMSD for experimental data withEq. (3). Relative RMSD values are calculated by Eqs. (4) and (5).

M. Parian et al. / Minerals Engineering 82 (2015) 25–35 33

The problem remaining is that with all methods theback-calculated chemical composition does not match perfectlywith the chemical assays of the commodity elements. The chal-lenge is that as resource geologists and metallurgist have a longtradition to work with chemical assays, they find it difficult to takeparallel mineralogical information that is not fully consistent withchemical assays. Weighting can be a solution for that but morework is needed to establish solid grounds for defining the weight-ing factors and to control that weighing does not cause the mineralgrades to drift too far away from the true mineral composition.

For a selection of the best possible option further informationregarding practical considerations such as sample preparation,costs, detection limit, and the information that method offers arenecessary (Table 9).

6. Conclusions

Conclusions from the work done are summarized below:

(1) Three different methods for the analysis of mineral gradeswere compared firstly in terms of the closeness (cf. trueness)and precision but also with respect to their applicability ingeometallurgy. Detection limit, sample preparation, analysistime, costs and additional information that they providewere included in the evaluation.

(2) A combined technique of quantitative X-ray diffraction andelement-to-mineral conversion has been introduced to over-come the limitations of each of the techniques. Thus, it issuggested to be suitable for geometallurgy for the analysisof mineral grades in bulk.

(3) The combined method gives an estimate on both magnetiteand hematite grades and can replace tedious Satmagan andwet chemical Fe2+ analysis.

(4) A problem occurring with all methods is thatback-calculated chemical composition from mineral gradesdoes not match perfectly with the elemental grades of com-modities received from chemical assays. This can be partiallysolved by combined method, however, this can be fullyavoided for certain elements by weighting, but this requiresfurther development.

Acknowledgments

The authors acknowledge the financial support from theHjalmar Lundbohm Research Centre (HLRC) and thank LKAB forproviding samples and analysis. The authors kindly thank the sup-port from Kari Niiranen, Therese Lindberg, and AndreasFredriksson from LKAB. Cecilia Lund (Luleå University of

Technology) helped in automated mineralogy and finalizing thearticle. Megan Becker (University of Cape Town) gave commentsand suggestions on the draft paper. They all are greatly appreci-ated. The authors are grateful to the ProMinNET research groupfor comments and advice provided during the meetings. The helpof Jukka Laukkanen from Geological Survey of Finland (GTK) inXRD analysis is appreciated.

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Table 9Comparison of different methods for obtaining mineral grades.

Parameter XRD with Rietveld Automated mineralogy EMCa Combined

Detection limit (wt.%) 1 0.01 0.01 0.01Sample preparation time

(minutes)45 480 0 45

Analysis time (minutes) 90 240 0 90Cost (approximate, US$) 60 200 0 60Experienced operator needed Yes Yes No YesExperienced mineralogist needed Yes Yes Yes YesPrecisionb 9.0–21.8 3.6 5.2 10.6Closeness (against XRF)b 38.4 32.5 21.6 24.7Closeness (against AM)b 56.5 – 110.0 76.8Additional information Crystalline structure of

mineralsTextural information (liberation, association, grain size, intergrowths,etc.)

– –

a EMC method used here is solution of underdetermined situation. Closeness (against AM) is not representative of all EMC cases.b Closeness and precision are the ‘‘a’’ of the model (Eq. (3)). It gives relative standard deviation directly for the grade. The smaller the value is the better is the method.

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M. Parian et al. / Minerals Engineering 82 (2015) 25–35 35

Paper II

Developing a particle-based processmodel for unit operations of mineralprocessing – WLIMS

Mehdi Parian ⁎, Pertti Lamberg, Jan RosenkranzMinerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden

a b s t r a c ta r t i c l e i n f o

Article history:Received 15 March 2016Received in revised form 16 May 2016Accepted 6 July 2016Available online 07 July 2016

Processmodels inmineral processing can be classifiedbased on the level of information required from the ore, i.e.the feed stream to the processing plant.Mineral processingmodels usually require information on total solid flowrate, mineralogical composition and particle size information. Themost comprehensive level of mineral process-ingmodels is the particle-based one (liberation level), which gives particle-by-particle information on their min-eralogical composition, size, density, shape i.e. all necessary information on the processedmaterial for simulatingunit operations. In flowsheet simulation, the major benefit of a particle-based model over other models is that itcan be directly linked to any other particle-based unitmodels in the process simulation. This study aims to devel-op a unit operationmodel for awet low intensitymagnetic separator on particle property level. The experimentaldata was gathered in a plant survey of the KA3 iron ore concentrator of Luossavaara-Kiirunavaara AB in Kiruna.Corresponding feed, concentrate and tailings streams of the primary magnetic separator were sampled, assayedand mass balanced on mineral liberation level. The mass-balanced data showed that the behavior of individualparticles in the magnetic separation is depending on their size and composition. The developed model involvesa size and composition dependent entrapment parameter and a separation function that depends on themagnet-ic volume of the particle and the nature of gangue mineral. The model is capable of forecasting the behavior ofparticles in magnetic separation with the necessary accuracy. This study highlights the benefits that particle-based models in simulation offer whereas lower level process models fail to provide.

© 2016 Elsevier B.V. All rights reserved.

Keywords:Wet magnetic separatorParticle trackingParticle-based model

1. Introduction

Minerals and particles are the key elements in mineral processingoperations and simulation. Bothmineral properties and particle size de-fine the selection of a process and particles govern the process perfor-mance. However, the full potential of using particles in mineralprocessing simulation has not been accomplished yet. This is partlydue to lack of analyzing instruments to collect information on particlelevel as well as lack of mass balancing techniques and data reconcilia-tionmethods capable to work with themineral liberation level. The de-velopment of automated mineralogymethods (Donskoi et al., 2010; Guet al., 2014) has facilitated collecting particle level information. Addi-tionally, data reconciliation and mass balancing techniques improvedfrom the traditional approach of balancing solids and elements(Hodouin, 2010) to reconciling and adjusting particle populations(Lamberg and Vianna, 2007). These developments have built a

foundation to take mineral processing unit models and simulation to anew level.

Taking a step back and looking at the bigger picture, where the feedhas not reached the mineral processing plant yet, a holistic view of ge-ology, mining and mineral processing exists. This approach is knownas geometallurgy, a rapidly expanding area of geology and mineral pro-cessing to create spatially based models for production management(Lamberg, 2011). It requires geological and resource characterizationinformation to be collected in a way to build predictive models for amineral processing circuit.

As to the level of details, geometallurgical predictive models can bedivided into three categories whether the smallest block in the simula-tion is an entire processing circuit (black box model), a section (e.g.comminution circuit) or a single unit operation (e.g. individual flotationcells). Another way of classifying geometallurgical models is based onthe level to that the feed stream properties are described. A streamcan have several attributes including flow rates and particle size classes.A bulk stream can be considered as a set of sub-streams eachrepresenting a particle size class. If there are no size classes available,then unsized or bulk information is used. The flow rates in a stream,from lowest to highest level of detailedness, are solids, elements, min-erals and particles. Obviously, the study goal defines the selection of

International Journal of Mineral Processing 154 (2016) 53–65

⁎ Corresponding author.E-mail address: mehdi.parian@ltu.se (M. Parian).

http://dx.doi.org/10.1016/j.minpro.2016.07.0010301-7516/© 2016 Elsevier B.V. All rights reserved.

Contents lists available at ScienceDirect

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the level and size information. For instance, sized solids are often usedto model and simulate comminution circuits whereas bulk-mineral in-formation is common in flotation.

The selection of a modeling level comes with certain restrictions(Table 1) that limit its usability when expanding it outside the scopewhere the model is created and calibrated. For instance, while a model onsolids flowrate level is enough for equipment sizing in the basic engineeringstageof anoreproject, it cannotbeused for estimating theperformanceof aseparator unit. In the grindability type criterion, material is divided intogrindability types, e.g. hard and soft, and these typeswill behave differentlyin comminution circuit. Clearly, the feed stream that is defined only bygrindability types cannot be adopted directly, for example, in a magneticseparator model, which at least requires elemental or mineral distribution.Inminerals by behavioral types (in bulk or by size) level, eachmineral is di-vided into behavioral types. For example in flotation modeling, thefloatability component approach divides each mineral to fast floating,slowfloatingandnon-floating type (RungeandFranzidis, 2003).Onparticlelevel (ormineral liberation level), the assumption is that, similar particles (interms of the particle's attributes such as composition, size and shape) be-have similarly regardless of fromwhich part of the ore they originate. In aprocess or circuit simulation, the ideal situation is where all unit operationmodels work on a same level. If not, then transformation functions ormodels must be used where some of the required stream properties aregenerated based onexisting information of the streamand additional infor-mation given in a model.

The purpose of this paper is to develop a particle-based unit opera-tion model for geometallurgical purposes by using wet low intensity

magnetic separation (WLIMS) as a case study. The aim is that a parti-cle-basedmodel can forecast composition and flow rates (i.e. recovery)of the magnetic concentrate and tailings for any new feed stream if theparticle level information is available. This type of models can becoupled with any other particle-based unit models in mineral process-ing and recycling (Castro et al., 2005). This approach ensures that allnecessary information is passed through the streams for each unit oper-ation and all process streams including the final products carry particlelevel information (particle size distribution, mineral liberation distribu-tion and etc.). This demands high level information for the plant feedsince all required properties in any processing unit downstream mustbe generated mostly from that. The mineralogical approach togeometallurgy (Lamberg et al., 2013) aims to provide such a high levelinformation to mineral processing simulation. Therefore, a particle-based model of mineral processing units can effectively work in thetheme of geometallurgy to address variations in the ore body in orderto provide a robust production forecast.

2. Models for wet magnetic separators

Literature on magnetic separators focuses on design and operationof the unit with recommendations for improving their performance(Cui and Forssberg, 2003; Dobbins et al., 2009; Oberteuffer, 1974;Svoboda and Fujita, 2003). Models suitable for flowsheet simulationare quite a few, mostly empirical, and rarely based on physical or chem-ical principles behind the process. In the following, various wet

Table 2Magnetic separator models including model level and considered operational parameters.

Model Level Feed properties used in model Input parameters (givenby user)

Output Reference

Davis tubesrecoveryfunctions

Elemental Iron grade Empirical functions foriron recovery

Iron recovery Schulz (1963)

Dobby and Finch Phase behaviortype by size

Magnetic susceptibility and particle size distribution of thefeed

M50 and B, ML Recovery in size class Dobby and Finch(1977)

Davis and Lyman Mineralbehavior type

Feed rate of magnetics (dry) Drum speed, feed andsqueeze pan clearances

Magnetite loss,Concentrate density

Davis and Lyman(1983)

USIM PAC Mineral by size Mineral composition of the feed by size fractions Recovery of minerals insize fractions

Recovery and grade ofminerals in size fractions

Söderman et al.(1996)

King andSchneider

Particle For each particle: magnetic volumetric grade, particle size By-pass function Recovery of particles King andSchneider (1995)

Rayner andNapier-Munn

Mineralbehavior type

Volumetric feed rate, gangue fraction, magnetic volumesusceptibility, magnetic density, the volume of solids

Slurry viscosity in pickupzone

Magnetite loss in tailing Rayner andNapier-Munn(2003b)

Pseudo-liberation Mineralbehavior typeby size

Magnetite grade, particle size distribution Calibration parameters Magnetite recovery Ersayin (2004)

Metso Particle Not specified Not specified Not specified Murariu (2013)

Table 1Modeling levels and their limitations in minerals processing. The model is valid as long as the feed stream assumptions are met.

Level Feed stream assumptions Example of application

Bulk Solids Each particle will behave identically regardless of its size and composition Solid splitter model, equipment scale-up, basic engineeringElement Mineralogy, particle size distribution and liberation distribution are fixed Recovery function model for elementsMineral Particle size distribution and liberation distribution are unchanged Mineral splitter modelBehavioral type Particle size distribution is unchanged. Similar behavioral types will behave

identicallyGravity separation model

Sized Solids Each particle of given size will behave identically Comminution model, Size classification model, equipmentscale-up

Grindabilitytype

Each particle type of given size will behave identically Comminution model

Element Mineralogy and liberation distribution are unchanged Recovery function model in size classesMineral Liberation distribution is unchanged Mineral splitter model in size classesBehavioral type Similar behavioral types will behave identically in narrow size fraction Flotation model (fast and slow floating materials in size classes),

Gravity separation model in size classesParticle Similar behavior of particles of same composition and size Principally applicable to all unit models

54 M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

magnetic separator models are reviewed and compared against themodeling levels given in Table 1.

In magnetite ore processing, the Davis Tube test is traditionally usedto develop recovery and grade models. Its development goes back to1921 when a test previously performed manually mechanized (Schulz,1963). Commonly, the models give the concentrate quality and iron re-covery based on iron grade in the feed. The approach has proved to bepractical for judging amenability of an ore tomagnetic separation. How-ever, themodel is valid as long asmineralogy, ore texture, and distribu-tion of particle size and liberation in the feed remain unchanged.

The empirical model of wet high intensity magnetic separator(WHIMS) by Dobby and Finch (1977) indicates that the recovery of par-ticles into the magnetic concentrate is dependent on the magnetic sus-ceptibility and size of particles. Their empirical model was defined asfollows:

RM x;dp� �

¼ C þ B� log10ML

M50

� �ð1Þ

if MLbM50 � 10−0:45B then C ¼ 0:05 ð2Þ

if M50 � 10−0:45B ≤ML ≤M50 � 10

0:45B then C ¼ 0:5 ð3Þ

if MLNM50 � 100:45B then C ¼ 0:95 ð4Þ

where RM is the recovery of particles having of size dp and volumetricmagnetic susceptibility of x; and M50 is the magnetic cut point atwhich the recovery is 50%.M50 and B aremachine parameters and inde-pendent of the treatedmaterial.ML is an empirical parameter calculatedfrom a formula that is related to mass fraction of magnetic material inthe feed, and magnetic and hydrodynamic force (King, 2012). Experi-mental test work is necessary to determine the distribution of particlesize and magnetic susceptibility in the feed.

Davis and Lyman (1983) defined the feed stream using a binary sys-tem of magnetic and non-magnetic particles split into size classes andstudied the effect of several operational variables like feed rate, drumspeed and magnetite/non-magnetite particle size distribution on anEriez full-scale high gradientwetmagnetic separator. A two componentmodel for the magnetite loss was described based on operational vari-ables. The model lacks the ability to forecast the concentrate grade.

King and Schneider (1995) developed an empiricalmagnetic separa-tor model that already uses particle properties. In the model, the distri-bution of particles between the concentrate and tailing is a function ofthe volumetric abundance of the magnetic phase in each particle. Thefraction of particles that ends up in the tailings stream is described byfollowing formula:

t gv;dð Þ ¼ ∝ dð Þ þ 1−∝ dð Þð Þr gvð Þ ð5Þ

where d is the particle size, ∝(d) is the bypass fraction of particles in thefeed that report directly to the tail. r(gv) is the primary classificationfunction based on volumetric grade of magnetic phase in the particle(gv). The bypass function is modeled from experimental data using thereciprocal of natural exponential functionwith two coefficients. The pri-mary classification function is modeled by a Rosin-Rammler distribu-tion function and is only a function of particle composition, or moreexactly the volumetric grade of the magnetic phase in a particle. Themodelwas implemented in theMODSIM simulation software. However,the size of a particle in classification function was not considered.

The magnetic separator model in the USIM PAC simulator is definedbased on the recovery of minerals in size fractions. The user defines re-coveries to the magnetic concentrate for each mineral by particle sizefractions based on experimental results. An application example wasgiven in the context of designing an iron ore beneficiation plant in Kiru-na where a statistical model for a wet low intensity magnetic separator(WLIMS)wasdeveloped (Söderman et al., 1996). The authors simplifiedthe model by assuming that recovery of magnetite per size class is notaffected by minor changes in the head grade, feed rate or particle sizedistribution of the feed.

Fig. 2. Schematic procedure of preparing survey samples for analysis.

Fig. 1. Schematic view of approach for developing a unit model.

55M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

Rayner and Napier-Munn (2000) developed a model to predict thepercentage loss ofmagnetic particles for awet drummagnetic separatorin a dense medium application. The model is represented by a floccula-tion rate and a residence time (Rayner and Napier-Munn, 2003a). Thefeed stream is described by the behavior type for magnetic particlesand ferrosilicon as the dense medium. The size of the particles was notconsidered in this model.

A simplified approach called pseudo-liberation approach for simu-lating the effect of liberation in WLIMS was proposed by Ersayin(2004). The assumption behind the model was described as increasinggrade of magnetite in the feed results in decreasing the degree of liber-ation of gangue minerals. For a given ore and plant, the pseudo-libera-tion model uses empirical data and cubic spline functions to generatea plant operating surface as a magnetic separator model.

Metso has developed amodel for the LIMS that couples discrete ele-mentmethod (DEM), computational fluid dynamics (CFD) and finite el-ement method (FEM) (Murariu, 2013). In the model, each particle is

treated separately but details on how the model predicts the behaviorof particles in the unit operation are not given. According to Murariu(2013) the model can be used to study the effect of operational param-eters and geometry of LIMS on the separation efficiency. Although themodel is not empirical, characterization of the feed in particle level isthe requirement. The usage of theMetsomodel in flowsheet simulationhas not been demonstrated in literature.

The models, as summarized in Table 2, are able to predict metallur-gical performance to some extent. Themajority of themodels have beendeveloped for optimization purposes with strict adoption to the feedtype.Moreover, the availablemodels are not able tomake use of particlelevel information. The closest model among availablemodels to providesuch a feature is the King and Schneider (1995) model. However, themodel considers particle size only for calculating the bypass to the tail-ings. Therefore, the development of a WLIMS particle-based model canbe a starting point to generate more particle-based models for otherprocessing units of mineral processing.

Fig. 3. Comparison of chemical composition between XRF assays against back calculated from IncaMineral modalmeasurements. Values on the graph are showing corresponding R2 valuefor each element.

Table 3Average chemical composition of minerals (“the mineral matrix”) as wt.% and their specific gravity.

Magnetite Quartz Apatite Biotite Albite Actinolite Calcite Titanite Titano-magnetite Anhydrite

Mgt Qtz Ap Bt Ab Act Cal Ttn Ttn-Mgt Anh

F % 0.00 0.00 3.72 0.00 0.00 0.00 0.00 0.00 0.00 0.00S % 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 23.55Na % 0.00 0.00 0.00 0.02 5.11 0.02 0.00 0.00 0.00 0.00Mg % 0.01 0.00 0.07 10.26 0.00 10.09 0.00 0.00 1.94 0.00Al % 0.05 0.00 0.00 6.91 10.78 0.99 0.00 0.00 2.60 0.00Si % 0.00 46.72 0.00 19.60 33.98 25.30 0.00 14.32 0.02 0.00P % 0.00 0.00 16.06 0.00 0.00 0.00 0.00 0.00 0.00 0.00K % 0.00 0.01 0.00 6.55 0.00 0.11 0.00 0.00 0.00 0.00Ca % 0.00 0.01 40.39 0.00 0.04 7.55 37.17 20.44 0.00 29.43Ti % 0.05 0.00 0.00 2.24 0.01 0.01 0.00 24.41 12.95 0.00V % 0.04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00Mn % 0.00 0.00 0.00 0.04 0.01 0.04 0.00 0.00 0.71 0.00Fe % 72.43 0.02 0.16 10.77 0.01 8.00 0.00 0.00 49.44 0.00S.g.a 5.2 2.7 3.2 2.9 2.6 3.0 2.7 3.6 5.2 3.0

a Specific gravity.

56 M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

3. Methodical approach

Before starting to develop a processmodel, one needs to identify anddecide on the level of detailedness needed for the purpose. Amodel canbe established for the whole circuit, part of the circuit or a process unit.Once the smallest process entity is defined, model level based onachievable detail of feed stream (Table 1) and expectations from themodel can be selected.

Inmineral processing, developing and calibrating processmodels re-quires experimental work. The tests and corresponding analyses mustbe designed to meet the criteria of selected level; process/section/unit,element/mineral/particle, and bulk/sized. As the purpose of this studyis to develop particle-based unit models for several mineral processingunits in iron ore processing, the experimental work was based on aplant survey for an entire concentrator plant. However, at this stageonly data around the primary magnetic separator was used here asthe case study for developing particle-based unit models.

Before experimental data can be used in model development, thedata must be mass-balanced. The mass balancing must be done on thesame level the model is aiming to operate. For example, to address theliberation issues in the performance of a plant, the level of data collec-tion and mass balancing needs to be on the particle composition level.

Once data reconciliation is done, the input and output of the unit isprovided for model development. Principally, a mineral processingunit model is a set of mathematical functions representing the unitthat uses the relevant input data such as feed properties and operatingconditions for forecasting the performance of the unit. The modelinglevel and the model's purpose usually specify the input and output

parameters. The output of themodel can be qualitative or a quantitativevalue. The unit models based on qualitative output are usually devel-oped by unit manufacturers to reflect the effects of changes in theunit. On the other hand, a particle-based unit model is built to take par-ticle properties as the input and provide the same level of output infor-mation. This ensures that the unit models can be coupled together andbe used in flowsheet simulation.

The model should be developed in such way that unimportant de-tails are neglected. The model can be developed based on empirical ob-servations, or first principles behind the process, or by a combination ofboth. If the model uses a transfer function as the mathematical repre-sentation fitted to describe input and outputs, then a black box modelis in use.

After development, the model needs to be compared against obser-vations; this is called verification. The next step, the validation, is whenthe model is used to forecast the performance of the process based onobservations not used in the modeling stage. Once a unit modelhas been verified and validated, it is ready to be used in simulation(Fig. 1). This paper focuses on model development and verification.

4. Experimental

4.1. Samples

The plant survey was done at one of the Luossavaara-KiirunavaaraAB (LKAB) iron ore processing plants in Kiruna, Northern Sweden.While the plant was operating at steady state, selected streams in theplant were sampled during a two hours period. The sampling protocolat LKAB was followed. Incremental sampling was performed aroundthe circuit during the samplingperiod. Sampleswere taken at 10minuteintervals and added to the same bucket after each sampling interval. Thecutter width was at least 3 times the diameter of the largest particles inthe stream so as not to bias against their collection. Prior to sampling adummy sample was taken and the sampler emptied out as it would befor the proper sample.

Additionally, all the information available from the control roomwascollected during the sampling campaign. For two of the streams, sam-pling was repeated three times in order to measure the experimental

Fig. 4. Comparison of mineral grades between measured and balanced data. Values on the graph are showing corresponding R2 value for each mineral.

Table 4Bulk balanced values for WLIMS (mineral grades in weight percentages). For mineral ab-breviations see Table 3.

Streams Solids Mgt Qtz Ap Bt Ab Act Cal Ttn

t/h % % % % % % % %

Feed 454 83.8 0.83 3.16 3.50 2.85 3.86 1.76 0.28Conc. 387 98.0 0.05 0.48 0.56 0.13 0.55 0.11 0.08Tail. 68 2.20 5.25 18.48 20.33 18.34 22.76 11.21 1.44

57M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

error and to control the quality of the sampling. In this paper, samplesaround the primary WLIMS (feed, concentrate and tailings) are usedto develop a particle-based model for the magnetic separator. TheWLIMS feed comes from the overflow of a screw classifier and the con-centrate is sent to a pebble mill for further grinding.

4.2. Sample preparation

The survey samples were prepared according to the procedureshown in Fig. 2. The sample preparation was started with weightingthe samples in wet and dry state (steps 2–4), followed bydeagglomeration and splitting on a rotary splitter to produce sub-sam-ples for further sizing, ensuring there was 5–10 kg per sample to assuresufficient coarser particles per sample (step 5). The pulp samples weredried in room temperature (3). The first split was stored for laterusage (8), the second for bulk chemical analysis by X-ray fluorescence(XRF) (6) and the third for wet sieving (7) followed by drying. Sievingprovided four size fractions: +125, −125 + 63, −63 + 38, and−38 μm. Each size fraction from sieving (9) was split into two parts,one for a XRF analysis (11) and the other one for preparing resinmountsfor optical and scanning electron microscopy.

4.3. Analytical methods

X-ray fluorescence analyses of the samples were done at the chem-ical laboratory of LKAB using the company's standardized methods(MagiX FAST, PANalytical). Chemical analysis of the samples was usedas a quick sanity check to evaluate the quality of modal mineralogy byautomated mineralogy. Epoxy samples on size fractions were preparedat Kemi University of Applied Science. Scanning electron microscopy(SEM) and automated mineralogy analysis on epoxy samples weredone by using aMerlin SEM (Zeiss Gemini - FESEM)with Oxford Instru-ment EDS detector at Luleå University of Technology, Sweden. The SEMsystem was coupled with the IncaMineral data acquisition system byOxford Instruments in order to combine and store backscattered detec-tor images with EDS information during automated mineralogy into ajoint database (Liipo et al., 2012).

In average, N20,000 particles were measured in each size fraction,which sums up to around 300,000 particles in three studied streams.Identifying of minerals, reporting of mineral grades and back-calculat-ing of chemical compositions were done by post-processing the rawdata. The mineral list shown in Table 3 was used as the reference forthe program and back calculation of chemical composition of samples.Chemical composition of minerals was taken from Lund et al. (2013)and verified by EDS analysis.

Mass balancing, data reconciliation, particle tracking, and LIMSmodeling were done using the modeling and simulation software HSCChemistry 8 by Outotec and MATLAB by Mathworks.

5. Results

5.1. Quality of data and measurements

Standard deviation for XRF and automated mineralogy measure-ments in repeated samples were calculated according to Parian et al.(2015). The standard deviation for XRF assays follows the equation

STDXRF ¼ �0:007ffiffiffixp

ð6Þ

Table 5Population and mass distribution of particles in streams.

Stream Particle Population (number of particles) Mass distribution %

Feed Liberated 69,056 69.55Binary 22,240 30.10Ternary 280 0.32Complex 27 0.06

Concentrate Liberated 81,068 72.46Binary 20,846 27.41Ternary 210 0.14Complex 15 0.00

Tailing Liberated 81,277 67.46Binary 20,755 30.70Ternary 881 1.41Complex 327 0.55

Fig. 5. Parity chart showing measured particle type (bin) mass in the feed, concentrate and tailing streams after advanced binning against mass balanced particle types (bin) after theparticle tracking.

58 M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

where x is the elemental grade in wt.%. Standard deviation for mineralgrades measured by automated mineralogy follows the equation

STDAM ¼ �0:208ffiffiffixp

ð7Þ

where x is the mineral grade in wt.%. Eq. (7) was used for setting stan-dard deviations during mass balancing the data for minerals.

To evaluate the quality of automated mineralogy, back calculatedchemical compositions were compared against chemical assays (Fig.3). Generally, good overall correlation was observed. However, minorelements such as vanadium (V), manganese (Mn) and potassium (K)show weak correlation between chemical assays and back calculations.This could be due to either error in XRF analysis at low concentration orinaccuracy in the chemical composition of minerals (Table 3).

5.2. Mass balancing and data reconciliation

Mass balancing and data reconciliation improve the reliability ofmeasurements and can under certain circumstances even enable the es-timation of unmeasured streams and variables. It is a requirement forestimating the metallurgical performance of the circuit, for diagnosisof process bottlenecks, and for modeling the process. Well establishedmethods exist for mass balancing and data reconciliation of mineralprocessing data and several software packages have been developedfor performing these tasks (Hodouin, 2010).

Particle mass balancing is the state-of-the-art technique as devel-oped by Lamberg and Vianna (2007) for mineralogical mass balancing.It transfers the mass balancing concepts of common chemical assaysto themineral level and finally to themineral liberation level. Themeth-od requires delicate considerations to provide consistent results and toovercome missing liberation data. The following steps need to be in-cluded when extending the mass balancing to the particle level (i.e.mineral liberation level):

1) Bulk mass balance by minerals

Fig. 7. Recovery of various binary particles with magnetite, error bar shows two standard deviation. Error in recovery was calculated by Monte Carlo simulation. High errors in someparticle bins are due to low number of particles in the bin. The arbitrary trend curve shows magnetite content in particle and recovery relationship.

Fig. 6. Schematic view of counter-current WLIMS.(Modified after Stener (2014)).

59M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

2) Sized mass balance by minerals3) Particle mass balance (by so-called particle tracking)

As a first step, unsized data was used for mass balancing total solidand mineral flowrates in bulk. The result from the bulk mass balancingwas then used as a constraint whenmass balancing theminerals in sizefractions. This stepwise procedureminimizes the error propagation andensures that bulk and sized mass balances are consistent.

The adjustment of mineral grades in mass balancing for most min-eralswasminor as shown in Fig. 4,where the parity line indicates no ad-justment. Adjustment of anhydrate and titano-magnetite was relativelyhigher compared to others and therefore information on these traceminerals is less reliable. This was mainly due to precipitation ofanhydrate in tailing buckets and false identification of titano-magnetiteduring automated mineralogy. Titanium bearing minerals such astitanite and rutile exists as the lamellae in magnetite grains (Lund,2013), causing the identification of some of the magnetite grains falselyas titano-magnetite. To resolve this problem, titano-magnetite in eachparticle was lumped together with the magnetite and the anhydratephasewas removed. Each particle compositionwas normalized after re-moving the anhydrate phase. Afterwards, mass balancing was redone(Table 4).

The particle tracking technique (Lamberg and Vianna, 2007) aims atadjusting liberation data tomatchwithmass balance results in bulk andsize fractions. The particle tracking is a stepwise procedure that startswith adjusting the mass proportion of the particles in order to matchmodal composition received from bulk and sized mass balancing. It isfollowed by the basic binning, which involves the classification of parti-cles by size and composition into narrow liberation classes (bins). Inprincipal, the number of bins can be as many as the possible combina-tion of phases in particles and grade classes. Practically, in the basic bin-ning stage the population of various particles in the stream defines hownarrow the size classes should be and which combinations of phases inparticles have to be considered. Population andmass distribution of par-ticles in the studied samples showed that liberated and binary particlesaccount for over 99% of the population (Table 5).

In some streams, some bins may have no or very few particles mak-ing the mass balancing result unreliable. In the following stage, the ad-vanced binning, the bins with low numbers of particles are globallycombined (i.e. in all the streams in a similar way) in order to reach asound number of particles in each bin. In this work, the advanced bin-ning was first done for the feed stream and the minimum number ofparticles in each bin was set to 25. This equals to amaximum of 20% rel-ative standard deviation for the mass proportion of the particle type(bin) in question. The other streams were binned in the same way byusing the feed stream as a reference. In the final stage, the mass propor-tion of each bin (particle type) was adjusted to reach the mass balancein the whole circuit by keeping the total solids flow rates as constraints.Additionally, the particle flow rate of each bin was balanced amongfeed, concentrate and tailing by considering a weighting factor calculat-ed from the number of particles observed in each bin. In this study, theparticle tracking resulted in themass balancing of 702 different kinds ofparticles around theWLIMS (Fig. 5). Once the particle types were massbalanced in streams, it was possible to calculate the recovery of eachparticle type.

5.3. Developing a process model for WLIMS

In the WLIMS, the rotating drum with the magnet is partially sub-merged into a slurry tank where it lifts out the magnetic particles.Based on the tank design and the feed slurry flow three types of setupscan be distinguished: concurrent, counter-current and counter-rotation.Selection of the type of magnetic separator for treating an ore isgoverned by feed particle size, throughput, and concentrate grade andrecovery (Stener, 2014).

Based on the type of the magnetic separator, slurry tank and mag-netic arc, several different zones can be defined. For example, the coun-ter-current magnetic separator can be divided into three zones. Thepick-up zone is where the fresh slurry feed encounters the drum. Thescavenger zone is a shallow zone close to the tailings outlet where thedrum's rotation is opposite to the slurry flow. The dewatering zone orcleaning zone is where the drum pushes the concentrate up to the dis-charge and the concentrate water flows back to the tank (Fig. 6).

When ferromagneticmaterial is exposed to themagnetic field, mag-netic ordering occurs based on intrinsic property of the material whichdefines spontaneous magnetization (Svoboda, 2004). The other phe-nomenon happening is the growth of magnetic domains. Dependingon the size of the particle and the strength of the magnetic field, themagnetic particle can consist of single or multiple magnetic domains.If the external field is strong enough or the particle is fine enough(b0.1 μm) particle magnetization becomes homogenous; this is calledmagnetic saturation. Even when the saturated particle is outside of themagnetic field, the particle will not become completely demagnetized.

Magnetized particles in the slurry tend to gradually gather intogroups and form flocs or aggregates. This is calledmagnetic flocculation.Beforemagnetic saturation is reached, the strength of theflocs increaseswith the growth in field strength and effective permeability. The mag-netic content of the particles, the fineness and as well as the nature ofthe non-magnetic material affect the effective permeability (Lantto,1977). It is believed that the magnetic flocculation plays a crucial rolein the recovery of fine magnetic particles.

5.3.1. Physical explanations for observations

5.3.1.1. Recovery of binary magnetite bearing particles. The major masspopulation of particles in the concentrate is formed by liberated and

Fig. 9. Stereological effect on recovery of particles in coarse and fine size fractions. Withsimilar texture, stereological bias is higher in small particles than in coarse ones.

Fig. 8. Recovery of liberated gangue particles in various sizes. Error bars show twice thestandard deviation.

60 M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

magnetite rich binary particles, as expected. For modeling purposes, theaim is to find an equation for the recovery of particles into themagneticconcentratewhen its composition and size is known. Therefore, in Fig. 7the recovery of particles is plotted against composition. Firstly, recoveryis directly related to the magnetite content in the particle. For liberatedmagnetite particles, no matter of the size, recovery is 100%. Secondly, itcan be seen that the recovery of magnetite particles in coarse size frac-tions is higher than those in fine size fractions (Fig. 7). This ismainly dueto higher magnetic force on coarsemagnetite particles and their impor-tant contribution to increase the effective permeability of flocs. For ex-ample, in the case of apatite, particles with around 10% magnetitehave a recovery of around 22% in the fine size fraction (b37 μm), butthe same particles in coarse size fraction (N125 μm)have N70% recoveryto the concentrate. Similar behavior can be seen with other binary par-ticles with magnetite.

5.3.1.2. Recovery of liberated gangue particles. Liberation measurementsrevealed that there are liberated non-magnetic particles in the concen-trate and themass balancing confirms that there is a positive relation be-tween the liberated gangue particle size and the recovery into theconcentrate (Fig. 8). For apatite, fully liberated particles contribute witharound 30% of the total apatite in the concentrate. For other minerals,this value varies. Recovery of fully liberated gangue minerals in the con-centrate can be due to stereological bias, entrainment or entrapment.

a) Stereological biasA stereological bias in 2-dimensional particle image analysis meansthat particles that are regarded as liberated in sections, can actuallybe composite particles in three dimensions. If this is the case thenthe recovery should show a decrease by increasing particle size. Rel-atively speaking in a similar texture a fine-grained particle in coarsesize fraction changes to coarse-grained particle in fine size fraction,as depicted in Fig. 9. This is analogous to that in fine textures the ste-reological bias is smaller (Leigh et al., 1996; Spencer and Sutherland,2000). Therefore, stereological bias as a possible reason for this ob-servation can be excluded.

b) Entrainment phenomenaEntrainment means that particles are dragged into the concentratewith water. This effect is stronger for fine particles than for coarseones (Neethling and Cilliers, 2009), i.e. opposite to the observation.Therefore, also this explanation is rejected.

c) EntrapmentAs discussed earlier, in a flocculation process magnetite particles at-tach to each other. During this process, liberated gangue mineralscan be trapped between magnetic particles. The entrapment ofnon-magnetic particles has been previously reported as enclosuresin the flocs (Lantto, 1977). In the dewatering step (Fig. 6) whenthe drum pushes the flocs up toward the concentrate discharge,water inside the flocs drains back to the tank and takes some ofthe fine liberated gangue particles with (drainage). Madai (1998)has shown that for fine particles the drag force is stronger thanits counter force, the magnetic force. Therefore fine particleshave higher probability to escape from the flocs than coarserparticles. On the other hand, the small porosity size in the flocshinders the coarse gangue particles to be drained out from theflocs. Therefore, the coarse liberated gangue particles have higherchance to be trapped in the flocs and to end up in the concentrate(Fig. 10).

5.3.2. Semi-empirical model of WLIMSEven though observations show a clear correlation between the re-

covery of particles and the physical processes, it is not possible to devel-op a pure physical model. This is mainly due to numerous and complexsub-processes involved in the separation. Further, the data availablefrom the plant survey describes only one operational point. Therefore,themodel developedhere is semi-empirical in nature and tries to repro-duce recovery curves atmineral liberation level. Requirements to be for-mulated for such a model are that (i) it should be flexible to adapt tolinear or curve shaped recoveries, (ii) should have reasonably low num-ber of parameters, and (iii) should reflect physical sub-processes in thesystem. At a later stage, themodel can be further developed to consideroperational variables.

A flexible and relatively simple way to model the recovery patternsof binary particles is to use the incomplete beta function Ix(a,b)(Abramowitz and Stegun, 1965). The incomplete beta function is de-fined as follows:

Ix a; bð Þ ¼ ∫xata−1 1−tð Þb−1dt ð8Þ

If for the sake of simplicity, the a parameter is fixed at 1, variouscurve shapes can be generated by changing only the b variable alone.

For the entrapment, the observation shown in Fig. 8 suggests thatthe probability of entrapment increases by size and nature of ganguemineral. A simple linear relationship based on the particle size can beapplied for each mineral as follows:

RE ¼ E1dþ E2 ð9Þ

where RE is the recovery due to entrapment, d is the particle size, and E1and E2 are the constants. This linear model is applied to predict the en-trapment of different sizes of liberated gangue particles.

Table 6Linear regression models for b and RE. x in the function is the size of particle in microns.

Binary particle Mgt-Qtz Mgt-Ap Mgt-Bt Mgt-Ab Mgt-Act Mgt-Cal Mgt-Ttn

Regression model for b 0.0408x 0.1174x + 1 0.1190x + 1 0.0261x 0.1040x + 1 0.0057x 0.0180xRegression model for RE 6E−06x 0.10x 0.11x 6E-03x 0.11x 8E−03x 3E−03x

Fig. 10.Effect of drainagewater in dewatering zone towash outfinegangueparticles. Grayparticles aremagnetic particles and bright ones are gangueparticles. Drainageflow shownby the straight arrow toward bottom of the tank.

61M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

To model the recovery of various magnetite binary particles in theWLIMS concentrate, the following function is used:

Rx ¼ Ix 1; bð Þ ð10Þ

where x is the grade of magnetite in the particle and b is a spread value.Depending on the mineral type that is binary with magnetite, the b canvary from 0.01 and 30. Finer size fractions generally have smaller bvalue than coarser size fractions. The trend of increasing b values fromfine size fractions to coarse size fractions shows the spread of recoverycurves. Therefore, the spread value in Eq. (10) is dependent on the par-ticle size, the susceptibility of non-magnetic portion of the particle,shape of the particle, and specific gravity of the particle. Finally, the re-covery model by considering entrapment becomes as follows:

R ¼ Rx þ 1−Rxð Þ � RE ð11Þ

Fitting the Eq. (11) with the experimental points gives various bvalues for compositionally different binary particles in different sizefractions. During the data fitting, each particle type recovery wasassigned a weight factor calculated from the number of particles fallinginto the particle bin type. In addition, the highest and lowest b values at95% confidence level were calculated for the particles in each size frac-tion. In general, a linear regression describes the increase of b values re-spect to the particles size. A similar approach was perused forcalculatingRE. The results of the regressionmodels for b and RE are listedin Table 6.

The results indicate that binary pairs of magnetite with gangue canbe divided into two groups. The first group is magnetite binary particleswith apatite, biotite, and actinolite and the second group is magnetitebinaries with quartz, albite, calcite and titanite. For each group an

average regression model for b and RE can be selected and applied tothe model as follows:

Firstgroup : R ¼ Ix 1;1þ 0:12dð Þ þ 1−Ix 1;1þ 0:12dð Þð Þ � 0:11d ð12Þ

Secondgroup : R ¼ Ix 1;0:02dð Þ ð13Þ

where x is the magnetite grade of the particle, d is the particle size.

6. Verification of the model

To verify the developedmodel, themodel was compared against ob-servations in two levels. In the first level the comparison was madeagainst the bulk and sized mineral flow rates. In the second level thecomparison was made on liberation distribution in the concentrate.

6.1. Verification based on bulk and sized level

Comparison of solid flow rates and mineral grades from observa-tions and model indicates that the model forecasts well the solid andmineral flowrates (Table 7). However, in the finest size fraction, the dif-ferences between model and observation are higher than in the othersize fractions and in the bulk. This could be related to the unpredictablebehavior of fine particles in the process. This can also be seen in the re-covery of fine minerals in finest fraction (Fig. 11).

6.2. Verification based on mineral liberation level

Evaluation of the model at particle level was started by comparingthe liberation curves for magnetite particles. As shown in Fig.12, themodel well describes the liberation of magnetite particles. However,the mode of occurrence of minerals in particles is not well describedfor certainminerals (Table 8 and Table 9). The differences for quartz, al-bite, calcite, and titanite are higher than for the other minerals. This isbasically arising from using simple linear regression model for b valuesinmodel for this group ofminerals. However, more observations of par-ticles are required to form a better model for this group of minerals.

7. Discussion

Missing mineral liberation information and a lack of mass balancingtechniques for multiphase particles has hindered the development ofunit operation process models to be based on particle properties(Table 1). Particle level information provides an excellent opportunityto relate particle properties to physical sub-processes and to develop amodel for forecasting the performance of any unit operation.

Table 7Solid and mineral flow rates in bulk and sized fractions from model and observations.

Conc. Fraction Solidt/h

Mgt%

Qtz%

Ap%

Bt % Ab%

Act%

Cal%

Ttn%

Obs. Bulk 387 98.0 0.06 0.48 0.57 0.14 0.55 0.11 0.080–37 μm 116.9 98.8 0.06 0.13 0.39 0.03 0.21 0.34 0.0037–63 μm 68.5 98.2 0.03 0.56 0.47 0.19 0.48 0.00 0.0363–125 μm 109.5 97.7 0.05 0.66 0.68 0.16 0.60 0.01 0.11+125 μm 91.7 97.1 0.09 0.67 0.73 0.19 0.99 0.02 0.18

Model Bulk 385 98.0 0.06 0.47 0.51 0.07 0.50 0.05 0.090–37 μm 115.5 98.0 0.01 0.19 0.31 0.02 0.20 0.03 0.0237–63 μm 68.5 98.6 0.04 0.49 0.39 0.04 0.37 0.03 0.0763–125 μm 109.4 98.0 0.05 0.59 0.55 0.05 0.50 0.04 0.11+125 μm 92.2 97.4 0.15 0.68 0.80 0.20 1.00 0.09 0.18

Fig. 11. Recovery of minerals in size fraction from observations (left) and model (right).

62 M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

The developed particle-based WLIMS model can forecast recoveryand product quality of any new feed stream if the particle level informa-tion is available. Process simulators and unit operation models that op-erate at particle level exist and are becomingmore common. In addition,simulation of a process where the model level is at particle level staysstraightforward, i.e. input and output streamof themodel can be direct-ly used by any other unit models. For example, the hydrocyclonemodelby Donskoi et al. (2005), which uses particle level information, can becoupled with the developed WLIMS model. In addition, developmentof more of suchmodels is on-going for other unit operations such as flo-tation (Minz et al., 2013) and comminution (Mwanga et al., 2015). Thisapproach ensures that all necessary information is passed between unitoperations and is accessible for all process streams including the finalproduct streams.

Notably for the purpose of geometallurgy, the liberation level modelis suitable only if the geological model provides information on ore tex-tures level and if there is a mechanism to transfer this information togenerate multiphase particles with compositional information in thecomminution stage. The example of such a characterization was givenby Lund (2013), who obtained detailed mineralogical data and com-bined it with a particle-based model.

The developed model can be used in optimization for example bytesting the effect of grinding fineness and detaching of flocs beforesending the concentrate to the cleaning stage. From the curve shapescoarser grinding gives higher recovery but lower grade compared tofine grinding. Detachment of the flocs could potentially decrease the en-trapment. Further development is needed to relate the model parame-ters to the operational parameters or include certain sub-processes ofmagnetic separation if themodel is intended to be used for process con-trol or to investigate the effects of operational conditions.

Observations at particle level as well as physical theory imply thatmagnetic separation is a complex process that is controlled by both op-erational conditions and the feed stream properties. Studying and

characterizing the feed stream at particle level provides insight aboutthe performance of a magnetic separator that previously was not possi-ble to reach accurately. The developed semi-empirical model of WLIMSdescribes the recovery of particles based on two mechanisms; recoveryof particles due tomagnetic volume and entrapment. This was achievedthrough applying the particle tracking technique. However, there areseveral other factors that need to be addressed.

7.1. The effect of mineral nature, grain size and shape

The relationship between particle size and recovery of fully liberatedgangue particles can be explained by the entrapment phenomenon. Asseen in Fig. 8, there are slight differences between the gangue minerals,i.e. apatite, actinolite, and biotite show entrapment higher than the rest.In the case of apatite, fine magnetite inclusion (b1 μm) were observedin the apatite in the concentrate, which under normal condition of auto-mated mineralogy was not possible to detect. On the other hand, apatitein the tailings seems not to have magnetite inclusion as those found inthe concentrate. This also can be true for actinolite and biotite sincesuch an observation has been reported previously (Niiranen, 2015). De-tection of fine magnetite inclusion can be easily missed in the measure-ments and data processing of automated mineralogy, hence magneticsusceptibility measurement of present minerals and individual particles,if possible, would be needed to verify whether the liberated gangue par-ticles end up to concentrate because of their magnetic susceptibility rath-er than entrapment. While higher susceptibility due to magnetiteinclusion probably plays a major role, the effect of grain shape shouldnot be neglected. Actinolite and biotite, can vary in shape and are oftenelongated that makes their release from flocs harder. In addition, angularparticles have naturally strongermagnetic forces at the corners and edges.

The spread factor b in Eq. (10), describing how close the recoverycurves are for different size fraction, is closely correlated to particlesize, the susceptibility of non-magnetic portion of the particle, to

Table 8Mode of occurrence of minerals in the concentrate from observations. Each row describesthe association of named mineral with the minerals stated on columns in percentages.

OBS Mgt Qtz Ap Bt Ab Act Cal Ttn

Mgt 98.14 0.10 0.55 0.52 0.07 0.35 0.07 0.12

Qtz 75.79 9.42 1.23 3.37 0.40 3.55 0.70 0.60

Ap 59.88 0.07 32.62 0.71 0.49 0.97 0.25 0.01

Bt 66.33 0.33 0.50 27.99 0.60 0.78 0.16 0.32

Ab 41.75 0.96 0.95 1.09 45.63 2.15 1.44 0.22

Act 54.10 0.43 0.67 0.86 0.82 36.52 0.22 0.18

Cal 49.72 0.79 1.29 3.40 1.22 0.71 40.62 0.27

Ttn 91.32 0.46 0.05 1.47 0.96 0.95 0.51 1.50

Shaded cells indicate the mass proportion of liberated particles.

Fig. 12. Liberation curve for magnetite particles from observations (left) and model (right).

Table 9Mode of occurrence of minerals in the concentrate from the model.

Model Mgt Qtz Ap Bt Ab Act Cal Ttn

Mgt 97.93 0.10 0.59 0.53 0.11 0.39 0.10 0.12

Qtz 88.00 5.92 0.13 0.15 0.02 0.39 0.01 0.02

Ap 63.12 0.03 32.21 0.04 0.02 0.06 0.01 0.01

Bt 72.19 0.02 0.09 23.52 0.08 0.22 0.05 0.01

Ab 71.34 0.02 0.10 0.59 17.25 1.31 0.02 0.03

Act 61.43 0.05 0.06 0.13 0.12 33.19 0.03 0.01

Cal 88.90 0.05 0.12 0.21 0.11 0.34 7.84 0.11

Ttn 95.15 0.02 0.02 0.12 0.07 0.38 0.03 0.00

Shaded cells indicate the mass proportion of liberated particles.

63M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

shape of the particle, and specific gravity of the particle. The smaller thegrain size is, the lower the magnetic force on the material becomes,resulting in weakening and shortening of the flocs (Lantto, 1977). Onthe other hand, coarse magnetic particles increase the strength of theflocs and the length of the chains, thus resulting in an increase of totalrecovery. The nature of gangue minerals, magnetic susceptibility ofgrains, shape and total susceptibility of particles affect theflocs' effectivepermeability. For particles with sharp corners, porosity in the flocs in-creases and the total effective permeability becomes smaller comparedto when flocs are packedwith rounded particles. Specific gravity of par-ticles may have a high impact during the cleaning stage. Particles withlower specific gravity tend to follow drainage water more easily thanothers.

7.2. The effect of feed quality

As seen in observations, the entrapped liberated gangue particles inthe concentrate are one of the sources of impurities in the products.While formation of the flocs is stronger in high grade magnetite oreand is crucial for the recovery offineparticles, releasing gangue particlesfrom these flocs is highly unlikely. Unless the flocs becomedemagnetized or detached, entrapped gangue particles inside the flocsfind their way to the concentrate. Mechanical detachment of the flocscan be momentarily but may be enough to let gangue particles escapefrom the flocs.

The studied ore is such a high grade and shows high recovery notonly in the first magnetic separation but also in the whole process.This raises the question whether liberation information is really neededfor the process simulation. However, in producing high quality productsthe recovery is not the main concern but the impurities are, thus thegrade of gangue minerals in the concentrate. For a high quality ironproduct, the requirements for certain impurities are tight and must bemet (LKAB, 2014). For example, phosphorus and silicon contents ofthe product are the determinative criteria meaning that relatively highliberation is needed to reach a pure product. In some iron depositseven sulphur existmainly in the form of sulphideswhich is problematicespecially when monoclinic (thus magnetic) pyrrhotite is present(Arvidson et al., 2013).

Conversely, in processing of low grade ore, the mineral liberationcan cause a recovery issue as well. It is expected that the strength offormed flocs in low grade feedwill beweaker and the loss of binary par-ticles with magnetite and fine magnetite particles accordingly behigher.

7.3. The effect of stereological bias

As it is known, 2-dimensional measurement of liberation which in-herently is defined in 3-dimension is biased estimate of the liberation.The liberation is always overestimated and themagnitude of the overes-timation depends on ore texture. The bias exist for liberation estimation,however the bias affects the model parameters in less degree. In calcu-lation ofmodal parameters, instead of using absolute value of liberation,the term liberation recoverywas used. Thismeans the overestimation ofliberation presents itself in feed and concentrate which to some extendcancel each other. In this way, themodel can take the uncorrected liber-ation data as well as corrected liberation data as an input and gives thesame quality of the liberation.

8. Conclusion

Using particle tracking technique for the first time demonstratedthat the behavior of magnetite-gangue particles in magnetic separationis not only dependent on the particle size but also on nature of thegangue mineral. Particles containing gangue minerals such as biotite,actinolite, and apatite are showing similar behavior in WLIMS whereothers such as albite, quartz, and calcite are having different behavior

respect to the first group. The origin of differences in behavior seemsto be tiny magnetite inclusions in the first group. Also the entrapmentphenomenon is greater in the first group than in the second group.

The developed model requires that the feed stream is described atparticle level and each particle must have information on its size andmineral composition. Even though the model lacks operating parame-ters it can be used for any WLIMS. Entrapment parameters and spreadvalues for each mineral by size must be calibrated. When calibratedfor certain operational conditions the parameter value should notchange as the feed composition change.

Benefits of the developed model are that it is portable and does notneed continuous calibration according tofluctuation in feedmineralogy,particle size distribution and liberation characteristics. The developedmodel requires that the feed is characterized on mineral liberationlevel. In geometallurgy, validated methods to provide such informationthrough thewhole ore body don't exist and therefore fully utilization ofthe model requires that such a concept and model is developed.

Acknowledgment

The authors acknowledge the financial support from the HjalmarLundbohm Research Centre (HLRC) and thank LKAB for providing sam-ples and analysis. The authors kindly thank the support from KariNiiranen, Mikko Kauppinen and Andreas Fredriksson from LKAB. Theauthors would like to show their gratitude to all personal helping insample preparation at LKAB. Cecilia Lund's and Bertil Pålsson's helpfrom Luleå University of Technology is kindly appreciated.

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65M. Parian et al. / International Journal of Mineral Processing 154 (2016) 53–65

Paper III

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Ore texture breakage characterization and fragmentation into multiphase particles Mehdi Parian*, Abdul Mwanga, Pertti Lamberg and Jan Rosenkranz * Corresponding author, Minerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden; Tel. +46-920-492556; Fax +46-920-97364, e-mail: mehdi.parian@ltu.se.

Minerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden

Keywords: Textural characterization, iron ore, mineral liberation, breakage, particle population

Abstract The ore texture and the progeny particles after a breakage in the comminution are the missing link between geology and mineral processing in the concept of geometallurgy. A new method called Association Indicator Matrix based on co-occurrence matrix was introduced to analyze the mineral association of ore texture and particles. The Association Indicator Matrix can be used as a criterion to classify ore texture and analyze breakage behavior of ore texture. Within the study, the outcome of breakage analysis with Association Indicator Matrix was used to generate particle population of iron ore texture after crushing. The particle size of forecasted particles was taken from experimental and frequency of breakage in phases was defined based on Association Indicator and liberation of minerals. Comparison of liberation distribution of iron oxide minerals from experimental and forecasted population shows a good agreement.

1. Introduction Ore texture characterization concept in geology focuses on the geological aspects of the texture such as ore formation and genesis (Craig, 2001; Nyström and Henriquez, 1994). For geometallurgical purposes, ore texture characterization should be quantitative and provide quantitative information regarding progeny particles formed in comminution and their composition, thus on liberation distribution (Petruk, 1988). The significance of ore texture on beneficiation and other downstream processes is recognized and has been evaluated in mineral processing (Bonifazi et al., 1990; Donskoi et al., 2008; Gaspar, 1991). Qualitative or categorical geological classification is not sufficient for mineral processing. The mineralogical approach to geometallurgy requires information on ore textures to enable quantitative evaluation of mineral liberation distribution and the required crushing and grinding energies for mineral liberation.

1.1 Terminology The terminology used for describing mineral liberation and breakage has not been harmonized therefore the definitions of the key terms are given below (see Figure 1):

Particle: A unity consisting of single or multiple grains and single or multiple phases (particles 1, 2 and 3).

Grain: A unit composed of only one mineral that has a clear interfacial surface with other grains (A and B grains in particles 1 and 3).

Liberated particle: A particle consisting of only one phase (particles 2 and 3). Degree of liberation: Mass proportion of mineral of interest occurring as liberated particles in

2

the particulate material. Mineral liberation: a) An action where minerals are liberated (comminution).

b) A broad term which describes the mode of occurrence of mineral in particulate material.

Liberation distribution: Mass distribution of mineral of interest in particle population. Preferential breakage: When breakage and cracking more frequently occurs in one phase (King,

2012). Random breakage: When breakage and cracking are not favored by any phase or boundary

region.

1)BA

2)B

3)B B B

Figure 1. Composite particle and liberated particle.

Definition of what encompasses ore texture varies among geologists and metallurgists (Leigh, 2008). A comprehensive review of the definitions for ore textures is given by Vink (1997) and Bonnici (2012). The common definition for ore texture refers to volume, grain size, shape, spatial distribution and association of each mineral in the ore, thus in intact, pristine stage, i.e. in the unbroken material. The other issue is in what scale textural information needs to be collected. Microtexture term is used for grain-scale features like mineral inclusions in another grain, mesotexture for hand specimen sizes, and macrotextures for scales larger than mesoscale (Richmond and Dimitrakopoulos, 2005). Ore texture is a generic term that refers to all scales.

1.2 Ore texture measurement Ore texture measurement is commonly performed on thin sections, polished slabs, or drill cores depending on the required scale and details for intact ore or particulate samples. Optical microscopy, scanning electron microscopy (SEM), hyperspectral imaging, and x-ray diffraction mapping are common methods to acquire spatial distribution of phases in a sample. Generally, the mineral map is generated, and parameters of interest are calculated. Image analysis tools are commonly used to measure and quantify ore textural attributes (Nguyen, 2013; Pérez-Barnuevo et al., 2012; Zhang and Subasinghe, 2012).

Ore texture and particle composition information is a critical part of the mineralogical approach to geometallurgy. The ore texture and the progeny particles after a breakage in the comminution are the missing link between geology and mineral processing in the concept of geometallurgy. Generally, ore texture is quantified in terms of descriptors (such as covariance function, proximity function and linear intercept length distribution (Zhang and Subasinghe, 2012)). However, these descriptors are mostly developed for binary systems, and there is no extension for three-dimensional ore texture volume. In this study, ore textures and particles are quantified by association indicator to show the trend of ore texture breakage in crushing.

1.3 Mineral liberation modeling In the concept of liberation modeling, various approaches are known. The first approach is to model liberation independently from size reduction modeling and assuming that liberation process is related to the texture of the ore and the target size (Gaudin, 1939; Wiegel and Li, 1967). Usually, the main parameters in this liberation model are the average grade of phases and the size ratio between particles and grains. This approach is also called texture modeling and is achieved by superimposing

3

particles mesh over texture image. This approach further developed from simple textures to consider a variety of ore textures (Barbery, 1991) or transformation of textures to simple forms (Meloy and Gotoh, 1985). In this, the key parameters are the volumetric grade of the ore mineral and the interfacial surface area between phases which is related to the grain size.

The second approach was developed by extending the theory of liberation (Andrews and Mika, 1976; Wiegel, 1976). These authors have considered the problem of simultaneously accounting for liberation and breakage in a batch mill. Other approaches have been reported in the literature such as integration of liberation, size reduction and process modeling (Bax et al., 2016; Khalesi, 2010).

A fundamental part of liberation models is how the ore texture is defined or is characterized to be used for developing predictive liberation models. The second part of liberation model is how the mineral distribution in particles is defined. This can be described by distribution functions without measurement or measured on by images analysis techniques. A majority of liberation models are based on binary system (i.e. an ore mineral embedded in a gangue matrix), and they lack the capability of forecasting multiphase particles. A comprehensive review of liberation models and their development in 80’s and before was given by Barbery and Leroux (1988). Another important part of liberation modeling is how actually fragmentation (breakage) happens. As discussed earlier, a simple approach is to superimpose particle patterns over textures. A recent review of mineral liberation and liberation in comminution is given by Mariano et al. (2016).

Practical implementation of mineral liberation models in the mineral processing is rare. This is because the models are mainly for binary systems and taking models to the multiphase system is too complicated. However, in simplified ore textures (binary system) the models have been tested and compared against experimental data (Barbery and Leroux, 1988; Choi et al., 1986; Finch and Petruk, 1984; Hsih and Wen, 1994; Leigh et al., 1996; Schneider et al., 1991).

In simulation software in mineral processing, MODSIM has implemented complete Andrews-Mika liberation modeling. HSC Chemistry since version 7.1 (Outotec, 2012) has included liberation model as built-in comminution models. Traditional comminution models describe the product particle size distribution and internally the software forecast the liberation distribution of the product if the liberation information on the feed stream is given (Lamberg and Lund, 2012). This is done by keeping the liberation distribution within the size fractions unchanged, and the changes are applied only to mass proportions of different size fractions. As the mineral grades between the particle size fractions may be different, the shift in mass proportions of the particle size fractions would change the mineral grades in bulk. Therefore, there is extra reconciliation step to conserve the bulk mineral balance between the feed and product.

2. Materials and methods

2.1 Samples Various AQ (core diameter 27 mm) and BQ drill cores (36.5 mm) of iron ore with variation in ore textures were selected from Kiruna and Malmberget ore bodies. The samples were cut along the core axis and were scanned by the flatbed scanner. Afterward, the drill cores were cut in intervals of two centimeters. Two pieces were used for preparing epoxy block; other pieces went through the crushing process. These pieces were crushed in laboratory jaw crusher with closed side setting opening of 3.35

4

mm. The crushing product was sieved, and subsamples of each size fraction were selected to make epoxy samples for particle measurements (Figure 2).

Drill core sample

Axial cut

Drill core scanning

Cut in pieces (20 mm)

Two pieces for ore textural study Crushing (-3.35 mm)

Sizing

Resin mounts for size fractions

Figure 2. Schematic procedure of preparing samples for ore textural study.

Routine analysis of ore textural samples is affected by required details, image resolution, time and cost of analysis. Optical and SEM based automated mineralogy are the common methods of obtaining ore textural image. The image is treated by image processing tools to extract textural and mineralogical information.

Ore textural study was done in optical and scanning electron microscopy. The aim was to analysis particulate and intact rock samples to generate the mineral map. Afterward, the mineral map was used for retrieving textural attributes and liberation.

For eight drill cores, mineral maps were created for intact ore and particulates samples after crushing. Crushed sample sieved and sized in 1.68-3.35 mm, 0.85-1.68 mm, 0.43-85 mm and 0.30-0.43 mm size fractions. Measurement of -0.30 mm size fraction was skipped due to the high liberation of minerals in all samples.

2.2 Analysis

2.2.1 Image acquisition Image acquisition of ore texture was performed by mosaic capturing of field images by automated stage optical microscopy (Zeiss Axio Imager) and SEM backscatter detector (AZtec - Zeiss Merlin). The whole image of the samples was generated by stitching field images by built-in programs. Minerals relating to specific gray level in backscatter image were identified by EDS analysis of the phases at that gray level. This data was used later in assigning phases in mineral maps.

5

2.2.2 Image processing Image processing is a rapidly advancing area of retrieving information from images. The technique is used to classify objects in the image (such as grains, particles or phases) and retrieve a wide range of features. In an ore textural study, captured images are used for phase discrimination, calculation of object shape factors, mineral grades, and the association between phases. In this study, image processing sequences including phase discrimination, object separation, feature extractions were done by writing code in MATLAB. The code can analyze ore texture and particulate samples to give numeric ore textural features and liberation. The extension of the code can generate particle population from ore texture by defining breakage pattern and particle size distribution.

Phase separation Phase separation began by assigning multiple threshold values according to a range of gray level of each phase in the sample. The image pixels corresponding to each threshold interval was assigned a new value representing a phase. In particulate samples, the epoxy region was assigned a zero value for simpler processing of objects during imaging processing.

Composition and liberation Obtaining a mineral map of ore texture or particulate sample facilitates the calculation of mineral grades and liberation. Generally, the area of each phase (number of pixels occupied by the phase) in a particle or whole texture are calculated to obtain information on the composition of the particle. To convert this value to weight percentages, the density of minerals is used as weight factors in the calculation of composition.

The other important factor that can be useful in characterizing breakage and also interest in some aspect of mineral processing (such as flotation and leaching) is liberation by exposed surface area of particles. In each particle, this is calculated by normalizing measured shared boundary between phases and background (epoxy).

Mineral association Association of minerals can be estimated based on the proportion of minerals in the particles. However, this approach for the intact ore texture only gives mineral grades of texture. Therefore, an alternative method is to calculate the interfacial surface area between minerals in the intact ore texture or particle as an indication of association.

An image can be considered as a matrix of pixel values. An easy and straightforward way of estimating association in the image is using co-occurrence matrix. A mineral map with n phases (n pixel values) will have n × n size co-occurrence matrix. Each cell of the matrix, C(i,j), is correspondence to the number of times that the cell i is situated with cell j in the defined offset. Here, for calculation of association, the co-occurrence matrix is the sum of cell values for 0-360° in intervals of 45° (Figure 3).

6

315°

0°

45°90°135°

270°225°

180°

Figure 3. The schematic matrix of pixels showing different orientations for offsets.

For example, for a simple case with three-pixel values as below with one-pixel distance offset, the corresponding co-occurrence for various orientations is as Table 1.

1 2 3

Figure 4. An image matrix with three cell values

Table 1. Table of co-occurrences, showing the abundance of co-occurrence cells in different orientations for Figure 4.

Co-occurrence 0° 45° 90° 135° 180° 225° 270° 315° Sum 1 – 1 2 1 3 0 2 1 3 0 12 1 – 2 2 3 3 3 2 1 4 4 22 1 – 3 3 1 0 1 1 3 1 3 13 2 – 1 2 1 4 4 2 3 3 3 22 2 – 2 4 1 2 1 4 1 2 1 16 2 – 3 2 4 2 1 2 1 1 1 14 3 – 1 1 3 1 3 3 1 0 1 13 3 – 2 2 1 1 1 2 4 2 1 14 3 – 3 2 1 4 2 2 1 4 2 18

Therefore, the co-occurrence matrix for Figure 4 is:

=

181413141622132212

C

(1)

The co-occurrence matrix can be normalized to give an indication of association based on the abundance of a phase interfacial in the sample. This can be done by normalizing non-diagonal cells, row or column wise. This is called association indicator matrix (AIM). For example, for above example, AIM is:

−−

−=

9.511.489.381.611.379.62

CAIM

(2)

7

The non-diagonal values are the association indicators. For the above example, phase one has 62.9% association with phase two and 37.1% with phase three. In the particles, the exposed surface of particles may consider in the calculation. This can be done by including the background (epoxy) as another phase. This also makes the calculation of the surface exposure of minerals straightforward.

Limitations The optical image was planned to be used for discrimination of hematite and magnetite in the samples. Even though hematite and magnetite could be distinguished easily in the optical image, imperfect image stitching by built-in programs lead to incorrect registration of image objects (Figure 5). Additionally, uncorrected uneven illumination in the image fields presented another obstacle in the image processing of the data (Figure 6). These problems could have been fixed by correcting uneven illumination in the field images as well as aligning field images in a proper way. However, AZtec system for capturing backscatter images does not provide an easy way to access field images.

Figure 5. Imperfect image registration. The optical image (left), BSE image (middle), Blend of Optical and BSE images (right).

Figure 6. The uneven illumination effect in the stitched images (left side optical image, right side BSE image).

3. Results

3.1 Association indicator for ore texture characterization The analysis of 8 drill cores of iron ore in terms of modal composition and association indicator shows variations in ore textures (Table 2). The average grain size of gangue phases was estimated in optical image microscopy while grain size of magnetite and iron oxide (magnetite and hematite) was measured by image processing technique.

8

Table 2. Phases, mineral grades, Association indicator matrix of ore textures and average grain size (80% passing size).

Sample Phase Grades (wt%)

Association indicator matrix (%)

Average grain size (µm)

E

Biotite Amphibole

Apatite Magnetite

3.17 2.67 2.04

92.13

−−

−−

28.4286.3687.2041.5477.2782.1792.4043.2464.3445.3144.2111.47

400 600 400 881

F

Quartz Feldspar Apatite

Magnetite

0.17 1.10 1.35

97.38

−−

−−

34.7949.1517.565.8817.918.295.5403.2902.1637.4432.1731.38

100 200 300 894

G

Quartz Feldspar Apatite

Magnetite

0.92 0.72 0.29

98.07

−−

−−

45.1368.4887.3685.5267.3148.1596.4186.618.5128.3689.382.59

200 300 300

1905

D1

Quartz Feldspar Biotite Apatite

Magnetite

5.52 12.88 10.27 7.24

64.09

−−

−−

−

10.2288.3518.2684.1546.4125.2922.1508.1419.2463.1063.4655.1827.1313.498.3462.4798.1020.502.1979.64

100 200 200 300 504

A2 Quartz Apatite

Hematite

2.18 1.87

95.96

−−

−

90.7910.2095.8305.1696.5604.43

200 300

1486

A1 Quartz Apatite

Iron oxide

4.23 3.86

91.90

−−

−

65.3535.6441.6859.3138.7962.20

300 500

1218

B2

Quartz Feldspar Apatite

Iron oxide

3.48 2.32 1.88

92.32

−−

−−

38.2018.5245.2795.5354.2751.1846.3993.762.5243.2669.689.66

400 400 600

1629

C1 Feldspar Apatite

Iron oxide

1.28 6.90

91.82

−−

−

56.7344.2687.8013.1994.5906.40

100 700

1192

The association between magnetite and apatite in magnetite samples is in order of F > E > D1 > G while the association between apatite and magnetite is F > E > G > D1. Even though D1 has the highest apatite grade the association between magnetite and apatite is less than E and F samples with high-grade magnetite. Consideration of both modal composition and association indicator gives insight about the assemblage of phase in the texture. Approximately in all samples, apatite is highly

9

associated with magnetite and iron oxide phase regardless of apatite or magnetite grade. Also, considering grain size of phases, except in D1 sample that has roughly even grain size distribution, in the rest of the samples magnetite and hematite grains are coarser than the grains of other phases.

As many of the samples have high iron oxide grade and mineral liberation is expected to be very high in these, only four of the samples with a high amount of gangue phases namely E, D1, A1, and C1 were selected for further studies.

3.2 Association indicator for particle characterization The AIM can be used for characterizing breakage behavior of particles and estimating the association of minerals based on the interfacial perimeter in the particle. The association indicator for particles is a unique way of assessing particle population. The AIM values for different type of particles are listed in Table 3. For example, particles P1 and P2 have a similar composition, but they have different AIM values. In the AIM of particles, surrounding area of particles (e.g. epoxy, free space) is considered as an additional phase. In this way, the exposed surface of particles is considered in the AIM. The first row of the AIM shows liberation by exposed surface.

A B C

P1

P3P2

P3

Figure 7. Particles with different composition and interfacial perimeter

Table 3. Comparison of association indicators for various type of particles.

Type Composition AIM Type Composition AIM

P1 [ ]252550

−−

−−

440564444120406042850

P2 [ ]252550

−−

−−

173350173350202060252550

P3 [ ]251065

−−

−−

0336701000

15246133067

A [ ]00100

−−

−−

0000000010000100

3.3 Ore texture and breakage characterization Characterization of ore texture before and after breakage provides valuable insights about the fracture pattern in comminution, the population of particles for specific ore texture and their relation to parent ore texture. Characteristic of ore textures from simplest to more sophisticated way can be considered by analysis of particle size distribution after breakage, distribution of liberations and analysis of changes in associations. In the context of the mineralogical approach to geometallurgy, predicting the particle population from ore texture is a critical step to establish an interface between geology and mineral processing. This is also subject of interest in mineral processing for liberation analysis and comminution processes.

10

3.3.1 Particle size distribution after breakage Particle size distribution of comminuted ore textures in one stage crushing, and 100% less than 3.35 mm are demonstrated in Figure 8. Generally, the crushed samples approximately have similar particle size distribution.

Figure 8. Cumulative particle size distribution of particles after one stage crushing (left) and after 100% crushing less than

3.35 mm (right).

Modeling of particle size distribution of the comminuted sample is a well-established area and not new. However, to compare the size distributions numerically and also enable generating the particle size distribution for further purposes, the particle size distributions were fitted with Rosin-Rammler distribution function as follows:

−−×=

n

DDDf

2.63

exp1100)( (3)

where

f(D): Cumulative weight percentage of particles passing size D

D: The particle size

D63.2: The particle size where the distribution value is 63.2%

n: A factor describing the spread of the distribution

The parameter values of particle size distributions (Table 4) suggests that more or less all the ore textures show similar particle size distribution after crushing. In general, textures with finer grain size have wider particle size distributions (lower n values) such as D1 and F samples. This data is used later for generating particle size distribution for forecasting particles.

Table 4. Parameters for Rosin-Rammler equation.

One stage crushing crushing 100% less than 3.35 mm D63.2 n D63.2 n

E 1.90 1.31 1.62 1.56 D1 3.32 0.90 1.16 1.06 A1 2.47 1.09 1.25 2.37 C1 2.48 1.08 1.38 1.47

10 -1 10 0 10 1 10 2

Upper size (mm)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

pass

ing

(%)

E

D1

A1

C1

10 -1 10 0 10 1 10 2

Upper size (mm)

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

pass

ing

(%)

E

D1

A1

C1

11

3.3.2 Distribution of particle types after breakage The distribution of particle types (by composition) in the samples shows that most of the samples have very high liberation even in the coarsest size fractions, > 1 mm (Figure 9). Major liberation contribution is from iron oxide minerals. Even in the multiphase particles, iron oxide is the major contributor. Among the samples, D1 sample has the highest amount of locked particles.

Figure 9. Distribution of particles by liberated, binary and complex particles in weight percent in size fractions. Liberated

particle counted as >95 wt% of the phase of interest.

3.3.3 Association Indicator distribution for binary and complex particles Distribution of particle association indicator has significance in defining the breakage behavior of particles. By comparing the association indicator in the intact sample and in crushed one conclusion on randomness versus degree of preference in breakage can be made. This value is an estimation how the breakage separates one phase from another compared to original ore texture.

Before analyzing the Association Indicator for different phases, it is important to understand how the breakage pattern affects the Association Indicator values. In simple cases as demonstrated in Table 5, when breakage is a phase-boundary fracture, phases reach a liberated state in coarse particle sizes. This means the interfacial area between phases disappear and consequently, association indicator values become zero. On the other hand, the association with the background (exposed surface) reaches to its maximum i.e. 100% Association Indicator value.

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100E

Biotite

Amphibole

Apatite

MagnetiteBinary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100D1

Quartz

Feldspar

Biotite

Apatite

MagnetiteBinary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100A1

Quartz

ApatiteIron oxide

Binary

Complex

1680-3350 (µm)

850-1680 (µm)

425-850 (µm)

300-425 (µm)

0

10

20

30

40

50

60

70

80

90

100C1

Feldspar

ApatiteIron oxide

Binary

Complex

12

In a case of preferential breakage in one phase, Association Indicator value for the phase where breakage occurs decreases for non-liberated particle compared to original particle while Association Indicator value of the phase with no breakage remains same. In the case of boundary-region breakage, Association Indicator values for the phases decrease respect to parent particle while due to generating free surface Association Indicator values between phases and background increases. An indication of this type of fracture is observing a significant number of non-liberated particles in fine size fractions.

Table 5. A simple demonstration of the effect of breakage type on variation in AI values for particles (A and B are phases and C is the free space). DOL is the degree of liberation.

Parent particle0 Breakage Progeny particles1 AI change DOL A DOL B

BA

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Looking at the distribution of Association Indicator values between phases, for example, magnetite and apatite in Figure 10, the Association Indicator value for apatite-magnetite after breakage compared to ore texture has not been changed significantly, however for magnetite-apatite the Association Indicator decreases in finer size fractions. These indicate that the breakage between magnetite and apatite (two major phase in D1 sample) is a combination of boundary-region and preferential in magnetite phase. The part that should not be neglected is the contribution of detachment breakage. Since the liberated particles are not considered in this graph, no conclusion can be made about this type of breakage. However, if the surface liberation of one phase increases dramatically simultaneously by decreasing particle size without leaving locked particles behind, that could be an indication of detachment process.

13

Figure 10. Distribution of Association Indicator values for magnetite and apatite in D1 samples.

To investigate changes of Association Indicator values for different phases, the term AI50 is introduced. The AI50 is the value of the Association Indicator for 50% of the population of locked particles (median value). AIM50 is the association indicator matrix filled for AI50 values for each cell. AIM50 can be generated for each size class of locked particles and compared against AIM of the original ore texture. This can be used to evaluate breakage and trend of separation of two specific phase from each other.

The graphs (Figure 11-14) show the changes in AI50 values for different paired phases. AI50 for a phase and background (epoxy) demonstrates the abundance of a phase free surface in locked particles. The trend along with the liberation of the phase show the generation of free surface for the specific phase in size fractions.

Figure 11. Changes in AI50 from ore texture to size fractions for E sample.

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Figure 12. Changes in AI50 from ore texture to size fractions for D1 sample.

Figure 13. Changes in AI50 from ore texture to size fractions for A1 sample.

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Figure 14. Changes in AI50 from ore texture to size fractions for C1 sample.

A significant trend in all samples is the association between iron oxide minerals and gangue phases. The AI50 value in size fractions decreases from ore texture while the iron oxide free surface in locked particles increases. This indicates that in these samples, the breakage is mostly preferential in iron oxide phase. Additionally, increased mass proportion of free particles (thus liberation degree) is another reason to support preferential breakage.

3.4 Forecasting the particle population from ore texture Ore texture mapping and breakage behavior of ore are the critical steps for forecasting the particle population. Experimental work and analysis that has been done on the ore textures can be utilized for forecasting particle population. The particle size distribution of particles modeled by Rosin-Rammler equation along with the degree of breakage either preferential in phase or random estimated by breakage characterization are the main parameters for forecasting liberation distribution.

Simple assumptions can be made to reduce the complexity of forecasting particle population. For example, rectangular particle shapes are used, selectively or randomly positioned particles over ore textures is used to generate particles. The size of particles is taken from modeled particle size distribution. Schematically, the approach that is applied here is shown in Figure 15.

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Figure 15. Schematic view of generating particle population from ore texture.

3.4.1 Assigning breakage frequency To assign preferential breakage in a phase or entirely random breakage, breakage probability function was used for selecting pixels on the mineral map of ore texture. For example, if the breakage is known to be preferential in some specific phases, a probability function can be generated based on the degree of breakage to position random particles selectively over ore texture. To ensure that the particle has the surface exposure for that particular phase, the corner of the rectangle was selected for the anchor to position on the mineral map. For given ore texture D1, by random breakage and 100% preferential breakage in magnetite phase, the liberation distribution of magnetite in size fractions would be as Figure 16.

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Figure 16. Modeled liberation distribution of magnetite in size fractions for random breakage (left) and 100% preferential

breakage in magnetite (right).

From the degree of liberation distribution and AIM values in size fractions, the degree of breakage can be roughly estimated as given in Table 6 for the studied samples. For example, the degree of liberation of D1 sample is around 74% for magnetite and 4% for apatite in the fine fractions while AIM50 for these phases indicates that surface exposure of the phases in the locked particles is increasing in the fine fractions as well. This is suggesting that for the liberation of magnetite and apatite, preferential breakage in these phases are the main contributor for liberation. If we assume that the main breakages in the sample are either preferential in phases or random (no preferences in any way), it is safe to use a degree of liberations as a rough estimate to position rectangle corner in phases. For the D1 sample, this would be 4% chance to place rectangular corner in apatite phase, 74% chance for magnetite phases and 21% chance to have no preferential positioning (random).

Table 6. The probability distribution for preferential breakage in a specific phase and random breakage established based on the degree of liberation.

Breakage E D1 A1 C1 Quartz - 0.1 1.3 - Feldspar - 0.1 - 0.5 Biotite 0.3 0.8 - - Amphibole 0.0 - - - Apatite 1.2 4.4 5.0 5.2 Iron oxide 88.1 73.5 83.3 83.2 Random 10.4 21.1 10.4 11.1

Applying preferential and random breakage over ore textures yields particle population. Approximately one million particles were generated for each sample.

3.4.2 Adjusting liberation to match modal mineralogy Generating particles by this method does not necessary give the same modal composition as the experimental work for some size fractions specifically for finer fractions. However, the liberation distribution is still close to the experimental liberation. The differences in modal composition and degree of liberation of some minerals could be due to the way that the particles are generated. In realistic breakage with classification stage, when particle breaks preferentially in one phase, non-liberated progeny particles are generated as well. This means that non-liberated particle still has a chance to break to fully liberated particles in finer size fractions, but this cannot be considered in the particle generation approach. In current particle generation, grade of the phase with highest

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preferential breakage increases in finer fractions. This specifically is true for the finest size fraction. Possible explanation is the resolution of the mineral map that in certain point particle size is reached. This means many fine particles are consist of only a few pixels or even one pixel. This can be fixed by the approach that was introduced by Lamberg & Vianna (2007) to adjust the mass proportion of particles to match the known bulk modal composition. This is not a perfect solution, but it solves the inconsistency between liberation distribution of particles and modal composition. The modal composition of selected samples from experimental and texture breakage with the adjusted composition are listed in Table 7-Table 10. In general, similar composition can be reached for all samples only by adjusting the mass proportion of particles.

Table 7. The modal composition of E sample from experimental (Exp.) and generated particles after adjusting liberation (Adj.).

Fraction Biotite (wt%) Amphibole (wt%) Apatite (wt%) Magnetite (wt%) Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj.

>1680 1.64 1.57 1.51 1.52 0.90 1.42 95.95 95.49 850-1680 0.97 0.92 0.62 0.75 0.45 0.89 97.95 97.43 425-850 1.00 0.96 0.50 0.70 0.58 0.95 97.92 97.39 300-425 1.30 1.26 0.57 0.86 1.72 1.85 96.40 96.03

Table 8. The modal composition of D1 sample from experimental (Exp.) and generated particles after adjusting liberation (Adj.).

Fraction Quartz (wt%) Feldspar (wt%) Biotite (wt%) Apatite (wt%) Magnetite (wt%) Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj. Exp. Adj.

>1680 6.22 6.71 23.08 22.63 5.33 5.30 6.43 6.40 58.9 58.87 850-1680 3.63 4.08 13.02 12.49 5.64 5.65 9.38 9.38 68.3 68.29 425-850 1.50 1.51 2.07 2.58 7.15 6.94 5.76 5.77 83.5 83.30 300-425 1.50 1.76 2.78 3.22 7.28 6.96 6.03 5.87 82.4 82.19

Table 9. The modal composition of A1 sample from experimental (Exp.) and generated particles after adjusting liberation (Adj.).

Fraction Quartz (wt%) Apatite (wt%) Iron oxide (wt%) Exp. Adj. Exp. Adj. Exp. Adj.

>1680 6.67 6.46 3.90 4.42 89.43 89.12 850-1680 2.92 3.08 1.93 2.28 95.15 94.64 425-850 5.06 4.99 5.92 5.64 89.02 89.37 300-425 2.63 2.85 6.90 6.45 90.48 90.71

Table 10. The modal composition of C1 sample from experimental (Exp.) and generated particles after adjusting liberation (Adj.).

Fraction Feldspar (wt%) Apatite (wt%) Iron oxide (wt%) Exp. Adj. Exp. Adj. Exp. Adj.

>1680 1.52 1.49 3.26 3.76 95.22 94.75 850-1680 0.73 0.69 1.57 2.06 97.70 97.25 425-850 1.10 0.92 4.03 4.42 94.88 94.67 300-425 1.26 1.03 7.33 7.21 91.42 91.77

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3.4.3 Comparison of liberation of iron oxide minerals As the major phase in the samples is iron oxide mineral and its liberation is critical for mineral processing plant performance, the iron oxide liberation distribution comparison is made between experimental and forecasted particles. Generally speaking, in most of the samples, the trend of iron oxide liberation is predicted well (Figure 17). However, particle population of magnetite samples (E and D1) presents better liberation distribution than those where both magnetite and hematite are present. In overall, this suggests that the ore texture is a major factor controlling the liberation distribution in crushing.

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Figure 17. Liberation distribution of iron oxide minerals from experimental (left) and forecasting particles (right)

4. Discussion Image processing methods are widely used for ore texture and particle characterization, however, liberation by composition and exposed surface are still the dominated methods for liberation and particle characterization. One of the shortcomings of the existing methods for association and liberation distribution is the inability to compare the particle texture against the original ore texture numerically. Textural descriptors that are commonly used for particles (Pérez-Barnuevo et al., 2012) are to show the complexity of texture or identification, but they lack the capability to relate particles to the parent texture in a way that can be used for the breakage analysis and forecasting.

The association indicator matrix (AIM) can be regarded as an extension of pioneer work by Lund et al. (2015) to account for a grade of mineral in the particle in the assessment of association. The suggested method could not consider phase boundaries or exposed surface. Therefore, the applicability of association index was limited especially when there were disseminated grains or inclusion in the particle. Current method accompanied by particle composition can store valuable information about the distribution of interfacial areas between phases and liberation distribution by composition and exposed surface.

The merits of association indicator over absolute value of interfacial area or common co-occurrence matrix are not only that it is less sensitive to scale, for example, due to fractal effect, but also values can be compared to different textures as well as particles and can be used as criteria for textural classification.

The cell values in the AIM also gives relevant information about how the phases are occurring in the ore texture. For example, if the AI value goes near 100%, it is an indication that one phase is mainly accompanied by another phase, for instance as inclusions. Also, if the purpose is to identify or categorize new textures, the AIM can be used as a criterion.

The other potential strong point of AIM is the capability of evaluating the nature of breakage of given ore texture for further generation of full particle population. This was demonstrated by four drill core samples where liberation distribution of iron oxide minerals was compared. In general, results for magnetite samples were closer to experimental data. This could be because in iron oxide samples hematite and magnetite are lumped together, and same breakage frequency as magnetite was used for hematite.

Generated mineral map of ore texture from drill core mapping was used as an input for generating particles. The particle size distribution from crushing was used for generating various size of rectangles

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that were superimposed on the mineral map. For positioning the rectangles over the mineral map, breakage probability was used. The assumption was that the preferential breakage in the phase is the cause of the liberation of minerals and random breakage can yield both liberated and non-liberated particles. The obstacle in this approach is that grade of mineral with highest preferential in finer size fractions progressively increase. Therefore, liberation adjustment step was required to match modal composition in size fraction according to experimental.

The value of the developed method is that it links original texture and mineral liberation. The approach generates full particle population which can be directly used in particle-based process simulations.

5. Conclusions To best of our knowledge, the association indicator was introduced for the first time and used for characterization of breakage. In addition, following points were introduced and applied in this work:

• In the studied samples, the analysis of the AI values indicates that the breakage is preferential in the iron oxide phases specifically in magnetite. This was further investigated by generating particles based on defined breakage. This can be done by establishing breakage probability function.

• The full particle population was generated based on applying breakage on ore texture mineral map. The mass proportion of generated particles was adjusted to match the known modal composition of the samples. The outcome was satisfactory.

• The particle population forecasting has a great potential use in mineralogical approach to geometallurgy as the forecasting the liberation distribution from texture is a critical issue there. This work is intended to be used for filling the gap between geology and mineral processing in the mineralogical approach to geometallurgy.

6. Acknowledgment The authors acknowledge the financial support from the Hjalmar Lundbohm Research Centre (HLRC) and thank LKAB for providing samples. The authors kindly thank the support from Kari Niiranen from LKAB.

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Lund, C., Lamberg, P., Lindberg, T., 2015. Development of a geometallurgical framework to quantify mineral textures for process prediction. Miner. Eng. 82, 61–77. doi:10.1016/j.mineng.2015.04.004

Mariano, R.A., Evans, C.L., Manlapig, E., 2016. Definition of random and non-random breakage in mineral liberation - A review. Miner. Eng. 94, 51–60. doi:10.1016/j.mineng.2016.05.005

Meloy, T.P., Gotoh, K., 1985. Liberation in a homogeneous two-phase ore. Int. J. Miner. Process. 14, 45–55. doi:10.1016/0301-7516(85)90013-4

Nguyen, K., 2013. A New Texture Analysis Technique for Geometallurgy, in: Proceedings of the Second AusIMM International Geometallurgy Conference. Brisbane, QLD, Australia, pp. 187–190.

Nyström, J.O., Henriquez, F., 1994. Magmatic features of iron ores of the Kiruna type in Chile and Sweden: ore textures and magnetite geochemistry. Econ. Geol. 89, 820–839. doi:10.2113/gsecongeo.90.2.473

Outotec, 2012. HSC Chemistry 7.1 – Chemical reaction and equilibrium software with thermochemical database and simulation module. ISBN 978-952-9507-12-2.

Pérez-Barnuevo, L., Pirard, E., Castroviejo, R., 2012. Textural descriptors for multiphasic ore particles. Image Anal. Stereol. 31, 175–184. doi:10.5566/ias.v31.p175-184

Petruk, W., 1988. Ore characteristics that affect breakage and mineral liberation during grinding, in: Proceeding of Process Mineralogy VIII: Applications of Mineralogy to Mineral Beneficiation Technology, Metallurgy, and Mineral Exploration and Evaluation, with Emphasis on Precious Metal Ores. Phoenix, Arizona, US, pp. 181–193.

Richmond, A., Dimitrakopoulos, R., 2005. Multi-scale stochastic modelling of ore textures at the George Fisher mine. CIM Bull. 1–8.

Schneider, C.L., Lin, C.L., King, R.P., Miller, J.D., 1991. Improved transformation technique for the prediction of liberation by a random fracture model. Powder Technol. 67, 103–111. doi:10.1016/0032-5910(91)80032-E

Vink, L., 1997. Textures of the Hilton North Deposit, Queensland, Australia, and their relationship to liberation. Doctoral Thesis: University of Queensland.

Wiegel, R.L., 1976. Integrated Size Reduction-Mineral Liberation Model. AIME Trans. 260, 147–152.

Wiegel, R.L., Li, K., 1967. A random model for mineral liberation by size reduction. Soc. Min. Eng. AIME 179–189.

Zhang, J., Subasinghe, N., 2012. Extracting ore texture information using image analysis. Miner. Process. Extr. Metall. 121, 123–130. doi:10.1179/1743285512Y.0000000011

Paper IV

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Process simulation in mineralogy-based geometallurgy of iron ores Mehdi Parian*, Pertti Lamberg, and Jan Rosenkranz

* Corresponding author, Minerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden; Tel. +46-920-492556; Fax +46-920-97364, e-mail: mehdi.parian@ltu.se.

Minerals and Metallurgical Engineering, Luleå University of Technology, SE-971 87 Luleå, Sweden

Keywords: Geometallurgy, mineral liberation, particles, process modeling, simulation

1. Abstract The mineral processing simulation models can be classified based on the level that stream in plant and unit models is described. The levels of modeling in this context are: bulk, mineral or element by size, and particle. The particle level modeling and simulation utilizes liberation data in the feed stream and is more sensitive to the variations in ore quality. Within the paper, results of simulation for two texturally different magnetite ore are demonstrated at bulk, mineral by size and particle level. The models were calibrated for one ore and then in the simulation applied directly to the other ore. For the second ore the simulation results vary between the different levels. This is because, at the bulk level, the model assumes that magnetite, as well as other minerals, do not change their behavior if ore texture and grinding fineness are changed. At the mineral by size level, the assumption is that minerals behave identically in each size fraction even the ore texture changes. At the particle level, the assumption is that similar particles behave in the same way. The particle level approach gives more realistic results, and it can be used in optimization, thus finding the most optimal processing way for different geometallurgical domains. Even in the high grade iron ores where iron minerals are highly liberated the particle level shows its power in the prediction of impurity levels well.

2. Introduction Variation in the quality of feed to a plant has been a challenge for mineral processing operations. A prior quantitative understanding of the characteristics of the feed over the lifespan of the mining operation is the solution to successful production planning, circuit design, optimization, and troubleshooting. Also, demands for effective utilization of ore bodies and proper risk management in the mining industry have emerged an interest in geometallurgy.

A mineralogy-based geometallurgical modeling employs quantitative mineralogical information, both on the deposit and in the process. The geological model must describe the minerals present, give their chemical composition, report their mass proportions (modal composition) in the ore body and describe the ore texture. The process model must be capable of using mineralogical information provided by the geological model to forecast the metallurgical performance of different geological volumes, such as samples, ore blocks, geometallurgical domains or blends prepared for the plant feed for different periods from hourly and daily scale to weekly, monthly and annual production.

2

As to the level of details, predictive models of mineral processing can be divided into three categories based on the size of the smallest block in the simulation. In the least detailed level, the entire processing circuit (black box model) is modeled in a single operation, sections (e.g. comminution circuit and flotation circuit) is used at a moderate level, and single unit operations (e.g. individual flotation cells) is used at the detailed level. In geometallurgy, it is common to use models which predict the full process with simple equations (black box models). For example in Hannukainen iron ore deposit, the iron recovery into the iron concentrate has been defined with a simple equation based on iron and sulfur head grade (Equation (1),SRK Consulting (2014)).

)1)(96.1()1(5.98 )6(06.0 +×−×−×= −×

FeSeR Fe

Fe (1)

Models describing the process section wise are also common especially in comminution circuits when throughput or comminution energy usage is being forecasted. Geometallurgical models going to unit operation level are rare. This is mainly due to the difficulty of obtaining quantitative results from geology to work at unit level as well as the lack of interface to connect geological data to mineral processing unit level.

Another way of classifying the models used in the mineral processing simulation is based on the level that the feed stream to the plant and unit operations is described. The flowrates information in a stream, from lowest to the highest level of detailedness, are total solids, chemical elements, minerals, and particles. Each of these properties can be further divided to be part of certain size class. Thus bulk stream is divided into different sub-streams each representing a particle size class. Obviously, the study goal defines the selection of the properties and size information. For instance, solids by size (i.e. total solids flowrate of narrow particle size class) are often used to model and simulate comminution circuits whereas bulk mineral information is common in froth flotation. The selection of a modeling level comes with certain restrictions (Table 1) that limit its usability when expanding it outside the scope where the model is created and calibrated.

Table 1. Modeling levels and their assumptions in minerals processing. The model is valid and can be extended outside the calibration point as long as the feed stream assumptions are met.

Level Feed stream assumptions Example of application

Bulk (B)

Solids (BS) Each particle will behave identically regardless of its size and composition

Solid splitter model, equipment scale-up, basic engineering

Element (BE) Mineralogy, particle size distribution, and liberation distribution are fixed

Recovery function model for elements

Mineral (BM) Particle size distribution and liberation distribution are unchanged

Mineral splitter model

Behavioral type (BB)

Particle size distribution is unchanged. Similar behavioral types will behave identically

Gravity separation model

Sized (S)

Solids (SS) Each particle of given size will behave identically

Comminution model, Size classification model, equipment scale-up

Grindability type (SG)

Each particle type of given size will behave identically

Comminution model

Element (SE) Mineralogy and liberation distribution are unchanged

Recovery function model in size classes

3

Mineral (SM) Liberation distribution is unchanged Mineral splitter model in size classes

Behavioral type (SB)

Similar behavioral types will behave identically in narrow size fraction

Flotation model (fast and slow floating materials in size classes), Gravity separation model in size classes

Particle (SP) Similar behavior of particles of same composition and size

Principally applicable to all unit models

Another critical dimension of a process model is what input parameters it takes, what are the limitations are and how it was developed. Empirical models are solely based on the data without any explanation of physical or chemical process governing the system. Phenomenological models are based on the data, but the theory of the process to some extent is used to define to correlate the equations and used parameters. Finally, the fundamental models are solely based on physical and chemical properties and sub-processes in the system without the need of experimental data. Fundamental models, which try to consider all involving elements in the process, have not yet found their place in flowsheet simulation. This is mainly due to many sub-processes has taken place even in simple mineral unit operation (e.g. pumping), a big number of particles in the system and huge demand on computational resources.

This study focuses on flowsheet simulation for geometallurgy of iron ores. Process unit models to be studied are selected based on applicability at particle level for iron ore beneficiation and flowsheet simulation. The first purpose is to identify where appropriate models exist and where development is needed and second is to evaluate advantages and disadvantages of simulation at particle level compared to other levels.

3. Review of unit operation models for simulation of magnetite ore beneficiation plant at mineral and particle level

Minerals and particles are the fundamental elements in mineral processing operations and simulations. Both mineral and particle properties define the selection of a process and the process performance. However, the full potential of using particles in mineral processing simulation has not been accomplished yet. This has been partly due to lack of analyzing instruments to collect experimental information at particle level as well as the lack of mass balancing techniques and data reconciliation methods capable of working with the mineral liberation level when processing the experimental data to define model parameters of a unit process in question. Also, unit operation models which predict the behavior of individual (also multiphase) particles based on their properties are largely missing.

The development of automated mineralogy (Gu et al., 2014) has facilitated collecting particle level information. Additionally, data reconciliation and mass balancing techniques improved from the traditional approach of balancing solids and elements (Hodouin, 2010) to reconciling and adjusting particle populations (Lamberg and Vianna, 2007). These developments have built a foundation to take mineral processing unit models and simulation to a new level.

For the magnetic separation models reader is referred to a reviewed and model development of Parian et al. (2016). For other commonly used unit models, a review of existing models regarding modeling level (Table 1) is given in the following sub-chapters.

4

3.1 Size classification models Particle size classification in mineral processing is mostly done by screening or hydrodynamic classifiers. In screening the separation of particles is affected by their sizes (as well as the size and the shape of the aperture in screen) while hydrodynamic classifiers use the motion of particles. Hydrocyclone and spiral classifier fall into the second category. For them the particle properties are fundamentally required to model classifiers however for screens, the size distribution of particles can be sufficient.

An extensive review of the hydrocyclone models and their applications are available in the literature (Barrientos and Concha, 1990; Chen et al., 2000; Frachon and Cilliers, 1999; Heiskanen, 1997; Kraipech et al., 2006; Svarovsky, 2000). In a context of flowsheet simulation in mineral processing, the number of suitable hydrocyclone models is limited. This is because solution from fundamental modeling of hydrocyclone is computationally intensive (Nageswararao et al., 2004). The remaining models are empirical or phenomenological models that require experimental work to obtain material specific constants. An example of a hydrocyclone model that used for considering particles and ore texture is a study by Donskoi et al. (2005). He used revised Plitt’s hydrocyclone model (Flintoff et al., 1987) in USIM PAC simulation package and defined a various class of particles (density based) in size fractions as a separate phase. This data was used to predict recovery of minerals, total iron, and masses in the hydrocyclone underflow.

A common method of representing separation efficiency by size is by efficiency curve (Napier-Munn et al., 2005). It relates mass proportion of each particle size in the feed which reports to the particle size. None of the above-listed models can truly treat particles individually and give different behavior for particles being similar in size but different in composition (density).

3.2 Comminution models In iron ore beneficiation, the purpose of the comminution is mostly to liberate iron ore minerals from gangues. Further comminution to finer than liberation normally is unnecessary unless there is a particle size requirement for the product such as fine magnetite concentrate for pelletizing process. Comminution equipment in the mineral industry are many and differ in design and application. It is not possible nor is the objective of this study to cover all crushing and grinding models. Emphasize is made on models which are capable of delivering stream properties for flowsheet simulation instead power consumption, operating conditions or optimization. This means size distribution and liberation models which can be applied for size reduction processes. Considering modeling levels given in Table 1, only sized level models (S) are valid.

In the most simplified case, particle size distribution of discharge stream can be modeled by fitting particle size distribution functions such as Rosin-Rammler, lognormal or logistic distribution (see King 2012) for the product. Based on the experimental work and observations the best distribution function can be selected to model particle size distribution of the discharge stream. The distribution functions as such cannot forecast the size distribution if there are changes in federate, grinding conditions, residence time or material properties (like particle size distribution, mineralogy, ore texture). Some studies (Mwanga, 2016) have used an approach where P80 from Bond equation has been used to forecast the full particle size distribution by Rosin-Rammler equation by keeping the parameter describing the steepness of the cumulative distribution curve fixed. This kind of model can be described as a forecast of particle size distribution experimentally.

5

Population balance model (Austin et al., 1984) is versatile and has a wider range of forecasting capability than the one described above. Once the model is calibrated, it can forecast the product particle size distribution even if the particle size distribution of the feed changes. It is based on the mass balances by particle size comprising a selection function (S) and the breakage function (B). The equation in cumulative form is defined as follows:

dy

ytyMyxByS

ttxM

x∫∞

∂∂

=∂

∂ ),(),()(),(

(2)

where:

),( txM : Cumulative mass of particles finer than size x )(yS : The selection function which shows the mass fraction of size y which is going to be fragmented

),( yxB : The cumulative breakage function which is the fraction of particles of size y which are fragmented to give particles of size less than x

The equation (2) in discrete form changes to

∑−

=

+−=1

1, )()(

i

jjjjiii

i tMSbtMSdt

dM

(3)

The most popular of breakage function models are based on a mixture of two separate populations (Equation (4)). However it can be even simplified as one population. A general and simplified representation of the selection function is in the form of equation (5).

( )

ba

yxK

yxKyxB

−+

= 1),(

(4)

aKxxS =)( (5)

If one takes simplified forms of selection and breakage functions, the solution of equation (2) becomes well-known Rosin-Rammler distribution.

tAxa

exMtxM −= )0,(),( (6)

Size-mass balance models can relatively well predict particle size distribution of a mill product even if the particle size distribution of the feed changes. However, the model is not capable of predicting neither mineral grade by size nor liberation distribution.

In the concept of liberation modeling, various approaches are known. The first approach is to model liberation independently from size reduction modeling and assuming that liberation process is related to the texture of the ore and the target size (Gaudin, 1939; Wiegel and Li, 1967). Usually, the main parameters in this liberation model are the average grade of phases and the size ratio between particles

6

and grains. This approach is also called texture modeling and is achieved by superimposing particles mesh over texture image. This approach further developed from simple textures to consider a variety of ore textures (Barbery, 1991) or transformation of textures to simple forms (Meloy and Gotoh, 1985). In this, the key parameters are the volumetric grade of the ore mineral and the interfacial surface area between phases which is related to the grain size.

The second approach was developed by extending the theory of liberation (Andrews and Mika, 1976; Wiegel, 1976). These authors have considered the problem of simultaneously accounting for liberation and breakage in a batch mill. Other approaches have been reported in the literature such as integration of liberation, size reduction and process modeling (Bax et al., 2016; Khalesi, 2010).

A fundamental part of liberation models is how the ore texture is defined or is characterized to be used for developing predictive liberation models. The second part of liberation model is how the mineral distribution in particles is defined. This can be described by distribution functions without measurement or measured on by images analysis techniques. A majority of liberation models are based on binary system (i.e. an ore mineral embedded in a gangue matrix), and they lack the capability of forecasting liberation distribution for multiphase particles. A comprehensive review of liberation models and their development in 80’s and before was given by Barbery and Leroux (1988).

Another important part of liberation modeling is how actually fragmentation (breakage) happens. As discussed earlier, a simple approach is to superimpose particle patterns over textures. A recent review of mineral liberation and liberation in comminution is given by Mariano et al. (2016).

Practical implementation of mineral liberation models in the mineral processing is rare. This is because the models are mainly for binary systems and taking models to the multiphase system is too complicated. However, in simplified ore textures (binary system) the models have been tested and compared against experimental data (Barbery and Leroux, 1988; Choi et al., 1986; Finch and Petruk, 1984; Hsih and Wen, 1994; Leigh et al., 1996; Schneider et al., 1991). The results of these studies are encouraging, but the application of the binary system is limited specifically nowadays that ore bodies grades are declining, and deposits are becoming more complex.

In simulation software used in mineral processing, MODSIM includes complete Andrews-Mika liberation modeling. HSC Chemistry since version 7.1 (Outotec, 2012) has included liberation model as built-in comminution models. Traditional comminution models describe the product particle size distribution and internally the software forecast the liberation distribution of the product if the liberation information on the feed stream is given (Lamberg and Lund, 2012). This is done by keeping the liberation distribution within the size fractions unchanged, and the changes are applied only to mass proportions of different size fractions. As the mineral grades between the particle size fractions may be different, the change in mass proportions of the particle size fractions would change the mineral grades in bulk. Therefore, there is extra reconciliation step to conserve the bulk mineral balance between the feed and product.

3.3 Flotation models It is known that kinetic model well describes the batch flotation results. In batch flotation modeling with its specific assumptions, such as perfect mixing, full particle suspension and capture efficiency, the rate of flotation is directly related to remaining floatable material in the cell (King, 2012). The flotation rate equation in differential form is:

7

nkCdtdC

=−

(7)

where n denotes the order of the equation. In the simplest form, the first order kinetic, the equation (7) becomes:

kteCC −= 0 (8)

By the assumption that a fraction of each mineral is non-floatable and considering the ultimate recovery 𝑅𝑅∞, the form of equation in terms of recovery of the mineral in batch flotation and perfect mixer (industrial single tank cell) becomes

( )kteRR −∞ −= 1 (9)

ktktR+

=1

(10)

To find the constants, experimental data must be fitted with the equation (9). The extension of the first order kinetic model (Equation (9)) is the Klimpel model which has the rectangular rate distribution instead of uniform rate as the classic first order kinetic model (Dowling et al., 1985). The Klimpel (1980) kinetic model is defined as follow:

−−=

−

∞ kteRR

kt11

(11)

The Klimpel model has been used for analysis of more than 300 flotation tests at WEMCO® and was found to fit experimental data reasonably well (Parekh and Miller, 1999).

Kelsall (1961) presented a kinetic based flotation model consisting slow and fast floating rate constant. Comparing to classic first order kinetic model, Kelsall’s model was considered to offer a better estimate. Later his model modified by Jowett (1974) to consider ultimate recovery as follow:

( )( ) ( )( )tktk sf eeRR −−∞ −+−−= 111 ϕϕ

(12)

A comprehensive survey of flotation models exists in the literature (Dowling et al., 1985; Mavros and Matis, 1991; Runge and Franzidis, 2003; Wang et al., 2015). The other approach of flotation modeling are the models considering environment effects. These models remark the relation between metallurgical performance and environment variables (Gorain et al., 1999; Mathe et al., 1998; Tabosa et al., 2016; Vera et al., 2002; Wang et al., 2016). Compared to other unit processing models, flotation models are more mature in reaching to particle level modeling (Lamberg and Vianna, 2007; Savassi, 2006; Welsby et al., 2010).

3.4 Summary of the process unit models for particle-based simulation In the concept of particle-based simulation, a minimum requirement for a unit model is the capability to work in particle size level and address relevant particle properties for the unit process. This means that

8

even some of the existing unit operation models are not designed to be used for mineral liberation data they can still be used in particle-based simulations with some considerations. For example, even though Efficiency Curve or Plitt’s hydrocyclone model is not particle-based in nature, the particle population can be used to generate the bulk information needed to calculate the cut size of a hydrocyclone. Mineral liberation information would be required in some areas, including magnetic separation and flotation. Regarding this study, magnetic separation model must perform simulations on liberation level. The applicability and limitation of existing unit operation models for the mineralogical approach are summarized in Table 2.

Table 2. Applicability of current unit models in particle-based simulation.

Area Model Considerations Magnetic separation King and Schneider (1995), Parian et al.

(2016) -

Comminution HSC Chemistry: combined fixed particle size distribution and liberation model

Assumes liberation in narrow size fractions remains unchanged

Particle size classifier Fixed particle size distribution The only size of particles is considered to affect separation

Hydrocyclone Efficiency curve/Efficiency curve by mineral

Does not take into account particle/mineral densities

Flotation HSC Chemistry, Lamberg & Vienna Kinetic constants for multiphase particles deviates from linear behavior

4. Materials and methods

4.1 Samples The data that is used for plant simulation falls into two categories. The first set of data is from plant survey that has been done at one of the LKAB’s iron ore processing plants in Kiruna, Northern Sweden. Sample preparation and mass balancing of plant data in a mineral by size level are as described at Parian et al. (2016). The second set of data is the result of ore texture mapping and fragmentation to generate particle population as a feed stream to the flowsheet. Two magnetite drill core samples with variation in ore texture are used to generate two different liberation distribution. The procedure for generating particles from drill core ore texture was explained at Parian et al. (submitted to Journal).

4.2 Analysis Chemical analyses of the survey samples were done at the chemical laboratory of LKAB. The data was used to achieve mineral grades in the stream by Element-to-Mineral conversion method described in Parian et al. (2015). Afterward, the plant data was mass balanced in a mineral by size levels. Mass balancing and data reconciliation was done using the modeling and simulation software HSC Chemistry 9 by Outotec and MATLAB by Mathworks. In the mass balancing of liberation data Particle Tracking technique (Lamberg and Vienna, 2007) was used.

The flowsheet was drawn in HSC Chemistry 9.1 Sim module and is used to demonstrate different levels of modeling according to Table 1. The newly made particle based WLIMS model (Parian et al., 2016) was also adopted in HSC Chemistry 9.1 Sim to be used for the simulation.

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5. Results and discussion

5.1 Plant Circuit A flowsheet used here consist of comminution and concentration circuits and is based on LKAB Kiruna concentration plant (Samskog et al., 1997; Söderman et al., 1996). A circuit is a general form of the process that LKAB uses in Kiruna for the beneficiation of magnetite ore. The feed to the plant is the product of crushing and cobbing plant. The beneficiation process consists of three major steps including comminution, magnetic separation and apatite flotation. The comminution circuits include autogenous grinding followed by the spiral classifier and pebble milling coupled with hydrocyclone (Figure 1).

Figure 1. Magnetite beneficiation plant flowsheet for demonstration of different levels of modeling and simulation

5.2 Process units The process unit models used in the simulation in different modeling levels are gathered in Table 3. The results from the mass-balancing of the plant data were used for defining the model parameter values of different models.

Table 3. The model that is used in the simulation of flowsheet at different levels.

Unit Bulk model Mineral by size model Particle level model Autogenous Mill Perfect mixer (Fixed) PSD HSC comminution model

with decoupled size reduction and liberation models

Trommel Mineral splitter/mass splitter

Efficiency curve / Efficiency curve by mineral

Efficiency curve/efficiency curve by mineral

Mixer Perfect mixer Perfect mixer Perfect mixer Pebble Mill Perfect mixer (Fixed) PSD HSC comminution model

with decoupled size reduction and liberation models

WLIMS Mineral splitter Mineral by size splitter Developed WLIMS model

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(Parian et al. 2016) Spiral classifier Mineral splitter Efficiency curve/efficiency

curve by mineral Efficiency curve/efficiency curve by mineral

Hydrocyclone Mineral splitter Efficiency curve/efficiency curve by mineral

Efficiency curve/efficiency curve by mineral

Flotation Flotation kinetics by mineral

Flotation kinetics by mineral by size

Particle based kinetic flotation model

5.3 Plant feeds Two different magnetite ore were selected to be used for simulation. The first ore is the actual feed to the plant during the survey (Ore A). The second ore is one of the studied drill cores samples which was studied by Parian et al. (submitted) (Ore B). The procedure for generation of particle population from second ore is described in Parian et al. (submitted). The two ores are texturally different thus have different mineral grades and liberation distribution (Table 4, Figure 2). The assumptions that are used here are that mineral compositions and particle size distribution after crushing for both ores are same.

The ore B was selected because it represents an ore which is significantly lower in the head grade and texture is much more fine-grained giving lower liberation degree at given particle size (Figure 2). Also, the Ore B would represent the plant feed in a case where cobbing is not used.

Table 4. Modal composition of plant feed samples. Ab = albite, Act = actinolite, Ap = apatite, Bt = biotite, Cal = calcite, Mgt = magnetite, Qtz = quartz.

Ab Act Ap Bt Cal Mgt Qtz Ttn Ore A 3.01 3.43 2.48 3.50 0.91 85.57 0.96 0.14 Ore B 12.88 0.00 7.24 10.27 0.00 64.09 5.52 0.00

Figure 2. Liberation curves of magnetite in the Ore A (left) and Ore B (right).

0 20 40 60 80 100

Magnetite (wt%) in particle

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

yiel

d (%

)

0-38 µm

38-53 µm

53-75 µm

75-150 µm

150-300 µm

300-600 µm

600-1700 µm

1700-3350 µm

0 20 40 60 80 100

Magnetite (wt%) in particle

0

10

20

30

40

50

60

70

80

90

100

Cum

ulat

ive

yiel

d (%

)

0-38 µm

38-53 µm

53-75 µm

75-150 µm

150-300 µm

300-600 µm

600-1700 µm

1700-3350 µm

11

5.4 Simulation for Ore A Mass balancing results were used for calibrating models at bulk mineral and mineral by size levels. For simulation at particle level, models described in Table 3 were used and adjusted to match experimental and mass balancing results. In overall, for Ore A, three levels of simulation give the same grade and recovery for all minerals for the final concentrate of the plant with the calibrated parameters. The effect of coarse grinding was investigated by increasing product particle size in grinding circuit (pebble mill and hydrocyclone). The simulation reveals that even in coarse product magnetite recovery and grade is still preserved.

Table 5. Results of the simulations at different levels: composition of the magnetite concentrate (Grade wt%) and mineral recoveries. For mineral symbols, see Table 4.

Grinding Level Ab Act Ap Bt Cal Mgt Qtz Ttn

Fine (P80 = 38 µm)

Bulk Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Size Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Particle Recovery (%) 13.87 17.17 23.02 13.19 17.80 95.62 0.00 99.70 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.22 0.00 0.17

Coarse (P80 = 72 µm)

Bulk Recovery (%) 13.86 17.25 22.99 13.23 17.80 95.60 0.00 99.79 Grade (wt%) 0.50 0.70 0.68 0.55 0.19 97.21 0.00 0.17

Size Recovery (%) 18.84 24.21 20.41 16.38 17.47 95.59 0.00 99.79 Grade (wt%) 0.67 0.98 0.60 0.68 0.19 96.71 0.00 0.17

Particle Recovery (%) 10.17 22.33 23.23 16.24 26.54 95.81 0.00 99.74 Grade (wt%) 0.36 0.91 0.68 0.67 0.29 96.92 0.00 0.17

5.5 Simulation for Ore B For the simulation of Ore B, the calibrated parameters that were used at bulk mineral, mineral by size and particle levels for Ore A, were used. The results show that at bulk mineral and mineral by size levels, the mineral recoveries are similar as for the Ore A in fine grinding (Table 6). This is a property of models which define the behavior of minerals on unsized or size based: regardless of the plant feed the mineral recoveries (and distribution in the full process) is similar, but the grades change. When the head grade lowers, the concentrate grade drops as well.

At the liberation level, the result is, however, different. Similar particles behave in the same way as in the base case, but because the mass proportion of particles (thus liberation distribution) is different in the plant feed for the Ore A and Ore B, the final result will differ for both grades and recoveries. The particle level simulation forecasts slightly lower grade and recovery for the Ore B as for the Ore A. Compared to bulk and mineral by size level the particle level simulation forecast lower gangue recovery thus higher magnetite grade.

12

Table 6. Results of the simulations at different levels for the ore B: composition of the magnetite concentrate (Grade wt%) and mineral recoveries. For mineral symbols see Table 4.

Grinding Level Ab Act Ap Bt Cal Mgt Qtz Ttn

Fine (P80 = 38 µm)

Bulk Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Size Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Particle Recovery (%) 7.68 0.00 17.60 9.28 0.00 89.29 3.21 0.00 Grade (wt%) 3.13 0.00 2.02 0.90 0.00 93.58 0.37 0.00

Coarse (P80 = 72 µm)

Bulk Recovery (%) 14.28 0.00 21.16 15.72 0.00 95.60 0.00 0.00 Grade (wt%) 5.29 0.00 2.21 1.39 0.00 91.12 0.00 0.00

Size Recovery (%) 19.80 0.00 18.85 19.66 0.00 95.58 0.00 0.00 Grade (wt%) 7.18 0.00 1.92 1.70 0.00 89.20 0.00 0.00

Particle Recovery (%) 6.79 0.00 15.22 13.89 0.00 89.62 7.26 0.00 Grade (wt%) 2.75 0.00 1.73 1.34 0.00 93.34 0.83 0.00

Comparison of simulations for ores A and B demonstrates the difference between mineral and particle level modeling and simulation. In the ore B, the results from the particle level simulation give more plausible result than the mineral and mineral by size level. This is due to the fact that the parameters are calibrated based on the liberation of particles instead of general calibration to the ore at bulk mineral and mineral by size level. At the particle level, the assumption is that similar particles behave in the same way whereas in the mineral level the assumption is that mineral behaves identically regardless of texture and particle composition. Although no verification and validation for results of ore B were provided, however the simulation results in particle level comparatively to other levels is more credible.

6. Conclusions The mineralogical approach of geometallurgy requires quantitative mineralogical data from geology model to be able to perform in its best form. It is common that for estimation of plant metallurgical response black box models or simple equation is used. However, this approach is not sensitive to the material changes. In the best case, they can adopt the changes in the head grade but not in variation in textures. Within this study, it is shown that simulation at mineral levels with calibrated parameters to the ore feed is only valid for ore having similar liberation characteristics. However, calibrated parameters at particle levels are based on the liberation of particles and are capable of giving more reliable estimates. In iron ore, the forecasts for the iron grade and recovery do not differ significantly, but for the impurity levels, the particle level simulation gives more reliable results. Also, the particle level enables optimization, thus finding optimal processing conditions, e.g. grinding fineness, for different textural ore types and geometallurgical domains.

7. Acknowledgment The authors acknowledge the financial support from the Hjalmar Lundbohm Research Centre (HLRC) and thank LKAB for providing samples and analysis. The authors kindly thank the support from Kari Niiranen from LKAB.

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