Department of Civil, Environmental and Natural...

DOCTORA L T H E S I S

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

Development of a Geometallurgical Testing Framework for ore Grinding and

Liberation PropertiesISSN 1402-1544

ISBN 978-91-7583-737-6 (print)ISBN 978-91-7583-738-3 (pdf)

Luleå University of Technology 2016

Abdul-R

ahaman M

wanga D

evelopment of a G

eometallurgical Testing Fram

ework for ore G

rinding and Liberation Properties

Mineral Processing

Abdul-Rahaman Mwanga

Development of a geometallurgical testing framework for ore grinding and liberation properties

Abdul-Rahaman Mwanga

Doctoral Thesis in Mineral Processing

Division of Minerals and Metallurgical Engineering

Department of Civil, Environmental and Natural Resources Engineering

Luleå University of Technology

SE-971 87 LULEÅ

Sweden

Luleå University of Technology

Printed by Luleå University of Technology, Graphic Production 2016

ISSN 1402-1544 ISBN 978-91-7583-737-6 (print)ISBN 978-91-7583-738-3 (pdf)

Luleå 2016

www.ltu.se

Cover illustrations: The effect of varied feed properties (texture variation), on breakage properties, energy required for grindability and liberability during comminution.

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ABSTRACT

Efficient measurement methods for comminution properties are an important prerequisite for testing the variability of an ore deposit within the geometallurgical context. This involves the investigation of effects of mineralogy and mineral texture on the breakage of mineral particles. Breakage properties of mineral particles are crucial for the liberations of minerals and the energy required for that.

For process optimization and control purposes, comminution indices are often used to map the variation of processing properties of an entire ore body (e.g. Bond work index). Within the geometallurgical approach this information is then taken up when modelling the process with varying feed properties.

The main focus of this thesis work has been to develop a comprehensive geometallurgical testing framework, the Geometallurgical Comminution Test (GCT), which allows the time and cost efficient measurement of grinding indices and their linkage to mineralogical parameters (e.g. modal mineralogy or mineral texture, mineral liberation).

In this context a small-scale grindability test has been developed that allows estimating the Bond work index from single pass grinding tests using small amounts of sample material. Verification of the evaluation method and validation was done with different mineral systems.

For selected samples the mineral liberation distribution was investigated using automated mineralogy. By transferring the energy-size reduction relation to energy – liberation relation new term liberability has been established.

As part of the experimental investigations, mineralogical parameters and mineral texture information were used for predicting breakage and liberation properties. Patterns for describing the breakage phenomena were established for a set of iron oxide ore samples. The determined breakage patterns indicated that the specific rate of mineral breakage slows down when reaching the grain size of mineral particles, thus allowing maximizing mineral liberation significantly without wasting mechanical energy.

Keywords: Grindability test, mineral texture, breakage properties, mineral liberation, process modeling, geometallurgy.

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ACKNOWLEDGEMENTS

I would like to appreciate and thank my supervisors Professor Jan Rosenkranz and Professor Pertti Lamberg for their guidance and valuable contribution throughout this research work. I am grateful to be their student at the MiMeR (Minerals and Metallurgical Research Laboratory) and to be able to conduct almost all my experiments which have has made this work possible.

The financial support of the CAMM Centre of Advanced Mining and Metallurgy at Luleå University of Technology is gratefully acknowledged. Special acknowledgement goes to LKAB process mineralogy team particularly to Kari Niiranen, Therese Lindberg and Charlotte Mattsby for organizing sampling, supporting sample assays and readiness for the discussions when developing the method. Cecilia Lund is thanked for discussions on geological and mineralogical information of the Malmberget deposit. Kurt Aasly, Friederike Minz, Ingjerd Bunkholt and Alireza Javadi Nooshabadi are thanked for providing samples.

The help of Ulf Nordström, Pierre-Henri Koch, Mehdi Amiri Parian, and Bertil Pålsson in experimental work and analyses is appreciated. ProMinNET researchers have provided valuable comments. The Mineral Resource Institute Dodoma (MRI) and Tanzania Ministry of Energy and Minerals are acknowledged for allowing me to come to Sweden for studies.

Special thanks go to all my friends at the Division of Minerals and Metallurgical Engineering Dr. Anders Sand, Mehdi Parian, Pierre-Henri Koch, Victor Lishchuk, Erdogan Umur Kol, Jane Mulenshi, Tommy Karlkvist, Dr. Hesham Ahmed, Dr. Mohammad Khoshkhoo, Samira Lotfian, Kamesh Sandeep, Suchandra Sar and Asmaa El-Tawil for their company and encouragement during my study.

Finally, my heart-felt appreciations go to my lovely family Mwavita Lai Samizi my wife, my son Abdul Hamid and my daughters Asia, Asma and Mariam, my mummy Sauda Makuta, grandmother Saada Salim Kisombe and my uncles Khalid Makuta, Adinani Makuta, Yahaya Makuta, Sadiq Salim Swai and Hamadi Swai for their understanding and patient for being far away from them for long time.

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List of Papers

The thesis is based on the following papers:

I. Mwanga, Abdul, Rosenkranz, Jan, Lamberg, Pertti. Testing of Ore Comminution Behavior in the Geometallurgical Context – A review. (Published)

II. Mwanga, Abdul, Lamberg, Pertti and Rosenkranz, Jan. Comminution test method using small drill core samples. (Published)

III. Mwanga, Abdul, Rosenkranz, Jan and Lamberg, Pertti. Development and experimental validation of the Geometallurgical Comminution Test (GCT).(Submitted)

IV. Mwanga, Abdul, Parian, M, Lamberg, Pertti and Rosenkranz, Jan. Comminution modeling using mineralogical properties of iron ores.(Submitted)

The following papers are not included in the thesis:

Other contributions

1. Mwanga, Abdul, Rosenkranz, Jan and Lamberg, Pertti. A Comminution Model for Linking Size Reduction with Energy and Mineral Liberation. Proceedings of the 14th European symposium on comminution and classification, 2015, Gothenburg Sweden.

2. Mwanga, Abdul, Lamberg, Pertti and Rosenkranz, Jan. Liberability: A new approach for measuring ore comminution behavior. Conference in process mineralogy, 2014, Cape Town South Africa.

3. Mwanga, A., Rosenkranz, J., Lamberg, P., Conference papers, 2014. Developing ore comminution test methods in the geometallurgical context, Conference in Minerals Engineering, Luleå Sweden.

4. Lamberg, P., Parian, M. A., Mwanga, A., and Rosenkranz, J., 2013. Mineralogical mass balancing of industrial circuits by combining XRF and XRD analysis, Conference in Minerals Engineering, Luleå Sweden.

5. Lamberg, P., Rosenkranz, J., Wanhainen, C., Lund, C., Minz, F., Mwanga, A., and Amiri Parian, M., 2013. Building a Geometallurgical Model in Iron Ores using a Mineralogical Approach with Liberation Data, Geomet 2013, The second AUSIMM International Geometallurgy Conference, Brisbane.

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Extended Abstracts

6. Mwanga, A., Rosenkranz, J., Lamberg, P., and Koch, P., 2013. Simplified Comminution Test Method for Studying Small Amounts of Ore Samples for Geometallurgical Purposes, Resources and Mining Geology Conference, Cardiff UK.

7. Koch. PH; Mwanga. A., Lamberg .P, Pirard. E., 2013. Textural Variants of Iron Ore from Malmberget: Characterisation, Comminution and Mineral Liberation, Exploration, Resources and Mining Geology Conference, Cardiff UK.

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CONTENTS

Part 1 1

1. Introduction 3

1.1. Background 3

1.2. Objectives of the thesis and research questions 6

2. Breakage properties and link to comminution modeling 6

3. Geometallurgical testing for ore grindability 10

3.1. Bench-scale grindability tests 10

3.1.1. Bond grindability test 10

3.1.2. Variations of the Bond grindability test 11

3.1.3. Evaluation of grindability tests 11

3.2. Pilot and bench-pilot scale tests 12

3.3. Indirect methods for determining comminution behavior 13

3.4. Summary and conclusions 13

4. Methodological approach for the development and validation of the GCT 14

4.1. Characterization of samples within a geometallurgical framework 14

4.2. Development of the GCT grindability test 17

4.2.1 Experimental validation 20

4.2.2 Samples and applied methods 20

4.2.3 Analysis and developed validation correlation of the GCT 23

4.2.4 Single pass grindability behavior between GCT and Bond mill 26

4.3 Incorporation of liberation into the GCT 28

4.4 Investigation of the linkages between mineralogy and breakage behavior 32

4.4.1 Breakage behavior and modeling 32

4.4.2 Linkage between mineral grains size and specific rate of breakage 34

4.4.3 Modal mineralogy by size 38

4.4.4 Mineral distribution and breakage patterns by size 40

4.4.5 Modeling mineral grade by size in the mill product 42

4.4.6 Modeling the mineral distributions by size 44

x

5. Discussion 45

6. Conclusions and further work 49

7. References 51

Part II 57

Paper I

Paper II

Paper III

Paper IV

1

Part I

- Development of a geometallurgical testing framework for ore grinding and liberation properties -

2

3

1. Introduction

1.1. Background

Considerable efforts in research have been made over time to generate useful knowledge develop and tools for mineral processing. Comminution theories are one example of that, and are used for describing particle size reduction and liberations of mineral particles. Mineral liberation is a parameter fundamental to beneficiation plant performance. For efficient concentration and the quality of the final concentrate product, composite particles of different mineral phases must break into the different mineral phases in order to allow for separation of the particles in downstream processing. Only sufficient liberation of the composite particles guarantees efficient separation of valuable minerals from the gangue. By connecting mineral liberation information with a comminution model the optimal conditions can be examined a priori. However, this remains a challenge since mineral composition and texture information (e.g. the mineral grain sizes) have not been efficiently used to predict the liberation of mineral particles during comminution yet.

Usually mineral liberation models are developed based on the particle grade and size. The liberation model by Andrews and Mika (1975) is such an example of a model that can be used to model the comminution of multi-component mineral systems. The model describes the relationship between product size and liberation and can be used within process simulation. However, the entire characterization of an ore requires a quite large number of data which makes its application complicated. Nevertheless, this concept has been used when simulating breakage based on population balances, as done by King (2001) or Schneider (1995).

Comminution circuits are often the bottle neck in a mineral processing plant, i.e. they define the plant material throughput. Figure 1 is a typical simplified comminution circuit consisting of the crushing unit, tumbling mill closed with hydrocyclones for particle size classifications. Normally the target for the comminution circuits is to produce a certain size distribution and at the same time maximize the throughput. If a material is very hard it normally means that the throughput must be decreased in order to reach a targeted particle size. Further, there are some process variables that can be adjusted .e.g. rotational speed in mills, amount of grinding media in the mill (as steel balls) and the cut size in classification steps. If a high throughput is maintained to the expense of particle size reduction the consequence will be a poorer mineral liberation and subsequently lower recovery in separation due to increased losses by locked particles. Therefore, it is very important to design the comminution circuit in the right way, select proper types of unit operations and size the equipment correctly for reaching targeted throughput and particle size distribution.

The design and control requires extensive testing and for that reason representative ore samples are needed. Four different purposes of tests in mineral processing can be identified: (i) testing for flowsheet development, (ii) testing for sizing the operational units, (iii) testing for validating the metallurgical performance and (iv) variability testing. The latter has vital importance for the geometallurgical modeling and simulations.


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Flowsheet development aims to define the right technology and circuit to be used. In comminution this includes tests to compare different processing alternatives like autogenous grinding, semi-autogenous grinding, ball mill grinding, rod mill grinding, high pressure grinding rolls, as well as for investigating suitable pre-treatment methods, e.g. microwave treatment (Amankwah, Khan, Pickles, and Yen, 2005) or high voltage electric pulses (Shi, Zuo, and Manlapig, 2013). At this stage testing is often done in relatively small scale, typically with samples of 10-100 kg. Unit sizing requires specific tests for each technology. This is commonly done after flowsheet selection and sample sizes are slightly larger, i.e. 100-500 kg. Validating the metallurgical performance requires even larger scale testing using pilot plants. Here, sample sizes reach 10-500 tons and feed rates of 1-10 t/h are used. Pilot tests last from several days to several weeks and consider the entire process flowsheet, i.e. besides comminution also concentration stages and even dewatering.

Jaw Crusher

AG Mill

Ore

Mill feed Mill discharge

Cyclone

Cyclone underflow

Product

Ore type1 Ore type2

Ore type3

Comminution model for simulating ore body performances Multi-objective

optimisation:-Throughput-Energy-PSD-Liberation-Downstreamprocess requirements

Product

Variations

Figure 1. Simplified flowsheet of a typical comminution circuit.

For geometallurgical purposes the outcome of the experimental work has to serve as an input to process modeling, i.e. the comminution test results need to be linked to the parameters used in the comminution process models. Within process modeling different levels of modeling depth are used. Simple approaches use defined size distribution functions based on single parameters as energy for grinding or machine-specific size reduction ratios.

More sophisticated, rigorous models apply population balancing methods. Here the entire breakage distribution function needs to be constructed based on experimental test work or by sampling and back-calculation from continuous comminution tests even at industrial scale. In this context it has to be noted that a comprehensive framework for determination of size reduction and energy for size reduction as well as mineral liberation analysis using advanced automated mineralogy is still missing within experimental work and process modeling.

Rock mechanical tests, particle breakage tests, and bench-scale grindability tests are the commonly used comminution tests methods that have potential to be used in geometallurgical context and have been reviewed earlier (Mwanga et al., 2015). The listed tests are conducted with quite large samples which make the number of different samples to be included in a geometallurgical testing program comparatively small. To find out about the ore-related variations in comminution properties and also other

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mineral processing properties it is customary to run a larger number of variability tests, also described as geometallurgical testing. In this regards, a number of ore samples is collected and characterized with respect to their chemical composition, mineralogy, as well as comminution properties and processing properties related to separation (see Table 1). For comminution testing the available test methods use comparatively large ore samples, i.e. the availability of special geometallurgical tests for comminution in small scale are limited. This hinders the detailed mapping of ore variability using small samples as for instance drill core samples. Some of the established test methods used in geometallurgy are simple drop weight tests (Napier-Munn et al, 1996; Narayanan, 1985), rotary breakage tests (e.g. Shi et al, 2009) and abbreviated tests as the SMC test (Morrell, 2004).

Table 1. Typical number of tests needed in a geometallurgical mapping program (Williams and Richardson, 2004).

Type of the test Number of samples Chemical assays 10000+ Mineralogy 10000+ Grinding 100-300 Metallurgical tests(e.g. flotation) 100-301

Mineral processing properties within an ore body can vary a lot and bring several challenges during production. For instance for the Collahuasi concentrator, Alruiz et al. (2009) and Suazo et al. (2010) showed how the plant throughput and copper recovery varied strongly between different so-called geometallurgical domains, i.e. areas of the ore body where metallurgical properties are similar. With current practices the throughput is mostly determined by solely fixing the particle size of the mill product which is questionable when there is a big variation in micro-structure (texture) or liberation size within a deposit. However, comminution characterization studies that take into account mineral information are very rare (Kim, Cho and Ahn, 2012).

This thesis describes the development of a geometallurgical framework for testing ore grindability and liberability behavior. The method was extended to the modeling of the breakage of mineral distribution of various class sizes by using mineralogical and mineral textures. Samples from the Malmberget and Kiruna iron oxide ore deposits in Northern Sweden were used to demonstrate the linkages of the mineral compositions and grain size with breakage of mineral particles (e.g. specific rate of breakage). The mineral breakage patterns were used for the predictions of the degree of mineral liberations. This provided an insight on the way of achieving high efficiency measurement and modeling in geometallurgical context.


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1.2. Objectives of the thesis and research questions

The main objectives of the thesis were to

1. Develop a comminution test method that is time and cost efficient for characterizing the comminution properties of an ore sample involving mineralogy and mineral texture.

2. Investigate the effects of mineralogical properties of ore samples based on industrial case studies, e.g. oxide ores (case of Malmberget and Kiruna iron ores) and sulphide ores, including measurements of the Bond work index by using a single pass grindability test.

3. Unify mineralogical and comminution models and parameters to describe the variations of ore comminution behavior in an ore body.

The research questions to be answered in this study in the geometallurgical sense have been:

1. Can the efficiency of the Bond grindability test (in terms of samples size and time) be improved by changing the geometry of the test mill to a small diameter and by a single-pass batch test?

2. Is there an efficient way to integrate mineral liberation into the Bond test method and related process modeling?

3. Can samples with similar grindability and modal mineralogy but different liberability be distinguished from each other by mineral textures, e.g. mineral grain size?

2. Breakage properties and link to comminution modeling

Breakage of rock material is a complex phenomenon that affects the mechanical system (i.e. mechanical energy responsible for fracturing) for breaking the mineral particles as well as liberation of minerals. Mechanical forces are usually used to break the bonds of the mineral matrix of composite particle into mineral phases. During comminution, the breakage of mineral particles can occur along the grains boundaries (.i.e. less forces is required for that) or across the grains where large forces are required to break the grains depending on the composition and grain size of mineral particle. In fact, these phenomena have effects on mineral liberation and have been categorized as random and non-random breakages (King, 2001).

The central challenge has been how to link material properties (texture and other mineralogical properties) to the mechanical system (equipment, design and process parameters) in order to model comminution and liberation of various mineral particles. Amongst others, the heterogeneity of mineral texture and mineralogy of rock particles make the description of breakage of mineral particles complex, such that it has been a challenge to have energy- efficient mechanical system for size reduction. There have

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been efforts to develop empirical models in order to describe the breakage of mineral particles and mineral liberations. The efforts for improving the modeling of mineral breakage and liberation by Wei and Gay (1999) that used experimental data from Schneider (1995) for defining a texture-related dispersion function are one example. According to Wei and Gay (1999), liberation models based on ore texture are useful for mill design but not for grinding circuit performances and simulations. When liberation models are developed it is important to introduce assumptions regarding the fracturing phenomena due to the presence of different modes of breakage as investigated by Fandrich et .al. (1997). Fandrich observed dependence between breakage behavior and particle grade distribution for iron oxide ores when using particle bed breakage test. According to Fandrich the observed breakage behavior is related to preferential breakage of the binary iron ore oxides. In this case particle bed comminution was used. According to the work of Vizcarra et al. (2010) liberation of minerals is independent of breakage mechanisms for sulphide minerals with different texture characteristics. The conclusion by Vizcarra et al. (2010) that particle-bed comminution does not enhance liberation properties of metalliferous ores is contrary to other researchers as Özcan and Benzer (2013), Dhawan (2012) and Wang (2012), and Phaninra et al. (2011) who concluded that the bed breakage mechanism enhances the liberation of minerals.

Many studies for breakage and liberation models are based on random fracture of particles. Besides the breakage mechanisms also the mechanical strength affects the liberation properties of a mineral particle, i.e. comminution behavior will depend on particle composition. King (2001) suggested for this breakage mode the term “differential breakage” to describe the effects on progeny size distribution resulting from changing the particle composition during ore comminution. Gay (2004a) developed a liberation model for comminution process based on preferential breakage and the probability of a progeny particle of certain size and composition based on the feed particle of certain size and composition. In addition to that, Gay (2004b) used also a simple texture based model. This liberation model still requires more work to be practically used for quantifying liberation properties of an ore based on texture information, although it has good foundation to quantitatively explain liberation properties based on mineral texture.

In order to model comminution (i.e. breakage properties of mineral particle), one approach has been to describe the change in one representative particle size during processing. An example of this approach is the utilization of the size reduction ratio. If defined by the maximum particle size the P max,F max, xxRR can be used to calculate

the product size distribution using for instance a Gaudin-Schuman distribution function.

Pmax,xx

xQ (1)

RRFmax,xx

xQ (2)


8

where is a material and machine dependent parameter.

Also energy-size relations as for example the Bond equation can be used in the same manner when information about the starting particle size x80,F, the energy E and the ore’s work index Wi (Rosenkranz, 2000) are provided:

P80,xx

xQ a (3)

iW,E,a

P80,xx

xQ (4)

where a and are material and machine dependent parameters.

A more detailed description is possible by using so-called population balance methods where the entire particle size distribution is considered. Here the distribution of material of one starting particle size to smaller sizes during crushing or grinding is described by the breakage distribution. Different mathematical formulations are available that need to be fitted to experimental data, e.g. the cumulative distribution function of Broadbent and Callcott (1956)

j

i

d

d

i e11.58dB (5)

where B(di) is the cumulative mass of materials finer than di, and dj > di. Another distribution type that is frequently used has been defined by Austin (1972). The function has three parameters , and for describing ore specific breakage behavior:

y

x1

y

xyx,B (6)

Besides describing in which size fractions the fragments from breakage end up also the fraction of material that undergoes size reduction has to be quantified. This selection function S, or specific rate of breakage when describing comminution as a kinetic process, is a function of machine properties and material properties, especially depending on particle size.

9

b

S0x

xxS 0 (7)

According to the unit operation different balance types are used to formulate the population balance model for different process conditions, i.e. for single pass breakage, for ideally mixed mills or for plug flow. In the case of the ideally mixed mill one receives for the mass fraction in the i-th size fraction in the mill product

1

1

i

jjj,ijmeaniimeanii pbSpSfp (8)

where f is the mass fraction in the feed, S the specific rate of breakage and b the breakage distribution coefficient. The mean residence time mean is defined by

MM

mean (9)

Depending on the feed rate to the comminution equipment, the appearance rate of a size class i from previous class is experimentally established and used in the model to predict the comminution properties of an ore. The triangular matrix structure of the model provides the rates at which the size fractions discharge from the mill discharge. The model involves a diagonal matrix that describes the breakage rate of each component in the mill. For complex system or equipment empirical models are used to enhance the function-ability of the model to the entire equipment (King, 2001).

Another modeling approach is to determine the breakage distribution function based on t10 of the particle distribution size from a single particle breakage tests e.g. drop weight test at different breakage energy levels, compare chapter 2. The t10 function is expressed as:

Ebexp1At10 (10)

The values of A and b in conjunction with a population balance model can be used to simulate the performance of mineral process. During the test, variations in breakage rates and energy consumption are analyzed and used for better process control, circuit design, circuit modeling and simulation, throughput forecast and sizing comminution equipment (Weedon and Wilson, 2000). Narayanan (1985) suggested that the higher the value of A*b the softer is material subject to comminution and vice- versa. These parameters give an insight on hardness of the ore deposit without considering the liberation properties of mineral particles. On other hand variations in A*b are reported to be useful for geometallurgical modeling and mapping of a deposit.


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Some attempts have been made for combining mineralogy with comminution properties (Bonnici et al., 2008; Hunt et al. 2013; Vatandoost, 2009). It has been proposed that detailed and accurate information on modal mineralogy and mineral textures fully describes the comminution and concentration properties of an ore sample (Lund, 2013; Shea and Kronenberg, 1993; Lamberg et al. 2013; Lund et al. 2013). Mineral composition and texture (i.e. the grain size) have been used to predict the breakage properties of an ore but are not fully used to predict the liberation of mineral particles during comminution. For this purpose an integrated breakage model is needed that links the energy used to reduce the size of the mineral particles with the mineral liberation achieved during comminution. Such a liberation model for forecasting the degree of mineral liberation has to be based on mineral texture information in order to meet the requirements of geometallurgy.

3. Geometallurgical testing for ore grindability

3.1. Bench-scale grindability tests

3.1.1. Bond grindability test

The Bond test is used to analyze the grindability of a material. The test applies a standardized ball mill of 305 mm (12 in.), both in diameter and length, with a grinding media charge of certain size distribution and operated at a defined speed (Bond, 1961). The sample amount is defined by the bulk volume of 0.7 liters, consisting of particles smaller than 3.35 mm. The test is conducted as a dry locked-cycle test with sieving of the mill product after each stage. Fines are replaced by an equal amount of fresh feed material in order to simulate a closed circuit, and grinding times are varied in order to reach a simulated circulating load of 250%. For these tests, usually samples of up to 10 kg smaller than 3.35 mm are required. From the grinding test the Bond ball mill work index Wi (in kWh/t) is determined (Bond, 1961):

0.23 0.82

80, 80,

1.1 44.5

10 10i

SP F

W

x Gx x

(11)

where xS is the screen aperture in microns, G is the grindability (in grams of product per mill revolution), and x80,F and x80,P are the 80% passing particle sizes in m for the mill feed and product, respectively. The test results are used to calculate the change in particle size during grinding based on the grinding work input W (in kWh/t) and to size mills to achieve a desired size reduction using the Bond formula, also referred to as Bond’s law, as a process model (Bond, 1952):

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80, 80,

10 10i

P F

W Wx x

(12)

3.1.2. Variations of the Bond grindability test

The Bond test was originally developed for determining ball mill grindability but has been adapted also to other mill types. Bond defined an additional test routine for rod mill grinding using a 305 mm × 610 mm standard mill requiring up to 20 kg samples. Test conditions differ, e.g., the circulating load is changed to 100%, and also the Bond equation for calculating the rod mill work index is slightly different. In order to describe comminution in AG/SAG mills and high pressure grinding rolls (HPGR) based on the Bond test method requires model extensions by empirical relations. For instance, Barratt provided an empirical formula for a SAG circuit involving three work indices for crushing, rod mill and ball mill grinding (Barratt, 1989). The SPI (SAG Power Index) is another related index used to determine the ore comminution behavior in AG/SAG mills. The index is obtained from a batch test in a mill of 305 mm × 102 mm operated with steel balls of 25 mm in diameter. The feed ore sample is crushed material <12.7 mm. The test was originally developed by Starkey et al. in 1994 and reviewed by Amelunxen et al. in 2014 (Starkey et al., 1994; Starkey et al., 2006). Grinding time and power draw are measured for grinding the ore sample to an 80% passing product particle size of 1.7 mm. With respect to modeling, the SPI test has been extended to ore body profiling and the design of SABC milling circuits (Bennet et al., 2001; Dobby, 2001) and is further used in the CEET software (Kosick et al., 2001). In the past, several attempts have been made to simplify the Bond procedure. One approach has been to change the test from locked-cycle to a pure single-pass batch test in order to minimize the time, effort and sample amount needed, by developing new test mills, e.g., Outokumpu’s Mergan mill (Niitti, 1970) or the NSBM (Nematollahi, 1994), or by modifying the test procedure, such as by changing the test to wet grinding (Tüzün, 2001), or by reducing the number of test cycles based on certain assumptions and complemented by simulations for ball mill and rod mill grindability, see (Magdalinovica, 1989; Tavares et al., 2012) and JK Bond Ball Mill Lite test (Kojovic and Walters, 2012). In the Modbond grindability test, an open circuit dry batch test run is used for estimating the work index after calibration against the standard Bond ball mill test (Kosick et al., 1999).

3.1.3. Evaluation of grindability tests

In grindability tests, a combination of impact and attrition is applied to a bulk of material. The original Bond test procedure is quite tedious, as several grinding cycles are necessary to reach the steady state of the simulated closed circuit. Furthermore, the sample amount required in the test is large, and is more problematic when only drill cores are available. Sample preparation is involving pre-crushing and screening.


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The test is reliable and has a good repeatability if the procedure and test mill comply with the standard. One of the major advantages is surely the huge data base that has been developed during the last six decades. With respect to process modeling, the coupling between the work index and the particle size reduction can be used together with an approximation function for particle size distribution. Attention must be paid to the applicability of the function type for the individual case. The particle size range of the mill product is suitable to also perform mineral liberation analyses. Table 3 summarizes the characteristics of the different grindability test methods.

Table 2. Grindability tests.

Adverse ( ), Acceptable (O), Advantageous (+)

Original Bond Ball Mill

Original Bond Rod Mill

Simplified Bond e.g., Mergan Mill

Simplicity O O + Repeatability + + +

Sample preparation O O O Time exposure and costs O

Sample amount O Link to modeling + + + Mineral liberation + + +

3.2. Pilot and bench-pilot scale tests

Comminution test work on bench-pilot or pilot scale is done by using different types of crushers and mills depending on the intended process design. Typically these tests include:

Cone crushers; High pressure grinding rolls (HPGR); Tumbling mills: ball mills, AG and SAG mills; Stirred media mills, e.g., IsaMill or vertical stirred mills.

Stress type and stress rate are based upon the respective machine type. The tests usually require preparing tens to hundreds of kilograms of sample material and are done in batch or continuous mode. Sample preparation normally comprises pre-crushing and screening to the initial size distribution, as well as sample splitting. Sampling from the test mill or comminution circuit provides the data necessary for determining breakage probabilities and grinding rates, as well as breakage distributions received from back-calculation when applying population-balance methods. Using the data from liberation analyses allows for describing the particles based on their mineral composition (Lamberg et al., 2007). Pilot and bench-pilot scale tests are used to verify the metallurgical performance of a designed circuit. In the geometallurgical context, these results can be used in calibrating the small scale test results to full scale operation.

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3.3. Indirect methods for determining comminution behavior

Another way of obtaining information about rock mechanical strength is to evaluate the core drilling process with corresponding instrumentation, also referred to as measurement while drilling (MWD). Alternatively, drill cuttings can be evaluated. Variations of the conditions at the drill bit, such as torque, normal or bending forces, result from changes in rock hardness. Despite the huge data sets that are continuously collected in a large number of operations, the MWD data is seldom used for assessing the comminution properties of ore bodies. One of the obstacles is the lack of reliable on-line information about the condition of the drill bit, which is needed for correcting the recorded down-hole measurements by the dynamic process of drill bit wear. Petrophysical data from multi-sensor drill core logging have also been used for calibration against measures of ore breakage parameters and grindability obtained from conventional destructive comminution tests (Vatandoost, 2010). Using density, magnetic susceptibility and seismic wave parameters from Australian copper-gold deposits, the Bond mill work index and the crushability parameters obtained from drop weight testing, could be predicted with acceptable accuracy. In conjunction with recent advances in quantitative mineralogical analyses, the development in geometallurgical characterization today tends towards the identification of correlations between ore comminution behavior and mineralogical properties. The strategy is to reduce the number of comminution tests necessary for characterizing a deposit and to arrive at a more generic description of mechanical properties based on the occurring minerals (Mwanga et al., 2013).

3.4. Summary and conclusions

Grindability tests are well established and provide a huge amount of reference data. The Bond equation links comminution energy and resulting particle size reduction, thus already providing a comminution process model. With respect to geometallurgical testing, a clear disadvantage lies in the timely effort needed for conducting the Bond test and the comparatively large sample amount. Steps have been undertaken to simplify the procedure. Future development should target on modified Bond grindability tests where the sample amount needed is significantly minimized.

Pilot and bench-pilot scale tests are principally not suitable for mapping of the ore’s comminution variability but can be employed in the calibration of small scale tests and at a later stage of a mine development project. Here tumbling mills as well as tests with stirred media mills and HPGR are of relevance.

Indirect measurements have not been used to a large extent yet but are promising and further development is warranted.


14

4. Methodological approach for the development and validation of the GCT

4.1. Characterization of samples within a geometallurgical framework

Within this work a novel framework has been defined for testing ore comminution and liberation properties of an ore deposit, the Geometallurgical Comminution Test (GCT) (Figure 2). This involves a set of broad, simple, cheap and efficiency test methods that can be used for developing new tools (.e.g. a process simulator) when assessing the variability within a deposit before full implementation of the process and grinding operations. With respect to the process chain this represents explicitly a one stage grinding test at comminution testing level.

Recently, there has been further progress in the development of methods to enhance ore characterization in geometallurgy. Many of these approaches have been mainly focusing on hardness of ore (crushability and grindability) or mapping mineralogical variability of an ore and throughput based on crushability index. For example Vatandoost’s (2010) work on petrophysical properties of a rock and their effect on ore comminution behavior emphasize measuring the hardness of a rock. Bonnici et al (2008) provided detailed characterization of a porphyry copper ore mainly based on mineralogical variability within a deposit by showing a qualitative correlation between textural parameters and liberation properties of an ore.

Linking the mineralogical and liberation properties of a given material to the process performance by applying automated mineralogy as a tool for solving mineral processing problems (e.g. Sutherland, 1991) has contributed to geometallurgy to become an industrial tool for improving resource efficiency. Advances in analytical but also methodical analyses have made geometallurgy an active and emerging field of studies for many researchers (Newton and Graham, 2011). As geometallurgical techniques become more sophisticated a profound framework is needed for

Examining the variables or variability of a given deposit at different levels of the process units by using the mineralogical properties of the material.

Evaluating the test results from a given deposit vs. full simulation of the material responses and suggests new experiments and optimization strategies for the effectivization of mine operations.

Because mineralogical properties of the material directly affect the downstream separation processes such as flotation or magnetic separation, the concept of geometallurgical testing should not be limited to one level but be integrated into the entire process to fully describe the ore variability for a given deposit towards the end product (including units as .e.g. flotation, extraction). The majority of available test methods (see Table 3) are usually conducted individually due to lacking knowledge of what variables can be used to link the different levels of unit processes, even though putting the testing framework in different levels has benefits in the geometallurgical context.

15

Table 3. Collected methods commonly used for testing ore process variability in different levels in geometallurgy

Rank Test method Objectives Level 1 (comminution &liberation) JKCi hardness proxy

Hardness standard Comminution variability Paired testing with classic DWI &BWI

Drop Weight Test (A*b) Bond Work Index (BWi)

Hardness Testing JKCi Test with QA/QC

Whole rock analysis - Borate Fusion / XRD

Level 2 (concentration &extraction)

Metal Recovery Testing Recovery & grade variability Rougher / cleaner

Mineralogy - XBSE / PMA Ore Blending / Flotation Poisoning

Tests 3 Bench / Plant scale-up 3

Grade Engineering Grade Engineering Test (ore upgrading)

Rheology Testing Settling test on tails.

Level 3 (environmental assessment) Acid Producing Potential Prediction

Mineralogy - XBSE / BMA & XRD Variability on acid mine

drainage Cu/Ni

S(sulphide) - LECO Carbonate - LECO

ABA static test

However, a comprehensive answer to how the mineralogical variables would affect the entire chain of the processing is often missing. In the developed conceptual framework (Figure 2) mineralogical variables have been used to describe the grinding and liberation properties of the materials in a wider context. The same concept can be extended to other levels in order to specify the behavior and examine the limitations for the variables when testing the ore variability in the geometallurgical programs.

The dotted line in Figure 2 indicates additional information added to the original GCT test method which was described by Mwanga et al (2015). The purposes of adding more information has been to broaden the method and to be able to generalize the measurement of Bond work index by using single pass grinding procedure considering the variations of the different ore types.


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8) Grinding test

9) Sizing

1.) Sample

2) Sample prep

3) 1 pass crushing

4) Sizing

4A) Report crushability index as size reduction ratio

5) Crushing 100 % < 3.35 mm

6) Splitting

7) Particle size analysis

10) Report P80, PSD

B1) Take one size fraction

B 2) Liberation analysis

B 3) Report Lib % and AI

A 1) Sample prep for other assays

A 2) Chemical assay

A 3) XRD

A 4) Modal mineralogy

A 5) Grain size of the main minerals

11) Report the mass passing 106 m screens at 2 and 5 minutes grinding time

Figure 2. Flow chart for a novel testing framework in geometallurgy

The 106 m screen was selected as a basis for measuring grindability. This is in close accordance with the Bond law that describes the energy required to grind materials from infinity size to 100 m.

Characterization of samples properties puts challenges before gaining benefits in managing the resource efficiency by geometallurgical programs. This involves measurement of the process parameters and analyses of the mineral properties (.i.e. mineralogical properties) as well as their linkage to the subsequent processes for the recovery of valuable minerals depending on the processes conditions. The ultimate outcome of the analyses and testing is the identification of the variability of material response to the process. On the other hand the data from analyses is needed for the modeling of the geometallurgical systems. The later one serves as a tool for predicting the process behavior given the mineralogical and process parameter (.e.g. grain size vs. breakage properties).

For an efficient test framework, information about mineralogy and texture is crucial and needed for controlling and monitoring the beneficiation plant in geometallurgical context. This is usually done by using image analysis techniques based on SEM and optical microscopy, XRF and XRD for mineral and phase identification. For variability testing, the timely efforts and costs are crucial. Depending on the requirement of the individual test method the sample amount required can be large, i.e. higher efforts and

17

costs for analyses become a constraint when testing the variability of a deposit. Besides the analyses and testing requirement, the testing framework should provide suitable parameters for process modeling in order to be able to simulate the variability of a given deposit. From simulation important variables for process optimization are obtained after testing the given deposit.

4.2. Development of the GCT grindability test

Selected samples of different grinding properties were used to develop a rapid and novel geometallurgical testing procedure for estimating the Bond work index. The Bond law of comminution was used for the development and the test results were evaluated with respect to accuracy and precisions against the standard Bond work index (i.e. work index determined from the original Bond test). For conducting a geometallurgical program suitable comminution test methods have to provide not only material properties but also the relevant parameters that can be used within process modeling and simulation. In the following, some principles of comminution process modeling are discussed in order to point out how the linkage between test work and modeling looks like.

The entire test programme involves crushability and grindability test work as well as mineralogical analyses for both entire samples as well as selected sieve fractions (Mwanga, 2015b). Results received from the GCT test programme comprise modal mineralogy, particle size distributions, work indices and mineral liberation analysis.

As part of the test procedure a small scale batch grindability test has been defined as a shortcut test method for estimating the Bond ball mill work index. For this test a small laboratory ball mill is used that has a volume of ca 1.4 liters only. The mill is running on the same percentage of critical speed as the original Bond mill, thereby fulfilling the criteria of kinematic similarity as described by a constant Froude number (Steiner, 1996). Also the volume fraction of mill volume occupied by the ball charge has been kept similar to the original Bond mill. Grinding media is in the same size range as in the Bond test, while the number of steel balls is adjusted to the mill size. Preliminary tests were done with one magnetite ore sample but were limited in their validity due to the fact that a coherent methodical framework for test conduct and evaluation of results was missing (Mwanga et al., 2105b).

The suggested batch grindability test involves the following steps:

Sample preparation: Preparation of 220 g sample material, pre-crushed in a laboratory jaw crusher to 100% passing 3.35 mm. The chosen sample size is adapted to the size of drill core sections or fractions of drill cores and even allowing for repetitions with smaller samples. To simplify sample preparation and energy measurements, the test uses a constant sample mass as it is the case also for other grindability test, for instance in the Hardgrove test or the Zeisel test (Böhm et al., 2015).

Test execution: Dry batch grinding test of the sample is done using cumulatively 2, 5, 10, 17 and 25 minutes grinding times. After each grinding time sample is dry sieved for particle size analysis and returned to the mill for further grinding.


18

Particle size: The particle size distributions are numerically evaluated for the 80% passing size. Additionally the sample amount below the target product size is determined corresponding to the grindability analysis within the Bond procedure.

Energy for grinding: Recording of the gross electrical power draw during the grinding test is done using a conventional energy meter. To overcome the limited precision of the meter an energy-time relation has been established for the experimental setup. The mechanical power provided to the mill is back-calculated using efficiency data for both electrical engine and mechanical drive (Mwanga et al., 2016). The calculation takes into consideration that the mill is running at reduced speed and load. As the test is run at constant sample weight and mill parameters (number of revolutions, grinding media), the energy supplied to the mill per unit time is assumed to be constant.

Evaluation: Experimental data evaluation and GCT work index calculation as described in the following paragraphs using spreadsheet calculation.

The evaluation of the grinding test results is then based on the Bond formula for calculating the specific energy for grinding W:

FPi xx

WW,80,80

1010 (13)

with

iW : Work index, in kWh/t

Px ,80 : 80% passing size of the mill product, in m

Fx ,80 : 80% passing size of the mill feed, in m

Potential differences in the shape of the product particle size distribution compared to a locked-cycle test with screen are neglected in the calculation of the Px ,80 value. Further,

for a given feed size the change in specific grinding energy is proportional to the reciprocal of the square root of the Px ,80 value:

1010 80

80

P,

P,

xWk

xkW (14)

where

k : Constant, in kWh/t

19

The proportionality constant k divided by 10 is denoted as the GCT work index and can be determined using the several data pairs of W and Px ,80 for the different grinding times.

Like the Bond work index, the GCT work index is a material dependent parameter.

The suggested approach to data evaluation takes up the earlier formulation of the Bond equation, where energy is expressed by gram per number of mill revolutions passing the target particle size:

1001611 820

i.

BBond,i

PG

.W (15)

Figure 3 shows the typical linear course of curve that is described by Equation (14) for an iron oxide ore sample after transformation of the x-axis. The straight line is not continuing through the origin but intersects with the y-axis in the negative intercept. This can be interpreted as an infinitely large starting particle size. The selected time steps provide a larger resolution in the beginning of the test. By calculating the slope from several points of time, a timely averaged value is received for k and the GCT work index, respectively. The latter is important with respect to those cases where deviations from the linear course can be observed.

The derived GCT work indices are higher than the Bond work index from the standard test. This might be explained by the different evaluation methods but also by the lower energy intensity in the small ball mill. By introducing appropriate correction factors, the GCT work index can then be correlated to the original Bond work index based on common target product particle size of 106 m, which can be regarded as the finest size for dry grinding, compare section 4.2.4.


20

0

10

20

30

40

50

60

70

0,03 0,035 0,04 0,045 0,05 0,055 0,06 0,065 0,07

Gross

specifice

nergy[kWh/t]

1/Square root of 80% passing size (product, value in μm)

2 min.

5 min.

10 min.

17 min.

25 min.

Figure 3: Linear relation between specific energy and mill product size (magnetite sample).

4.2.1 Experimental validation

For validation of the small scale grindability test procedure and the development of a correlation between the GCT work index and the standard Bond work index, grinding tests were carried out with fifteen samples from different types of deposits in the Nordic countries having wide mineralogical variations. For each sample the full Bond grindability test was conducted following the Bond standard test procedure and results from that were compared with the GCT grindability test. The target product size in all the tests was kept constant at 106 μm (150 mesh) which was related to the liberation size of most mineral samples. Full Bond grindability tests were done in a standard ball mill with an internal diameter of 305 mm and a length of 305 mm. Ball charge and ball size distribution as well as mill speed followed the original Bond procedure of locked-cycle tests (Bond, 1961).

4.2.2 Samples and applied methods

Different mineral samples were collected from mines in Sweden, Norway and Finland that can be categorized into three major groups:

The first category was a group of oxide ores including magnetite and hematite from iron ore deposits in Northern Sweden. Originally, these ore samples were the starting point for developing the GCT and main focus when analyzing ore comminution behavior in the geometallurgical context, i.e. magnetite dominated ore (FAR) and hematite dominated ore (HAR) were collected after pre-

21

concentration in the cobbing plant in Malmberget and used as reference samples during the entire investigation. Composite magnetite (MGT) and hematite (HMT) ore samples were received via belt cut from the processing plant in Malmberget and introduced to the investigation plan to study the effect of sample variations in geometallurgical comminution testing. The samples from the Kiruna iron field ore deposit is known as magnetite-apatite deposit having fine grained magnetite. The mineral include besides _Fe oxides actinolite, K-feldspar, albite, phlogopite, chlorite, titanite, quartz, and talc (Niiranen, 2015). The texture characteristics of magnetite sample KA3 are simple and distinct from Malmberget samples. The Kiruna sample represents a belt cut of SAG mill feed material (KA3).

The second category were sulphide ore samples which comprise gold deposits, porphyry copper and massive sulphide deposits from Boliden mine sites (KSM and RSM). Other samples falling into this category were dominated massive zinc (RS1) and massive chalcopyrite-pyrite (RS2) from another ore deposit in the Skellefteå area. The occurrences of the massive sulphide are associated with felsic pyroclastic rocks, quartz porphyries and minor mafic volcanites (Weihed et al., 1992). Porphyry copper deposits from the Skellefteå field consist of large rounded sub-grained quartz phenocrysts with minor biotite and chlorite minerals. Samples RS1 and RS2 have variations in distribution of Sb-bearing minerals. A gold-quartz mineralization sample from Västerbotten (BAU) was also included into the investigation. Within this category even black schist Ni Nickel sample (NIT) from Talvivaara in Eastern Finland was included as a special type of sulphide deposit. The sample contained pyrrhotite, pyrite, sphalerite, pentlandite, violarite, chalcopyrite and graphite. The main silica minerals were quartz, mica, anorthite and microcline (Riekkola-Vanhanen, 2010). The other sample from Sotkamo in Finland (AGF) contained silver minerals with a different mineralogy compared to the Talvivaara deposit. The main mineral in the AGF sample was quartz, which was relatively coarse grained compared to the fine grained occurring in NIT.

The third category was a group of non-metallic minerals that included pure quartz, calcite and olivine. The quartz and calcite sample were received from two different mines in Norway. The quartz was received from Elkem quartzite deposit having a simple mineralogy. The calcite sample from Brønnøysund in Northern Norway contained coarse grained calcite marble (Olden, 2015) as a major phase with inclusions of silicates and sulphide minerals. Graphite and silicates were the main contaminants for the quality of the calcite product. Further, an olivine sample from also Norway was used in the investigation. Because of its natural properties (low density and high magnesium content) the olivine is used as an additive in metallurgical processing.


22

A summary of the sample description is given in Table 4.

Table 4: Samples used for test validation

No. Identifier Description Main minerals Minor minerals

1 FAR Processed magnetite sample, Malmberget, Sweden

Magnetite Biotite, apatite

2 MGT Belt cut magnetite sample, Malmberget, Sweden

Magnetite Biotite, albite and apatite

3 HAR Processed hematite sample, Malmberget, Sweden

Hematite Biotite, actinolite

4 HMT Belt cut hematite sample, Malmberget, Sweden

Hematite Magnetite, biotite, quartz

and apatite 5 KA3 Magnetite sample, Kiruna, Sweden Magnetite Feldspar 6 KSM Complex copper ore, Boliden, Sweden Quartz Chalcopyrite 7 RSM Complex copper ore, Boliden, Sweden Quartz Chalcopyrite,

pyrite and sphalerite

8 RS1 Rockliden massive zinc sulphide samples, Sweden

Sphalerite Quartz

9 RS2 Rockliden massive chalcopyrite-pyrite, Sweden

Chalcopyrite-pyrite

Quartzite

10 CAL Calcite sample, Brønnøysund, Norway Calcite - 11 AGF Silver gold sample, Finland Quartz sphalerite and

galena 12 BAU Quartzite dominating mineral gold sample,

Sweden Quartz Pyrite

13 QRZ Quartz sample Quartz - 14 OLI Olivine sample Olivine - 15 NIT Black schist nickel sample, Talvivaara,

Finland Quartz Pentlandite,

chalcopyrite and sphalerite

In Table 5 more sample properties are provided for further characterization. Mohs hardness and density were calculated as weighted averaged values based on modal mineralogy. The mineral composition of the samples was received from XRD analysis or from XRF results used in combination with a numerical element-to-mineral conversion, respectively. The average grain sizes of the main minerals in each sample were determined by means of optical microscopy.

23

Table 5: Sample properties based on mineralogical analysis

No. Identifier Hardness Mohs [-]

Density [g/cm3]

Grain size [ m], main

mineral 1 FAR 6.51 5.10 500 2 MGT 6.20 4.84 350 3 HAR 6.57 4.75 600 4 HMT 6.47 4.95 800 5 KA3 6,30 4.82 150 6 KSM -1) -1) 500 7 RSM 6.64 3.19 250 8 RS1 6.30 2.93 200 9 RS2 6.54 2.82 200 10 CAL 3.00 2.71 1500 11 AGF -1) -1) 100 12 BAU 6.99 2.65 500 13 QRZ 7.00 2.62 300 14 OLI 6.75 3.32 600 15 NIT 6.89 3.12 30

1) Not available

4.2.3 Analysis and developed validation correlation of the GCT

In order to assess the repeatability of the measurement by GCT, at least three experiments for each sample were performed. Figure 4 is an example that illustrates the reproducibility of the GCT ball mill from different operators before validations of the GCT testing conditions. A good reproducibility for the GCT testing conditions can be observed.

0

10

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30

40

50

60

70

80

90

100

10 100 1000 10000

Cum

mul

ativ

e pe

rcen

tage

pas

sing

(%)

Particle size (μm)

Author FAR-10 min product

Students FAR-10 min product

LTU technician FAR-15 minproductStudent FAR-15 min product

Author HAR- 10 min product

Student HAR -10 min product

LTU technician FAR- 17 minProductAuthor FAR -17 min product

LTU technician- 25 min product

Author FAR-25 min

LTU technician FAR- 5 minproductAuthor FAR-5 min product

LTU technician FAR feed

FAR feed

Student HAR feed

HAR feed

Figure 4. Comparison of the GCT grinding responses for the two different samples on repeatability from different operators (GCT was operated on the same conditions for different operator and different time).


24

Table 6 summarizes the work indices received from the two types of grindability tests. As an estimate of the strength of the relationship between linear slope model and the measured data the coefficients of determination are provided.

Table 6: Summary of work indices

No. Identifier 80% passing size feed

[ m]

Slope factor [-]

Coefficient of determination

[-]

GCT work index

[kWh/t]

Bond work index

[kWh/t] 1 FAR 1024.0 1601.51 0.9796 160.15 16.71 2 MGT 1309.9 1580.21 0.9664 158.02 16.62 3 HAR 880.8 1955.31 0.9934 195.53 20.36 4 HMT 1410.7 1828.80 0.9835 182.88 17.10 5 KA3 1832.2 814.03 0.9124 81.40 7.34 6 KSM 1806.8 1286.88 0.9779 128.69 12.43 7 RSM 2092.5 1216.84 0.9433 121.68 11.22 8 RS1 2202.1 657.97 0.9691 65.80 6.30 9 RS2 2190.8 677.97 0.9731 67.80 7.21 10 CAL 2005.0 920.90 0.9796 92.09 7.70 11 AGF 1868.6 799.00 0.9964 79.90 7.90 12 BAU 2172.3 1597.86 0.8956 159.79 14.94 13 QRZ 1874.8 1068.95 0.8790 106.89 15.09 14 OLI 2172.3 2995.02 0.9948 299.50 25.69 15 NIT 2233.8 1933.15 0.9944 193.31 15.45

Comparing the results from the two grindability tests revealed that there is a linear relationship between the work indices. When taking into account the geometric scaling factor between small mill and Bond mill and a correction of the GCT work indices for mill drive and engine efficiency, a remaining linear correlation factor of 4.0 can be derived from the experimental data. The model for estimating the Bond work index from GCT test data is then given by:

411GCT,iBondestimated,i WW (16)

where

Mill drive and engine efficiency, = 0.64

Geometric scaling factor, = 2.65

Figure 5 shows the measured Bond work indices versus the estimated (calculated) work indices received from the GCT, confirming the linear correlation assumed in the model. For the metal ore samples, the relative error between the two values was within a range of 0.70% to maximal 8.8%, with an average of 5.1%. This is in the same range as reported in literature for abbreviated Bond test of 2 to 3 grinding cycles while the experimental variation of the full Bond test is denoted with ±3.5%.

25

The three samples of industrial minerals, however, showed larger deviations. Complementing the tests with these samples with smaller sample mass to compensate for the lower density did not show significant differences. Also, some of the metal ore samples had densities in the same range. From that it has to be concluded that a more complex dependency on texture and mineralogy is controlling the comminution behavior. The estimation of the Bond index could be improved by adjusting the linear correlation factor or by introducing another model parameter in equation (16).

The results received from the tests were also compared with the mineral composition and related properties of the samples as described in Table 6. The deviation between original Bond index and the estimate from the GCT showed certain patterns towards density and grain size. However, the number of the samples and their variety did not allow describing the dependency in a quantitative way.

1,0

10,0

1,0 10,0

Bond

workinde

x[kWh/t

Calculated work index from GCT [kWh/t]

Figure 5: Comparison between standard Bond test and GCT results after calculation.

The test can be further optimized with respect to timely effort by reducing the number of time steps. As discussed above, this is much depending on the individual sample. This can involve shorter tests as in the case of FAR (see Figure 8), or even longer grinding as for the NIT sample. When applying the test to a group of similar samples, as it is the case when testing for the variability of an ore body, further adjustment of the grinding time is possible by identifying shorter time periods for describing the linear correlation.

In order to assess the repeatability of the measurement by GCT, at least three experiments for each sample were performed. Based on the measured particle size distributions and the interpolation for determining the 80% passing particle size, the relative error was approximately 1.4%. Otherwise, the GCT testing procedure involves


26

errors from sample preparations, i.e. splitting and weighing, and from measuring specific grinding energy. All in all, the experimental results could be reproduced within good precision.

However, looking at the entire chain from sampling over testing to geometallurgical modeling it must be concluded that the whole procedure is very much determined by the quality of the sample selection. I.e., errors within sampling affecting representativeness cannot be compensated by higher accuracy of the test and model.

The entire error from GCT testing procedure includes errors from sample preparations (.i.e. splitting and weighing), error from grinding tests (i.e. errors due to measurement of specific grinding energy and time when start and stop the tests). However these errors have no detrimental effects on the measurement of the Bond work index. The uncertainty error from size measurement (i.e. X80, product) has effects on the Bond work index. This error is associated with losses during sieving and it was considered as an important variable in the evaluations of the relative uncertainty in the GCT test method. The accuracy and reliable analyses were obtained by analyzing the relative errors associated by the GCT.

4.2.4 Single pass grindability behavior between GCT and Bond mill

In a first step, the grinding tests were analyzed with respect to the grinding progress and in order to exclude possible anomalies. Figure 6 shows the results from the small scale grinding tests for all the 15 samples in terms of material retained on the product screen at the target size 106 μm. The time intervals were according to the suggested grinding times for the GCT. It can be seen that all the grinding curves were monotonously decreasing with increasing within the grinding time, i.e. none of the mineral samples showed indications for overgrinding or agglomeration and coating effects during the test.

10

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70

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90

100

0 5 10 15 20 25 30

Seiv

e re

sidu

re o

n 10

6 μm

scre

en (%

)

Grinding time (minutes)

FAR

Mgt

HAR

Hmt

KA3

KSM

RSM

RLS1

RLS2

CAL

AGF

BAU

QRZ

OLI

NIT

Figure 6: Grinding curves for all samples, target size 106 m.

27

Comparing with the original Bond tests, the GCT grinding curves were running below the curves obtained with the large mill (see Figure 7), thus indicating lower energy intensity.

0

10

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30

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90

100

0 5 10 15 20 25

Perc

enta

ge r

etai

n in

> 1

06 μ

m sc

reen

(%)

Grinding time (min)

Bond mill vs FAR sample

GCT mill vs FAR sample

Figure 7: Compare Grinding curves for FAR sample, target size 106 m between Bond and GCT ball mill.

Further, the linear relation between energy for grinding and the 80% passing product particle size was examined. Figure 8 depicts the results for all samples analogous to Figure 3. The majority of samples directly follow the assumed linearity. In some cases, the linearity develops after an initial phase. This is particularly pronounced in the case of the NIT sample from Finland, where significant grinding action is taking place only after 17 minutes. Accordingly, the suggested number of time steps was extended in this case.

0

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80

100

120

140

160

180

0.02 0.04 0.06 0.08 0.1 0.12

Gro

ss sp

ecifi

c en

ergy

(Kw

h/t)


FARMGTHARHMTKA3KSMRSMRS1RS2CALAGFBAUQrtzOLINIT

Figure 8: Check for linear relation specific energy vs. mill product size.


28

4.3 Incorporation of liberation into the GCT

The liberability approach can be measured within a small scale comminution test developed in this work. This approach provides a wide description of multi-dimensional problem by combining mineral liberation, grinding energy and particle size reduction (Mwanga et al. 2015). This requires efficient process model and parameters that predict liberation properties of mineral particles. Hence complement the value of Bond grindability test when applied to geometallurgy.

Besides the particle size reduction and energy required the test framework also involves mineral liberation. In Malmberget the degree of liberation (i.e. mass proportion of mineral particles containing more than 95% of the mineral in question) shows negative relationship with particle size, as expected (Figure 10). In a simplistic approach, particles are broken and energy used to break particles is measured and compared with progeny size distribution. By assuming that the liberation distribution is conserved within narrow size fractions, the degree of liberation in the bulk is predicted by the model in equation (19).

Three major steps are required for prediction of the degree of mineral liberation (see Figure 9).

Receive a characteristic size P80 from grinding test or calculate it by Bond equation

Use Rosin-Rammler model to convert the received P80 to full particle size distribution

Select one key size fraction from progeny size distribution : should be closed to the expected liberation size fraction

e.g. 53- 75 μm

1. Liberation by size2. Mineral grade by size

(assays of magnetite)3. Size distribution (%

mass) by size

Apply liberation model to calculate liberation distribution

Step 2: Convert a given P80 of a mill product to full particle size distribution

Size distribution (% mass distribution)

Bulk mineral Liberation at given P80

Step 1: Establishment of mineral liberation by size

Mineral Liberation by size

Step 3: Combine step 1 and 2 with magnetite grade (assays) to predict magnetite liberation in the bulk

Figure 9. Steps required for prediction of degree of liberation at a given P80.

To describe the liberation by size, particles were first generated by grinding the materials to give a certain particle size distribution, which was analyzed by sieving. The black and white mark in Figure 10 represents the measured degree of magnetite liberation from

29

selected one key size fraction. This should be close to the expected liberation size and for the Malmberget magnetite ore the size fraction of 53-75 microns was selected. The measured degree of liberation was used to calculate (equation 17) the changes in liberation per size ( slope) by assuming that at very fine particle size the magnetite particle is 100 % liberated (full liberated).

gmX

100XsfLiB

LiB S (17)

Where,

SLiB is the degree of liberation per average size of the selected size fraction (% / m). It is describing the rate of change of mineral liberation per size,

LiBXsf is the degree of mineral liberation for the selected fraction which is closed to expected liberation size (%),

Xgm is the geometric mean size of the selected size fraction for liberation analyses ( m).

The slope in equation (17) was used to establish a liberation model which describes the degree of liberation by size as shown in Figure 10. The degree of liberation in the bulk sample was calculated from the size fractions as weighed averages using a linear model equations established in Figure 10.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600 700

Deg

ree

of m

agnet

ite

liber

atio

n (

%)

Particle size ( m)

Fa-Fsp

8C

8F

6F

4F

2F

Figure 10. Comparison of liberation distribution of Magnetite mineral after grinding for various mineral texture samples from Malmberget.


30

The characteristic size of 80% passing (P80) of a mill product was calculated by using equation 18. In the calculation the Bond work index received from grinding tests (Geometallurgical comminution test) and fixed feed size distribution (F80) were used. The received mill product size (P80) is converted to a full particle size distribution by using the RRSB according to equation (19) and taking the parameter describing the variance of the distribution.

F80,x

1

P80,x

1i10WE (18)

where,

Wi is a work index of material (kWh/t),

E is the grinding energy (kWh/t),

X 80,p and X 80,F are mill product and feed size ( m), respectively.

By changing the comminution energy the size distribution is changing and the liberation distribution in the bulk is changing accordingly. The Rosin-Rammler-Sperling-Bennet distribution function in equation (19) is used to enhance the changes of size distribution.

100

n

63.2X

xexp1RRSB (19)

where,

RRSB is a Rosin-Rammler-Sperling-Bennet distribution (%), X is the size of a particle ( m), X63.2 % is the characteristic size describing 63.2 % quartile of the distribution in the population of particles ( m) and n is a parameter which described the variance of the distribution (dimensionless unit).

To estimate how the liberation changes with grinding energy a simple approach was used. Calculations were done for each sample individually following the steps in Figure 9. In the first, a set of grinding energies was selected and for each of these the P80 was estimated by using the Bond equation (18). In this calculation the Bond work indices received from the tests were used. The P80 was converted to a full particle size distribution by using the Rosin-Rammler equation and applying the parameters describing the variance of the distribution of the grinding product (see Table 7). A new D63.2 parameter to give identical P80 as received from the Bond equation was searched by least squares fitting. Finally, to get an estimate for the degree of liberation of magnetite it was assumed that the degree of liberation within the narrow size fractions remains constant and the overall value is a product of each size fraction by their mass proportions (see equation 20).

31

n

1i Mgt%LiBwt %

bulkLiB (20)

where,

LiBbulk is the calculated degree of mineral liberation in the bulk in a given P80 for the n size fractions, % wt is the percentage mass (%) at size i, LiB is calculated degree of liberation at size i, % Mgt is magnetite grade in size i (%).

The liberation characteristics of the size fraction were measured using automated mineralogy. Based on the measurement on size fraction 53-75 microns the degree of liberation of magnetite was estimated in the other size fractions by applying a linear equation which passes through the measured point and the point (0,100). The degree of liberation in the bulk sample was calculated from the size fractions as weighed average.

The liberability interchange (i.e. the transfer the energy-size reduction relation to energy-liberation) provides an efficient way of using the liberation measurement (i.e. one size fraction while assuming that liberation is conserved within narrow size fraction) in order to assess the ore comminution behavior. This distinguishes this approach from others .e.g. the approach by King (1976) where many size fractions are required in order to describe the response of grindability to liberation of different material properties .e.g. texture. Because the main purpose of grinding is to achieve the required liberation the liberability information will clearly tie the technical and economical ways in order to utilize the resource in an optimal manner. This has potential to change the processing plants in their operational principles from targeting a certain particle size to defined mineral liberation. The samples in Table 7 are examples that have been used to test the concept of liberability and which be divided into two classes of texture i.e. coarse grained texture (8C) and fine grained texture (8F, 6F, 4F&2F).

Table 7. Parameters for determination of the degree of liberation

Sample 2F 4F 6F 8F 8C Texture type 2 4 6 8 8 Grain size Fine Fine Fine Fine Coarse Size fraction 53-75 microns Magnetite wt.% 13.3 88.6 59.0 85.0 90.2 Magnetite Lib% 78.0 88.6 85.2 94.5 95.3 Grinding test product 80% passing 125.3 132.3 126.7 129.9 140.3 Rosin-Rammler D63.2 81.2 96.6 93.4 96.3 103.5 Rosin-Rammler alpha 1.7 1.7 1.7 1.7 1.7

Figure 11 is a modification of the liberability curves (Mwanga et al, 2015) that show that ore texture classes 8C and 8F have similar liberability and different grindability .The reason for similarities and differences between two class textures is that the two classes (8C and 8F) have closely the same magnetite content and different magnetite grain size.


32

The remained three texture classes (2F, 4F and 6F) have different magnetite grade and grain size and they have shown different liberability behavior as expected. The higher the magnetite content the better is the liberability and the opposite is true.

60

65

70

75

80

85

90

95

100

5 6 7 8 9 10 11

Deg

ree

of liber

atio

ns

of m

agnet

ite

in t

he

mill pro

duct

(%

)

Applied specific grinding energy (kWh/t)

8C

2F

8F

4F

6F

Figure 11. Liberability based on the variation of magnetite mineral texture.

4.4 Investigation of the linkages between mineralogy and breakage behavior

4.4.1 Breakage behavior and modeling

Traditionally comminution efficiency is assessed based on the achieved progeny size distribution against applied mechanical energy. In conjunction with recent advances in quantitative mineralogical analyses, the development in geometallurgical characterization today tends towards the identification of correlations between ore breakage properties and mineralogical properties of a given deposit. The approach uses modal mineralogy and mineral texture to describe the variability in terms of process responses (Mwanga et al 2015).

The lack of knowledge on how grain size and mineral composition affect breakage rate and how such parameters control the breakage phenomenon, and ultimately liberation of mineral particles, requires a profound understanding of the relationships between mineral grade and texture before modeling comminution properties of a given materials. In this study, the focus was to investigate the influence of mineral texture (grain sizes) and mineral compositions on specific rate of breakage. In fact, the investigations try to answer the questions what affect the Austin model parameters for specific rate of breakage and

33

how mineralogical data can be used to determine the specific rate of breakage and degree of mineral liberation.

Two samples of the same magnetite grade (FAR and KA3) but different magnetite grain size were used to examine whether the grain size of mineral particle affect the breakage properties of a given materials (compare Figures 12A, 12B and 12C). Within this investigation the sample F, which has significantly different magnetite grain size but the same mineral densities as sample FAR, was used to test the hypothesis that material with similar modal composition (the same magnetite grade) have the same breakage properties. Figure 12A illustrate the main effects of changing the grain size on the specific rate of breakage. It can be observed that the finer the grain size the faster is the rate of breakage. In the coarse size fractions there is no systematic order of the effects that can explain the reason of the differences between KA3 and FAR samples. The similarities between FAR and F in the size fraction 2380-3350 m are due to similar magnetite grain size. The observed opposite effect between FAR and KA3 in the three coarsest size fractions reflects the fundamental effects of energy dissipation considering the mineral grain packing (i.e. mineral grain arrangement).

0.01

0.1

1

30 300 3000

Spec

ific

rate

of b

reak

age

(per

min

ute)

Particle size (μm)

KA3- 150 μm mganetite grainsize

F - 80 μm magnetite grain size

FAR - 500 μm magnetite grainsize

Figure 12A. Test results showing how different can specific rate of breakage of materials of the same magnetite grade but different magnetite grain size.

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

2380 1680 1190 850 600 425 300 212 150

Den

sity

in th

e pa

rtic

le (g

/cc)

Tested particle size (μm)

B)

0

10

20

30

40

50

60

70

80

90

100

2380 1680 1190 850 600 425 300 212

Gra

de o

f mag

netit

e in

the

part

icle

(%)

Particle size selected for grinding (μm)

C)

Figure 13B & C. B) = comparison of feed mineral density (i.e. solid density) for three samples (FAR, KA3&F) for the sizes used to investigate the specific rate of breakage& C) = Comparison of feed magnetite composition for FAR &

KA3 for the sizes used to investigate the specific rate of breakage.


34

4.4.2 Linkage between mineral grains size and specific rate of breakage

Starting from specific rate of breakage, a simple approach was chosen to include grain size and mineral composition into existing Austin model of specific rate of breakage. Later, the approach was extended to the determination of the mineral breakage distribution pattern based on mineral grades (see section 4.4.3 - 4.4.4).

The experimental investigation of mineral breakage patterns were carried out using mill feed from crushing and the mill products (see Figure 13). From the experiment eleven different size fractions for each product were obtained and analyzed for the mineral grades and solid densities. The solid densities for sample D3 and B1 were not determined because of the shortage of sample material for each size fraction required for the measurement. Figure 13 shows the experimental set up for investigating breakage properties of mineral particles based on mineralogy and mineral texture (S is the sieving stage of the materials).

For the case of specific rate of breakage nine different size fractions were used to perform experiments for mono-sized particles (220 g sample for each size fraction) over time to measure the rate of disappearance of the materials and later on used to determine the specific rate of breakage according to Austin model. The steps used in the measurement of specific rate of breakage were the grinding times 1, 3, 5, 7 and 9 minutes.

Size range(μm)

C product G product

Number of samples

300-212 1 1 2

212-150 1 1 2

150-106 1 1 2

106-75 1 1 2

75-38 1 1 2

Crushing (C)Grinding (G)

S

3.35 mm screen

100 % < 3.35 mm300 μm screen

Samples for Liberation analyses

Liberation:100 % < 300 μm

A piece of drill core

Reject:(100 % >300 μm)

S

0-3350 μm screen

Figure 13. Experimental set up for the investigations of grindability test and breakage properties of materials.

Using the Austin approach, compare equation (21), the size for breakage was investigated based on the first order kinetics and the model was used to determine the specific rate of breakage Si as a function of size.

tSexp0WtW iii (21)

35

where

0Wi : divided by mass fraction at time zero

tWi : mass fraction of size class i at time t

The determined specific rates of breakage from experimental investigations were fitted to the Austin model in equation (22).

id1

0d

id

oS

iS (22)

where

Si: Specific rate of breakage of size fraction i, in time-1

di: Particle size

d0: Reference particle size (1 mm as suggested by Austin)

A good agreement between experimental and modeled pattern can be observed (see Figure 14). The fitted Austin model parameters (see Table 8) were used to further evaluate the effects of mineral texture and mineralogy on the breakage properties of different material.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

100 1000

Spec

ific

rate

of b

reak

age

(per

min

ute)

Particle size (μm)

Experimental FAR

Modeled FAR

Experimental HAR

Modeled HAR

Experimental Mgt-ore

Modeled Mgt-ore

Experimental Hmt-ore

Modeled Hmt-ore

Experimental KA3

Modeled KA3

Experimental F

Modeled F

Figure 14. A plot of compared the experimental and modeled specific rate of breakage by using Austin model.

In order to describe the intrinsic properties of particle breakage it is therefore important to consider the effects of mineral grains and compositions of the materials, as these affect the Austin model parameters for specific rate of breakage. In this sense, the specific rate of breakage was assumed to be a function of mineral texture (i.e. grain size) and modal mineralogy. From the investigations of the set of iron ore samples, the calculated Austin


36

model parameters (So, , and ) were compared with minerals grain sizes, mineral densities, Mohs-hardness and mineral composition of materials. Table 8 and 9 summarize the Austin model parameters

Table 8. Austin model parameters and mineralogical properties of iron ore samples

Model parameter FAR Mgt-ore KA3 HAR Hmt-ore F So 1.42 0.926 1.095 0.342 1.29 0.889 Alpha( ) 2.069 1.93 1.445 1.371 2.182 1.415 Mu( ) 0.54 0.581 0.658 0.942 0.435 0.882 Lambda( ) 2.459 2.398 2.455 2.227 2.337 2.533

Grain size of dominating Fe oxide( m) 500 350 150 600 800 80 Grain size of the gangue minerals( m) 200 120 150 360 150 200 Fe oxide grade (%) 83.1 74.5 86 71.5 71.2 92 Average mineral density(g/cc) 5.1 4.8 4.8 4.7 4.9 5.2 Average Mohs-hardness 6.5 6.2 5.6 6.2 6.3 6

The evaluation of the Austin model parameters with respect to the directions of the influence of the mineralogical and mineral grain size parameters is summarized in Table 9. Weak correlations were found when considering the contribution of the individual dependent parameters (i.e. mineral density, Mohs-hardness and grain sizes of minerals), indicating that the effects depend on more than one mineralogical parameters. These parameters were combined to improve the correlation between Austin model parameters and mineralogical properties of a given material.

Table 9. Model parameters - Correlation matrix for specific rate of breakage

Model

parameter

Mineralogical parameters and their direction of influence vs. Austin model parameters

‘‘O’’=weak correlation, ‘‘ ’’= correlation, ‘‘-’’= no correlation

So= Specific rate of breakage at maximum particle size, = Particle size exponent alpha , = Exponent for rate of decrease of selection function lambda & = Size coefficient for maximum breakage rate mu, Yi=grain size of magnetite or hematite minerals, Yj=grain size of the gangue minerals

Density (g/cc) Fe grade (%) Mohs-hardness H Yi/Yj

So O - O

- -

O - O

O O

Starting from the model parameter S0, the specific rate of breakage at maximum particle size showed positive correlation with average density of dominating Fe oxide (hematite or magnetite) according to the empirical model given by

326.91116131.46848213.15803oS (23)

Where,

S0 is the specific rate of breakage at maximum particle size; is the average density of the dominating Fe oxide.

37

In the case of the model parameter , the correlation between grain sizes and modal composition is given by

0.3159036YY

0.1506195.50411870.398085j

i2 (24)

Where is the particle size exponent, Yi is the grain size of the dominating Fe oxide and Yj is the grain size of the gangue minerals (weighed average).

The model parameter correlates with grade of dominating minerals according to the equation.

1.503452grade Fe0.011265 (25)

Where is the exponent for rate of decrease of selection function, Fe grade is the grade of the dominating Fe oxide in the sample.

The parameter in the Austin model usually indicates where the maximum specific rate of breakage passes, .i.e. it defines the turning point of specific rate of breakage. In this context, it accounts the complex transformation of the slope and the position of the peak depending on the entire mineralogical properties of a given material. In this correlation, mineral density was found to be suitable parameter for describing the parameter according to the equation

197.0319779.26667827.988962 (26)

Where is the size coefficient for maximum breakage rate, is the average density, respectively.

The models developed for the 4 coefficients seem to describe the data in an acceptable way, see Figure 15.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cal

cula

ted

Fitted to measured data

S0

Alpha

Mu

Lambda

Figure 15. Comparison of calculated coefficient model parameter vs. fitted to measured data.

However, when using the coefficient models in a forward calculation of Si = f(di) the representation of the curves over size is only limited in some cases (see Figure 16). This has to do with the high sensitivity of the Austin model towards changes in the model parameters, particularly in the case of S0 and . This led to the conclusion that the Austin model for the specific rate of breakage may not be the optimal mathematical description when trying to link the model parameters to mineral properties within coefficient models.


38

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Spec

rat

e of

bre

akag

e [t

ime-

1]

Particle size [mm]

FAR exp

FAR mod

Mgt exp

Mgt mod

KA3 exp

KA3 mod

HAR exp

HAR mod

Hmt exp

Hmt mod

F exp

F mod

Figure 16. Comparison of modeled specific rate of breakage based on forward calculation received from using

mineralogical properties vs. measured specific rate of breakage of different texture samples of iron ores.

4.4.3 Modal mineralogy by size

State-of-the art comminution models are incapable to predict the grade differences between the particle size fractions. This is serious deficiency especially when mineral processing circuit involves splitting of material by size: e.g. gravity concentration for coarse size fractions common in gold circuits, split flotation used in nickel sulphide or cobbing in coarse particle sizes of magnetite ores.

Within the sample set both magnetite and hematite ore showed grade by particle size pattern where the highest magnetite / hematite grade is found to be in the medium particle size range, i.e. between 250 and 1200 microns. The pattern can be divided into three particle size ranges, accordingly. The coarse size range from 1200 to 2400 microns represents very hard particles and in magnetite ore they are compositionally close to the average ore whereas in hematite ore they are poor in hematite but rich in actinolite, orthoclase and albite. The middle range between 250 to 1200 microns is enriched in magnetite and hematite and corresponds to hard material to fracture. The third size range, below 250 microns represents a soft component.

In a coarse grained sample the grade pattern with Fe oxide mineral enrichment in the middle particle size ranges is a prominent feature (Figs. 17A and 18A). In the fine grained ore the pattern looks different; almost opposite with middle particle size showing lowest Fe oxide grade (Fig. 19A). Quite naturally most of the gangue minerals show a mirror image to Fe oxides. However, biotite is clearly enriched in the fine particle sizes which can be explained by soft nature of the mineral.

39

60

65

70

75

80

85

90

95

100

10 100 1000 10000

Mag

netit

e gr

ade/

Mod

al m

iner

alog

y (%

)

Particle size (μm)

Mgt grade feed

Mgt grade mill product

Average Mgt feed

A)

0

1

2

3

4

5

6

7

8

9

10 100 1000 10000

Gan

gue

min

eral

gra

des

(%

)

Particle size ( m)

Ap in the feed

Ab in the feed

Bt in the feed

Ap in the mill product

Ab in the mill product

Bt in the mill product

B)

Figure 17. A) = Grade of magnetite by size in the mill feed and the product for FAR sample, B) = Grade of gangue minerals by size in the mill feed and the product for FAR sample.

If the particle breakage was homogeneous such grade trends would not be seen; thus the grade patterns are an evidence of heterogeneous breakage.

Even the coarse grained and fine grained ore showed different mineral by particle size pattern that still have one common feature: the maximum Fe oxide grade is roughly aligning with the grain size of Fe oxide. Explanation for the observed pattern is that Fe oxides rich particles break down easily until they compose of single mineral grains. This forms a barrier for particle breaking and thus enrichment for mineral grades.

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Hm

t gra

de/ M

odal

Min

eral

ogy

(%)

Particle size (μm)

Hmt grade inthe feed

Hmt grade inthe millproduct

Average Hmtgrade in thefeed

A)

0

5

10

15

20

25

10 100 1000 10000

Gan

gue

min

eral

gra

de

(%)

Particle size ( m)

Ab in the feed

Ap in the feed

Bt in the feed

Qrtz in the feed

Orth in the feed




Qrtz in the mill product

Orth in the mill product

B)

Figure 18. A) = Grade of hematite by size in the mill feed and the product for HAR sample, B) = Grade of gangue minerals by size in the mill feed and the product for HAR sample.


40

60

65

70

75

80

85

90

95

100

10 100 1000 10000

Mag

netit

e gr

ade

(%)

Particle size (μm)

Mgt grade in the feed

Mgt grade in mill product

Average Mgt grade in the feed

A)

0

2

4

6

8

10

12

14

16

18

10 100 1000

Gan

gue

min

eral

gra

de (%

)

Particle size (μm)

Qrtz in theDi in the feClintonite Qrtz in theDi in the mClintonite

B)

Figure 19. A) = Grade of magnetite by size in the mill feed and the product for KA3 sample, B) = Grade of gangue minerals by size in the mill feed and the product for KA3 sample.

4.4.4 Mineral distribution and breakage patterns by size

For different mineral texture the breakage distribution patterns are represented in Figure 20. Fine grained samples show similar gradients (KA3 and D3) opposite to the coarse grained ores (compare Figures 20A, B, C & D). As expected, texture properties align with breakage properties of minerals. For example for sample FAR the resistance against mineral breakage is increasing in the order of Apatite>Albite/Biotite> Mgt/Hmt (i.e. Apatite is least resistance for comminution whereas Mgt/Hmt have the highest resistance); again, indicating the existence of selective breakage (compare Figure 20). For HAR and B1 samples the order is Mgt>Hmt i.e. in a magnetite-hematite system the magnetite breaks selectively first. For the D3 sample there is no preferred order of breakages.

A)

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Perc

enta

ge p

assi

ng (%

)

Particle size (μm)

Mgt in the feed

Mgt in the product

Ab in the product

Ap in the product

Bt in the product

Hmt in the product

B)

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Perc

enta

ge m

iner

al p

assin

g (%

)

Particle size (μm)

Mgt feed

Mgt in the product

Qrtz

Di

Clintonite

41

0.3

0.5

0.7

0.9

1.1

1.3

1.5

1.7

10 100 1000 10000

FeO

gra

de in

the

feed

/FeO

in th

e m

ill p

rodu

ct

Particle size (μm)

FARHARKA3D3B1

C)

D)

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Perc

enta

ge m

iner

al p

assi

ng (%

)

Particle size (μm)

Mgt in the feed

Mgt in the product

Ab in the product

Tremolite

Enstatite

E)

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Perc

enta

ge m

iner

al p

assi

ng (%

)

Particle size (μm)

Hmt in the feed

Hmt in the product

Mgt in the product

Mgt in the feed

F)0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Perc

enta

ge m

iner

al p

assin

g (%

)

Particle size (μm)

Hmt in the feed

Hmt in the product

Ab in the product

Ap in the product

Bt in the product

Mgt in the product

Or in the product

Qrtz

Figure 20. Mineral distribution by size from different texture minerals received from Kiruna and Malmberget iron ore deposits FAR- Coarse grained magnetite high grade magnetite, KA3- Fine grained magnetite high grade magnetite, C) - Patterns showing the observed breakage spectrum at 25 minutes grinding time from five different mineral textures, D3-

Fine grained magnetite low grade magnetite, B1- Extremely coarse grained hematite high grade magnetite, HAR- Coarse grained hematite high grade magnetite.

The decreasing rate can be observed when comparing mass of solids passing versus mineral grade in the corresponding sizes of the mill product (i.e. the point of maximum grade of the mill product in Figure 21). It implies that the mineral particles break down to progenies that distribute to the smaller particle sizes, and accumulation for each mineral can be found where particle size meets the grain size of the mineral. This occurs to the expense of decreasing the breakage rate of corresponding mineral particles (i.e. percentage passing of solid material significantly decreases).


42

0.4

0.6

0.8

1

1.2

1.4

1.6

0 0.2 0.4 0.6 0.8 1 1.2

Rat

ios o

f fee

d F

eO g

rade

/mill

pro

duct

FeO

gra

de

Ratios of feed solid mass/mill product solid mass

FARHARB1D3KA3

Figure 21. Plot of mineral grade vs. percentage passing of the solid material in the mill product

As shown in Figure 22 it appears that the size with maximum mineral breakage rate correlates with the size of the mineral grains e.g. magnetite. Different samples show different turning point (size at which breakage efficiency decreases) depending on the mineral grain sizes (see Figure 21C & 22). Based on observations, the particle size at which the mineral grade reaches the maximum is the liberation size of the mineral.

B1

D3KA3

HAR

FAR

y = 205.85e0.002x

R² = 0.9821

120

1200

0 200 400 600 800 1000 1200

Size

at w

hich

bre

akag

e of

FeO

gra

de st

art t

o de

crea

se (μ

m)

Grain size of the dominating i.e. FeO (μm)

Figure 22. Correlation between grain sizes of the dominating mineral vs. size at which the breakage efficiency start to decrease.

4.4.5 Modeling mineral grade by size in the mill product

Prediction of mineral grade by size of the material in the mill during grinding is presently not established. An important question is whether properties of feed (i.e. mineral grade & grain sizes) can be used for predictions, and whether this can be done based on bulk sample or is the information on feed mineralogy by particle size required. From experimental observations, it is clear that the mineral grade patterns for coarse grained magnetite and hematite can be easily predicted from sized information. For fine grained

43

texture the pattern resembles the random breakage nature of a given material. This range of patterns complicates the predictions of mineral grade by size when using the empirical models. The observations suggested that strong grade differences by size can be found if there is difference in grain sizes of minerals. If the grain sizes are similar the pattern is expected to be flat.

The observed patterns of the mineral grade by size reflect the non-linear trends which allow the experimental data to fit a non-linear function similar to Gaudin-Schuman distribution function given by

fgtp,g (27)

Where gp,t is the mineral grade of a given material at time t in the mill product, gf is the feed grade, and are constant model parameters for a given material. These parameters (see Table 10) were calculated by using the feed grade for each size and fitted to the measured grade of the mill product at 25 minutes grinding time before related to the grain sizes of mineral particles.

Table 10. Parameters used to predict the grade of magnetite or hematite in the mill product

Parameter FAR KA3 D3 B1 HAR 0.32 0.00 0.26 1.16 0.61 22.09 82.21 21.30 0.52 6.15

Grain size of Fe oxide ( m) 500 150 200 1000 600 Grain size of gangue mineral ( m) 200 150 200 600 360 Geometric mean size for Fe oxide and

gangue grains ( m) 316 150 200 775 465

The fitted model parameter and were compared to the mineral grain size in order to identify a correlation. The model parameter showed an inverse relation to the average grain size of the minerals (Fig. 23). The larger the grain size the smaller is the value of the model parameter of a given material for grinding.

FAR

KA3

D3

B1

HAR

y = 178.85e-0.007x

R² = 0.9586

0.1

1.0

10.0

100.0

0 100 200 300 400 500 600 700 800 900

Mod

el p

aram

eter

s

Average grain size (geometric mean) of valuable grain and gangue minerals (μm)

A)

FAR

KA3

D3

B1

HAR

y = -0.231ln(x) + 1.0105R² = 0.996

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90

Mod

el p

aram

eter

Model parameter

B)

Figure 23. A) = Model parameter as a function of the mineral grain size, B) = Model parameter as a function of parameter .


44

Once the parameters and are known they are anticipated into the model (see equation 27) to predict the grade of mineral for each size in the mill product given the feed grade properties. A good correlation can be seen between measured and predicted magnetite/hematite grade for coarse grained magnetite/hematite minerals (compare to Figure 24). Significant deviation can be observed for fine grained high grade magnetite for KA3 sample as expected. It should be noted that for high grade fine grained magnetite, the model cannot predict well the grade of minerals by size in the mill product. This reflects the nature of grade by size pattern observed from experimental data in the previous section (see section 4.3).

30

40

50

60

70

80

90

100

30 40 50 60 70 80 90 100

Obs

erve

d m

agne

tite/

hem

atite

gra

des a

t 25

min

utes

gri

ndin

g tim

e (%

)

Predicted magnetite/hematite grades (%)

FARKA3D3HARB1

Figure 24. Predictions of mineral grades based on initial mineral grade in the feed in different size classes.

4.4.6 Modeling the mineral distributions by size

To assess the breakage of mineral particles by composition it is crucial to understand the distribution of the mineral by size. From the experimental investigations of the different mineral texture it was observed that mineral distribution by size follows the normal comminution size distribution curves. Such distribution is often well described by the Rosin-Rammler distribution function with two model parameters n and 63.2x .These parameters account for the variability of the shape of the curves depending on the properties of the mineral particles.

Accordingly, the observed experimental data were fitted to the Rosin-Rammler function to calculate the distributions of minerals by size (MD) according to

N

63.2xix

exp-1100ij,MD (28)

where,

where,

ij,MD = Mineral j distributed at size class i

Xi = selected size class i

63.2x = Rosin-Rammler model parameter describes particle size at 63.2 % passing.

45

N = Rosin-Rammler model parameter describes the spread of distribution (slope for the distribution curve)

= Model parameter for correcting the model errors of the mineral distribution.

The Rosin-Rammler function with the additional parameter fits well the experimental data (Figure 25).The model parameters in equation 28 are dependent on material properties e.g. grain size of the mineral particles. Therefore, to predict the mineral distribution by size it is necessary to first find the relationship between calculated model parameters (see Table 3) and mineralogical properties of a given mineral particles. By knowing the grain size of the valuable and gangue minerals, the model parameters can be calculated and used in the modified Rosin-Rammler function in order to describe the distribution of the magnetite or hematite minerals by size. Figure 25 is an example illustrating how well magnetite/hematite distribution can be predicted from different texture of mineral particles at 25 minutes grinding time in the GCT ball mill.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Obse

rved

mag

net

ite

or

hem

atite

dis

trbution (

cum

mula

tive

pas

sing

%)

Predicted magnetite or hematite distribution (cummulative passing %)

FAR-predicted Mgt

B1-predicted Hmt

D3-Predicted Mgt distribution

KA3-predicted Mgt distribution

HAR-predicted Hmt distribution

Figure 25. Observed magnetite or hematite mineral distributions vs. predicted one.

Once this is established, various analyses can be made e.g. analyses for breakage of minerals (see Figure 20) from different texture for breakage efficiency recognition. Hence the idea of investigating the influence of mineralogical properties of a given material becomes important for the determination of model parameters. The correlation between model parameters versus mineralogy are established, functions for approximate the model parameters are also determined. These functions are used to calculate the model parameters and later on implemented into the Rosin-Rammler to predict the distribution of mineral content (.i.e. % cumulative mineral passing) by size.

5. Discussion

Controlling the kinetic rates of grindability of the material by using single pass grinding conditions (GCT) offers a breakthrough concerning the measurement of the Bond work index according to the requirement of the geometallurgy. In geometallurgy, time and


46

costs for sample characterization are important as variability studies require large amounts of data to provide optimal solutions for even complex deposits. According to Williams and Richardson (2004), Morrell (2009) building up information about variations of an ore body requires comprehensive testing (due to a large number of samples i.e.>1000 that are required to be analyzed). This brought several challenges in the geometallurgical programs including measurement efficiency and linking of mineralogical information into process models. Over time the Bond grindability test procedure has been modified and improved by several researchers (Armstrong, 1985, Wills and Bruce, 1966 and Smith and Lee, 1968 refer to Wills and Napier-Munn, 2006), but still much effort and large sample amounts are need to measure the Bond work index.

One of the greatest advantages of the developed GCT grindability test is that it avoids the need for several grinding cycles as needed for Bond grindability conditions (.i.e. steady state). The results from this study confirm the validity of the short cut method for estimating the Bond work index (BWI) by using the GCT single pass-based procedure within a shorter period of time.

The assumption that energy for grinding is proportional toP80,x

1, reflects that BWI

depends on material properties and is valid only by limit. This is partly due to the effects of heterogeneous mineral texture and partly due surface coating of mineral particles. For materials with complex mineralogical intergrowth it was observed that the calculated value of BWI tend to be over-estimated. For example, sample NIT contains complex mineralogy (i.e. fine quartz mineral grains, graphite materials and some coarse pyrite grains). In this regards the linear slope had limitations to estimate the BWI. Many approaches used in geometallurgy have focused on the hardness of ore (crushability and grindability) or mapping mineralogical variability of an ore separately. For example Kojovic et al (2010) developed a test method for mapping hardness of an ore and throughput based on crushability index with no emphasis on mineralogical and liberation properties. Likewise Vatandoost (2010) work on petrophysical properties of a rock on ore comminution behavior emphasizing on measuring the hardness of a rock. Bonnici et al (2008) provided detailed characterization of a porphyry copper ore mainly based on mineralogical variability within a deposit by showing a qualitative correlation between textural parameters and liberation properties of an ore. The GCT opens a window for use of the available mineral properties i.e. Mohs hardness, mineral density and mineral grains (i.e. a framework for testing various properties of materials on process behavior). These are for instance used to approximate theoretical values of the ore grinding behavior. Within the GCT, liberability of difference minerals is also considered which make it more powerful and robust. The robustness of GCT is due to its ability to provide accurate and reliable measurement of the Bond work index (i.e. BWI ± 5 % error). It also provides the measurement of the Bond work index with short time about 90 % efficient time saving and it handles small amount of sample compare to Bond procedure.

47

Mineral association is another aspect that affects the liberation and grinding properties of an ore as observed by Bonnici et al (2008). Mineral associations affect the type of particles that may be recovered in the concentrate, which has been observed by Petruk (1990) as an important part of better minerals separations. These parameters are very important but very challenging to quantify. It should be noted that, in the developed framework an association index has been included in the framework but has not been used to evaluate the comminution responses from various samples neither modeling the comminution system or the entire beneficiation system. This means that the framework presented here provides an insight and directions for the quantification of mineralogical parameters with respect to comminution and provides a platform for proper integration between mineralogical and comminution parameters in the context of geometallurgical modelling and simulation.

Within the developed GCT framework, a lot of information can be extracted from the sample given the amount of sample needed for the analyses and testing from individual sample. In fact, much information can be provided for the investigation, development and simulation of material properties of an ore deposit. The first part of testing framework provides mineralogical characterizations and when combined with the testing of ore grindability, the liberability and the limiting breakage properties can be identified and dealt with appropriately. Actually, broad knowledge about mineralogical effects on breakage and liberation properties provides an insight to grinding-liberation phenomena and, hence an alternative way of modeling comminution systems can be provided.

The available testing methods .e.g. comminution methods have not been able yet to explain what happens when starting to break the grains of the mineral phases. This has fundamental importance when considering the energy consumptions and dissipation as well as liberation of minerals. In the GCT it has partly been shown that for iron ores (e.g. magnetite, hematite), high energy is required to break the coarse grains when applying ball milling. Further, ores with similar grindability may have different liberability (Mwanga et al, 2015). This suggest that for proper geometallurgical mapping and modelling it is important to combine liberation distribution and grindability to investigate variations of an ore body and related process performance depending on the modal mineralogy and mineral texture (micro structure). The GCT helps to efficiently analyze comminution parameters and links them with mineralogical parameters. This has been shown for the case of iron ore when quantitatively describing ore comminution behavior. Nevertheless, the nature of these phenomena requires further investigation and extension towards other beneficiation process performance (.e.g. flotation).

In this work, several approaches were analyzed in order to improve the reliability for estimating of the Bond work index by GCT. The third law of comminution was used thereby assuming that energy for grinding is coupled with achieved product size. One distinct feature of the proposed procedure as compared to the conventional procedure of simulating the closed circuit is that it reduces processing time compared to reaching steady state as defined by Bond. This was done to avoid the necessity of using large sample amount and reduce the efforts for sample preparations. The rate at which the


48

particle size is reduced while increasing energy was assumed to be constant for the same materials and one material can be distinguished from another by the different slopes. Factors accounting for the mechanical energy, geometric effects and efficiency factors are used to estimate the Bond work index.

The findings from breakage and liberation of minerals show that modal mineralogy and mineral grain size affect the patterns for the mineral breakage distribution. These parameters identify the limit for efficient comminution of a given mineral texture and presumably the degree of mineral liberations in a ball mill. In this study, a model to describe the breakage phenomenon of minerals was developed and by using the model it could be observed that the breakage of minerals slows down when comminution reaches a size of maximum mineral distribution which was about the size of dominating mineral grain. This quantitative relationship reflects a simple approach for the descriptions of ore comminution behavior from various mineral textures in the geometallurgical modeling context.

Further, correlations between the Austin model parameters and the mineral texture as well as modal composition were observed. The preliminary interpretation for such correlation is that minerals of similar composition e.g. magnetite grade may have different breakage properties depending on the grain size of the magnetite and gangue minerals. Here, the breakage of coarse grain materials reaches its maximum distribution in the coarser sizes and therefore these particles are liberating their mineral grains earlier than fine grains. This phenomenon adds to the understanding of the breakage nature of mineral grains and grinding limits during ball milling. A model for breakage pattern of mineral distributions predicts where to find the yield of the individual grains for various texture properties of different ore. After maximum distribution towards the fine sizes, mineral phases (grain phases) are transformed into single mineral grain (yield into individual grain) thereby increasing grinding energies. When this happens in comminution the degree of mineral liberation increases.

According to Austin (1982), King (2001), the specific rate of breakage increases with increasing sizes and after passing a maximum the specific rate of breakage slows down due to inefficiency of the nipping of the large particles between the grinding media for breakage. The elucidation on breakage inefficiency is based on particle size without taking into account mineralogical variability and mineral texture as essential properties affecting the specific rate of breakage. In this study it was observed that the specific rate of breakage for fine grained slows down earlier than coarse grained minerals. The mineralogical properties of the feed describe the ore comminution behavior by a correlation with comminution parameters (e.g. specific rate of breakage). These findings showed the link between mineralogy and ore comminution behavior. This can be used where knowledge about mineralogy (i.e. mineral grades, grain size of main mineral, and density, and Mohs hardness) exists.

49

6. Conclusions and further work

A single pass-based geometallurgical comminution test method has been developed and validated against several samples of high variability. Experimental results from this study offered an important insight on prediction of the grindability behavior of the materials in geometallurgical context by using mineralogical information of the feed samples. The GCT is valid for the estimation of the Bond work index and can be used in geometallurgical programs. For the Malmberget iron ore samples, the liberability is depending on the grade and grain size of magnetite. A significant difference between grindability and liberability can be observed.

With respect to kinetic modeling of the specific rate of breakage, variations in grain size and mineral grades affect and control the breakage properties of a given material. Comparison between breakage behavior of various texture for iron ores revealed that grain size, and mineral composition can be used to empirically approximate the specific rate of breakage. Experiments also showed that particles of the same magnetite grade can have different specific rate of breakage. Such ores are distinguished from each other by mineral textures, and the mineral grain size is the most significant parameter in that. Looking on mineralogical parameters, the degree of mineral liberation depends on the particle composition and can change the target size of the progeny size distribution. The implications from the experimental results are that samples with similar modal mineralogy may have different breakage properties. With regards to mineralogical properties of the feed, further studies are suggested for better understanding the fundamental properties of mineral texture (.e.g. the crystal parameters, energy dissipation) and their effects on grindability phenomena of comminuted materials.

The breakage phenomenon of the minerals is governed by mineral texture and mineral distribution in different size classes. For the studied iron ores the patterns for mineral breakage distributions showed that efficiency of mineral breakage slows down when the breakage is reaching the grain size of a mineral particle/grain. Within the pattern, the grain size of minerals indicates a suitable size for efficient comminution and liberation of minerals. The overall conclusion is that modal mineralogy, grain size, solid densities of mineral particles determine the degree of mineral liberation. The findings from this study elucidate how mineral texture and other mineralogical properties of the ore particles affect comminution behavior and breakage phenomenon of various mineral particles. For generalization more data from other ore types such as sulphide ore are required for rigorous process modeling. Including mineral grain distribution into the deposit model will enable prediction of energy efficiency (throughput) and provide a modeling framework for geometallurgical simulation of various ore deposit.

Based on the work presented the answers to the research questions are:

The efficiency of the Bond grindability test (in terms of samples size and time) can be improved by reducing the size of the geometry of the original Bond mill. This is the first time the test mill has been significantly reduced in size to handle


50

sample sizes of 220 g, i.e. crushed samples and even parts of drill cores in the range of some hundred grams can be tested for grindability.

Liberability is an efficient and novel way of integrate mineral liberation into the Bond test method when modeling comminution processes.

Samples with similar grindability and modal mineralogy may have different liberability. Such ores are distinguished from each other by mineral textures, and the mineral grain size has been identified to be the most important parameter in that.

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Part II


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Paper I

Testing of Ore Comminution Behavior in the Geometallurgical Context – A review Abdul Mwanga, Jan Rosenkranz and Pertti Lamberg

Minerals, Volume 5, 2015, pages 276-297 DOI: 10.3390/min5020276.

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Testing of Ore Comminution Behavior in the Geometallurgical Context- A review

Mwanga, A., Rosenkranz, J., Lamberg, P.

Minerals and Metallurgical Engineering Laboratory Luleå University of Technology, Sweden

Abstract

Comminution tests are an important step in the proper design of ore beneficiation plants. In the past test work has been conducted for particular representative reference samples. Within geometallurgy the entire ore body is explored in order to also identify the variation within the resource and to establish spatial geometallurgical domains that show the different response to mineral processing. Setting up a geometallurgical program for an ore deposit requires extensive test work. Methods for testing the comminution behavior have therefore to be more efficient in terms of time and cost but also with respect to sample requirements. Also the integration of the test method in the geometallurgical modeling framework is important. This paper provides an overview of standard comminution test methods used for the investigation of ore comminution behavior and evaluates their applicability and potential in the geometallurgical context.

Keywords: Geometallurgy, comminution behavior, metallurgical testing.

1. Background

Before concentrating metal ores have to be crushed and ground in order to liberate the metal bearing minerals. A sufficient size reduction is not only the prerequisite for any downstream physical separation. Comminution is also the processing step within mineral processing having the highest energy demand and in practice being much often the limiting factor for plant capacity. Reliable testing of the ore’s comminution behavior, i.e. information about the particle size distribution after fracture, the achieved mineral liberation as well as the comminution energy needed, is therefore an important step in the proper design and control of ore beneficiation plants.

In the past the process design has usually been based on particular representative reference samples that were analyzed and tested at different scale but did not describe all the mineralogical variations occurring in an ore body. The limited picture received from that is a potential cause for insufficient mineral liberation or on the contrary for too fine grinding leading to low recovery and selectivity in physical separation [1], and thus resulting in poor plant performance and limited production capacity.


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During the last years geometallurgy has evolved as a new interdisciplinary approach. Geometallurgy combines geological and metallurgical information to create a spatially-based predictive model for mineral processing to be used in production management [2]. Within the geometallurgical approach the entire ore body is explored in order to identify the variation within the ore body and to establish spatial geometallurgical domains that show different response to mineral processing. Using the geometallurgical domains in the design and control of ore beneficiation plants allows for higher flexibility towards changes in the plant feed when mining different parts of the ore [3].

Setting up a geometallurgical program for an ore deposit requires extensive test work that on the one hand pays back by improved plant operation, but on the other hand is time consuming and correspondingly costly. Also the best possible utilization of the available sample material is a crucial point as chemical and rock mechanical analyses are also requiring samples and thereby limiting the available amount. Accordingly the need of efficient geometallurgical testing gives a stimulus for developing new fast comminution test methods or for the revision of existing test procedures, respectively. Also improved process models need to be established that subsequently make use of the additional information provided by the geometallurgical approach.

This paper provides an overview of standard test methods used for the investigation of ore comminution behavior and evaluates their applicability and potential in the geometallurgical context. Besides the test work itself also the provision of suitable parameters for process modeling is considered.

2. Criteria for evaluation

The term comminution behavior comprises the complex interaction of material properties and process parameters. In practice different comminution test methods are used for different applications (Figure 1). As the comminution properties change with particle size different tests ranging from crushing to grinding and very fine grinding are employed accordingly. Also the type of mechanical stress applied in a certain crusher or mill type, i.e. compressive or impact stress, as well as the stress intensity and rate have to be considered in the selection of a suitable test method.

Finally the applicability of a comminution test will depend on the project stage and the available sample amount, ranging from drill core sections or hand-picked single particles used in the early stages of the resource evaluation and in laboratory scale to pilot scale tests where the metallurgical performance is verified and several tens or hundreds of kilograms are used. At larger scales also the effort in terms of time and costs per test is increasing. This third dimension will limit the test work to certain methods for the different scales during the individual project stages.

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CoarseFineUltrafine

Bench scale

Lab scale

GeoMet levelCompression

ImpactAttrition

Pilot andbench pilot scale

Figure 1 Dimensions in test categorization

For geometallurgical purposes the outcome of the experimental work has to serve as an input to process modeling, i.e. comminution test results need to be linked to the parameters used in the comminution process models. Within process modeling different levels of modeling depth are used. Simple approaches use defined size distribution functions based on single parameters as energy for grinding or machine-specific size reduction ratios. More sophisticated, rigorous models apply population balancing methods. Here the entire breakage distribution function needs to be constructed based on experimental test work or sampling and back-calculation from continuous comminution tests even at larger scale [4]. In this context it has to be noted that a closed methodology that not only comprises size reduction and energy for size reduction but also incorporates mineral liberation within experimental work and process modeling is still missing.

As discussed above a geometallurgical program imposes particular requirements on the efficiency and manageability of test methods. A comminution test for geometallurgical purposes should therefore fulfill several technical and economic criteria:

Simplicity – The test should be relatively simple and easy to execute. It should use instruments that are available in common analytical and mineral processing laboratories.

Repeatability – The test should be repeatable and not depending on the individual person conducting the test.

Sample preparation - Sample preparation should be possible with low efforts and possible to do with basic skills or after short training.


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Time exposure and costs – The test should be fast and inexpensive, i.e. for execution times of one hour it should be possible to conduct 1000 tests within half a year.

Sample amount – The amount of sample per test should be < 0.5 kg. Preferentially rejects from chemical assays should be enough.

Link to modeling – Tests should provide parameters that can directly be used in process modeling and simulation.

Mineral liberation – Tests should be easy to extend in order to include mineral liberation information.

Another criterion is given by the precision and the statistic quality of the test results. With respect to accuracy a proper quantification is not an easy task as the entire chain of sampling and sample preparation together with the test and analysis method needs to be considered. Statistic quality is a parameter that from the perspective of geometallurgy has not only to be judged with respect to the repetition of single tests but in relation to generating a comprehensive data set for the entire geometallurgical program, i.e. there is a compromise between the quality of single measurement and the quantity of measured points.

3. Review of existing test methods

In the following commonly used comminution test methods having potential to be used in geometallurgical context are reviewed against the criteria listed above. The tests are classified in three groups: 1) rock mechanical tests, 2) particle breakage tests, and 3) bench-scale grindability tests.

3.1 Rock mechanical testing

Rock mechanical tests for rock strength are conducted by means of universal test machines or simplified instruments. Loading takes place at comparatively low velocities. The instrumentation of the test machine allows recording of the load applied to the sample and the displacement over time. Several standard test methods are used that differ in the loading conditions applied [5].

Samples consist of drill core sections, parts of drill core sections and single particles (crab samples) that are cut to regular shape but also irregular shaped particles. Measured strength parameters depend not only on modal mineralogy but also on textural effects and anisotropy [6].

3.1.1 Compression tests

In compression tests the drill core sample is pressed between the two parallel planes of the test machine, which are then loaded up to failure of the specimen. Data for the applied load and the resulting displacement is recorded over time, providing the maximum load for calculating the compressive strength. Sample preparation comprises

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careful cutting of the specimen’s top and bottom planes in order to prevent bending effects during the test.

Displacementtransducer

Load cell

Rock sample

Figure 2: Uniaxial unconfined compression test

In case the specimen is not further supported the test is referred to as unconfined compressive strength (UCS) test (Figure 2). For triaxial compression tests the drill core specimens are cut to the required length and then enveloped on the lateral surface by a membrane that seals the specimen from the surrounding pressure medium, usually oil, that provides the radial support. When increasing the axial compressive load also the oil pressure is increased in parallel up to failure of the specimen.

A similar experimental setup is used in the point load test (PLT), see Figure 3. Instead of using parallel planes here the compressive load is applied between the tips of two cones, putting a point load on the specimen. Test instruments are quite compact and can even be used in field work.

From the point load test the point load strength index Is50 is obtained that needs to be corrected to the standard equivalent core diameter De of 50 mm if other specimen are used.

250 eDPIs (in psi) (1)

with the failure load P in lbf (pound force) and De in inches. The point load strength index can be transferred into uniaxial compressive strength using a linear conversion factor that needs to be determined for a particular ore [7].


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Load cell

Rock sample

Figure 3: Point load test

3.1.2 Indirect tensile strength test

Using cylindrical of a specimen as slices from drill cores and loading these radially by compression forces between two sockets (plates, cushioned plates, curved clamps) gives an indirect tensile stress and an according deformation in orthogonal direction. This experimental setup is also known as the Brazilian test (Figure 4).

Load cell

Rock sample

Figure 4: Brazilian test

The sample is stressed under the linear compressive load that induces the tensile stress. Assuming that the material is homogeneous, isotropic, and linearly elastic before failure [8] the failure is expected at maximum tensile stress. The corresponding tensile strength is then calculated by

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tDP

t2

(2)

where P is the failure load, D the specimen diameter, and t the thickness of the test specimen.

3.1.3 Evaluation of rock mechanical tests

Using results from rock mechanical tests for describing comminution behavior is an attractive approach as no additional test work and sample material is needed. Also the necessary sample amounts are small.

All the tests discussed above apply slow compressive stress in a well-defined way, meaning that the repeatability of the method is given, though the interpretation has to take into account the textural effects and inhomogeneity in samples from natural mineral resources. The conduct of the test is rather simple and can partly be done in the field. More effort has to be put on proper samples preparation, e.g. when sawing drill cores. The fragments received are usually too coarse for using them as such in quantitative mineralogical analyses.

It has been shown that mechanical parameters of rock samples can be used to describe and model comminution processes at least in the case of crushing [9], [10], [11]. For this purpose mechanical strength expressed by the maximum load at the point of failure needs to be transformed into quantities that can be used within the design of crushing stages. Usually empirical ore-specific correlations are provided for calculating crushing index or crusher reduction ratio from UCS or PLT strength values.

The evaluation of the different rock mechanical tests with respect to the criteria defined in section 2 is summarized in Table 1.

Table 1. Rock mechanical tests

adverse (–), acceptable (o), advantageous (+)

UCS PLT Brazilian

Simplicity + + +

Repeatability O O O

Sample preparation – O –

Time exposure and costs O O O

Sample amount + + +

Link to modeling – – –

Mineral liberation – – –


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3.2 Particle breakage tests

3.2.1 Drop weight test

3.2.1.1 Simple drop weight test

In the drop weight test a weight is lifted to a certain height and then released to fall on an ore sample, which is arranged on a rigid anvil underneath (Figure 5). The fragments from the sample are afterwards collected and analyzed by their particle size to receive a breakage distribution. The test sample can comprise single particles, a part or an entire drill core section or several particles as received from pre-crushing. Several apparatus have been presented [12], [9], [13]. For conducting particle bed fracture tests with fine particles the anvil is replaced by a die [14].

Anvil

Rock sample

Drop weight

h

Figure 5: Drop weight tester

Different impact levels and amounts of specific comminution energy can be obtained by varying the drop weight, the falling height or the sample mass. The energy provided to the ore sample can be described by the potential energy of the drop weight at the initial height:

hgmE dw (3)

where mdw is the mass of the drop weight and h the distance between the drop weight and the top of the specimen.

For evaluating the breakage distribution a method has been developed that links the breakage distribution and comminution energy to the modeling of particle size reduction

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[15]. The percentage passing 1/n of the starting particle size can be related to the comminution energy by:

specEbn eAt 1 (4)

where Espec is the specific energy in kWh/t and A and b are ore-specific parameters determined by model fitting the experimental data obtained from tests with different energies. Typically the t10-value is used as a fineness index to characterize a certain ore sample. In process modeling and simulation an average set of A and b is used assuming that particles of different size will break in a similar way.

For determining the several tn curves five different initial particle sizes in the range of 13.2 to 63 mm and 3 energy levels need to be investigated giving a total of 15 tests. This drop weight test as defined by the Julius Kruttschnitt Mineral Research Centre therefore normally requires 75 to 100 kg of sample material.

In order to reduce the sample amount and the number of particle size fractions an abbreviated drop weight test, called SAG Mill Comminution (SMC) test, has been suggested [16]. Using only a single size fraction, i.e. particles or parts cut from drill cores in the size range 19/22 mm, the necessary sample amount can be reduced to 5 kg. The test provides the parameters A and b as well as a Drop Weight Index (DWi in kWh/t) but not the t-values.

3.2.1.2 Instrumented drop weight test

The simple drop weight test has been improved by adding instrumentation. A well-established instrumented drop weight test is the Ultra-fast load cell device (UFLC) developed at the University of Utah [17], [18], [19] (Figure 6).

Drop weightPhoto diode

LaserRock sample

Strain gauge

Figure 6: Ultra-fast load cell


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A sample, consisting of individual particles or a bed of particles, is placed on a vertical steel bar and then hit by the falling weight. As with the split Hopkinson pressure bar (see 3.2.3) the bar is instrumented by a pair of strain gauges for detecting the impact wave that allows for inference on the load applied to the sample. Based on load-time profiles and the calculated deformation the transferred energy can be calculated.

A portable impact load cell, using the same principles as in the Ultra-fast load cell, has been developed by Bourgeois et al. [20] for in-situ quantification of ore breakage properties. The so-called SILC – Short Impact Load Cell is reduced in height and weighs only 30 kg.

Anvil

Rock sample

Drop weight

h

Load cell

Displacementtransducer

Figure 7: Micro-stamping device

Based on the principle design of the simple drop weight test another instrumented drop weight tester has been designed [21] and initially used for the investigation of particle compaction processes. Here the drop weight itself is instrumented by a load cell and an inductive displacement transducer that yield time-dependent measurement profiles for the entire sequence of primary impact and subsequent rebounds. The comminution energy transferred to the sample is received from integration of the load-displacement relation.

3.2.2 Twin pendulum tests

In twin pendulum tests a single particle is fractured between two pendulum-mounted hammers that are released from a certain height. Figure 8 shows the experimental setup for the Bond twin pendulum test [22]. A single particle is mounted on a socket and then simultaneously hit by the hammers. The procedure is repeated until the particle breaks, thereby incrementally increasing the deflection angle of the hammers.

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Bond defined a crushing work index by:

p

Bi

CCW 5.53

(5)

where p is the particle density in g/cm3 and CB the impact energy per particle thickness

dp in J/mm for the last pendulum deflection angle of :

pB dC 1117

(6)

Also the twin pendulum test has been extended by adding instrumentation that allows the recording of the pendulum motion [23], [24]. Lifting only one pendulum and mounting the particle on the other allows for determining the energy transferred to the sample by evaluating the rebound movements of the two pendulums after collision.

Rock sample

Hammers

Figure 8: Bond twin pendulum tester

3.2.3 Split Hopkinson pressure bar test

The split Hopkinson pressure bar, originally developed for testing stress propagation in materials from the detonation of explosives, has been used for fracturing a sample particle between two horizontally mounted steel bars called the incident bar and the transmitted bar, compare Figure 9. The mechanical stress is induced by a loading system, i.e. a gas gun, and the travel of the deformation waves is recorded with strain gauges. The signals provide information about load-displacement profiles and allows for energy balancing.

Even though the experiments with the Hopkinson pressure bar are laborious there has been a phase of intensive development of the test method, leading to the Modified Hopkinson Pressure Bar for higher resolution [25] or the CSIRO Hopkinson pressure bar for larger specimen [26] having a vertical assembly like the Ultrafast load cell.


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Rock sample

Strain gauge

Ridgid block Gas gunIncident bar

Transmitted bar

Figure 9: Split Hopkinson pressure bar

3.2.4 Rotary single impact tester

In single impact tests the stress applied to a sample results from the collision with one single tool. This can be achieved either by accelerating the sample against a plate using gravitational forces or the acceleration forces from a gun, or by advancing the sample with a fast moving tool, commonly realized in a rotor-stator impact system.

Such a rotary impact tester design was first presented by Schönert et al. [27] and has meanwhile been commercially adapted also for ore testing [29], [30]. Figure 10 shows a schematic of the rotor–stator impacting system. Particles are fed to the evacuated impact chamber by centrifugal action via several channels in the rotor. The surrounding stator has a saw tooth profile that allows for a perpendicular impact of the particles. Compared to other particle breakage tests significantly more particles can be tested in a given time.

Rotor

Stator ring

Feeding channel

Figure 10: Rotary impact tester

The probability for breakage can be described as a function of the impact energy using a Weibull distribution [28]:

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min,exp1 kinkinmat EExkfS (7)

where fmat is a material constant, x the initial particle size, k the number of impacts, and Ekin and Ekin,min the kinetic energy impact and the energy threshold without fracture, respectively.

The specific kinetic energy is described by

2

21 vEkin

(8)

Comminution test are used to determine the parameters within the probability for breakage and the breakage distribution.

3.2.5 Evaluation of particle breakage tests

Particle breakage tests use impact stress for striking the sample. Except for the rotary breakage test the mounting of the sample and the conduct of the tests are in most cases quite tedious. Repeatability is more affected by the sample characteristics than by the test method.

Table 2: Particle breakage tests


Drop weight

UFLC Twin Pendulum

Split Hopkinson bar

Rotary breakage

Simplicity O – – – –

Repeatability O O – O +

Sample preparation

–1) – O – O

Time exposure and costs

–1) – O – O

Sample amount –1) – O – O

Link to modeling + O + O +

Mineral liberation O O O O O

1) based on the JK drop weight test

The necessary sample amounts are small if using cut drill core samples. Testing fractionated material from crushing and screening requires significantly more material. This is particularly the case if not only the initial particle size is varied but also different energy levels are tested, e.g. when using the concept of tn-values for process modeling.


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Depending on the initial sample size the fragments received after breakage are usually too coarse for using them as such in quantitative mineralogical analyses, i.e. only for the case of ultra-fast load cell or when using small bars with the split Hopkinson pressure bar test sufficiently small particles are generated that are meaningful to investigate for mineral liberation.

3.3 Bench-scale grindability tests

3.3.1 Bond test

The Bond test is used to analyze the grindability for a material. The test applies a standardized ball mill of 305 mm (12 in.) both in diameter and length with a grinding media charge of certain size distribution and operated at a defined speed. The sample amount is defined by the bulk volume of 0.7 liters, consisting of particles smaller than 3.35 mm. The test is conducted as a dry locked cycle test with sieving of the mill product after each stage. Fines are replaced by an equal amount of fresh feed material and grinding times are varied in order to reach a simulated circulating load of 250%. Usually samples of 10 kg smaller 3.35 mm are required.

From the grinding test the Bond ball mill work index Wi is determined [31]:

FPS

i

xxGx

W

,80,80

82.023.0 1010

5.441.1

(9)

Where xS is the screen aperture, G the grindability (in grams of product per mill revolution), and x80,F and x80,P are the 80% passing particle sizes in m for the mill feed and product, respectively.

The test results are used to calculate the change in particle size during grinding based on the grinding work input W using the Bond formula, also referred to as Bond’s law, as a process model [32]:

FPi xx

WW,80,80

1010

in kWh/t (10)

3.3.2 Variations of the Bond test

Besides for determining ball mill grindability the Bond test has been adapted to other mill types. Bond also defined a test for rod mill grinding using a 305mmx610mm standard mill requiring up to 20 kg sample. Test conditions are differing, e.g. the circulating load is changed to 100%, and also the Bond equation for calculating the rod mill work index is slightly different. For describing comminution in AG/SAG mills and HPGR using the Bond test method requires model extensions by empirical relations.

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In the past several attempts have been made in order to simplify the Bond procedure. One approach has been to change the test from locked cycle to a pure single pass batch test in order to minimize the timely effort and also the sample amount needed, by developing new test mills, e.g. Mergan mill [33] or NSBM [34], or by modifying the test procedure [35], [36].

3.3.3 Evaluation of grindability tests

In grindability tests a combination of impact stress and attrition is applied to a bulk of material. The original Bond test is quite tedious as several grinding experiments are necessary to reach the stationary state of the simulated closed circuit. Also the sample amount appears quite high if only drill cores are available. Sample preparation is limited to pre-crushing and screening.

The test is reliable and has a good repeatability if procedure and test mill comply with the standard. One of the major advantages is surely the huge data base that has been developed during the last decades. With respect to modeling the coupling between the work index and the particle size reduction can directly be used together with a size distribution function. Attention has to be paid to the applicability of the function type for the individual case. The size range of the mill product can be used as such to conduct mineral liberation analyses.

Table 3: Grindability tests


Original Bond ball mill

Original Bond rod mill

Single pass e.g. Mergan mill

Simplicity O O +

Repeatability + + +

Sample preparation O O O

Time exposure and costs – – O

Sample amount – – –

Link to modeling + + +

Mineral liberation + + +

3.4 Pilot and bench-pilot scale tests

Comminution test work on bench-pilot or pilot scale is done by using different types of crushers and mills. Typically this comprises:

Cone crushers


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High pressure grinding rolls (HPGR)

Ball mills

Stirred media mills, e.g. IsaMill or vertical stirred mills

Stress type and stress rate are based upon the respective machine type.

Tests require several tens to hundreds of kilograms sample material and are done in batch or continuous mode. Sample preparation usually comprises pre-crushing and screening for adjusting the initial size distribution, as well as sample splitting.

Sampling from the test mill or circuit provides the data base for determining breakage probabilities or grinding rates as well as breakage distributions from back-calculation using population balance methods. Using the data from liberation analyses allows for describing the particles based on their mineral composition [37].

Pilot and bench-pilot scale tests are used to verify the metallurgical performance of a designed circuit. In the geometallurgical context these result can be used in calibrating the small scale test results towards full scale operation.

3.5 Indirect methods for determining comminution behavior

Another way of obtaining information about rock mechanical strength is to evaluate the core drilling process by according instrumentation, also referred to as measurement while drilling (MWD). Alternatively also drill cuttings can be evaluated. Variations of the conditions at the drill bit, as for instance torque, normal or bending forces, result from changes in the rock hardness.

Despite of the huge data sets that are continuously collected in a large number of operations the MWD data is seldom used for assessing the comminution properties of ore bodies. One of the obstacles is the lack of reliable on-line information on the condition of the drill bit, which is needed for correcting the recorded down hole measurements by the dynamic process of drill bit wear off.

Also petrophysical data from multi-sensor drill core logging has been used for calibration against measures of ore breakage parameters and grindability that were received from conventional destructive comminution tests [38]. Using density, magnetic susceptibility and seismic wave parameters from Australian copper-gold deposits the Bond mill work index and the crushability parameters received from drop weight testing could be predicted with acceptable accuracy.

In conjunction with recent advances in quantitative mineralogical analyses the development in geometallurgical characterization today is towards identifying correlations between ore comminution behavior and mineralogical properties. The idea behind is to reduce the number of comminution tests necessary for characterizing a deposit and to arrive at a more generic description of mechanical properties based on the occurring minerals [39].

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4 Conclusions

Table 4 summarizes the findings from the evaluation of the individual test methods. None of the tests is fulfilling all criteria but by emphasizing the requirements on sample amount and effort for conducting the tests as well as modeling issues several methods can be identified to be promising for the further development of geometallurgical comminution test.

Results from rock mechanical tests should only be used where already available. But as the results cannot be used directly correlations need to be found for the description of ore crushing properties. Generally speaking, rock mechanical tests should not be part of a geometallurgical program as they do not provide information about grinding behavior down to the particle liberation level.

Table 4: Summary table, relevance for geometallurgy

Fracture test method – O + Relevance

Unconfined compressive strength test 3 2 2

Point load test 2 3 2 ( )

Brazilian test 3 2 2

Drop weight test 1) 3 3 1 ( )

Ultra-fast load cell test 4 4 0

Twin Pendulum test (Bond CWI) 2 4 1

Split Hopkinson bar test 4 3 0

Rotary breakage test 1 4 2

Bond ball mill test (Bond BWI) 2 2 3 ( )

Bond rod mill test (Bond RWI) 2 2 3 ( )

Single pass test, e.g. Mergan mill 1 2 4

1) based on the JK drop weight test

Particle breakage tests have a potential to be used within geometallurgy in case they are not depending on too large sample amount and high effort. This is for instance the case for the SMC test based on the standard drop weight testing where only single size samples are required. Also the rotary breakage test is promising despite the need for the technically and monetarily intensive test machines.


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Grindability tests are well established and provide a huge amount of reference data. The Bond equation links comminution energy and resulting particle size reduction thus already providing a comminution process model. With regard to geometallurgical testing a clear disadvantage lies in the timely effort for conducting the Bond test and the comparatively large sample amount. Here the route for further development should be put towards modified Bond tests with the objective of significantly minimizing the sample amount needed.

Considering different dimensions, like particle sizes, mechanical stress and comminution techniques described in chapter 2 it can be stated that it is practically impossible to have a single universal method for determining ore comminution behavior in the geometallurgical context. Figure 11 shows the test methods existing today with their placement in the matrix as introduced in Figure 1 but without using the dimension of stress type.

The further development in geometallurgical comminution test methods will have to focus on replacing the remaining interrogation marks either by developing entirely new comminution test methods or by enhancing the existing methods.

…? …?SMC…?

DWTRBT

BBWIBRWI

BCWI

CoarseFineUltrafine

Pilot andbench pilot scale

IsaMilltest

Ballmilltest

HPGRtest

Bench scale

Lab scale

GeoMet level

Figure 11: Available comminution tests

5 Acknowledgements

The financial support of the CAMM Centre of Advanced Mining and Metallurgy at Luleå University of Technology is gratefully acknowledged.

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[26] Fandrich, R.G., Clout, J.M.F., Bourgeois, F.S. (1998). The CSIRO Hopkinson Bar Facility for Large Diameter Particle Breakage, Minerals Engineering, 11 (1998) 9, pp. 861 – 869.

[27] Schönert, K., Marktscheffel, M. (1986). Liberation of composite particles by single particle compression, shear and impact loading, Proceedings of the 6. European Symposium Comminution, Nürnberg, pp. 29 – 45.

[28] Vogel, L., Peukert, W. (2003). Breakage behaviour of different materials – Construction of a master curve for the breakage probability, Powder Technology 129 (2003), pp. 101 – 110.

[29] Kojovic, T., Shi, F., Larbi-Bram, S., Manlapig, E. (2008). Julius Kruttschnitt Rotary breakage tester – Any ore, any mine, Proceedings Metallurgical Plant Design and Operating Strategies (MetPlant 2008), pp. 91 – 103.

[30] Shi, F., Kojovic, T., Larbi-Bram, S. Manlapig, E. (2009). Development of a rapid particle breakage characterisation device – The JKRBT, Minerals Engineering 22 (2009), pp. 602 – 612.

[31] Bond, F.C. (1961). Crushing and grinding calculations, British Chemical Engineering, 6 (1961) 6, pp. 378 – 385.

[32] Bond, F.C. (1952). The Third Theory of Comminution. Transactions of the AIME No 193, Mining Engineering, pp. 484 – 494.

[33] Niitti, T. (1970). Rapid Evaluation of Grindability by a Simple Batch test, Proceedings International Mineral Processing Congress, Prague, pp. 41 – 46.

[34] Nematollahi, H. (1994). New Size Laboratory Ball Mill for Bond Work Index Determination, Mining Engineering Vol. 46. No. 4. pp. 352 – 353.

[35] Tüzün, M.A. (2001). Wet Bond Mill Test, Minerals Engineering, 14 (2001) 3, pp. 369 – 373.

[36] Tavares, L.M., de Carvalho, R.M., Guerrero, J.C. (2012). Simulating the Bond rod mill grindability test, Minerals Engineering 26 (2012), pp. 99 – 101.

[37] Lamberg, P., Vianna, S.M.S. (2007). A technique for tracking multiphase mineral particles in flotation circuits, Proceedings of VII Meeting of the Southern Hemisphere on Mineral Technology, Ouro Preto, Brazil, pp. 195-202.

[38] Vatandoost, A. (2010). Petrophysical Characterization of Comminution Behavior, PhD thesis University of Tasmania, Australia.

[39] Mwanga, A. Rosenkranz, J. Lamberg, P., P.-H. Koch (2013). Simplified Comminution Test Method for Studying Small Amounts of Ore Samples for Geometallurgical Purposes. Preprints AusIMM Exploration Resource and Mining Geology Conference ‘13, Cardiff, UK, pp. 45 – 48.


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Paper II

Comminution test method using small drill core samples Abdul Mwanga, Pertti Lamberg and Jan Rosenkranz

Minerals Engineering, Volume 72, 2015, pages 129-139 DOI: 10.1016/j.mineng.2014.12.009

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Comminution test method using small drill core samples

Abdul Mwanga *, Pertti Lamberg and Jan Rosenkranz

Minerals and Metallurgical Engineering Laboratory, Luleå University of Technology, SE-971 87 Luleå, Sweden; E-Mail: [email protected], [email protected],

[email protected]

* E-Mail: [email protected]; Tel.: +46-920-49; Fax: +46-920-97364.

Abstract Comminution tests aim to measure the comminution properties of ore samples to be used in designing and sizing the grinding circuit and to study the variation within an ore body. In the geometallurgy context this information is essential for creating a proper resource model for production planning and management and process control of the resource’s exploitation before and during production.

Standard grindability tests require at least 10 kg of ore sample, which is quite a lot at early project stages. This paper deals with the development of a method for mapping the variability of comminution properties with very small sample amounts. The method uses a lab-scale jaw crusher, standard laboratory sieves and a small laboratory tumbling mill equipped with a gross energy measurement device. The method was evaluated against rock mechanics tests and standard Bond grindability test. Within this approach textural information from drill cores is used as a sample classification criterion.

Experimental results show that a sample of approximate 220 g already provides relevant information about the grindability behavior of iron ores at 19 % mill fillings and 91% fraction of the critical mill speed. The gross energy measured is then used to calculate an equivalent grinding energy. This equivalent energy is further used for predicting the variations in throughput for a given deposit and process.

Liberation properties of the ore connected to grindability elaborates energy required for grinding and significances of it when deciding to move to higher grinding energy considering the improvement of liberation of the desired mineral. However, high energy significantly enhanced the degree of liberation of magnetite and is expected to improve the concentrate grade after downstream treatment. The higher the magnetite content the better is the liberability of magnetite and the lower the energy required to liberate the desired mineral. Liberability of magnetite is also affected by texture classes containing low magnetite content. A methodology that combines this information has been developed as a practical framework of geometallurgical modeling and simulation in order to manage technical and economic exploitation of resource at early, project stages and during mining operations.

Keywords: Geometallurgy; grindability; mineral liberation; liberability; comminution test


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1. Introduction Ore testing is an important part of the geometallurgical experimental framework and modeling. Tests are used in characterization of ore processing behavior at different process stages, such as comminution. Several test methods are available for testing comminution behavior but they require comparatively large (>10 kg) samples. In the early stage of resource evaluation only drill core samples are available while for metallurgical testing only half or quarter of the drill core is left. Therefore commonly samples collected for the testing are composite samples representing a broad mineralogical variation within them. This hinders the detailed mapping of ore variability using drill core samples. Some of the methods used in geometallurgy are the JK Tech drop weight test (Napier-Munn et al, 1996; Narayanan, 1986), JK Rotary Breakage Test (JKRBT; Shi et al, 2009) and SMC test (Morrell, 2004). For detailed characterization of metallurgical properties along the mineralogical variability small-scale comminution test methods are needed.

Mineral processing properties within an ore body can vary a lot and bring several challenges for production. For the Collahuasi copper mine Alruiz et al. (2009) and Suazo et al. (2010) showed that the plant throughput and the copper recovery significantly vary between the geometallurgical domains. In geometallurgical programs, like for the Collahuasi mine, it is common that the comminution circuit throughput is determined by fixing the particle size of a comminution product. This is questionable when there is a big variation on micro-texture or liberation size within a deposit, e.g. as shown by Lund (2013) in Malmberget iron ore. However, comminution characterization studies that would take into account mineral information are very rare (Kim, Cho, and Ahn, 2012; Kim and Cho, 2010; Schreier and Groger, 1999).

This study aims at establishing a comminution test method for geometallurgy and evaluating it with a case study from Malmberget iron ore, Northern Sweden. Another aim of the study is to demonstrate how and why modal mineralogy, mineral textures and liberation should be considered already in comminution tests.

2. Comminution tests most suitable for geometallurgy A short review on existing comminution tests is here done to estimate their directly usability and easiness to modify for geometallurgical purposes. A suitable geometallurgical comminution test should fulfill the following requirements:

1. The test should be relatively simple and use instruments available in common analytical and mineral processing laboratories.

2. The test should be repeatable and not dependent on person.

3. The test should be easy to execute so that technicians with basic skills in sample preparation should be able to do it with short training.

4. The test should be fast (max 1 hour) and inexpensive.

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5. The amount of sample per test should be less than 0.5 kg; preferentially the test could use assay rejects.

6. The test, or rather a combination of tests, should give measured values on both crushability and grindability.

7. It should be possible to use the parameters derived from the test directly in the modeling and simulation of a comminution circuit.

8. It should be easy to extend the test to include mineral liberation information .

Comminution tests are here classified into three groups, compare Table 1: 1) Geological and rock mechanics tests, 2) Single particle breakage tests and 3) Grindability and bed breakage tests. Another dimension in the classification is the particle size range. As shown by Hukki (1962) comminution energy vs. size reduction equation changes by particle size. In the coarse range the energy required for size reduction is smaller than for finer particle sizes. Three different particle size areas following the different comminution laws can be identified: A) coarse range (crushing, >1 cm, Kick, 1885), B) middle range (grinding, 0.1-1 cm, Bond, 1952) and C) fine range (fine grinding, < 100 microns, von Rittinger, 1867).

Rock mechanics test are used to measure the mechanics strength of the rock in the coarse particle size range (A). They are commonly used in geotechnical studies. The most potential ones for geometallurgical tests are point load test and unconfined compressive tests. They are used for testing small scale drill core samples. It has been shown that the mechanical strength of rock measured from point load can be correlated with comminution parameters (Akram and Bakar, 2007; Flores, Limitada, and Minería, 2005). These kinds of tests are simple and can quickly generate information about the hardness of an ore and therefore are relevant for geometallurgical mapping. However, they require reasonable large sample amounts and the measured parameters cannot be directly used in comminution or throughput models (Flores et al., 2005).

Single particle breakage tests such as JK Drop Weight tests, SAG Mill Comminution test (SMC) by Morrell (2004), pendulum and ultra-fast load describe the crushability (fracture behavior) of the materials in coarse-middle particle sizes (A-B) using empirical parameters which are further used in specifically developed process models (Napier-Munn et al. 1996). As these tests are used especially in designing and optimizing autogenous or semi-autogenous grinding circuits they use large samples, typically >10 kg, which makes it difficult to be practically used in geometallurgical programs (Bailey et.al. 2009). The JK Rotary Breakage Test has been developed to rapidly assess the hardness of the materials (Shi et al 2009 (Hunt et al., 2008). Despite the JKRBT capability to measure hardness of the materials and general suitability for geometallurgical programs (Table 1) it is still very new for that purpose.

Grindability tests are done for multiple particles to characterize the material properties in milling in a middle particle size range (B). The most widely used is the Bond grindability test (Man, 2002). The test has been further improved for wet grinding and


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different type of circuits (Armstrong, 1985; Wills and Bruce, 1966; Smith and Lee, 1968; refer Wills and Napier-Munn, 2006). However, the test is not very suitable for geometallurgy, because it requires large sample (>10 kg), and the test takes several hours to complete.

Table 1. Common fracture test methods having potential for geometallurgical tests. Requirements (see text)- 1) Simplicity, 2) Repeatability, 3) Sample preparation, 4) Time exposure and cost, 5) Sample amount, 6) Parameters can be used in modeling and simulation, 7) Can be extended to mineral liberation.

Fracture test method Suitability criteria for geometallurgical test (- = adverse, O = acceptable, + = advantage)

Reference

1 2 3 4 5 6 7

Unconfined compressive strength test

[1] + O - O + - -

Point load test [2] + O O O + - - Brazilian test [3] + O - O + - - Drop weight test [4] O O - - - + O Ultra-fast load cell test [5] - O O O - + O Twin Pendulum test (Bond CWI) [6] - - O O O + O Split Hopkinson bar test [7] - O - - - O O Rotary breakage test [8] - + O O O + O Bond ball mill test (Bond BWI) [9] O + O - - + + Bond rod mill test (Bond RWI) [10] O + O - - + + Single pass test, e.g. Mergan mill [11] + + O O - + + [1] Rusnak & Mark 2000; [2] Farah, 2011; [3] Claessona and Bohloli, 2002; [4] Brown, 1992; [8] Shi et al. 2009; [5] Weichert and Herbst, 1986, Abel et al., 2009; [7] Fandrich et al.1998; [6] Narayanan, 1985; [9] Bond, 1951 and 1962, Man 2002); [11] Niitti 1970.

A literature survey and simple evaluation showed that no single fracture test method fulfills all eight criteria (Table 1). Putting an emphasize on criteria for modeling and simulation (criterion 6 in Table 1) and liberation (criterion 7), three tests were identified having the best potential for further development towards a comminution test for geometallurgy using small drill core samples: Bond ball mill test, instrumented drop weight test and Rotary Breakage Test (RBT). Here, the Bond test was selected as a base as it has been used for almost a century. It is an accepted industrial standard resulting in large databases of test results (Bond work index, BWI). The test is easy to conduct without requiring special equipment. It also seems to be easy to extent the test to the liberation level.

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3. Materials and methods

3.1Samples Samples for this study (Table 2) were collected from Malmberget iron ore located in Northern Sweden. In the Malmberget iron field more than 20 separate ore bodies are known and production is coming from several different underground operations (Lund, 2013). Ore is processed in the Malmberget concentrator in two lines: one for magnetite dominated ore (FAR) and another for hematite dominated ore (HAR). Lund (2013) developed a preliminary geometallurgical classification of the ore body based on modal mineralogy and mineral textures (see also Lamberg and Lund, 2012; Lamberg et al., 2013; Lund et al. 2013). This model, however, did not take into account comminution properties.

Table 2. Mineralogical, mineral texture and comminution properties of characterized samples. Sample 1F 2F 3F 4F 5F 6F 7C 8F 8C FAR HAR Main Fe mineral Mgt* Mgt* Mgt* Mgt* Mgt* Mgt* Mgt* Mgt* Mgt* Mgt* Hmt* Texture type 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 8.0 - -

Grain size F F F F F F C F C - -

FeO wt.% 5.5 10.0 22.0 28.0 57.0 55.0 55.0 80.0 80.0 62.9 51.1 Mgt grain size (μm) 44.0 75.0 95.0 61.0 64.0 74.0 106.0 32.0 180.0 - -

Modal composition % Magnetite 14.8 54.6 59.1 84.4 90.5 87.6 2.7 Hematite 0.5 70.8 Albite 53.7 28.0 29.9 1.8 1.1 2.0 4.6 Actinolite 15.8 7.5 5.8 3.2 4.8 2.6 0.0 Apatite 0.0 0.2 0.1 0.7 0.9 1.2 4.4 Orthoclase 2.3 6.2 1.5 0.4 0.1 1.6 2.6 Biotite 0.0 0.0 0.0 0.0 0.0 2.5 5.2 Others 2.0 5.5 Strength of the rock UCS (N/mm2) 84.1 27.3 63.0 16.4 47.1 58.1 20.0 36.3 20.1 - -

Crushing properties Reduction ratio 5.6 8.4 6.4 6.4 8.9 7.8 8.8 9.2 - - Grindability properties F80 of the test (μm) 2822 2115 2456 1893 2609 1983 2221 2237 2065 2980 1033 P80 of the test (μm) 109 125 113 132 127 127 N/A 130 140 258 977 Estimated Bond work index(kWh/t) 9.0 9.3 10.1 9.5 10.0 10.4 N/A 10.3 11.0 10.9 13.5 Mgt*= magnetite, Hmt*= hematite

Two sample sets were collected. The first one consists of drums of composite magnetite and hematite ore samples which were collected from the Malmberget process plant on 11th and 12th of April in 2012. These samples represent sample types and sample sizes used normally in comminution characterization. As the plant feed includes country rock (wall rock dilution) the ore samples used in the study consisted of the FAR and HAR concentrates from the cobbing plant. For more information of the Malmberget process


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and flowsheet see Alldén et al. (2008), Tano et al. (1999) and Öberg and Pålsson (2004). The second sample set includes small drill core pieces from different textural variants of Malmberget ore type Fsp (Feldspar breccia) classified by Lund (Koch, 2013; Lund, 2013). The Fsp Malmberget is a composite sample of different texture types and was used as a reference for that reason. They represent typical samples for a geometallurgical program. The textural classification used for Malmberget follows the one developed by Lund (2013). The classification has two dimensions: magnetite grain size (fine/coarse) and relationship and mass proportions of melanocratic and leucocratic parts. Melanocratic material is rich in magnetite and it brecciates the leucocratic albite-orthoclase-rich magnetite-poor matrix. The textural types are by increasing magnetite grade (Table 2) as follows: (1) disseminated, (2) banded, (3) waving veins, (4) patchy, (5) granules, (6) clustered, (7) small veins, '(8) massive ore'. Here the division between fine and coarse grained texture is put to 100 microns (the average grain size of magnetite). Besides the above listed minerals the sample usually includes actinolite and apatite. In the second sample set the magnetite grade shows negative correlation with albite and actinolite grades. Apatite grade shows positive correlation with magnetite grade. Most of the samples are classified as fine grained.

3.2Experiments The experimental work is divided into three parts. The first part describes the work done to downscale the Bond ball mill grindability test to be applicable for small drill core samples. The second part incorporates modal mineralogy, mineral textures and mineral liberation for the geometallurgical testing. The third part brings the geometallurgical test to the practical level, i.e. the full procedure is developed and described. In addition mechanical test results are compared with results from the developed test.

Rock mechanical tests were conducted using two different experimental set-ups. The point load test (PLT) was carried out according to D5731-08 standard (ASTM 2011). Quarters of drill core were clamped between the tops of cone-shaped tools giving a point load on the outer perimeter of the specimen. For the unconfined compressive test (UCS) the specimen was pressed between two parallel planes of a universal testing machine. Fracture patterns observed were variable and usually not symmetric.

Crushing tests were done with a laboratory scale jaw crusher (model Retsch Type BB mach. no. 31648). Fixed closed size setting of 3.35 mm was used. For the crushing tests the sample was passed through the crusher only once. For the sample preparation for the grinding test the sample was continuously sized using a 3.35 mm sieve and the oversize was crushed again until all the material passed the sieve.

The grinding tests were evaluated according to the Bond approach by using the recorded electrical energy consumption meter (corrected by the mechanical efficiency of the device) together with the change in the 80% passing particle size in order to determine grindability which describes specific work index of a given ore.

The grinding experiments were conducted using two different ball mills (see Figure 1): A standard Bond ball mill (22 L) and a Capco Jar ball mill (1.4 L; Figure 1). The mass

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of steel balls (kg) was calculated based on degree of mill filling, ore density (4800 kg/m3) and mill volume. The steel ball size distributions used in the experiments ranges from four to 50 per cent for the smallest and biggest steel ball diameter sizes (mm), respectively (Table 3).

Figure 1. Laboratory mills of different sizes used in the study.

Table 3. Size distribution of steel grinding media used in Bond ball mill grindability test and in down-scaled test with a small mill.

Diameter of a ball (mm) Distribution by weight (%)

Number of balls in a small mill

36.0 15 1 28.5 51 7 21.8 29 9 15.0 4 5

3.3Assays Mineralogical analyses on modal composition and liberation distribution were made using scanning electron microscope (SEM) based automated mineralogy. Zeiss Merlin SEM and IncaMineral system (Liipo et al., 2012) for automated mineralogy were used. In modal and liberation analyses the minerals were identified and classified using back-scattered electron image and EDS analysis. Magnetite grain size was estimates were done by optical microscopy (Lund, 2013).


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4. Results

4.1Downscaling the Bond ball mill test for geometallurgy The starting point selected for the new grindability test was the Bond ball mill grindability test (Figure 2). The test is a locked cycle test which simulates a closed continuous comminution circuit (Figure 2). The test starts with 0.7 liters sample, corresponding to 3.4 kg FAR (iron ore sample), and the test is repeated until steady state is reached. Normally this takes at least six grinding-screening cycles. The test aims for 250% circulating load at a defined screen cut size close to 100 μm. After each grinding step the mill product is sized and material passing 100 microns screen is removed and replaced by an equal amount of fresh feed material to maintain 3.4 kg of sample in the tumbling mill. The grinding time is adjusted after each round to reach 250 % circulation load and a steady-state condition.

Figure 2. Schematic flowsheet of the Bond ball mill grindability test. Test needs more than 10 kg sample.

The average mass per number of revolution of the undersize materials of the last three cycles of the grinding test is used to determine the grindability and the work index according to the Bond formula in equation 1. Totally the test uses about 10 kg of sample and it takes usually at least one working day to be completed. Figure 3 shows how steady state was reached with the magnetite ore sample (FAR).

FPGP

BWI

bpi1010

5.441.1822.023.0

(1)

Where:

BWI = Bond work index, kWh/t Gbp = Average mass in gram of undersize material produced per number of

revolution for the last three cycles. Pi = cut screen size (100 μm) F = Particle size 80 % passing of fresh feed, wt. % P = Particle size 80 % passing final undersize (passing cut screen size), wt. %

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0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 1 2 3 4 5 6 7

Grin

dability(g/revolution)

Number of grinding cycle

Grindability approximate steadystate grinding condition

Grindability profile for sixdifferent grinding cycles

Figure 3. Grindability curve of the Bond ball mill grindability test with the Malmberget

iron ore sample (FAR).

To be applicable for geometallurgy the test should be faster and it should use smaller sample (< 2 kg). Therefore a solution was searched by doing the test in single pass with electrical energy measurement, similarly to the Mergan test (Niitti, 1970) but with a significant smaller mill and sample size.

In down-scaling the Bond ball mill grindability test, the principle was to keep the impact effects similar in the Bond and in a smaller mill (Table 4). Therefore ball sizes and their size distribution was kept constant. The total ball charge was defined by keeping the ball charge filling fixed (19%). The target was to minimize the sample size and therefore to find the smallest possible mill fulfilling the conditions on similar impact effect. The diameter vs. length of the mill was not fixed because the aim was to find a suitable commercially available laboratory mill. Also the length of the mill does not affect the impact of ball charge inside a mill. To maintain similar type of mechanical stress and ball hitting location inside the tumbling mill, ball trajectories and ball impact velocities were calculated based on throw angle and tangential velocity of rotating mill. Calculations showed that a CAPCO laboratory 1.4 l stainless steel ball mill model 2 variable speed (Ref. 337SS, www.capco.co.uk) with 115 mm mill internal diameter gives similar conditions as the Bond mill with similar critical speed. The sample size was defined by keeping the proportion between ball and sample weight similar for both mills. The mill speed was maintained at 91% of the critical speed.


94

Table 4. Parameters for down-scaling the Bond ball mill test.

Parameters Condition for downscaling

Standard Bond ball mill

Small ball mill

Mill dimensions

1 Diameter (mm) To be changed 305 115

2 Length (mm) To be changed 305 132

Ball charge 3 Percentage mill volume fillings by ball charge (%)

Fixed 19 19

4 Average ball size (mm) Fixed 27 27

5 Ball charge (kg) Scaled by filling (3)

21.9 1.33

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

7 Sample size (kg) Scaled by ratio (6)

3.4 0.220

8 Sample particle size distribution (mm)

Fixed <3.35 <3.35

Operational conditions

9 Speed, vs. critical (%) Fixed 91 91

10 Grinding time (minutes) To be changed 10.5 17.0

11 No of revolutions/minute To be changed 70 114

12 Test type To be changed Locked cycle Single pass

13 Mill product sizing Fixed Standard sieve series

Standard sieve series

The Bond mill gives bigger impact because of its large diameter compared to the small ball mill. By prolonging the grinding time in the small ball mill the material experiences higher number of impacts. Sample FAR was used to determine the grinding time in the smaller mill that gives identical particle sized distribution in the mill discharge compared to the Bond test. It was found that 17 minutes grinding time in single pass gives similar particle size distribution for the mill discharge (80% passing size, P80 = 259 μm) as the Bond test procedure after reaching the steady state (see Figure 4). This was therefore selected as a standard condition for further testing in the small ball mill.

95

0

10

20

30

40

50

60

70

80

90

100

10 100 1000 10000

Cumulativepe

rcen

tage

passing(%

)

Particle size (μm)

Feed

Mill discharge of Bond testprocedure approximatesteady state at 10.5 minBatch test small mill 220 gvs 17 min

Batch test small mill 220 gvs 10 min

Batch test small mill 220 vs25 min

Figure 4. Comparison of particle size distribution of the product from small ball mill for different grinding time vs. Bond test procedure. Sample: FAR.

By shifting the Bond grinding conditions to the small ball mill the kinetics are changed because of the differences in geometry. Another thing to consider is the change from a closed circuit test to single pass test. Therefore a scale factor is needed to equalize the results with the Bond test. From geometrical relationship the kinetic scale factor (square root of the ratio of the diameter of large to small ball mill) between the Bond and the small mill is 1.63. This is reached by considering the geometric similarities of the standard bond ball mill (L) and modeled small ball mill (S) and geometric scaling factor

( D ) is exactly defined by the 2.65mm 115mm 305

mill ball small ofDiameter mill Bond ofDiameter

.

For receiving the same fracture effects the impact from ball motion has to follow the similarity principles(i.e. dimensionless factor impact between two mill =1). Here the impact velocity of a grinding ball at a certain throw angle is used. In the

formulation of this dimensionless factor the Froude number lg

vFr , i.e. the ratio

between inertia to gravitational forces, has been considered as a suitable quantity for describing the grinding ball movement inside a tumbling mill, with the mill diameter being the characteristic length is in this case.

Applying the principles of the Buckingham Pi theorem gives

lgv,

ll

ii

i (2)

where

li : Characteristics length of the Bond ball mill and in this study it is DL


96

lii : Characteristics length of the small ball mill and in this study it is DS

v : Velocity of the grinding ball at throw

g : Gravity constant

The dimensionless factor for the impact velocity is defined by

SDgSimpv

LDgLimpv

impact (3)

Where;

Vimp( ) L : Impact velocity of large mill (Bond ball mill) at any throws angle

Vimp ( ) S : Impact velocity of modeled mill (small ball mill) at any throw angle

Keeping the kinematic similarity between the two mills the expression for the scale factor is calculated as

DSDLD

S impvL impv

(4)

With the FAR iron ore sample the measured specific energy with 17 minutes grinding time is 10.56 kWh/t. The measured Bond work index with full Bond test gave 10.6 kWh/t. By applying back calculation with the Bond energy equation 5 the calculated work index with the small mill is 10.87 ± 0.42 kWh/t (2 ). This confirms that scale-down factor of 1.63 from the geometry can be applied and is used in this study for the estimation of the Bond work index.

801

801104321 FP

EfEfEfEfk

EBWI (5)

Where BWI = Bond work index (estimated), E = measured specific energy in the small mill, P80 = the product 80% passing size (microns), F80 = the mill feed 80% passing size (microns) and k = scale factor defined by square root of the ratio of the diameter of Bond to

small ball mill equal (1.63) Ef1 = correction factor for dry grinding (1.3; Rowland and Kjos, 1978; Mular et

al., 2002). Ef2 = correction factor efficient diameter (1.842) (Rowland and Kjos, 1978;

Mular et al., 2002). Ef3 = Ball mill efficient factor (0.835) (Rowland and Kjos, 1978; Mular et al.,

2002). Ef4 = Efficient factor for fineness (0.95) (Rowland and Kjos, 1978; Mular et al.,

2002).

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Four different samples of know Bond work indices were used to validate the developed test method (Figure 5). It can be clearly seen that there is strong correlation between the BWI from the standard grindability test and the BWI obtained from the small ball mill test with small amount of sample. It implies that the BWI of the small ball mill with fixed grinding time describes relative grindability correctly.

Quartzite

massive sulphide ore

HAR

FAR

y = 0.8007x + 2.5834R² = 0.9953

9

10

11

12

13

14

15

9 10 11 12 13 14 15

Bond

workinde

xby

stan

dard

metho

d(kWh/t)

Estimated Bond work index by small ball mill (kWh/t) Figure 5. Comparison of Bond work index from standard grindability test methods and estimated Bond work index by small ball mill.

4.2Linking comminution properties and mineralogy with special reference to mineral liberation

Grindability, expressed as estimated Bond work index, does not appear to correlate with crushability, expressed the crusher reduction ratio (Figure 6). Looking against mineralogical parameters it can be found that the higher the content of magnetite the higher is the reduction ratio (easy to crush) while in grinding the opposite is the case: The higher the magnetite content the higher is the P80 of the grinding product (and therefore the harder it is to grind). When applying multivariate statistics for the small mill data set it can be found that the mill product size (P80) is controlled by the magnetite grade and the magnetite grain size according to following empirical equation 6 (see also Figure 7).

118micronssizegrain Mgt *0.054%wt Mgt*0.139micronsP80 (6)

Direct relationship means that the larger the grain size of magnetite the higher is the P80 and therefore the harder is the material to grind. As the P80 is between 110 and 140 microns in coarse grained materials, where the magnetite grain size is >100 microns, the


98

grinding action is partly used to break individual magnetite grains and presumably this is why the material appears to be very hard to grind. The purpose of ore grinding is to liberate and with the coarse grained sample the particle size in the mill product is already well below the average magnetite grain size and most probably also of liberation size, i.e. the size where the mineral occurs liberated enough for the downstream processes. For the geometallurgical context the grindability of the material is not exactly the proper measurement since for different material the degree of liberation of the mineral may be very different. Therefore the grindability is here extended to mineral liberation and a new term liberability is introduced: It is defined as the relative ease with which an ore mineral can be liberated by grinding.

8

9

10

11

12

5 6 7 8 9 10

Estim

ated

Bon

d w

ork

inde

x(kW

h/t)

Size reduction ratio in crushing

1F2F

3F

4F5F

6F8F

8C

Figure 6. Crushability (size reduction ration in a single pass crushing) vs. grindability of Malmberget samples Weak positive correlation indicates that samples easy to crush (having high size reduction ratio) seem to be difficult to grind (high work index).

In a composite sample of feldspar breccia from Malmberget the degree of liberation (i.e. mass proportion of mineral in particles containing more than 95% of mineral in question) shows inverse relationship with particle size, as expected (Figure 8). The relationship is close to linear and passes through the point 0 microns particle size and 100% liberation. Linear relationship cannot be generalized and the size liberation function needs to be calibrated individually for each ore type. It is not very practical to introduce a liberability term in geometallurgy if this means that for each sample after grinding several size fractions must be analyzed for liberation. Therefore an alternative approach was developed. Firstly, a key size fraction was selected for liberation measurement. This should be close to the expected liberation size and for the Malmberget ore a size fraction of 53-75 microns was selected. The liberation characteristic of the size fraction was measured with automated mineralogy. Based on

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the measurement on the selected size fraction the degree of liberation of magnetite was estimated in the other size fractions by applying a linear equation which passes through the measured point and the point (0,100). The degree of liberation in the bulk sample was calculated from the size fractions as weighed average. In the Fabian Fsp sample from Malmberget (analyzed by Lund, 2013; Figure 8) the estimated degree of liberation in the bulk sample (when using only one size fraction and linear liberation model) differs only 1% from the actual measured one.

180 μmmagnetite grain

32 μmmagnetitegrain




y = 0.1424x + 122.28R² = 0.5188

100

110

120

130

140

150

160

0 20 40 60 80 100 120

Millprod

uct,

80%pa

ssing,m

icrons

Magnetite grade (wt %) Figure 7. Mill product size P80 after grinding in small –scale ball mill at the same conditions.

The grinding test gave a certain particle size distribution, which was measured by sieving. The degree of liberation for the bulk sample was estimated as described above. To estimate how the liberation changes with grinding energy a simple approach was used (a-f in the following refer to a worked out example given in Table 6). Calculations were done for each sample individually. Firstly a set of grinding energies were selected and for each of them (a) the P80 (b) was estimated by using the Bond equation (Equation 7). In the calculation the Bond work index received from the tests (c) and fixed (d) F80 were used. The energy vs. particle size relationship for different textural types of Malmberget is shown in Figure 9.

80

180

110FP

BWIE (7)


100

The received P80 (b) was converted to a full particle size distribution by using the Rosin-Rammler equation and taking the parameter describing the variance of the distribution (e) from the 17 minutes grinding product (Table 5). A new D63.2 parameter (f) to give identical P80 as received from the Bond equation was searched by least squares fitting. Finally to get an estimate on the degree of liberation of magnetite it was assumed that the degree of liberation within the narrow size fractions remains constant (g) and the overall value is a product of each size fraction by their mass proportions (h). The liberability graph, i.e. the liberation degree vs. specific grinding energy is shown in Figure 10.

0

10

20

30

40

50

60

70

80

90

100

0 100 200 300 400 500 600

Degree

oflib

eration,%

Particle size, microns

Mgt

Fsp

Act

Ap

Figure 8. Particle size versus degree of liberation of the main minerals in Malmberget,

a composite sample of Fabian Fsp (feldspar breccia ore type, Lund, 2013).

Table 5. Parameters for the determination of degree of liberation considering mineralogical composition of samples from Malmberget. Sample 2F 4F 6F 8F 8C Texture type 2 4 6 8 8 Grain size Fine Fine Fine Fine Coarse Size fraction 53-75 microns Magnetite wt.% 13.3 88.6 59.0 85.0 90.2 Magnetite Lib% 78.0 88.6 85.2 94.5 95.3 Grinding test product 80% passing 125.3 132.3 126.7 129.9 140.3 Rosin-Rammler D63.2 81.2 96.6 93.4 96.3 103.5 Rosin-Rammler alpha 1.7 1.7 1.7 1.7 1.7

101

0

2

4

6

8

10

12

0 50 100 150 200

Specificgrinding

power

(kWh/t)

Product particle size, 80 % passing (μm)

8C2F8F4F6F

Figure 9. Specific power prediction for target size for magnetite liberation from five different mineral texture classes of Malmberget iron ore deposit.

0

2

4

6

8

10

12

60 70 80 90 100

Specificgrinding

power

(kWh/t)

Degree of liberation of magnetite from in product (%)

8C

2F

8F

4F

6F

Figure 10. Specific power prediction for degree of liberation of magnetite ore of Malmberget iron ore from five different mineral texture classes.


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Table 6. Worked example of how the grinding energy to degree of liberation relationship was established. meas = measured, calc = calculated; for (a)-(h) see text. Parameter

Measured with grinding test (t=17 min)

Forecasted for given energy (example 9 kWh/t)

E kWh/t 10.59 (meas) 9.00 (a) BWI kWh/t 11.04 (c, calc) 11.04 (c)

F80 microns 2064.9 (d, meas) 2064.9 (d)

P80 microns 71.95 (meas) 93.36 (b) Rosin-Rammler D63.2 microns 53.56 (meas) 68.36 (f) Rosin-Rammler alpha 1.68 (e, meas) 1.68 (e)

(meas

) (g) (h) (g)

Size fraction Mass

% Mgt Lib% Mass% Mgt Lib%

Bulk 96.2 (calc) 95.2 (h) 0-38 microns 43.0 98.0 (calc) 31.1 98.0 38-53 microns 19.6 96.7 (calc) 16.8 96.7 53-75 microns 20.2 95.3 (meas) 21.0 95.3 75-106 microns 12.9 93.4 (calc) 18.7 93.4 106-150 microns 3.9 90.6 (calc) 10.0 90.6 150-212 microns 0.4 86.7 (calc) 2.2 86.7

Significant difference is observed between the liberability and the grindability (see Figure 9 and Figure 10). For example, grindability indicates that two high grade samples, 8F (fine grained) and 8C (coarse grained), require quite different grinding energy but when the mineral liberation is set as a target the ores appear to be very similar. Because the main purpose of grinding is to achieve the required liberation the liberability information will clearly tie the technical and economical ways in order to utilize the resource in an optimal manner. This has potential to change the plants in their operational principles from targeting a certain particle size to defined mineral liberation.

4.3Novel GCT- The Geometallurgical comminution test Based on the work done a small-scale test method for mapping variation of ore comminution properties in geometallurgy was established and the flow chart is shown in Figure 11. The test includes a separate crushability stage very similar to JKMRC test (Kojovic et al., 2010). For the crushability the procedure is optional and preliminary and must be further tested.

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8) Grinding test

9) Sizing

1.) Sample

2) Sample prep

3) 1 pass crushing

4) Sizing

4A) Report crushability index as size reduction ratio

5) Crushing 100 % < 3.35 mm

6) Splitting

7) Particle size analysis

10) Report P80, PSD

B1) Take one size fraction

B 2) Liberation analysis

B 3) Report Lib % and AI

A 1) Sample prep for other assays

A 2) Chemical assay

A 3) XRD

A 4) Modal mineralogy

Figure 11. Flow chart of the GCT – the geometallurgical test for comminution.

The test is designed for drill core samples and each sample is ideally a 30 cm long piece of a drill core half (step 1, Figure 11). In magnetite ore this equals to about 500 g sample. In the sample preparation stage (step 2) the drill core is cut to about 2x2 cm pieces. The pieces are then crushed by the laboratory jaw crusher at closed side setting 3.35 mm (step 3). If also crushability is to be determined then after one pass crushing, the crusher product is sized (step 4). Otherwise the crusher product is split with 3.35 mm sieve and oversize is crushed again (step 5). This is continued until all material passes the 3.35 mm sieve. This should give a product with 80% passing close to 1 mm. The crushed sample is split to 2-3 parts (step 6). One is used for sieving to obtain F80 (step 7). One part is used for the grinding test (step 8). The grinding test is performed as described in chapter 4. When using the Capco jar mill 337SS the sample size is 220 g and the ball charge is 1.3 kg with diameters given in Table 4. Grinding time of 17 min. is suggested but should be verified for each ore body separately. With these conditions electrical energy meter is not required because the reading will be identical in all the tests. The target P80 should align with the Bond tests and therefore some other grinding time might be used. But the idea of the test is to use a fixed time for a given ore body and geometallurgical program. (step 9) After grinding, the material is sized and the results are calculated: 80% passing particle size, estimated Bond work index and the Rosin-Rammler distribution parameters. One size fraction slightly coarser to the expected liberation size is used to determine the degree of mineral liberation and mineral associations. The size distribution is determined using a sieve series form 3.35 mm down to 38 μm following the 2 series.

The comminution test designed is suited to the normal sample preparation scheme used for chemical assays. The crusher product can be split and one part can be used for determining the bulk chemical composition of the sample e.g. with X-ray fluorescence.


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For the modal mineralogy an element to mineral conversion method can be applied (Lund et al., 2013, Whiten, 2007) but one may need to use additional techniques like X-ray diffraction (A2, Lamberg et al. 2013; Parian and Lamberg, 2013)) and SEM based automated mineralogy (A3).

In the grinding test (step 8) the used sample size is defined by mass rather than volume as in the Bond test. Therefore the volume of the sample can be significantly varying in e.g. massive sulphide and iron ores. However, this is considered as one part of material properties in this methodology.

The outcome of the test results when combined with chemical assays are then:

A. Chemical composition of the sample B. Crushability index as a reduction ratio (F80/P80) C. Grindability index as P80 and calculated BWI D. Degree of liberation for the key minerals and their association indices

(Lamberg et al. 2012; Lund, 2013) E. Modal mineralogy F. Liberability curves (Figure 10 and Figure 12)

To be cost effective within the geometallurgical program one might come to a solution where chemical assays are done for all samples, crushability and grindability for 50% of samples and liberation analysis for 10% of samples.

1) Experimental data1.1 Feed particle size1.2 Estimated Bond work index (W)1.3 Particle size distribution the test product (P80, Rosin-Rammler parameters)1.4 ) Degree of liberation of one key size fraction

2) Estimate liberation by size

3) Estimate liberation by size

2.1 Estimate the degree of liberation in each size fraction assuming linear relationship between the degree of liberation and particle size. Assume that at 0 point particle size liberation is 100 %.

3.1 Take new energy (E)3.2 Using Bond formula calculate P803.3 Particle size distribution the test product3.4 Using Rosin-Rammler equation to calculate full particle size distribution3.5 ) Calculate the degree of liberation in the bulk sample using new particle size distribution (3.2) and the degree of liberation by size (2.1)

Figure 12. Flow chart to calculate particle size distribution and degree of liberation for any given grinding energy.

5. Discussion The developed test method aims to characterize the essential comminution properties of small samples in a single (combined) test. This is an ambitious goal since most of the geometallurgical programs use different tests for different particle sizes. It is common to do separate characterization tests for crushing, SAG grinding and ball mill grinding (e.g.

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Bulled and Lozano, 2009; Bergholtz and Schreder, 2004; Flores et al., 2005; Keeney et al 2011; Montoya et al., 2011; Harbort et al. 2013). Even though the Bond work index generally speaking has a positive correlation with SAG grindability indexes like A*b (e.g. Bulled and Lozano, 2009) the difference is so significant that it is rare to use the Bond test only as an estimate for the full grindability in geometallurgical programs (Oyarzún and Arévalo, 2011; Philander and Rozendaal, 2011b). Vatandoost (2009, 2010) developed petrophysical methods to be used for proxies for comminution characterization. This approach is very practical for geometallurgical mapping but it misses important information about mineral liberation.

In geometallurgical programs comminution characterization aims to provide a reliable model to be used to forecast plant throughput. As the comminution circuits consists of several different type of comminution units like crushers, SAG mills and ball mills also the models must be capable in to treat these units separately but in a circuit. Parameters like scat handling (e.g. does the circuit includes a pebble crusher), transfer size between the SAG and the ball mill and handling of slimes may be more important for the throughput than the actual grindability. This addresses that the methodology developed here can’t provide all this important information needed for reliable forecasting. Rather the developed test is designed to be used in early project stages for identification of variability in the comminution properties. This information is to be used in geometallurgical domaining. After this the sampling and testing can be done in larger scale to economically and efficiently serve circuit design, sizing of the unit operations and to model and simulate the throughput. This ensures the quality of the process as circuit configurations are based on material properties and their variations as given by the geometallurgical program.

Linking of the liberation and comminution characteristics in geometallurgy is not very common. Philander and Rozendaal (2011a, 2011b) compared grindability and liberation of zircon at the Namakwa Sands mine resulting in a successful expansion program. Instead many different kinds of liberation models have been developed before geometallurgy has come up as a concept (e.g. Gay, 1999; King and Schneider, 1998; King, 1979; Wei and Gay, 1999, Gay 2004). Most of the liberation models require a good quality textural picture to start with. This is a limitation when thinking of geometallurgical programs. Scanning drill holes with pixel sizes of some microns would be required and with currently available techniques this is impossible or at least very slow and costly (Leichliter et al. 2012; Hunt et al., 2008). If such a picture is available then there are additional limitations like that the existing liberation models assume non-preferential breakage, that they can be used only in binary systems (i.e. two minerals: valuable and others) or that they require an ore-specific Kernel function (King, 1967).

The methodology proposed here requires validation for each deposit to prove that the assumptions lying behind the test do hold. These are that (i) the bulk liberation can be estimated only using one size fraction and that (ii) the assumption that liberation within a narrow size fractions is constant regardless of particle size distribution of the bulk material (Vizcarra et al. 2010). How to combine liberation and size reduction in the comminution models is also an open issue. Current crusher and grinding models provide


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forecast on particle size distribution, grinding energy and throughput dependency but they are not capable to forecast how the grade varies by size neither the liberation distribution of the products. Before the developed test method can be linked with process simulations reliable mineral by size and mineral liberation models on comminution needs to be developed.

The question how much energy is needed to achieve required liberation when the feed composition (texture) is changing is crucial and important for production planning. An interesting observation from this study is that there is a significant difference between grindability and liberability at the same grinding energy when the mineral texture is different. It implies that domaining an ore body based on grindability (hardness) may mislead the ore classification and may result in ineffective resource utilization. Therefore it is important to collect information on mineral liberation, grinding energy and particle size relationships before the geometallurgical domains are defined.

Mineral liberation may not be sufficient information because the associating minerals and the type of particles is important for downstream processes in order to produce a salable product. Lamberg and Lund (2012) and Lund (2013) developed a methodology on how to incorporate full liberation information into the geometallurgical model but the concept was missing grindability. The developed methodology has potential to fill this gap. Comminution mechanisms and texture characteristics should be seen as drivers for the prediction of the liberation properties of minerals. The possibility of using different breakage mechanisms on different mineral texture has a potential to improve resource efficiency.

6. Summary and Conclusions Comminution test methods commonly used in geometallurgy require large samples and are time demanding and therefore expensive. Small scale comminution tests are needed to be applied early in the ore characterization for collecting information on the variability of crushability and grindability for proper geometallurgical domaining. A review of existing rock fracture testing showed that none of the available methods fulfills the criteria set for proper geometallurgical testing. The most promising ones were found to be small scale Bond ball mill test, instrumented drop weight test and rotary breakage tester (RBT).

The Bond grindability test was scaled down to use about 220 g of sample and it was changed to a single pass. The work index calculated from experimental results by small ball mill agrees well with Bond work indices. The developed test method was complemented with a crushability test and with mineral liberation measurements on one selected size fraction in order to establish quantitative information about the relation between grindability and mineral liberation, i.e. liberability curves.

The developed test (GCT) makes possible to use small sample amount and to do about 10 times more measurements in given time compared to traditional Bond ball mill test. Preliminary results from the Malmberget case study show that the comminution properties are related to modal mineralogy and mineral texture (i.e. grain size of

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magnetite). A new finding is that samples with similar grindability and modal mineralogy may have different liberability.

The developed method is still a prototype and before applying it routinely in geometallurgical programs the following studies are suggested:

Study how accurate the estimated Bond work index is compared to full scale Bond grindability test using different ore samples.

Study whether the crushability test can be used for estimating SAG characterization parameters like A*b.

Study whether the degree of liberation can be estimated reliably for the bulk samples based on one size fraction also with other ore types.

Study whether the observation and assumption that liberation in narrow size fractions is independent of overall particle size distribution holds with different ore types.

Study how the mineral grade varies by size and how large this effect is for evaluating the degree of liberation for full sample based on analysis on one size fraction.

Study how grindability and liberation information can be combined in process simulations using the concept proposed by Lamberg and Lund (2012) and Lund (2013).

7. Acknowledgements The financial support of the CAMM Centre of Advanced Mining and Metallurgy at Luleå University of Technology is appreciated. We are grateful to Kari Niiranen, Therese Lindberg, Charlotte Mattsby (LKAB) Cecilia Lund, Ulf Nordström, Pierre-Henri Koch, Mehdi Amiri Parian, Friederike Minz, Bertil Pålsson, Alireza Javadi Nooshabadi (Luleå University of Technology), Kurt Aasly and Ingjerd Bunkholt (Norwegian University of Science and Technology) for their advice and support.

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Lund, C., Lamberg, P., and Lindberg, T., 2013.Practical way to quantify minerals from chemical assays at Malmberget iron ore operations – An important tool for the geometallurgical program. Minerals Engineering, 49, pp. 7–16.

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Paper III

Development and experimental validation of the Geometallurgical Comminution Test (GCT) Abdul Mwanga, Jan Rosenkranz and Pertti Lamberg Submitted to Journal of Minerals Engineering 2016

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Development and experimental validation of theGeometallurgical Comminution Test (GCT)

Abdul Mwanga , Jan Rosenkranz, Pertti Lamberg

Minerals and Metallurgical Engineering Laboratory, Luleå University of Technology,SE 971 87 Luleå, Sweden

*) Corresponding author, e mail: [email protected]

Abstract

Based on the requirements and available sample amounts in geometallurgical studiesof ore variability, a small scale batch grindability test has been developed, theGeometallurgical Comminution Test (GCT). The test requires 220 g of sample materialand can be conducted within 2.5 to 3 hours. Test results are evaluated using amodified Bond equation together with a linear correlation factor. The test andevaluation method have been validated against several ore types.

Keywords: Geometallurgy, comminution test, grindability, small scale test

1 Introduction

Time and accuracy of measurements of ore comminution behavior are most relevantwhen setting up an appropriate geometallurgical program, e.g. for predicting thethroughput of a mineral beneficiation plant for varying ore properties. Establishedcomminution test methods require comparatively large amounts of sample materialand are time demanding and therefore costly [Mwanga, 2015a]. Particularly within thegeometallurgical mapping of mineral deposits, where the number of samples requiredfor realistic variability testing of an ore body is relatively large (typically, the number ofsamples required for realistic variability testing of an ore body is larger than 1000[Walters et.al., 2006]) and, in turn, the size of the samples is usually very limited (e.g.to drill core sections or parts of drill cores) efficient comminution test methods arerequired.

Test methods used for characterizing ore comminution behavior range from rockmechanical tests over various particle breakage tests to bench scale grindability tests.The latter group of tests includes the well known Bond test method [Bond, 1952;Bond, 1961], which is still the most used approach in the design and analysis ofcomminution circuits. Grindability tests, while having certain limitations, are wellestablished and provide a huge amount of reference data. In the context ofgeometallurgical modelling, the Bond formula, which links comminution energy and


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resulting particle size reduction with capacity, provides the advantage of a short cutmethod for modeling of comminution processes.

The Bond test applies a standardized ball mill of 305 mm (12 inch), both in diameterand length, with a grinding media charge of certain size distribution and operated at adefined speed. The sample amount is defined by the bulk volume of 0.7 liters,consisting of particles smaller than 3.35 mm. The test is conducted as a dry lockedcycle test with sieving of the mill product after each stage. Particles finer than thetarget product size are replaced by an equal amount of fresh feed material, andgrinding times are varied in order to reach a simulated circulating load of 250 % atsteady state. For reaching this point usually seven to eight grinding cycles arenecessary that require samples of approximately 10 kg. After determination of thefeed and circuit product particle size distribution, the Bond work index is thencalculated using Bond’s empirical equation:

F,P,

.B

.i

Bond,i

xxGP

..W

8080

820230 11

45411

(1)

where

iP : Target screen size in the test, in μm

BG : Grindability, gram per number of revolutions passing iP

P,x80 : 80% passing size of the mill product, in μm

F,x80 : 80% passing size of the mill feed, in μm

Besides its long processing time and the significant sample mass requirement, is hasalso to be considered that the Bond test is subject to some uncertainty related to thevariable number of grinding cycles for reaching steady state, the circumstance thatenergy is not really measured, and its susceptibility to procedural error due to thehuman factor in testing.

Several suggestions have been made over years to modify the Bond test in order tominimize the timely effort and sample amount needed while keeping the requiredlevel of reliability. More particularly, this involved (i) the development of single pass orbatch comminution tests instead of simulating a locked cycle grinding process, (ii) theutilization of smaller grinding mills together with the original Bond test procedure, (iii)or the reduction of the number of test cycles based on certain assumptions and/orcomplemented by simulations for determining an estimate of the Bond ball mill

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grindability. Further, it can be mentioned that also tests for wet grinding weredeveloped to overcome the problems related to very fine dry grinding [Tüzün, 2001].

Berry and Bruce [1966] used an ordinary laboratory mill for comparing the wetgrinding of two ore samples, where one was a reference sample of known Bond workindex. For identical sample weights of 2 kg, grinding time and operating conditionsthey applied Bond’s Third Law of Comminution for calculating an estimate for the Bondball mill index of the unknown ore.

Smith and Lee used an earlier version of Bond’s empirical formula (eq. 4) forcalculating the work index based on the batch test grindability. Dry batch tests weredone in a ball mill identical to the Bond test mill. Based on grinding tests for differenttarget particle sizes and minerals, the grindability data received from Bond test andbatch test were compared.

A simple batch test for wet and dry grinding was developed by Outokumpu [Niitti,1970]. For this purpose a laboratory mill, the so called Mergan mill, was constructedhaving smaller dimensions compared to the Bond mill. The mill was equipped withvariable speed and a mechanical torque measurement that was integrated in the milldrive. The test conditions differed from the Bond test in terms of sample amount (5 kg)and initial particle size distribution, as well as with respect to the mill filling grade.Batch grindability was calculated from the measured energy consumption.

Yap et al. [1982] used a laboratory batch ball mill for a wet batch test to approximatethe Bond work index, also known as the Anaconda simplified method. In the test ca.2kg of sample material were used in a ball mill of 251 mm in diameter. The receivedbatch work index was assumed to be proportional to the Bond index for a constanttarget particle size of 100 μm.

Nematollahi [1994] developed a test method similar to the original Bond testprocedure but using a down scaled ball mill. By reducing the diameter and length ofthe so called New Size Ball Mill (NSBM) by one third compared to the original Bondmill, the required sample amount for locked cycle grindability tests could be reducedfrom 10 kg to 3 kg. The Bond equation as given in eq (1) was adjusted accordingly.

Also for the SGS Modbond grindability test an open circuit dry batch test was used forestimating the Bond work index after calibration against the standard Bond ball milltest [Kosick et al., 1999]. The test itself involved the Bond ball mill and reducedsamples sizes of 1.2 kg pre crushed to minus 3.35 mm.

Kapur [1970] developed a stage wise simulation of the Bond grinding cycles.Grindability was calculated and used in an empirical model for estimating the workindex. Later, Karra [1981] modified the approach in order to allow for larger amountsof feed material finer than the target particle size. Also Magdalinovica [1989] usedsimulation of the Bond test to reduce the number of test cycles needed. Based on afirst order kinetic model a grinding rate constant was determined and then used to


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calculate the grindability from only 2 cycles corresponding to ca 5 kg of sample.Opposite to Kapur who used the target screen size, measured particle size distributionswere evaluated.

A shortened procedure for the Bond grindability test was also suggested by Kojovic[2012]. The so called JK Bond Ball Mill Lite Test (JK BBL) is a locked cycle grindabilitytest conducted using the standard Bond laboratory ball mill. As distinct to the Bondgrindability test, the test consumes approximately 2.5 kg of sample, i.e. half of themass needed in the full test, due a reduced number of two to three locked cycles. The80% passing is either predicted simply from the closing screen size or measured bythree sieves.

As an alternative to testing, correlations of the Bond index with sample propertieshave been investigated. Vatandoost [2010], for instance, used petrophysical data frommulti sensor drill core logging were used to correlate Bond grindability and work indexwith density, magnetic susceptibility and seismic wave parameters. He showed thatthe Bond mill work index of an Australian copper gold ore could be predicted.

From the analysis of the different test modifications and their performanceparameters it can be concluded that an efficient and at the same time small scalecomminution test is still missing for geometallurgical testing with very small samples.Therefore, a novel batch grindability test, the Geometallurgical Comminution Test(GCT), is suggested here, which is characterized by the following requirements:

Minimize the necessary sample amount to what is available in geometallurgicaltesting,

Significantly reduce the processing time and related costs, Exclude or minimize process related errors during test conduct, Use a small and inexpensive standard laboratory mill.

2 Description of the GCT test method

In order to provide a comminution test method suitable to analyzing even small drillcore samples the GCT – Geometallurgical Comminution Test programme has beendeveloped at Luleå University of Technology. The entire test programme involvescrushability and grindability test work as well as mineralogical analyses for both entire,samples as well as selected sieve fractions [Mwanga, 2015b]. Results received from theGCT test programme comprise modal mineralogy, particle size distributions, workindices and mineral liberation analysis.

As part of the test procedure a small scale batch grindability test has been defined as ashortcut test method for estimating the Bond ball mill work index. For this test a smalllaboratory ball mill is used that has a volume of ca 1.4 liters only. The mill is running onthe same percentage of critical speed as the original Bond mill, thereby fulfilling thecriteria of kinematic similarity as described by a constant Froude number [Steiner,

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1996]. Also the volume fraction of mill volume occupied by the ball charge has beenkept similar to the original Bond mill. Grinding media is in the same size range as in theBond test, while the number of steel balls is adjusted to the mill size. Preliminary testswere done with one magnetite ore sample but were limited in their validity due to thefact that a coherent methodical framework for test conduct and evaluation of resultswas missing [Mwanga et al., 2105b].

The suggested batch grindability test involves the following steps:

Sample preparation: Preparation of 220 g sample material, pre crushed in alaboratory jaw crusher to 100% passing 3.35 mm. The chosen sample size isadapted to the size of drill core sections or fractions of drill cores and even allowingfor repetitions with smaller samples. To simplify sample preparation and energymeasurements, the test uses a constant sample mass as it is the case also for othergrindability test, for instance in the Hardgrove test or the Zeisel test [Böhm et al.,2015].

Test execution: Dry batch grinding test of the sample is done using cumulatively 2,5, 10, 17 and 25 minutes grinding times. After each grinding time sample is drysieved for particle size analysis and returned to the mill for further grinding.

Particle size: The particle size distributions are numerically evaluated for the 80%passing size. Additionally the sample amount below the target product size isdetermined corresponding to the grindability analysis within the Bond procedure.

Energy for grinding: Recording of the gross electrical power draw during thegrinding test is done using a conventional energy meter. To overcome the limitedprecision of the meter an energy time relation has been established for theexperimental setup. The mechanical power provided to the mill is back calculatedusing efficiency data for both electrical engine and mechanical drive [Mwanga etal., 2016]. The calculation takes into consideration that the mill is running atreduced speed and load. As the test is run at constant sample weight and millparameters (number of revolutions, grinding media), the energy supplied to themill per unit time is assumed to be constant.

Evaluation: Experimental data evaluation and GCT work index calculation asdescribed in the following paragraphs using spreadsheet calculation.

The evaluation of the grinding test results is then based on the Bond formula forcalculating the specific energy for grinding W:

FPi xx

WW,80,80

1010 (2)

with


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iW : Work index, in kWh/t

Px ,80 : 80% passing size of the mill product, in μm

Fx ,80 : 80% passing size of the mill feed, in μm

Potential differences in the shape of the product particle size distribution compared toa locked cycle test with screen are neglected in the calculation of the Px ,80 value.

Further, for a given feed size the change in specific grinding energy is proportional tothe reciprocal of the square root of the Px ,80 value:

1010 80

80

P,

P,

xWk

xkW (3)

where

k : Constant, in kWh/t

The proportionality constant k divided by 10 is denoted as the GCT work index and canbe determined using the several data pairs of W and Px ,80 for the different grinding

times. Like the Bond work index, the GCT work index is a material dependentparameter.

The suggested approach to data evaluation takes up the earlier formulation of theBond equation, where energy is expressed by gram per number of mill revolutionspassing the target particle size:

1001611 820

i.

BBond,i

PG

.W (4)

Figure 1 shows the typical linear course of curve that is described by Equation (3) foran iron oxide ore sample after transformation of the x axis. The straight line is notcontinuing through the origin but intersects with the y axis in the negative intercept.This can be interpreted as an infinitely large starting particle size. The selected timesteps provide a larger resolution in the beginning of the test. By calculating the slopefrom several points of time, a timely averaged value is received for k and the GCT workindex, respectively. The latter is important with respect to those cases wheredeviations from the linear course can be observed.

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The derived GCT work indices are higher than the Bond work index from the standardtest. This might be explained by the different evaluation methods but also by the lowerenergy intensity in the small ball mill. By introducing appropriate correction factors,the GCT work index can then be correlated to the original Bond work index based oncommon target product particle size of 106 μm, which can be regarded as the finestsize for dry grinding, compare section 4.

0

10

20

30

40

50

60

70

0,03 0,035 0,04 0,045 0,05 0,055 0,06 0,065 0,07

Grosss

pecific

energy

[kWh/t]


2 min.

5 min.

10 min.

17 min.

25 min.

Figure 2: Linear relation between specific energy and mill product size (magnetite sample).

3 Experimental validation

For validation of the small scale grindability test procedure and the development of acorrelation between the GCT work index and the standard Bond work index, grindingtests were carried out with fifteen samples from different types of deposits in theNordic countries having wide mineralogical variations. For each sample the full Bondgrindability test was conducted following the Bond standard test procedure and resultsfrom that were compared with the GCT grindability test. The target product size in allthe tests was kept constant at 106 μm (150 mesh) which was related to the liberationsize of most mineral samples.


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4.4Test equipment and procedure

The small scale grindability test was performed by using a Capco jar mill, type 337SS,with a steel ball charge of 1.3 kg and an average ball diameter of 28 mm. The inner milldiameter was 115 mm. The mill speed was set to 91% of critical speed (114 rpm) usingvoltage control. Figure 2 shows the setup with the small ball mill as used in the test.

Figure 3: Small scale laboratory mill used in the tests.

Full Bond grindability tests were done in a standard ball mill with an internal diameterof 305 mm and a length of 305 mm. Ball charge and ball size distribution as well as millspeed followed the original Bond procedure of locked cycle tests [Bond, 1961].

4.5Test material

Different mineral samples were collected from mines in Sweden, Norway and Finlandthat can be categorized into three major groups:

The first category was a group of oxide ores including magnetite and hematitefrom iron ore deposits in Northern Sweden. Originally, these ore samples werethe starting point for developing the GCT and main focus when analyzing orecomminution behavior in the geometallurgical context, i.e. magnetitedominated ore (FAR) and hematite dominated ore (HAR) were collected afterpre concentration in the cobbing plant in Malmberget and used as referencesamples during the entire investigation. Composite magnetite (MGT) andhematite (HMT) ore samples were received via belt cut from the processingplant in Malmberget and introduced to the investigation plan to study theeffect of sample variations in geometallurgical comminution testing. The

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samples from the Kiruna iron field ore deposit is known as magnetite apatitedeposit having fine grained magnetite. The mineral include besides _Fe oxidesactinolite, K feldspar, albite, phlogopite, chlorite, titanite, quartz, and talc[Niiranen, 2015]. The texture characteristics of magnetite sample KA3 aresimple and distinct from Malmberget samples. The Kiruna sample represents abelt cut of SAG mill feed material (KA3).

The second category were sulphide ore samples which comprise gold deposits,porphyry copper and massive sulphide deposits from Boliden mine sites (KSMand RSM). Other samples falling into this category were dominated massivezinc (RS1) and massive chalcopyrite pyrite (RS2) from another ore deposit inthe Skellefteå area. The occurrences of the massive sulphide are associatedwith felsic pyroclastic rocks, quartz porphyries and minor mafic volcanites[Weihed et al., 1992]. Porphyry copper deposits from the Skellefteå fieldconsist of large rounded sub grained quartz phenocrysts with minor biotite andchlorite minerals. Samples RS1 and RS2 have variations in distribution of Sbbearing minerals. A gold quartz mineralization sample from Västerbotten (BOT)was also included into the investigation. Within this category even a blackschist Ni Nickel sample (NIT) from Talvivaara in Eastern Finland was included asa special type of sulphide deposit. The sample contained pyrrhotite, pyrite,sphalerite, pentlandite, violarite, chalcopyrite and graphite. The main silicaminerals were quartz, mica, anorthite and microcline [Riekkola Vanhanen,2010]. The other sample from Sotkamo in Finland (AGF) contained silverminerals with a different mineralogy compared to the Talvivaara deposit. Themain mineral in the AGF sample was quartzite, which was relatively coarsegrained compared to the fine grained occurring in NIT.

The third category was a group of non metallic minerals that included purequartz, calcite and olivine. The quartz and calcite sample were received fromtwo different mines in Norway. The quartz was received from Elkem quartzitedeposit having a simple mineralogy. The calcite sample from Brønnøysund inNorthern Norway contained coarse grained calcite marble [Olden, 2015] as amajor phase with inclusions of silicates and sulphide minerals. Graphite andsilicates were the main contaminants for the quality of the calcite product.Further, an olivine sample from also Norway was used in the investigation.Because of its natural properties (low density and high magnesium content) theolivine is used as an additive in metallurgical processing.

A summary of the sample description is given in Table 1.


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Table 2: Samples used for test validation

No. Identifier Description Main minerals Minorminerals

1 FAR Processed magnetite sample, Malmberget,Sweden

Magnetite Biotite, apatite

2 MGT Belt cut magnetite sample, Malmberget,Sweden

Magnetite Biotite, albiteand apatite

3 HAR Processed hematite sample, Malmberget,Sweden

Hematite Biotite,actinolite

4 HMT Belt cut hematite sample, Malmberget,Sweden

Hematite Magnetite,biotite, quartzand apatite

5 KA3 Magnetite sample, Kiruna, Sweden Magnetite Feldspar6 KSM Complex copper ore, Boliden, Sweden Quartzite Chalcopyrite7 RSM Complex copper ore, Boliden, Sweden Quartzite Chalcopyrite,

pyrite andsphalerite

8 RS1 Rockliden massive zinc sulphide samples,Sweden

Sphalerite Quartzite

9 RS2 Rockliden massive chalcopyrite pyrite,Sweden

Chalcopyritepyrite

Quartzite

10 CAL Calcite sample, Brønnøysund, Norway Calcite11 AGF Silver gold sample, Finland Quartz sphalerite and

galena12 BAU Quartzite dominating mineral gold sample,

SwedenQuartz Pyrite

13 QRZ Quartz sample Quartz14 OLI Olivine sample Olivine15 NIT Black schist nickel sample, Talvivaara,

FinlandQuartz Pentlandite,

chalcopyriteand sphalerite

In Table 2 more sample properties are provided for further characterization. Mohshardness and density were calculated as weighted averaged values based on modalmineralogy. The mineral composition of the samples was received from XRD analysisor from XRF results used in combination with a numerical element to mineralconversion, respectively. The average grain sizes of the main minerals in each samplewere determined by means of optical microscopy.

Table 3: Sample properties based on mineralogical analysis

No. Identifier HardnessMohs [ ]

Density[g/cm3]

Grain size[μm], mainmineral

1 FAR 6.51 5.10 5002 MGT 6.20 4.84 3503 HAR 6.57 4.75 6004 HMT 6.47 4.95 8005 KA3 6.30 4.82 1506 KSM 1) 1) 5007 RSM 6.64 3.19 250

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8 RS1 6.30 2.93 2009 RS2 6.54 2.82 20010 CAL 3.00 2.71 150011 AGF 1) 1) 10012 BAU 6.99 2.65 50013 QRZ 7.00 2.62 30014 OLI 6.75 3.32 60015 NIT 6.89 3.12 301) Not available

5 Results from test work and discussion

5.1 Analysis of the experimental data

In a first step, the grinding tests were analyzed with respect to the grinding progressand in order to exclude possible anomalies. Figure 3 shows the results from the smallscale grinding tests for all the 15 samples in terms of material retained on the productscreen at the target size 106 μm. The time intervals were according to the suggestedgrinding times for the GCT.

It can be seen that all the grinding curves were monotonously decreasing withincreasing within the grinding time, i.e. none of the mineral samples showedindications for overgrinding or agglomeration and coating effects during the test.Comparing with the original Bond tests, the GCT grinding curves were running belowthe curves obtained with the large mill, thus indicating lower energy intensity.

10

20

30

40

50

60

70

80

90

100

0 5 10 15 20 25 30

Ret

aine

d m

ater

ial o

n 10

6 μm

scre

en (%

)


FAR

Mgt

HAR

Hmt

KA3

KSM

RSM

RLS1

RLS2

CAL

AGF

BAU

QRZ

OLI

NIT

Figure 4: Grinding curves for all samples, target size 106 μm.

Further, the linear relation between energy for grinding and the 80% passing productparticle size was examined. Figure 4 depicts the results for all samples analogous toFigure 1. The majority of samples directly follow the assumed linearity. In some cases,


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the linearity develops after an initial phase. This is particularly pronounced in the caseof the NIT sample from Finland, where significant grinding action is taking place onlyafter 17 minutes. Accordingly, the suggested number of time steps was extended inthis case.

0

20

40

60

80

100

120

140

160

180

0.02 0.04 0.06 0.08 0.1 0.12

Gro

ss sp

ecifi

c en

ergy

(Kw

h/t)


FARMGTHARHMTKA3KSMRSMRS1RS2CALAGFBAUQrtzOLINIT

Figure 5: Check for linear relation specific energy vs. mill product size.

5.2 Establishing a correlation between the work indices

Table 3 summarizes the work indices received from the two grindability tests. As anestimate of the strength of the relationship between linear slope model and themeasured data the coefficients of determination are provided.

Table 4: Summary of work indices

No. Identifier 80% passingsize feed[μm]

Slope factor[ ]

Coefficient ofdetermination

[ ]

GCT workindex

[kWh/t]

Bond workindex

[kWh/t]1 FAR 1024.0 1601.51 0.9796 160.15 16.712 MGT 1309.9 1580.21 0.9664 158.02 16.623 HAR 880.8 1955.31 0.9934 195.53 20.364 HMT 1410.7 1828.80 0.9835 182.88 17.105 KA3 1832.2 814.03 0.9124 81.40 7.346 KSM 1806.8 1286.88 0.9779 128.69 12.437 RSM 2092.5 1216.84 0.9433 121.68 11.228 RS1 2202.1 657.97 0.9691 65.80 6.309 RS2 2190.8 677.97 0.9731 67.80 7.2110 CAL 2005.0 920.90 0.9796 92.09 7.7011 AGF 1868.6 799.00 0.9964 79.90 7.9012 BAU 2172.3 1597.86 0.8956 159.79 14.9413 QRZ 1874.8 1068.95 0.8790 106.89 15.0914 OLI 2172.3 2995.02 0.9948 299.50 25.6915 NIT 2233.8 1933.15 0.9944 193.31 15.45

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Comparing the results from the two grindability tests revealed that there is a linearrelationship between the work indices. When taking into account the geometric scalingfactor between small mill and Bond mill and a correction of the GCT work indices formill drive and engine efficiency, a remaining linear correlation factor of 4.0 can bederived from the experimental data. The model for estimating the Bond work indexfrom GCT test data is then given by:

411GCT,iBondestimated,i WW (5)

where

Mill drive and engine efficiency, = 0.64

Geometric scaling factor, = 2.65

Figure 5 shows the measured Bond work indices versus the estimated (calculated)work indices received from the GCT, confirming the linear correlation assumed in themodel. For the metal ore samples, the relative error between the two values waswithin a range of 0.70% to maximal 8.8%, with an average of 5.1%. This is in the samerange as reported in literature for abbreviated Bond test of 2 to 3 grinding cycles whilethe experimental variation of the full Bond test is denoted with ±3.5%.

The three samples of industrial minerals, however, showed larger deviations.Complementing the tests with these samples with smaller sample mass to compensatefor the lower density did not show significant differences. Also, some of the metal oresamples had densities in the same range. From that it has to be concluded that a morecomplex dependency on texture and mineralogy is controlling the comminutionbehavior. The estimation of the Bond index could be improved by adjusting the linearcorrelation factor or by introducing another model parameter in equation (5).

The results received from the tests were also compared with the mineral compositionand related properties of the samples as described in Table 2. The deviation betweenoriginal Bond index and the estimate from the GCT showed certain patterns towardsdensity and grain size. However, the number of the samples and their variety did notallow describing the dependency in a quantitative way.


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1,0

10,0

1,0 10,0

Bond

workinde

x[kWh/t

Calculated work index from GCT [kWh/t]

Figure 6: Comparison between standard Bond test and GCT results after calculation.

The test can be further optimized with respect to timely effort by reducing the numberof time steps. As discussed above, this is much depending on the individual sample.This can involve shorter tests as in the case of FAR (see Figure 1), or even longergrinding as for the NIT sample. When applying the test to a group of similar samples, asit is the case when testing for the variability of an ore body, further adjustment of thegrinding time is possible by identifying shorter time periods for describing the linearcorrelation.

In order to assess the repeatability of the measurement by GCT, at least threeexperiments for each sample were performed. Based on the measured particle sizedistributions and the interpolation for determining the 80% passing particle size, therelative error was approximately 1.4%. Otherwise, the GCT testing procedure involveserrors from sample preparations, i.e. splitting and weighing, and from measuringspecific grinding energy. All in all, the experimental results could be reproduced withingood precision.

However, looking at the entire chain from sampling over testing to geometallurgicalmodeling it must be concluded that the whole procedure is very much determined bythe quality of the sample selection. I.e., errors within sampling affectingrepresentativeness cannot be compensated by higher accuracy of the test and model.

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6 Conclusions

A single pass grindability test for geometallurgical testing has been developed andvalidated against full Bond grindability tests for fifteen different ore samples. The testresults from the GCT reveal that the method itself is precise and capable ofreproducing a work index. The suggested evaluation method for estimating the Bondwork index from the GCT work index is possible with a relative error of on average5.1%. Compared to the full Bond grindability test the following advantages can behighlighted:

The test uses a very small roller driven laboratory ball mill in conjunction withan ordinary energy meter.

The test involves a sequence of up 5 grinding tests with in total 25 min. grindingtime. Together with sample preparation and sieving the entire test can beconducted in 2.5 to 3 hours.

The required sample size is only 220 g, i.e. for the first time crushed samplesand parts of drill cores in the range of some hundred grams can be tested forgrindability.

The authors want to point out that the suggested test method is not meant to replacethe standard Bond test. It is intended as a complementary approach when workingwith small scale samples as in the geometallurgical context.

7 Acknowledgements

The financial support of the CAMM Centre of Advanced Mining and Metallurgy at LuleåUniversity of Technology is gratefully acknowledged. Further, Mr. Erdogan Kol isacknowledged for the provision of the energy grinding time relation.

8 References

Berry, T.F., Bruce, R.W. (1966). A Simple Method of Determining the Grindability ofOres, Canadian Mining Journal, Vol. 87, pp. 63 65.

Böhm, A., Flachberger, H. (2006). Überblick über Methoden der Mahlbarkeitsprüfung,BHM, 151. Jg. (2006), Heft 6

Bond, F.C. (1952). The Third Theory of Comminution, Transactions of the AIME Min.Eng. 1952, 1983, pp. 484 494.

Bond, F.C. (1961). Crushing and grinding calculations, Br. Chem. Eng. 1961, 6, pp. 378385.

Kapur, P.C. (1970). Analysis of the Bond Grindability Test, Trans. IMM, Vol. 79, pp. C103 108.


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Karra, V.K. (1981). "Simulation of the Bond Grindability Test. CIM Bulletin, Vol. 74, No.827, pp.195 199.

Kojovic, T. and Walters, P. (2012). Development of the JK Bond Ball Lite Test (JK BBL),In: Proceedings of the GEOMET2012 International Seminar on Geometallurgy,Santiago, Chile, December 2012; pp. 46 47.

Kosick, G. and Bennett, C. (1999). The Value of Orebody Power Requirement Profilesfor SAG Circuit Design, In: Proceedings of the 31st Annual Meeting of the CanadianMineral Processors, Ottawa, Canada, January 1999; pp. 241 254.

Magdalinovica, N. (1989). Procedure for Rapid Determination of the Bond Work Index,International Journal of Mineral Processing 1989, 27, pp. 125 132.

Riekkola Vanhanen, M. (2010). Talvivaara Sotkamo Mine – bioleaching of apolymetallic nickel ore in subarctic climate. In: Proceedings 2010 of NovaBiotechnological, pp. 7 14.

Mwanga, A., Rosenkranz, J., Lamberg, P. (2015a). Testing of Ore ComminutionBehavior in the Geometallurgical Context: A Review, Minerals 5 (2015), pp. 276 297.

Mwanga, A., Lamberg, P., Rosenkranz, J. (2015b). Comminution test method usingsmall drill core samples, Minerals Engineering 72 (2015), pp. 129 139.

Mwanga, A., Rosenkranz, J., Lamberg, P., Kol, E. (2016). Reference manual for the GCT– Geometallurgical Comminution Test, Luleå University of Technology.

Nematollahi, H. (1994). New Size Laboratory Ball Mill for Bond Work IndexDetermination, Minerals Engineering 46 (1994), pp. 352 353.

Niiranen, K. (2015). Characterization of the Kiirunavaara Iron Ore Deposit for Mineralprocessing with a focus on the high silica ore type B2. Montanuniversität Leoben,Austria, 2015.

Niitti, T. (1970). Rapid Evaluation of Grindability by a Simple Batch test, In Proceedingsof the International Mineral Processing Congress, Prague, Czechoslovakia, 1–6 June1970; pp. 41 46.

Olden, B.I.(2015). The implications of sulphides in GCC feed and the potential for theirremoval during alkaline amine flotation. PhD thesis, Norwegian University of Scienceand Technology, Norway.

Steiner, H.J. (1996). Characterization of laboratory scale tumbling mills, InternationalJournal of Mineral Processing, 44 45 (1996), pp. 373 382.

Tavares, L.M.; de Carvalho, R.M.; Guerrero, J.C. (2012). Simulating the Bond rod millgrindability test, Minerals Engineering 26 (2012), pp. 99 101.

Tüzün, M.A. (2001). Wet Bond Mill Test, Minerals Engineering 14 (2001), pp. 369 373.

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Vatandoost, A. (2010). Petrophysical Characterization of Comminution Behavior, PhDthesis University of Tasmania, Australia.

Walters, S., Kojovic, T. (2006) Geometallurgical Mapping and Mine Modelling (GeMIII)–The way of the Future. Proceedings SAG2006 Conference, Vancouver, Vol IV, pp. 411425.

Weihed, P.; Bergman, J; Bergström, U. (1992). Metallogeny and tectonic evolution ofthe Early Proterozoic Skellefteå district, Northern Sweden. Precambrian Research, 58(1992), pp. 143 167.

Yap, R.F., Sepulveda, J.L., Jauregui, R. (1982). Determination of the Bond Work Indexusing an ordinary laboratory batch ball mill. In: Design and Installation of ComminutionCircuits, SME, 176 203.


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Paper IV

Comminution modeling using mineralogical properties of iron ores Abdul Mwanga, Mehdi Parian, Pertti Lamberg and Jan Rosenkranz

Submitted to Journal of Minerals Engineering 2016

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Comminution modeling using mineralogical properties of iron ores

A. Mwanga, M .Parian, P. Lamberg and J. Rosenkranz

Minerals and Metallurgical Engineering Laboratory

Luleå University of Technology, SE-971 87 Luleå, Sweden; E-mail: [email protected]

Abstract The objectives of comminution modeling are to reliably forecast the size and liberation distribution of mineral particles and the required comminution energy. The current state-of-the-art comminution models provide a calculation of particle size distribution, grinding energy and throughput dependency without a broad understanding of neither how the mineral grade varies by size nor the liberation distribution of the product. The underlying breakage mechanisms affect the liberation of mineral grains and are dependent on modal mineralogy and mineral texture (micro structure). It has also been a challenge to model comminution systems to predict the optimal energy and size for better mineral liberation because of the variability of the mineral particles properties i.e. grains arrangement and compositions. A detailed mineralogical study was carried out in order to broaden the understanding of the nature and distribution of comminuted particles in a ball mill product. Focusing on iron ore samples the study showed how the particle breakage rate decreases when the particles are reaching the grain size of a mineral grain. Below that size comminution does not increase mineral liberation and therefore in most of the cases passing over that boundary is only a waste of energy. The study involving iron ores from Malmberget and Kiruna, northern Sweden, showed that certain shortcuts can be applied to physically model the mineral liberation distribution of the particles in a ball mill based on the mineral grade-by-size pattern from a geometallurgical program. In Malmberget and Kiruna the mineral grade-by-size pattern is depending on the mineral distribution and grain size of gangue as well as magnetite or hematite minerals. A significant difference between mineral breakage of the same grade and gangue minerals can be observed.

1. Introduction Mineral liberation is the prerequisite for successful ore concentration. It should be regarded as a driver for energy efficient comminution and high quality production of final product in the extraction of minerals. In the flowsheet design, it is important to know the degree of liberation required for certain product quality with each technology alternatives. To select the process technology and flowsheet among different options requires knowledge on how grindability and corresponding mineral liberation varies within the ore body. Presumably the most optimal economic operation point is neither at fixed particle size distribution nor at fixed liberation degree. Increasing the degree of liberation of the mineral comes with a cost related to comminution energy and potential problems in fine particle separation. As this can cause a decrease in throughput it must come with an improvement in recovery. Instead liberability is a proper way to describe the multi-dimensional problem since it combines mineral liberation, grinding energy and particle size relationships (Mwanga et al. 2015). This requires efficient process model and parameters that predict liberation properties of mineral particles.


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Several models have been developed to describe the liberation properties of mineral particles by using texture and grade information (Wiegel and Li, 1967; Andrews and Mika, 1975; King 1979; Klimpel and Austin 1983; Schneider, 1995; Spencer and Sutherland, 2000; Gay, 2004a, Gay, 2004b; Stamboliadis, 2008; Lamberg and Lund, 2012). For example, King (1979) uses the Andrew-Mika diagram together with a kernel function to develop a model describing the correlation between the parent and progeny particle compositions. Most of the models use the texture and liberation information from particle images to quantitatively predict the degree of mineral liberation at any given particle size distribution. Most of the models assume random breakage of mineral particles, only in few cases non-random breakage is used. In these models the Andrew-Mika diagram is first used to describe the attainable region of mineral grade by size. By using conservation of mass suitable parameters are determined and integrated into a population balance model to forecast the liberation of minerals. It seems that non-random breakage (phase-boundary, liberation by detachment and boundary-region breakage) is difficult to apply and still not well examined.

Mineral texture is an essential ore property that affects the breakage and liberation properties of materials during comminution. As shown by many researchers, the challenge of using texture to quantitatively predict ore comminution behavior is to quantify the pattern that accounts for breakage of mineral grains during comminution (King and Schneider, 1998; Hsih and Wen, 1994; Gaudin, 1939; Gay, 1999). Despite the several studies in this field, linking the grain size (mineral texture) to the mineral breakage and liberation distribution has not come to an acceptable level. Simple evidence is that already the grade-by-size information is practically seldom included in the comminution models. However, without this information the higher level information, i.e. liberation distribution, is practically impossible to forecast.

This paper establishes and demonstrates a relationship between mineral grain size, mineral breakage distribution pattern and degree of mineral liberation of comminuted particles. This quantitative relation reflects the simplest approach to prediction of mineral liberation from various textures of iron ores in the geometallurgical context.

2. Materials and methods

2. 1 Samples The samples for the study came from the Malmberget and Kiruna iron ore deposits located in Northern Sweden. In the Malmberget iron ore field more than 20 separate ore bodies are known and production is coming from several different underground operations (Lund, 2013). Ore is processed in the Malmberget concentrator in two lines: one for magnetite dominated ore (FAR) and another for hematite dominated ore (HAR). The first geometallurgical model of the ore body based on modal mineralogy and mineral textures was developed by Lund (2013; see also Lund 2012, Lamberg et al. 2013, and Lund et al. 2013). This model, however, did not consider comminution properties.

For this study a composite magnetite (Mgt-ore) and hematite (Hmt-ore) ore sample were taken from belt cut of Malmberget process plant. Additionally, samples from drill cores representing ore types D3 and B1 (see Niiranen 2015) were used to develop the mineral breakage distribution patterns. In the D3 sample, the grain sizes of gangue minerals and magnetite are similar. This is opposite to the B1 sample. The sample KA3 from Kiruna is a fine grained magnetite (see Figure 1a). In all the samples, the gangue

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minerals include actinolite, phlogopite, chlorite, titanite, quartz, talc albite and K-feldspar (Niiranen 2015). According to Lund (2013), textural classification for the Malmberget ore has two dimensions: magnetite grain size (fine/coarse) and the mass proportions of melanocratic and leucocratic parts. Melanocratic material is rich in magnetite while the leucocratic breccia shows an albite-orthoclase-rich magnetite-poor matrix. The textural types are compared in Figs. 1 to 3.

a) KA3 fine grained magnetite high grade associated with gangue minerals (silica minerals)

b) FAR Coarse grained magnetite high grade associated with gangue minerals (silica minerals)

Figure 1. Fine and coarse grained magnetite ore samples, KA3 (left) and FAR (right).

Hmt-ore coarse grained hematite high grade associated with magnetite

B1-coarse grained hematite high grade associated with magnetite &gangue minerals HAR-coarse grained hematite high grade associated with

gangue minerals Figure 2. HAR and B1 sample are coarse grained. Hematite is present in HAR.


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a) D3 fine grained magnetite low grade associated with gangue minerals(silica minerals)

b) Mgt-ore coarse grained magnetite High grade associated with gangue minerals(silica minerals)

Figure 3. Samples D3 and Mgt-ore show clear difference in the magnetite grain size.

The sample F (see Figure 4) was used to test the developed empirical models that describe the Austin model parameters for specific rate of breakage, see section 3. The coarse size fractions of the sample (i.e. 2380-3350 μm) show clusters and massive particles of fine grained magnetite. In the size fractions < 2380 μm fine grained magnetite is associated with coarse grained gangue minerals (e.g. apatite).This forms the major part of the whole samples.

F- Typical gangue in fine grained high grade magnetite F- Typical fine grained high grade magnetite Figure 4. Sample F fine grained magnetite used to test the model for describing the specific

rate of breakage by using the texture properties of a given material. On the left is a fine grained magnetite associated by coarse grained gangue minerals.

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2.2 Chemical and mineralogical analyses The chemical composition of the samples was determined by X-ray fluorescence at LKAB using their standardized method (see Lund et al. 2013). The modal composition was calculated by element-to-mineral conversion techniques using the HSC Chemistry 7.1 software and a calculation routine developed by Lund et al. (2013). The grain sizes of minerals were measured by using optical microscopy. The x-ray diffraction (XRD) measurements were done at GTK MINTEC research center in Outokumpu, Finland. The mineral phase identifications and quantitative estimates for samples KA3, D3 and B1 were carried out at LTU by using Rietveld quantitative analyses with Panalytical HighScore software. The solid density for each feed size fraction was measured by AccuPycII 1340 V1.09 at LTU. These measurements were used to identify samples of similar properties before comparing with measured specific rate of breakages.

2.3 Experimental set up The experimental investigation of mineral breakage patterns was carried out using mill feed from crushing and the mill products (see Figure 4). From the experiment eleven size fractions were obtained for each product and analyzed with respect to the mineral grades and solid densities.

For the case of specific rate of breakage nine different size fractions were used to perform comminution tests with narrow starting size fractions (220 g sample for each size fraction) over time to measure the rate of disappearance of the materials and later on used to determine the specific rate of breakage according to the Austin model (Austin et al., 1982). The grinding times used to measure the specific rate of breakage were 1, 3, 5, 7 and 9 minutes, respectively.

Size range(μm)

C product G product

Number of samples

300-212 1 1 2

212-150 1 1 2

150-106 1 1 2

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75-38 1 1 2

Crushing (C)Grinding (G)

S

3.35 mm screen

100 % < 3.35 mm300 μm screen

Samples for Liberation analyses

Liberation:100 % < 300 μm

A piece of drill core

Reject:(100 % >300 μm)

S

0-3350 μm screen

Figure 5. Experimental set up for investigating breakage properties of mineral particles based on

mineralogy and mineral texture (S is sieving stage of the materials).

3. Assessing the breakage efficiency of mineral particles

3.1 Mass balancing by size Figure 6 and 7 summarize the experimental results from various mineral textures used in this study. Figure 6 is a typical plot from the experiment representing the rate of disappearance of different size classes of materials selected for breakage in a tumbling


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mill. As expected in breakage the particles disappear at constant rate (denoted as first-order kinetics). A deviation from first-order is observed for the size class 2.38-3.35 mm. Austin et al. (1982) and Tavares et al. (2009) have reported similar deviations for large particle sizes. According to these authors the reason for such a deviation is that coarse size fractions are not well nipped between balls during grinding. The slope from the plot was used to calculate the specific rate of breakage Si according to Austin kinetic model given by

tSexp0WtW iii (1)

where

0Wi : divided by mass fraction at time zero

tWi : mass fraction of size class i at time t

0.0

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0 1 2 3 4 5 6 7 8 9 10

Wi(t

)/Wi(0

)


2.38-3.35 mm

1.68-2.38 mm

1.19-1.68 mm

0.85-1.19 mm

0.6-0.85 mm

0.425-0.3 mm

0.3-0.425 mm

0.212-0.3 mm

0.15-0.212 mm

Figure 6. First-order plot for KA3 iron ore sample for nine different size classes used for studying the specific rate of breakage.

The selected interval between the particle sizes classes for breakage was chosen according to the 2 geometric series which allows calculation of specific rate of breakage at a narrow size fraction. It can be seen that the specific rate of breakage exhibits nonlinear dependence on particle size that can be described by the Austin model (Austin, 1984):

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id1

0did

oS

iS (2)

where

Si: Specific rate of breakage of size fraction i, in time-1

di: Particle size

d0: Reference particle size (1 mm as suggested by Austin)

The parameters So, , and are the model fitting parameters that describe patterns of the specific rate of breakage shown in Figure 7.

If the specific rate of breakage is plotted against the relative particle vs. grain size of the main mineral (magnetite or hematite), it can be observed that the specific rate of breakage of fine grained magnetite minerals decreases earlier than the coarse grained mineral particles (Figure 7). The relative particle-grain size (relative scale) is defined by

gXiX

iscale,R (3)

where

Rscale,i : Relative size for size class i selected for breakage

Xi: Size class i selected for breakage

Xg: Grain size of a given mineral particles

Different mineral texture (i.e. different grain size) showed difference breakage properties (see Figure 7 and 8A) irrespective of their similar magnetite grade (compare figure 8A, 8 B and C).


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0.01

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reak

age

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min

ute)

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KA3

FAR

HAR

Hmt-ore

Mgt-ore

F(drill core sample)

Figure 7. Specific rate of breakage vs. relative size

Traditionally comminution efficiency is assessed based on the achieved progeny size distribution against applied mechanical energy. In conjunction with recent advances in quantitative mineralogical analyses, the development in geometallurgical characterization today tends towards the identification of correlations between ore breakage properties and mineralogical properties of a given deposit. The approach uses modal mineralogy and mineral texture to describe the variability of process responses (Mwanga et al 2015).

Mineral texture and modal composition have been discussed by King (1998), Gay (2004b), and Wiegel (1967) as important factors to describe comminution properties of a given materials but the mechanisms involved in the model are too complex for practical applications. The lack of knowledge on how grain size and mineral composition affect breakage rate and how such parameters control the breakage phenomenon and finally liberation of mineral particles requires profound understanding of the relationship between mineral grade and texture before modeling comminution properties of a given materials. In this study, the focus has been to investigate the influence of mineral texture (grain sizes) and mineral compositions on specific rate of breakage. In fact, the investigation tries to answer the questions of what affects the parameters in Austin’s model for the specific rate of breakage and how mineralogical data can be used to determine the specific rate of breakage and degree of mineral liberation.

Two samples of the same magnetite grade (FAR and KA3) but different magnetite grain size were used to examine whether the mineral grain size affects the breakage properties of the given materials (compare Figures 8A, 8B and 8C). Within this investigation the sample F, which has significantly different magnetite grain size but the same mineral densities as the sample FAR, was used to test the hypothesis that materials with similar

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modal composition (the same magnetite grade) have the same breakage properties. Figure 8A illustrates the main effects of changing the grain size on the specific rate of breakage. It can be observed that the finer the grain size the higher is the specific rate of breakage. In the coarse size fractions there is no systematic order of the effects that can explain the reason of the differences between KA3 and FAR samples. The similarities between FAR and F in the size fraction 2380-3350 μm is due to similar magnetite grain size. The observed opposite effect between FAR and KA3 in the three coarsest size fractions reflects the fundamental effects of energy dissipation considering the mineral grain packing (i.e. mineral grain arrangement).

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KA3- 150 μm mganetite grainsize

F - 80 μm magnetite grain size

FAR - 500 μm magnetite grainsize

Figure 8A. Test results showing how different can specific rate of breakage of materials of the same magnetite grade but different magnetite grain size.

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C) Figure 8B & C. B) = comparison of feed mineral density (i.e. solid density) for three samples (FAR,

KA3&F) for the sizes used to investigate the specific rate of breakage& C) = Comparison of feed magnetite composition for FAR & KA3 for the sizes used to investigate the specific rate of breakage.


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3.2 Linkage between mineral grains size and specific rate of breakage Starting from the specific rate of breakage, a simple approach was chosen to include grain size and mineral composition into the existing Austin model for the specific rate of breakage. Later, the approach was extended to the determination of the mineral breakage distribution pattern based on mineral grades (see section 3.3-3.4).

Using the Austin approach, compare equation (1), the size for breakage was investigated based on the first order kinetics and the model was used to determine the specific rate of breakage Si as a function of size. The determined specific rates of breakage from experimental investigations were fitted to the Austin model in equation (2). A good agreement between experimental and modeled pattern can be observed (see Figure 9). The fitted Austin model parameters (see Table 1) were used to further evaluate the effects of mineral texture and mineralogy on the breakage properties of different material.

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Modeled HAR

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Experimental Hmt-ore

Modeled Hmt-ore

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Modeled KA3

Experimental F

Modeled F

Figure 9. A plot of compared the experimental and modeled specific rate of breakage by using Austin model.

In order to describe the intrinsic properties of particle breakage it is therefore important to consider the effects of mineral grains and compositions of the materials, as these affect the Austin model parameters for specific rate of breakage. In this sense, the specific rate of breakage was assumed to be a function of mineral texture (i.e. grain size) and modal mineralogy. From the investigations of the set of iron ore samples, the calculated Austin model parameters (So, , and ) were compared with minerals grain sizes, mineral densities, Mohs-hardness and mineral composition of materials. Table 1 and 2 summarize the Austin model parameters

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Table 1. Austin model parameters and mineralogical properties of the investigated iron ore samples

Model parameter FAR Mgt-ore KA3 HAR Hmt-ore

F

So 1.420 0.926 1.095 0.342 1.290 0.889 Alpha( ) 2.069 1.930 1.445 1.371 2.182 1.415 Mu( ) 0.540 0.581 0.658 0.942 0.435 0.882 Lambda( ) 2.459 2.398 2.455 2.227 2.337 2.533 Grain size of dominating Fe oxide(μm) 500 350 150 600 800 80

Grain size of the gangue minerals(μm) 200 120 150 360 150 200

Fe oxide grade (%) 83.1 74.5 86.0 71.5 71.20 92.0

Average mineral density(g/cc) 5.10 4.80 4.80 4.70 4.90 5.20

Average Mohs-hardness 6.50 6.20 5.60 6.20 6.30 6.00

The evaluation of the Austin model parameters with respect to the directions of the influence of the mineralogical and mineral grain size parameters is summarized in Table 2. Weak correlations were found when considering the contribution of the individual dependent parameters (i.e. mineral density, Mohs-hardness and grain sizes of minerals), indicating that the effects depend on more than one mineralogical parameters. These parameters were combined to improve the correlation between Austin model parameters and mineralogical properties of a given material.

Table 2. Model parameters - Correlation matrix for specific rate of breakage

Model

parameter

Mineralogical parameters and their direction of influence vs. Austin model parameters

‘‘O’’=weak correlation, ‘‘ ’’= correlation, ‘‘-’’= no correlation

So= Specific rate of breakage at maximum particle size, = Particle size exponent alpha , = Exponent for rate of decrease of selection function lambda & = Size

coefficient for maximum breakage rate mu, Yi=grain size of magnetite or hematite minerals, Yj=grain size of the gangue minerals

Density (g/cc) Fe grade (%) Mohs-hardness H Yi/Yj

So O - O

- -

O - O

O O

Starting from the model parameter S0, the specific rate of breakage at maximum particle size showed positive correlation with average density of dominating Fe oxide (hematite or magnetite) according to the empirical model given by

6326.9111131.46848213.15803oS (4)

Where,


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S0 is the specific rate of breakage at maximum particle size; is the average density of the dominating Fe oxide.

In the case of the model parameter , the correlation between grain sizes and modal composition is given by

3159036.0150619.05041187.5398085.0 2

j

i

YY (5)

Where is the particle size exponent, Yi is the grain size of the dominating Fe oxide and Yj is the grain size of the gangue minerals (weighed average).

The model parameter correlates with grade of dominating minerals according to the equation.

1.503452grade Fe0.011265 (6)

Where is the exponent for rate of decrease of selection function, Fe grade is the grade of the dominating Fe oxide in the sample.

The parameter in the Austin model usually indicates where the maximum specific rate of breakage passes, .i.e. it defines the turning point of specific rate of breakage. In this context, it accounts the complex transformation of the slope and the position of the peak depending on the entire mineralogical properties of a given material. In this correlation, mineral density was found to be suitable parameter for describing the parameter according to the equation

197.0319779.26667827.988962 (7)

Where is the size coefficient for maximum breakage rate, is the average density, respectively.

The models developed for the 4 coefficients seem to describe the data in an acceptable way, see first Figure 10.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Cal

cula

ted

Fitted to measured data

S0

Alpha

Mu

Lambda

Figure 10. Comparison of calculated coefficient model parameter vs. fitted to measured data.

However, when using the coefficient models in a forward calculation of Si (di) the representation of the curves over size is only limited in some cases (see Figure 11). This has to do with the high sensitivity of the Austin model towards changes in the model parameters, particularly in the case of S0 and μ. This leads to the conclusion that the Austin model may not be the optimal mathematical description in this case.

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rat

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akag

e [t

ime-

1]

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FAR exp

FAR mod

Mgt exp

Mgt mod

KA3 exp

KA3 mod

HAR exp

HAR mod

Hmt exp

Hmt mod

F exp

F mod

Figure 11. Comparison of modeled specific rate of breakage based on forward calculation received

from using mineralogical properties vs. measured specific rate of breakage of different texture samples of iron ores..

4. Modal mineralogy by size State-of-the art comminution models are not capable to predict the grade differences between the particle size fractions. This is a serious issue particularly when modeling mineral processing circuits involving splitting of material by size: e.g. gravity concentration for coarse size fractions common in gold circuits, split flotation used in nickel sulphide or cobbing in coarse particle sizes of magnetite ores.

Within the sample set both magnetite and hematite ore show grade by particle size pattern where the highest magnetite / hematite grade is found in the middle particle size range, i.e. between 250 and 1200 microns. The pattern can be divided into three particle size ranges, accordingly. The coarse range from 1200 to 2400 microns represents very hard particles and for the magnetite ore they are compositionally close to the average ore whereas for the hematite ore they are poor in hematite but rich in actinolite, orthoclase and albite. The middle range between 250 to 1200 microns is enriched in magnetite and hematite and corresponds to hard material to fracture. The third size range, below 250 microns represents a soft component.

In a coarse grained sample the grade pattern with Fe oxide mineral enrichment in the middle particle size ranges is a prominent feature (Figs. 12A and 13A). In the fine grained ore the pattern looks different; almost opposite with middle particle size showing lowest Fe oxide grade (Fig. 14A). Quite naturally most of the gangue minerals show a mirror image to Fe oxides. However, biotite is clearly enriched in the fine particle sizes which can be explained by the soft nature of the mineral.


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des

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Ab in the feed

Bt in the feed




B)

Figure 12. A) = Grade of magnetite by size in the mill feed and the product for FAR sample, B) = Grade of gangue minerals by size in the mill feed and the product for FAR sample.

If the breakage was homogeneous such grade trends would not be seen; thus the grade patterns are an evidence of heterogeneous breakage.

Even the coarse grained and fine grained ore show different mineral by particle size pattern they still have one common feature: the maximum Fe oxide grade is roughly aligning with the grain size of Fe oxide. An explanation for the observed pattern is that Fe oxide rich particles break down easily until they are composed of single mineral grains. This forms a barrier for particle breaking and thus enrichment for mineral grades.

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B)

Figure 13. A) = Grade of hematite by size in the mill feed and the product for HAR sample, B) = Grade of gangue minerals by size in the mill feed and the product for HAR sample.

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Qrtz in the feedDi in the feedClintonite in the feedQrtz in the mill productDi in the mill productClintonite in the mill produc

B)

Figure 14. A) = Grade of magnetite by size in the mill feed and the product for KA3 sample, B) = Grade of gangue minerals by size in the mill feed and the product for KA3 sample.

4.1. Mineral distribution and breakage patterns by size

For different mineral texture the breakage distribution pattern is represented in Figure 15. Fine grained samples show similar gradients (KA3 and D3) opposite to the coarse grained ores (compare Figure 15 A, B, C & D). As expected texture properties align with breakage properties of minerals. For example for sample FAR the resistance against mineral breakage is increasing in the order of Apatite>Albite/Biotite> Mgt/Hmt (i.e. Ap is least resistance for comminution whereas Mgt/Hmt have the highest resistance); again, indicating the existence of selective breakage (compare Figure 15). For HAR and B1 samples the order is Mgt>Hmt i.e. in a magnetite-hematite system the magnetite breaks selectively first. For D3 sample there is no preferred order of breakages.

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Qrtz

Figure 15. Mineral distribution by size from different texture minerals received from Kiruna and

Malmberget iron ore deposits FAR- Coarse grained magnetite high grade magnetite, KA3- Fine grained magnetite high grade magnetite, C) - Patterns showing the observed breakage spectrum at 25 minutes

grinding time from five different mineral textures, D3- Fine grained magnetite low grade magnetite, B1- Extremely coarse grained hematite high grade magnetite, HAR- Coarse grained hematite high grade

magnetite

The decreasing rate can be observed when comparing mass of solid passing vs. mineral grade in the corresponding sizes of the mill product (i.e. point of maximum grade of the mill product in Figure 16). It implies that mineral particles break down to progenies that distribute to the smaller particle sizes, and accumulation for each mineral can be found where particle size meets the grain size of the mineral. This occurs by the expense of decreasing the breakage rate of corresponding mineral particles (i.e. percentage passing of solid material significantly decreases).

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d F

eO g

rade

/mill

pro

duct

FeO

gra

de

Ratios of feed solid mass/mill product solid mass

FARHARB1D3KA3

Figure 16. Plot of mineral grade vs. percentage passing of the solid material in the mill product

As shown in Figure 17 it appears that the size with maximum mineral breakage rate correlates with the size of the mineral grains e.g. magnetite. Different samples show different turning point (size at which breakage efficiency decreases) depending on the mineral grain sizes (see Figure 15C & 16). Based on observations, the particle size at which the mineral grade reaches the maximum is the liberation size the mineral.

B1

D3KA3

HAR

FAR

y = 205.85e0.002x

R² = 0.9821

120

1200

0 200 400 600 800 1000 1200

Size

at w

hich

bre

akag

e of

FeO

gra

de st

art t

o de

crea

se (μ

m)

Grain size of the dominating i.e. FeO (μm) Figure 17. Correlation between grain sizes of the dominating mineral vs. size at which the breakage

efficiency start to decrease.

4.2. Modeling mineral grade by size in the mill product

Prediction of mineral grade by size of the material in the mill during grinding is presently not established. An important question is whether properties of feed (i.e. mineral grade & grain sizes) can be used for predictions, and whether this can be done based on bulk sample or is the information on feed mineralogy by particle size required? From experimental observations, it is clear that the mineral grade patterns for coarse grained magnetite and hematite can be easily predicted from sized information. For fine grained texture the pattern resembles the random breakage nature of a given material. This range of patterns complicates the predictions of mineral grade by size when using


150

the empirical models. The observations suggested that strong grade differences by size can be found if there is difference in grain sizes of minerals. If the grain sizes are similar the pattern is expected to be flat.

The observed patterns of the mineral grade by size reflects the non-linear trends which allow the experimental data to fits non-linear function similar to Gaudin-Schuman distribution function given by

fgtp,g (8)

Where gp,t is the mineral grade of a given material at time t in the mill product, gf is the feed grade, and are constant model parameters for a given material. These parameters (see table 3) were calculated by using the feed grade for each size and fitted to the measured grade of the mill product at 25 minutes grinding time before related to the grain sizes of mineral particles.

Table 3. Parameters used to predict the grade of magnetite or hematite in the mill product

Parameter FAR KA3 D3 B1 HAR 0.32 0.00 0.26 1.16 0.61 22.09 82.21 21.30 0.52 6.15

Grain size of Fe oxide (μm) 500 150 200 1000 600 Grain size of gangue mineral (μm) 200 150 200 600 360 Geometric mean size for Fe oxide and gangue grains (μm) 316 150 200 775 465

The fitted model parameter and were compared to the mineral grain size to find a correlation between them. The model parameter showed an inverse relation to the average grain size of the minerals (Fig. 18). The larger the grain size the smaller is the value of the model parameter of a given material for grinding.

FAR

KA3

D3

B1

HAR

y = 178.85e-0.007x

R² = 0.9586

0.1

1.0

10.0

100.0

0 100 200 300 400 500 600 700 800 900

Mod

el p

aram

eter

s

Average grain size (geometric mean) of valuable grain and gangue minerals (μm) A)

FAR

KA3

D3

B1

HAR

y = -0.231ln(x) + 1.0105R² = 0.996

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 10 20 30 40 50 60 70 80 90

Model

par

amet

er

Model parameter

B)

Figure 18. A) = Model parameter as a function of the mineral grain size, B) = Model parameter as a function of parameter .

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Once the parameters and are known they are anticipated into the model (see equation 8) to predict the grade of mineral for each size in the mill product given the feed grade properties. A good correlation can be seen between measured and predicted magnetite/hematite grade for coarse grained magnetite/hematite minerals (compare to Figure 19). Significant deviation can be observed for fine grained high grade magnetite for KA3 sample as expected. It should be noted that for high grade fine grained magnetite, the model cannot predict well the grade of minerals by size in the mill product. This reflects the nature of grade by size pattern observed from experimental data in the previous section (see section 4).

30

40

50

60

70

80

90

100

30 40 50 60 70 80 90 100

Obs

erve

d m

agne

tite/

hem

atite

gra

des a

t 25

min

utes

gri

ndin

g tim

e (%

)

Predicted magnetite/hematite grades (%)

FARKA3D3HARB1

Figure 19. Predictions of mineral grades based on initial mineral grade in the feed in different size classes.

4.3. Modeling the mineral distributions by size To assess the breakage of mineral particles by composition it is crucial to understand the distribution of the mineral by size. From the experimental investigations of the different mineral texture it was observed that mineral distribution by size follows the normal comminution size distribution curves. Such distribution is often well described by Rosin-Rammler distribution function with two model parameters n and

63.2X .These

parameters account for the variability of the shape of the curves depending on the properties of the mineral particles.

Accordingly, the observed experimental data were fitted to the Rosin-Rammler function to calculate the distributions of minerals by size (MD) according to

N

i

xx

2.63

exp-1100ij,MD (9)

where,

ij,MD = Mineral j distributed at size class i


152

Xi=selected size class i

63.2X = Rosin-Rammler model parameter describes particle size at 63.2 % passing.

N = Rosin-Rammler model parameter describes the spread of distribution (slope for the distribution curve).

= Model parameter for correcting the model errors of the mineral distribution.

The Rosin-Rammler function with model parameters fit well the experimental data (Fig. 20). The model parameters in equation 9 are dependent on material properties e.g. grain size of the mineral particles. Therefore, to predict the mineral distribution by size it is necessary to first find the relationship between calculated model parameters (see Table 3) and mineralogical properties of a given mineral particles. By knowing the grain size of the valuable and gangue minerals, the model parameters can be calculated and used in the modified Rosin-Rammler function to describe the distribution of the magnetite or hematite minerals by size. Figure 20 is an example illustrating how well magnetite/hematite distribution can be predicted from different texture of mineral particles at 25 minutes grinding time in the GCT ball mill.

0

10

20

30

40

50

60

70

80

90

100

0 10 20 30 40 50 60 70 80 90 100

Obse

rved

mag

net

ite

or

hem

atite

distr

bution (

cum

mula

tive

pas

sing

%)

Predicted magnetite or hematite distribution (cummulative passing %)

FAR-predicted Mgt

B1-predicted Hmt

D3-Predicted Mgt distribution

KA3-predicted Mgt distribution

HAR-predicted Hmt distribution

Figure 20. Observed magnetite or hematite mineral distributions vs. predicted one.

Once this is established various analyses can be made e.g. analyses for breakage of minerals (see Figure 15) from different texture for breakage efficiency recognition. Hence the idea of investigating the influence of mineralogical properties of a given material becomes important for the determination of model parameters. The correlation between model parameters vs. mineralogy are established, functions for approximate the model parameters are also determined. These functions are used to calculate the model parameters and later on implemented into the Rosin-Rammler to predict the distribution of mineral content (.i.e. % cumulative mineral passing) by size.

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Table 3. Summary results of model parameters

Parameter KA3 D3 B1 FAR HAR X63.2 (μm) 78.43 104.44 242.29 116.24 170.88 N 0.36 0.50 3.36 1.43 1.53

5.15 0.52 2.85 0.00 0.00 Xvalue (μm) 150 200 1000 500 600 Xgangue (μm) 150 200 600 200 360 Average size (μm) 150 200 775 316 465

Starting from model parameter 63.2X , a strong correlation between grain sizes of the

main mineral, thus Fe oxide, was observed as shown in Figure 21. The model parameter N is also positively correlated to the grain size of valuable minerals. Considerable non-linear dependence with grain size of the valuable minerals can be observed for the model parameter .

0.00

1.00

2.00

3.00

4.00

5.00

6.00

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200

N,

X63

.2 (μ

m)

XG,Value (μm)

X63.2 (μm)

N (-)

(-)

Figure 21. Rosin-Rammler model parameter describes the size at 63.2 % vs. grain size of the gangue

minerals. XValue= grain size of valuable Fe oxide mineral (i.e. dominating mineral grain in the sample), X63.2= Rosin-Rammler model parameter describes particle size at 63.2 % passing.

From correlation plot, a model parameter 63.2X can be given by

152.58X0.183463.2X value (10)

where

valueX = Estimated average grain size of the main mineral, thus Fe oxide

The parameter N can be approximated by a function given by

0.2579valueX0.0035N (11)

In the case of the , an approximation function can be defined by

6.4021valueX0.02282valueX0.5102 (12)


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Regarding the parameter , it should be noted that the average value of 2% can be arbitrarily used as a suitable value for modeling the cumulative percentage passing of magnetite or hematite (iron ores with grain size between 150 – 1000 μm). This is considered as a model error for the extreme case materials e.g. KA3.

5. Discussions The findings from this study show that modal mineralogy (mineral composition) and texture, i.e. mineral grain size, predicts the patterns for the mineral breakage distribution. These parameters identify the efficiency limit for comminution of a given mineral texture and presumably the degree of mineral liberations in a ball mill. In this study a pattern describing the breakage phenomenon of minerals was established and it shows how the breakage rate of minerals decreases when the comminution reaches the mineral grain size. At this size the mineral reaches maximum grade when studied against particle sizes. This quantitative relationship reflects the simplest approach to predictions of mineral liberation of various mineral textures in the geometallurgical modeling context. This observation serves a qualitative tool to predict mineral grade by size patterns and predict the liberation size of a mineral from the grade by particle size information.

The question how particles break is crucial for predicting liberation of mineral particles and comminution energy. A strong correlation between the Austin model parameters and the mineral texture, and modal composition was observed. The preliminary interpretation for such correlation is that particles with similar minerals composition (e.g. magnetite grade) may have different breakage properties depending on the grain size of the minerals present. Here, the breakage of coarse grain materials reaches its maximum breakage rate and mineral grade in coarser sizes and therefore liberating its mineral grains earlier than in fine grained material. This phenomenon leads to the understanding of the breakage nature of mineral grains in ball milling. A model for breakage pattern of mineral distributions predicts where the maximum grade of different minerals for various textures can be achieved. The breakage rate of multigrain particles is high and the rate is degreasing strongly when particles are transformed into single mineral grain particles. This suggests that liberation size of minerals can be considered as dynamic non-linearity point in comminution.

With the current state-of-the art comminution model, the specific rate of breakages are determined experimentally and fitted to the Austin model assuming that the rate of breakage is size dependent. The experimentation for the determination of specific rate of breakage is simple but requires effort (time) and large sample amount. The fitted model parameters are related to material properties (mineralogical and mineral texture). Yet the concept of linking the mineralogy and mineral texture to the breakage of mineral particles has not fully been used to enhance the efficiency of the available comminution model. According to Austin (1982), King (2001), specific rate of breakage increases with increasing sizes indefinitely and when passes maximum the specific rate of breakage decreases due to inefficiency of the nipping of the large particles between the grinding media for breakage (i.e. specific rate of breakage is machine parameter dependent). This elucidate that breakage is dependent on machine properties but does not take into account particle properties i.e. mineralogical variability and mineral texture as crucial properties that affect the specific rate of breakage. It was also observed that the specific rate of breakage for fine grained decreases earlier than coarse grained minerals. The current interpretation for that phenomenon is that the fine grained

155

reaches the maximum rate of breakage to their grain size and start to experience resistance due to strength nature of fine particles depending on the composition of a given particle.

A combined approach has been used in this study; including modeling the breakage properties of mineral particles based on mineralogical data to provides breakage patterns of different mineral texture. With respect to the modeling, experiments were used to evaluate the consistence of the breakage patterns from various mineral textures of different iron ores. Mineralogical information (mineral composition, mineral density and Mohs-hardness) with mineral texture (grain sizes), empirically shows strong correlations with the Austin model parameters. This suggests that mineralogical properties of a given material can be used to determine the values of the Austin model parameters. These values can be later used to calculate an estimate on the specific rate of breakage for different sizes of a given ore. Validation is required for the model to be used with other type of materials.

The approach used here provided preliminary model for predicting the mineral grade by size of the mill product by knowing the mineral grade by size from crusher product (i.e. feed to ball mill). The forecast of mineral grade by size in the mill product or SAG mill product by using the bulk grade from crusher product is still an open question. Associated minerals are another parameter that affects liberation and grinding properties of an ore as observed by Bonnici et al (2008). Mineral associations affect the type of particles produced in comminution, which has been observed by Petruk (1990) as an important part of assessing the minerals separations. These parameters are important but very challenging to quantify. The modeling approach presented here does not fully answer the questions of the effects of mineral association on degree of mineral liberation. It rather provides an insight and directions for the quantification of mineralogical parameters with respect to comminution and provides a platform for proper integration between mineralogical and comminution parameters in the context of geometallurgical modelling and simulation.

6. Summary and Conclusions

The state-of-the art kinetic model is a suitable model for evaluating the breakage properties of a given particle. The particle heterogeneity (i.e. variations in grain size, grades) affects and controls the breakage properties of a given material. Comparison between breakage behavior of various texture for iron ores revealed that grain size, and mineral composition can empirically approximate the specific rate of breakage. Experiments showed that materials with similar modal composition (magnetite grade) but different texture have different specific rate of breakage.

Observations show that the breakage rate of particles decreases as the particle size reaches the grain size of a mineral. The grade by particle size pattern gives an estimate on liberation size and therefore can be used to define a suitable size for efficient comminution and liberation of minerals.

The overall conclusion is that modal mineralogy, hardness of minerals, their grain sizes, and bulk density control the breakage behavior of mineral material and are therefore necessary attributes for comminution and geometallurgical modeling. The findings from this study elucidate how mineral texture and mineralogical properties of a mineral


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particle affects ore comminution behavior and breakage phenomenon of various mineral particles. For generalization, more data from other ore types is required.

7. Acknowledgements Authors are grateful for LKAB and especially Kari Niiranen, Therese Lindberg for their help in collecting samples and providing sample analyses. The financial support of the CAMM Centre of Advanced Mining and Metallurgy at Luleå University of Technology is gratefully acknowledged.

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