Figure 3-7: Influence of % of critical speed (top) and % of mill filling (bottom) on power consumption. ... Figure 3-9: Schematic illustration of a tumbling mill. .... Figure 5-14: Effect of ball size and mill filling on grinding efficiency (U=100% and.
EFFECT OF OPERATIONAL VARIABLES ON BALL MILLING
Daniel Mendonça Francioli
Projeto de Graduação apresentado ao Curso de Engenharia de Materiais
da Escola
Politécnica,
Universidade Federal do Rio de Janeiro, como parte dos requisitos necessários à obtenção do título de Engenheiro de Materiais.
Orientador:
Prof. Luís Marcelo Marques Tavares
Coorientador: Prof. Rodrigo Magalhães de Carvalho
Rio de Janeiro EFFECT OF OPERACIONAL VARIABLES ON BALL MILLING Fevereiro de 2015
ii
Francioli, Daniel Mendonça Effect of operational variables on ball milling/ Daniel Mendonça Francioli. – Rio de Janeiro: UFRJ/ Escola Politécnica, 2015. XVIII, 72, p.: il.; 29,7 cm. Orientador: Luís Marcelo Marques Tavares Coorientador: Rodrigo Magalhães de Carvalho Projeto de Graduação – UFRJ/ Escola Politécnica/ Curso de Engenharia de Materiais, 2015. Referências Bibliográficas: p. 68-71. 1. Comminution. 2. Energy efficiency. 3. Ball milling. I. Tavares, Luís Marcelo Marques e Carvalho, Rodrigo Magalhães de. II. Universidade Federal do Rio de Janeiro, Escola Politécnica, Curso de Engenharia de Materiais. III. Effect of operational variables on ball milling.
iii
“In a gentle way, you can shake the world.” Mahatma Gandhi iv
To my parents, family and friends. v
Acknowledgments
I would like to thank the following persons for helping me during my undergraduate degree. •
My family, Marco, Rachel, André, Brenno, Ignez and Nylson, for their encouragement, advice and friendship throughout all my life.
•
My girlfriend Rita, for her support and patience during these last months and also for her loving care.
•
My group of friends, Friends Metalmat, for affording great unforgettable laughs along our undergraduate study years.
•
My advisors, Professors Luis Marcelo Tavares and Rodrigo Carvalho, for their constant support, advice and suggestions. I am extremely grateful to consider them not only as advisors but also as great friends.
•
LTM undergraduate and postgraduate students, for their support and incredible knowledge exchange.
•
LTM staff, for their crucial support during experimental work.
•
Professor Malcolm Powell and Research Fellow Dr. Mohsen Yahyaei, from JKMRC/UQ, for their enduring advice and invaluable encouragement.
•
Pedra Sul Mineração Ltda, for providing the samples for the experimental work.
•
Fundação Coppetec and ThyssenKrupp Steel Europe, for the financial support.
•
CNPq (Brazilian Research Agency), for providing financial support during the Science without Borders Program.
•
And every other person without whom this project would not be possible.
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Resumo do Projeto de Graduação apresentado à Escola Politécnica/ UFRJ como parte dos requisitos necessários para obtenção do grau de Engenheiro de Materiais.
EFEITO DAS VARIÁVEIS OPERACIONAIS NA MOAGEM Daniel Mendonça Francioli Fevereiro/ 2015
Orientador:
Luís Marcelo Marques Tavares
Coorientador: Rodrigo Magalhães de Carvalho
Curso: Engenharia de Materiais Moinhos de bolas são equipamentos de cominuição usados na indústria mineral em larga escala. Contudo, apesar da enorme aplicabilidade, moinhos de bolas são considerados equipamentos de baixa eficiência energética. Testes laboratoriais com utilização de moinhos tubulares em batelada têm sido fundamentais para um melhor entendimento da influência das variáveis que afetam seu desempenho. Esses testes, aliados a ferramentas adequadas de análise, permitem elucidar os efeitos das diversas variáveis bem como fornecer subsídios para otimizar a sua operação. A análise conjunta dos resultados dos experimentos e de simulações computacionais usando o método dos elementos discretos (DEM) forma a base para a validação e calibração do modelo matemático mecanicista desenvolvido no Laboratório de Tecnologia Mineral da COPPE/UFRJ. O presente trabalho consistiu na realização de experimentos em um moinho de dimensões 30 x 30 cm de modo que variáveis operacionais foram alteradas, gerando mudanças na granulometria final do minério assim como na energia consumida. A análise dos resultados mostrou que há melhora na eficiência energética do processo com aumento do tamanho dos corpos moedores e graus intermediários de enchimento do moinho e porcentagem de sólidos. A utilização do DEM através do software EDEM® possibilitou uma melhor análise do movimento da carga dentro do vii
moinho. Ainda assim, para que os resultados simulados atinjam total confiabilidade ainda é necessário um profundo entendimento sobre qual é a real contribuição de finos de minério tanto no movimento da carga quanto na potência. O modelo mecanicista da UFRJ mostrou excelente concordância com dados experimentais relacionados à quebra de partículas grossas de minério quando corpos moedores de 40 mm foram utilizados. Contudo, o próprio modelo ou os parâmetros específicos relacionados ao minério ainda necessitam de ajustes para que seja possível fazer predições da cominuição de finos.
Palavras-chave: cominuição, eficiência energética, moagem
viii
Abstract of Undergraduate Project presented to POLI/UFRJ as a partial fulfillment of the requirements for degree of Materials Engineer.
EFFECT OF OPERATIONAL VARIABLES ON BALL MILLING Daniel Mendonça Francioli February/ 2015
Advisors:
Luís Marcelo Marques Tavares Rodrigo Magalhães de Carvalho
Course: Materials Engineering (BEng) Ball mills have large applicability in the mining industry. At the same time, ball mills are considered as low efficient equipment. Laboratory tests using tumbling mills for batch grinding have been crucial to a better understanding of the variables that affect their development. These tests, when allied to adequate analysis tools, are able to elucidate all effects from operational variables on ball milling and also provide information for their operation optimization. The combined analyses of experimental data with computational simulations using the discrete element method (DEM) forms a challenge basis for the validation and calibration of the mechanistic model developed at the Laboratório de Tecnologia Mineral (LTM) from COPPE/UFRJ. This work consisted on experimental batch grinding tests with a 30 x 30 cm ball mill in which operational variables were altered. The change of these parameters resulted in direct variation on the final product size as well as on the average power consumption. Therefore, it was possible to verify enhanced process efficiency for bigger grinding media and intermediate degree of both mil filling and percentage of solids. The use of DEM through the software EDEM® provided an outstanding tool for analyzing charge movement inside ball mills. However, in order to achieve absolute trust in the results from the simulations, it is still necessary a sophisticated understanding of the actual contribution of the fine ore both on the charge movement and on the power consumed during the milling process.
ix
The UFRJ mechanistic model showed excellent agreement with experimental data regarding the breakage of coarse particles when steel balls of 40 mm were used. Nonetheless, either the model itself or the specific parameters used, which are related to the ore, still needs adjustments, which aim at improving the prediction on the breakage of intermediate and fine particles.
Keywords: Comminution, energy efficiency, ball milling.
x
Table of Contents Acknowledgments ....................................................................................................... vi List of Figures ........................................................................................................... xiii List of Tables ............................................................................................................ xvii Nomenclature ........................................................................................................... xviii 1.
Introduction ........................................................................................................... 1
2.
Objective ............................................................................................................... 4
3.
Review of the literature ......................................................................................... 5 3.1.
Comminution .................................................................................................. 5
3.2.
Comminution laws .......................................................................................... 6
3.2.1.
Size specific energy (SSE) as a measure of energy efficiency ................... 9
3.3.
Particle breakage mechanisms .................................................................... 10
3.4.
Grinding ........................................................................................................ 12
3.4.1. 3.5.
4.
Power in ball mills ...................................................................................... 14 Comminution modeling ................................................................................. 18
3.5.1.
Discrete element method (DEM) ............................................................... 20
3.5.2.
UFRJ mechanistic model overview ........................................................... 22
Materials and methods ....................................................................................... 25 4.1.
Batch grinding............................................................................................... 25
4.1.1.
Measurements ........................................................................................... 28
4.1.1.1. 4.1.2.
Size analyses ............................................................................................ 30
4.1.3.
Experimental method................................................................................. 34
4.1.4.
Experimental repeatability ......................................................................... 36
4.2. 5.
Different mill design ................................................................................ 30
Simulation software (EDEM® & LTM Analyst) .............................................. 37
Results and discussion ....................................................................................... 41 5.1.
Batch grinding............................................................................................... 41
5.1.1.
Power ........................................................................................................ 41
5.1.2.
Particle size distribution ............................................................................. 46
5.1.3.
Fines generated and grindability ............................................................... 50
5.1.4.
Effect of mill internal design....................................................................... 55
5.2. 5.2.1.
Simulation ..................................................................................................... 56 Power calculated from DEM simulations ................................................... 56 xi
5.3.
Comparison between experimental and simulated data .............................. 60
5.3.1.
UFRJ mechanistic model (Particle breakage) ........................................... 60
5.3.2.
DEM (Power) ............................................................................................. 62
6.
Conclusions ........................................................................................................ 65
7.
Future work ......................................................................................................... 67
8.
References ......................................................................................................... 68
9.
Appendix A – power comparison ........................................................................ 72
xii
List of Figures Figure 3-1: Rittinger, Kick and Bond applicability regions. Adapted from Hukki (1962). .............................................................................................................................. 8 Figure 3-2: Comminution energy efficiency calculated using ratio between operating and Bond work indices: unfilled data points from Morrell (2004) and filled points from Ballantyne et al. (2014)............................................................................... 10 Figure 3-3: Different types of stress application mechanisms inside comminution equipment. Bigger balls circles grinding media and smaller ones representing ore particle. Adapted from Chieregati (2001)...................................................... 11 Figure 3-4: a) Shattering process; b) Fracture by cleavage. Adapted from King (2001). ................................................................................................................ 11 Figure 3-5: Surface fragmentation (chipping and abrasion). Adapted from King (2001). ................................................................................................................ 12 Figure 3-6: Examples of movement of the media inside a ball mill simulated using DEM: centrifuge (left), cataract (middle) and cascade (right). ............................ 13 Figure 3-7: Influence of % of critical speed (top) and % of mill filling (bottom) on power consumption. Gray area indicates the usual range used in the industry. Adapted from Kelly and Spottiswood (1982). ..................................................... 15 Figure 3-8: Illustration of the torque required to turn a mill. Adapted from King (2001). ............................................................................................................................ 16 Figure 3-9: Schematic illustration of a tumbling mill................................................... 17 Figure 3-11: Schematic diagram of the collision event of the mechanistic model (Tavares and Carvalho, 2009). ........................................................................... 23 Figure 3-12: Schematic illustration of the input information for the mechanistic model (Tavares, 2015). ................................................................................................. 24 Figure 4-1: Laboratory ball mill settings. .................................................................... 28 Figure 4-2: 3-D model of the 30x30 cm laboratory ball mill (left) and the lifter profile (right). ................................................................................................................. 29 Figure 4-3: Typical data extracted from the torque sensor. ....................................... 29 xiii
Figure 4-4: Mill design 1 (bigger lifters) and mill design 2 (smaller lifters). ................ 30 Figure 4-5: Ro-tap® sieving equipment. ..................................................................... 32 Figure 4-6: Sympatec® equipment installed at LTM facilities. .................................... 33 Figure 4-7: Distributions resulted from Sympatec® software program. ...................... 34 Figure 4-8: Experimental procedure. ......................................................................... 35 Figure 4-9: Different size analysis techniques for 1 minute grinding depending on the size interval of the particles. ............................................................................... 35 Figure 4-10: Size analyses of duplicate cases using different ball size: 15 mm (top left), 25 mm (top right), 40 mm (bottom left) and distribution (bottom right). ...... 36 Figure 4-11: Breakage rate of 8 mm size class (left) and variation of power with time (right) of duplicate tests. ..................................................................................... 37 Figure 4-12: Snapshot of EDEM simulation where balls are colored by their kinetic velocity (J=30%, φc=75% and db=25 mm). ........................................................ 39 Figure 4-13: Power draw of the ball mill (J=30%, φc=75% and db=25 mm). ............. 40 Figure 4-14: Velocity profile (left) and particle frequency (right), (J=30%, φc=75% and db=25 mm). ......................................................................................................... 40 Figure 5-1: Variation of power with time for tests with different ball sizes: Dry (left) and wet (right). (J=30%, φc=75% and U=100%). ............................................... 42 Figure 5-2: Effect of mill filling on power consumption (φc=75% and U=100%). ....... 43 Figure 5-3: Variation of power with grinding time for different percentage of the critical speed (J=30%, U=100% and db=25 mm). ............................................... 44 Figure 5-4: Variation of power with percentage of critical speed for different powder fillings (J=30%, φc=75% and db=25 mm). .......................................................... 45 Figure 5-5: Effect of 100% powder filling on power for different mill filling percentages. Ball size: 15 mm (left) and 40 mm (right). ..................................... 45 Figure 5-6: Size analyzes of each batch grinding step (J=30%, U=100% and φc=75%). Top-left: db=15 mm log-log scale; bottom-left: db=15 mm semi-log
xiv
scale; Top-right: db=40 mm log-log scale; bottom-right: db=40 mm semi-log scale. .................................................................................................................. 47 Figure 5-7: Size distribution after 10 minutes of grinding using different ball sizes (J=30%, U=100% and φc=75%). ........................................................................ 48 Figure 5-8: Product size after five minutes grinding using db=15 mm (left) and db=40 mm (right). (J=30%, U=100%, φc=75%)............................................................. 49 Figure 5-9: Effect of powder filling (left) and mill filling (right) on size distribution after ten minutes grinding using 25 mm balls (left) and ball distribution (right). .......... 49 Figure 5-10: Effect of rotational speed on size distribution after ten minutes grinding using U=80% (left), U=100% (middle) and U=120% (right) (db=25 mm and J=30%). .............................................................................................................. 50 Figure 5-11: Graphic representation of productivity and grindbility calculations of cases 20 - 22. ..................................................................................................... 51 Figure 5-12: Charge (balls) frequency extracted from LTM Analyst showing different impact zone caused by different speed: φc= 85% (left) and φc= 67.5 (right). .... 51 Figure 5-13: Effect of ball size and percentage of solids on grinding efficiency. Dry data is the average of duplicate cases (J=30%, U=100% and φc=75%). .......... 54 Figure 5-14: Effect of ball size and mill filling on grinding efficiency (U=100% and φc=75%). ............................................................................................................ 54 Figure 5-15: Effect of mill design on grinding efficiency (J=30%, db=25 mm and φc=75%). ............................................................................................................ 55 Figure 5-16: Effect of percentage of critical speed on power from simulation using different contact parameters. (J=30% and db=25 mm). ...................................... 57 Figure 5-17: Effect of ball size and mill filling on power from simulation using different contact parameters. ............................................................................................ 57 Figure 5-18: Collision energy spectra of balls-balls (left) and balls-liner (right) pairs with different mill filling percentage (db=40 mm and φc=75%)............................ 58 Figure 5-19: Collision energy spectra of balls-balls (left) and balls-liner (right) pairs with different ball sizes (J=20% and φc=75%). ................................................... 58
xv
Figure 5-20: Particle frequency profiles extracted from LTMAnalyst showing different charge movement caused by different ball sizes: 15 mm (left), 25 mm (middle) and 40 mm (right). .............................................................................................. 59 Figure 5-21: Particle frequency profiles extracted from LTMAnalyst showing different charge movement behavior obtained from different mill designs running at same operational conditions: Mill design 1 (left) and Mill design 2 (right) (J=30%, db=25 mm and φc=75%). .............................................................................................. 59 Figure 5-22: UFRJ mechanistic model predictions for different mill filling: J=30% (left) and J=40% (right). (U=100%, db=40 mm and φc=75%). .................................... 61 Figure 5-23: UFRJ mechanistic model predictions for smaller ball sizes: db=15 mm (left) and db=25 mm (right). (U=100%, J=30% and φc=75%). ............................ 61 Figure 5-24: Comparison between disappearance of top size class from simulation and experimental data. ....................................................................................... 62 Figure 5-25: Comparison of the charge movement: experimental (left), simulation using EDEM® and post-processing using LTM Analyst (J=30%, φc=75% , db=25 mm and for the experimental case, U=100%). .................................................. 63 Figure 5-26: Power consumption for different percentage of mill filling (db=25 mm, φc=75% and experimental data with U=100%). ................................................. 64 Figure 5-27: Comparison between simulated and experimental power consumption (J=30%, db=25 mm and U=100%). ..................................................................... 64 Figure 7-1: Particle frequency extracted from LTM Analyst showing charge movement caused by different designs and rotational speeds: Mil design 1 (left) with φc=50% and Mill design 2 (right) with φc=75% (J=30% and db=25 mm). ... 67 Figure 9-1: Power comparison (experimental x center of gravity x energy loss) for different mill filling percentages and grinding media size (φc=75%). ................. 72
xvi
List of Tables Table 4-1: Experimental details (grinding media only). .............................................. 26 Table 4-2: Standard ball size distribution based on that from the Bond Wi test (equivalent to 20% of the mill filling). .................................................................. 26 Table 4-3: Relationship between mill filling and total mass of balls. .......................... 26 Table 4-4: Experimental details (dry grinding) ........................................................... 27 Table 4-5: Experimental details (wet grinding)........................................................... 28 Table 4-6: Size intervals selected for the experimental analyses. ............................. 31 Table 4-7: Batch grinding time intervals for tests including ore powder..................... 34 Table 4-9: Material parameters used for EDEM simulations (Dem Solutions Ltd.).... 38 Table 4-10: Contact parameters for steel-steel surfaces (middle) and contact parameters to compensate the existence of ore particles. ................................. 38 Table 5-1: Fines generated and grindability from dry tests using 25 mm balls and 30% of mill filling. ................................................................................................ 52 Table 5-2: Fines generated and grindability from all experimental tests: dry grinding (left) and wet grinding (right). .............................................................................. 53
xvii
Nomenclature AG
Autogenous grinding
CFD
Computational Fluid Dynamics
CNPq
Conselho Nacional de Desenvolvimento Científico e Tecnológico
COPPE
Instituto Alberto Luís Coimbra de Pós-Graduação e Pesquisa em Engenharia
DEM
Discrete Element Method
FEM
Finite Element Method
JKMRC
Julius Kruttschnitt Mineral Research Centre
LTM
Laboratório de Tecnologia Mineral
SAG
Semi-autogenous grinding
SPH
Smoothed-particles Hydrodynamics
SSE
Size specific energy
UFRJ
Universidade Federal do Rio de Janeiro
UQ
The University of Queensland
xviii
1. Introduction Particle size reduction operations, called comminution, are extremely important to achieve a concentrated high-grade product. Nowadays, the mineral industry is facing some of its most challenging obstacles: •
Ore quality is gradually getting worse. In other words, easy extraction of high concentration resources is becoming limited. As ore grades continue to decline, the cost to produce mineral commodities rises.
•
Mineral processing operations are making great effort to keep up with the same quality productivity as ore quality decreases.
These challenges require a full understanding of all mineral processing operations and equipment so that process optimization becomes a viable solution. Comminution is known as an energy intensive process. In fact, many researches tried to estimate the energy consumption due to comminution operations. Schönert (1986) estimated that comminution is responsible for between 2 and 3% of the energy produced in the world. In his recent work, Napier-Munn (2014) indicated that this estimation is reduced to 1.8%. He also showed impressive numbers related to energy consumption from several mineral beneficiation industries: approximate calculations indicate cement grinding is responsible for 185 billion kWh of energy consumption whilst coal stone crushing indicates consumption of 20 billion kWh. Wills (1997) indicated that comminution could be responsible for 70% of mineral beneficiation costs. Among all comminution steps, grinding in tumbling mills is known to be energy inefficient. The most commonly used tumbling mill in the industry is the ball mill, which is named after its grinding media, steel balls. Rotational movement provides the rise of the charge inside the mill and subsequent impact, resulting in particle breakage. They are able to reduce size particles on a relatively wide range of particle sizes, hence their wide applicability in the industry and research laboratories. Many distinct methodologies have been proposed to assess and predict ball mill performance and energy requirement, being the one based on the Bond work index (BWi) the most popular. In order to optimize ball milling it is important to first properly understand the effect of operational variables on grinding. Mill filling, powder filling, mill rotational speed and size of the grinding media are some of the most important operational variables of a ball mill. Recently, mechanistic approaches found their way into comminution modeling for being able to describe detailed relationships between 1
physical environment inside the mill and the product discharged from the mill, overcoming limitations of previous models (Tavares and Carvalho, 2009). To achieve this level of detail, mechanistic models used the discrete element method (DEM) to describe the mechanical environment of the mill (Mishra and Rajamani, 1992, Weerasekara et al., 2013). Combined analyses between batch experimental grinding tests and modeling approaches may be the best path for comminution processes optimization. The validation of these models will lead to a powerful and efficient tool for breakage prediction, new equipment design and energy consumption estimation. The impressive usability and the energy inefficiency associated to ball mills over the years are the motivational foundations of this work. The possibility of giving a step further on understanding this complex yet thrilling process enhances the motivation to improve the efficiency of this traditional and solid equipment by providing substantial resources to future optimization studies. A concise discussion of the contents of each chapter follows. CHAPTER 2 indicates the objectives of this work in a clear form. CHAPTER 3 reviews some aspects of comminution regarding mineral liberation and particle breakage mechanisms, ball milling operations, power draw calculation methods and the advances in comminution modeling. A description of the UFRJ mechanistic model and information about the discrete element method (DEM) can also be found in this chapter. CHAPTER 4 details the experimental methods presented in this work. It indicates the material used for batch grinding tests and the software used for the simulations. Information regarding the methodology used for power measurements and size distribution analyses are presented as well as the tool used for simulation post processing. CHAPTER 5 discusses the influence of operational variables such as grinding media size, mill filling, percentage of the critical speed, powder filling and solids percentage on power consumption and on particle size distributions. A detailed comparison between experimental and simulation data is presented indicating the possible limitations of the techniques used.
2
CHAPTER 6 summarizes the results and concludes the work. It shows which areas are established and which still need further understanding. CHAPTER 7 proposes extra tests, which aim at gaining deeper insights into the effect of mill design and powder filling on ball milling.
3
2. Objective The aim of this work is to evaluate the effect of operational variables on ball mills through batch grinding and simulation tools, providing resources to improve mechanistic modeling approaches of tumbling mills.
4
3. Review of the literature In this chapter, a review of the well-known comminution laws is presented as well as a description of the breakage mechanisms of particulate solids, including body and surface breakage. In addition, grinding processes, especially ball mill operations, are detailed. The calculation of power in ball mills and the energy efficiency of these equipment are reviewed. Finally, an overview on comminution modeling using the discrete element method as basis for the UFRJ mechanistic model is presented.
3.1. Comminution In mineral processing, valuable ore minerals need to be liberated from the gangue in order to achieve a product with desirable grade after concentration processes. The release of these valuable minerals is obtained through comminution. Comminution is the term used for size reduction due to the application of energy. It consists of three steps: rock blasting, crushing and grinding. These processes demand high-energy consumption and it is estimated that around 2% of the global electricity generated is spent during comminution (Schönert, 1986, Fuerstenau and Abouzeid, 2002, Napier-Munn, 2014). In fact, at an ore beneficiation plant, comminution can be responsible for up to 70% of production costs, either due to power consumption or equipment degradation and consumption of wear parts (Wills, 1997). Crushing stages are responsible for a significant size reduction and can be carried out in three or four stages. Primary crushing feed stream can have particle sizes as coarse as 1000 mm and the last crushing stage can deliver particles sizing 10 mm or even smaller. After being crushed, the material go to grinding circuits resulting in a reduced particle sizes of hundreds or a few micrometers. Particle size distribution of the product must be well controlled aiming at maximizing the efficiency of further concentration stages. Tumbling mills are grinding equipment widely used in mineral processing. The most used tumbling mills are: ball, autogenous (AG), semi-autogenous (SAG) and rod. Despite their low energy efficiency, ball mills are robust equipment extensively used in grinding circuits, probably due to the fact they operate from laboratory to industrial scale. They are also able to process a large scale of particle size (Napier-Munn et al., 1996). The grinding media inside ball mills, steel balls, are elevated among the charge 5
and then impacted against the particles by centrifugal and gravity forces. The collisions promote breakage due to body or surface breakage (Carvalho, 2014).
3.2. Comminution laws Comminution processes have always been correlated to energy consumption, which represents a major percentage of mineral beneficiation costs. It was clearly observed that in order to produce finer particles more energy was needed. Then, a general equation was proposed, in which a relation between particle fragmentation and energy consumption is inversely proportional to a particle size power-function, given by (Napier-Munn et al., 1996): 𝑑𝐸 = −𝐾
!! !!
(3-1)
where: 𝑑𝐸 is the additional energy required to produce a size reduction dx; 𝑥 is the particle size; 𝐾 and 𝑛 are ore constants. The greatest challenge of quantifying grinding energy is the fact that the mill absorbs most of the energy applied and only a small percentage is directed to actual particle fragmentation. Over the history, semi-empirical energy-size reduction relationships were proposed by Rittinger, Kick, and Bond, known as comminution laws. •
First Law of Comminution (𝑛 = 2) – proposed by Rittinger in 1867, this relation
indicates that the energy consumption is proportional to the increase in surface area generated by crushing or grinding processes. It is known that surface area is inversely proportional to particle size, resulting in the following equation: 𝐸=𝐾
! !!
−
! !!
(3-2)
where 𝑥! and 𝑥! are feed and product particle size respectively.
6
•
Second Law of Comminution (𝑛 = 1) – proposed by Kick in 1885. It assumes
that the energy consumed is proportional to the volume reduction of the particles involved and it can be given by: !!
𝐸 = 𝐾 𝑙𝑛
(3-3)
!!
These two laws brought forth an extensively controversy between Rittinger’s and Kick’s followers. In fact, Rittinger’s approach is extremely simplified since it assumes that all energy is transferred to the charge and it does not consider deformations that might happen prior to the breakage event (Bond, 1985). On the other hand, although Kick’s theory showed to be adequate for homogeneous materials, it also miscalculates the actual energy required in practice. •
Third Law of Comminution (𝑛 = 3 2) – proposed by Bond in 1952. This law
assumes that the energy consumed to reduce particle size is proportional to the square root of the new area produced and inversely proportional to particle size, known as: 𝐸=𝐾
! !!
−
!
(3-4)
!!
where 𝐾 is the Work Index (𝑊𝑖), which was proposed by Bond and it is determined experimentally in the laboratory. 𝑊𝑖 is the energy required, in kWh/t, to reduce 1 tonne from a large size (infinite) to a point where 80% of the material passes the 100 microns sieve. This point is commonly referenced as d80: 𝑊𝑖 = 𝐾
! !""
− 0 => 𝐾 = 10𝑊𝑖
(3-5)
The third law of comminution can then be written as:
𝐸 = 10𝑊𝑖
! ! !!"
−
! ! !!"
(3-6)
Bond´s comminution law can be applied for crushers, rod and ball mills. Consequently, the 𝑊𝑖 is different depending on the equipment and it must be measured separately. The standard Bond’s laboratory test to determine 𝑊𝑖 was designed to produce an index that would correctly predict the power required by a test with specified parameters. Thus, in order to apply Bond’s equation to industrial mills, which differ from the standard meant by Fred Bond, a series of efficiency factors should be taken into consideration (King, 2001).
7
Although Bond was successful at theoretically proving his assumption, it is known nowadays that Equation (3-6) is an empirical relation that provides good fit to results from grinding experiments. Moreover, Bond’s theory is still commonly used as a tool for sizing crushing and grinding equipment in the industry. It is also recognized that this methodology may present discrepancies around 20% in respect to the actual energy consumption in the case of ball mills (Herbst and Fuerstenau, 1973) and even higher in the case of crushers (Tavares and Silveira, 2008) Attempts to modify these laws, which aimed at proposing a single general equation and ceasing any ambiguity, were unsuccessful for a large range of particle sizes. Hukki (1962) pointed out different applicability regions regarding each comminution law as shown in Figure 3-1.
Figure 3-1: Rittinger, Kick and Bond applicability regions. Adapted from Hukki (1962).
It was identified that Kick’s relation is more appropriate for crushing processes whilst Rittinger’s can be related to fine grinding. Although Bond’s method also shows a limited
8
applicability region, it is applicable for particle size intervals that are regularly used in grinding operations.
3.2.1. Size specific energy (SSE) as a measure of energy efficiency The size specific energy is the energy required to produce new particles of a certain size. Ballantyne et al. (2014) proposed the size of -75 μm particles as a basis to calculate the SSE. Musa and Morrison (2009) indicated linear relationship between new -75 μm material generated and cumulative comminution energy consumption. It was explained previously that the Bond work index is used until nowadays as a method for calculating energy efficiency of grinding circuits. However, this methodology is based on 𝑃!" , which is a size marker of a particle size distribution that is close to the top size particles. It can be a problem when predicting AG/SAG grinding circuits since these equipment tend to produce a large amount of fines without reducing 𝑃!" (Ballantyne et al., 2014). According to Levin (1992), the percentage of -75 μm may be a more variable quantity and hence, SSE may be a more appropriate measure of fineness. Ballantyne et al. (2014) confirms that SSE is more effective regarding energy efficiency calculations because it is related to the generation of fines and not the reduction in the top size. It was also found by Ballantyne et al. (2012) that the operating work index and SSE are linearly related. Figure 3-2 compares observed and predicted specific energy calculation for ball and AG/SAG mills. Data presented on the chart are originated from Ballantyne and Powell (2014) and Morrell (2004). Sixty percent of the plants analyzed by Ballantyne et al. (2014) had circuit efficiencies below 65%, which indicates the need and potential for energy efficiency improvement.
9
Figure 3-2: Comminution energy efficiency calculated using ratio between operating and Bond work indices: unfilled data points from Morrell (2004) and filled points from Ballantyne et al. (2014).
3.3. Particle breakage mechanisms Mineral breakage happens when the particle breakdown limit is reached resulting in smaller progeny distribution. Depending on the input particle size and the desired particle product size, different comminution equipment are selected as each of them uses different stress application mechanisms. The main stresses involved in comminution equipment are illustrated in Figure 3-3. The magnitude of the stresses applied together with the right information of ore characteristics should indicate the type of fragmentation the particle would suffer.
10
Figure 3-3: Different types of stress application mechanisms inside comminution equipment. Bigger balls circles grinding media and smaller ones representing ore particle. Adapted from Chieregati (2001).
In general, stresses are applied in comminution rapidly, providing enough energy to cause particle failure. Breakage through rapid application of stresses, or “impact”, occurs in several mineral processing equipment, for instance, impact crushers or autogenous, ball and rod mills. Compression results in lower rate of stress application, resulting in slower propagation of cracks inside the particle, as in jaw and cone crushers. Breakage through shattering results in an intense fragmentation of the parent particle producing a wide range of progeny size, which is extremely common after impact events. Cleavage, another fragmentation mechanism, happens when the intensity of energy applied is lower. It results in a progeny with many coarse particles, as well as fines generated from the location of the stresses.
Figure 3-4: a) Shattering process; b) Fracture by cleavage. Adapted from King (2001).
11
Breakage of particles may be, additionally, classified into two distinct modes: body breakage and surface breakage. Surface fragmentation occurs when the energy applied is not high enough to cause body breakage. This happens, for instance, frequently inside autogenous mills where coarse particles act as grinding media. Surface fragmentation results in finer products and does not cause significant change in parent particle volume and size (King, 2001). It occurs via two mechanisms: chipping and abrasive wear (Francioli et al., 2014). Chipping happens when there is formation of subsurface lateral cracks (Hutchings, 1993), resulting in the chipping off of a small volume of the particle. Abrasion, in which almost no surface damage can be seen, is caused by applications of either low energy stresses or shear stresses generated by the rolling or sliding of the particles against each other or another rougher surface.
Figure 3-5: Surface fragmentation (chipping and abrasion). Adapted from King (2001).
3.4. Grinding Grinding processes of tumbling mills consist on the rotation of the mill at the horizontal axis. Usually, mills are filled partially with grinding media, ore particles and sometimes water. The movement of the media inside the mill can be indicated by the energy applied and the mill geometry (liner, lifters and mill diameter). Lifters prevent slipping of the charge in the mill reducing the amount of energy wasted during the grinding process and improve the breakage mechanisms by enhancing the number of collisions. The dimensions of the lifters have great influence in charge motion and grinding efficiency.
12
The rotation speed that results in the movement of the grinding media adjacent to mill shell during the entire mill rotation is called critical speed. Ball mills can operate in two distinct regimes depending on the rotation speed: cascade and cataract, as illustrated in Figure 3-6. Cascade motion is more likely to result in breakage through attrition whereas cataract would favor collisions and, thus, body breakage.
Figure 3-6: Examples of movement of the media inside a ball mill simulated using DEM: centrifuge (left), cataract (middle) and cascade (right).
The critical speed in rotations per minute can be given by, Critical speed =
!".! !! !!!
(3-7)
where 𝐷! is the mill internal diameter and 𝑑! is the diameter of the grinding media particles, both in meters. Very commonly, the speed a mill is operated is called fraction of critical speed, 𝜑! . Industrial milling usually work between 65-82% of the critical speed, but sometimes values as high as 90% or lower than 65% are used (King, 2001). Mill filling is the percentage of the mill volume occupied by the grinding media and the interstices between them. This operational variable can be written as, Mill filling: 𝐽 =
!!" !! ∗ !!!"
(3-8)
where 𝑉!" is the volume of the grinding media inside the mill and 𝑉! is the volume of the mill. 𝑓! is the fractional volume of the interstices between the grinding media, usually 𝑓! has a value of 0.4 (Austin and Concha, 1994). The charge inside a mill can be given by, Charge: 𝑓! =
!!" !! ∗ !!!"
(3-9)
13
where 𝑉!" is the volume of the material inside the mill. The powder filling gives the correlation between the charge of material and the charge of grinding media: Powder filling: 𝑈 =
!! !! ∗ !
(3-10)
In addition, grinding processes can be classified as dry or wet, when water is part of the charge inside a mill. Although 30% less energy is used in wet grinding processes, the costs related to drying may compensate the final expense. Moreover, the wear of grinding media and grinding mills are typically 3 to 5 times greater during wet grinding (Tavares, 2009b).
3.4.1. Power in ball mills Ball mills are one of the greatest energy consumption equipment in mineral processing, which leads to a high demand of technological development that might result in increasing energy efficiency. For instance, Cleary (2000) indicates that the power consumption for a 5x7 m ball mill can reach 3.5 MW and only 1 to 5% of this power is directed to size reduction. Energy consumption and breakage rate are the best parameters to define grinding performance. Figure 3-7 illustrates how some operational variables influence energy consumption. The effect caused by the variation of the critical speed can be seen. As the speed increases the center of mass of the charge inside the mill is dislocated towards the mill wall. However, when the speed gets closer to the critical speed the center of mass is dislocated to the mill center as the charge starts to centrifuge.
14
Figure 3-7: Influence of % of critical speed (top) and % of mill filling (bottom) on power consumption. Gray area indicates the usual range used in the industry. Adapted from Kelly and Spottiswood (1982).
The variation of mill filling can also influence power consumption. More energy is needed when there is an increase of the mass inside the mill. On the other hand, the variation of the center of mass as the percentage of mill filling changes also plays a major role. For greater mill fillings the center of mass is dislocated towards the mill center, reducing energy consumption.
15
In order to improve grinding efficiency it is crucial to understand how power is consumed during grinding processes. The following equation indicates the torque required to turn a mill (King, 2001): 𝑇𝑜𝑟𝑞𝑢𝑒: 𝑇 = 𝑀! 𝑔𝑑! + 𝑇!
(3-11)
where 𝑀! is the mass of the charge inside the mill, 𝑔 is the gravitational force, 𝑑! is the distance from the center of gravity to the mill center and 𝑇! is the torque required to overcome friction, as shown in See Figure 3-8.
Figure 3-8: Illustration of the torque required to turn a mill. Adapted from King (2001).
Then, the mill power is given by: Power: 𝑃 = 2π𝑁𝑇
(3-12)
where 𝑁 is the mill rotation frequency. Austin (1990) and Morrell (1996) proposed models that decouple gross and net power of tumbling mills: Gross power = No load power + Net power
(3-13)
16
Figure 3-9: Schematic illustration of a tumbling mill.
No-load power is the power consumed by an empty mill and it accounts for frictional and mechanical losses. According to Morrell (1996), it can be calculated by: !.!" No load power = 1.68𝐷! φ! (0.667𝐿! + 𝐿)
!.!"
𝑘𝑊
(3-14)
where 𝐷! and 𝐿 are physical characteristics presented in Figure 3-9. In Equation (314), 𝐿! is the mean length of the conical ends as it is shown below: 𝐿! =
!! !!
(3-15)
!
The net power is calculated from: Net power = 𝐾𝐷 !.! 𝐿! ρ! θξ
(3-16)
where 𝐿! is the effective length of a mill, ρ! is the specific gravity of the charge, θ is a parameter related to the fractional mill filling and ξ is another parameter related to the percentage of critical rotation speed. Depending on the type of discharge, 𝐾 assumes a specific value. Austin (1990) and Morrell (1996) suggested different values of 𝐾 for each condition. Moreover, they indicated different approach for calculations of 𝐿! , θ and ξ. •
Austin’s approach:
𝐿! = 𝐿 +
!.!"#
!!
!! (!!!.!"!! ) !! !!
!!
θ = 𝐽! (1 − 1.03𝐽! )
!.!"# !.! !.!!!!
−
!.!"# !!.! !.!!!!
(3-17)
(3-18) 17
ξ = φ! 1 − •
!.! ! !!!"!!
Morrell’s approach:
𝐿! = 𝐿 + 2.28𝐽! (1 − 𝐽! ) θ=
(3-19)
!! !
!! (!!!! ) !!
ξ = φ! 1 − 1 − φ!"# exp (−19.42φ!"# + 19.42φ𝒄 )
(3-20) (3-21) (3-22)
where 𝐽! is the total fractional mill filling, which includes the percentage of the mill volume occupied by the grinding media and the ore. In Equation (3.21), Ψ can be calculated by: Ψ = 2(2.986φ! − 2.213φ!! − 0.4927)
(3-23)
and, φ!"# = 0.954 − 0.135𝐽!
(3-24)
According to King (2001) and Tavares (2009a), both approaches deliver approximately the same estimates of net power consumed by tumbling mills.
3.5. Comminution modeling The concept of comminution modeling emerged as a computational mechanism, which aims at understanding comminution processes with a detailed approach. There are two types of modeling that achieved large applicability in industrial processes. The first type, known as phenomenological models, predicts product size distribution through prior knowledge of operational variables and feed particle size distribution. They describe mill operations as a first order rate process and they generally consider the grinding equipment as a perfect mixing reactor.
18
Breakage event Operational
Feed
conditions
Product
Figure 3-10: Black box models. Adapted from Napier-Munn et al. (1996).
Through an engineering tool, called the population balance model, researchers were able to describe successfully comminution processes in tumbling mills (Austin et al., 1984). The population balance model can be simplified as a mass balance over a range of sizes through calculations of breakage rates and appearance functions, classification and transport in mills. The size-discretized model when applied for batch grinding can be described by Austin et al. (1984): !!! (!) !"
= −𝑠! 𝑡 𝑤! 𝑡 +
!!! !!! 𝑏!" 𝑠!
𝑡 𝑤! 𝑡
(3-25)
where 𝑤! is the mass fraction of particles in size class i, s is the selection function and b is the breakage function. The selection function represents the specific breakage rate depending on the size of the particle and the breakage function describes the breakage behavior of a particle after being fractured and its fragments are distributed among smaller size classes. Coarser particles are usually classified in size class 1, whilst finer particles are classified as N. The grinding process in size class i is related to the disappearance of particles in this very size class and the appearance of smaller particles coming from coarser classes. The coarser size interval has the advantage of having only the disappearance function and Equation (3.25) can then be simplified as: !!! (!) !"
= −𝑠! 𝑤! 𝑡
(3-26)
19
where 𝑠! is the breakage rate in size class 1 (coarsest class). This simplification allows the assumption of identifying grinding process as being a first order kinetic process. As 𝑠! does not vary with time, it can be estimated by: log
!! (!) !! (!)
=−
!! ! !.!
(3-27)
Examples of specific breakage rate for the first size class can be found further in this work (Figure 4-11). For decades, the traditional population balance model, which in the case of the batch grinding may be described by Equation 3.25, has been used as a basis for modeling mills and researchers added their individual semi-empirical relationships contributions to fit the technique. However, the model itself encounters great difficulty to simulate the process under different conditions from those used to fit its parameters (Carvalho and Tavares, 2013). In addition, another limitation lies in its inherent incapacity to describe how operating and design variables used in milling influence size reduction. Weerasekara et al. (2013) also commented on the incapacity of the traditional population balance model, given that it is a phenomenological model, of predicting the performance of new or novel equipment. In order to overcome the limitations of the traditional population balance model, new formulations, known as mechanistic models, were proposed. Those types of models are very complex and they require great computational capacity. They can describe detailed relationships between physical conditions inside the mill and the product. Tavares and Carvalho (2009) and Tavares and Carvalho (2010) proposed a mechanistic model that maintains mass balancing capabilities of the population balance model and also presents a deeper insight of the effect of operating and design variables. Their model is able to decouple material from mill contributions in the process. In order to achieve this level of detail, the Discrete Element Method is used to describe the mechanical environment of the mill.
3.5.1. Discrete element method (DEM) Mishra and Rajamani (1992) were the first to use the discrete element method in the minerals industry as a tool to simulate grinding media motion. DEM has been widely accepted not only in comminution but also to simulate environments where granular 20
materials are used, such as rock and powder mechanics. Today, DEM technique has proved to be a powerful tool for the development of mechanistic modeling in comminution. Some of the characteristics of DEM are: •
It simulates particle motion through Newton’s equations of motion;
•
It simulates particle contact (collisions) through contact laws;
•
Used for energy efficiency calculations;
•
Used for equipment design and optimization;
•
It needs intense computational power;
•
It can provide data for simulating size reduction in comminution machines.
Carvalho (2014) explains the calculation algorithm of the DEM in three stages. A list of interactions regarding the particle neighborhood is periodically built through a search mesh. The collision forces are also evaluated by the use of the contact model and, finally, the forces involved on each particle are summed followed by the integration of motion equations, which are related to mass, inertia momentum of the particle, and its linear and angular velocities. DEM simulations of tumbling mills started as a two dimensions technique. Millsoft® is an example of 2-D software dedicated to tumbling mills (Mishra and Rajamani, 1992). 3-D tools, such as EDEM®, came out with the advances of computational power. Recently, DEM found its way on coupling to other simulation techniques, for instance: DEM-FEM (finite element method), DEM-CFD (computational fluid dynamics) and DEM-SPH (smoothed particles hydrodynamics) (Bagherzadeh Kh et al., 2011, Chu et al., 2009). The use of these coupled techniques allow the simulations of different environments in distinct applications such as particle breakage, crack propagation and motion and slurry discharge from a mill. The power consumption calculated through DEM regarding charge motion does not include the effect of slurry movement in the charge or the mechanical losses in the motor or couplings. Cleary (2001) stated that power measures taken from real mills will be greater than the power obtained from DEM simulations. The use of DEM for ball, AG and SAG mills simulations can provide prediction of power consumption with an error of less than 10%. In addition, it is able to predict the movement of the charge inside the mill and it also gives important information on lifters and liners wear and degradation (Mishra, 2003). Many researchers directed their work into validating DEM simulations by comparing simulated results with experimental data. Cleary and Hoyer (2000) used a centrifugal mill and changed fill levels with very close agreement in terms of power prediction.
21
Another study comparing simulations to experimental data was conducted by Makokha et al. (2007) using a ball mill with different lifter profiles. Good agreement was achieved regarding shoulder and toe positions as well as power draw at sub-critical speeds. Morrison et al. (2006) carried out tests on a pilot AG mill and concluded that the error in power draw predicted using DEM was 3.1%. According to Carvalho (2014), the main set of information extracted from DEM to be used on grinding predictions is the collision energy spectrum. The energy spectrum can be captured by normal and tangential (shear) energy loss calculations or by kinetic energy calculations immediately after the collision event. These two methods give significant difference in the results, as claimed by (Powell et al., 2008). Independently of the method, the extraction of the collision energy spectrum after a simulation using DEM needs an enormous amount of data, and several post-processing techniques have been proposed to better evaluate collision energy information. In fact, Weerasekara et al. (2013) agrees that the revealing of the nature of the collisions energy spectra is one of the most important success of the discrete element method. The concept of incremental breakage was also developed as DEM simulations provided information on the high number of weak collisions inside tumbling mills, which are responsible for particle failure. Experimental studies indicated that failure by accumulation of damage over weak collisions consumes more energy than failure by a single high-energy impact, suggesting a cause for tumbling mills energy inefficiency (Weerasekara et al., 2013).
3.5.2. UFRJ mechanistic model overview Mechanistic models are those that are capable to decouple the contributions of the machine from the material being processed in such a way that the micromechanics are described in great detail. In milling, these models are capable of decoupling the contributions of the mill and the ore, so that they can describe detailed information of physical conditions inside the mill. The UFRJ mechanistic model showed to be a potential candidate to overcome other limitations of other mechanistic model approaches (Carvalho, 2014). One of the greatest strengths of the UFRJ approach lies in the fact that it recognizes the weakening of the particles that survive collisions during milling, described by the model by Tavares and King (2002) using the damage
22
accumulation model. It considers that particle properties change with time due to both low-energy and high-energy impacts. As stated by Carvalho (2014), the model has inputs from fundamental ore breakage properties and it uses information from collision energy spectrum from DEM simulations. To simulate breakage on ball mills, previous work conducted by Tavares and Carvalho (2009) and Tavares and Carvalho (2010) proposed to consider the ball mill as a perfect mixing reactor, in which the material properties are equally distributed. The ball mill model assumes that a certain volume of particles will be captured between grinding media and the energy transferred is divided among the captured particles after each collision. However, the energy provided by the impact results in different breakage mechanisms, which depends on the magnitude on the impact and on the ore properties. Figure 3-11 presents a schematic overview of the breakage possibilities after each impact. The captured particles may suffer body breakage or surface breakage due to chipping and/or abrasion mechanisms.
Figure 3-11: Schematic diagram of the collision event of the mechanistic model (Tavares and Carvalho, 2009).
The model couples DEM and empirical/phenomenological models that describe the outcome of each breakage event as illustrated in Figure 3-12.
23
Figure 3-12: Schematic illustration of the input information for the mechanistic model (Tavares, 2015).
The model assumes that the normal component of the collision is entirely responsible for the breakage. Previous studies conducted at LTM showed good agreement between the UFRJ mechanistic model results with experiments when predicting nonfirst order rates of coarser particles of a laboratory batch ball mill test. Furthermore, the effect of operating and design variables in ball milling has been investigated by Carvalho and Tavares (2013). They simulated the batch grinding of narrow size samples with the mechanistic model over a wide range of operational variables. Their predictions were in general agreement with the literature. Finally, the model was also extended to other applications such as vertical impact crusher (Cunha et al., 2013), SAG mills (Carvalho, 2014) and material handling (Tavares and Carvalho, 2011).
24
4. Materials and methods In this chapter, the experimental settings and procedures are presented. Batch tests in a ball mill that were conducted are divided in two sets: tests with only steel grinding media as charge and tests with grinding media and ore filling the voids left by the media. The equipment used for torque and power measurement and size distribution analyses are detailed. The simulation parameters using the software EDEM® are explained as well as the tool developed in LTM to extract simulation data.
4.1. Batch grinding Batch grinding in laboratory tumbling mills have been essential for a better understanding of the effect of operational variables on grinding operations. Experimental batch tests, when coupled to the right analyses tools, are able to deliver crucial information for process optimization. First, batch tests using only grinding media (steel balls) as charge inside the mill were conducted. Some operational variables were changed as it can be seen in Table 4-1. Mill filling, powder filling and the critical speed were calculated using Equations (3-7), (3-8), (3-9) and (3-10). A grinding media charge composed of balls of different diameters (size distribution) used in some cases were calculated according to a modified ball size distribution related to the standard Bond 𝑊𝑖 test. The mass of each ball size interval was recalculated to 30% and 40% of the mill filling by maintaining the same mass proportion as presented in Table 4-2 and Table 4-3.
25
Table 4-1: Experimental details (grinding media only). Case #
Ball diameter (+/-‐2 mm)
Mill filling (%)
8
Percentage of critical speed (%)
Mill frequency (RPM)
75
59.4
20
9
15
30
10
40
11
20
75
60.5
12
30
67.5
54.4
30
75
60.5
14
30
85
68.6
15
40
75
60.5
75
62.2
75
60.5
13
25
16
20
17
40
30
18
40
5 6
20 Distribution
7
30 40
Table 4-2: Standard ball size distribution based on that from the Bond 𝑾𝒊 test (equivalent to 20% of the mill filling). Ball diameter (mm)
Total number of balls
Nominal
Interval
36.5
35-‐39
36
30.2
29-‐31
62
25.4
25-‐28
12
19.1
19-‐23
61
15.9
15-‐16
114
Table 4-3: Relationship between mill filling and total mass of balls. Mill filling (%)
Ball mass (Kg)
20
19.8
30
29.8
40
39.8
Then, in the following tests, powder was added to the charge. The material used for the experimental batch tests was a granulite rock provided by the Brazilian Company Pedra Sul/Petra, located in Matias Barbosa, Minas Gerais State. Its specific gravity – 2.69 g/cm3 – was determined from picnometry tests at LTM. This rock has considerably high mechanical strength, which prevents it from degrading during handling and screening operations associated to the experimental testwork. As such, it represents an ideal material for investigating grinding kinetics in the laboratory. Moreover, another sample of this ore has been previously characterized by (Tavares and Neves, 2008).
26
The material was first sieved as the size range in the feed to the tests was selected to be +1.18-9.50 mm and later a pile was formed to allow separation of representative samples for each batch experiment. In order to study the effect of mill filling, powder filling, percentage of critical speed, ball size and percentage of solids many different tests were required and a specific organized plan was followed. Case number 24 (25 mm ball size, 30% mill filling, 100% powder filling and 75% of the critical speed) was selected as the base condition and all other tests were varied according to the progress of the results and the need to evaluate tests with different operational variables. Table 4-4 and Table 4-5 list all batch tests that were conducted with their respective detailed variables.
Table 4-4: Experimental details (dry grinding) Case #
Ball diameter (mm)
Mill filling (%)
Powder filling (%)
20
Percentage of critical speed (%) 67.5
80
21
75
22
85
23
67.5
24 24 (2) 25
30
100
25
75 75 85
26
67.5
27
120
28
75 85
29
20
100
75
30
40
100
75
31
20
100
75
30
100
75
30
100
75
33
40
100
75
19
20
100
75
30
100
75
32 32 (2)
34 34 (2)
40
Distribution
30
100
75
35
40
100
75
36
20
100
75
36 (2)
20
100
75
30
100
75
37 (2)
30
100
75
38
40
100
75
37
15
27
Table 4-5: Experimental details (wet grinding) Case # 40 41 42 43 44 45
Ball diameter (mm) 25 40 Distribution
Percentage of solids (%)
Mill filling (%)
Powder filling (%)
Percentage of critical speed (%)
30
100
75
65 75 65 75 65 75
4.1.1. Measurements Figure 4-1 illustrates the settings of the laboratory ball mill used in the batch grinding tests. The mill has 30 x 30 cm and eight metallic lifters. The lifters were designed to give an aggressive milling response regarding breakage rate. Their dimensions are presented in Figure 4-2. The size of the lifters provides intense cataract movement of the charge inside the mill under normal grinding conditions (Figure 3-6).
Figure 4-1: Laboratory ball mill settings.
28
Figure 4-2: 3-D model of the 30x30 cm laboratory ball mill (left) and the lifter profile (right).
The torque sensor is able to measure torque and power variations over time with 0.1% error by using the software from Lorenz Messtechnik® (Krimmel). Tests running with an empty mill result in torque values varying close to zero N.m, what allows assuming that the torque measured later during the batch tests is entirely due to the charge movement. Figure 4-3 is an example of data extracted from the software. Initial and final peaks from both torque and power curves indicate the start of the mill rotational movement and the activation of the breaks respectively. In order to work with the data, these peaks were not considered in the calculations and the average value of the remained data of torque and power were extracted for further analyses.
Figure 4-3: Typical data extracted from the torque sensor.
29
4.1.1.1. Different mill design Some tests using another mill design were carried out at LTM. The dimensions of the mill remained the same (30 x 30 cm), but only 6 lifters with different dimensions (27 x 6 cm) were used. A 3-D drawing of both ball mills is presented in Figure 4-4.
Figure 4-4: Mill design 1 (bigger lifters) and mill design 2 (smaller lifters).
With design number 2, the following parameters were used: 25 mm ball size, 75% φ! , 30% of mill filling, and several powder filling conditions as presented in Table 4-1 and Table 4-4.
4.1.2. Size analyses Sieving has been the method of particle size analysis in laboratories around the world. Regular screening is composed of a series of screens with size factor 2 or
!
2, which
is able to provide mass distribution over a wide range of sizes. However, screening analyses also may require tremendous amount of time, especially for fine particles screening when wet screening is usually needed. Three different methods were used for separation of the material after the grinding process. The total size analyses include the size intervals shown in Table 4-6. 30
Table 4-6: Size intervals selected for the experimental analyses. Size (mm)
Initial size range
•
9.5 8.0 6.3 4.75 3.35 2.38 1.70 1.18 0.850 0.600 0.425 0.300 0.212 0.150 0.106 0.075 0.053 0.038 0.027 0.020 0.013 0.009 Bottom
Screening (Produtest)
®
Screening (Ro-tap sieve shaker)
®
Sympatec (Mytos)
Solotest® (Produtest) (+4.75-9.5 mm) & Ro-tap® (+0.425-4.75 mm):
Both Produtest and Ro-tap® are automated sieve shakers with large processing capacity. Produtest is particularly suitable for sieving coarser material and larger quantities of sample whilst Ro-tap® is suited for analyzes of finer material. The latter supports seven sieves series. The standard time of a sieving batch is 15 minutes and its rotation movement results in a quick efficient sieving. After every Ro-tap® analysis, the material held in the bottom sieve was quartered so that only 20g would be analyzed in Sympatec®.
31
®
Figure 4-5: Ro-tap sieving equipment.
•
Sympatec® (Mytos) (
