Delft University of Technology
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Specialization: Transport Engineering and Logistics
Report number: 2015.TEL.7954.
Title:
State-of-the-art in modelling particle
breakage
Author:
Hasim Korkmaz
Title (in Dutch)
Het modelleren van de grootte reductie van deeltjes
Assignment: literature Confidential: no
Supervisor:
Dr.ir. Dingena Schott
Student: H. Korkmaz Assignment type: Literature Supervisor (TUD):
Dr.ir. Dingena Schott
Creditpoints (EC): 10 Specialization: TELReport number: 2015.TEL.7954. Confidential: No
Subject: State-of-the-art in modeling particle breakage
Wood pellets are compressed small (approx.1mm) parts of wood in a cilindrical shaped form. The amount of material to be traded in the coming years is expected to increase steeply as co-firing wood pellets with coal is one way to meet the sustainability criteria set by the European Commission. A known characteristic of wood pellets is that it contains a lot of small particles, and that this is a quality and explosion risk in material handling.
During bulk handling of wood pellets and other materials forces act on the particles. Depending on the brittleness of particles they will remain or break in to or many more parts. The smaller parts are unwanted because of quality reasons and because they might cause dust and increase risk for explosions.
The aim of our ongoing research in two research projects (BiologikNL and Bioforce) is to model wood pellets and especially the breakage of wood pellets in relation to the handling process. For that, the first step is to create an overview of the state-of-the-art in modeling particle breakage with Discrete Element Method.
Your assignment is to investigate and make an overview of the literature on particle breakage, particle size reduction, grinding and related areas. That comprises amongst others (but is not limited to) addressing the following questions:
- Describe the methodology and theory of modeling particle breakage?
- How is the mechanical strength influencing the particle breakage in reality and in modeling? - What is the relation between particle breakage and dust generation?
- What is the degree of validation described in the available literature? - Classify and compare the literature found.
It is expected that you conclude with a recommendation for further research based on the results of this study.
The report should comply with the guidelines of the section. Details can be found on blackboard.
The supervisor,
Summary
Breakage of particles is nothing else than reducing a particle in two or more smaller particles. This process is sometimes intended and sometimes unwanted. Smaller particles can be wanted because of further applications. Sometime particle breakage is unwanted because they might cause dust. Dust can be unhealthy and increase risk for explosions.
The discrete element method (DEM), originally developed by Cundall and Strack, 1970, is a numerical method to calculate the motion and collisions of particles. Also particle breakage can be simulated using DEM. In reality it is not possible to make measurements during a process where breakage occur, only the results before and after can be measured. With DEM it is possible to simulate the steps in between. There are several methods to implement particle breakage in the discrete element
method. In this report the four most important methods of implementing particle breakage in DEM are described. Also two methods are described of simulating particle breakage without using DEM.
The first method for implementing particle breakage in DEM is the two dimensional packing method. This method is developed by Astrom and Herrmann, 1998. The two dimensional packing method uses only two dimensional circular discs. The second method is the simple breakage method, developed by Cleary, 2001. This method uses three dimensional particles. The simple breakage method is more extensive and has less limits in breakage. The third method is developed by Lichter, 2009 with almost no limits left, except the phase between the first force on a particle and the breaking of a particle, the so called post breakage fragment size, was not implemented. The fourth method, octahedral shear stress breakage method, developed by Li, 2014 has implement this post breakage fragment size and developed the most complete method up to now. One important thing missing in in the octahedral shear stress breakage method is the dust generation.
There are also two different methods to simulate particle breakage without using DEM. The first one is control oriented modelling, developed by Atta and Gustafson, 2013. This method makes use of vectors and matrix multiplications. The second one is the real-time algorithm model of Hulthen and Evertsonn, 2011. This method can control the closed side settings and eccentric speed in real time. The
algorithms are continuously evaluated and automatic adapted to the process.
A problem with almost all the information about the particle breakage methods obtained from available literature is the validation process. Two of the six models are validated correctly by the actors self. The other actors did not spend much attention to the validation process. A reason for this can be the limitations of the process by the availability of quality data from reality measurements.
Another subject of this report is the mechanical strength of particles. The mechanical strength of a particle changes when particles break. DEM is also able to calculate the new mechanical strength of the smaller particles. The mechanical strength is usually calculated by DEM with the bonded sphere
4 approach. This method detect the breakage of particles automatic and then calculates the new
mechanical strength. This is adapted in all mentioned breakage methods in this literature assignment. Dust generation on the other hand, is implemented in none of the mentioned methods. This because the development of implementing dust generation has begun in 2013. At this moment a coupling method of DEM and Computational Fluid Dynamics is used to simulate dust generation. This coupling method is expected to be used in the near future to simulate dust generation during breakage.
It can be concluded, from the first to the last method for simulating particle breakage there are less and less limits. The most complete method is the octahedral shear stress breakage developed by Li, 2014. Almost all conditions are taken into account to simulate as realistic as possible. Still there is one important subject missing, the dust generation. At this time researchers are working on implementing the dust generation in the DEM using Computational Fluid Dynamics.
Summary (in Dutch)
Het breken van deeltjes is niks anders dan het reduceren van een deeltje in twee of meerderen kleinere deeltjes. Dit proces is soms gewild en soms niet gewild. Kleinere deeltjes zijn bijvoorbeeld gewild voor verdere toepassingen. Soms is het reduceren van deeltjes niet gewild omdat het kan zorgen voor stofvorming. Stof kan ongezond zijn en de risico voor explosie laten stijgen.
De Discrete Element Method (DEM), ontwikkeld door Cundall en Strack, 1970, is een numerieke methode om de bewegingen en botsingen van deeltjes te berekenen. Ook kan het breken van deeltjes gesimuleerd worden met DEM. In werkelijkheid is het niet mogelijk om metingen te doen aan het breken van deeltjes, alleen de resultaten vooraf en achteraf kunnen gemeten worden. DEM maakt het mogelijk om de stappen tussenin te simuleren. Er zijn verschillende methoden om het breken van deeltjes te implementeren in DEM. In dit rapport worden de vier belangrijkste methoden om het breken van deeltjes in DEM te implementeren besproken. Ook worden er twee methoden om het breken van deeltjes te simuleren beschreven die geen gebruik maken van DEM.
De eerste methode voor het implementeren van het reduceren van deeltjes in DEM is de ‘two dimensional packing’ methode. Deze methode is ontwikkeld door Astrom en Hermann, 1998. In de two dimensional packing methode worden alleen twee dimensionale cirkels gebruikt. De tweede methode is de ‘simple breakage method’ methode, ontwikkeld door Cleary, 2001. Deze methode maakt gebruik van drie dimensionale deeltjes. De simple breakage methode is meer uitgebreid en heeft minder limieten in het reduceren van deeltjes. De derde methode is ontwikkeld door Lichter, 2009 en heeft bijna geen beperkingen over, alleen de fase tussen het eerste kracht op het deeltje en het breken van het deeltje, de zo genoemde post breakage fragment size, is niet geïmplementeerd. De vierde methode, octahedral shear stress breakage, ontwikkeld door li, 2014 heeft deze post breakage fragment size wel geïmplementeerd en heeft de meest complete methode tot nu toe. Een belangrijk onderwerp wat hier nog mist is de stofvorming.
Er zijn ook twee anderen methoden voor het simuleren van het afbreken van deeltjes zonder gebruik te maken van DEM. De eerste is de ‘control oriented modelling’, van Atta en Gustafson, 2013. Deze methode maakt gebruik van vectoren en matrix vermenigvuldigingen. De tweede ‘real-time algorithm’ model is ontwikkeld door Hulthen en Evertsonn, 2011. Deze methode heeft controle over de geslote zijde instellingen en de excentrieke snelheid in realiteit. De algoritme wordt continu geëvalueerd en automatisch aangepast aan het proces.
Een probleem met bijna alle informatie over de methoden verkregen uit literatuur is het validatie proces. Twee van de zes methoden zijn correct gevalideerd door de auteurs zelfs. De andere auteurs hebben niet veel besteed aan het valideren. Dit kan zijn omdat er weinig kwalitatieve data is van de werkelijkheid metingen.
6 Een ander onderwerp van dit rapport is de mechanische sterkte van deeltjes. De mechanische sterkte van een deeltje veranderd wanneer een deeltje breekt. DEM is in staat om deze nieuwe mechanische sterkte van het deeltje te berekenen. De mechanische sterkte wordt meestal berekend door DEM met de ‘bonded sphere approach’. Deze methode detecteert het breken automatisch en berekend de nieuwe mechanische sterkte. Dit wordt gebruikt in alle bovengenoemde methoden. Stofvorming daarentegen wordt in geen van de bovengenoemde methoden gebruikt. Dit is omdat het ontwikkelen van het simuleren van stofvorming in DEM is begonnen in 2013. Op dit moment wordt een koppeling tussen DEM en ‘Computational Fluid Dynamics’ gebruikt om stofvorming te simuleren. De verwachting is dat deze methode in de toekomst word gebruikt om stofvorming te simuleren bij het afbreken van deeltjes.
Er kan worden geconcludeerd dat de methoden steeds minder beperkingen hebben naarmate de tijd. De meest complete methode tot nu toe is de ‘octahedral shear stress Breakage’ van Li, 2014. Bijna alles is in rekening gebracht om zo realistisch mogelijk te simuleren. Er mist alleen nog 1 belangrijke onderwerp, stofvorming. Op dit moment zijn onderzoekers bezig met het implementeren van stofvorming tijdens het reduceren van deeltjes in DEM met behulp van ‘Computational Fluid Dynamics’.
Contents
Summary ... 3
Summary (in Dutch) ... 5
1 Introduction ... 10
2 What is DEM ... 13
3 Theory of particle breakage ... 15
3.1
Particle strength and DEM ...15
3.1.1
Mechanical strength general ...15
3.1.2
Mechanical strength estimation ...16
3.1.3
Mechanical strength in DEM ...17
3.2
Comminution models ...18
3.2.1
Comminution mechanisms ...18
3.2.2
Virtual comminution model ...19
3.3
Dust generation ...19
3.3.1
Risks ...19
3.3.2
Testing methods ...20
3.3.3
Relation of particle breakage with dust generation ...21
3.3.4
Dust generation in modelling ...21
3.3.5
Single particle settlement ...22
4 Methodology of modeling particle breakage ... 23
4.1
Two dimensional packing ...23
4.1.1
Theory behind the two dimensional packing method ...23
4.1.2
Fracture mode ...24
4.1.3
Fragment-size distribution ...24
4.1.4
Validation ...25
4.1.5
Amount of citations ...26
8
4.2.1
Simple breakage model ...26
4.2.2
Validation ...27
4.2.3
Amount of citations ...28
4.3
Fast breakage model ...28
4.3.1
Early models ...28
4.3.2
Fast breakage model ...28
4.3.3
Validation ...30
4.3.4
Amount of citations ...31
4.4
Octahedral shear stress breakage ...31
4.4.1
Particle replacement method ...31
4.4.2
Method of H.Li ...31
4.4.3
Validation ...33
4.4.4
Amount of citations ...34
5 System modelling ... 35
5.1
Control oriented modelling ...35
5.1.1
Three activities ...35
5.1.2
The proposed model ...36
5.1.3
Mixed materials model ...37
5.1.4
Validation ...38
5.1.5
Amount of citations ...38
5.2
Real-time algorithm...38
5.2.1
Control system ...39
5.2.2
Real time algorithm ...39
5.2.3
Validation ...40
5.2.4
Amount of citations ...41
6 Future DEM models ... 42
7 Conclusion ... 44
10
1 Introduction
Particle Breakage is nothing more than reducing a particle in two or more smaller particles and is an important subject in the industry sector because the energy supply, transport and further use. For example milling processes typically use about 5% of the supplied energy for particle breakage (Cleary, 1999). The aim by milling processes is to reduce the sizes producing maximum throughput and minimum operational costs. Here for controlling the particle breakage is important.
Particle breakage occur in a lot of industries like mining, cement, aggregate, power and chemical industry. Breakage is needed for different reasons; the mining industry reduces the particles to expose the valuable minerals so as to enable their recovery; the cement industry reduces particles to prepare the raw material and grinding the clinker; the aggregate industry reduces to produce an aggregate to a strength and shape specification; in the power industry coal is ground to promote rapid and
complete combustion and in the chemical industries ground particles are reduced to enable chemical reactivity. All these examples are intended breakage. Another example of intended breakage is breakage to transport. As seen in figure 1 the rock is too big to transport. In this case this rock needs to be reduced for a better transport.
Figure 1: Transportation of a rock. (Delft, 2015)
Particle breakage also can be unwanted. An example is breakage on a conveyor belt (figure 2). Here particles are broken due to vibrations on the conveyor belt and also due to collision by transshipment to the stockpile. A problem occurring in this situation is dust generation. Dust is a releasable, freely moving disintegrated smaller particle and is defined as a particle with an aerodynamic mean diameter less than 100 μm and a terminal settling velocity lower than 0.25 m/s (Saleh, 2013). Dust can be dangerous and unhealthy.
Figure 2: Transportation on a conveyor belt. (Google, 2008)
Breakage of particles occur when the ultimate strength is reached. The strength of a particle is strongly dependent of the internal structure. Experimental characterization of these microscopic information is difficult. The discrete element method (DEM) is an effective tool to calculate the mechanical strength of each particle individually. Breakage of a particle can affect the mechanical strength of the daughter particles (He, 2015). DEM is also able to calculate these characteristics. Therefore simulating particle breakage with DEM is very interesting.
There are different methods to implement particle breakage into the DEM. In this report the different methods will be described with its advantages and disadvantages. Below the research and sub questions are presented.
Research question:
Which methods are developed to model particle breakage using DEM and what is the theory behind these models?
Sub question:
1. What is DEM?
2. What is the theory behind particle breakage?
3. Which methods are existing to model particle breakage using DEM?
4. Are there other methods to model particle breakage without using DEM?
12 6. What is the degree of validation in the available literature?
7. What are the advantages and disadvantages of the models?
8. What are further plans for modelling particle breakage?
In this report first of all some information about DEM will be given. Second the theory behind particle breakage will be described. Third the models for particle breakage using DEM will be explained. In this chapter also the validation and the amount of citations of the models are treated. After this other models for modelling particle breakage without using DEM will be described. Finally further plans will be handled and a conclusion and recommendation will be given.
2 What is DEM
The discrete element method (DEM) is a numerical method to calculate the motion and collisions of particles. DEM is a particle based method which means that particulate materials are modelled by modelling individual particles and defining its (interaction) properties on a particle level. DEM has become widely accepted as an effective method of addressing engineering problems in granular and discontinuous materials, especially in granular flows, powder mechanics, rock mechanics, and comminution. With DEM obtaining a lot of output parameters are possible, for example; speed, throughput, size distribution, power usage and forces on a geometry. Figure 3 shows a belt conveyor modelled with a program which is using the discrete element method, the program is named EDEM. The different colors are different speeds of the particulate materials.
Figure 3: EDEM model (Solutions, 2015)
DEM is a model which detect contacts between particles and geometry, calculates the interaction forces and calculate the new positions based on Newton’s second law. There are a lot of simulation settings like time step, contact model, coefficient of restitution and particle size distribution, to simulate the reality as good as possible. Fundamentally, DEM solves Newton's equations of motion to resolve particle motion and uses a contact law to resolve inter-particle contact forces. Forces are typically integrated explicitly in time to predict the time history response of the material using an appropriate quadrature method. The DEM includes a family of techniques that use radically different treatments for the element geometry and the form of the contact forces. The Hertz-Mindlin
14 model and is thus well suited to the non-cohesive interactions which are to be used within the
computational models (Edinburgh, 2005). The model uses a spring-dashpot response to normal contact between particles and/or geometry, a Coulomb friction coefficient μ for shear interactions and a second spring-dashpot response to tangential or rolling friction interaction.
Figure 4: Hertz Mindlin contact model (Edinburgh, 2015)
To make simulations as real as possible the breakage of particles has to be modelled. DEM is able to simulate the breakage of particles. In reality it is not possible to make measurements during a process where breakage occur, only the results before and after can be measured. With DEM it is possible to predict the steps in between. This is important to get insight of the process, predict the wear in the geometry and calculate the power consumption.
3 Theory of particle breakage
Particle breakage occur in a lot of industries and in different stages. In this chapter the theory behind particle breakage will be described. First of all the strength of the particle will be handled with a basic description of the mechanical strength of materials. Also the implementation of particle breakage in DEM will be described. Second the different comminution models will be described and finally the relation of breakage with dust generation will be explained.
3.1 Particle strength and DEM
In this paragraph the basis of particle mechanical strength and the implementation in DEM is described. The mechanical strength of a particle is strongly dependent of the internal structure. Experimental characterization of these microscopic information is difficult. The discrete element method is an effective tool to calculate the mechanical strength of each particle individually. Breakage of a particle can affect the mechanical strength of the daughter particles (He, 2015). DEM is also able to calculate these characteristics.
3.1.1 Mechanical strength general
Fragmentation of brittle solids is one of the most fundamental problems in applied mechanics and is of considerable scientific and industrial interests. It is a phenomena with a wide range in the industry from big rocks till small processing industries like pharmaceutical. The mechanical strength of a particle is the ability to withstand an applied load without failure. To predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus
and Poisson's ratio. Figure 5 shows she stress-strain curve of a tensile test. Material strength refers to the point (yield stress) on the engineering stress-strain curve beyond which the material experiences deformations that will not be completely reversed upon removal of the loading and as a result the member will have a permanent deflection. The ultimate strength refers to the point on the curve corresponding to the stress that produces fracture.
16
Figure 5: stress-strain curve (Google, 2014)
3.1.2 Mechanical strength estimation
A lot of experimental and theoretical efforts have been made to estimate the required force to break a brittle solid into fragments with desirable size distribution. The experiments are done by compression on two ways, statically and dynamically. With these tests the characteristics of a material are given like deformability, hardness, crushing strength and tensile strength (Chau, 2000). The double impact test is a test to investigate the energy required for fragmentation and correlation is made between the static and dynamic energies required for fragmentation. The double impact test uses a sphere
between two flat plates to compress. The calculation are the same as the Hertz contact stress with the theoretical analysis by Hiramatsu and Oka, 1966. This model obtained an analytic solution for an isotropic sphere under diametral point loads, which were modeled as uniform normal stress acting diametrically on two small areas on the surface of the sphere (Hiramatsu and Oka, 1966). The
predictions of the failure load for various sizes and strengths of spheres agree very well with the static experiments. Comparisons of the static and dynamic tests show that the impact energy required for fragmentation of a sphere can be approximated as 1.5 times of that for the static test (Chau, 2000). The maximum contact force is larger in the static case than in the dynamic case, the energy required to fracture the sphere is larger under dynamic condition than under static condition. As expected, the dynamic impact energy needed for fragmentation increases monotonically with the size and strength of the spheres. However, the contact time at failure does not exhibit a clear trend with the changes in size and strength of the spheres. Figure 6 shows the comparison of the experimental and theoretical results.
Figure 6: Theory and experiment comparison (Chau, 2000)
3.1.3 Mechanical strength in DEM
The discrete element method is an effective way to investigate particle behavior because it treats particle individually and explicitly considers the particle characteristics, material properties and the particle forces. As seen in the previous chapters the mechanical strength differs with the different particle sizes. This has to be implemented in DEM. Here for the size and shape of primary particles is of relevance. Agglomerates consisting of nanoparticles exhibit much greater strength than
agglomerates made of micron-sized particles (Spettl, 2015). Also the microstructure plays a central role in the crushing of rocks or their mechanical behavior, which is influenced by the shape of primary particles.
The bonded-particle model (BPM) is an approach to simulate the mechanical behavior of agglomerates numerically using DEM, where the agglomerate microstructure is specified by a dense packing of spheres that are bonded together. Usually,agglomerate microstructures are generated such that these packing’s of primary particles have similar properties as observed experimentally in real agglomerates. In this method, DEM simulations are used to evaluate the mechanical behavior of spherical
agglomerates whose microstructure is generated according to a flexible stochastic model (Spettl, 2015). Realizations of the proposed stochastic microstructure model are suitable as input to the BPM and primary particles are spherical, non-overlapping and connected by bonds. Advantages of the proposed stochastic model are precise control about the microstructure. The stochastic model is used to generate agglomerates with specific micro structural properties.
To calculate the new mechanical strength of the particles first the breakage need to be detected. Here for an automated method to analyze thecompression results of all agglomerates statistically is used. Available data for breakage detection is the force-displacement curve for every agglomerate. Below a figure is shown of the force-displacement curve. A suddenly drop in the force means a breakage in this curve.
18
Figure 7: Force displacement curve. (Spettl, 2015)
3.2 Comminution models
There are different models and theories about comminution for particle breakage. In this paragraph the different comminution mechanisms will be described. Also the virtual comminution model will be handled.
3.2.1 Comminution mechanisms
There are three types of comminution mechanisms (Cleary, 1999) to predict the particle size distribution after exit.
1. Breakage by high energy normal collisions.
When steel balls or large rocks impact at high speed on each other or the geometry breakage by high energy normal collisions occur. This could be useful but also wear will appear, this is undesirable.
2. Attrition
In both the avalanching region and near the shell in the region where material is being lifted, the shearing action produces attrition where small fragments are rubbed from the larger ones.
3. Low energy crushing near the shell
In granular material the force is transmitted via a small number of chains of particles, the members of which experience very large instantaneous forces. The intensity of the force increase with the depth into the charge. If these forces produce tensile forces within the particle that exceed their yield stress then they are crushed.
Cleary, 1999 used DEM to calculate quantities such as the rate of particle-particle and particle-wall normal and shear work and use the as indicators of the breakage and the attrition. This allows comparison of comminution performance for different configurations.
3.2.2 Virtual comminution model
The virtual comminution model has provided a breakthrough in technology advancement, whereby crusher variables can be investigated in a yet more detailed manner without the need for the expensive and lengthy testing. The virtual comminution model provides the necessary tool to reduce development times through providing enhanced design confidence.
This method treats each particle of the feed being modeled as a separate entity, following the motion and calculating forces and energy applied to each particle as it travels through the crusher. When the required breakage energy threshold has been reached, the particle breaks and daughter particles are generated.
The data required to determine the probability of breakage, and the resultant fragmentation, is derived from the results of drop weight breakage tests on the ore being modeled. The virtual crusher comminution model represents the first true microscale model, that can provide details of the crushing environment, and that can be examined in three dimensional space (Lichter, 2009). This makes it possible to investigate a wider range of crushing conditions in a relatively short period of time and to decide what combination provides the best application results.
3.3 Dust generation
Dust is generated in process steps such as transport, fluidization, drying processes, shearing, attrition, collision and bulk packing (Rhodes, 2008). With the breakage of particles a lot of dust will be
generated. In this paragraph the risks of dust generation, the testing methods and the relation with breakage will be described.
3.3.1 Risks
A large majority of raw materials and final product in the industry are constituted of powders. This has advantages and disadvantages. The advantage of powders compared with fluid are transport facilities, storage and volume reduction. The disadvantage of using powder is the dust generation. Dust can be dangerous and unhealthy. Dust emission leads to several risks related to economics, health, hygiene, product quality and process safety (Nguyen, 2013). The level of risk associated with dust particles depends on chemical composition and particle size. Depending on the specific nature of the material, dust may contain toxic contaminants. So it is unhealthy for human being. Also when people breathe in too much dust it is dangerous for the lungs. Forms of asthma can occur and it is bad for the eyes of
20 human beings also. People die earlier by heart and vascular disease due dust. Here for it is important to control the dust process and keep it as low as possible. If this is not possible people who are working in such an area have to wear a masker and glasses. There are several measures depending on the process to prevent dust generation. For example a dust filter can be used. In some cases it’s hard to reduce the dust generation. In this case it is also possible to spray water over the material which will lower the dust on the material.
Recently, a number of research groups have carried out studies that are relevant to the dust generation problem (Weerasekara, 2013). One significant issue is that the frictional and wearing properties are not well-known at a typical atmosphere, temperatures, and pressures. This is a risk because without these information it is difficult to control the process. Also it make it more difficult to predict the wear in machines and geometries. This is a disadvantage because optimizing the process is not possible. If this dust generation can be implemented in the DEM model this could be a solution to control the process.
A second major problem is the danger of explosion. When using a material with danger for explosion, for example sulfur, several characteristic parameters has to be controlled carefully. These are
including minimum ignition temperature, minimum ignition energy, lower explosive limit, maximum explosion pressure, explosion index and limit oxygen concentration (Yanqiua, 2014).
3.3.2 Testing methods
The amount of dust generation in density (kg/m3) can be tested with many different methods such as
the drop test, fluidization test and the rotating drum test (Saleh, 2013). The main steps of all the methods are:
1. Taking a representative sample of the powder
2. Applying constraints to the sample
3. Releasing the dust
4. Sampling the emitted dust
5. Analyzing the emitted dust
These test are unfortunately limited to specific situations. This is mainly due to the difficulty to adapt the process a powder undergoes in a given process to another one. Therefore, there is still a need to develop new tests for proper assessment of dust emission (Saleh, 2013). An ideal test should be able to:
1. Cover a wide range of stresses encountered in practical situations and various processes. This condition is necessary for the extension of the test to a larger variety of industrial situations.
2. Determine the intrinsic amount of dust contained in a powder
If these two requirement are combined in one test the result will be usable for dust generation in real processes.
3.3.3 Relation of particle breakage with dust generation
It is known that the particle breakage process can bring out dust. So it can be concluded that there is a relation of dust generation with particle breakage. This relation itself is not investigated explicitly in the available literature. However, there is literature available of modelling dust generation in DEM. The next paragraph will describe the modelling of dust generation in DEM. The relation of particle breakage with dust generation is a good option to investigate in the near future.
3.3.4 Dust generation in modelling
Dust generation is a complicated process to be studied due to great number of variables to be considered, so any related theoretical or numerical simulation is forced to implement many
simplifications. Furthermore, there are numerous methods to study such a problem. One of them is the newly introduced Computational Fluid Dynamics and Discrete Element Method (CFD-DEM)
coupling method. This method is expected to be used extensively in near future (Bagherzadeh, 2014).
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. CFD is an approved method and has applications in many engineering fields. In case of fluid-solid interaction modelling, CFD can take advantage of both Eulerian-Eulerian and Eulerian-Lagrangian approaches. Eulerian-Eulerian approach takes the solid particles as a continuum interpenetrating and interacting with continuous gas (Deng, 2013). This model allows momentum exchange between the fluid and solid phases, but also considers the effect of the particle solid fraction on the fluid phase.
Numerical approach combining the Computational Fluid Dynamics and Discrete Element Method prove to be advantageous. This coupling method is a state-of-the-art simulation technique, increasingly used to study the physics of multiphase flow related to various industrial problems. CFD-DEM coupling method follows the Eulerian-Lagrangian approach. The coupling of this method is described in steps:
1. The DEM solver calculates the particles positions and velocities.
2. For each particle, the corresponding cell in the CFD mesh is determined.
3. For each cell, the volume fraction as well as a mean particle velocity is determined.
4. Based on this information, the momentum exchange terms between the gas phase and
22 5. Using the momentum exchange terms the fluid flow is calculated.
6. The fluid forces acting on the particles are calculated and sent to the DEM solver.
7. The routine is repeated from 1
In this method the motion of individual particles is obtained by solving Newton’s second law.
3.3.5 Single particle settlement
Multiphase flow is a simultaneous flow of materials with different states or materials with different chemical properties but in the same phase (Bagherzadeh, 2014). There are a lot of investigations according this subject but still the hydrodynamics of such complex flows is partially understood. A very simple version of a multiphase flow problem is the single particle settlement (SPS) problem. The fluid dynamic drag on a sphere and the terminal settling velocity of a single spherical particle in fluid are of interest in numerous fields. Improvements in predictions could be useful in mathematical modelling of particle behavior to be used for modelling all particle processes, specifically in dust liberation field of research. It is important to be able to estimate terminal velocity of particles as it can be used in studies for particle size reduction and suspension. In many phases in bulk handling size reduction happens which might finally lead to generation of micro sized particles.
The first step of the SPS is to identify various particle interaction forces. The forces can be sorted in two main groups of driving forces and damping forces. The only driving force for the case of SPS is the force of gravity (Bagherzadeh, 2014). This force make the particle settle downward. On the other hand damping forces, opposing the gravity force and acting upwards, include buoyancy force, drag force, virtual mass force, Basset force and lift forces.
4 Methodology of modeling particle breakage
There are different methods to implement breakage in the DEM model. The different methods are developed over the time and used in the discrete element method. In this chapter the theories of the four methods of modeling particle breakage using DEM will be described with its advantage and disadvantages.
4.1 Two dimensional packing
The earliest model with particle breakage implemented in the DEM simulation consist of 2D circular discs and simple breakage criteria. In this model progeny particles are being packed into the space left by a breaking parent particle (Astromm and Herrmann, 1998). This method is called the two dimensional packing method. This paragraph will describe the theory behind the two dimensional packing method. Also the validation process and the amount users of the method will be handled.
4.1.1 Theory behind the two dimensional packing method
The two dimensional packing method is a method with a numerical two-dimensional model for the fragmentation of a granular medium under pressure. The grains and fragments are modelled as elastic circular discs. In the simulation a few grains are placed at random in a two dimensional box (Herrmann, 1998). By overlap of the grains they repel each other with a force (eq. 1).
(1)
The radius of the overlapping grains are ri and rj, ds is the distance between the center of the grains
and E the Young's modulus. The wall of the box are elastic also. Decreasing the size of the box will give a pressure.
There are two different types of fragmentation criteria which the grain break in this method.
1: A threshold value for the pressure on a grain and
24 Type 1 is quite natural as the pressure is the total compressive force on a grain. Type 2 is more delicate because if the grains are stiff and smooth the contacts will be almost pointlike, which will lead to a high stress concentration.
4.1.2 Fracture mode
The fracture mode means how an individual particle fragments. All fragments are modelled as circular disc and the total mass has conserved during fragmentation. There are 3 problems with choosing a fracture mode:
1. The number of fragments at each breaking should be kept low so that many breakings can be made in each simulation
2. The fragments should be chosen so that they can packed in such a way that local pressure decreases at a breaking
3. The breaking mechanism should at least to some extent mimic the real event.
It is impossible to satisfy all the 3 points. So two different criterions are used:
1. Split a grain in two equal size fragments.
2. Pack 12 fragments of three different sizes into the area of the broken grain and place the rest of the mass just outside the surrounding grains.
Criterion 1 violates problem 2 and criterion 2 violates problem 1 but satisfies problem 2 and 3. After some simulations the biggest difference between the two modes is that some grains remain unbroken using mode 2. This is because when using mode 2 the radius are decreasing fast and the small radius surround unbroken grain, which adopt the pressure so the big grain will not break (figure 8).
Figure 8: a=mode 1, b=mode 2 (Herrmann, 1998)
4.1.3 Fragment-size distribution
There have been many investigations devoted to understanding the fragment-size distribution. There are two distributions which appear, the log-normal and power-law distribution (Astromm and
Herrmann, 1998). The origin of the log-normal size distribution is quite easy to understand. If all grains and fragments break independently of each other and with a constant probability per unit time, then the number of breakings per unit mass will have a normal distribution. If at each breaking a fragments are formed, then the number c(i) of fragments that have gone through i breakings is given by equation 2.
(2)
N0 is the original number of particles, and ī the average number of breakings per mass-unit. The reduction in the particle radius is shown in equation 3.
= * (3)
By combining equation 2 and 3 a log-normal distribution is obtained.
With the power-law distribution it is possible to fill the entire space with fragments even if they have a difficult shape like circles. This can be done by choosing the right exponent and arranging the
fragments on a fractal set (Falconer, 1990). In experiments, power-law distributions commonly result from highly energetic impacts such as explosions, but also ongoing fragmentation can lead to a power-law size distribution.
4.1.4 Validation
Since the DEM method offers such strong advantages in modelling and understanding comminution, it is essential that both the DEM methods be properly validated. Validation is limited both by the
availability of suitable good quality data and by the preparedness of groups and software developers to take responsibility for validating their predictions (Weerasekara, 2013). It is important to
differentiate between validation of the methods and of the software implementation. It is easily possible for problems to occur in either area. That one DEM code is validated indicates that it is possible for such a prediction to be made accurately and that the test code can do this but this does not mean that all DEM software will reproduce this level of accuracy. Each one needs to be
independently validated (Weerasekara, 2013).
The two dimensional packing method is the first method which has implemented breakage into the DEM model. In this paper there is no clear description of the validation process. The actors only looked at one breakage example from reality and made a model on the basis of these results.
Afterwards the actors used different parameters with the model but did not validated the examples. In future methods this is also coming back. The actor who used the two dimensional packing method, mention that the validation has to be done again.
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4.1.5 Amount of citations
This article is cited 33 times. This article is mostly cited in 2015, 7 times. The mostly citing journals of this article is: Granular Matter, 8 times. There is no researcher who did cited this article more than one time.
4.2 Simple breakage
In this paragraph the method for breakage by Cleary, 2001 will be given. High energy impact breakage and compressive breakage under the toe of the charge are taken into account by this breakage model.
4.2.1 Simple breakage model
The simplest method to model both impact and compression breakage into DEM is to construct macro particles from small sub-particles (Cleary, 2001). Doing this allows detailed analysis of particle
breakage under a range of conditions. The disadvantage of this method is that the computational cost is linearly dependent on the number of sub elements (Cleary, 2001). For example a 3D industrial scale mill simulation uses about 106 particle. An alternative method is to use a rule base to identify the
conditions under which particles would be expected to fracture and then replace the fracturing parent particle with an appropriate assembly of daughter particles packed into the space occupied by the parent.
The parent and daughter fragments are spherical and their sizes are chosen using geometrical criteria to optimally pack the space occupied by the parent particle and a minimum fragment size is
nominated. Figure 9 shows a collision of two particles. The parent particle dissipate enough energy to fracture and replace by the daughter fragments. The daughter fragments are now free to move, collide and break again.
Figure 9: Simple breakage method (Cleary P, 1999)
An example is the rotating box. The box is filled partially and rotated, what will give impact at the particles. If the energy is high enough the particles will break. The process is shown in the figure below. The grey colors are the daughter particles which are broken.
Figure 10: rotating box (Cleary, 2001)
4.2.2 Validation
In this method calibration and validation is done. Experimental validation of DEM predictions for a centrifugal mill is done which showed excellent agreement both for the charge motion and the power draw. Comparison with quality experimental data allows to understand the accuracy of various types of DEM models and the penalties associated with the various assumptions made by the models. Such validation exercises are critical in establishing the accuracy of existing models and improving their accuracy in the future. Calibration of the energy and force thresholds used in determining whether
28 breakage occurs for specific particles according to these mechanisms is not at all straight forward. Quantities that can be experimentally measured such as the impact energy for breakage using the drop weight test and fracture toughness, compressive breakage measures are not easily related to the calculated quantities used in DEM breakage models. Another critical issues is that for compressive breakage, tests such as with uniaxial, biaxial or triaxial tests are all performed at slow or very slow strain rates since they were designed for measuring rock properties in geo mechanical situations. In crushers, the strain rates are several orders of magnitude higher than in traditional rock mechanics testers (Cleary, 2014).
4.2.3 Amount of citations
This paper is cited 154 times in other papers. 56 times of these citations, Cleary is also a writer. So it can be said that the paper is used 98 times by other researchers without co-operation by P. Cleary. R.D. Morrison is the one who cited the paper the most, 14 times.
4.3 Fast breakage model
A standard Dem approach cannot be applied to systems where size reduction is an important element in the flow of particles. Lichter, 2009 has therefore developed a breakage model that incorporates elements of population balance modeling techniques to describe breakage as function of the loads on the individual rocks (Lichter, 2009). This physics based virtual comminution (see 3.2.2) model will enable engineers to optimize the design development of future crushers.
4.3.1 Early models
The early models handled in the previous paragraphs like the simple breakage method and the two dimensional packing method used rocks constructed as glued together by contacts that will not let go till specific tensile stress. This technique provides good data but it is restricted in its application due to the very high computational costs. This model is therefore used for coarse crushing applications or 2D models. 2D models can provide useful data but it is not suitable for providing absolute performance data. The new method has largely overcome the limitations of these old models. The new method is called the fast breakage model.
4.3.2 Fast breakage model
The first difference with the simple breakage method and the two dimensional packing method is that in this model polyhedral particle are used. ‘‘Glued” spheres, or non-spherical particles generated with the use of super quadratics, have the implicit non ideality that they cannot conserve both mass and volume when broken (Lichter, 2009). The virtual comminution model described here therefore uses
randomly shaped convex polyhedral particles. The breakage model uses a population balance model (PBM) approach (Herbst, 2003).
The DEM simulation provides the energy applied to every particle in a system, either by collision with other particles, or with the crusher bowl liner or mantle. If the energy of a contact is determined to be sufficient to break a particle, the particle is broken instantaneously into the sizes calculated from the solution of a set of ordinary differential equations, constituting the energy specific PBM (Lichter, 2009). Each daughter particle behaves as a separate particle and can break again when the applied energy is sufficient.
(4)
(5)
Equations 4 and 5 describe the primary ore breakage. The first equation describes the fracture rate and the second the size distribution of daughter fragments. These functions are simplified into a functional form that contains three parameters to describe the selection function, and three
parameters to describe the breakage function. SiE is the normalized selection function and is primarily
an ore characteristic, di is the geometric mean of size fraction i, and the breakage function Bij is the
fraction passing size di from the breakage of particles in the size fraction [dj, dj+1]. The breakage
characteristics like the energy specific PBM, impact energy and the resultant fragmentation are determined by a single particle drop weight test. Figure 11 shows an example of a cone crusher modelled with the fast breakage model.
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Figure 11: Cone crusher (Lichter, 2009)
4.3.3 Validation
The actors (Lichter, 2009) of this method did take the validation process very serious. In the paper some examples of the validation process are described in detail. The actor almost validated everything like, crusher throughput, crusher power draw, crushing force and product size distributions. The first example described in detail is the validation process with a pilot laboratory test conducted on a B90 cone crusher for the throughput. The B90 is a small continuous laboratory scale cone crusher. First a very hard material, sorilla granite, is used. The test are done at Metso Minerals in Finland. The measured throughput during validation test was 40.7 kg/min and the model calculated 41.5 kg/min. This agreement is excellent.
The validation of the breakage is more difficult because a minimum particle size has to be
implemented in the model. This minimum size has to be chosen carefully because it has a big effect on the particle size distribution. The results from the simulation were compared to continuous pilot scale crushing tests conducted at Metso Minerals in the USA. Of interest with this validation exercise is the distinct change in the breakage parameter estimates as a function of the size fraction in the feed. Two simulations were completed, one using the breakage parameter estimates from 50 mm rock, and the second using the parameter estimates from 25 mm rock. The measured throughput for the test was 121 tph. The simulated throughput with the two sets of ore properties were 111 tph and 131 tph. Current models allow such differences in the breakage parameters to be included in a single
4.3.4 Amount of citations
This paper is cited 17 times. This is not much comparing with the two previous methods. Jens Lichter did not cited this article by itself one more time. P.W. Cleary did cited this paper the most, 3 times. This paper is mostly cited in engineering, earth and planetary subjects.
4.4 Octahedral shear stress breakage
The cone crusher is the most common type of mineral comminution machine that is used widely in mineral and aggregate extractive industries to crush medium or above medium sized rocks. Huiqi Li first studied the particle flow in a chute without implementing breakage of the particles in the DEM model (Li, 2012). After this the breakage of particles is implemented in the DEM model in 2014 (Huiqi Li, 2014). In this paragraph the method of Li, 2014 will be described, named octahedral shear stress breakage. Octahedral means that a particle is subjected to diametrical point loads, equal in three mutually orthogonal directions
4.4.1 Particle replacement method
The particle replacement method (PRM) has been used to model particle breakage by Lichter, 2009. The PRM approach replaces the predicted failed parent particle by a number of new and smaller fragments. The achievement of a critical octahedral stress induced in a particle was used as the breakage criterionin the application. The breakage criterion and breakage function were determined from the results of a series of experimental compression tests performed on a feed of different sizes of granite rock samples. For a given particle feed size distribution, the performance of the
computational crusher model was validated by evaluating the effects on the predicted product size distribution. However, in that study the rock particles were described by polyhedral models and the fracture criterion and the parameters used to determine the distribution of the resultant post breakage fragment sizes were not discussed. In the method of H.Li it was decided to employ the octahedral shear stress breakage criterion for the simulations.
4.4.2 Method of H.Li
The method of Li, 2014 avoids particle fracture under a high hydrostatic stress but low deviatoric stress, for example, if a particle is subjected to three equal orthogonal diametrical point loads, it would not break. The octahedral stress is expressed in equation 6.
32 In this equation Q1, Q2 and Q3 are the principle stresses in the three directions. The particles would break and replaced when the computed octahedral shear stress exceeds its strength. The Weibull (Weibull, 1951)statistical distribution is one of the most commonly used tools to describe the fracture of materials. Therefore in this study the rock particles were given strengths for a given size described by the Weibull distribution.
In the simulation a sphere is used as particle. The contact model Li, 2014 used is the linear contact model. Energy dissipation at contacts was modelled by a viscous damping model characterized by a critical damping ratio. The critical damping ratio was calibrated by comparing the results of model simulation drop tests with corresponding laboratory drop tests (Li, 2014).
In the simulation huge local pressure spikes were generated by the overlaps of particles in the size distribution function. The imposed elastic energy caused by the overlap needs to be accommodated after every update of particle breakages. Otherwise, all the fragments will break infinitely under the artificially created huge pressure. To solve this problem, Li, 2014 defined a freeze state to release the artificial energy. The cone crusher model will be set into the freeze state once breakage occurs with the following assumptions (Li, 2014):
- When new particles are generated, all other particles are initially given zero rotational and translational velocities. The locations of the boundaries (the walls of the crusher model) are fixed.
- In this state, all of the particles are temporarily assigned an artificially large mass to minimize the motions caused by collision.
- The new particles are given an artificially low stiffness to minimize the energy release generated by the overlaps.
- The viscous damping system is removed and a high local damping coefficient of 0.9is added to accelerate the stabilization of the new particles.
- Gravity is removed.
Figure 12: Schematically process flow (Li, 2014)
4.4.3 Validation
The literature of this method did not spend much to the validation process. The validation is done and the results are shown in a graph for the speed of marked peddles and clearance time but not for the breakage and the details are not described. The first validation is for the speed of marked peddles with the closed side settings set to 50mm and the bite angle at 18 degrees. The closed side setting is the smallest length in the closed position of the crusher. The bite angle is the angle subtended between the concave and the mantle (see figure 13).
Figure 13: Crusher: D=Closed side setting, B=Bite angle, C-left=Mantle, C-right=Concave. (Metso, 2010)
In figure 14 the results are seen of an experimental setup and the simulation with a vertical deposition and an inclined deposition. It is seen that the inclined deposition agrees better with the experimental data.
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Figure 14: validation speed of peddles (Li, 2014)
Also a validation is done for the clearance time in seconds. This is the time all peddles leave the chute. Here the bite angle is taken at 18, 20 and 22 degrees and the closed side setting is set to 40mm. The experimental and simulation results are compared in figure 15. There are no further validations for the breakage process.
Figure 15: validation clearance time. (Li, 2014)
4.4.4 Amount of citations
This method is cited 7 times. 5 times in 2015 and 2 times in 2014. P.W. Cleary also cited this paper. Also this paper is not cited more than 1 time by one researcher.
5 System modelling
Till now four method are described to implement particle breakage in the DEM. In this chapter two model will be described to simulate particle breakage without using DEM. Also these two model are not only describing the process of particle breakage but it is the description of the whole system. The first model which will be described in this chapter is control oriented modelling, the second one is real-time algorithm.
5.1 Control oriented modelling
This method is a dynamic method for prediction the output size of cone crushers. It represents the material distributions as vectors and the operations as matrix multiplications, and is also known as matrix analysis approach. In this paragraph the theory of control oriented modelling will be described.
5.1.1 Three activities
There are three activities that describe the behavior of crushers. These are: breakage, selection and classification. The overall behavior of the crusher is a repetition of these activities, which can be represented as matrix multiplication in the case of the discontinuous function approach (Atta, 2013). The breakage matrix B is a lower triangular matrix, in which the entry represent the mass proportion of particles from the size class that ends up in size class, after breakage. The selection matrix S is a diagonal matrix, where each entry represents the probability of breakage of a particle in the size class. The classification matrix C is a diagonal matrix, where each entry represents the fraction of material from the size class in a particular zone that is prevented from moving to the next zone. The crusher is divided into three zones and each zone has its own input and output. The breakage function, the classification function and the selection function were discretized into matrices according to the size classes as seen in equation 7.
(7)
Here m is the number of size distribution classes. In this literature m is chosen as maximum 24 classes. The largest size class is 167.27mm. The matrix and crusher are simulated using Matlab Simulink.
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5.1.2 The proposed model
The crusher is divided into N zones and by using the matrix representation the output size distribution can be predicted using the inflow to the zone as an input to the model. Figure 16 shows the different zones. In this figure the mantle is 1.2m high, the CSS is 3 cm and the stroke and bed height are different in all zones.
Figure 16: Multi zone approach: CSS= closed side setting, b=bed height, s=stroke. (Atta, 2013)
At each zone all the 3 actions will be performed and all the zones will be combined after. This is the so called multi zone approach. Figure 17 shows a schema of the process where Bi is the breakage matrix,
Si the selection matrix, Ci the classification matrix, Ui the vector representing the input mass size
distribution, Zi representing the output mass size distribution and Xi is representing the mass size
distribution inside the zone while Firepresents the material that is retained in the zone, after applying
the actions of selection and breakage on it.
The equation governing the operation of the zone are summarized and shown in equation 8-13 with βi
the fraction of material pass down out of the material that are classified to pass down, Li the length of
the zone, Mi the maximum mass a zone can contain and α is a linear action on all the materials Zithat
are qualified to pass to the next zone. This factor will determine the percentage of material to flow after the classification action.
(8) (9) (10) (11) (12) (13)
Now the overall model is obtained and showed in the figure 18.
Figure 18: Overall model. (Atta, 2013)
5.1.3 Mixed materials model
The advantage of control oriented modelling is that it is also possible to model different types of materials. This makes the equation more difficult but it is possible. Figure 19 shows the scheme of the
38 process with different types of materials. Here is assumed that each material has its own breakage function but the same selection matrix and classification matrix.
Figure 19: Mixed material model. (Atta, 2013)
5.1.4 Validation
Here the validation process is not treated. There is only a referral to another literature written by Lee and Evertson (Lee, 2010). In this papers is seen that the results of the control oriented modelling is the same as the experiments in the paper of E.Lee. Also all parameters are the same as the
simulation. So the validation is done but nothing is explained in the paper.
5.1.5 Amount of citations
This article is cited 2 times. One time by Delaney G.W., Morrison R.D., Sinnott M.D., Cummins S. and Cleary P.W. and the other time by Karelovic P., Putz E. and Cipriano A. About the application of this method nothing is written in the paper. It is written that this model is in by Matlab Simulink but further information about the application is not given.
5.2 Real-time algorithm
This method uses a system for controlling the closed side setting of the crusher and thereby the size reduction of particles. As explained in previous chapters the closed side setting is the smallest outlet in the crusher in a closed position. With a frequency converter also the eccentric speed can be adjusted in real time in addition to the closed side setting. The eccentric speed affects the dynamic interaction between the rock material and the crusher liners. Especially the number of compressions the material
is exposed to is affected and also the local compression of the rock material is affected, thus the particle-size distribution of the product. The eccentric speed has also a great impact on the product properties. The eccentric speed affects the number of compressions that the material is exposed to and thus the particle-size distribution of the product. Similarly, the eccentric speed also indirectly affects the shape of the product.Eccentric speed also affects crusher capacity. Real-time feedback data on the sellable product streams can be obtained by applying mass-flow sensors to the process. In this paragraph the theory behind the real-time algorithm will be described.
5.2.1 Control system
This method reports the development of a monitoring and control system including a two variable online algorithm for the selection of the set point for eccentric speed with respect to the current closed side setting. The different product yields from the crusher were monitored by mass-flow meters and continuously evaluated by a fitness function. A model for the outcome of the crushing stage, with the two parameters, eccentric speed and closed side setting, was fitted mathematically to the
measurement data. However, since the process varies continuously, due to the wear of crushers and screens and feed material variations, the performance landscape is also continuously varying. Therefore, an Evolutionary Operation (EVOP) approach was adopted, wherein the variations are instead used to continuously find an operating point closest to the optimal (Hulthen, 2011). Practical crushing operations encounter a wide range of variables like natural variations of the rock material properties in the feed, wear of the equipment, weather and unwanted stops. So when implementing real-time control of a crushing plant, monitoring of the status of the actual process is crucial. It is difficult to measure product properties in real-time at a plant due to the high capacities, the dirty environment and the wide range of product sizes.
5.2.2 Real time algorithm
The models used in the real-time algorithm for closed side settings and eccentric speed, both build upon the behavior of the process with a closed loopreturn flow of the oversize particles. The assumed appearance of the model is shown in equation 14 where y is the crushing stage output (product yield), x1 is the eccentric speed, x2 is the time since the last closed side setting adjustment and a till f are constants:
(14)
This model was fitted to the model described above and simultaneously use it for optimal crusher operation. Therefore, an EVOP (Hulthen, 2011) approach was implemented on the crusher with two variables. The closed side setting is adjusted regularly by a hydraulic motor, either on manual command or automatically. This is typically done every two or three hours of operation. When the liners become worn the crusher must be empty of material before the closed side setting can be adjusted. The closed side setting is adjusted by stopping the feed, unclamping the thread, turning the
40 top shell, clamping, and restarting the feed. This takes six to ten minutes before the process is up and running in steady-state mode again. Therefore, this adjustment can only be done a couple of times during a shift. Every operation time period between adjustments can therefore be defined as a run in an EVOP context. Taking the model and the crusher-type limitations into consideration, three
parameters have been resolved here:
1. Power draw when adjusted, if the power draw is high, the closed side setting is small. This implies high reduction but decreased capacity.
2. Eccentric speed when the run is started.
3. Speed change, how much the eccentric speed should be changed, every ten minutes.
The EVOP algorithm clearly pointed out the direction for the dynamic optimal speed. Compared with earlier algorithms, this EVOP algorithm is less noise sensitive. However, it cannot react to short term variations, changes in the raw-material feed. Once detailed modeling has provided sufficient process insight the EVOP can be replaced by another algorithm for set point selection.
5.2.3 Validation
The data obtained for the validation is all recorded in phases. The phases are shown in figure 20.
Figure 20: EVOP phases. (Hulthen, 2011)
Figure 21: Results EVOP. (Hulthen, 2011)
The standard deviations during the runs were relatively high, on average 14% of the measured values. Box and Draper, however, state that large experimental error often indicates a lucrative source of improvement and it is probable that large effects can be detected (Box, 1998).
The correlation coefficient between the average power draw and the performance value is 0.845, which clearly indicates a link in the form of the amount of size reduction achieved. However, the correlation coefficient between the maximum power draw and the performance value was only 0.588, which is low.
5.2.4 Amount of citations
This method is cited 4 times. P.W. Cleary did cited this article one time in 2015 also. Another two know actor from this literature assignment who cited this method are M.D. Sinnott and K.T. Atta.
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6 Future DEM models
One of the challenges remaining for DEM modelling is the need to adequately take account of the fine particles in milling applications (Weerasekara, 2013). These particles represent a reasonable volume of the charge, modify the collisional and transport behavior of the coarser mill charge components and are the key component about which the user wishes to make predictions in terms of their size
reduction and transport. The CFD-DEM coupling method is a good start but it has to be improved further.
Figure 22: CFD-DEM Coupling method (Dastidar, 2015)
Another area that represents a challenge for the future is in describing realistically comminution in highly confined conditions, such as those found inside a high pressure roll crusher. This machine poses the additional challenge of requiring a mechanical coupling that will allow predicting the response of the movable rolls to the conditions existing inside the packed bed. Most important in the future is the uptake of the DEM outputs into standard comminution models used in design and optimization of equipment and processes. A primary barrier is the gap between the detailed and complex outputs of the DEM simulations and the simplistic, or even non-existent, collision and energy profiles used in the industrial semi-empirical models (Weerasekara, 2013). It is considered worthwhile to review the application of the simple contact models for future DEM simulation of comminution systems, as the contact mechanics are inadequate for detailed analysis of the collision and breakage events. With the massive improvements in computational capability the time may be ripe to take up a new level of more physically meaningful contact models.
