the future of comminution modelling

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The future of comminution modelling M.S. Powell a, , R.D. Morrison b a Mineral Processing Research Unit, University of Cape Town, PB Rondebosch, 7700, South Africa b JKMRC, the University of Queensland, Indooroopilly, Queensland, 4068, Australia Received 5 May 2006; received in revised form 17 August 2006; accepted 18 August 2006 Available online 4 October 2006 Abstract The current status of the modelling of comminution processes is assessed in light of its capabilities and weaknesses. The principles required for a major upgrade in modelling capability are proposed. The use of advanced computational techniques to provide detailed information on the mechanical environment in comminution devices, linked in with correctly designed breakage tests, underpin this development. These will lead us into more fundamentally correct models that include mineral liberation and can be applied to the design of novel comminution devices. © 2006 Elsevier B.V. All rights reserved. Keywords: Comminution; Modelling; Computational methods; DEM; Breakage testing; Liberation 1. Introduction It is appropriate to consider the future of comminution modelling in this special issue, as Prof. Peter King has always been a leading thinker in this area. He has always worked towards major advances in comminution models and their potential applicability. It is well past time to move on from the slide rules and log tables that limited the comminution models to single- number descriptions. The comminution design, opera- tion, and modelling world has clung to these as though they have holy significance. While these methods have the virtue of simplicity, they have many shortcomings when applied to real designs. Perhaps an instructive parallel occurs in structural engineering. Even though there are many analytical so- lutions for ideal beams at ideal loading and constraint conditions, almost every engineering company will use detailed finite element analysis to examine any design under serious consideration for construction. The underlying driver in both cases is the enormous (and continuing) reduction in the real cost of compu- tation. This drives more complex (and hopefully better) measurement and models. In a keynote address presented at the IMPC (King, 1993) king noted that a fundamental understanding of the basic micro-processes associated with the dynamics of particulate systems their transport and fracture is still lacking. He followed this by stating “…the really significant advances in comminution technology in the forthcoming decade will only come from the exploitation of basic fundamental understanding of the fracture process to improve industrial comminution processes.King postulated that breakage in a complex system “… can be synthesised from the universal single-particle breakage functions once the patterns of energy distribu- tion and stress application are known. These key Int. J. Miner. Process. 84 (2007) 228 239 www.elsevier.com/locate/ijminpro Corresponding author. Tel.: +27 21 6503861; fax: +27 21 650 5501. E-mail address: [email protected] (M.S. Powell). 0301-7516/$ - see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.minpro.2006.08.003

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Page 1: The Future of Comminution Modelling

84 (2007) 228–239www.elsevier.com/locate/ijminpro

Int. J. Miner. Process.

The future of comminution modelling

M.S. Powell a,⁎, R.D. Morrison b

a Mineral Processing Research Unit, University of Cape Town, PB Rondebosch, 7700, South Africab JKMRC, the University of Queensland, Indooroopilly, Queensland, 4068, Australia

Received 5 May 2006; received in revised form 17 August 2006; accepted 18 August 2006Available online 4 October 2006

Abstract

The current status of the modelling of comminution processes is assessed in light of its capabilities and weaknesses. Theprinciples required for a major upgrade in modelling capability are proposed. The use of advanced computational techniques toprovide detailed information on the mechanical environment in comminution devices, linked in with correctly designed breakagetests, underpin this development. These will lead us into more fundamentally correct models that include mineral liberation and canbe applied to the design of novel comminution devices.© 2006 Elsevier B.V. All rights reserved.

Keywords: Comminution; Modelling; Computational methods; DEM; Breakage testing; Liberation

1. Introduction

It is appropriate to consider the future of comminutionmodelling in this special issue, as Prof. Peter King hasalways been a leading thinker in this area. He has alwaysworked towards major advances in comminution modelsand their potential applicability.

It is well past time to move on from the slide rules andlog tables that limited the comminution models to single-number descriptions. The comminution design, opera-tion, and modelling world has clung to these as thoughthey have holy significance. While these methods havethe virtue of simplicity, they have many shortcomingswhen applied to real designs.

Perhaps an instructive parallel occurs in structuralengineering. Even though there are many analytical so-lutions for ideal beams at ideal loading and constraint

⁎ Corresponding author. Tel.: +27 21 6503861; fax: +27 21 650 5501.E-mail address: [email protected] (M.S. Powell).

0301-7516/$ - see front matter © 2006 Elsevier B.V. All rights reserved.doi:10.1016/j.minpro.2006.08.003

conditions, almost every engineering company will usedetailed finite element analysis to examine any designunder serious consideration for construction.

The underlying driver in both cases is the enormous(and continuing) reduction in the real cost of compu-tation. This drives more complex (and hopefully better)measurement and models.

In a keynote address presented at the IMPC (King,1993) king noted that “a fundamental understanding ofthe basic micro-processes associated with the dynamicsof particulate systems – their transport and fracture – isstill lacking”. He followed this by stating “…the reallysignificant advances in comminution technology in theforthcoming decade will only come from the exploitationof basic fundamental understanding of the fractureprocess to improve industrial comminution processes.”King postulated that breakage in a complex system “…can be synthesised from the universal single-particlebreakage functions once the patterns of energy distribu-tion and stress application are known”. These key

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statements demonstrate a conviction that the processmust be better understood in order to be better modelled.

2. Modelling status

The following is a brief overview of the status andpotential for development of comminution modelling.This overview is not intended to be comprehensive orcomplete, and the authors apologise in advance to themany investigators whose work is not mentioned. Themotivation for this outline is to set the scene for pro-spective areas for comminution research over the nextdecade, not to provide a comprehensive summary of allcomminution models.

2.1. Power-based models

The wonderfully elegant Bond descriptions (Bond,1952, 1961) are used and abused with little or noconsideration of their origins or intended use. Fred Bonddid a great job of correlating a well-controlled laboratorytest to the standard rod and ball mills of his time. He neverproposed these to cover all milling applications under thesun. Bond always made very clear his key requirement/assumption that the cumulative feed and product sizedistributions plot as at least approximately parallel lineson log–log or Rosin–Rammler axes. The need to modifythe Bond correlations is evident in the many variationsand ‘improvements’ developed over the years, to coverlarger mills, wider ball size ranges, changes to mill speed,etc. Morrell (2004) has recently published on the weak-ness of these improvements and provided the most up-dated and reasonable modification to the Bond Techniqueto improve its predictive capability.

The most notable downfall of the application of theBond method was its inappropriate application to SAGmill design, with calamitous results with respect to millsizing. It was also found that the techniques fall apartwhen applied to fine grinding devices, such as towermills. However, AG/SAG mills, crushers and many finegrinding devices do not satisfy the Bond requirement ofparallel size distributions.

A number of new empirical testing and modellingtechniques, generally based on correlations between alaboratory or pilot test and the full-scale application,were developed in answer to the shortfalls of the Bondtechnique by investigators such as MacPherson (1989)and Starkey and Dobby (1996). Alternatively, a numberof standard laboratory tests, such as BBWI, BCWI, JKDWT, etc., were correlated to the performance ofoperating mills via empirical relationships. Designerssuch as Siddall of Oreway Minerals (Siddall et al., 1996)

and Barratt (1989) successfully used this technique. Thecorrelations are usually restricted to in-house use, as theycarry the designer's intellectual property and businessvalue. The user has to basically have faith in the out-comes—usually based on a track record of the designer.

The strength, and limitation, of these empirical tech-niques is the credibility of their database. That is, thecorrelation between measured production data and thelaboratory or pilot tests on the same ore type. Thestrength is that if the design operation is in the sameregime as the database, then the predictions are generallygood. The limitation is if the new design is outside of thedatabase range, then predictions are likely to be un-reliable. The weakness is that it is dangerous to use thesetechniques to extrapolate to very new operating condi-tions or ore types, let alone new types of applications.

2.2. Population balance-based models

As comminution modelling progressed in the 1970s,and the investigators strove to describe a wider range ofequipment, a step change in the concept of modellingwas introduced. The fine work of investigators such asAustin et al. (1984), Herbst and Fuerstenau (1980),Whiten (1972), Morrell et al. (1993) (to mention but afew) moved modelling a large step forward with theintroduction of the population balance model (PBM).

If we consider the notional contents of any commi-nution device, we can reduce what is happening insidethe machine to three relationships. The first is theproportion of a specified particle type which is selectedfor breakage per unit of residence time. This is usuallycalled the selection function. The second is the degree towhich the selected particle type undergoes breakage.This is called the appearance or breakage function. Notethat it relates to an event not to a time or rate. The productof the selection function and the appearance function iscommonly called the breakage rate. The third relation-ship describes the selection of particles which are to beremoved from the process. This is called the dischargefunction. If it describes the proportion of a particular typeto be removed per unit time, then it is a discharge rate.

Many researchers use these terms interchangeablywithout clear indication ofwhich sense is intended, hence,the level of confusion over the PBM. With careful defi-nition, it is a quite general description and can be appliedto whatever types of particles we can distinguish—eventhough the standard usage is particle size.

Breakage within a ball or rod mill is reasonably selfsimilar with size and the PBM can be used to generatequite simple models of size reduction. Where appropri-ate, various mixing conditions can also be applied to the

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mill contents. For a detailed comparison of PBM asdeveloped by researchers worldwide, see chapter 2 ofNapier-Munn et al. (1996). The PBM along with themeasured self-similarity of breakage with progressivesize reduction leads to the concept of a breakage andselection function which underlies all the current modelsand forms a powerful framework for a self-consistentmodel. A key to this is the appearance function, that is, adescription of the size distribution of a particle once it isbroken. This is ore-specific, and an issue with applyingthese models has always been obtaining the appearancefunction of the ore under consideration. Exhaustivelaboratory test work by the above list of authors was usedto establish the breakage and appearance functions andprove the validity of the theory. However, these cannotbe directly obtained in industrial test work. The appear-ance function of coarser material was obtained throughpendulum breakage tests developed in the 1980s(Narayanan, 1983, 1985) that were replaced in 1992 bythe simpler drop weight breakage tests, as tested andimplemented at the JKMRC (Napier-Munn et al., 1996).The appearance function at fine sizes (less than a fewmillimetres) can currently only be obtained throughlaborious batch milling tests, so in reality, it is seldomobtained.

In 1962 the Australian Mineral Industries ResearchAssociation (AMIRA) P9 project was established, withthe JKMRC as the primary investigators, to pursue “Theoptimisation of mineral processes by modelling andsimulation”. The project, which is ongoing to this date,initiated an extensive research campaign that has made amajor contribution to the applied modelling of commi-nution devices. A significant development was a newmodel for SAG and AG mills developed by Leung et al.(1987) and later extensively enhanced by Morrell andMorrison (1989). An updated version of the model thatenhances the mechanistic nature of the model and isintrinsically dynamic was developed by Valery (Valeryand Morrell, 1995; Valery, 1998). The dynamic modelhas been applied in industry by Valery (1998), Schroderet al. (1997), Schroder and Holtham (2004), and others.

Within the AMIRA P9 project, a number of otherdevices were modelled, notably the crusher, the high-pressure grinding roll, the tower mill, and a simplified ballmill model (Napier-Munn et al., 1996). These modelsbuilt on thework of other researchers worldwide, who haddeveloped many of the principles, such as presented inKing (2001). All of these models build on the PBM andbreakage and selection functions, plus they utilise a semi-mechanistic approach. The SAG/AGmill model utilises acombined impact and abrasion appearance function that isstrongly particle size and energy dependent.

Whiten developed the ingenious t10 concept thatrelated the degree of breakage to the input energy, andthis led to the well-known A, b, and ta breakage param-eters (Narayanan, 1983; Narayanan and Whiten, 1988;Andersen and Napier-Munn, 1989; Napier-Munn et al.,1996). The crusher model uses the same technique, butwithout the abrasion component. This gives an excellentprediction of size reduction, and a prediction of powerdraw (Narayanan, 1985; Kojovic et al., 1997) baseddirectly on the drop weight test data, until packed bedinter-particle crushing begins to dominate. The standardcrushing models utilise only a breakage and classifica-tion function and assume that all materials left in thechamber after selection for discharge are subject to thesame force and energy of breakage. This simplificationmay be an additional reason for the breakdown of themodels under packed bed conditions.

An essential parameter for all of the comminutionmodels is the discharge function or the rate at whichmaterial leaves the device. The general form of the equa-tion is Pi=disi, where i refers to a particular size range, Pis the product, d the discharge function, and s the contentsof the device. The product from a device can bemeasured,but as d and s are both unknowns, at least one has to bemeasured to derive the other. This is feasible (but hardwork) in pilot applications, but generally not feasible inindustrial applications. A good strategy to overcome thisis to lump the discharge function into the breakage rate, asimplemented by Whiten in the ball mill model (Napier-Munn et al., 1996). The PBM is then used to derive themill contents, s, by fitting a breakage rate for each size, ri,to form the breakage function. For SAGmill modelling, itis not feasible to hide the discharge function in the break-age function, as the breakage is explicitly worked out as afunction of input energy. A simple discharge function wasderived by Leung et al. (1987), to account for gratedischarge. In fitting the SAG mill model, the dischargefunction and breakage function are interdependent andhave to be resolved stepwise in an iterative manner. How-ever, it is clear when working with these models that thebreakage rate function is not unique, as it is dependentupon both s and d, which are interdependent, and it issensitive to changes in d. It has been found that this causesmajor issues when scaling and modelling. The dischargeefficiency is dramatically different in pilot- and full-scaleSAG/AG mills, and sufficiently realistic scaling relation-ships do not yet exist.

It can be seen that the major issues with fittingbreakage rates is that they are both ore and machinedependent, are a function of interdependent variables, andmay well be an artifact of the modelling technique ratherthan an estimate of the rates of breakage in a comminution

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device. The breakage rates are used to absorb all theunknowns, and then are used to scale between differentapplications. Although this works remarkably well overlimited and controlled changes (as proven by the world-wide success of this technique), one must always startwith an application that is closely similar in both ore typeand general dimensions to ensure successful design simu-lations, or survey the application under consideration toreliably model it.

High-pressure grinding rolls can be successfullymodelled by a combination of conventional crusher inthe pre-crushing zone, compressed bed breakage, and abypass of the bed. The simulation of the compressed bedbreakage is dependent upon scale-up from laboratory orpilot tests, based on the equivalent operating pressures.

2.3. Energy-based models

A noticeable exception to the general PBM modelsare the energy-based models that can be used in impactcrushers, such as the vertical or horizontal shaft impactcrushers. With these the energy of each impacting par-ticle can be explicitly calculated and it is reasonable toassume that the impacts are independent, and that eachparticle receives a single impact. Utilising standard dropweight test data the breakage product is well modelled inan explicit manner (Napier-Munn et al., 1996). However,the models cannot predict the product for more complexdevices, such as the Barmac crusher, that utilise inter-particle impacts and the range of impact energies re-quires more sophisticated models. These are well suitedto the computational techniques presented in the nextsection.

2.4. Computationally intensive techniques

Many problems in science and engineering can beconsidered as a series of small zones which are related toone another by a set of (relatively) simple rules. The userspecifies a grid of points, appropriate boundary condi-tions and a set of starting values. A similar calculation isthen carried out for each grid point in turn, the values areupdated and a test for convergence or stability is applied.When the test is satisfied, the simulation is complete.These methods can be made quite general but requiresubstantial computation.

Computational fluid dynamics and finite elementmethods exactly fit this scheme. An interesting variationis to use a particle as a point on a “moveable grid” andsubject it to motion according to its interactions withsurrounding particles and boundaries. A powerful tech-nique based on this meshless method is the discrete

element method (DEM), as proposed by Cundall andStrack (1979). This was applied for the first time tocomminution devices by Mishra (1991) and Mishra andRajamani (1994) in their pioneering work of modellingcharge motion in mills. Mishra (2003a) provides a usefulreview of the techniques underlying the application ofDEM to milling.

A more recent variation is to consider a fluid as anassemblage of pseudo-particles and this is calledsmoothed particles hydrodynamics (SPH). SPH hasproved to be very useful for simulation of fluids whichchange physical properties as a variable such as tem-perature changes (Cleary, 1998a). The interaction rulescan also depend on the relationship between the fluidparticles. Hence, non-Newtonian fluids can also be mod-elled with the interactions related to shear at any point in aslurry. This provides a link between fluid transport andfine particles in a slurry, using the slurry viscosity modeldeveloped by (Shi and Napier-Munn, 1996, 2002).

Clearly the practical limit for these approaches is the“cost of computation”. With computer power doublingabout every 18 months (“Moore's Law”) for at least thelast 20 years, these approaches have become much morefeasible although computational limits are still impor-tant. It became feasible to undertake simple two-dimen-sional (2D) DEM and CFD simulations in the late 1980s.Because of Moore's Law these applications rapidlygained in speed and size of feasible problem, withapplication to 3D starting in the mid-1990s.

Both CFD and DEM can produce complex images asoutput. Particles or cells can be coloured according tovelocity (or any other simulated variable) and even out-put as animated images with suitable simulated lighting.Because humans are well adapted to receiving high bandwith visual information, there is a tendency – evenamong researchers – to accept these images as “reality”.Objective verification and testing of the predictions ofnumerically intensive computer codes is absolutelyessential, an area in which Powell et al. have appliedconsiderable effort (Powell and Nurick, 1996a,b,c;Govender et al., 2002, 2004).

Cleary et al. (2001) reported a detailed comparisonbetween measured mill charge position and particlevelocity in a scaled 600-mm-diameter AG mill. Thesesimulations used 250,000–300,000 particles for acomplete size-based description of the scaled chargeover a wide range of operating conditions. The resultsdemonstrated that 2D simulation with circles could onlypredict over a very narrow range. 2D simulation with“shaped” particles was an improvement but 3D simula-tion with spheres predicted similar charge shapes andparticle velocities over a wide range of conditions. This

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was a surprising result as the experimental chargeconsisted of crushed rock and was strongly non-spherical. While this success in prediction is reassuring,it does not imply that the collision models are in any way“exact.” Further work is continuing to test simplecollisions in detail (Chandramohan and Powell, 2005).

An analysis of normal and shear (tangential) energydistribution for spheres with the same size distribution(from top size of 180mmdown to 20mm) as an industrialSAG mill was carried out by Cleary et al. (2001) Theresults did produce a reasonable estimate of net power attwo different operating conditions. However, they did notcorrelate in any obvious way with the JKMRC SAGmodel estimates of impact and abrasion energy. Moreinterestingly, the predicted impact energy spectra con-tained almost no impacts of sufficient energy to breakeven a 20-mm particle in a single event according toparticle strength as measured by a JK Drop Weight test.

To examine this issue in more detail, a simulation of a“Hardinge” style 6 ft by 2 ft (1.8 m by 0.6 m) pilot AG/SAG was run for 350,000 particles to match a measuredsize distribution from 150 mm to 5 mm. Within thecharge, collision histories were tracked for a selection ofparticles within each size fraction. As for the large mill,collisions which might produce even moderate breakagein a single impact were still rare.

In applying the DEM outputs to predicting the break-age product from mills, Datta and Rajamani (2002)applied the impact energy spectra derived from 2DDEMsimulations to batch ball mill modelling. The authorssimplified the breakage environment by assuming thatthe main form of energy transfer in a batch ball mill wassimilar to the energy transfer achieved by dropping ballsonto a bed of four layers of particles. They reported thatthe progeny of a small batch mill could be predicted fromthe product of the bed breakage tests and the impactenergy distribution as predicted by the DEM simulation.The authors suggested that shear could be added if asuitable bed shear test could be used to characterise theore breakage. Mishra (2003b) reviews the application ofDEM to milling, which picks up no more advancedpractical applications to product size prediction than thatof Datta and Rajamani (2002). Most recently, Herbst(2004) has published on the methodology of utilising theoutputs of the discrete element method (DEM) to en-hance the modelling of SAG mills. These are still es-sentially the same PBM methods, with an energydistribution function and scaling relationship derivedfrom the DEM used to derive the breakage.

Djordjevic et al. (2003) have demonstrated that DEMtechniques are well suited to extend the explicit modelsfor impact crushers. DEM techniques have also been

applied to the modelling of stirred mills (Cleary et al.,2006b; Sinnott et al., 2006) by assuming that all break-age is due to shear and utilising the shear energies cal-culated form the DEM.

2.5. Wear issues

DEM provides detailed estimates of the forcesbetween particles and the equipment surfaces. Hence,wear rates based on various frictional interactions can beused to estimate relative wear and evolution of keycomponents such as SAG mill lifters (Herbst andNordell, 2001; Cleary 1998b; Kalaya et al., 2005).Wear should also be calibrated in terms of wear materialand ore, such as the procedure being developed byRadziszewski (2001).

2.6. Mineral liberation

It has long been the holy grail of comminution mod-elling to incorporate liberation, for after all, that is theobjective of comminuting the particles in mineral pro-cessing. A number of investigators have contributed tothis goal, but the models have been limited by assump-tions of random breakage, and are generally applicable toa specific ore and process. Until the 1990s a majorlimitation to developing liberation models was the limitedcapability of collecting data, and this seriously hamstrungthis goal. With scanning electron microscope (SEM)techniques becoming more accessible, this allowed theacceleration of research in this area.

Peter King has been dedicated to this objectivethroughout his long career. From pioneering work at theUniversity of the Witwatersrand, King (1979) wrote hislandmark paper on linking liberation and comminution(King and Schneider, 1998). This paper tackles non-random breakage through a generic approach within thePBM framework. Six non-random breakage processesare defined: selective phase breakage; differential break-age; preferential breakage; liberation by detachment; andboundary-region fracture. These are well defined in thepaper and are considered to be the most useful and rig-orous definitions of the modes of non-random fracture.

In this work, it was demonstrated how to simplify thegeneral solution to non-random breakage and introduceany of the six processes in a manageable manner. Thesolution is bounded by the regions of feasible liberationand particle size, as expressed in the Andrews–Mikadiagram. It is shown how this solution changes dra-matically with the non-random breakage. Application ofthe technique is tested on ores, with good correspondenceof outcomes. The power of this technique is that it can be

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applied to any comminution model that is structuredwithin the PBM framework.

It is considered that this route represents the wayforward of incorporating liberation into comminutionmodelling in a universally applicable manner. King andSchneider do warn that “The mode of stress applicationin the grinding mill can influence the liberationcharacteristics of an ore”. That is, the mode of non-random breakage is a function of breakage mode, such ascompression versus impact. So the next challenge lies inlinking the liberation modelling to breakage testing.

With the routine use of mineral liberation techniquessuch as the JK-FEI-MLA (Cameron et al., 1998;Guerney and Gu, 1999) and QemScan (Gottlieb et al.,2000) becoming more common, the full evolution ofnon-random breakage models is a realistic objective.

Although the liberation modelling shows promise it isbarely used. The PBM is structured to deal with size, andthe liberation outputs are tacked on top of the commi-nution model outputs. The technique provides a limitedpredictive capability so long as the breakage mode doesnot vary, but essentially has to be recalibrated for eachnew application.

2.7. Breakage testing

In a general sense, the current breakage testing tech-niques are a simplified imitation of the major perceivedmodes of breakage that occur in the comminution equip-ment. Although useful, we must accept that they arecrude. Regardless of the actual modes in the equipment, acorrelation is developed with the equipment and integrat-ed into the models. These correlations can be quite suc-cessful, provided that they are used in the window overwhich the correlation was developed. However, as thewindow is widened, more and more factors are added andthe original vision of a simple correlation is lost. This is anexplicit indication that the test does not correlate with theconditions in the equipment. The Bond Work Index andStarkey Power Index are examples of this.

The JKMRC drop-weight test simulates impactbreakage and the associated abrasion test simulates lowstress abrasion. DEM simulation indicates that most likelyalmost no breakage in an AG/SAG mill is due to singleimpact breakage (Cleary and Morrison, 2004). It is alsoclear that there is a wide range of abrasion that occurs at aconsiderably higher stress than in the laboratory test. Thus,even this well-used breakage test that is based on theagreed major modes of breakage requires improvement.

The current testing techniques are seen as a majorlimitation to the modelling progress, as they do not cor-rectly reproduce the modes of breakage found in

comminution equipment and do not have the flexibilityto do so.

As a result of the outputs of DEM simulations, adetailed investigation of incremental breakage is inprogress at the JKMRC (Whyte, 2005) and at theUniversity of Cape Town (Bbosa et al., 2006). Shi andKojovic (private communication, P9N AMIRA report 5)have developed a new breakage testing technique thatcan rapidly test a large sample of particles at accurateenergies over a wide range and incorporate measure-ments of incremental breakage. This links in well withthe work on probability of breakage that Vogel andPeukert (2003) developed and is currently beingmodified to be incorporated into existing model struc-tures by Shi and Kojovic (in press).

2.8. Model limitations

A major pitfall of the comminution model develop-ment has been that each type of equipment has differentmodels, with different structures and limited overlap ofthe key principles. Each new piece of equipment seemsto attract a new researcher with an all new model. Thismeans that advances in modelling techniques filter onlyslowly across the board, and many research groups andinvestigators are involved in incrementally updating theplethora of models.

The current form of the models can take model outputsto a point but no further. The models are essentially adescription of the output of the equipment, not of theprocess. The PBM is not actually a model, it is a frame-work that maintains mass integrity. It has turned out to bea major and essential step in the advance of comminutionmodelling, but does not describe the breakage process; itmerely keeps track of the product.

The authors are of the opinion that the modelledbreakage rate has no physical significance; rather, it ismerely a construct of the model structure and the as-sumptions made regarding selection and dischargefunctions. Those who have worked with these modelswould have noted that strange breakage rates are derived,especially at the extremes of size. For example, theclassic wave format of the SAG/AG mill breakage ratecurve gives an extremely high breakage rate for thecoarsest rocks, yet they are known to be reduced slowlyby abrasion. It is also apparent that the fitted rates arestrongly dependent upon the fitted discharge function fora device. The breakage rates are used to absorb allunknowns and inaccuracies of the models and hold bothequipment and ore information.

Power or energy input is not directly used in themodels. Although some models do predict a power draw,

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this is quite independent from the calculation of thebreakage product, which is driven by breakage and selec-tion functions. Even SAG mill models that use an energytype driver do not correlate this to the mill power draw.

No models truly incorporate liberation. Some usefuladvances have been made in correlating liberation to thedegree of breakage, but these are always a tack-on, themodels do not intrinsically predict the liberation pro-perties of the product particles. For models to have apredictive capability – as opposed to a back-fitted cor-relation – the mineralogical liberation information needsto be a direct output of the breakage events in the com-minution device. Other than the application to the batchgrinding equation, King and Schneider (1998), no cur-rent models can accommodate this.

3. So where to from here?

The authors see the future of comminution modellingtaking a step change from empirical, single-numbermodels to

• mechanistically based models,• driven by energy input,• and the mechanism/particle interface,• with distributed breakage functions,• utilising available computational power,• with mineralogical liberation integral to the models.

The models will model breakage as a result of simu-lated interactions within the equipment, rather than asequipment outputs. It will then be possible to apply themodels to any piece of equipment. The models will trulyseparate ore and machine properties. They will not bedriven by breakage functions; they will instead be particlebased. Each particle will be subjected to a local collisionenvironment, that will determine what will happen to it.The product of the equipment is the sum of the productsfrom all the individual breakage interactions.

4. How may this be achieved?

It is necessary to dissect the process. Measuring theoutcome of the pieces of equipment will never give thefull picture, as there are too many interacting processes.It is necessary to understand and model the processesindependently and then assemble them into a compre-hensive model. The outcomes can then be tested againstthe equipment. This is a fundamental change in thephilosophy of modelling, where the equipment is notused to develop the models—which is the intuitivelyobvious route to follow.

The population balance (PB) will still be a criticalstructure underlying all modelling, tracking the productsand ensuring the integrity of the outcomes, but will notbe a model. The PB will be used as a framework inwhich the mechanistic models of the processes will behoused. An excellent example of this exists in thechemical engineering field of crystallisation, which hasboth formation and breakage of particles, feed, andproduct streams in a reactor (Hounslow et al., 2005).

Powell (2006) has proposed the development of aUnified Comminution Model to achieve this goal.

4.1. Internal equipment mechanics

In moving to models that are based on the mechanicsof the equipment, it is clearly necessary to develop agood understanding of the mechanical environment in-side each comminution device. To achieve this, it isnecessary to measure, model, and simulate the mechan-ics of particle motion in the devices. Computationaltechniques are used to produce the simulated outputs,and it is essential that these outputs are validated beforethey are applied to comminution modelling. The particleinteractions can be used to derive the rate at which eachparticle is hit, with what force, and by what. This is whatdetermines the damage and breakage of particles. Thesimulation outcomes can be bundled into distributionsrepresenting a history of the mechanical environment foreach class of particle. The classes are size, ore type,density, mineralogy, degree of liberation, etc. This canthen yield a manageable volume of data that is used topredict the rate of breakage of each class of particle in thecomminution device.

One of the more difficult areas in applying DEM toreal grinding processes is to predict the interactionbetween fine ore particles and the grinding media (inPBM terms this is the selection function). The authors areof the opinion that this issue has not yet been satis-factorily addressed. In wet mills this is linked with thetransport and slurry suspension of the particles. Thesimplified contact models (e.g., spring and dashpot) aresufficiently efficient numerically to enable simulationswith large numbers of particles to be carried out oncurrently available high end desktop computers. How-ever, these models provide at best a gross approximationof what might happen in a collision where breakageoccurs. It may be necessary to implement independentbreakage detection and adjust the collision model ac-cordingly. Some of the inferences made that are based onDEM outputs may be more a consequence of simplifiedcollision models than the actual process. It is the opinionof the authors that this whole area of contact and energy

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transfer and breakage is a key research aspect in themeaningful application of computational techniques toprediction of the progeny of comminution devices.

4.2. Transport

An adequate description of the transport of theparticles through and out of the device is an essentialpart of a model. This determines the residence time ofparticles, and where they will reside and for how long inthe various regions in a device. This discharge ratedetermines the limit to the feed rate of a device, so is thekey feed rate controller.

It is suggested that initially for slurry and air sweptdevices the flow can be measured under realistic con-ditions in laboratory tests, and these outputs fed intomechanistic models of the flow environment for eachdevice. The more generic the laboratory tests, the widerthe applicability of the data. Appropriate mechanisticmodels can then be used to customise the flow to par-ticular pieces of equipment. Thus, it is proposed that thedevelopment of these flow relationships should not be byequipment type, e.g., grate discharge SAG mill, but byflow mode. Thus, for an SAG mill, the modes would beflow through the cascading mill charge, flow through thegrate holes, flow along pulp lifters, flow out the dischargeaperture, flow back through grate holes into the mill. Theflow characteristics of each mode are independentlystudied and then combined through the use of a mecha-nistic model. The same test results can then be applied to adifferent piece of equipment, provided that the flowmodes are the same, by utilising a newmechanistic modelthat describes the physical environment of that device.

In the longer term, the flow needs to be studied andmodelled in a fundamental manner so as to have a trulypredictive capability, such that it can be applied to newtypes of devices. For this coupled particle–fluid compu-tational techniques are required, such as smoothed particlehydrodynamics (SPH), computational fluid dynamics(CFD), or Lattice Boltzmann techniques linked withDEM techniques. These techniques exist and are alreadyapplied in some areas of research and industry (Potapovet al., 2001), but require further development and testing,and do have an extremely high computing power over-head, that is, simulations currently take in the order ofweeks. Cleary et al. (2006a) have demonstrated its ap-plication to milling.

For dry large particle applications, such as crushers,the DEM techniques are adequate to simulate the flowand discharge of the device.

For positive displacement devices, such as rolls andHPGR crushers, no special transport function is required.

4.3. Breakage testing

The route to correct breakage testing techniques is totest the breakage modes found in the equipment, andunder the correct range of forces and rates of inter-action. A fine illustration of this is the HPGR, whereexcellent scale-up is achieved from pilot to full scale,as they can be operated at the same pressure. This is notachievable for the cascading action in tumbling mills,as laboratory mills have forces that are orders of mag-nitude less than the full-scale mills. For some equip-ment, a small-scale laboratory or pilot test that mimicsthe full-scale equipment may be the best breakagetesting technique, provided that the realistic forces andrates of interaction are achieved. But for most equip-ment, this is not achievable, and the tests are lockedinto being equipment specific.

The analysis of the mechanical environment in thecomminution equipment will inform the design of break-age testing techniques. The testing techniques must coverthe modes of breakage and the interaction forces that arefound in the equipment. It is proposed that the testsshould measure the distribution of breakage products,rather than reducing them to an over-smoothed average.Hitting 20 apparently identical particles each with thesame force will produce 20 size distributions. Currently,these are combined into one. However, breaking a singleparticle does not produce an adequately defined progenydistribution. Two different ore types may yield the sameaverage product size distribution, but if one ore is a lotmore variable in structure, it will give a far wider range ofdistributions and, thus, in reality give a considerablywider product size distribution than the more homoge-nous ore. This has implications for classification, sliming,oversize carry-over, and undoubtedly for liberation andrecovery.

Liberation should be measured as an integral part ofthe breakage tests. This will reveal the liberation as afunction of the breakage mode and the energy/forceenvironment. The outcomes are only likely to be usefullyaccurate for properly designed breakage tests. That is,liberation is usually a function of how you got there, notjust the final product size distribution, as discussed byKing and Schneider (1998). To successfully incorpor-ate liberation information into the breakage testing out-puts, fast and relatively cheap analysis techniques arerequired—not a strong point of traditional liberation analy-sis, although it is undoubtedlymoving in that directionwithsystems like the JK-FEI MLA and QemScan. It issuggested that techniques such as X-ray micro-tomogra-phy, that can deal with particles down to about 100 μm insize, will play a central role. These combined with MLA

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and assaying can be used to reveal the liberation at finersizes.

With the development of more sophisticated breakagetests, sight must not be lost of the need for simple andcheap indicator tests that can be used to check for orevariability and indicate where more detailed tests arerequired in an ore body.

The involvement of geologists and mineralogists(especially the new breed of process mineralogists) toquantitatively correlate mineralogical variation in the orebody to its breakage and liberation properties is anessential long-term goal. The emergence of the geo-metallurgist, who will make extensive use of processmineralogy, should fulfil the position of the ‘deposit toproduct’ integrator.

The fundamental modelling of breakage is a wholenew approach that will hopefully enter in the modellingtechniques that follow this next major step on improvingcomminution modelling. While these fundamental mod-els are being developed, they can be expected to provideimproved understanding to the breakage process and thisknowledge will supplement and bolster the testing andmodelling techniques.

4.4. Non-mechanical breakage

This applies to techniques such as pulsed microwaveheating, which hold great promise as comminutionenhancing devices. It is proposed that the new higherquality breakage tests can be applied to the ores pre- andpost-such treatment. The breakage tests would thenprovide an accurate measure of the resultant effect ofthe treatment, and this can be related to the modes ofbreakage. The resultant predictions can then be integratedinto the mechanical environment, using the new commi-nution models.

The modelling of these non-mechanical modes ofbreakage can start with empirical relationships, but thetrue modelling is a whole new arena of materials fracturemodelling.

4.5. Mine-to-mill

Comminution starts at the rock face; thus, comminu-tion modelling should be linked to the mining technique.Part of the requirement to achieve this is to develop acommon language and purpose between the two currentlysegregated fields of application and research. Althoughsome progress has been made in this arena, with excellentindustrial success, this is undoubtedly an area that requiresconsiderable input to achieve a properly integratedapproach.

5. Where will the new generation of models take us?

A step change in capability will be the fully predictivestructure of the models; this means that novel devices canbe designed and trialled through thorough andmeaningfulsimulation prior to any laboratory work. The concept ofthe Virtual Comminution Device (VCM) has been pro-posed by Morrison to facilitate the rapid prototype devel-opment of new equipment and concepts in comminutiondesign. The VCM should also allow the optimisation ofexisting designs in terms of the desired modes of break-age, as determined by improved understanding of break-age and liberation, instead of merely aiming to minimisewear, correct what are clearly poor operation practices, oridentify circuit constraints.

This technology will be linked into predictive wearmodelling of liners, which will present a tremendousopportunity to save on the cost of wear components. Butwell beyond this, a prediction of the evolution of wearprofiles will enable the design to be based onmaximisingthe operating efficiency over the complete wear cycle ofliners.

With such sensitivity to breakage modes and withliberation integrated into the models, they will be ideallypositioned to link to up- and downstream integratedoptimisation.

Modelling of liberation is seen as one of the mostimportant aspects of the step change in modelling capa-bility—noting that it will be integral to the predictivecapabilities of the models, not a post-modelling add-on.Additionally, the capability of predicting other properties,such as micro-cracking and surface state, that can belinked to downstream recovery processes can readily beincorporated into the model structure, provided the re-quired information is modelled or fitted as a sub-process.

As the models will be capable of dealing with in-dividual particle classes, they will intrinsically cope withwidely varying ore blends, and the consequences ofblending.

Integrated circuit design can become a reality. Withliberation linked to the recovery process the modellingobjective can be to design the optimal circuit forrecovery—rather than size reduction.

Integral power prediction in the models will ensurethat the specific power consumptions are a consistentand meaningful output.

The intrinsic dynamic nature of the models will assistin the design of the most operable and stable circuitconfigurations, with the capability of avoiding bottlenecks; simulating realistic variations in feed type, size,and blend; and simulating the effect of downtime onvarious sections of the circuit.

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Faster commissioning can be obtained through moreaccurate design and a better understanding of the op-erating window and variation of the circuit. This canensure that the circuit is ramped up to full capacity farmore rapidly, leading to lower capital and operating costs.

6. Conclusions

The proposed direction for the future of comminutionmodelling may appear rather ambitious, but it has bothshort-term benefits in potential to improve existing mod-els and long-term benefits. Rather than the short-termview of models with limited use and life span, theresearch can build in a coherent and consistent directionthat brings continuous improvement and the long-termobjective of a step-change in modelling capability. Themassive increase in computing power over the past de-cade, and extending into the future, and the enormousimprovement in measurement techniques, such as micro-tomography and quantitative mineral liberation analysis,are the tools that can enable such an approach.

In order to make a major contribution to mineralprocessing, new comminution models must model theprocess and not the outcome of specific equipment. Thebreakage testing techniques must be able to characterisethe breakage modes found in comminution equipmentand incorporate liberation in the analysis of theproducts, with both breakage and liberation related tothe mode of breakage. Utilising computational techni-ques to simulate the mechanical breakage environment,the models will incorporate the breakage test outputs topredict product size distribution and liberation. Mech-anistic transport models will complete the simulations.

The models will be able to predict the performance ofnovel devices by simulating the mechanical environmentwith computational techniques and then simulating thebreakage and transport outputs. They will enable theexploration of the most energy efficient ore reductionroute integrated with the optimal liberation route. Toobtain full benefit from this technique the classificationmodelling must come up to speed along the same lines,and the models of the recovery processes need to be ableto link into the liberation data.

Right now, over 80% of this is achievable with currentmodelling and analytical techniques and the authors feelthat computational techniques are advancing rapidly andwill soon be able to produce adequate data resolution,further enhanced by constant improvements in comput-ing power.

Currently, it is the basics not the advanced modellingthat is lagging in development. Inadequate ore breakagetesting techniques are seen as the major limitation to

major progress in comminution modelling. It is imper-ative that in this endeavour, we researchers take fulladvantage of new measurement techniques, such as fastand routine MLA analysis, and tomographic analysis ofmineral structure, fracture, and liberation in coarserparticles. As researchers we are also obliged to use theenormously improved computational power that is everbecoming available, to better understand the process—and to not delude ourselves with pretty pictures that mayonly reinforce our existing preconceptions.

King (1993) rounds off his visionary paper with theconclusion that “… it will be the application of veryfundamental physical principles that is likely to bring themajor advances in comminution modelling”. Theprogress may not have been as significant as he hopedin the decade since then, but it is undoubtedly in thatdirection. It is proposed that a concerted effort by com-minution researchers in a common direction shouldensure that the dream of the new comminution models isbrought to fruition in the next decade.

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