predicting breakage and the evolution of rock size and shape distributions in ag and sag mills using...

Minerals Engineering xxx (2013) xxx–xxx

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Minerals Engineering

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Predicting breakage and the evolution of rock size and shape distributionsin Ag and SAG mills using DEM

G.W. Delaney a, P.W. Cleary a,⇑, R.D. Morrison b, S. Cummins a, B. Loveday c

a CSIRO Mathematics, Informatics and Statistics, 71 Normanby Road, Clayton, Victoria 3168, Australiab University of Queensland, JKMRC, SMI 40 Isles Road, Indooroopilly 4068, Australiac School of Chemical Engineering, University of KwaZulu-Natal, Durban, Private Mail Bag X54001, South Africa

a r t i c l e i n f o

Article history:Available online xxxx

Keywords:AG/SAG pilot millingIncremental breakageDiscrete element modellingComminution

0892-6875/$ - see front matter Crown Copyright � 2http://dx.doi.org/10.1016/j.mineng.2013.01.007

⇑ Corresponding author.E-mail address: [email protected] (P.W. Cleary)

Please cite this article in press as: Delaney, G.W.DEM. Miner. Eng. (2013), http://dx.doi.org/10.1

a b s t r a c t

Applying DEM to prediction of tumbling mill performance is challenging because several different modesof breakage are active in the process. As our knowledge of breakage and computational capacity improve,it is worth revisiting previous simulation tasks which did not produce a satisfactorily realistic descriptionof a measured process. At SAG 2006, we reported the simulated and measured outcomes of treating a wellcharacterised ore in a 1.2 m diameter mill. This well instrumented, pilot scale mill at the University ofKwaZulu-Natal has been combined with some new approaches to ore testing to allow different modesof breakage to be tested. The mill design allows the rate of generation of fine material to be measuredin close to real time for autogenous and SAG mill charges. The updated simulation model estimates massloss with particle evolution and embeds the cumulative damage and breakage. To more clearly delineatethe effects of different types of breakage, surface wear has not been included in these simulations. Thesimulated results are compared with the measured results. The cumulative damage model is more real-istic for SAG operation but is inadequate for AG. Hence, any realistic model must incorporate severalbreakage mechanisms. Issues such as relating modelling inputs to particle breakage characterisation dataand the accuracy of the predictions of the models are discussed.

Crown Copyright � 2013 Published by Elsevier Ltd. All rights reserved.

1. Introduction

Discrete Element Method (DEM) is a computational methodthat is used for predicting the flow of particulates in circumstanceswhere their collisions are the dominant physical process. Overtime, it has been used to investigate several different aspects ofmill performance with use being more mature in some areas thanothers. Its earliest use for modelling of SAG mills was in twodimensions (2D) by Rajamani et al. (1996) who used it for lifter de-sign by predicting media overthrow. The most common area of usehas been in understanding the flow patterns, energy utilisation andpredicting power draw (Mishra and Rajamani, 1992, 1994; Cleary,1998, 2001a, 2004, 2009a; Herbst and Nordell, 2001; Morrison andCleary, 2008; Cleary et al., 2008) and many authors since thenincluding for example the comminution special issue edited byCleary and Morrison (2008). Axial particle transport has been ex-plored to a lesser degree (Cleary, 2006, 2009b) and dry particleSAG mill discharge (Cleary, 2004). Slurry flow and distributionhas also received relatively little investigation because of the needto couple the DEM model to a CFD model with recent studies byCleary et al. (2006), Cleary and Morrison (2012), by Jayasundara

013 Published by Elsevier Ltd. All r

.

, et al. Predicting breakage and016/j.mineng.2013.01.007

et al. (2011) for an Isamill and flow from the pulp chamber havebeen presented by Lichter et al. (2011). The distribution of very fineparticles in ball mills has also only recently started to be consid-ered (see Cleary and Morrison, 2011)

The least investigated aspect of mill performance using DEM isthat of particle breakage which is perhaps surprising since this isthe basic purpose of these mills. Applying DEM to prediction oftumbling mill performance is challenging because several differentmodes of breakage are active in the process. The most common ap-proach has been to use DEM to provide data from which selectionfunctions can be calibrated for use in more traditional populationbalance models – either steady state or batch (Tuzcu and Rajamani,2011; Tavares and de Carvalho, 2009). The accuracy of such modelsis limited by the ability to adequately characterise the collisionalenvironment and the limited physics captured by the populationbalance models. To be able to accurately predict, from first princi-ples, breakage, product size distribution and resident particle sizedistribution in the mill including axial variation, the breakageand its controlling mechanisms and transport need to be includeddirectly in the DEM model. This was first proposed by Cleary(2001b) who used a replacement strategy where compressive orimpact breakage mechanisms fracture a parent particle into finerprogeny all of which are represented in the DEM model. This modelwas limited by the use of spherical parent and progeny and the

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the evolution of rock size and shape distributions in Ag and SAG mills using

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Table 1Key operating parameters of the pilot mill.

Mill diameter 1.2 mMill length 0.31 mLifters 14 – 40 � 40 mmMill speed 30 rpmTest 1 30% Autogenous loadTest 2 20% Autogenous loadTest 3 10–10% SAG rock–ballRock charge 1.5–4.5 kg at an sg of 2.65Ball charge 80 mm nominal at an sg of 7.85

2 G.W. Delaney et al. / Minerals Engineering xxx (2013) xxx–xxx

limited ability to characterise the breakage properties. As ourknowledge of breakage and computational capacity improve, it ispossible to include increasingly realistic descriptions of the break-age process directly in the DEM model.

In general AG and SAG mill researchers have hypothesized thatat least two breakage mechanisms are active in a SAG mill – arounding of particles producing fine progeny and more vigorousbreakage producing angular progeny. The mathematical model incommon use (Leung et al., 1987; Morrell and Morrison, 1996) pro-vides a continuum between abrasion of large particles and impactbreakage of small particles combined with a set of empiricallydetermined grinding rates.

Normalising these types of breakage using the standard JKMRCimpact (Drop Weight) and abrasion tests (Napier-Munn et al.,1996) and derivatives (Morrell, 2004) has enjoyed considerablesuccess as a tool for equipment selection as well as circuit optimi-zation. Therefore one might reasonably expect that DEM simula-tions of grinding mills would confirm this underlying model.However, this supposition is not supported by DEM results (Clearyand Morrison, 2004). The impact energy available to particles lar-ger than a few millimetres is much too small to do much impactdamage in a single impact. Therefore a more detailed study hasbeen undertaken both of rock characterization and ways to sepa-rately measure and model the breakage mechanisms active inAG/SAG milling environments.

At SAG 2006, we reported (Morrison et al., 2006) the simulatedand measured outcomes of treating a well characterised ore in a1.2 m diameter mill. This well instrumented, pilot scale mill atthe University of KwaZulu-Natal has been combined with somenew approaches to ore testing to allow different modes of breakageto be tested. It showed that autogenous mill loads of various sizesand shapes could be reasonably predicted by abrasive mass lossproportional to the estimated frictional energy experienced byeach particle after particle chipping and rounding had stabilised.However, this approach was inadequate for SAG operation whereincremental damage produces more non-trivial body breakageand quite different progeny size distributions.

Here we extend the model to include breakage due to incre-mental damage (Morrison et al., 2007; Whyte, 2005) with parentparticles (both round and non-round) being broken based on thecumulative energy absorption above the E0 elastic threshold forcreating incremental damage. This can be combined with the fourother existing breakage/mass loss mechanisms to provide a com-putational capacity that can, in principle, fully predict the evolu-tion of the mill particle size distribution and product sizedistribution. This paper extends the work reported in Morrisonet al (2011) by modelling AG and SAG operating conditions usingincremental damage alone and compares the simulated and exper-imental results. Issues such as relating ore characterisation andmeasurement of inputs to the particle breakage models and theaccuracy of the predictions of the models are discussed.

2. Experimental mill and ore characterisation

A substantial sample of a uniform, fine grained ore was col-lected in conjunction with detailed surveys of an industrial SAGoperation. The sample was characterized using JKDWT abrasionand Bond ball work indices. Further repetitive DW test work wascarried out at much lower energies to investigate incrementalbreakage of this ore (Morrison et al., 2007; Whyte, 2005). A sampleof the ore was also tested in a 1.2 m by 0.3 m long semi-batch pilotmill. Key operating parameters for this mill are provided in Table 1.

This mill was developed by Loveday and Hinde (2002) to cali-brate and test abrasion based AG/SAG model (Loveday and Whiten,2004). This mill was of interest for this project because it providesfor rapid removal of progeny as it is generated, and tracking of the

Please cite this article in press as: Delaney, G.W., et al. Predicting breakage andDEM. Miner. Eng. (2013), http://dx.doi.org/10.1016/j.mineng.2013.01.007

mass of each particle in the charge. Hence, detailed DEM predic-tions of the comminution processes can be compared against themeasured results for individual (or small groups) of particles inthe charge. In addition to the mass of surviving particles, the prog-eny from each type of comminution were collected, weighed andsized. This provides a mass balance around the mill.

3. Comminution processes – breakage mechanisms

The first few minutes of operation with a fresh charge causes ra-pid rounding of initially angular particles and a relatively coarseproduct. The DEM code can estimate the mass of each survivingparticle from an accelerated wear rate but not the size distributionof the resulting progeny.

The production rate of progeny then decreases to a more or lesssteady state production rate of much finer progeny. The rate ofwear can be modelled based on inter-particle friction/shear.

When balls are added to the charge, the number of impactswhich exceed E0 increases and the ore particles begin to accumu-late incremental damage (as discussed in detail in the nextsection).

So we postulate five mechanisms as occurring in SAG mills (andsome ball mills):

� Body breakage (single impact breakage through the particle –the traditionally conceived mechanism occurring in tumblingmills but in reality infrequent in a large SAG mill and com-pletely absent in the pilot mill used here).� Incremental damage (body breakage due to accumulated dam-

age or fatigue from many weak collisions).� Attrition (mass loss by abrasion of the surface of rounded rocks

as other parts slide over them).� Rounding (preferential and higher abrasive mass loss from the

corners of blocky particles).� Chipping (loss of corners and asperities by small scale body

breakage for irregular shaped particles).

All five mechanisms have been implemented in the DEM codedescribed in Cleary (2004, 2009a). However, for the results re-ported in this paper, only the incremental damage/breakage mech-anism is active and has been used in the prediction of the rock sizedistribution. The collision model used in this work is a linearspring-dashpot model. Details of this and other collision modelscan be found in Thornton et al. (2011, 2013) for elastic and inelasticcollisions.

4. Modelling breakage by incremental impact damage

The basic hypothesis of incremental breakage is:

� At less than some specific energy (E0), no body damage occursas all deformation is elastic.� At higher energies, the particle accumulates incremental dam-

age (Ei � E0) and the probability of survival decreases until it



0102030405060708090

100

Number of Impacts

Cum

ulat

ive

Frac

tion

Bro

ken

20%

30%

40%

50%

1 2 3 4 5 6 7 8 9 10

Fig. 1. �19 + 16 mm preliminary test results for breakage caused by successiveimpacts at various percentages of the minimum energy required to cause breakagein a single impact. (After Morrison et al., 2007).

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100

Number of Impacts

Cum

ulat

ive

Frac

tion

Bro

ken

30%

40%

50%

1 2 3 4 5 6 7 8 9 10

Fig. 2. �26.5 + 22.4 mm preliminary test results for breakage caused by successiveimpacts at various fractions of the minimum energy required to cause breakage in asingle impact. (After Morrison et al., 2007).

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

Size (mm)

Cum

ulat

ive

Perc

ent P

assi

ng

7 hits - total 0.28 kWh/t



One hit at 1 kWh/t

One hit at 0.25 kWh/t

0.10 1.00 10.00 100.00

Fig. 3. Comparison of progeny size distributions for single and multiple impacts for31.5 � 26.5 mm particles each at an energy level of 50% of the minimum requiredfor breakage in a single impact (after Morrison et al., 2007).

G.W. Delaney et al. / Minerals Engineering xxx (2013) xxx–xxx 3

breaks (where Ei is the energy absorption by the i-th collision ofthe particle).

A model based on this needs three components:

� An estimate of the probability of breakage for each impact.� A rule for accumulation/severity of breakage.� A progeny distribution model (or breakage function).

Morrison et al. (2007) reported on various approaches to mod-elling incremental damage for this ore type. A satisfactory modelfor the probability of breakage, degree of breakage and likely prog-eny size distribution was developed based on the standard JKMRCimpact breakage model (Napier-Munn et al., 1996) and the work ofVogel and Peukert (2004) with modifications suggested by Shi andKojovic (2007).

In summary, the probability of survival after a series of k equalimpacts is predicted by:

S ¼ 1� expf�fmat � x � kðWm;kin �Wm;kinÞg ð1Þ

where S is the breakage portion, Wm,kin is the single impact energy,Wm,min is the no damage energy, x is the diameter of particle, k is thenumber of impacts, fmat is the material parameter.

The likely severity of breakage can be estimated in terms of thenet energy absorbed by the particle.

The Vogel and Peukert (2004) equation provides a useful modelto test. In slightly modified form, the probability of selection for Sbreakage is after i events. For more detail, see Morrison et al.(2006).

S ¼ 1� exp �b0X

i

½Ei � E0� !

ð2Þ

Note that [Ei � E0] may not be less than zero and b0 is a materialparameter which may contain a particle size component. The prob-ability of survival after i events is simply (1 � S).

PðSurvival=iÞ ¼ exp �b0X

i

½Ei � E0� !

ð3Þ

Whyte (2005) carried out a series of preliminary tests on16 � 19 mm and 22 � 26 mm size fractions of a broad rock sizedistribution at four energy levels. These provide a manageablesub-set to test the survival model.

Breakage testing in this range of energies is unusual because theresults of single impact testing appear to become erratic. For theearly experiments, some preliminary testing was carried out todetermine the energy level which would almost certainly causebreakage in a single impact. Once this level was established, sepa-rate sets of particles were subjected to successive impacts at frac-tions of this energy level.

Figs. 1 and 2 show the fractions of survivors after 1–10 hits at20%, 40%, 60% and 80% of the specific energy required to causebreakage in a single impact. Fig. 1 shows that at an impact energylevel of 20% of that required for single impact breakage 80% of theparticles have not been broken after 10 successive impacts. At 30%,40% and 50% of the energy required for breakage in a single impact,50% of the particles break after only two impacts. This behaviourhas major implications for the energy efficiency of tumbling mills.

Fig. 3 shows the size distribution of the progeny after 7, 8 and 9weak impacts (given by the blue1, magenta and yellow curvesrespectively) and for single impact breakage at higher energies(given by the purple and cyan curves). With each successive weak

1 For interpretation of color in Figs. 3 and 5, the reader is referred to the webversion of this article.


impact there is a moderate amount of breakage as particles faildue to accumulation of incremental damage and the progeny sizedistribution becomes finer (moves progressively to the left). The sizedistribution from the incremental damage after 8 and 9 impacts ap-pears to be quite similar to that achieved in a single impact. This sug-gests that a similar process of crack extension occurs regardless ofwhether it is one event or several impacts. However, there will usu-ally be very little excess energy (above the elastic threshold) and sothe degree of breakage achieved will be of low severity for each im-pact. The progeny from incremental impact breakage are indistin-guishable from those generated by single impact breakage(Morrison et al., 2007) except that they will likely occur at lowseverity as shown in Fig. 3. Note however, that the total energy input



t75t50

t25

t10

t4

t2

0

20

40

60

80

100

0 10 20 30 40 50

t (

% P

assi

ng)

n

Breakage Index, t (%)10

Fig. 4. tn vs degree of breakage as given by t10 (after Whiten and Narayanan, 1988,for a range of ore types).

Table 2Parameters used for the DEM simulations.

Normal spring stiffness 200,000 N/mShear spring stiffness 100,000 N/mDensity of rock 2650 kg/m3

Density of ball 7850 kg/m3

Coefficient of restitution (rock–rock) 0.3Coefficient of restitution (rock–ball) 0.5Coefficient of restitution (ball–ball) 0.8Friction (rock–rock, rock–ball and ball–ball) 0.5


required is higher when several impacts are required due to the en-ergy absorption under the elastic threshold. The single hit at0.25 kW h/t, the single hit at 1 kW h/t and the multiple impact (7,8 and 9 hits) progeny are clearly very similar and can be describedby the spline curves and/or a string of particles as described above.

The commonly used JKMRC relationship for severity of breakagecan be modified in the same way:

t10 ¼ A 1� exp b0X

i

½Ei � E0� ! !

ð4Þ

where t10 is the fraction of the mass of the original particle whichwill pass through an aperture of 1/10 of the original particle size– after the impact event.

E0 is the threshold energy per unit of particle mass below whichthe particle essentially does not accumulate any impact damage.

This incremental damage model is used in the DEM model togive the simulation results presented in Section 7. The probabilityfor breakage to occur in the simulation is determined from Eq. (2)and then the resulting progeny from such a breakage event are pre-dicted using the JKMRC breakage map (Whiten and Narayanan,1988). The breakage map shown in Fig. 4 can be used to estimatea full size distribution at any value of t10. Any vertical line drawnin Fig. 4 represents a complete cumulative size distribution for thatspecific value of t10.

A new method has been developed to generate a set of DEMparticles which closely match a measured size distribution or asimulated breakage function. The size distribution is calculatedusing a spline curve fitted to the values shown in Fig. 4.

tðkÞ ¼ AðkÞ 1:0� exp ðbðkÞÞX

i

Ei � E0

! !ð5Þ

where A(k) and b(k) are coefficients for a set of k = 6 size classesfrom t2 to t75, which have been determined from drop weight tests.When a particle breakage event occurs, first the reduced parent sizeis calculated by extrapolation of the predicted t(1) and t(2) values.The model then iteratively determines the size of the next progenyparticle by using the left over mass to calculate t(next) which isthen substituted into the size distribution curve. The progeny modelhas been calibrated for breakage energies E0 > 0.3 kW h/t and at lowbreakage energies the distribution curve becomes such that physi-cally unrealistic progeny sizes can be predicted which violate massconservation. In such cases, an estimate of the reduced parent size


can still be determined from interpolation of the t(1) and the origi-nal parent size. The resulting set of progeny particles are thenpacked into the volume of the parent particle. The progeny genera-tion, packing and replacement of the parent are performed in theDEM simulation as an instantaneous event since the timescale fora particle to break is substantially shorter than any of the flow re-lated timescales. Eq. (5) is a general form of breakage behaviour thatapplies broadly to mineral rocks. The ore specific behaviour isdetermined by the parameters A(k), b(k), and E0 which need to bemeasured or estimated for each ore type.

Note, that in our DEM simulations we can specify a minimumsize of progeny fragment which we will resolve within the simula-tion. But we also track the full predicted size distribution for eachbreakage event. The summation of these is then a prediction of thebreakage products created by the mill. In this way we can, in prin-ciple, predict the full size distribution for both the particles whichare resolved in the simulation, and also the unresolved finematerial.

5. Calibration of abrasion test results

The standard JKMRC abrasion test mill is 300 mm in diameterand 300 mm in length and has four 10 mm square lifters. It isoperated at 53 rpm. The material properties used in the DEM sim-ulation are shown in Table 2. The charge consists of 3000 g of�55 + 38 mm ore – which in this case comprised 17 particles.In the DEM simulation of this abrasion mill, the impact and fric-tion energies dissipated during collisions were accumulated.Fig. 5 shows the probability distribution of the observed collisionenergy level (blue diamonds) and the cumulative energy distribu-tion starting from the highest energy levels (magenta squares).This data is collected when the flow is at steady state and for asufficient period to produce statistically well averaged collisiondistributions. Almost all (99%) of the energy applied to the parti-cles occurs in quite a narrow range from about 0.08 to 0.6 J/kg(which is the energy absorbed by the particle per unit mass ofthe particle). The remaining impacts are much more numerousbut might at best only cause smoothing of small asperities. How-ever, as we will see later, smoothing is an essential component ofbreakage.

The standard calibration parameter ta relates to the productionof particles finer than one tenth of the original particle size of55 � 37.5 mm. For a more detailed description of the test, see Na-pier-Munn et al. (1996). For DEM simulation, the degree of massloss of the large particles is of most interest. The large particleswere weighed at the end of the test and their overall wear rateswere estimated from mass lost. This wear rate of large particleswas not as repeatable as the ta value and ranged from 60 to120 g for three 10 min tests of fresh samples.

The abrasion mill is expected to be dominated by shear, so theshear energy absorption by the particles was used to calibrate thedegree of abrasive wear expected in the 1.2 m diameter mill interms of mass lost per unit of energy dissipated.



0102030405060708090

100

Upper Bin Level J/kg

Perc

ent o

f Col

lisio

ns

Impacts per 10 seconds

Cumulative Energy %

0.0000001 0.0001 0.1 100

Fig. 5. The collision energy distribution (diamonds) and the cumulative collisionenergy distribution (squares) of the particles in the abrasion mill predicted by DEM.

Fig. 6. Shows the motion of spherical particles in the 1200 mm pilot mill for test 1when just using the abrasion model for producing mass loss.

0

1000

2000

3000

4000

5000

6000

Mass of each feed particle (g)

Mas

s of

eac

h pr

ogen

y

part

icle

(g)

Mass (f)DEM est at 720s

0 1000 2000 3000 4000 5000 6000

Fig. 7. Measured (blue diamonds) and predicted (magenta squares) particle massesfor Test 1 (after Morrison et al., 2006). (For interpretation of the references to colourin this figure legend, the reader is referred to the web version of this article.)

0500

1000150020002500300035004000

Mass of each feed particle (g)

Mas

s of

eac

h pr

ogen

y

part

icle

(g)

Mass (f)

DEM at 720s

0 1000 2000 3000 4000 5000

Fig. 8. Measured and predicted particle masses for Test 2 (after Morrison et al.,2006).

0500

1000150020002500300035004000

0 1000 2000 3000 4000Mass of each feed particle (g)

Mas

s of

eac

h pr

ogen

y

p

artic

le (g

)

Mass (f)

DEM at 720s

Fig. 9. Measured and predicted particle masses for Test 3 (after Morrison et al.,2006).


6. Prediction of ore size change in a pilot mill from abrasion

The pilot mill used here is the Loveday mill which is:

� 1.12 m � 0.31 m, with,� 53 particles with mass and diameter measured before the

experiment and at the end so we can look at the exact mass lossof each particle.� Grates in front of each lifter to allow removal fines preventing

re-breakage, giving a mass loss of fine per unit time.� Rotation rate is 30 rpm.

Tests were performed for 10 min for three different charges:

1. 30% AG charge.2. 20% AG charge.3. SAG charge with 10% rocks and 10% balls.

DEM simulations were run exactly matching these conditions.The abrasion wear rate of each particle in the simulation is propor-tional to the shear energy it accumulates in each collision scaled bythe abrasion test mill wear rate. The model produces a particlemass distribution as an output. The simulated mill containing 53particles is shown in Fig. 6 for Test 1 with a 30% rock charge.

The predictions of the final masses of the charge particles forthe autogenous cases in Tests 1 and 2 and comparisons to theexperimental results are shown in Figs. 7 and 8. As might be ex-pected, there is significant scatter in the experimental data. Someof the scatter is likely due to misidentification of progeny in thecharge. There is a systematic over-prediction of the final sizes ofthe particles in the simulation. The rate of wear is under-predictedby about three times. Hence the higher intensity frictional eventsin the pilot mill achieve more wear than the similar shear energyin the abrasion test mill. However, the trends and general variationseem quite comparable for Tests 1 and 2. Using a calibrationparameter would produce a very close match to the DEM predic-tions for Tests 1 and 2. The collision conditions in Tests 1 and 2 failto achieve the required threshold energy for impact damage to oc-cur. Hence a simple shear model seems appropriate for predictingthis size of AG mill.

Test 3 (10% Rock and 10% Balls) shows a quite systematic devi-ation between the simulation and the experiment (Fig. 9). There isa very large over prediction of the sizes of the smaller particles.This is likely due to the smaller particles accumulating significantincremental damage. This behaviour is not captured by the fric-tion/abrasion model. Some of the total collision energies for smal-ler particles achieve about half of the specific energy required forimpact damage measured in DW test in Whyte (2005), where a va-lue of E0 = 0.008 kW h/t was found (where this is again the energyabsorbed per unit mass of the particle). Given the variety of loadingconditions in the mill charge, the required energy level may be

Please cite this article in press as: Delaney, G.W., et al. Predicting breakage and the evolution of rock size and shape distributions in Ag and SAG mills usingDEM. Miner. Eng. (2013), http://dx.doi.org/10.1016/j.mineng.2013.01.007


Fig. 11. Measured and predicted particle masses for Test 1.


reduced. Further work on damage thresholds carried out by Bbosa(2007) found that smoothed particles have a much lower damagethreshold than ‘‘as broken’’ particles – even if the smoothing is car-ried out at very low energies. Bbosa tested smoothed particles of asiliceous ore quite similar to the one used for this test work. The A �b values from several Drop Weight Tests of each siliceous ores ran-ged from 34 to 40. Both of these ores have been milled autoge-nously further confirming that they are similar enough for thepurposes of this paper. Ideally, progressively smoothed particlesof the same ore would be tested. Bbosa found that E0 ranged from0.001 to 0.0015 kW h/t (3.6–5.4 J/kg) or about one tenth of theWhyte estimate of 0.008 kW h/t for unsmoothed particles. In thenext section, we will use the Bbosa estimates to test if an incre-mental breakage model can better predict the size evolution ofthe charge particles in the mill.


7. Prediction of ore size change in a pilot mill using incrementalbreakage

Next we performed DEM simulations of the three test condi-tions using non-spherical particles and the incremental breakagemodel described in Section 4. The rock particles used in the simu-lation were super-quadrics with shape factors (determining theblockiness of the particles) ranging from m = 3.0 to 6.0, and aspectratios from a = 0.5 to 1.0. The steel balls were represented asspheres (See Fig. 10). Due to the uncertainty in the exact value ofE0 to use for the material in the experiments, simulations were per-formed using values of E0 = 3.6 J/kg and E0 = 5.4 J/kg. These werechosen from results obtained from impact tests using siliceousore similar to that used in this test work (Bbosa, 2007).

Fig. 11 shows the predicted final masses of the charge particlesin the simulation and the experiment for the AG test case 1. Thelower E0 value of 3.6 J/kg (0.001 kW h/t) tends to under predictthe final sizes of the smaller particles and slightly over predictthe sizes for the larger particles. The higher E0 value of 5.4 J/kg(0.0015 kW h/t) gives a more linear variation in the final sizesand compares well with the final sizes seen in the experiments,with an overall small over prediction in the final sizes of theparticles.

Fig. 12 shows the predicted final masses of the charge particlesin the simulation and the experiment for the AG test case 2. Herethe lower E0 value substantially under predicts the final sizes ofthe charge particles. The prediction for the higher E0 value is verygood across the full size range of the particles.

Fig. 10. Shows the motion of the non-spherical rock particles and the sphericalsteel balls in the 1200 mm pilot SAG mill for test 3 when incremental damage isused as the model for mass loss.



For the SAG case (Fig. 13), the higher E0 value generally overpredicts the final sizes of the particles, except for the three smallestparticles, which are predicted to have final masses below the spec-ified resolved limit for the particles in the simulation of less than�13 g. In the experiment there is uncertainty in the final sizes ofthe smallest particles, with clear difficulty identifying the particlesas demonstrated by some of the particles being predicted to havegrown. For the lower E0 value, the simulation results are quite closeto the experiment. The agreement is very good for the midsizedcharge particles between 1500 g and 2500 g. There is some un-der-prediction for the masses of the upper third of the size rangesand again some under prediction of the final sizes for the smallestgrain sizes. The experimental results are well bounded by the twosets of DEM predictions which gives reasonable confidence in themodel predictions and for the possible range of E0. The use of the



Fig. 14. Measured and predicted fine material for Test 3.


incremental breakage model for the SAG case shows a considerableimprovement over the abrasion model reported by Morrison et al.(2006). It much better captures the non-linearity in the final sizesof the charge particles, with larger amounts of damage being pre-dicted for the smaller particles.

A comparison of the size distribution for the measured fineproduct (below 22 mm) from the mill and the prediction of fineprogeny from the DEM simulation for case 3 (SAG mill) is shownin Fig. 14. The match is clearly exceedingly poor, with the DEMmodel predicting vastly coarser ‘‘fine’’ progeny. The differences ob-served are a combination of the energy range used in the measure-ment of the t10 progeny distribution and the absence of theabrasive mechanisms contributions. The incremental breakagemodel, using the relatively high collision energy data, is able topredict the amount of mass loss of the parent particles but is notable to predict the fineness of the progeny. This will require char-acterisation of the progeny over larger ranges of collision energiesin future work. This also shows that although the use of an incre-mental breakage model is able to strongly improve the predictedevolution of the larger rocks with very plausible wear rates atlow values of E0, it alone is not capable of describing the entire pro-cess in terms of progeny produced.

8. Discussion

The three modes of breakage provide some insight into the en-ergy efficiency of tumbling mills:

� Mode 1 (rounding) produces fine material at a low energy cost.� Mode 2 (surface wear) produces fine material at a much-

reduced rate for similar energy per mill resolution. That is, itis much less energy efficient.� Mode 3 (incremental breakage) expends energy as elastic defor-

mation until E0 is exceeded, with the energy < E0 only ‘‘heating’’the charge. Hence the autogenous mode will generally be quiteinefficient in this mode of breakage. Changing to SAG mode cansignificantly lift the collisional energies (in particular for smal-ler particles) above E0, causing damage to be accumulated untilbreakage occurs.

At the E0 levels measured by Bbosa for well-rounded particles,Eqs. (3) and (4) provide a description of wear rates by modes 2and 3 as a single process. Based on the simulation results, the ac-tual value of E0 (or distribution of values) at which incrementaldamage begins to accumulate is critical to impact breakage and re-moval of critical size material from the charge. Published work on‘‘rough’’ particles overestimates E0 by as much as ten times.Accepted lab tests for impact breakage use very much higher ener-gies – at least in part to avoid the (apparent) scatter, which comes


into play at lower energy levels. The resulting variation due tosmall numbers of particles which are assumed to have both uni-form breakage properties and a uniform initial degree of damageis probably a factor for both experimental and simulated results.

However, Fig. 14 suggests that modes 2 and 3 produce very dif-ferent progeny. Therefore, it will be more appropriate to modelmode 2 as proportional to friction with very fine progeny resultingand mode 3 using the standard JK breakage map. This would pro-vide an analogous approach to the JKMRC AG/SAG model (Napier-Munn et al., 1996) with a dynamic balance between abrasion andimpact (i.e. mostly incremental) breakage.

The requirement to smooth particles before very much damageleading to breakage can occur also has important implications forthe dynamic behaviour of AG and SAG mills – particularly at startup. If particles have not had enough time to become round andsmooth, they will require much higher impacts before damage willbegin to accumulate and there are very few such impacts available.

Prediction of the rough to smooth transition of ore particlesmay potentially require highly detailed characterisation of eachparticle. However, as each test produced similar shaped size distri-butions of progeny in the rounding phase, there may be a simplerapproach.

This analysis underpins work by Musa and Morrison (2009)which compared comminution devices in terms of the energy re-quired to duplicate the comminution achieved with a JK-dropweight tester. AG/SAG mills cluster at around 40% efficient – i.e.they need about 2.5 times as much energy as a DWT to generatea similar quantity of fine material.

9. Conclusions

The results for a DEM model of particle size evolution in a pilotAG/SAG mill using an abrasion model were seen to make reason-able predictions for the overall trend in the size reduction of thecharge particles in the AG mill. However, using only an abrasionwear rate calibrated from the results of the JKMRC pilot mill, themodel under predicted the rate of wear by about three times. Forthe SAG case, the disagreement between the simulation and exper-iment was greater. This was due to the model not incorporating theeffects of incremental impact damage to the particles.

Conversely, the predictions of particle size reduction from theDEM simulations using an incremental damage model alone im-proved on those from the abrasion model, in particular for theSAG case. The incremental damage model was able to predict thegreater degree of damage observed for the smaller particles withinthe mill. The results demonstrated the sensitivity to the choice ofE0 value used, with significant variation seen between the two val-ues tested. There is uncertainty too regarding the exact definitionof E0 in terms of which collisional energy contributions should beincluded. Here we have considered the total collision energy indetermining the cumulative energy used to calculate the probabil-ity of breakage and the progeny that are produced. While the DEMincremental damage model gives good predictions for the size evo-lution of the charge particles, it predicted a vastly coarser size dis-tribution for the ‘‘fine’’ product particles produced by the mill.Therefore, it will be more appropriate to model mode 2 (abrasion)as being proportional to friction with very fine progeny resultingand mode 3 using the standard JK breakage map (producing coar-ser progeny). This would provide an analogous approach to theJKMRC AG/SAG model (Napier-Munn et al., 1996) with a dynamicbalance between abrasion and impact (i.e. mostly incremental)breakage. Combining these two modes of wear will be tested in fu-ture DEM modelling. The importance of the material characterisa-tion and modelling of mode 1 (rounding) mechanisms is also nowclear and remains a challenge for the future.




The simulation model presented here provides insight into thebreakage mechanisms, which apply to particles in a small pilotscale AG/SAG mill. An overall conclusion of this work is that tum-bling mills are intrinsically inefficient for at least two reasons.Firstly, a great deal of the energy of interaction between ballsand rocks is consumed as elastic deformation – that is, it is lessthan E0. Secondly, many of the impacts which do cause damageonly exceed E0 by a small margin and a high proportion of the en-ergy in the interaction is still lost as elastic deformation.

Acknowledgements

This project was carried out under the auspices and with thefinancial support of the Centre for Sustainable Resource Processing(CSRP), which was established and supported under the AustralianGovernment’s Cooperative Research Centres Program.

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