A GENERIC DYNAMIC MODEL INCORPORATING A 4D APPEARANCE FUNCTION FOR TUMBLING MILLS

Ping Yu1, *Weiguo Xie1, Lian X. Liu1, Nirmal Weerasekara1, Benjamin Bonfils1 and Malcolm Powell1

1 the University of Queensland, Julius Kruttschnitt Mineral Research Centre, Sustainable Minerals Institute, Indooroopilly, Brisbane, QLD 4068, Australia

* Corresponding author: w.xie@uq.edu.au

ABSTRACT

A mill model structure based on the population mass balance framework incorporating breakage characteristics, slurry and solids transport, product classification and discharge and energy consumption was reported in XXVII IMPC and named the Generic Tumbling Mill Model Structure Version I (GTMMS I). In this work, a new 4D (four dimensional) appearance function sub-model based on the experimental results of the JK Rotary Breakage Tester (JK RBT) was developed to describe the breakage characteristics and was applied to this new model structure. The newly developed 4D appearance function model has fewer fitting parameters and is more generic in nature. Most importantly, it is applicable to both high and low energy impact breakage. It is therefore much more versatile in comparison to the existing JKMRC t10-tn

appearance function and the size-dependant JK M-p-q t10-tn appearance function. In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. With DEM results providing energy distribution information inside the mill directly, the selection function and the back-calculation method used in the existing JKSimMet modelling method are not needed in this model structure. With the above two revolutionary innovations, the previous model structure was upgraded to the Generic Tumbling Mill Model Structure Version II (GTMMS II). Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation. A case of the dynamic grinding of a SAG mill was studied to validate the GTMMS II. The model simulation results agreed well with the plant data. With the newly developed 4D appearance function model, the incorporation of DEM energy distribution and transport function, the Generic Tumbling Mill Model Structure Version II (GTMMS II) is an important step forward towards mechanistic modelling of tumbling mills.

KEYWORDS

Generic Tumbling Mill Model Structure Version II (GTMMS II), Tumbling mill, Breakage characterisation, 4D appearance function, Discrete Element Method (DEM), Transport function, dynamic model

INTRODUCTION

Comminution processes consume most of energy in the mineral processing plants. At least 1.3% of Australia’s electricity output is consumed in the comminution of copper and gold ores (Ballantyne, Powell, & Tiang, 2012). It is estimated that comminution consumes 1-4 % of all electrical power generated in the world and 7-10% of that in Australia (Napier-Munn, 2013). Tumbling mills, such as ball mill, rod mill, pebble mill, autogenous (AG) mill, semi-autogenous (SAG) mill and tube mill, which are widely used in comminution process, use the largest share of comminution energy in most plants. Thus the modelling of tumbling mills and optimisation of their grinding circuits can play a significant role in reducing the energy consumption in comminution.

There are two kinds of tumbling mill models: non-mechanistic and mechanistic models (Yu, Xie, Liu, & Powell, 2014). The non-mechanistic models do not consider the fundamental physical mechanism in the comminution process. However, mechanistic models focus on the comminution process, considering the fundamental physical laws in the process and the interactions between the particles and elements in the mill. Austin, Menacho, and Pearcy (1987) developed a general model for SAG/AG mills. The specific rate of breakage (also known as the selection function) was composed of three regions: normal breakage, abnormal breakage, and self-breakage. Powell (2006) summarized the limitations of the current comminution models and proposed a conceptually new model – the unified comminution model (UCM) – with the hypothesis that comminution is a generic process of ore breakage independent of the equipment and that the mechanical breakage environment can be modelled fundamentally. Govender, Tupper, and Mainza (2011) developed a mechanistic cell model based on combining space and time-averaged Navier–Stokes equations to simulate the slurry transport in dynamic beds.

Firstly developed by Cundall and Strack (1979), and then applied to tumbling mills by Mishra and Rajamani (1992), the Discrete Element Method (DEM) was regarded as one of the ‘High-Fidelity Simulation (HFS) tools’ based on the basic physics theories for the simulation and optimization of comminution operations (Herbst & Lichter, 2006). Recently, the DEM has been applied to provide full range of information on the mill mechanical environment and the information needed in liner wear modelling (Weerasekara, Powell, Cole, & Favier, 2010).

In the previous work, an integrated, mechanistic mill model structure for tumbling mills has been developed (Yu et al., 2014). It was based on the population mass balance framework combining the JK M-p-q tn appearance function, transport function and other sub-models. That model structure has been labelled as the Generic Tumbling Mill Model Structure Version I (GTMMS I). In this work, it is upgraded to the Generic Tumbling Mill Model Structure Version II (GTMMS II). A new 4D (four dimensional) appearance function sub-model based on JK RBT experimental results was developed to describe the breakage characteristics and was included in this new model structure. In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation.

GENERIC TUMBLING MILL MODEL STRUCTURE VERSION II (GTMMS II)

The generic integrated tumbling mill model structure version II is illustrated in Figure 1. In common with the Generic Integrated Tumbling Mill Model Structure Version I, it uses Population Balance Method (PBM) as the heart of the framework because the PBM, tracking the production of progeny particles, is a generic relationship in almost all types of grinding mills. There are two significant upgrades in the model structure version II: the JK M-p-q t10-tn appearance function model in GTMMS I is replaced by the 4D (four dimensional) appearance function model; the Discrete Element Method (DEM) energy distribution model takes the place of the JK updated selection function. These two upgrades make the new Model Structure more mechanistic and generic. The sub-models contained in Figure 1 are expanded in below section.

Figure 1: Schematic of the Generic Integrated Tumbling Mill Model Structure Version II

4D Appearance Function ModelAn appearance function describes the breakage characterisation of an ore. The t10-tn model has

been widely used in practice (King, 2001; Napier-Munn, Morrell, Morrison, & Kojovic, 1996). In the model structure version I (Yu et al., 2014), the JK updated appearance function, JK M-p-q t10-tn method, was used to characterise the product size distribution after breakage (Kojovic, Hilden, Powell, & Bailey, 2012; Shi & Kojovic, 2007):

[Beginning of the document][Automatic section break]00001()

00002()where t10 is the cumulative percentage passing at an aperture of 1/10 th of the original ore particle

size. M is maximum possible value of t10 in impact (per cent), Fmat is the material property (kgJ-1m-1) = f(X,p,q), p and q are ore-specific constants, X is the average input ore particle size (mm), E cs is the specific breakage energy (kWh/ton).

Within the model structure version II, the traditional JK M-p-q t10- tn approach for appearance function is not used. Instead, the full product size distribution is related to the original sizes of ore X (mm), ore characteristics, and input specific comminution energy Ecs (kWh/ton). For a given ore, the cumulative percentage passing at a sieve size class is determined by X, Ecs, and the sieve size class x (mm).

00003()The cumulative percentage passing is a three-variable function and can be plotted in a X-Ecs-x 3D

coordinate system. The 4th dimension of “passing” can be illustrated by a colour bar in this 3D graph. Thus we get a virtual 4D graph which can describe product size distributions under different combinations of X, Ecs and x. Eq. 00003() is called the 4D appearance function model. This is an appearance function

covering a wider range of different X and Ecs. The derivation of 4D appearance function is demonstrated as follows:

Based on 42 sets of breakage test data from JK Rotary Breakage Tests (JK RBT) for Cadia Ore, a 3D scatter graph was obtained (Figure 2). The Ecs range is from 0.05kWh/t to 2.5kWh/t and the original size range is from 7.3mm~24.4mm. Because there were only 42 sets of the raw experimental data, the interpolation method was used to enrich the original data.

The following shows the derivation of the 3-variable appearance function using Eq.00003(). For a given Ecs and X, the cumulative percentage passing can be estimated using the P80-m Weibull distribution (Wills & Napier-Munn, 2006):

00004()where, P80 is the size that the cumulative percentage passing of 80% (mm) is. x is the sieve size

class (mm). The P80 parameters can be interpolated out from the original test data using reverse-interpolation method. The reason to choose P80 is because the P80 size is often used as a product size measure in industry. Given P80 calculated and the cumulative percentage passing is derived from the experimental data, the parameter “m” can be calculated using Eq.00004(). Based on the experimental data trends for Cadia ore and the interpolated data, two empirical relationships for P80 and the parameter “m” in Eq.00004() were developed using the multi-variable function regression and fitting techniques:

00005()

00006()where, α,β,γ,δ,a,b,c are fitting parameters. X is the original ore size (mm), X top is the largest size

of the original sizes. The Ecs is the specific comminution energy (kWh/t). Ecstop is the biggest Ecs value among all the Ecs values at different X. Because of the non-dimensional forms in Eq.00005() and Eq.00006(), the model has a good scalable ability. All the parameters can be divided into two groups: α,β,γ,δ contributing to P80 and a,b,c contributing to ‘m’. P80 represents the fineness of the breakage. The less the P80 values, the finer the product sizes. The parameter ‘m’ indicates the shape of the product size distribution (PSD). The bigger the ‘m’ value, the steeper the PSD curves, and the narrower range in product sizes. The smaller the ‘m’ value, the flatter the PSD curves, and the wider range in product sizes. P80 decreases when the specific energy Ecs increases and the original ore size X decreases, indicating finer products. Parameter ‘m’ increases when the specific energy Ecs decreases and the original ore size X decreases, implying the steeper PSD curve shapes and the smaller range in product sizes.

Eq.00004(), 00005() and 00006() form a 4D full appearance function model for a given ore (Cadia in this case). For any given X and Ecs, P80 and ‘m’ can be calculated with Eq.00005() and 00006(). Substituting P80 and ‘m’ into Eq.00004(), cumulative percentage passing can be obtained. The proposed 4D full appearance function model has been compared with the existing JK M-p-q t10-tn model. Parameters M, p and q have been fitted by using Eq.00001() and Eq.00002(). The tn family curve data in Figure 3 for Cadia ore were calculated based on the raw experimental data.

510

1520

25

01

230

5

10

15

20

25

Original Size X (mm)

Cumulative Percentage Passing 3D Graph

Ecs (kWh/ton)

Sie

ve S

ize

x (m

m)

Cum

ulat

ive

Per

cent

Pas

sing

%

10

20

30

40

50

60

70

80

90

100

Figure 2: 42 sets of Cadia test data

0 5 10 15 20 25 30 35 40 45 500

10

20

30

40

50

60

70

80

90

Breakage Index t10 (%)

tn p

assi

ng (%

)

tn .vs. t10 degree of breakage

t2t4t10t25t50t75

Figure 3: tn family curves

4a): Original data interpolated from experimental data

4b): Fitted with M-p-q t10-tnmodel 4c): Fitted with the 4D appearance model

Figure 4: Comparison of JK M-p-q t10-tn model and the 4D appearance function model

Comparing Figure 4a, Figure 4b and Figure 4c, it is apparent that the 4D appearance function model is more accurate than the JK M-p-q t10-tn model because the former is closer to the original data. The product size distribution (PSD) curves for typical combinations of the original ore size X and the specific energy Ecs are also compared between the JK M-p-q t10-tn model and the 4D appearance function model. It can be seen from Figure 5 to Figure 7 that the JK M-p-q t10-tn model cannot accurately predict size distribution of low energy impact breakage whilst the 4D model can estimate the size distribution for low energy breakage well. In general, the JK M-p-q t10-tn model can predict high energy impact breakage well. However for smaller original ore sizes in both Figure 5 and Figure 6, the tn model’s prediction accuracy for impact breakage deteriorates. For the new 4D full appearance function model, it can be seen that it predicts both the low energy incremental breakage and high energy impact breakage accurately. Thus the 4D appearance function model can be employed to replace the existing JK M-p-q t10-tn model to calculate the breakage characteristics in grinding processes.

Figure 5: Size distribution comparison for low energy impact

X=7.3mm Ecs=0.05KWh/t

Figure 6: Size distribution comparison for high energy

impact X=7.3mm Ecs=2.5KWh/t

Figure 7: Size distribution comparison for high energy impact

X=10.3mm Ecs=2.5KWh/t

DEM Energy Distribution ModelThe energy size distribution (Ecs-size class curve) is a function to display the specific energy

distributed by size classes, which shows how the power is assigned to the different size classes. In the Generic Tumbling Mill Model Structure Version I, the JK back-calculated selection function was used to describe the energy distribution.

007()

where, Ecsi: Ecs in i size class; Ecs: Specific Comminution Energy kWh/t; : Selection function, related to comminution probability. The back calculation method will inevitably push errors to the selection function. However, with the aid of the Discrete Element Method (DEM), energy distribution for each size can be calculated directly. The selection function isn’t needed anymore with the DEM energy distribution model integrated into the generic model structure.

According to the DEM theory, in unit time (1 second) for one particle:

008()

where, En: normal energy (kWh); Et: Tangential energy (kWh); Eall: total energy per particle in one size class (kWh)

009()

where, En,i: the normal energy per collision (kWh/ collision); Fn,i: number of collisions per particle per second (Normal Frequency); N: number of energy classes per size class; En: total normal energy per particle per second (kWh/particle/second).

0010()where, Eti: the tangential energy per collision (kWh/ collision); F t,i: number of collisions per

particle per second (Tangential Frequency); N: number of energy classes per size class; En: total tangential energy per particle per second (kWh/particle/second)

0011()

0012()

where, M: mass per particle (Kg/particle); Ecsni : specific normal energy (kWh/ton); Ecsti : specific tangential energy (kWh/ton). The total energy per particle in one size class (kWh) Eall:

0013()

For all the particles in the size class:

0014()

where, Esum: total energy in that size class (kWh); No: number of particles in that size class; M: mass per particle

0015()

where, Msum: mass in that size class. For the total specific energy in that size class:

0016()

where, Ecssum: specific energy in that size class (kWh/ton).

Eq.0016() provides a practicable estimation for the total specific energy distribution. Figure 8 is a typical DEM energy distribution curve for a SAG mill. Because of the limitation of computational power of the computer, the smallest size class which the DEM can reach is about 4 mm. However, in practical application, the smallest size class can reach tens of microns. In order to extend the applicable scope of DEM, the following reasonable assumption is adopted: the size classes 2~5 mm have the highest specific energy, according to breakage rate distribution theory that the breakage rate peaks in the range of 2~5 mm (T. J. Napier-Munn et al., 1996). Particles less than 2 mm more probably behave like ‘water’ and tend to flow with the water before they are broken or break others. The breakage probability decreases with the decreasing size. For particles of 2~5 mm, all the particles bigger than them have a contribution to their breakage. The DEM research also proves that the particles at smaller size classes experience higher energy than the larger ones (N. Weerasekara & Powell, 2010). Based on this assumption, a DEM energy distribution map was obtained for the case in this study (Figure 9).

Particle size (mm)100 101 102 103

Spe

cific

Ene

rgy

Ecs

(kW

h/to

n)

10-4

10-2

100

Specific Energy Distribution by DEM

Total specific energyTotal normal specific energyTotal tangential specific energy

Figure 8: Specific Energy distribution by DEM

0 50 100 1500

1

2

3

4

5

6

7

Particle size (mm)

Siz

e-S

peci

fic E

nerg

y (k

Wh/

t)

Specific energy distribution by DEM

Figure 9: DEM Specific Energy distribution for the case study

Besides the above two sub-models, the Generic Tumbling Mill Model Structure Version II (GTMMS II) has other sub-models and modules, such as the discharge function, transport function, dead slurry hold-up, power model and dynamic modelling strategy. Those sub-models and modules are described in the previous work (Yu et al., 2014).

RESULTS AND DISCUSSION

To validate the feasibility of the Generic Tumbling Mill Model Structure Version II that is integrated with the 4D appearance function model and the DEM energy distribution model, a case of the dynamic grinding of a SAG mill was studied. In this case, the internal length of the SAG mill is 6.6 m and the internal diameter is 5.0 m. The grate size Xg is 22 mm, and the fine size Xm is 2.5 mm. The mill feed is zero initially and a constant feed of 137.5t/h is added after the time zero point. The DEM energy distribution model was used to obtain the Ecs-size class energy distribution information. The feed ore sizes are known and they, together with the Ecs-size class distribution information and sieve sizes, are input into the 4D appearance function model. According to Eq.00004(), the cumulative percentage passing can be calculated. Besides these the classification function is given by Figure 10, the transport function and the power model were also applied into the model structure. The SAG mill is divided into four equal virtual segments to incorporate the transport functions, numbered from segment 1 closest to the inlet to segment 4 closest the outlet. The dead slurry hold-up is also considered in this integrated model structure. The model

structure is implemented in MATLAB codes. Finally the dynamic responses were obtained (Figure 11 and Figure 12).

Particle size Log(size)10-1 100 101 102 103

Cla

ssifi

catio

n fu

nctio

n %

0

20

40

60

80

100

Figure 10: The classification function

0 5 10 15 20 25 300

50

100

150

200

Flow

rate

(t/h

)

Time (hour)The dynamic response of product and slurry content to the feed

by the Generic Tumbling Mill Model Structure Version II

0 5 10 15 20 25 300

15

30

45

60

Vol

ume

(m3 )

Feed t/hProduct t/hSlurry Content m3

Figure 11: Dynamic simulation by the Generic Tumbling Mill Model Structure Version II

Figure 11 shows that when the feed steps up from zero to 137.5t/h, the mill contents and products also increase from zero gradually. After about 2.5 hours, the mill reaches the steady state where the product and the content will not change any more and the product rate equal feed rate. The slurry contents in the mill at the steady state is about 24 m3 and the total volume of the mill is 129.6 m3 (approximating the mill as a cylinder). Thus the total mill filling is about 19%. The dynamic response of the contents and products to the feeds in each segment is shown in Figure 12. The dynamic simulation results in each segment are corresponded to the total response in Figure 11. The products of the upstream segment are treated as the feeds of the downstream segment. It takes over 2.5 hours for the mill to stabilise. The overall slurry contents in the mill are the sum of the contents in each segment. When the contents stop increasing, the mill reaches the steady state. Except the last segment, the contents from the first segment to the later one along the length are reducing, providing the pressure drop driving the slurry flow (Figure 12). However, because of the barrier of the grate at the outlet, the volume in the last segment is a little bit higher than the upstream. In addition, because of the dead slurry hold-up, there is a lag between the feed and the product in the segments. The dead slurry hold-up will postpone the establishment of steady state because the slurry must fill the dead volume first before it can be discharged. The product size distributions of each segment are shown in Figure 13. It can be seen that as the ore particles travel along the length of the mill they become progressively finer. The transport function appears to describe the size reducing progress along the mill in a reasonable manner. The transport function has a strong influence on mill modelling (Figure 14). After implementing all the sub-models, such as the 4D appearance function model, the DEM energy distribution model, the classification and discharge model, the transport function model, and the power model, the dynamic simulation results of the Generic Tumbling Mill Model Structure Version II (GTMMS II) agrees well with the plant data (Figure 14). The prediction error of the GTMMS II for product size distributions in steady state is almost within ± 5% compared with the plant data (Figure 15).

0 5 10 15 20 25 300

100

200

Flow

rate

(t/h

)

Time (hour)

Segment 1

0 5 10 15 20 25 300

10

20

Volu

me

(m3 )

Feed t/hProduct t/hSlurry volume m3

0 5 10 15 20 25 300

100

200

Flow

rate

(t/h

)

Time (hour)

Segment 2

0 5 10 15 20 25 300

10

20

Volu

me

(m3 )

Feed t/hProduct t/hSlurry volume m3

0 5 10 15 20 25 300

100

200Fl

owra

te (t

/h)

Time (hour)

Segment 3

0 5 10 15 20 25 300

10

20

Volu

me

(m3 )

Feed t/hProduct t/hSlurry volume m3

0 5 10 15 20 25 300

100

200

Flow

rate

(t/h

)

Time (hour)

Segment 4

Feeds products and contents varying with time in different segments by the Generic Tumbling Mill Model Structure Version II

0 5 10 15 20 25 300

10

20

Volu

me

(m3 )

Feed t/hProduct t/hSlurry volume m3

Figure 12: Feed, product and content in each segment

Particle size Log(size)10-3 10-2 10-1 100 101 102 103

Cum

ulat

ive

perc

enta

ge p

assi

ng %

0

10

20

30

40

50

60

70

80

90

100

Product size distribution comparison between different segments

Segment 4Segment 3Segment 2Segment 1Feed

Figure 13: Product size distribution in each segment

Particle size Log(size)10-3 10-2 10-1 100 101 102 103

Cum

ulat

ive

perc

enta

ge p

assi

ng %

0

10

20

30

40

50

60

70

80

90

100

Product size distribution by GTMMS II

Plant dataGTMMS II With transport functionWithout transport functionFeed

Figure 14: Product size distribution simulation compared with plant data

In order to further verify the application feasibility of the Generic Tumbling Mill Model Structure Version II (GTMMS II), the step changes of feed in this SAG mill case were studied. The feed rate experiences a step change from 0 to 150t/h, keeps constant for a while and then goes down suddenly to 125t/h, keeps unchanged for a period of time, and then abruptly goes up to 195t/h, and afterwards keeps constant. The other working conditions are kept unchanged compared with previous case 1. This progress simulates three important operations in milling industry: start from zero feed, increasing feed and reducing feed. The reasonable results in Figure 16 show that the Generic Tumbling Mill Model Structure Version II (GTMMS II), which combines the 4D appearance function model, the DEM energy distribution model, and the transport function model, can work stably and reliably.

Figure 15: Product size distribution simulation error assessment

0 5 10 15 20 25 300

50

100

150

200

Flow

rate

(t/h

)

Time (hour)The dynamic response of products and slurry contents to the step change

of feeds by the Generic Tumbling Mill Model Structure Version II

0 5 10 15 20 25 300

15

30

45

60

Vol

ume

(m3 )

Feed t/hProduct t/hSlurry Volume m3

Figure 16: Dynamic simulation for feed step changes by the GTMMS II

CONCLUSION

Based on the previous work of the Generic Tumbling Mill Model Structure Version I (GTMMS I) and the experimental results of JK RBT Tests, a new 4D (four dimensional) appearance function model was successfully developed through a multi-variable function regression and fitting technique. The newly developed 4D appearance function model, with fewer fitting parameters, is more accurate than the existing JKMRC t10-tn appearance function and the size-dependant JK M-p-q t10-tn appearance function and is more generic in nature. Most importantly, it accurately models to both high and low energy impacts. It is therefore much more versatile in comparison to the existing JK appearance function models.

In addition, the Discrete Element Method (DEM) energy distribution model was integrated into the new model structure. With DEM results providing energy distribution information inside the mill directly, the selection function and the back-calculation method used in the existing JKSimMet modelling method are not needed any more. Based on the mechanistic modelling results, it is considered that the DEM energy distribution method is more applicable than the traditional selection function.

Furthermore, the new model structure is dynamic in nature with time-stepping technique for non-steady-state simulation. With the above significant upgrades, the previous model structure evolved to the Generic Tumbling Mill Model Structure Version II (GTMMS II). Dynamic grinding simulations of a SAG mill were used to evaluate the GTMMS II. The model simulations indicate that all the sub-models can be integrated well in the GTMMS II and the model simulation results agreed well with the plant data. Integrated with the newly developed 4D appearance function model, the DEM energy distribution model and the transport function, the Generic Tumbling Mill Model Structure Version II (GTMMS II) is more generic, accurate and versatile than existing models, which can be marked as a vital milestone towards mechanistic modelling of tumbling mills. Future work is undergoing to improve the 4D appearance model and further validate the model structure.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the financial support of the Commonwealth Scholarship from the Australian Government and Scholarships from the University of Queensland. The authors wish to acknowledge the partial financial support on supervision from AMIRA P9P project. The authors wish to acknowledge Dr Marko Hilden at JKMRC in the University of Queensland for his review on this paper and his valuable comments and suggestions.

REFERENCES

Austin, L. G., Menacho, J. M., & Pearcy, F. (1987). A general model for semi-autogenous and autogenous milling. Paper presented at the APCOM 87. Proceedings of the Twentieth International

Symposium on the Application of Computers and Mathematics in the Mineral Industries, Johannesburg, South Africa.

Ballantyne, G. R., Powell, M., & Tiang, M. (2012). Proportion of energy attributable to comminution. Paper presented at the 11th AusIMM Mill Operators’Conference 2012, Hobart, Tasmania.

Cundall, P. A., & Strack, O. D. L. (1979). A discrete numerical method for granular assemblies. Géotechnique, 29(1), 47-65.

Govender, I., Tupper, G. B., & Mainza, A. N. (2011). Towards a mechanistic model for slurry transport in tumbling mills. Minerals Engineering, 24(3–4), 230-235.

Herbst, J. A., & Lichter, J. K. (2006). Use of Multiphysics Models for the Optimization of Comminution Operations. Paper presented at the 3rd International symposium, Society for Mining, Metallurgy and Exploration.

King, R. P. (2001). Modeling and simulation of mineral processing systems. Linacre House, Jordan Hill, Oxford OX2 8DP United Kingdom: Butterworth-Heinemann

Kojovic, T., Hilden, M. M., Powell, M. S., & Bailey, C. (2012, 29-31 October). Updated Julius Kruttschnitt semi-autogenous grinding mill model Paper presented at the 11th AusIMM Mill Operators' Conference 2012 Hobart, Victoria

Mishra, B. K., & Rajamani, R. K. (1992). The discrete element method for the simulation of ball mills. Appl. Math. Modelling, 16(November), 598-604.

Napier-Munn, T. (2013). Comminution Energy and How to reduce it-Presentation publicised by Coalition for Eco Efficient Comminution (CEEC). Retrieved from http://ceec.thick.ly/wp-content/uploads/2013/01/Napier-Munn-CEEC-3-12.pdf

Napier-Munn, T. J., Morrell, S., Morrison, R. D., & Kojovic, T. (1996). Mineral comminution circuits : their operation and optimisation (First edition 1996,Reprinted with minor corrections 1999, 2005, 2005 ed., Vol. 2). Indooroopilly, Brisbane, Australia: Julius Kruttschnitt Mineral Research Centre, University of Queensland.

Powell, M. S. (2006, 03-08 Sep.). The unified comminution model—a conceptually new model. Paper presented at the IMPC 2006 Conference, Istanbul, Turkey.

Shi, F., & Kojovic, T. (2007). Validation of a model for impact breakage incorporating particle size effect. International Journal of Mineral Processing, 82(3), 156-163.

Weerasekara, N., & Powell, M. (2010). Exploring the breakage environment in mills with discrete element methods, In: XXV International Mineral Processing Congress - IMPC 2010 'Smarter processing for the future. Paper presented at the International Mineral Processing Congress, 6-10 September, 2010 Brisbane, QLD, Australia

Weerasekara, N. S., Powell, M. S., Cole, S., & Favier, J. (2010). Modeling breakage environment in tumbling mills using DEM and analyzing the outputs. Paper presented at the Discrete Element Methods - Simulation and discontinua: Theory and applications, DEM5: The Fifth International Conference on Discrete Element Methods University of London

Wills, B. A., & Napier-Munn, T. J. (2006). Wills' Mineral Processing Technology: an introduction to the practical aspects of ore treatment and mineral recovery (Seventh Edition ed.). Great Britain: Elsevier.

Yu, P., Xie, W., Liu, L., & Powell, M. (2014). Development of a Dynamic Mill Model Structure for Tumbling Mills, In: XXVIl International Mineral Processing Congress - IMPC 2014: Conference Proceedings Paper presented at the International Mineral Processing Congress - IMPC Santiago, Chile.