Comminution

Introduction

Because most minerals are finely disseminated and intimately associated with the gangue, they must be initially "unlocked" or "liberated" before separation can be undertaken. This is achieved by comminu- tion in which the particle size of the ore is progres- sively reduced until the clean particles of mineral can be separated by such methods as are available. Comminution in its earliest stages is carried out in order to make the freshly excavated material easier to handle by scrapers, conveyors, and ore carriers, and in the case of quarry products to produce mate- rial of controlled particle size.

Explosives are used in mining to remove ores from their natural beds, and blasting can be regarded as the first stage in comminution. Comminution in the mineral processing plant, or "mill", takes place as a sequence of crushing and grinding processes. Crushing reduces the particle size of run-of-mine ore to such a level that grinding can be carried out until the mineral and gangue are substantially produced as separate particles.

Crushing is accomplished by compression of the ore against rigid surfaces, or by impact against surfaces in a rigidly constrained motion path. This is contrasted with grinding which is accomplished by abrasion and impact of the ore by the free motion of unconnected media such as rods, balls, or pebbles.

Crushing is usually a dry process, and is performed in several stages, reduction ratios being small, ranging from three to six in each stage. The reduction ratio of a crushing stage can be defined as the ratio of maximum particle size entering to maximum particle size leaving the crusher, although other definitions are sometimes used.

Tumbling mills with either steel rods or balls, or sized ore as the grinding media, are used in

the last stages of comminution. Grinding is usually performed "wet" to provide a slurry feed to the concentration process, although dry grinding has limited applications. There is an overlapping size area where it is possible to crush or grind the ore. From a number of case studies, it appears that at the fine end of crushing operations equivalent reduc- tion can be achieved for roughly half the energy and costs required by tumbling mills (Flavel, 1978).

Stirred mills are now commonly used in mineral processing, though they have been present in other industries for many years (Stehr and Schwedes, 1983). They represent the broad category of mills which use a stirrer to provide motion to the steel, ceramic, or rock media. Both vertical and horizontal configurations exist, and since they can operate with smaller media sizes, they are far more suit- able for fine grinding applications than ball mills. Stirred mills are claimed to be more energy effi- cient (by up to 50%) than conventional ball mills (Stief et al., 1987). This is thought to be the result of having a narrower range of applied energy.

A relatively new comminution device, the high pressure grinding rolls (HPGR), utilises compres- sion breakage of a particle bed, in which energy efficient inter-particle breakage occurs (Schrnert, 1988). The reduction ratio obtained in a single pass through the HPGR is substantially higher than that obtained in conventional rolls crushers. Some evidence has also been reported for down- stream benefits such as reduced grinding strength and improved leachability due to microcracking (Knecht, 1994). The HPGR offers a realistic poten- tial to markedly reduce the comminution energy requirements needed by tumbling mills. Reports have suggested the HPGR to be between 20 and 50% more efficient than conventional crushers and mills (Esna-Ashari and Kellerwessel, 1988).

Comminution lO9

Pr inc ip les of c o m m i n u t i o n

Most minerals are crystalline materials in which the atoms are regularly arranged in three-dimensional arrays. The configuration of atoms is determined by the size and types of physical and chemical bonds holding them together. In the crystalline lattice of minerals, these inter-atomic bonds are effective only over small distances, and can be broken if extended by a tensile stress. Such stresses may be generated by tensile or compressive loading (Figure 5.1).

Figure 5.1 Strain of a crystal lattice resulting from tensile or compressive stresses

Even when rocks are uniformly loaded, the internal stresses are not evenly distributed, as the rock consists of a variety of minerals dispersed as grains of various sizes. The distribution of stress depends upon the mechanical properties of the indi- vidual minerals, but more importantly upon the presence of cracks or flaws in the matrix, which act as sites for stress concentration (Figure 5.2).

It has been shown (Inglis, 1913) that the increase in stress at such a site is proportional to the square root of the crack length perpendicular to the stress

Figure 5.2 Stress concentration at a crack tip

direction. Therefore, there is a critical value for the crack length at any particular level of stress at which the increased stress level at the crack tip is sufficient to break the atomic bond at that point. Such rupture of the bond will increase the crack length, thus increasing the stress concentration and causing a rapid propagation of the crack through the matrix, thus causing fracture.

Although the theories of comminution assume that the material is brittle, crystals can, in fact, store energy without breaking, and release this energy when the stress is removed. Such behaviour is known as elastic. When fracture does occur, some of the stored energy is transformed into free surface energy, which is the potential energy of atoms at the newly produced surfaces. Due to this increase in surface energy, newly formed surfaces are often more chemically active, and are more amenable to the action of flotation reagents, etc., as well as oxidising more readily.

Griffith (1921) showed that materials fail by crack propagation when this is energetically feasible, i.e. when the energy released by relaxing the strain energy is greater than the energy of the new surface produced. Brittle materials relieve the strain energy mainly by crack propagation, whereas "tough" materials can relax strain energy without crack propagation by the mechanism of plastic flow, where the atoms or molecules slide over each other and energy is consumed in distorting the shape of the material. Crack propagation can also be inhibited by encounters with other cracks or by meeting crystal boundaries. Fine-grained rocks, such as taconites, are therefore usually tougher than coarse-grained rocks.

The energy required for comminution is reduced in the presence of water, and can be further reduced by chemical additives which adsorb onto the solid (Hartley et al., 1978). This may be due to the lowering of the surface energy on adsorption providing that the surfactant can penetrate into a crack and reduce the bond strength at the crack tip before rupture.

Real particles are irregularly shaped, and loading is not uniform but is achieved through points, or small areas, of contact. Breakage is achieved mainly by crushing, impact, and attrition, and all three modes of fracture (compressive, tensile, and shear) can be discerned depending on the rock mechanics and the type of loading.

110 Wills' Mineral Processing Technology

When an irregular particle is broken by compres- sion, or crushing, the products fall into two distinct size r a n g e s - coarse particles resulting from the induced tensile failure, and fines from compres- sive failure near the points of loading, or by shear at projections (Figure 5.3). The amount of fines produced can be reduced by minimising the area of loading and this is often done in compressive crushing machines by using corrugated crushing surfaces (Partridge, 1978).

/ / / / / / /

/ / / / / /

Figure 5.3 Fracture by crushing

In impact breaking, due to the rapid loading, a particle experiences a higher average stress while undergoing strain than is necessary to achieve simple fracture, and tends to break apart rapidly, mainly by tensile failure. The products are often very similar in size and shape.

Attrition (shear failure) produces much fine material, and may be undesirable depending on the comminution stage and industry sector. Attri- tion occurs mainly in practice due to particle- particle interaction (inter-particle comminution), which may occur if a crusher is fed too fast, contacting particles thus increasing the degree of compressive stress and hence shear failure.

Comminution theory

Comminution theory is concerned with the rela- tionship between energy input and the particle size made from a given feed size. Various theories have been expounded, none of which is entirely satisfac- tory (Wills and Atkinson, 1993).

The greatest problem lies in the fact that most of the energy input to a crushing or grinding machine is absorbed by the machine itself, and only a small fraction of the total energy is available for breaking the material. It is to be expected that there is a

relationship between the energy required to break the material and the new surface produced in the process, but this relationship can only be made manifest if the energy consumed in creating new surface can be separately measured.

In a ball mill, for instance, it has been shown that less than 1% of the total energy input is available for actual size reduction, the bulk of the energy being utilised in the production of heat.

Another factor is that a material which is plastic will consume energy in changing shape, a shape which it will retain without creating significant new surface. All the theories of comminution assume that the material is brittle, so that no energy is adsorbed in processes such as elongation or contraction which is not finally utilised in breakage.

The oldest theory is that of Von Rittinger (1867), which states that the energy consumed in the size reduction is proportional to the area of new surface produced. The surface area of a known weight of particles of uniform diameter is inversely proportional to the diameter, hence Rittinger's law equates to

(1 1) E = K (5.1)

D2 D1

where E is the energy input, D~ is the initial particle size, D 2 is the final particle size, and K is a constant.

The second theory is that of Kick (1885). He stated that the work required is proportional to the reduction in volume of the particles concerned. Where f is the diameter of the feed particles and p the diameter of the product particles, the reduc- tion ratio R is f/p. According to Kick's law, the energy required for comminution is proportional to log R/log 2.

Bond (1952) developed an equation which is based on the theory that the work input is propor- tional to the new crack tip length produced in particle breakage, and equals the work represented by the product minus that represented by the feed. In particles of similar shape, the surface area of unit volume of material is inversely proportional to the diameter. The crack length in unit volume is consid- ered to be proportional to one side of that area and therefore inversely proportional to the square root of the diameter.

For practical calculations the size in microns which 80% passes is selected as the criterion of

Comminution 111

particle size. The diameter in microns which 80% of the product passes is designated as P, the size which 80% of the feed passes is designated as F, and the work input in kilowatt hours per short ton is W. Bond's third theory equation is

10w, 10w, W = (5.2)

47 where Wi is the work index. The work index is the comminution parameter which expresses the resistance of the material to crushing and grinding; numerically it is the kilowatt hours per short ton required to reduce the material from theoretically infinite feed size to 80% passing 100 l~m.

Various attempts have been made to show that the relationships of Rittinger, Kick, and Bond are interpretations of single general equations. Hukki (1975) suggests that the relationship between energy and particle size is a composite form of the three laws. The probability of breakage in comminution is high for large particles, and rapidly diminishes for fine sizes. He shows that Kick's law is reasonably accurate in the crushing range above about 1 cm in diameter; Bond's theory applies reasonably in the range of conventional rod-mill and ball-mill grinding, and Rittinger's law applies fairly well in the fine grinding range of 10-1000 I~m.

On the basis of Hukki's evaluation, Morrell (2004) has proposed a modification to Bond's equa- tion that sees the exponent of P and F in Equa- tion 5.2 varying with size as"

K M i K M i W =

pf(P) Ff(F)

where M i is the mater ia l index related to the breakage property of the ore and K is a constant chosen to balance the units of the equation. The

If the breakage characteristics of a material remain constant over all size ranges, then the calculated work index would be expected to remain constant since it expresses the resistance of material to breakage. However, for most naturally occurring raw materials, differences exist in the breakage characteristics depending on particle size, which can result in variations in the work index. For instance, when a mineral breaks easily at the boundaries but individual grains are tough, then grindability increases with fineness of grind. Consequently work index values are generally obtained for some specified grind size which typi- fies the comminution operation being evaluated (Magdalinovic, 1989).

Grindability is based upon performance in a care- fully defined piece of equipment according to a strict procedure. The Bond standard grindability test has been described in detail by Deister (1987), and Levin (1989) has proposed a method for deter- mining the grindability of fine materials. Table 5.1 lists standard Bond work indices for a selection of materials.

Table 5.1 Selection of Bond work indices

Material Work index Material Work index

Barite 4.73 Fluorspar 8.91 Bauxite 8.78 Granite 15.13 Coal 13.00 Graphite 43.56 Dolomite 1 1 . 2 7 Limestone 12.74 Emery 56.70 Quartzite 9.58 Ferro-silicon 10.01 Quartz 13.57

The standard Bond test is time-consuming, and a number of methods have been used to obtain the indices related to the Bond work index. Smith

application of the new energy-size relation has and Lee (1968) used batch-type grindability tests to been shown to be valid across the size r a n g e arrive at the work index, and compared their results covered by most modern grinding circuits, i.e. with work indices from the standard Bond tests,

0.1-100 mm.

Grindability Ore grindability refers to the ease with which mate- rials can be comminuted, and data from grindability tests are used to evaluate crushing and grinding efficiency.

which require constant screening out of under- size material in order to simulate closed-circuit operation. The batch-type tests compared very favourably with the standard grindability test data, the advantage being that less time is required to determine the work index.

Berry and Bruce (1966) developed a comparative method of determining the grindability of an ore.

Probably the most widely used parameter to The method requires the use of a reference ore of measure ore grindability is the Bond work index W~. known grindability. The reference ore is ground for

112 Wills' Mineral Processing Technology

a certain time and the power consumption recorded. An identical weight of the test ore is then ground for a length of time such that the power consumed is identical with that of the reference ore. If r is the reference ore and t the ore under test, then from Bond's Equation 5.2.

[,0 10] [,0 ,0] Wr-Wt-Wir -Wit

,/Er ,/ rr 4 tt VTtt Therefore [10 10] Wit- Wir (5.3)

4gr JEt JEt Reasonable values for the work indices are obtained by this method as long as the reference and test ores are ground to about the same product size distribution.

The low efficiency of grinding equipment in terms of the energy actually used to break the ore particles is a common feature of all types of mill, but there are substantial differences between various designs. Some machines are constructed in such a way that much energy is adsorbed in the component parts and is not available for breaking. Work indices have been obtained (Lowrison, 1974) from grindability tests on different sizes of several types of equipment, using identical feed materials. The values of work indices obtained are indica- tions of the efficiencies of the machines. Thus, the equipment having the highest indices, and hence the largest energy consumers, are found to be jaw and gyratory crushers and tumbling mills; intermediate consumers are impact crushers and vibration mills, and roll crushers are the smallest consumers. The smallest consumers of energy are those machines which apply a steady, continuous, compressive stress on the material.

Values of operating work indices, Wio, obtained from specific units can be used to assess the effect of operating variables, such as mill speeds, size of grinding media, type of liner, etc. The higher the value of W i, the lower is the grinding efficiency. The Wio can be obtained using Equa- tion 5.2, by defining W as the specific energy being used (power draw/new feed rate), F and P as the actual feed and product 80% passing sizes, and W i as the operating work index, Wio. Once corrected for the particular application and equipment-related factors, Wio can be compared on the same basis as grindability test results. This

allows a direct comparison of grinding efficiency. Ideally Wi should be equal to Wio and grinding efficiency should be unity. It should be noted that the value of W is the power applied to the pinion shaft of the mill. Motor input power thus has to be converted to power at the mill pinion shaft unless the motor is coupled direct to the pinion shaft.

While Bond is the best-known grindability test for rod and ball mills, in recent years the SPI (SAG Power Index) test has become popular for SAG mills. The SPI test is a batch test, conducted in a 30.5 cm diameter by 10.2 cm long grinding mill charged with 5 kg of steel balls. Two kilograms of sample are crushed to 100% minus 1.9 cm and 80% minus 1.3 cm and placed in the mill. The test is run with several screening iterations until the sample is reduced to 80% minus 1.7 mm. The time required to reach a P80 of 1.7 mm is then converted to an SAG power index Wsag via the use of a proprietary transformation (Starkey and Dobby, 1996):

n

The parameters K and n are empirical factors whilst Lag incorporates a series of calculations (unpub- lished), which estimate the influence of factors such as pebble crusher recycle load, ball load, and feed size distribution. The test is essentially an indicator of an ore's breakage response to SAG abrasion events. As with other batch tests, the test is limited by the fact that a steady-state mill load is never reached.

Simulation of comminution processes and circuits

Simulation of comminution, particularly of grinding and classification, has received great atten- tion in recent years, due to the fact that this is by far the most important unit operation both in terms of energy consumption and overall plant perfor- mance. Other aspects of mineral processing have not received the same intensive research accorded to grinding.

The Bond work index has little use in simula- tion, as it does not predict the complete product size distribution, only the 80% passing size, nor does it predict the effect of operating variables

Comminution 113

on mill circulating load, nor classification perfor- mance. The complete size distribution is required in order to simulate the behaviour of the product in ancillary equipment such as screens and classi- fiers, and for this reason population balance models are finding increased usage in the design, optimisa- tion and control of grinding circuits (Napier-Munn et al., 1996). One of the most successful applica- tions of these models has been through the mineral processing simulator, JKSimMet. A range of case studies can be found in the literature, coveting both design and optimization of grinding circuits. Recent examples include Richardson (1990), Lynch and Morrell (1992), McGhee et al. (2001), and Dunne et al. (2001). In the model formulation the particulate assembly that undergoes breakage in a mill is divided into several narrow size intervals (e.g. x/2 sieve intervals). The size reduction process is defined by the matrix equation:

p = K . f

where p represents the product and f the feed elements. The element Pij in the product array is given by:

Pij = Ki j " f j

where Kij represents the mass fraction of the parti- cles in the jth size range which fall in the ith size range in the product. The product array for n size ranges can thus be written as:

Product array The product array is only useful if K is known. The behaviour of particles in each size interval is characterised by a size-discretised selection, or breakage rate function, S, which is the proba- bility of particles in that size range being selected for breakage, the remainder passing through the process unbroken, and a set of size-discretised breakage functions, B, which give the distribution of breakage fragments produced by the occurrence of a primary breakage event in that size interval. S. f represents the portion of particles which are broken, ( 1 - S). f thus representing the unbroken fraction. K in Equation 5.4 is thus replaced by B, and the equation for a primary breakage process becomes:

p=B.S , f + ( 1 - S ) . f

The model can be combined with informa- tion on the distribution of residence times in

the mill to provide a description of open-circuit grinding, which can be coupled with information concerning the classifier to produce closed-circuit grinding conditions (Napier-Munn et al., 1996). These models can only realise their full potential, however, if accurate methods of estimating model parameters are available for a particular system. The complexity of the breakage environment in a tumbling mill precludes the calculation of these values from first principles, so that successful appli- cation depends on the development of efficient techniques for the estimation of model parame- ters from experimental data. The methods used for the determination of model parameters have been compared by Lynch et al. (1986). This comparison shows that, while all the modem ball mill models use a similar method for describing the breakage rate and the breakage distribution functions, each model has its own way of representing the material transport mechanisms.

Parameter estimation techniques can be classi- fied into three broad categories:

(a)

(b)

(c)

Graphical methods which are based mainly on the grinding of narrow size distributions. Tracer methods, involving the introduction of a tracer into one of the size intervals of the feed, followed by analysis of the product for the tracer. Non-linear regression methods, which allow all parameters to be computed from a min- imum of experimental data.

Rajamani and Herbst (1984) report the develop- ment of an algorithm for simultaneous estimation of selection and breakage functions from exper- imental data with the use of non-linear regres- sion, and present the results of estimation for batch and continuous operations. The estimated param- eter values show good agreement with parameters determined by direct experimental methods, and a computer program based on the algorithm has been developed. The program is said to be capable of simulating tumbling mill grinding behaviour for a specified set of model parameters, and of estimating the model parameters from experimental data. Wiseman and Richardson (1991) give a detailed review of the JKSimMet software package for simulating mineral processing operations, particu- larly comminution and classification. It is based on

114 Wills' Mineral Processing Technology

more than 25 years of modelling and simulation research and development at the Julius Kruttschnitt Mineral Research Centre (JKMRC). One of the main applications for the software package is the analysis and optimization of the performance of existing operations using experimental circuit data. Kojovic and Whiten (1994) outline a procedure for evaluating the quality of models typical of those used in mineral processing simulation.

Single particle breakage tests have been used by a number of researchers to investigate some salient features of the complex comminution process. A comparison of the results from single particle breakage tests with grindability and ball mill tests is given by Narayanan (1986). Application of the results from single particle breakage tests to modelling industrial comminution processes is described, and the necessity for further research into single particle breakage tests to develop a simple but comprehensive technique for estimating the breakage characteristics of ores is discussed. Napier-Munn et al. (1996) give a detailed descrip- tion of the single particle breakage tests developed at the JKMRC, and their application to the determi- nation of ore-specific parameters used in comminu- tion models.

Although selection and breakage functions for homogeneous materials can be determined on a small scale and used to predict large-scale performance, it is more difficult to predict the behaviour of mixtures of two or more components. Furthermore, the rela- tionship of material size reduction to subsequent processing is even more difficult to predict, due

to the complexities of mineral release. However, recent work has focused on the development of grinding models which include mineral liberation in the size-reduction description (Choi et al., 1988; Herbst et al., 1988). In terms of liberation models for comminution, King (1994) and Gay (2004) have made the most significant progress. Gay's entropy-based multiphase approach models particles individually rather than using the standard approach of using composite classes. The development of such liberation models is essential if true simulation of integrated plants is ever to be developed.

The Discrete Element Method (DEM) approach is recognized as an effective tool for modelling (in both two and three dimensions) the flow of granular materials in a variety of mining industry applica- tions, including the motion of grinding media in a mill. The technique combines detailed physical models to describe the motion of balls, rocks, and slurry and attendant breakage of particles as they are influenced by moving liner/lifters and grates.

The DEM has been used to model many indus- trial applications over the past decade. Of specific interest to comminution is the modelling of ball mills by Mishra and Rajamani (1992, 1994), Inoue and Okaya (1995), Cleary (1998), Datta et al. (1999) and SAG mills by Rajamani and Mishra (1996), Bwalya et al. (2001), Cleary (2001), Nordel et al. (2001), and Djordjevic (2004, 2005). One of the features of three-dimensional DEM simulation is the cutaway images of particle motion in the mill, an example of which is presented in Figure 5.4 for a 1.8 m diameter pilot SAG mill.

Figure 5.4 Example of ball and particle motion in a slice of a pilot SAG mill using three-dimensional DEM simulation (Courtesy CSIRO (Dr. Paul Cleary))

Comminution 115

Figure 5.5 Comparison of three-dimensional DEM with experiment for 75% critical speed, scale model 0.6 m diameter SAG mill (Courtesy CSIRO (Dr. Paul Cleary))

Modelling of SAG mills by DEM is leading to improved understanding of charge dynamics, and offers the potential to improve mill design and control, and reduce wear. This could lead to reduced downtime, increased mill efficiency, increased throughput, lower costs, and lower energy consumption. DEM has not yet advanced to the stage of surpassing the predictive capability of the current milling models, but the improved under- standing may in the short term lead to improved mechanistic models and design equations. Coupling of slurry to particles and adding direct prediction of particle breakage to the full scale DEM model are two of the major unresolved issues.

Validation of the predictions made by DEM is a critical part of understanding the effect of various modelling assumptions and for separating more accurate DEM variants from less accurate ones. Examples of such validations can be found in Cleary and Hoyer (2000) and Cleary et al. (2001). Govender et al. (2001) uses an automated three- dimensional tracking technique utilising biplanar X-ray filming for providing rigorous validation data on the motion of particles in an experimental small scale mill. Figure 5.5 shows a good agreement between DEM simulation and experiment in terms of the charge motion for a scale model SAG mill.

Though advances in computing power have enabled DEM simulations to tackle increasingly more complex processes, three-dimensional DEM simulation of large mills with many thousands of particles can be a time-consuming task. The speed of computation is determined principally by two parameters: number of particles involved and

material properties. Large-scale simulations, with over 100,000 particles can take weeks for a single simulation. The computational time step is deter- mined by the size of the smallest particle present in the model and material properties (elastic). These computational demands and lack of detailed exper- imental verification have limited the value of DEM techniques in the mining industry. Hence there is much effort around the world seeking to fill the vital gap linking computational results to rigorous experimental data. It is only with validated DEM that any confidence can be given to the predictive capability of such computational tools, especially when the predictive range lies beyond that for which the existing semi-empirical models were developed.

R e f e r e n c e s

Berry, T.F. and Bruce, R.M. (1966). A simple method of determining the grindability of ores, Can. Min. J. (Jul.), 63.

Bond, F.C. (1952). The third theory of comminution, Trans. AIMF, 193, 484.

Bwalya, B.W., Moys, M.H., and Hinde, A.L. (2001). The use of discrete element method and fracture mechanics to improve grinding rate predictions, Minerals Engng., 14(6), 565-573.

Choi, W.Z., Adel, G.T., and Yoon, R.H. (1988). Esti- mation of model parameters for liberation and size reduction, Min. Metall. Proc., 5 (Feb.), 33.

Cleary, P.W. (1998). Predicting charge motion power draw, segregation and wear in ball mill using discrete element methods, Minerals Engng., 11(11), 1061-1080.

116 Wills' Mineral Processing Technology

Cleary, P.W. (2001). Modelling comminution devices using DEM, Int. J. Numer. Anal. Meth. Geomechan., 25, 83-105.

Cleary, P.W. and Hoyer, D. (2000), Centrifugal mill charge motion and power draw: Comparison of DEM predictions with experiment, Int. J. Min. Proc., 59(2), 131-148.

Cleary, P.W., Morrison, R.D., and Morrell, S. (2001). DEM validation for a full scale model SAG mill, SAG2001 Conference, Vancouver, Canada, IV, 191-206.

Datta, A., Mishra, B.K., and Rajamani, R.K. (1999). Analysis of power draw in ball mills by discrete element method, Can. Metall. Q., 38, 133-140.

Deister, R.J. (1987). How to determine the Bond work index using lab. ball mill grindability tests, Engng. Min. J., 188(Feb.), 42.

Djordjevic, N. (2005). Influence of charge size distri- bution on net-power draw of tumbling mill based on DEM modeling, Minerals Engng., 18(3), 375-378.

Djordjevic, N., Shi, F.N., and Morrison, R.D. (2004). Determination of lifter design, speed and filling effects in AG mills by 3D DEM, Minerals Engng., 17(11-12), 1135-1142.

Dunne, R., Morrell, S., Lane, G., Valery, W., and Hart, S. (2001). Design of the 40 foot diameter SAG mill installed at the Cadia gold copper mine, SAG2001 Conference, Vancouver, Canada, I, 43-58.

Esna-Ashari, M. and Kellerwessel, H. (1988). Inter- particle crushing of gold ore improves leaching, Randol Gold Forum 1988, Scottsdale, USA, 141-146.

Flavel, M.D. (1978). Control of crushing circuits will reduce capital and operating costs, Min. Mag., Mar., 207.

Gay, S. (2004). Application of multiphase liberation model for comminution, Comminution '04 Confer- ence, Perth (Mar.).

Govender, I., Balden, V., Powell, M.S., and Nurick, G.N. (2001). Validating DEM - Potential major improvements to SAG modeling, SAG2001 Confer- ence, Vancouver, Canada, IV, 101-114.

Griffith, A.A. (1921). Phil. Trans. R. Soc., 221, 163. Hartley, J.N., Prisbrey, K.A., and Wick, O.J. (1978).

Chemical additives for ore grinding: How effective are they?, Engng. Min. J. (Oct.), 105.

Herbst, 1.A., et al. (1988). Development of a multicomponent-multisize liberation model, Minerals Engng., 1(2), 97.

Hukki, R.T. (1975). The principles of comminution: An analytical summary, Engng. Min. J., 176(May), 106.

Inglis, C.E. (1913). Stresses in a plate due to the presence of cracks and sharp comers. Proc. Inst. Nav. Arch.

Inoue, T. and Okaya, K. (1995). Analysis of grinding actions of ball mills by discrete element method, Proc. XIX Int. Min. Proc. Cong., 1, SME, 191-196.

Kick, F. (1885). Des Gesetz der Proportionalem wider- stand und Seine Anwendung, Felix, Leipzig.

King, R.P. (1994). Linear stochastic models for mineral liberation, Powder Tech., 81, 217-234.

Knecht, J. (1994). High-pressure grinding rolls - a tool to optimize treatment of refractory and oxide gold ores. Fifth Mill Operators Conf., AusIMM, Roxby Downs, Melbourne (Oct.), 51-59.

Kojovic, T. and Whiten, W.J. (1994). Evaluating the quality of simulation models, lIMP Conf., Sudbury, 437-446.

Levin, J. (1989). Observations on the Bond standard grindability test, and a proposal for a standard grind- ability test for fine materials, J.S. Afr. lnst. Min. Metall, 89 (Jan.), 13.

Lowrison, G.C. (1974). Crushing and Grinding, Butter- worths, London.

Lynch, A.J. and Narayanan, S.S. (1986). Simulation- the design tool for the future, in Mineral Processing at a Crossroads - Problems and Prospects, ed. B.A. Wills and R.W. Barley. Martinus Nijhoff Publishers, Dordrecht, 89.

Lynch, A.J. and Morrell, S. (1992). The understanding of comminution and classification and its practical appli- cation in plant design and optimisation, Comminu- tion: Theory and Practice, ed. Kawatra, AIME, 405-426.

Lynch, A.J., et al. (1986). Ball mill models: Their evolution and present status, in Advances in Minerals Processing., ed. P. Somasundaran, Chapter 3, 48, SME Inc., Littleton.

Magdalinovic, N.M. (1989). Calculation of energy required for grinding in a ball mill, Int. J. Min. Proc. 25 (Jan.), 41.

McGhee, S., Mosher, J., Richardson, M., David, D., and Morrison, R. (2001). SAG feed pre-crushing at ASARCO's ray concentrator: development, implementation and evaluation. SAG2001 Conf., Vancouver, Canada, 1, 234-247.

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

Mishra, B.K. and Rajamani, R.K. (1994). Simulation of charge motion in ball mills. Part 1: Experimental verifications, Int. J. Min. Proc., 40, 171-186.

Morrell, S. (2004). An alternative energy-size relation- ship to that proposed by Bond for the design and optimisation of grinding circuits. Int. J. Min. Proc. (in press).

Napier-Munn, T.J., Morrell, S., Morrison, R.D., and Kojovic, T. (1996). JKMRC, University of Queens- land, Brisbane, 413pp.

Narayanan, S.S. (1986). Single particle breakage tests: A review of principles and applications to comminution modelling, Bull. Proc. Australas. Inst Min. Metall., 291(June), 49.

Nordell, L., Potapov, A.V. and Herbst, J.A. (2001). Comminution simulation using discrete element method (DEM) approach- from single particle

Comminution 117

breakage to full-scale SAG mill operation, SAG2001 Conf., Vancouver, Canada, 4, 235-236.

Partridge, A.C. (1978). Principles of comminution, Mine and Quarry, 7(Jul./Aug.), 70.

Rajamani, K. and Herbst, J.A. (1984). Simultaneous estimation of selection and breakage functions from batch and continuous grinding data, Trans. lnst. Min. Metall., 93 (June), C74.

Rajamani, R.K. and Mishra, B.K. (1996). Dynamics of ball and rock charge in SAG Mills, SAG1996 Conf., Vancouver, Canada, 700-712.

Richardson, J.M. (1990). Computer simulation and optimi- sation of mineral processing plants, three case studies, Control 90, ed. Raj amani and Herbst, AIME, 233-244.

Sch6nert, K. (1988). A first survey of grinding with high-compression roller mills, Int. J. Min. Proc., 22, 401-412.

Smith, R.W. and Lee, K.H. (1968). A comparison of data from Bond type simulated closed-circuit and batch type grindability tests, Trans. SME/AIME, 241, 91.

Starkey, J. and Dobby, G. (1996). Application of the minnovex SAG power index at five canadian SAG plants, SAG1989 Conf., Vancouver, Canada, 345-360.

Stehr N. and Schwedes J. (1983). Investigation of the grinding behaviour of a stirred ball mill, Ger. Chem. Engng., 6, 337-343.

Stief, D.E., Lawruk, W.A., and Wilson, L.J. (1987). Tower mill and its application to fine grinding. Min. Metall. Proc., 4(1), Feb., 45-50.

Von Rittinger, P.R. (1867). Lehrbuch der Aufbereitungs Kunde, Ernst and Korn, Berlin.

Wills, B.A. and Atkinson, K. (1993). Some observations on the fracture and liberation of mineral assemblies, Minerals Engng., 6(7), 697.

Wiseman, D.M. and Richardson, J.M. (1991). JKSimMet - The mineral processing simulator, Proceedings 2nd Can. Conf. on Comp. Applications in the Min. Ind., ed. Paulin, Pakalnis and, Mular, 2, Univ. B.C. and CIM. 427-438.