Media Type Effect on Ginding Efficiency

XXV INTERNATIONAL MINERAL PROCESSING CONGRESS (IMPC) 2010 PROCEEDINGS / BRISBANE, QLD, AUSTRALIA / 6 - 10 SEPTEMBER 2010 3207

INTRODUCTION

It has been estimated that the amount of energy used in the comminution process is equivalent to 3 per cent of the world-wide energy as Pease (2007) estimated and is the reason optimisation of energy consumption in the comminution process has been and still is one of the main objectives of various researchers and operators.

At the moment the conventional grinding technologies of SAG and Ball Mills, are power ineffi cient. They use from 3 - 5 per cent, as Fuerstenau (2003) showed, of the total of the energy consumed to grind only. Recently some researchers indicate that the maximum grinding effi ciency is limited to about 20 per cent as Arentzen and Bhappu (2008) indicated.

On the other hand, it can be argued that the grinding effi ciency is much more important than the grinding media cost, since the benefi ts of obtaining a greater capacity of treatment are several times greater than the magnitude of the grinding media cost. It is in this sense the effects of grinding media density and optimal ball size play a major role in the optimisation of the grinding stage.

Other authors benchmark the power effi ciency according to the confi guration of the circuit; nevertheless there is not suffi cient evidence to demonstrate statistically that a given circuit design is consistently superior from the point of view of energy effi ciency as Morrell (2009) demonstrated.

In addition, the belief exists that the classic Inverse confi guration is intrinsically more productive than the alternative Direct confi guration, this under the context of the so-called “Fourth Law” of the Grinding/Classifi cation, which affi rms that “to obtain an effi ciency of optimal energy in the grinding total process, the content of fi ne particles in the mill charge must be as low as it is possible for a given grinding task”. Practically speaking, the Inverse confi guration will only be advantageous when the fl ow of fresh feed contains more than 30 per cent of ore particles fi ner than the specifi ed objective P80 size for the operation as Sepúlveda (2008b) found.

There is a potential to increase the apparent effi ciency of the energy use by signifi cantly increasing the circulating load and increasing the throughput (depending on each particular application). With

1. Senior Applications Engineer, Moly-Cop Adesur S A, 110 Santa Rosa Avenue, Santa Anita, Lima, Peru. Email: [email protected]

2. Senior Applications Engineer, Moly-Cop Adesur S A, 131 Jacinto Ibanez Street, Parque Industrial, Arequipa, Peru. Emails: [email protected]

MEDIA TYPE EFFECT ON GRINDING EFFICIENCY

L Guzmán1 and D García2

ABSTRACT

T he consumption of energy in the grinding process is signifi cant in both the amount used and the cost involved. Both imply that it is important to maximise the throughput for a given grinding task; which in turn implies it is important to maximise mill power draw, which is related to the effi ciency whereupon this power is used.

In order to optimise the process it is fi rst necessary to know the effects of the operative parameters on the ore grindability because it is the grinding effi ciency that is to be evaluated; that is to say, the effi cient use of the energy from the metallurgical point of view in conventional ball grinding, recognising that such concepts and criteria also apply to other types of applications such as semiautogenous grinding (SAG) and vertical mills.

It was demonstrated that it is possible to optimise the grinding process by means of the correct selection of grinding media that allows maximising the effectiveness (power draw) and the power effi ciency of the process (correct use). For example, simulations demonstrate that using forged steel grinding balls (high density) [compared to cast steel (lower density) balls and to high chromium white cast iron (lowest density) balls] increases throughput by 2.2 - 4.4 per cent and reduces the specifi c energy consumption by 2 - 3 per cent (at constant feed size and product size).

Keynotes: grinding media, process simulation, balls density, energy effi ciency

L GUZMÁN AND D GARCÍA


a high circulating load, the balls in the mill act preferably on heavier particles that still need to be fractured, avoiding at the same time the overgrinding of the fi nest particles as Sepúlveda (2008a) showed. There is also a similar maximum potential from improving the classifi cation effi ciency as Morrell (2008) found.

The present work proposes to determine the effects and relationships among energy – grindability – grinding media type in the grinding optimisation stage.

THEORETICAL BACKGROUND

Energy specifi c consumption

From the fi rst studies on comminution of ores in the middle of the last century, it has been recognised that a major role is played by “energy specifi c consumption” in determining the parameters of the process results. In other words, the amount of mechanical energy applied to each unit mass of particles to a great extent determines the fi neness of resulting fragments. That is to say, the energy specifi c consumption is not more than the net consumption of energy (kWh) by each t of processed fresh feed. As an illustration, note the experimental information shown in Figure 1, as Siddique (1977) found, which was obtained using batch tests of dry grinding with mills of 10, 15 and 30 inches of diameter. From these results, Figure 1 demonstrates the clear relationship that exists between the energy specifi c consumption and the resulting product fi neness in each test.

Bond’s law

Bond (1952) postulated an empirical law that has been termed the third law of the comminution, which is denoted by the following expression:

E WiWWP F

−WiWW⎡

⎣⎢⎡⎡

⎣⎣

⎤

⎦⎥⎤⎤

⎦⎦0

1

80

1

80 (1)

where:

Wi = ore work index or Bond work index and depends as much on the material as on the equipment used for each specifi c application. Wi consequently represents the specifi c consumption required to fracture very heavy particles, P80 = 100 microns.

E = Energy specifi c consumption, kWh/t

F80 = Size passing 80 per cent in feeding (microns)

P80 = Size passing 80 per cent in product (microns)

Wi = Bond work index, kWh/t

The Figure 2 shows the importance of the energy specifi c consumption as the determining parameter of the comminution process. In the previous equation, the parameters F80 and P80 represent the defi ned grinding task; that is to say, the objective is to transform particles of characteristic size F80

FIG 1 - Product Energy – Size Relation (Siddique, 1977).

XXV INTERNATIONAL MINERAL PROCESSING CONGRESS (IMPC) 2010 PROCEEDINGS / BRISBANE, QLD, AUSTRALIA / 6 - 10 SEPTEMBER 2010


3209

into particles of size smaller than P80. The Bond Index allow one then, by means of Equation 2 shown below, to determine the energy (kWh) required to grind each unit (t) of ore. This energy specifi c consumption is also determined by the relationship:

EP

M= (2)

where:

E = Energy specifi c consumption, kWh/t

P = Mill net power draw, kW

M = Mill throughput, t/h

Net power draw

It is obvious from equation 2 that any increase in P has to be translated in a benefi cial increase in M, improving therefore the mill operational effectiveness. Recognising this critical role of the mill power, it is of interest to have a suitable correlation with the mill dimensions and basic conditions of operation, such as the proposal by Hogg and Fuerstenau (1972).

P DL

DN SiSC AP

∗⎛⎝⎜⎛⎛⎝⎝

⎞⎠⎟⎞⎞⎠⎠

∗N ( )f ff0 238 3 5 ND⎝⎜⎝⎝ ⎠⎟⎠⎠

238 αSinSSAP ( )f f−ff (3)

where:

D = Effective grinding diameter, feet

L = Effective grinding length, feet

Nc = Rotational mill speed; expressed as a fraction

ρap

= Apparent density of the charge, t/m3

f = Apparent fi lling level (with interstitial voids)

α = charge lifting angle which defi nes the dynamic positioning of the centre of gravity of the mill load (the ‘kidney’) with respect to the vertical direction, typically with values in the range of 35° to 45°.

This correlation, derived from simple theoretical observations, has been demonstrated to be satisfactorily precise for all the practical effects and in particular for the present analysis (Figure 3).

Figure 3 shows the variation of the power based on the fi lling level; it can be appreciated that the maximum levels of power are obtained at ~47 per cent of fi lling. Nevertheless, in practice fi lling levels of 35 to 40 per cent are maintained since greater increases of charge level do not benefi t the treatment capacity.

Apparent density of the charge

Referring again to the equation of Hogg and Fuerstenau (Equation 3), it is important to note that apparent charge density (ρ

ap) is included (among the other variables that affect the power). It is the

0 0

0 50 200 250 300

/( 104

Sp

...0.0.0.000000...000 0000000000000

0000000000000 00050505055555500000550 00000000002020000000222 000022200 00050505052525555000222 0022250 000000000303030333333 000000000033 0

[1[1[[[111 (/(/((((((//// 00000011000111001044444444444

SSp

Sp

SSSSS Spp pp ppp p

10 Wi = 80

Dry Batch GrindingOre : CalciteSize : 100 % - 10 #

FIG 2 - Bond’s Law (Siddique, 1977).



ratio of the gross weight of the charge and the volume that is being occupied by the charge and which is represented by the following expression as Sepúlveda (2008a) showed:

ρρ ρρ ν

ap

ρρm p p

Jρρρρρ ρm

Jρ f Jν

J=

( )νfν ( )νf ( )bJ Jb

−J⎡⎣⎡⎡ ⎤⎦⎤⎤Jρρf− +J ( (4)

where:

ρap

= Apparent density of the charge, t/m3

fv = Volumetric fraction (°/1) of interstitial voids between balls and rocks (typically 40 per cent of

apparent volume occupied by the charge).

ρb = Balls density, t/m3

Jb = Apparent fi lling with balls

J = Total apparent fi lling, °/1

Jp = Interstitial slurry fi ling

ρm

= Ore density, t/m3

ρp = Slurry density, t/m3

In the special case of the Conventional Ball Mills, J = Jb and the Apparent charge density is calculated

as:

ρap

= ρb[(1 – f

ν) + ρ

pJ

pfν] (5)

Specifi c ball charge surface area for optimal grinding

Other studies (Muranda, 1990; Guzmán 2001) have demonstrated that the optimal ball size plays a fundamental role on the specifi c selection function (SiE) also referred to as the “breakage function”. Determining the optimal ball size results in the optimum surface area for optimal grinding (m2/m3) based on the feed size distribution and desired product size. (See Figures 4 and 5)

In Figure 4 it is important to note that depending on feed size (particle size, microns), there exists an optimal string size of grinding media (specifi ccaly for the ball mills) that maximises the ore grindability (specifi c selection function – SiE, ton/kWh) and then obtain the lower product size (P80). Figure 5 shows that for each application (feed size F80, microns) there exists an optimal specifi c grinding media surface area that maximises the throughput.

Grinding media density

Recognising the importance of the apparent charge density, it is important to determine the grinding media density using an effective methodology since, depending on the grinding ball composition and on the process of manufacture of the balls, not all balls attain the maximum theoretical density of steel of ~7.80 g/cm3 that is typical of forged steel balls. Using the Principle of Archimedes and with the aid of the spreadsheet Media Charge_Ball Size & Density of Moly-Cop Tools (Moly-Cop Tools,

FIG 3 - Eff ect of the fi lling level on the power.



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version 2.0) as Sepúlveda (2005) showed – it is possible to calculate the true density of a given sample. (See Table 1).

It is evident from Table 1 that forged grinding media have from 1.5 per cent to 3.8 per cent higher density than other medias. According to Equation 3 this would result to a greater power draw and therefore a greater throughput. In addition, the cast ball densities exhibit a higher standard deviation (0.0210) in comparison to the forged balls (0.0108) - this difference is inherent to the manufacturing process. Figure 6 shows the effect of the media type on the ore grindability (specifi c selection function).

FIG 4 - Ball size eff ect on the ore grindability.

Diameter Forged Steel Cast SteelCast White Iron

10 - 12% Cr Cast White Iron

18 - 20% Cr

CastWhite Iron30 - 33% Cr

1.0” 7.813 7.562 7.536 7.552

1.5” 7.805 7.691 7.560 7.551 7.555

2.0” 7.802 7.680 7.580 7.558 7.531

2.5” 7.812 7.657 7.603 7.565 7.512

3.0” 7.794 7.647 7.593 7.502 7.511

3.5” 7.804 7.512

4.0” 7.749 7.490

TABLE 1

Example of the grinding media density (g/cm3).

FIG 5 - Eff ect of the specifi c ball charge surface area on the grinding task.



STUDY CASE

On the basis of the previously raised considerations, simulations were carried out using an Inverse circuit of primary grinding (Figure 7), concentrating on the effect of the grinding media density on the power draw and its relation with the plant throughput, for which extensive use was made of the Ballsim simulator of software Moly-Cop Tools version 2.0.

Using the densities experimentally determined for different grinding media and using the spreadsheet “Mill power” in Moly-Cop Tools, version 2.0, that includes the model of Hogg and Fuerstenau, the power draw for the case in study was calculated and exhibits variations in power from 11152 kW to 11531 kW, depending on the grinding media type. (See Table 2 and Figure 8).

If we take as the basis the variations of power generated by each of the grinding media types and make additional simulations with respect to product size, we can obtain the results shown in Table 3.

Media T ype E ffect on G rindability

0.01

0.10

1.00

10.00

10 100 1 0 10000 100000P art (mic rons )

Senc

tion

(SiE

)

F orged

10-12% C r

18-20% C r

30-33% C r

FIG 6 - Eff ect of the media type on the grindability.

Moly-Cop Tools TMS imulation N° 0

R emarks

38.00 % S olids52.49 % - S ize 18151.4 P 80 5.00 ps i

B pf 0.270 B pw 0.316 8 # of C yclones

14.00 Vortex 5.43 Apex

ton/hr 1100.0F 80 3677 79.00 % S olids

W ater, 155.9 W ater, m3/hr m3/hr 463.8

G ros s kW 11336.5% B alls 33.00 C irc. Load 283.78

% C ritical 75.00 m3/hr 4187% S olids 76.00 % S olids 61.66

kW h/to// n 10.31W io 15.91

S imulacion de C alibracion0

FIG 7 - Inverse circuit of primary grinding.



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In results shown in Table 3, the product fi neness is found to vary with media density, with the higher density forged steel grinding balls producing a fi ner size product, and the lower density cast products (both steel and white irons) producing coarser products.

When the feed size and the product size (P80) were held constant, the mill throughput varies in its relationship to grinding media. The resultant throughputs are shown in Table 4.

In Table 4 it is evident that the higher density forged grinding media processed 1125 t/h which is equivalent to 2.2 per cent greater throughput than the cast steel grinding media, and 4.4 per cent greater throughput than the cast high Cr white iron grinding media of lower density. In addition, the specifi c energy consumption (kWh/t) for the forged steel was reduced by 0.5 - 0.8 per cent, indicative of a more effi cient process.

Grinding Media Density (g/cm3)Density Diff erence

(%)Gross Power (kW)

Power Diff erence (%)

Forged Steel 7.794 0.00% 11531 0.00%

Cast Steel 7.647 1.92% 11334 -1.71%

Cast White Iron10 - 12% Cr

7.593 2.65% 11268 -2.28%


7.502 3.89% 11152 -3.29%


7.511 3.77% 11164 -3.18%

TABLE 2

Determinations of power draw.

11000

1110011200

11300

1140011500

11600

11700

1180011900

12000

7.4 7.5 7.6 7.7 7.8 7.9

De ns ity (gr /cm// 3)

Po

wer

(K

w)

Forged

Cas t

HCr 12%

HCr 18%

HCr 32%

FIG 8 - Variation of power based on the grinding media density.

Grinding Media

Forged Steel Cast SteelCast White Iron


18 - 20% Cr


t/h 1100 1100 1100 1100 1100

F80 (microns) 3677 3677 3677 3677 3677

P80 (microns) 148.3 151 152.6 154.7 154.4

Energy Consumption (kWh/t) 10.48 10.31 10.24 10.14 10.15

WIO (kWh/t) 15.97 15.91 15.89 15.86 15.87

Reduction Ratio 2.53 2.46 2.43 2.39 2.39

Circulating Load (%) 278 284 286 289 289

TABLE 3

Simulations – product size.



Finally, knowing that the grinding media affect the ore grindability (specifi c selection function used in simulation), we made simulations relating both the effect of power and the ore grindability, obtaining the following (See Table 5).

In Table 5 the effects of the grinding media density on the power draw and the ore grindability are shown. The forged grinding media get up to 1142 t/h, which is equivalent to 3.7 per cent greater throughput in comparison to the cast steel grinding media and up to 7.2 per cent in comparison to the high chromium white cast iron grinding media of lower density. That is to say, using the higher density forged steel balls reduced the energy specifi c consumption between 2 - 3 per cent, which indicates a signifi cant improvement in the grinding process.

CONCLUSIONS

It was demonstrated that it is possible to optimise the grinding process by means of the correct selection of grinding media that allows maximising the effectiveness (power draw) and the power effi ciency of the process (correct use). For example, simulations demonstrate that using forged steel grinding balls (high density) [compared to cast steel (lower density) balls and to high chromium white cast iron (lowest density) balls] increases throughput by 2.2 - 4.4 per cent and reduces the specifi c energy consumption by 2 - 3 per cent (at constant feed size and product size). To accomplish this it is necessary to consider changes in the measurement procedure and evaluation of the grinding process not only considering terms of throughput, energy and steel consumption, but also including the analysis of the ore grindability which is a powerful tool of process optimisation.

Grinding Media



18 - 20% Cr


t/h 1125 1100 1090 1076 1078

F80 (microns) 3677 3677 3677 3677 3677

P80 (microns) 151 151 151 151 151


WIO (kWh/t) 15.83 15.91 15.94 15.98 15.98

Reduction Ratio 2.43 2.46 2.47 2.49 2.49


TABLE 4

Simulations – throughput.

Grinding Media



18 - 20% Cr


t/h 1142 1100 1078 1060 1070

F80 (microns) 3677 3677 3677 3677 3677

P80 (microns) 151 151 151 151 151


WIO (kWh/t) 15.57 15.91 16.12 16.06 16.07

Reduction Ratio 2.4 2.46 2.69 2.87 2.73


TABLE 5

Simulations – grindability and power eff ects.



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REFERENCES

Arentzen, C and Bhappu, R, 2008. High effi ciency ball mill grinding, Engineering and Mining Journal, Apr:62 - 68.

Bond, F, 1952. The third theory of comminution, AIME Trans., 193:484.

Fuerstenau, M, 2003. Principles of ore processing, pp 95 (SME).

Guzmán, L, 2001. Methodology of the torque mill with optimizing aims, thesis, University of San Agustín, Arequipa.

Hogg, R and Fuerstenau, D, 1972. Power relationship for tumbling mill, Trans SME-AIME, vol. 252:418 - 423.

Morrell, S, 2008. A method for predicting the specifi c energy requirement of comminution circuits and assessing their energy utilisation effi ciency, Miner. Eng. (21), 224 - 233.

Morrell, S, 2009. Predicting the overall specifi c energy requirement of crushing, high pressure grinding roll and tumbling mill circuits, Miner. Eng., 1 - 6.

Muranda, R, 1990. Methodology to determine optimal sizes of ball, thesis. University of Atacama, Copiapó.

Pease, J, 2007. Increasing the energy effi ciency of processing, in Proceedings Crushing and Grinding 2007 - Sept 2007, pp 1 - 28 (Brisbane).

Sepúlveda, J, 2005. Moly -Cop Tools version 2.0, Software for the assessment and optimization of grinding circuit performance. Personal communication, 1 July.

Sepúlveda, J, 2008a. The fourth law 25 years later. Mineralurgia 2008, pp 1 - 46, (Tecsup: Lima).

Sepúlveda, J, 2008b. Direct vs. reverse grinding circuit confi gurations: a quantitative assessment of their relative operational performance. Procemin 2008, pp 55 - 60, (Gecamin: Santiago).

Siddique, M, 1977. A kinetic approach to ball mill scale-up for dry and wet systems. MS thesis, Department of Metallurgical Engineering, University of Utah, Salt Lake City.

Media Type Effect on Ginding Efficiency

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