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DTD 5Powder Technology 15Modeling and simulation of a fully air swept ball mill in a

raw material grinding circuit

Hakan Benzer*

Dr. Hacettepe University Mining Eng. Dept. Beytepe, Ankara, Turkey

Received 27 May 2003; received in revised form 27 July 2004; accepted 1 November 2004Abstract

A raw material grinding circuit was modeled using plant data. Samples were collected from around the circuit and, following a crash stop,

from inside the mill. The size distributions of the samples were determined down to a few microns. Using the data from inside the mill a

modeling approach, based on perfect mixing, was developed. The modelling approach implicitly assumes that the mixture of feed materials

broken is homogenous from the breakage point of view. The air classification around the circuit was modeled using the efficiency curve

approach. In order to measure the success of the method the circuit performance was predicted by simulation studies while it was operating at

different conditions. The results were then compared with the measured data. It is concluded that modeling gives a useful quantitative

indication of what may occur in fully air swept mills.

D 2004 Elsevier B.V. All rights reserved.

Keywords: Cement; Modeling; Breakage; Ball mill; Air separator1. Introduction

Grinding is a high-cost operation consuming approx-

imately 60% of the total electrical energy expenditure in a

typical cement plant and 40% of this energy is for raw

material grinding [1].

In recent years, considerable steps have been taken to

improve comminution efficiency both in the development of

machines with the ability to enhance energy utilisation and

in the optimal design of grinding systems to enable more

efficient use of existing machines. But it is still necessary to

have a better knowledge of the effects of mill operating

variables if optimum performance is to be achieved. Many

variables can affect the efficiency and productivity of a dry

grinding line, such as the operating conditions of the

separators, air flow through the mill, aperture size of mill

partitions, feed rate, hardness of the feed material and ball

sizes in the mill compartments. Optimising these variables0032-5910/$ - see front matter D 2004 Elsevier B.V. All rights reserved.

doi:10.1016/j.powtec.2004.11.009

* Tel.: +90 312 297 7626; fax: +90 312 299 2155.

E-mail address: benzer@hacettepe.edu.tr.in the grinding lines is an important step in minimising the

cost of production.

The best way to optimize the grinding circuit to achieve

economic plant operation is by simulation, using proven

mathematical modeling techniques. Simulation is a valuable

tool in process technology if the process models are accurate

and if model parameters can be determined in a laboratory

or plant. It is now used extensively for the design and

optimisation of wet grinding circuits and has brought large

economic benefits [2]. It is likely that economic benefits are

also attainable in dry grinding.

The population balance model is the model used to

simulate the cement manufacturing process within normal

operating conditions, with the perfect mixing model as an

approach to set the balance in the mill. Mathematical

models of the dry ball milling operation have been

developed by many researchers [312]. Austin et al.

pioneered development of the mathematical model for a

full scale cement mill. His approach is based on the

concept of specific breakage rate and mill residence time.

The model considers the mill as equivalent to several

grinding stages with internal classification in series [3,6].0 (2004) 145154PTEC-06142; No of Pages 10

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Fig. 1. Simplified flowsheet and sampling points in the raw material grinding line.

H. Benzer / Powder Technology 150 (2004) 145154146This technique has been used and validated by some

researchers [7]. Viswanathan et al. developed a computer

based mathematical model called the bDistributed FractureModelQ. This model is a matrix model wherein thegrinding process is described as a sequence of events with

each event being represented by a distribution function and

the number of events occurring per unit time being

described by a selection function [8,9]. Zhang et al.

considered the cement mill model as a perfectly mixed ball

mill. The two compartment mill was described by a mass

balance model that incorporated a breakage function

determined from single particle tests on clinker [10].

These studies were successful in explaining existing

conditions but they did not have the capability of

explaining the effect of variables such as the internalFig. 2. The size distributions of the samples takpartition between two compartments because they did not

include comprehensive data on sizing distributions inside

the mill. Lynch et al. and Benzer et al. developed a

modeling approach for the two compartment cement mills

using extensive data around and inside the mill [1113].

This paper is concerned with the model of a fully air

swept ball mill operating in a raw material grinding circuit.

For simplicity, the approach assumes that different

components in the feed can be treated as if they all had

the same breakage and classification properties. The

Whiten perfect mixing model approach [14] was used for

the ball mill modeling. This method considers a ball mill,

or a section of it, as a perfectly stirred tank. The process

can be described in terms of transport through the mill and

breakage within the mill. The model is expressed as a sizeen from the raw material grinding circuit.

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Fig. 3. The size distributions of the samples from inside the mill.

H. Benzer / Powder Technology 150 (2004) 145154 147mass balance of the mill content and the breakage rate of

particles.

fi riPi

di

Xij1

aijriPi

di Pi 0 1

fi: feed rate of size fraction i (tonnes/h); pi: product flow

of size fraction i (tonnes/h); aij: the mass fraction of

particles of size j that appears at size i after primary

breakage; ri: the rate of material breakage for particle size

i; si: amount of size i particles inside the mill (tonnes); di:

the rate of discharge for particle size i.

If the breakage distribution function is known, calibrat-

ing the model to a ball mill involves the calculation of r/dFig. 4. The variation of the ball size distribution and mvalues using the feed and product size distributions obtained

under known operating conditions. This approach uses a

simple correction for variations in residence time, di is

scaled in terms of mill volume and volumetric feed rate, Q,

to the term di*.

di4 D2L

4Q

di 2

where D and L are the diameter and length of the mill. It

is assumed that % of the actual mill volume is used

effectively.

The changes in the other material and machine

properties are simulated by adjusting the combined r/d*ean ball size along the length of the raw mill.

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Fig. 5. The raw and adjusted size distributions of the streams in the grinding circuit.

H. Benzer / Powder Technology 150 (2004) 145154148function for the new set of operating conditions. The

following equation is used to simulate the effects of mill

diameter, mill load fraction, critical speed and work index

[15].

r=d SIMr=d FIT

DSIM

DFIT

0:5b

1 JSIM1 JFIT

b

JSIM

JFIT

CsSIM

CsFIT

b

WISIM

WIFIT

0:83

D: mill diameter; J: ball load fraction (0.30.45); Cs: mill

speed percentage of critical speed; WI: Bond Work Index

(kW h/tonne); FIT: identifies the calibrated conditions;

SIM: identifies the simulated conditions.

In this study the air classifiers are modelled using the

Tromp curve approach. The mathematical model selected is

capable of defining fish hook type efficiency curves. The

general form of the equation is presented below. b* isFig. 6. Schematic presentation of the modelintroduced to preserve the definition of d50c and it can be

calculated iteratively [16].

Eoai C1 bb4X exp a 1 exp ab4X exp a 2

4

where

X xid50c

In cases where the classification curve does not exhibit

fish hook behaviour, the parameter b is equal to zero and asimplified form of Eq. (4) is obtained.

Eoai Cexp a 1

exp aX exp a 2

5

Eoai: the mass fraction of material in the size range indexed

by i that is sent to the coarse classifier product; C: theof the raw material grinding ball mill.

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Fig. 7. The variation of rate/discharge function with particle size for different segments of the mill.

H. Benzer / Powder Technology 150 (2004) 145154 149proportion of feed particles which are subjected to the

classifying action within a classifier (=1bypass); a: amodel parameter defining the sharpness of classification; b:a model parameter defining the fish hook; b*: a modelparameter introduced to the model to preserve the definition

of d50c (i.e. d=d50c when E=(1/2)C); xi: particle size; d50c:

the corrected cut size which is defined as the size which

divides equally between underflow and overflow due to

classification only.

The calibration of the air classifier model involves the

back calculation of the best fit values for a, b, d50c and Cusing the plant data around the classifier.Fig. 8. The ball size distributions of the segments in the model structure.2. Sampling studies

The mill used in the study had inner dimensions of 4.4 m

diameter and 11.4 m length and was divided into two

compartments. The first 3 m of the mill was used as drying

chamber, the remaining 8.4 m was the grinding chamber.

The mill operated at 70% of the critical speed. The ball load

in the mill was 32% by volume, and 10030 mm balls were

used. The first 3 m of the grinding chamber was designed

with lifting liners and the rest with classifying liners. The

make-up feed consisted of 32% limestone, 67% clay and 1%

pyrite ash, with a mean specific gravity of 2.46 tonnes/m3.

The moisture content of make-up feed and the dry mass

flow rate of the combined mill feed were 9.65% and 138.1

tonnes/h, respectively.

Before sampling, steady state conditions were verified by

the plant staff. Samples were taken from the external

product streams while the mill was operating, then after a

crash stop both ball and material samples were taken insidethe mill along its length. The sampling points around the

circuit and inside the mill are shown in Fig. 1.

Sampling of the feed material was achieved by stripping

2 m long sections from the feed conveyor belt. Because of

physical limitations the air swept mill discharge could not be

sampled. The inside mill samples were taken in the grinding

chamber from nine points equally spaced along the mill

axis. At each point, the material on the surface was removed

and the ball and material samples were collected at a 25 cm

depth. Three to five kilograms of sample and at least 50

balls were collected from each sampling point.

Size distributions of the samples were determined by dry

sieving from 25 mm to 800 Am and a laser diffractometersizing technique was applied from 800 Am to about 2 Am.Only the mill feed samples were analysed by dry sieving

between 25 mm and 38 Am. The laser sizing results werecombined with the sieve analysis by distributing the analysis

to the bottom sieve undersize (800 Am), assuming that

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Fig. 9. The efficiency curve of the O-Sepa separator.

H. Benzer / Powder Technology 150 (2004) 145154150particle size as measured by the laser is the same as that

measured by sieving.

The size distributions of the samples from around the

circuit, and of those from inside the mill are given in

Figs. 2 and 3.

Fig. 3 shows that material became finer and finer along

the mill length from the feed end to the discharge end, but

possibly because of insufficient air sweeping and/or grate

classification the material accumulated at the discharge end

of the mill (8.4 m) was coarser than that at the 6 and 7 m

sampling points.Fig. 10. The efficiency curve of the air sweeThe variation of the ball size distribution and the mean

ball size along the mill length is presented in Fig. 4. The

classifying action of the liners gives a coarser ball mix at the

feed end and a much finer ball mix at the discharge end.

This is an advantage since larger balls are effective in

breaking coarser feed, and smaller balls are more effective

on fine material.

Size distributions of the samples around the circuit and

inside the mill samples were used in the mass balancing and

modeling studies. The standard Bond Work Index Test me-

thod was performed to characterize the material grindabilityping action, showing expanded scale.

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Table 2

The operating conditions of the O-Sepa classifier

H. Benzer / Powder Technology 150 (2004) 145154 151and it was found to be 6.12 kW h/tonne. The feed material for

the test were prepared by using the weight ratios in the plant.

Product tonnage from the separator (tonnes/h) 138.1

Separator rotor speed (rpm) 88.1

Separator power (kW) 6

Fan opening (%) 613. Mass balancing

For initial mass balancing, the mass flow rates of

separator rejects (belt scale weighing) and separator fines

were used. However, a close inspection of the data

showed that the belt scale reading of the separator coarse

stream was grossly erroneous. Therefore the mill dis-

charge was estimated using the data obtained from the

crash stop sampling survey. The size distribution of the

sample taken from in the mill at the discharge end were

used to estimate the size distribution of mill discharge.

Then a mass balance was obtained around the separator

by giving higher standard deviations to the mill discharge

stream. The calculated flow rates for the mill discharge

and separator reject streams were 293 and 141 tonnes/h,

respectively. The raw and adjusted size distributions are

shown in Fig. 5 indicating that the data required only

small adjustments.

However, it should be noted that, for proper mass

balancing either the belt scale measuring separator rejects

should be calibrated or, better, a sampling system should be

installed in the mill discharge line.Table 3

Operating conditions for the four surveys4. Modeling studies

4.1. Ball mill model

It was assumed that the raw material grinding mill

could be modelled by considering that the mill consisted

of three perfectly mixed ball mills in series, the last one

being in closed circuit with a classifier which represents

the air sweeping in the mill. As the size distributions of

the classifier fines and rejects indicate, only a small

proportion of particles larger than a certain size can be air

swept. This implies that the air sweeping acts as a

classifier.

The first perfectly mixed ball mill section in the series

corresponds to the initial section of the mill where lifting

liners are used (the first 3 m). The second covers most of the

length of the section with classifying liners extending up to

the region where the effect of classifying action of the air isTable 1

Efficiency curve model parameters of the air classification in the circuit

O-Sepa Air sweeping

C 91 96

a 1 2b 0 0b* 1 1d50c (mm) 0.09 6reflected in the size distribution of the sample taken from

that particular point (4.4 m). The third one is assumed to

operate in a closed circuit with the air sweeping acting as a

classifier (1 m). Schematic presentation of the raw mill

model is given in Fig. 6.

A standard BroadbentCallcott breakage distribution

function was used in the mill model [17]. Then the rate/

discharge (r/d) function for each size fraction was back

calculated. As shown in Fig. 7, the segment of the mill

having a distribution of balls had higher r/d values. The ball

size distributions of the segments in the mill are given in

Fig. 8.

It should be noted that by using the standard breakage

function it was assumed that the breakage pattern of the

feed material was constant. In order to set up the relations

between the operating parameters and the model parame-

ters in every case the breakage function must be

determined.

4.2. Air classification model

A separator model defines the efficiency (Tromp) curve

under particular operating conditions and its performance

can be assessed by examining the curve. The efficiency

curve of the O-Sepa separator in the raw material grinding

line is shown in Fig. 9. It provided very sharp separation.

The fish hook effect was not observed and the bypass

fraction was only 10%.

It was assumed that air sweeping within the closed circuit

has a classifying effect on the ground product. Based on the

estimated air swept fraction, an efficiency curve was drawn

to model this action (Fig. 10).

As expected, the classifying effect of air sweeping is

poor in terms of very fine material, but it is effective for the

coarse particles.Survey 1 Survey 2 Survey 3 Survey 4

Dry feed tonnage

(tonnes/h)

138.1 160 105 121

Moisture content (%) 9.65 9.5 10.7 8.83

Separator rotor

speed (rpm)

88.1 88.8 88.7 85.5

Mill power (kW) 2030 2062 2068 2012.8

Separator power (kW) 6 6 8 6

Fan opening (%) 61 62 61 62

Bond Work Index

(kW h/tonne)

6.12 6.12 8.67 8.67

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Fig. 11. Feed size distributions of the four sampling surveys.

H. Benzer / Powder Technology 150 (2004) 145154152Model fitting of the air classification in the circuit was

achieved by determining the model parameters of the

efficiency curve equation (Eq. (4)) for air sweeping and the

O-Sepa classifier. These parameters and the operating

conditions of the O-Sepa classifier are given in Tables 1

and 2, respectively.Fig. 12. Algorithm to seek the optimum cir5. Simulation studies

Simulation studies were carried out to verify the model

structure by predicting the mill product for different

operating conditions. For this reason sampling surveys were

carried out around the mill while it was operating at differentcuit conditions using the simulation.

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Fig. 13. Model predicted and observed product size distribution of the circuit at simulated condition 1 (Survey 2), simulated condition 2 (Survey 3) and

simulated condition 3 (Survey 4).

H. Benzer / Powder Technology 150 (2004) 145154 153conditions of feed size distribution, feed rate and grind-

ability (The plant has two different sources of feed material

having different grindabilities). The operating parameters

and the feed size distributions for different surveys are given

in Table 3 and Fig. 11, respectively. The data from Survey 1

was that used in the model fits discussed above.

The stages of model fitting and simulation studies are

shown in Fig. 12. Modelling studies were done only using

the data from Survey 1 and by using these model parameters

(r/d values) determined during the modeling studies and

adjusting them as necessary, the size distribution of the

circuit product was simulated for different conditions and

the results were compared with the observed data. The

effects of changes in operating parameters and grindability

were reflected in r/d* values using the expressions given in

Eqs. (2) and (3). The observed and calculated results are

given in Fig. 13. The comparison of the circulating loadsTable 4

Comparison of the circulating loads for the simulated and plant conditions

Plant conditions (tph) Simulated conditions (tph)

Survey 2 173 165

Survey 3 105 100

Survey 4 162 159calculated from the simulation results with the plant

conditions are given in the Table 4.

As can be seen from the figure and the table, the

differences between the observed and calculated results are

very small and all are well within acceptable limits. This

means that this modeling approach is a useful quantitative

indication of what may occur in fully air swept mills. With

more data set taken from the plants it would be possible to

develop the relations between the model parameters and the

mill operating conditions such as ball size distribution, mill

load and grinding circuit configuration.6. Conclusion

It can be concluded that the back calculation (fitting)

model for a fully air swept mill predicts the existing

performance very well in spite of the fact that it was

assumed that all the materials being ground had the same

breakage and classification properties.

The model can be developed further with more data sets,

which requires extensive sampling surveys from the plants,

and could then be used for optimization and design

purposes. The structure of the model gives the possibility

ARTICLE IN PRESSH. Benzer / Powder Technology 150 (2004) 145154154of evaluation of the effect of air sweeping, ball size and liner

configuration. In order to set up the relations between the

model parameters and the operating conditions, the true

breakage functions should be measured and used.

The classifying action of the liners changes the breakage

rate of the mill along the mill axis; the mid region having a

ball size distribution between 90 and 30 mm gave higher

rate/discharge (r/d) function compared with the r/d at the

feed and discharge ends of the mill.

The structure of the model permits calculation of the rate/

discharge function at every meter inside the mill. The effect

of changing ball size along the mill axis can be seen in the

changing rate/discharge function.

The air sweeping effect can be modeled using an

efficiency curve model, but it should be noted that in order

to control the circuit effectively, a sampling system should

be installed in the mill discharge line.

Nomenclature

aij The mass fraction of particle of size that appear atsize i after breakageC The proportion of feed particles which are sub-jected to the classifying action within a classifier

(=1bypass)

Cs Critical speed 55% to 80%

D Mill diameter (m)

d50c The corrected cut size which is defined as the sizewhich divides equally between underflow and

overflow due to classification onlydi The rate of discharge for particle size i

Eoai The actual efficiency expressed as the particlesreporting to overflowFIT Identifies the calibrated conditions

fi Feed rate of size fraction i (tonnes/h)

J Ball load fraction (0.30.45)

L Mill length (m)

pi Product flow of size fraction i (tonnes/h)

Q Volumetric feed rate (m3/h)

ri The rate of breakage for particle size i

SIM Identifies the simulated conditions

si Amount of size i particles inside the mill (tonnes)

WI Bond Work Index (kW h/tonne)

xi Particle size

a A model parameter defining the sharpness of

classificationb A model parameter defining the fish hookb* A parameter introduced to the model to preservethe definition of d50c (i.e. d=d50c when E=(1/2)C)Acknowledgement

The support during the sampling and experimental

studies provided by Dr. Levent Ergqn, Dr. Salih ErsayVn,Prof. Muammer Oner, Aysun Gqnlq and Ilkay B. Celik isgratefully acknowledged.References

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Modeling and simulation of a fully air swept ball mill in a raw material grinding circuitIntroductionSampling studiesMass balancingModeling studiesBall mill modelAir classification model

Simulation studiesConclusionAcknowledgementReferences