simulation of closed cement grinding circuit
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2
Simulation of Closed Cement Grinding Circuit
A. J. Lynch, M. ner, H. Benzer
ABSTRACT
1. Mathematical models of ball mills and air separators based on a sampling survey were used in a closed clinker grinding circuit. Mass balancing, modeling and simulation studies were carried out by using JKSimmet computer programme developed by JKMRC (Julius Kruttschnitt Mineral Research Center) Australia. In the light of the observations a new modeling approach was made for ball milling. Efficiency curve approach was used for separators. Simulation was then used to predict the effect of using smaller balls in the second chamber of the mill, and eliminating the static separator in the circuit The results indicated that reduction in the ball size had a considerable effect in circuit capacity. Also it was found that removing the static separator from the circuit would provide a 4.5 % increase in the capacity for the same fineness.
1. INTRODUCTION
Current world production of cement amounts to approximately 1.6 bilion t/year and the grinding process is consuming nearly 2 % of the electricity produced in the whole world(1). In terms of electricity consumption about 60% is used for grinding the raw material and cement clinker alone, that's why optimized mill control gains an importance to achieve economical plant operation(2). The design and control of grinding plants are complicated functions which exert a decisive influence on cement quality and consistency. In order to optimise the design and control of grinding equipment and to reduce operating costs, it is necessary to have better knowledge of the mode of operation of ball mills(3).
There are many variables which influence the performance of tube mill-air separator circuits which are commonly used for the grinding of clinker to produce cement. Some of the more important are ball size and load, air flow rates through the mill and separator, aperture sizes in the mill partitions, feed rate and hardness of the clinker, and separator speed.
Operating the circuit to ensure minimum energy consumption per tonne of cement while maintaining the cement quality at specification is an important objective and simulation is a valuable aid in achieving this.
Simulation is 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 widely for the design and optimisation of wet grinding circuits and has brought large economic benefits but its success had come because of the learning process involved in many years of development. It is possible that economic benefits are also available in dry grinding.
A research program is in progress at Hacettepe University, Turkey, to develop models of mills and separators used for dry grinding and to investigate the value of simulation. The approach is to build models based on extensive data collection from operating circuits but also using laboratory machines where appropriate. This paper is concerned with the model of a two compartment tube mill.
2. BALL MILL MODEL
Perfect mixing ball mill model is used for ball mill modelling(4).
0
1
=
-
+
-
=
i
i
i
i
i
j
ij
i
i
i
i
p
d
p
r
a
d
p
r
f
.
.
EMBED Equation.3
It includes two sets of model parameters, i. e. the breakage function (aij) and a combined breakage/discharge rate (ri/di) function.
It can be expressed in a generalised matrix form as follows;
[
]
f
A
I
R
D
R
D
P
.
.
.
.
1
1
1
-
-
-
+
=
The breakage function defines the material characteristics and is determined by laboratory tests using twin pendulum or drop weight test apparatus(5). The combined breakage rate/discharge rate function defines the machine characteristics and can be calculated when feed and product size distribution are known and breakage function is available. For the most ball mills r / d on particle size is a smooth curve which can be fitted to a spline function with four knots.
Calibration of a ball mill model is the calculation r / d values using the feed and product size distributions obtained under a particular operating conditions. Where the size distribution of the mill contents is available, breakage rates and discharge rates can be calculated separately(6).
3. SEPARATOR MODEL
Air classifiers are modelled using efficiency curve approach. The mathematical model selected for the study is capable of defining the fish hook type efficiency curves. The general form of the equation is presented below.
E
oa
EMBED Equation.3
-
+
-
+
=
)
2
)
exp(
)
.
.
exp(
)
1
)
)(exp(
.
.
1
(
*
*
a
b
a
a
b
b
X
X
C
where
X=
c
i
d
d
50
In cases where the efficiency curve does not exhibit fish hook behaviour, the parameter ( is equal to zero and a simplified form of an equation 6 is obtained.
E
oa
EMBED Equation.3
-
+
-
=
2
)
exp(
)
.
exp(
1
)
exp(
a
a
a
X
C
The calibration of the air classifier model involves the calculation of the best fit values (, (, d50c and C to the plant data. If fish hook behaviour does not exist, then (, d50c and C are calculated instead.
4. SAMPLING STUDIES
Circuit sampling from the individual flows and mill inside sampling after crush stop of the mill were made.
The simplified flowsheet of the circuit is given in Figure 1. where the sampling points are also indicated.
Individual samples were taken from clinker, limestone and gypsum comprising the new feed. Size distribution of each component was determined by sieving and the distribution of the new feed was computed using dry flowrates of each flow. An individual sample was also taken from the ground trass flow. The size distributions of samples taken from around the circuit were determined by using lazer sizing technique from 800 m down to 2 m.
After the circuit sampling was completed, the mill was crash stopped. The material samples were taken along the mill length per each meter. The load within the mill was also determined by measuring the width of the charge and perpendicular distance between the charge and liner surface.
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f
A
I
R
D
R
D
P
.
.
.
.
1
1
1
-
-
-
+
=
Osepa Sep. Tromp Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Particle size (mm)
Part. Coeff.
Figure 1. The mass flow rates of the streams of closed circuit
5. MASS BALANCING
During sampling period, the mass flow rate for the combined fresh feed (clinker+limestone+gypsum) and ground trass were 87.4 t/h and 26 t/h respectively. Based on these flowrates and size distributions, a separate mass balancing at each node, such as at final product bin, dynamic separator, dynamic separator feed bin etc., was carried out. Then these estimated flow rates were used for mass balancing of the whole circuit.
Since the air swept portion of the material could not be sampled at the mill discharge, the flow rate and size distribution of this stream was calculated using the mass flows of separator streams.
The mass balanced flow rates of the streams are shown in Figure 1. In mass balancing studies JKSimmet computer programme developed by JKMRC-Australia was used as in modelling and simulation studies.
6. MODELING STUDIES
6.1. Ball Mill Model
The crush stop tests indicated that the size distribution of the material inside the mill becomes finer along the length going from the feed to the partition ( grate ) end of the first compartment, but it gets slightly coarser just before the grates and the size distribution of the material on the other side of the partition is considerably finer than the last point in the first chamber.
Static Sep. Tromp Curve
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Particle size (mm)
Part. Coeff.
According to this, the first compartment can be modelled by two or three perfectly mixed ball mills in series, the last one being closed circuited by a screen. This implies that the partitions between the compartments acts as a screen not allowing particles larger than about 0.8 mm to pass through. No such effect was discernible in the second compartment. Therefore the second compartment is considered as one perfectly mixed ball mill. Two products are obtained from the mill i.e. air swept fraction and the overflow. It was assumed that this action can be modeled by having an imaginary classifier separating a retatively coarse and fine products, the latter being the air swept fraction. Based on these observations closed circuit grinding mill was modeled by two perfectly mixed ball mill, a screen, another perfectly mixed ball mill and a classifier (Figure 2).
6.2. Separator Model
A separator model defines efficiency curve(Tromp Curve) separators performance can be assessed by examining the curve. The efficiency curves of static and dynamic separators within the closed circuit grinding line are presented in Figure 3 and 4 respectively. It was assumed that air sweeping within the closed circuit has a classifying effect on the ground product. Based on estimated air swept fraction, an efficiency curve was drawn to model this action (Figure 5).
Grate Sep. Tromp Curve
0.7
0.8
0.9
1
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
Particle size (mm)
Part. Coeff.
Figure 3. The efficiency curve of static separator
Figure 4. The efficiency curve of dynamic separator
Figure 5. The efficiency curve of grate separator
The efficiency curve of the static separator indicates that its performance is poor. Only 60-65% of the coarsest particles (0.09-0.2mm) in the separator feed are separated into the seperator rejects, while about 55% of the very fine particles (-0.01mm ) are separated into the separator fines. However, since the amount of the coarsest particles in the feed is very low and separator rejects goes through a second stage classification in dynamic separator, this inefficiency is thought not to have significant effect in overall performance of the circuit.
The dynamic separator has a very sharp efficiency curve with a low bypass fraction of about 15%. However the fish hook effect is observed on the curve. This indicates that the agglomeration of the very fines occurs within the mill and/or separator. As expected, the classifying effect of air sweeping is poor in terms of very fines, but it is effective for the coarse particles.
2. 6.3. Calibrated Model Parameters
3. Practically, a ball mill model consists of two functions, i. e. breakage distribution and breakage rate/discharge rate (r/d) function. Breakage distribution is normally determined by carrying out laboratory test work as described earlier in Section 2. In this study, however, the breakage distribution was assumed to be similar to the one offered by Broadbent and Callcott(4). This is usually a good assumption. Its validity will be checked when the laboratory studies are completed. Therefore the calibration of the ball mill model meant the estimation of the best fit values of r/d function. The combined r/d function is a smooth curve which could be described by a cubic spline function defined by 3-4 knots. Since the feed size distribution to the mill is wide, it would be more appropriate to have 4 knots in this particular case. This meant that the calibration of ball mill model was the calculation of r/d values for selected particle sizes to obtain a satisfactory fit to the measured data. Four particle sizes were selected such that they cover the whole range of distribution. The initial selection of sizes required some modification. Therefore a trial and error approach was employed. A non-linear optimisation algorithm was used to determine the best fit values of the combined r/d function.
As described earlier the calibration of a classifier model is the calculation of the best fit values of the parameters describing the efficiency curve, i. e. d50c, (, C and, if required, (. The same approach was used to model the screening effect of the grates between the two compartments. Here again, a non-linear optimization algorithm was used.
The model parameters of the mill, and static separator and dynamic separator are given in Table 1,2 respectively.
Table 1. The Calibrated Model Parameters of the Closed Circuit Ball Mill
First
Compartment
Second compartment
Grate
Air Sweeping
Ball Mill 1
Ball Mill 2
Ball Mill 3
Size (mm)
Ln r/d
Size (mm)
Ln r/d
Size (mm)
Ln r/d
Parameter
Parameter
0.04
-0.1211
0.04
-0.3915
0.015
-5.31
C
100
C
0.2144
0.5
1.38
0.5
4.27
0.070
-0.7385
(
10
(
0.01
1.5
4.22
1.5
5.31
0.2
1.16
(
0
(
0
15
2.58
15
3.42
0.7
7.64
d50c
0.8295
d50c
0.062
Table 2. The Calibrated Model Parameters of the Static and Dynamic Separators
Parameter
Static Separator
Dynamic Separator
C
0.5939
0.7352
(
1.14
0.01
(
0
1.07
d50c
0.137
0.0484
7. SIMULATION STUDIES
Simulation studies were carried out for the following alternatives:
i. Effect of ball size in the second chamber
ii. The effect of removing the low efficiency static separator from the circuit. In this case the total mill discharge is fed to the dynamic separator.
i. Effect of ball size in the second chamber
The effect of ball size were investigated by changing ball size from the existing 27 mm to 15 mm. The results of simulation studies are shown in Table 3.
Table 3. Effect of ball size in the second chamber in closed circuit clinker mill.
Original
Simulated acc. to ball size
Simulated according
to tonnage
Max.Ball Size (mm)
27
15
15
15
15
Product Tonnage (t/h)
113
113
126
141.5
155
% retained on 40 m
24.2
18.5
20
21.7
23.1
% retained on 90 m
3.6
2.3
2.6
3.1
3.4
Circulating Load (t/h)
146
113
137
168
200
Mill Tonnage (t/h)
233
201
234
277
319.5
Simulation results showed that reducing ball size to 15 mm in the second chamber increases the fineness and decreases the mill tonnage and circulating load. The performance of the grate was kept constant in the simulation studies. Since the grate between the compartments was modeled as a screen, the effect of feed rate on the performance should be included in the model. This requires more experimental data from inside the mill for different capacities.
Fresh feed rate was increased to obtain same fineness by keeping the fresh feed (77%) to ground trass (23%) ratio constant. The results indicate that capacity of the circuit could be increased up to 155 t/h without deteriorating the fineness. However, in doing so the circulating load would be expected to increase to 200 t/h and it is likely that overloading would occur in the first chamber at this throughput. Therefore, for the capacities greater than 126 t/h, the simulation results should be treated cautiously.
ii. Removing static separator from the circuit
The performance of static separator was found to be low. Therefore, the flowsheet was modified on the JKSimmet and static separator was removed from the circuit. The mill discharge was then fed to dynamic separator. The results showed that this rearrangement in the circuit would increase product tonnage from 113t/h to 118t/h.
8. CONCLUSIONS
The modelling approach for the simulation of mill and separators have been proven to be satisfactory.
Mass balancing throughout the circuit was obtained with minor adjustments in the raw data indicating the sampling surveys were very good.
Existing performance of the mill and separators were excellently predicted by the models developed.
Simulation studies indicated that the performance of the mill could be increased using smaller balls in the second chambers.
The results also indicated that removing static separator from closed circuit clinker grinding and feeding mill discharge to existing dynamic separator would result in better performance.
For more comprehensive description of the cement grinding processes the following mathematical expressions should be developed for;
i. The effect of air sweeping within the mill.
ii. The performance of the grate between the compartments for varying capacities.
iii. The relationship between the geometrical and operating variables and the performance of the
air separators.
ACKNOWLEDGMENT
The support during the sampling and experimental studies provided by Dr. Salih Ersayn, Dr. Levent Ergun, Aysun Gnl and lkay B. elik is gratefully acknowledged.
REFERENCES
4. Norholm, A., September 1995, Notes on energy conservation, FL Smidth and Co. Seminar, Istanbul, Turkey
5. Zhang Y. M., Napier-Munn T.J., Kavetsky A., December 1988, Application of comminution and classification modelling to grinding of cement clinker, Trans. Instn. Min. Metall (Sect. C: Mineral Process. Extr. Metall.), 97, pp 207-214.
6. Flament G., Saint-Etienne, Cordonnier A., Tete P., August 1991, Modelling of grinding plants and grindability of materials in cement plant, World Cement, pp14-26.
7. Lynch A. J., 1977, Mineral Crushing and Grinding Circuits, Elsevier Pub. Amsterdam, 342p.
8. Narayanan S.S., 1985 Development of a laboratory single particle breakage technique and its application to ball mill modelling and scale-up, Ph.D. thesis, University of Queensland.
9. Napier-Munn T., Morrell S., Morrison R.D., Kojovic T., 1995, Mineral Comminution Circuits: Their Operation and Optimisation, published by JKMRC, Ed Napier-Munn, 342p.
Eoa
:
The actual efficiency expressed as the particles reporting to overflow
C
:
The proportion of feed particles which are subjected to the classifying action within a classifier ( = 1- bypass)
(
:
A model parameter defining the sharpness of classification
(
:
A model parameter defining the fish hook
(*
:
A dummy parameter introduced to the model to preserve the definition of d50c ( i.e d=d50c when E=(1/2)C )
di
:
Particle size
d50c
:
The corrected cut size which is defined as the size which divides equally between underflow and overflow due to classification only.
EMBED Equation.3
Sampling Points
87.4 t/h
141 t/h
198 t/h
29.7 t/h
15 t/h
113.4 t/h
26 t/h
239 t/h
99 t/h
14.4 t/h
Figure 2. Schematic description of the closed circuit grinding mill
Second Compartment
Grate
First Compartment
Feed
air swept
overflow
Classifier
Ball
Mill
3
Screen
Ball
Mill
2
Ball
Mill
1
14.4 t/h
Filter
Filter
99 t/h
Clinker
L.Stone
Gypsum
Dynamic