- Email: [email protected]
Performance of a fluidized bed jet mill as a function of operating parameters
ELSEVIER
Int. J. Miner. Process. 44-45 ( 1996)507-5 19
Perhmance
of a fluidized bed jet mill as a function of operating parameters M. Benz, H. Herold, B. Ulfik Bayer AG, ZF-7VG
3,51368 Leverkusen, Germany
Abstract Fluidized bed jet mills are used for the dry comminution in the pm range. The application of the jet mill ranges from deagglomeration purposes to grinding of hard materials. This indicates the wide field for the usage of this grinding technique. The comminution effect is based on particle--particle impact in expanding gas streams. A dynamic classifier is integrated in the fluidized bed jet mill. Then: are two parameters which can be used to control the performance of the fluidized bed jet mill: th: speed of the classifier rotor and the pressure of the gas used for grinding. As a characteristic value the “spin-number” was defined. The “spin-number” is given as the ratio of the circumferential speed of the classifier rotor and the flow-through velocity of the classifying gas in radial direction. Results of limestone grinding were presented. The comminution of limestone represents a grinding, process, not just a deagglomeration step. The fineness achieved, expressed by the mean particle diameter, can be modelled as a function of the “spin-number” and the pressure of the gas used for grinding. A similar dependency was found for the parameters of the RRSB-distribution, describing the shape and the position of the distribution. The dependencies could be backed-up with experiments performed with an easily grindable rubber chemical. A few experiments performed at the base-points of the working range of the fluidized bed jet mill enable to establish a characteristic field of performance for a given product. The knowledge of this characteristic field simplifies the selection of the optimum operation conditions of the fluidized bed jet mill for a given grinding task. Moreover it enables to include milling processes in more advanced process control systems.
1. Introduction
Fluidized bed jet mills are commonly applied to achieve mean particle sizes between 1 and 110 pm via grinding. These fine particles are required e.g. in pharmaceuticals to 030 l-75 16/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SD1 0301-7516(95)00062-3
508
M. Benz et al./Int.
J. Miner. Process. 44-45 (1996) 507-519
enable high resorption rates or to realize a widespread homogeneous distribution of a small amount of an agro-chemical on a huge area. The comminution in a jet mill is achieved by collision of particles of different velocities in expanding gas streams. The particles are carried into the gas streams either by injector nozzles, drop casing or by screw-feed units. The energy for comminution results from the impact of particles of different velocities. Collision with the walls of the grinding chamber contribute minimally to the performance of a jet mill. Jet mills in general include a classifying device, either static or dynamic. Static classifiers take the energy for size classification from the energy of the grinding gas streams, therefore classification and grinding cannot be regarded as independent operations. Changing the grinding performance always has an impact on the classification. On the other hand, dynamic classifiers like deflector wheels need external energy. Thus the classification is nearly independent of the grinding inside the mill. In both cases the classification works according to similar principles. Comminuted particles are carried with the gas stream inside the grinding chamber towards the outlet of the mill. In jet mills with static classification devices, the air is forced into a vortex, either by the design of the outlet in the center of the mill (spiral jet mill), or by introduction of turning edges (oval tube jet mills). In both cases, larger particles cannot follow the gas streamlines, the centrifugal forces drive them back into the grinding zone. With dynamic classifiers, the high speed of the classifier wheel causes the gas vortex and thus the particles have to follow the gas stream through the openings of the deflector wheel. Again, if the particle is still too large, it cannot follow the path of the air stream and is taken back into the grinding zone via centrifugal forces.
2. Objectives The object of this study was to obtain knowledge of the effect of operating parameters of a fluidized bed jet mill on the grinding performance. As operating parameters the grinding gas pressure and the speed of the deflector wheel were investigated. The evaluation of the results focused on the mean particle diameter achieved by comminution, as well as the shape of the particle size distribution. The overall aim was to establish characteristics between the two operating parameters and the performance of the jet mill. The separation of the influence of grinding pressure from deflector wheel speed will help to adjust the fluidized bed jet mill quickly to a new grinding task. Moreover, the mill can be run in the optimum range, i.e. grinding with the lowest consumption of grinding energy. The operational costs of the fluidized bed jet mill are dominated by the costs for high pressure air, therefore operating the mill with the optimum milling pressure immediately reduces operational costs. In addition fewer of the time-consuming trial-and-error experiments to reach the optimum operating range are necessary. The idea was to develop characteristic fields of performance, giving the dependence of a grinding result, such as mean particle diameter, as a function of the operational parameters of the mill. These characteristic fields should enable to include the perfor-
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
509
mance of fluidized bed jet mills in mathematical simulation of unit operations, and help to include milling processes in more advanced process control systems.
3. Methods and materials 3.1. Fluidized bed jet mill All experiments were performed on a 100 AFG ( Aeroplex-FlieObettGegenstrahlmi_ihle) of Alpine AG, Augsburg, Germany with an inner diameter of the grinding chamber of 100 mm. The original layout of the fluidized bed jet mill was changed in a way that the cyclone, installed in-line before the filter, was removed. In earlier experimental runs, the cyclone had caused problems in taking representative samples. On top of the grinding chamber a dynamic classifier Alpine 50 ATP (Alpine Turbop:lex) is installed with a classifier wheel of 50 mm diameter. The performance of the mill is controlled by the grinding pressure and the classifier speed. However the achievable fineness is more or less independent of the particle size distribution of the feed. The externally driven classifier runs with a constant speed, independent of the gas-phase concentration in the grinding chamber, as long as the classifier does not become overloaded. 3.2. Material Limestone “Juraperle 150/300” with dg7 of 250 pm and d,, of 140 pm was used in the experiments. Limestone is a standard compound for comminution experiments. It is cheap, easy to handle and non-toxic. 3.3. Particle size analysis Particle sizes for limestone after comminution were measured using a Mastersizer MS-20 laser diffraction instrument.
4. Experimental
approach
Three Laval-type nozzles were used with a minimum diameter of 1.95 mm. Compressed air was the grinding medium, the pressure was adjusted to 4, 6 and 10 bar, the deflector wheel was run between 2,000 and 22,000 rpm. The product was fed into the grinding chamber with a screw-feed unit, the rate varying between 1 and 15 kg/h. The resulting gas-phase concentrations Al.ranged from 0.02 to 0.3 kg product/kg air. 4.1. Experimental setup Before running the experiment, the optimum level of product in the mill had to be investig,ated. This level depends on the product; after finishing each run the level was
M. Benz et al./lnt. J. Miner. Process. 44-45 (1996) 507-519
510
checked. This constant level of product is important for several reasons. For a good performance the mill requires a certain amount of product in the grinding chamber to ensure sufficient impact probability. However, if there are too many particles inside the mill, the classifier gets overloaded, which enables larger particles to pass the classifier. The run time was fixed at 15 minutes; in addition a comparison with runs with extended times (30 minutes) was made to ensure that the mill was operated at steady-state. During the run, the following pressures were monitored: milling gas, inside the grinding chamber, for the flushing of the bearings of motor and classifier. Moreover the rpms of the classifier wheel and the electrical energy consumed by the classifier were measured.
5. Background 5.1. Classification
With the classifier as the main instrument to control the fineness of the product, a few remarks should be made on the parameters which influence its performance. This simplified approach is based on a balance of forces for a particle and requires a few assumptions which are as follows. There exists a particle of a given size dT, for which the sum of all forces is zero. This particle has a 50% chance of passing the classifier or being thrown back into the grinding chamber. This particle size is described as the cut size d, of the classifier. All particles are assumed to have the same velocity as the gas stream. At the outer diameter of the classifier wheel the velocity of the gas stream (u) equals the circumferential speed of the rotor. Assuming laminar flow around the particles the drag force can be expressed by the equation of Stokes (Bohl, 1986). This leads to the following equation for the cut size d,. d*=
Jyy$J
(1)
with u = circumferential gas velocity, u = radial gas velocity, r = radial position, a,, 8, = density of the particles, fluid, and or = viscosity. The circumferential speed is calculated according to Eq. 2. u-2.rr.r.n
(2)
More difficult is the evaluation of the radial gas velocity. It is not accessible to measurement, because the air used for flushing the bearings has a certain leakage rate. This flow cannot be neglected, but the amount it contributes to the overall gas flow cannot be evaluated. Therefore to achieve comparable conditions for all evaluations, the flow through the nozzles was calculated. The volumetric flow through Laval-type nozzles can be evaluated, knowing the area of the deflector wheel allows to calculate the radial gas velocity. The calculations were done based on thermodynamics and the assumption that the process can be regarded as isentropic. The mathematical evaluation was taken from Bohl (1986) and is described in detail there.
M. Benz et al./Int. J. Miner. Process. 44-45 (1996) 507-519
Limestone
10
1 Spin-number Fig.
u/v
1.Cut size dT as a function of the “spin-number”
I( / v.
This equation represents, on the one hand, the impact of classifier speed; the higher the rpms, the higher the circumferential velocity (~1, i.e. d, falls. On the other hand increasing the volumetric gas flow by changing the grinding gas pressure, increases the radial gas velocity (v) and dT rises. Earlier investigations have shown, that this equation describes the tendencies fairly up to 6-10 pm. However, particle diameters greater than 10 pm cannot be predicted at all. With these problems in mind an attempt was made to plot the cut size d, as a function of the “spin-number” (U/U>. Th’is number is defined as the ratio of the circumferential (u> to the radial (v) gas velocity. This approach was applied to data from classifiers. Muschelknautz and Brunner (1967) stated that the head loss in cyclones can be given as a function of u/u. In Fig. 1, dT is plotted as a function of u/v, with the gas-phase concentration p as a parameter. On a log-log scale the correlation between dT and u/v for a given gas-phase concentration p can be given by straight lines. Implying this number to the fluidized bed jet mill, the impact of the classifier is represented by the circumferential speed u, the gas pressure influences the radial gas velocity. Thus both operating parameters of the fluidized bed jet mill are incorporated in this number. 5.2. Particle size distributions To characterize the impact of comminution, the distribution of the particle sizes before and after the grinding step have to be characterized. Two different approaches are practical. One consists in picking typical values from the distribution curve as d,o, d,,, dgO, i.e. the diameters indicating that 10, 50 respectively 90% of the particles are smaller than the given diameter. These values offer good information on the range of particle
512
M. Benz et ul./
Int. J. Miner.
Process. 44-45
(1996) 507-519
sizes, however only limited knowledge of the shape of the particle size distribution can be inferred. The calculation of characteristic values such as d2,/d,, or Cd,, - d,o)/d,, gives more insight into the shape of the distribution. These values have the advantage that they are not model-based, no limitation from the range of application or from the assumptions of the model exists. Another approach is to include some empirical information in the data evaluation. In this case a formula can be given to describe the distribution function. The most common distributions in the literature are the GAUSS-, the Log-Normal- and the RRSB-distribution (Schubert, 1989). For particle collectives resulting from comminution, the RRSBdistribution (Rosin-Rammler-Sperling-Bennet) (Schubert, 1989) is frequently applied. Eq. 3 gives the percentage of particles greater than the particle d, as a function of two model parameters n’ and d’.
(3) With a few steps of mathematical =n’.lnd,-n’.lnd’
manipulation
Eq. 3 can be transformed
into Eq. 4.
(4)
Thus a linear dependency between ln(ln(lOO/R)) and lnd, can be established. Plotting the data with the appropriate axis grid easily leads to the parameters n’ as the slope and d’ with R set to 36.8%.
6. Results and discussion 6.1. Mean particle size
With the positive results for the dependency of dT as a function of u/v in mind, the idea came up to check if the mean particle diameter d,, of the fine particle fraction of the fluidized bed jet mill can be plotted in a similar way. In Fig. 2 a typical example of such a characteristic field of performance is shown. Plotted are the mean particle diameters d,, of limestone as a function of the “spin-number” u/v. Three different grinding pressures and three deflector wheel speeds were realized. Thus the “spin-number” u/v varied over one order of magnitude. It is obvious that, for a given grinding pressure, the “spin-number” increases with increasing deflector wheel speed, thus resulting in lower d,,-values. A higher grinding pressure shifts the line towards lower d,,-values for a constant u/v-value. The lines result from linear regression, done with the prefix of a common slope for all grinding pressures. Earlier data evaluation showed that the differences between the individual slopes appeared to be very small. The interpretation of the data for constant deflector wheel speed is more difficult, because of two competing effects. On the one hand, a higher grinding pressure with the appropriate Laval-nozzles leads to higher particle velocities. Therefore an extended
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
513
I
10 Limestone
. 3 . ??
. L .
.
.
-•-
4 bar
- -I-
6 bar
\ ‘\
??
k
.
??
\
+
b
‘.I
10 bar
\. . \ . -x\ \
‘*
‘1‘:
II
1 1
10 Spin-number
100 u/v
Fig. 2. Mean particle size as a function of the “spin-number”
U/ U.
amount of energy is available for crushing during particle-particle impact and this should lead to smaller particle sizes. On the other hand a higher grinding pressure causes a higher volumetric flow rate inside the mill, thus resulting in a higher carry-on stream of larger particles through the openings of the classifier. For grinding of limestone it seems that the increase in grinding energy is dominant especially at low deflector wheel speeds. At higher values, the sharp separation characteristic of the classifier takes over. However it has to be mentioned, that the analytical error is in the same order of magnitude as the differences between the single data points, this has to be kept in mind when interpreting these data. The most important fact that can be taken from Fig. 2 is that to achieve a given grinding task, changes in the grinding pressure and/or the deflector wheel speed can be made. For the user of the machine, it is important that a simple change of the classifier speed at a given grinding pressure can change the mean particle size decisively. This is important considering the operational costs of the fluidized bed jet mill. The main factor contributing to the costs is very often the high pressure gas consumption. Similar dependencies of the grinding result as a function of the “spin-number” u/u were found for parameters dN and the increase in specific surface area ASspez as indicated in Figs. 3 and 4. Especially for the &-values the differences between the data for different grinding pressures are relatively small and therefore the analytical error, resulting from sampling and data analysis, has to be kept in mind when interpreting the data. Again, the impact of varying grinding pressures for constant deflector wheel speeds cannot be predicted precisely because so far not enough data points are available to back up the evaluation of the slope of the line.
M. Benz et al./ ht. J. Miner. Process. 44-45 (1996) 507-519
514
100
Limestone
@
?? ‘
10
-e-
U . w, . 5 ’ .T
.‘h . I
.
4 bar
- -a-
.6 bar
- +
-10 bar
‘b> ib .
‘r ‘0
I,
1 1
10 Spin-number Fig. 3. &,-data
100 u/v
as function of the “spin-number”
u/v.
4.2. Particle size distribution
For many applications the whole particle size distribution is important. In most cases a narrow distribution is the aim. As mentioned above the dimensionless number g as the ratio of (d, - d&/d,, is an indicator for the sharpness of a particle size distribution.
+
’
,’
_J..‘- . I.
:
‘-‘;,I_
1
’ 1
I
,
_ -;
I111111
I
I I III
10 Spin-number
100 u/v
Fig. 4. Increase in specific surface area as function of the “spin-number”
u/o.
M. Benz et al./lnt. J. Miner. Process. 44-45 (1996) 507-519
515
I
10 Limestone
??
--m--6
??
..*.-lO
‘*.
4 bar bar bar
..!
1
10 Spin-number
100 u/v
Fig. 5. Parameter g as a function of the “spin-number” u/u.
For the limestone experiments, g ranged from 1.4 to 10. The smaller g, the narrower the distribution. In Fig. 5 the parameter g is given as function of u/v. Again each grinding pressure leads to an individual characteristic dependency. To achieve narrow distributions, a high “spin-number” u/v should be chosen. A higher classifier speed leads to a narrower distribution. Assuming that for the same “spin-number” u/v the performance of the classifier is similar, then a higher grinding pressure leads to a better result concerning the particle size distribution. Again no definite decision for the slope of the lines of constant classifier speed can be made. The (evaluation of the data with the method of RRSB showed results that are in accordance with the ones presented so far. In Figs. 6 and 7 the RRSB-parameters d and n’are given as a function of the “spin-number” u/v. d which is somehow comparable to an average particle size, indicates the same trends as d,, with problems as far as the impact of the grinding pressure on Cp for a given classifier speed is concerned. n’ characterizes a narrower distribution with a higher value. As demonstrated earlier with the parameter g, a higher “spin-number” u/v leads to narrower distributions. For a given u/v, the higher grinding pressure leads to greater n’-values. 6.3. Mathematical evaluation As the experiments so far have shown the “spin-number” u/v can be applied to characterize the cornmunition performance of a fluid&d bed jet mill very well. The next step was to develop mathematical equations for the demonstrated characteristic fields. It was indicated that in a log-log plot all the important parameters have a linear
516
M. Benz et ol./Int.
I
J. Miner. Process. 44-45 (1996) 507-519
Limestone
1
10
Spin-number Fig. 6. RRSB-parameter
100
u/v
d as function of the “spin-number”
dependency of the “spin-number” described with Eq. 5.
u/u.
u/u. A straight line in a log-log
scale can be
(5) 10
i
I
Limestone
L
-*
-4 bar bar
--m--6
--•-
0.1
-10 bar
I 1
10
Spin-number Fig. 7. RRSB-parameter
100
u/v
n’ as a function of the “spin-number”
u/u.
M. Benz et al./ ht. J. Miner. Process. 44-45 (1996) 507-519
517
lO[‘,,I~~,I”~I”‘I’,,~
,
/ Limestone
8 i
/ -1
/’ /’
1
I
6
-
4
-
/ Ji Ir
b
a ’Y
?? J. i
mm
??
.
??
??
2
-
4 bar 6 bar 10 bar
/f J’-
Ok”“““““““.” 0
Fig. 8. &,-data
2
versus d,,-prediction
4 d5,-Data, according
6 Brn to mathematical
8
10
evaluation.
Both values K, and K, can be taken from linear regression. As indicated in the figures., parallel lines for different pressures can be assumed within the range of analytical error. Therefore K, is the arithmetic mean value of the individual slopes K,. This assumption simplifies the further evaluation. So far with data available for 3 different pressures a linear dependency for K, from the pressure (p> can be assumed (Eq. 6). ti~o=(K,+K,-p)~(~)X5
(6)
K, and K, can be evaluated from a linear plot of K, versus p. The characteristic line for each grinding pressure can then be predicted. In Fig. 8 the &-data for limestone are plotted together with the &-data predicted according to Eq. 6. A 15% error is assumed for sampling and data analysis indicated by the error bars. Within the analytical error range a good fit of data and prediction is found. The same approach can be applied on the specific surface area and the parameters characterizing the shape of the distribution as g, d’ and n’. Only the values and the dimensions of the parameters change.
6.4. Remarks Similar experiments were performed with rubber chemicals. These compounds are easy to grind and the comminution is more or less a deagglomeration step. The rubber chemical displayed, besides the different particle size range and cornmunition pressure, the same trends. The “spin-number” u/u could be used in the same way for data evaluation.
M. Benz et al./ ht. J. Miner. Process. 44-45
518
(1996) 507-519
As possible errors during the data evaluation, the representative sampling has to be mentioned. Moreover the leakage of air - necessary for the flushing of the bearings of the deflector wheel - changes the actual flow of air through the deflector wheel. This impact on the “spin number” u/u could not be evaluated so far. 7. Summary A study of the impact of the operating parameters of a fluidized bed jet mill on the performance was done. Compounds of different grindability were tested, requiring comminution as well as deagglomeration. The results showed that the most important number to characterize the performance of the fluidized bed jet mill is the “spin-number” u/u, the ratio of the circumferential speed and the radial gas velocity at the classifier wheel. Identical u/u-values represent identical behavior of the classifier. In a log-log plot characteristic fields of performance can be established, where the impact of gas pressure and deflector wheel speed can be evaluated easily. The results showed that the change of the classifier speed has a stronger influence on the performance compared to changing the grinding pressure. This is important for an economical use of the fluidized bed jet mill, because the operational costs of the mill are often dominated by the consumption of high pressure gas. Mathematical equations were developed to enable a quick prediction of the milling performance at any given pressure and “spin number” u/v. The mathematical evaluation is valid for dsO, &, as well as for parameters characterizing the shape of a distribution as g, d and n’. 8. Nomenclature di:
5: U: l4:
r:
49 6,: r)F: n’, d’: d,: R: g: K,-K,:
Diameter indicating i% smaller than di Gas-phase concentration, kg product/kg grinding media Cut size for classifier Radial gas velocity at deflector wheel Circumferential velocity Radius of deflector wheel Particle and fluid density Fluid viscosity Parameters of RRSB-distribution Particle diameter Remaining amount for a given particle size Parameter indicating the shape of the distribution, (dm - d,,)/d,, Parameters for mathematical evaluation
Acknowledgements The authors would like to appreciate the assistance of Bayer Antwerpen and H. Schneider, W. Hijijk and R. Hammelrath for their careful performance of the experimental runs.
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
519
References Bohl, W., 1986. Technische Strijmungslehre. Vogel Buchverlag, Wiirzburg, pp. 182-194. Muschelknautz, E. and Brunner, K., 1967. Untersuchungen an Zyklonen. CIT, 39(9/10): 531-538. Schubert, H., 1989. Aufbereitung fester mineralischer Rohstoffe, Band I. VEB 1964, Deutscher Verlag fir Grundstoffmdustrie, Leipzig.
Int. J. Miner. Process. 44-45 ( 1996)507-5 19
Perhmance
of a fluidized bed jet mill as a function of operating parameters M. Benz, H. Herold, B. Ulfik Bayer AG, ZF-7VG
3,51368 Leverkusen, Germany
Abstract Fluidized bed jet mills are used for the dry comminution in the pm range. The application of the jet mill ranges from deagglomeration purposes to grinding of hard materials. This indicates the wide field for the usage of this grinding technique. The comminution effect is based on particle--particle impact in expanding gas streams. A dynamic classifier is integrated in the fluidized bed jet mill. Then: are two parameters which can be used to control the performance of the fluidized bed jet mill: th: speed of the classifier rotor and the pressure of the gas used for grinding. As a characteristic value the “spin-number” was defined. The “spin-number” is given as the ratio of the circumferential speed of the classifier rotor and the flow-through velocity of the classifying gas in radial direction. Results of limestone grinding were presented. The comminution of limestone represents a grinding, process, not just a deagglomeration step. The fineness achieved, expressed by the mean particle diameter, can be modelled as a function of the “spin-number” and the pressure of the gas used for grinding. A similar dependency was found for the parameters of the RRSB-distribution, describing the shape and the position of the distribution. The dependencies could be backed-up with experiments performed with an easily grindable rubber chemical. A few experiments performed at the base-points of the working range of the fluidized bed jet mill enable to establish a characteristic field of performance for a given product. The knowledge of this characteristic field simplifies the selection of the optimum operation conditions of the fluidized bed jet mill for a given grinding task. Moreover it enables to include milling processes in more advanced process control systems.
1. Introduction
Fluidized bed jet mills are commonly applied to achieve mean particle sizes between 1 and 110 pm via grinding. These fine particles are required e.g. in pharmaceuticals to 030 l-75 16/96/$15.00 0 1996 Elsevier Science B.V. All rights reserved SD1 0301-7516(95)00062-3
508
M. Benz et al./Int.
J. Miner. Process. 44-45 (1996) 507-519
enable high resorption rates or to realize a widespread homogeneous distribution of a small amount of an agro-chemical on a huge area. The comminution in a jet mill is achieved by collision of particles of different velocities in expanding gas streams. The particles are carried into the gas streams either by injector nozzles, drop casing or by screw-feed units. The energy for comminution results from the impact of particles of different velocities. Collision with the walls of the grinding chamber contribute minimally to the performance of a jet mill. Jet mills in general include a classifying device, either static or dynamic. Static classifiers take the energy for size classification from the energy of the grinding gas streams, therefore classification and grinding cannot be regarded as independent operations. Changing the grinding performance always has an impact on the classification. On the other hand, dynamic classifiers like deflector wheels need external energy. Thus the classification is nearly independent of the grinding inside the mill. In both cases the classification works according to similar principles. Comminuted particles are carried with the gas stream inside the grinding chamber towards the outlet of the mill. In jet mills with static classification devices, the air is forced into a vortex, either by the design of the outlet in the center of the mill (spiral jet mill), or by introduction of turning edges (oval tube jet mills). In both cases, larger particles cannot follow the gas streamlines, the centrifugal forces drive them back into the grinding zone. With dynamic classifiers, the high speed of the classifier wheel causes the gas vortex and thus the particles have to follow the gas stream through the openings of the deflector wheel. Again, if the particle is still too large, it cannot follow the path of the air stream and is taken back into the grinding zone via centrifugal forces.
2. Objectives The object of this study was to obtain knowledge of the effect of operating parameters of a fluidized bed jet mill on the grinding performance. As operating parameters the grinding gas pressure and the speed of the deflector wheel were investigated. The evaluation of the results focused on the mean particle diameter achieved by comminution, as well as the shape of the particle size distribution. The overall aim was to establish characteristics between the two operating parameters and the performance of the jet mill. The separation of the influence of grinding pressure from deflector wheel speed will help to adjust the fluidized bed jet mill quickly to a new grinding task. Moreover, the mill can be run in the optimum range, i.e. grinding with the lowest consumption of grinding energy. The operational costs of the fluidized bed jet mill are dominated by the costs for high pressure air, therefore operating the mill with the optimum milling pressure immediately reduces operational costs. In addition fewer of the time-consuming trial-and-error experiments to reach the optimum operating range are necessary. The idea was to develop characteristic fields of performance, giving the dependence of a grinding result, such as mean particle diameter, as a function of the operational parameters of the mill. These characteristic fields should enable to include the perfor-
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
509
mance of fluidized bed jet mills in mathematical simulation of unit operations, and help to include milling processes in more advanced process control systems.
3. Methods and materials 3.1. Fluidized bed jet mill All experiments were performed on a 100 AFG ( Aeroplex-FlieObettGegenstrahlmi_ihle) of Alpine AG, Augsburg, Germany with an inner diameter of the grinding chamber of 100 mm. The original layout of the fluidized bed jet mill was changed in a way that the cyclone, installed in-line before the filter, was removed. In earlier experimental runs, the cyclone had caused problems in taking representative samples. On top of the grinding chamber a dynamic classifier Alpine 50 ATP (Alpine Turbop:lex) is installed with a classifier wheel of 50 mm diameter. The performance of the mill is controlled by the grinding pressure and the classifier speed. However the achievable fineness is more or less independent of the particle size distribution of the feed. The externally driven classifier runs with a constant speed, independent of the gas-phase concentration in the grinding chamber, as long as the classifier does not become overloaded. 3.2. Material Limestone “Juraperle 150/300” with dg7 of 250 pm and d,, of 140 pm was used in the experiments. Limestone is a standard compound for comminution experiments. It is cheap, easy to handle and non-toxic. 3.3. Particle size analysis Particle sizes for limestone after comminution were measured using a Mastersizer MS-20 laser diffraction instrument.
4. Experimental
approach
Three Laval-type nozzles were used with a minimum diameter of 1.95 mm. Compressed air was the grinding medium, the pressure was adjusted to 4, 6 and 10 bar, the deflector wheel was run between 2,000 and 22,000 rpm. The product was fed into the grinding chamber with a screw-feed unit, the rate varying between 1 and 15 kg/h. The resulting gas-phase concentrations Al.ranged from 0.02 to 0.3 kg product/kg air. 4.1. Experimental setup Before running the experiment, the optimum level of product in the mill had to be investig,ated. This level depends on the product; after finishing each run the level was
M. Benz et al./lnt. J. Miner. Process. 44-45 (1996) 507-519
510
checked. This constant level of product is important for several reasons. For a good performance the mill requires a certain amount of product in the grinding chamber to ensure sufficient impact probability. However, if there are too many particles inside the mill, the classifier gets overloaded, which enables larger particles to pass the classifier. The run time was fixed at 15 minutes; in addition a comparison with runs with extended times (30 minutes) was made to ensure that the mill was operated at steady-state. During the run, the following pressures were monitored: milling gas, inside the grinding chamber, for the flushing of the bearings of motor and classifier. Moreover the rpms of the classifier wheel and the electrical energy consumed by the classifier were measured.
5. Background 5.1. Classification
With the classifier as the main instrument to control the fineness of the product, a few remarks should be made on the parameters which influence its performance. This simplified approach is based on a balance of forces for a particle and requires a few assumptions which are as follows. There exists a particle of a given size dT, for which the sum of all forces is zero. This particle has a 50% chance of passing the classifier or being thrown back into the grinding chamber. This particle size is described as the cut size d, of the classifier. All particles are assumed to have the same velocity as the gas stream. At the outer diameter of the classifier wheel the velocity of the gas stream (u) equals the circumferential speed of the rotor. Assuming laminar flow around the particles the drag force can be expressed by the equation of Stokes (Bohl, 1986). This leads to the following equation for the cut size d,. d*=
Jyy$J
(1)
with u = circumferential gas velocity, u = radial gas velocity, r = radial position, a,, 8, = density of the particles, fluid, and or = viscosity. The circumferential speed is calculated according to Eq. 2. u-2.rr.r.n
(2)
More difficult is the evaluation of the radial gas velocity. It is not accessible to measurement, because the air used for flushing the bearings has a certain leakage rate. This flow cannot be neglected, but the amount it contributes to the overall gas flow cannot be evaluated. Therefore to achieve comparable conditions for all evaluations, the flow through the nozzles was calculated. The volumetric flow through Laval-type nozzles can be evaluated, knowing the area of the deflector wheel allows to calculate the radial gas velocity. The calculations were done based on thermodynamics and the assumption that the process can be regarded as isentropic. The mathematical evaluation was taken from Bohl (1986) and is described in detail there.
M. Benz et al./Int. J. Miner. Process. 44-45 (1996) 507-519
Limestone
10
1 Spin-number Fig.
u/v
1.Cut size dT as a function of the “spin-number”
I( / v.
This equation represents, on the one hand, the impact of classifier speed; the higher the rpms, the higher the circumferential velocity (~1, i.e. d, falls. On the other hand increasing the volumetric gas flow by changing the grinding gas pressure, increases the radial gas velocity (v) and dT rises. Earlier investigations have shown, that this equation describes the tendencies fairly up to 6-10 pm. However, particle diameters greater than 10 pm cannot be predicted at all. With these problems in mind an attempt was made to plot the cut size d, as a function of the “spin-number” (U/U>. Th’is number is defined as the ratio of the circumferential (u> to the radial (v) gas velocity. This approach was applied to data from classifiers. Muschelknautz and Brunner (1967) stated that the head loss in cyclones can be given as a function of u/u. In Fig. 1, dT is plotted as a function of u/v, with the gas-phase concentration p as a parameter. On a log-log scale the correlation between dT and u/v for a given gas-phase concentration p can be given by straight lines. Implying this number to the fluidized bed jet mill, the impact of the classifier is represented by the circumferential speed u, the gas pressure influences the radial gas velocity. Thus both operating parameters of the fluidized bed jet mill are incorporated in this number. 5.2. Particle size distributions To characterize the impact of comminution, the distribution of the particle sizes before and after the grinding step have to be characterized. Two different approaches are practical. One consists in picking typical values from the distribution curve as d,o, d,,, dgO, i.e. the diameters indicating that 10, 50 respectively 90% of the particles are smaller than the given diameter. These values offer good information on the range of particle
512
M. Benz et ul./
Int. J. Miner.
Process. 44-45
(1996) 507-519
sizes, however only limited knowledge of the shape of the particle size distribution can be inferred. The calculation of characteristic values such as d2,/d,, or Cd,, - d,o)/d,, gives more insight into the shape of the distribution. These values have the advantage that they are not model-based, no limitation from the range of application or from the assumptions of the model exists. Another approach is to include some empirical information in the data evaluation. In this case a formula can be given to describe the distribution function. The most common distributions in the literature are the GAUSS-, the Log-Normal- and the RRSB-distribution (Schubert, 1989). For particle collectives resulting from comminution, the RRSBdistribution (Rosin-Rammler-Sperling-Bennet) (Schubert, 1989) is frequently applied. Eq. 3 gives the percentage of particles greater than the particle d, as a function of two model parameters n’ and d’.
(3) With a few steps of mathematical =n’.lnd,-n’.lnd’
manipulation
Eq. 3 can be transformed
into Eq. 4.
(4)
Thus a linear dependency between ln(ln(lOO/R)) and lnd, can be established. Plotting the data with the appropriate axis grid easily leads to the parameters n’ as the slope and d’ with R set to 36.8%.
6. Results and discussion 6.1. Mean particle size
With the positive results for the dependency of dT as a function of u/v in mind, the idea came up to check if the mean particle diameter d,, of the fine particle fraction of the fluidized bed jet mill can be plotted in a similar way. In Fig. 2 a typical example of such a characteristic field of performance is shown. Plotted are the mean particle diameters d,, of limestone as a function of the “spin-number” u/v. Three different grinding pressures and three deflector wheel speeds were realized. Thus the “spin-number” u/v varied over one order of magnitude. It is obvious that, for a given grinding pressure, the “spin-number” increases with increasing deflector wheel speed, thus resulting in lower d,,-values. A higher grinding pressure shifts the line towards lower d,,-values for a constant u/v-value. The lines result from linear regression, done with the prefix of a common slope for all grinding pressures. Earlier data evaluation showed that the differences between the individual slopes appeared to be very small. The interpretation of the data for constant deflector wheel speed is more difficult, because of two competing effects. On the one hand, a higher grinding pressure with the appropriate Laval-nozzles leads to higher particle velocities. Therefore an extended
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
513
I
10 Limestone
. 3 . ??
. L .
.
.
-•-
4 bar
- -I-
6 bar
\ ‘\
??
k
.
??
\
+
b
‘.I
10 bar
\. . \ . -x\ \
‘*
‘1‘:
II
1 1
10 Spin-number
100 u/v
Fig. 2. Mean particle size as a function of the “spin-number”
U/ U.
amount of energy is available for crushing during particle-particle impact and this should lead to smaller particle sizes. On the other hand a higher grinding pressure causes a higher volumetric flow rate inside the mill, thus resulting in a higher carry-on stream of larger particles through the openings of the classifier. For grinding of limestone it seems that the increase in grinding energy is dominant especially at low deflector wheel speeds. At higher values, the sharp separation characteristic of the classifier takes over. However it has to be mentioned, that the analytical error is in the same order of magnitude as the differences between the single data points, this has to be kept in mind when interpreting these data. The most important fact that can be taken from Fig. 2 is that to achieve a given grinding task, changes in the grinding pressure and/or the deflector wheel speed can be made. For the user of the machine, it is important that a simple change of the classifier speed at a given grinding pressure can change the mean particle size decisively. This is important considering the operational costs of the fluidized bed jet mill. The main factor contributing to the costs is very often the high pressure gas consumption. Similar dependencies of the grinding result as a function of the “spin-number” u/u were found for parameters dN and the increase in specific surface area ASspez as indicated in Figs. 3 and 4. Especially for the &-values the differences between the data for different grinding pressures are relatively small and therefore the analytical error, resulting from sampling and data analysis, has to be kept in mind when interpreting the data. Again, the impact of varying grinding pressures for constant deflector wheel speeds cannot be predicted precisely because so far not enough data points are available to back up the evaluation of the slope of the line.
M. Benz et al./ ht. J. Miner. Process. 44-45 (1996) 507-519
514
100
Limestone
@
?? ‘
10
-e-
U . w, . 5 ’ .T
.‘h . I
.
4 bar
- -a-
.6 bar
- +
-10 bar
‘b> ib .
‘r ‘0
I,
1 1
10 Spin-number Fig. 3. &,-data
100 u/v
as function of the “spin-number”
u/v.
4.2. Particle size distribution
For many applications the whole particle size distribution is important. In most cases a narrow distribution is the aim. As mentioned above the dimensionless number g as the ratio of (d, - d&/d,, is an indicator for the sharpness of a particle size distribution.
+
’
,’
_J..‘- . I.
:
‘-‘;,I_
1
’ 1
I
,
_ -;
I111111
I
I I III
10 Spin-number
100 u/v
Fig. 4. Increase in specific surface area as function of the “spin-number”
u/o.
M. Benz et al./lnt. J. Miner. Process. 44-45 (1996) 507-519
515
I
10 Limestone
??
--m--6
??
..*.-lO
‘*.
4 bar bar bar
..!
1
10 Spin-number
100 u/v
Fig. 5. Parameter g as a function of the “spin-number” u/u.
For the limestone experiments, g ranged from 1.4 to 10. The smaller g, the narrower the distribution. In Fig. 5 the parameter g is given as function of u/v. Again each grinding pressure leads to an individual characteristic dependency. To achieve narrow distributions, a high “spin-number” u/v should be chosen. A higher classifier speed leads to a narrower distribution. Assuming that for the same “spin-number” u/v the performance of the classifier is similar, then a higher grinding pressure leads to a better result concerning the particle size distribution. Again no definite decision for the slope of the lines of constant classifier speed can be made. The (evaluation of the data with the method of RRSB showed results that are in accordance with the ones presented so far. In Figs. 6 and 7 the RRSB-parameters d and n’are given as a function of the “spin-number” u/v. d which is somehow comparable to an average particle size, indicates the same trends as d,, with problems as far as the impact of the grinding pressure on Cp for a given classifier speed is concerned. n’ characterizes a narrower distribution with a higher value. As demonstrated earlier with the parameter g, a higher “spin-number” u/v leads to narrower distributions. For a given u/v, the higher grinding pressure leads to greater n’-values. 6.3. Mathematical evaluation As the experiments so far have shown the “spin-number” u/v can be applied to characterize the cornmunition performance of a fluid&d bed jet mill very well. The next step was to develop mathematical equations for the demonstrated characteristic fields. It was indicated that in a log-log plot all the important parameters have a linear
516
M. Benz et ol./Int.
I
J. Miner. Process. 44-45 (1996) 507-519
Limestone
1
10
Spin-number Fig. 6. RRSB-parameter
100
u/v
d as function of the “spin-number”
dependency of the “spin-number” described with Eq. 5.
u/u.
u/u. A straight line in a log-log
scale can be
(5) 10
i
I
Limestone
L
-*
-4 bar bar
--m--6
--•-
0.1
-10 bar
I 1
10
Spin-number Fig. 7. RRSB-parameter
100
u/v
n’ as a function of the “spin-number”
u/u.
M. Benz et al./ ht. J. Miner. Process. 44-45 (1996) 507-519
517
lO[‘,,I~~,I”~I”‘I’,,~
,
/ Limestone
8 i
/ -1
/’ /’
1
I
6
-
4
-
/ Ji Ir
b
a ’Y
?? J. i
mm
??
.
??
??
2
-
4 bar 6 bar 10 bar
/f J’-
Ok”“““““““.” 0
Fig. 8. &,-data
2
versus d,,-prediction
4 d5,-Data, according
6 Brn to mathematical
8
10
evaluation.
Both values K, and K, can be taken from linear regression. As indicated in the figures., parallel lines for different pressures can be assumed within the range of analytical error. Therefore K, is the arithmetic mean value of the individual slopes K,. This assumption simplifies the further evaluation. So far with data available for 3 different pressures a linear dependency for K, from the pressure (p> can be assumed (Eq. 6). ti~o=(K,+K,-p)~(~)X5
(6)
K, and K, can be evaluated from a linear plot of K, versus p. The characteristic line for each grinding pressure can then be predicted. In Fig. 8 the &-data for limestone are plotted together with the &-data predicted according to Eq. 6. A 15% error is assumed for sampling and data analysis indicated by the error bars. Within the analytical error range a good fit of data and prediction is found. The same approach can be applied on the specific surface area and the parameters characterizing the shape of the distribution as g, d’ and n’. Only the values and the dimensions of the parameters change.
6.4. Remarks Similar experiments were performed with rubber chemicals. These compounds are easy to grind and the comminution is more or less a deagglomeration step. The rubber chemical displayed, besides the different particle size range and cornmunition pressure, the same trends. The “spin-number” u/u could be used in the same way for data evaluation.
M. Benz et al./ ht. J. Miner. Process. 44-45
518
(1996) 507-519
As possible errors during the data evaluation, the representative sampling has to be mentioned. Moreover the leakage of air - necessary for the flushing of the bearings of the deflector wheel - changes the actual flow of air through the deflector wheel. This impact on the “spin number” u/u could not be evaluated so far. 7. Summary A study of the impact of the operating parameters of a fluidized bed jet mill on the performance was done. Compounds of different grindability were tested, requiring comminution as well as deagglomeration. The results showed that the most important number to characterize the performance of the fluidized bed jet mill is the “spin-number” u/u, the ratio of the circumferential speed and the radial gas velocity at the classifier wheel. Identical u/u-values represent identical behavior of the classifier. In a log-log plot characteristic fields of performance can be established, where the impact of gas pressure and deflector wheel speed can be evaluated easily. The results showed that the change of the classifier speed has a stronger influence on the performance compared to changing the grinding pressure. This is important for an economical use of the fluidized bed jet mill, because the operational costs of the mill are often dominated by the consumption of high pressure gas. Mathematical equations were developed to enable a quick prediction of the milling performance at any given pressure and “spin number” u/v. The mathematical evaluation is valid for dsO, &, as well as for parameters characterizing the shape of a distribution as g, d and n’. 8. Nomenclature di:
5: U: l4:
r:
49 6,: r)F: n’, d’: d,: R: g: K,-K,:
Diameter indicating i% smaller than di Gas-phase concentration, kg product/kg grinding media Cut size for classifier Radial gas velocity at deflector wheel Circumferential velocity Radius of deflector wheel Particle and fluid density Fluid viscosity Parameters of RRSB-distribution Particle diameter Remaining amount for a given particle size Parameter indicating the shape of the distribution, (dm - d,,)/d,, Parameters for mathematical evaluation
Acknowledgements The authors would like to appreciate the assistance of Bayer Antwerpen and H. Schneider, W. Hijijk and R. Hammelrath for their careful performance of the experimental runs.
M. Benz et al./lnt.
J. Miner. Process. 44-45 (1996) 507-519
519
References Bohl, W., 1986. Technische Strijmungslehre. Vogel Buchverlag, Wiirzburg, pp. 182-194. Muschelknautz, E. and Brunner, K., 1967. Untersuchungen an Zyklonen. CIT, 39(9/10): 531-538. Schubert, H., 1989. Aufbereitung fester mineralischer Rohstoffe, Band I. VEB 1964, Deutscher Verlag fir Grundstoffmdustrie, Leipzig.