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An experimental study of the packing of a coal heap
187
Pow&r Technology, 68 (1991) 187-193
An experimental N. Standish, Depamnent
(Received
A. B. Yu* and Q. L. He
of Materials
January
study of the packing of a coal heap
Engineering,
The University
of Wollongong,
P.O. Box 1144,
Wollongong,
N.S. W. 2500
(Australia)
25, 1991; in revised form May 12, 1991)
Abstract
An experimental study of the packing of a coal heap has been carried out. The overall bulk density of a coal heap is considered as a function of a number of variables, viz. flow rate, conveyor belt speed, the height of the disengagement point of the conveyor belt, coal particle density, moisture content, the size of the heap and coal particle size distribution. The effects of the dimensionless numbers resulting from dimensional analysis on the overall packing density of a coal heap have been experimentally examined and analysed. The results are considered to be useful in developing an empirical method for the estimation of the packing density of a large stockpile in practice.
Introduction
The bulk density of coal in a stockpile is an important economic parameter in coal industry. The accurate determination of large amounts of coal is generally expected in operations such as coal stacking, reclaiming and loading of ships. But in practice the overall bulk density and the total weight of a coal stockpile are usually estimated by historical or laboratory data, which usually give unreliable results as discussed in [l]. It is therefore very useful to develop a more scientific method for the estimation of the overall bulk density and hence the total weight of a stockpile. Such a method may be developed by considering the packing of coal in a stockpile since, in principle, the bulk density of a coal stockpile should be a function of the coal properties and stacking parameters involved. However, the packing behaviour of granular materials in a stockpile, as a typical unconfined packing, is not clearly understood even on reference to the many studies that have been done on the confined packings [2, 31. The purpose of this paper is therefore to experimentally explore the (packing) process parameters affecting the bulk density of a coal heap and obtain some first-hand information on the packing of a coal stockpile.
*Author to whom correspondence should be addressed at: CSIRO Division of Mineral and Process Engineering, P.O. Box 312, Clayton, Vie. 3168, Australia.
0032-5910/91/$3.50
Experimental
A reduced scale model was set up to simulate the packing process of a coal heap, which is schematically illustrated in Fig. 1. The conveyor belt was driven by an electric motor and the speed of the conveyor belt was adjusted by changing the driving gear ratio. The height of the conveyor belt was adjusted by changing the height of the supporting frame but the angle of the conveyor belt was constant, as indicated in Fig. 1. In the experiments, coal was filled into a hopper through which it was discharged onto a conveyor belt. The flow rate was controlled by adjusting the opening of the hopper. To obtain large flow rates or avoid blockages in the hopper which occurred when the moisture content of coal was high, the coal was sometimes charged directly onto the conveyor belt manually. Though this may have introduced some error in the steady control of the flow
Fig. 1. A schematic
diagram of the packing of a coal heap.
0 1991 -
Elsevier Sequoia, Lausanne
188 rate, the resultant effect on the packing of a stockpile was not considered significant. The coal used was sieved into a number of size fractions, i.e. + 5600, - 5600 + 4000, + 4000 + 2500, - 2 5 0 0 + 5 0 0 , - 5 0 0 tzm. The amount of coal in each fraction for an experiment was predetermined according to the Rosin-Rammler function and mixed together. The coal feed was then mixed with a measured amount of water to obtain a predetermined value of moisture content. Manual mixing was used as it was felt to be more effective than a drum mixer. Samples were taken according to the conventional cone and quarter and riffle methods [6]. The particle size distribution and the moisture content of the coal used in the experiment were actually determined by analysis of the samples. This procedure was believed to be necessary, as the particle size distribution and the moisture content of the coal mixture were usually different from those predetermined. The well-mixed coal was finally charged to form a conical heap by the process described above. The total weight of a coal heap was measured by an electronic balance with an absolute error of less than 0.1 g. The volume of a coal heap should in theory be determined by contour plot as described in [4]. For simplicity, however, the size of a heap was determined by measuring its average length and height, as the shape of a heap was approximately conical. These measurements can lead to the determination of the average diameter, angle of repose and volume of a heap. The bulk density of a coal heap is by definition the ratio of its total weight to volume. The diameters of most of the coal heaps were greater than 1.4 m and the reproducibility of the experiment was better than 5%. In some experiments, a specially designed rectangular sampling divider was inserted from the top into a heap in the direction of the conveyor belt. Then the divider was filled with cotton rags. The coal outside the box was removed and the bottom was slid in and fixed under the divider. A 'slice' of the stockpile was obtained. This slice of stockpile was sampled by means of the 'tube sampling' technique after gently putting the divider onto the floor and removing its cover. The analysis of the samples would give us some information on the packing density distribution and size segregation in a coal heap.
(3) Height of disengagement point, H (L) (4) Height of a heap, h (L), or Diameter of a heap, D (L) (5) Particle density, pp (M L -3) (6) Particle size distribution ( - ) (7) Moisture content, H20% (8) Gravitational constant, g (L s -2) The size distribution of coal is usually represented by the Rosin-Rammler function [5, 6], which is written as [6] F(x) = 1 - exp[ - ln(2)( d-~.sf ]
(1)
where F(d) is the cumulative weight fraction passing size d, do.5 is the median of a distribution, and n is a parameter. Therefore, the size distribution of coal is determined by a pair of data (n, do.5). Two parameters were examined in the present study. They are: (1) overall bulk density, Pa (M L -3) and (2) angle of repose, a. In order to simplify the problem involved, the effects of some parameters on the packing of coal heaps may have to be ignored. It is known that the packing of particle mixtures is not affected by their absolute sizes if the weak forces among particles can be ignored [2, 3]. As commercial coal particles are usually not pulverized coal and the particle sizes are not very small, for simplicity do5 was here not taken into consideration. Similarly, the resistance of air to the movement of the particles, i.e. the drag force, was also ignored. The other parameter which has not been included in the present study is the width of the flow stream of particles on the conveyor belt, because of the difficulty in controlling it. Perhaps there are other parameters which may have been unknowingly ignored or not realized in the present model experiment. However, as far as the parameters affecting the packing of a coal heap are concerned, the overall bulk density, Pa, and the angle of repose, a, of a coal heap can be generally written as:
Pa =f(W, V, H, h, pp, n, HzO%, g)
(2)
a=f(W, V, H, h, pp, n, HzO%, g)
(3)
In order to make the results applicable to real situations and to determine the general dependence of the packing properties of a coal heap on these parameters, dimensional analysis was employed. In this way, eqns. (2) and (3) can be respectively transformed to:
Parameters considered
~'1 =f(~'3, ~r,, v,, vr, Ir7) For the experimental conditions described above, the parameters which may affect the packing behaviour of a coal heap are: (1) Flow rate, W (M s -1) (2) Conveyor speed, V (L s-1)
rs,
(4)
(5)
where ~'i (i=1, 2, ..., 7) are dimensionless numbers which are defined in Table 1. Therefore, the effects of the pertinent parameters on the bulk density of a
189 TABLE
1
Dimensionless
numbers
Dimensionless
number
and
their
variable
ranges
in the experiment
h
V5PP
gH
E
W?
0.03
0.2
2.0
0.2
1.5
0.3
0.8
300.0
2.0
15.0
VZ
cy
definition minimum
value
maximum
value
_
coal heap can be studied by examining the effects of the above dimensionless numbers on rr,, i.e. the ratio of bulk density to particle density, which is also referred to as packing density or packing fraction [2, 31. The variable range of each dimensionless number in the present experiment is also listed in Table 1. The details of the experimental data can be found in [l]. In the following, the effects of the above dimensionless numbers on the overall packing density of a coal heap will be examined respectively.
Results
and discussion
As expected, there is a packing density distribution in a stockpile. This distribution, like overall packing density, changes with packing conditions. Analysis of the sample slices of some coal heaps by the sampling technique described above revealed that similar packing density distribution patterns in coal heaps can be observed. Figure 2 shows a typical result. It should be noted that the maximum packing density may sometimes shift slightly from the centre of the bottom of a coal heap. This shift may coincide with the trajectory of falling coal but it was not verified in the present
Fig.
2. Packing
density
distribution
in a heap
H,O%
n
investigation. However, the result in Fig. 2 clearly indicates that there is a packing density distribution, although the present work is limited to the discussion of the relationship between overall packing density and packing process parameters of a coal heap. In a confined packing, the increase in compaction force usually increases the packing density [2,3]. When particles fall onto the top of the existing packing material, there are impactions. Increasing the dropping height or the conveyor belt speed increases the compaction force. However the resultant increase in packing density in unconfined packings depends not only on the absolute value of the compaction force but also on the direction of the compaction force. Increasing the conveyor belt speed will increase the tendency of particles to move horizontally, which decreases the packing density. r,, as defined in Table 1, is proportional to the conveyor belt speed and inversely proportional to the vertical speed. Therefore, increasing r3 will decrease the overall packing density, as shown in Fig. 3. As the size of a heap, i.e. the height of the heap, increases, the relative dropping height (= H-h), i.e. the difference between the heights of disengagement point and the heap, will decrease, so that the effect
(D = 1600, h = 74 mm):
(0)
sampling
points;
(-)
iso-packing
density
line.
190
0.56
o’55 5
0.56
0.53 -
0
q
11~0.565
.
k0.764
0.49 -
a
0.50
0.47 -
0.0
0.2
0.1
0.3
0.3
0.4
X3
Fig. 3. The effect density.
of dimensionless
number
rj on overall
packing
Fig. 5. The effect density.
0.5 E 4
of dimensionless
0.6
number
0.7
r4 on overall
0.6
packing
coal heap is clearly shown in Fig. 5. Actually, the good reproducibility of the present experiment may be exemplified by the results in Fig. 5, where each line resulted from a number of measurements. The dimensionless number rr5 can be written as:
0.66 -
where 0.64 -
0.62 ' 10
?T,=
'
I 20
Fig. 4. Overall packing packing (h/H = 1).
h density
I
I
I
30
40
50
vs.
heap
height
under
cascade
of the dropping compaction on overall packing density becomes smaller and smaller. On the other hand, increasing the size of a heap may increase the ‘internal’ compaction force and hence the overall packing density simply because of the force of gravity. This effect can be observed under cascading packing conditions as shown in Fig. 4, which was obtained when the height of the disengagement point was kept the same as the height of the coal heap. Therefore, increasing r4 may have two opposite effects. As the size of a heap increases, the decrease in the dropping compaction plays a main role so that the overall packing density decreases; after the size of the heap has increased to a certain value, the increase in the ‘gravity compaction’ becomes more important, so that the overall packing density increases. The effect of rd on the overall packing density of a
H5’=PPdn W
It is obvious that an increase in r5 can be obtained by increasing the values of either r3 or n-8. Increasing r3 decreases overall packing density (see Fig. 3). However, in the experiment, the effect of each dimensionless number on packing density was studied while other dimensionless numbers were kept constant. Therefore increasing r5 can only be obtained by increasing rr8. The latter can be realized by increasing the height of the disengagement point, H, or decreasing the flow rate, W. Increasing the height will increase the compaction force referred to earlier, and a decrease in the flow rate implies a decrease in the loss of the compaction force, as the interactions among the particles in a stream may be reduced. As a result, the overall packing density will increase with increasing T, (or 7r8 as noted above), which can be seen in Fig. 6. The packing density in a confined packing is affected by particle size distribution [2, 31. Theoretically, the packing density of particles with the Rosin-Rammler size distribution is dependent on the value of n only, and the smaller the value of n, the higher the packing density [7,8]. However, in practice, due to the existence
191
0
100
200 K
Fig. 6. The effect density.
300
of dimensionless
number
r5 on overall
packing
0.56
0.54 A .r 0.52
f a
0.50
-
0.46
0.46
0.44 0.0
Fig. 7. The effect density.
0.5
1.0 It 6
of dimensionless
4
8
12
16
Moisture Content,%
0.56
g
0
5
1.5
number
rb on overall
2.0
packing
of the sub-size distributions, usually there is an intermediate value of n giving maximum packing density, as discussed in [9, 131. Figure 7 shows the effect of distribution parameter n on the overall packing density. It is evident from Fig. 7 that the overall packing density increases and then, after a certain value, decreases with increasing II. This result is similar to that obtained under confined packing conditions [13]. Therefore, there may exist a general agreement between the confined and unconfined packings. This agreement can be further examined in the discussion of the effect of moisture content on packing density. As shown in Fig. 8, the overall packing density of a coal heap is strongly affected by the moisture content of coal. The packing density decreases as mois-
Fig. 8. The effect density.
of dimensionless
number
QT,on overall
packing
ture content increases to -9%, and then increases. This result is very similar to the results reported in [lo] for confined packing. The effect of moisture content on packing density results from the formation of agglomerates and the change of friction force among the particles, as demonstrated in [3, lo]. However, another factor which should be considered here is the mechanism of the formation of a coal heap. It was observed in the present study that as the size of the heap increases, the avalanching of particles on the heap surface [ll] plays a more and more important role in the formation of a heap. Similar to the increase in conveyor belt speed, the avalanche may loosen the coal heap. Increasing the moisture content can increase the cohesive force among the particles, which results in an increase in avalanche size so that the overall packing density decreases. However, if the moisture content is higher than a certain value, the cohesive force among particles is so high that the failure zone and avalanche can not be easily formed, and the overall packing density increases. This consideration, though obtained from unconfined packing, may also be applicable to confined packing. However, this should be examined with further experiments. By inspection of all the above figures, it is evident that the most significant factor affecting the overall packing density is moisture content. This result is clearly demonstrated in Fig. 9, in which all the experimental results are included. As mentioned above, another parameter examined in the present work is the repose angle of a coal heap. It has been reported that the angle of repose of a coal heap is mainly affected by moisture content [12]. The present results are in good agreement with the previous results. As shown in Fig. 10, for any given particle size
192
Conclusions
0.4 1 0
I 4
6
12
16
Moisture Content, % Fig. 9. The effect of moisture content on overall packing density.
55 -
8 kil .$j 50 P 3 P
45 -
& !z.
The overall packing density and angle of repose of a conical heap of coal is affected by a number of factors, such as the charging method, the heap size, the material properties and the moisture content. Among the parameters considered in this investigation, the most significant is the moisture content. Although the packing of a coal heap is a case of unconfined packing, similarities between confined and unconfined packings can be observed, e.g. the effects of particle size distribution and moisture content on packing density are similar to each other. This similarity suggests that in both packings the overall packing density is governed by the same mechanisms, such as the compaction, deposition, size segregation etc., although the relative roles played by each mechanism in the two packings may differ. This consideration should be further investigated, since the present investigation is limited to the relatively simple packing phenomena of a stockpile. The effects of the packing parameters represented by some dimensionless numbers on the overall packing density and the angle of repose of a conical coal heap have been established in this investigation. In principle, the results presented in this paper should be generally applicable to stockpile systems, irrespective of the granular materials involved. In fact, these results have been formulated as given in [14]. Based on these formulae, it may be possible to develop a general empirical method for the estimation of the overall packing density of an industrial stockpile.
40 -
Acknowledgement 35 1
I
I
I
I
0
5
10
15
20
Moisture Content,% Fig. 10. The effect of moisture content different particle size distributions.
on repose
angle for
distribution, increasing the moisture content increases the angle of repose to a maximum value, and any further increase in moisture content may decrease the angle of repose. However, it appears that the effect of particle size distribution on repose angle should be considered, as Fig. 10 indicates that the increase in the angle of repose with the moisture content depends on the particle size distribution involved. Other dimensionless numbers may also have some effects on the repose angle, but compared with the strong effects of moisture content and particle size distribution, all of them can be ignored without much error.
The assistance of the Department of Primaty Industries and Energy in providing funds through a NERDDP grant is gratefully acknowledged. One of the authors (A. B. Yu) is also grateful to CSIRO for providing a postdoctoral fellowship.
References N. Standish, 7Jre Bulk Density of Australian Export Coal, Final Research Report to NERDDP, 1990. W. A. Gray, The Packing of Solid Particles, Chapman and Hall, London, 1968. R. M. German, Particle Packing Characteristics, Metal Powder Industries Federation, Princeton, NJ, 1989. M. H. Elfick, J. G. Fryer, R. C. Brinker and P. R. Wolf, Elementaty Surveying, 7th edn., Harper and Row, Sydney, 1987. G. Herdan, Small Particle Statistics, 2nd edn., Buttenvorths, London, 1960. T. Allen, Particle Size Measurement, 3rd edn., Chapman and Hall, London, 1981.
193 7 T. Itoh, Y. Wanibe and H. Sakao, J. Jpn. Insr. Metals, 50 (1986) 740. 8 A. B. Yu and N. Standish, Proc. 2nd World Congr. Particle Technol., Sept. 19-22, 1990, Kyoto, Japan, Vol. 1, pp. 95-101. 9 A. B. Yu and N. Standish, A Study of the Packing of Panicles with a Mimre Size Distribution: I & II, Research Report, Dept. of Mat. Eng., Univ. of Wollongong, 1990. 10 Y. Lu, M. Met. Thesis, Dept. of Materials Engineering, University of Wollongong, 1989.
11 J. A. Drahun
and
J. Bridgwater,
Powder
TechnoL,
36 (1983)
39. 12 E. F. Wolf and H. L. Hohenleiten, Trans. Am. Sot. Mech. Engm, 67 (1945) 585. 13 N. Standish, A. B. Yu and R. P. Zou, Powder Technol., 68 (1991) 175. 14 A. B. Yu and (1991).
N. Standish,
Bulk Solids
Handling,
II, No. 3
Pow&r Technology, 68 (1991) 187-193
An experimental N. Standish, Depamnent
(Received
A. B. Yu* and Q. L. He
of Materials
January
study of the packing of a coal heap
Engineering,
The University
of Wollongong,
P.O. Box 1144,
Wollongong,
N.S. W. 2500
(Australia)
25, 1991; in revised form May 12, 1991)
Abstract
An experimental study of the packing of a coal heap has been carried out. The overall bulk density of a coal heap is considered as a function of a number of variables, viz. flow rate, conveyor belt speed, the height of the disengagement point of the conveyor belt, coal particle density, moisture content, the size of the heap and coal particle size distribution. The effects of the dimensionless numbers resulting from dimensional analysis on the overall packing density of a coal heap have been experimentally examined and analysed. The results are considered to be useful in developing an empirical method for the estimation of the packing density of a large stockpile in practice.
Introduction
The bulk density of coal in a stockpile is an important economic parameter in coal industry. The accurate determination of large amounts of coal is generally expected in operations such as coal stacking, reclaiming and loading of ships. But in practice the overall bulk density and the total weight of a coal stockpile are usually estimated by historical or laboratory data, which usually give unreliable results as discussed in [l]. It is therefore very useful to develop a more scientific method for the estimation of the overall bulk density and hence the total weight of a stockpile. Such a method may be developed by considering the packing of coal in a stockpile since, in principle, the bulk density of a coal stockpile should be a function of the coal properties and stacking parameters involved. However, the packing behaviour of granular materials in a stockpile, as a typical unconfined packing, is not clearly understood even on reference to the many studies that have been done on the confined packings [2, 31. The purpose of this paper is therefore to experimentally explore the (packing) process parameters affecting the bulk density of a coal heap and obtain some first-hand information on the packing of a coal stockpile.
*Author to whom correspondence should be addressed at: CSIRO Division of Mineral and Process Engineering, P.O. Box 312, Clayton, Vie. 3168, Australia.
0032-5910/91/$3.50
Experimental
A reduced scale model was set up to simulate the packing process of a coal heap, which is schematically illustrated in Fig. 1. The conveyor belt was driven by an electric motor and the speed of the conveyor belt was adjusted by changing the driving gear ratio. The height of the conveyor belt was adjusted by changing the height of the supporting frame but the angle of the conveyor belt was constant, as indicated in Fig. 1. In the experiments, coal was filled into a hopper through which it was discharged onto a conveyor belt. The flow rate was controlled by adjusting the opening of the hopper. To obtain large flow rates or avoid blockages in the hopper which occurred when the moisture content of coal was high, the coal was sometimes charged directly onto the conveyor belt manually. Though this may have introduced some error in the steady control of the flow
Fig. 1. A schematic
diagram of the packing of a coal heap.
0 1991 -
Elsevier Sequoia, Lausanne
188 rate, the resultant effect on the packing of a stockpile was not considered significant. The coal used was sieved into a number of size fractions, i.e. + 5600, - 5600 + 4000, + 4000 + 2500, - 2 5 0 0 + 5 0 0 , - 5 0 0 tzm. The amount of coal in each fraction for an experiment was predetermined according to the Rosin-Rammler function and mixed together. The coal feed was then mixed with a measured amount of water to obtain a predetermined value of moisture content. Manual mixing was used as it was felt to be more effective than a drum mixer. Samples were taken according to the conventional cone and quarter and riffle methods [6]. The particle size distribution and the moisture content of the coal used in the experiment were actually determined by analysis of the samples. This procedure was believed to be necessary, as the particle size distribution and the moisture content of the coal mixture were usually different from those predetermined. The well-mixed coal was finally charged to form a conical heap by the process described above. The total weight of a coal heap was measured by an electronic balance with an absolute error of less than 0.1 g. The volume of a coal heap should in theory be determined by contour plot as described in [4]. For simplicity, however, the size of a heap was determined by measuring its average length and height, as the shape of a heap was approximately conical. These measurements can lead to the determination of the average diameter, angle of repose and volume of a heap. The bulk density of a coal heap is by definition the ratio of its total weight to volume. The diameters of most of the coal heaps were greater than 1.4 m and the reproducibility of the experiment was better than 5%. In some experiments, a specially designed rectangular sampling divider was inserted from the top into a heap in the direction of the conveyor belt. Then the divider was filled with cotton rags. The coal outside the box was removed and the bottom was slid in and fixed under the divider. A 'slice' of the stockpile was obtained. This slice of stockpile was sampled by means of the 'tube sampling' technique after gently putting the divider onto the floor and removing its cover. The analysis of the samples would give us some information on the packing density distribution and size segregation in a coal heap.
(3) Height of disengagement point, H (L) (4) Height of a heap, h (L), or Diameter of a heap, D (L) (5) Particle density, pp (M L -3) (6) Particle size distribution ( - ) (7) Moisture content, H20% (8) Gravitational constant, g (L s -2) The size distribution of coal is usually represented by the Rosin-Rammler function [5, 6], which is written as [6] F(x) = 1 - exp[ - ln(2)( d-~.sf ]
(1)
where F(d) is the cumulative weight fraction passing size d, do.5 is the median of a distribution, and n is a parameter. Therefore, the size distribution of coal is determined by a pair of data (n, do.5). Two parameters were examined in the present study. They are: (1) overall bulk density, Pa (M L -3) and (2) angle of repose, a. In order to simplify the problem involved, the effects of some parameters on the packing of coal heaps may have to be ignored. It is known that the packing of particle mixtures is not affected by their absolute sizes if the weak forces among particles can be ignored [2, 3]. As commercial coal particles are usually not pulverized coal and the particle sizes are not very small, for simplicity do5 was here not taken into consideration. Similarly, the resistance of air to the movement of the particles, i.e. the drag force, was also ignored. The other parameter which has not been included in the present study is the width of the flow stream of particles on the conveyor belt, because of the difficulty in controlling it. Perhaps there are other parameters which may have been unknowingly ignored or not realized in the present model experiment. However, as far as the parameters affecting the packing of a coal heap are concerned, the overall bulk density, Pa, and the angle of repose, a, of a coal heap can be generally written as:
Pa =f(W, V, H, h, pp, n, HzO%, g)
(2)
a=f(W, V, H, h, pp, n, HzO%, g)
(3)
In order to make the results applicable to real situations and to determine the general dependence of the packing properties of a coal heap on these parameters, dimensional analysis was employed. In this way, eqns. (2) and (3) can be respectively transformed to:
Parameters considered
~'1 =f(~'3, ~r,, v,, vr, Ir7) For the experimental conditions described above, the parameters which may affect the packing behaviour of a coal heap are: (1) Flow rate, W (M s -1) (2) Conveyor speed, V (L s-1)
rs,
(4)
(5)
where ~'i (i=1, 2, ..., 7) are dimensionless numbers which are defined in Table 1. Therefore, the effects of the pertinent parameters on the bulk density of a
189 TABLE
1
Dimensionless
numbers
Dimensionless
number
and
their
variable
ranges
in the experiment
h
V5PP
gH
E
W?
0.03
0.2
2.0
0.2
1.5
0.3
0.8
300.0
2.0
15.0
VZ
cy
definition minimum
value
maximum
value
_
coal heap can be studied by examining the effects of the above dimensionless numbers on rr,, i.e. the ratio of bulk density to particle density, which is also referred to as packing density or packing fraction [2, 31. The variable range of each dimensionless number in the present experiment is also listed in Table 1. The details of the experimental data can be found in [l]. In the following, the effects of the above dimensionless numbers on the overall packing density of a coal heap will be examined respectively.
Results
and discussion
As expected, there is a packing density distribution in a stockpile. This distribution, like overall packing density, changes with packing conditions. Analysis of the sample slices of some coal heaps by the sampling technique described above revealed that similar packing density distribution patterns in coal heaps can be observed. Figure 2 shows a typical result. It should be noted that the maximum packing density may sometimes shift slightly from the centre of the bottom of a coal heap. This shift may coincide with the trajectory of falling coal but it was not verified in the present
Fig.
2. Packing
density
distribution
in a heap
H,O%
n
investigation. However, the result in Fig. 2 clearly indicates that there is a packing density distribution, although the present work is limited to the discussion of the relationship between overall packing density and packing process parameters of a coal heap. In a confined packing, the increase in compaction force usually increases the packing density [2,3]. When particles fall onto the top of the existing packing material, there are impactions. Increasing the dropping height or the conveyor belt speed increases the compaction force. However the resultant increase in packing density in unconfined packings depends not only on the absolute value of the compaction force but also on the direction of the compaction force. Increasing the conveyor belt speed will increase the tendency of particles to move horizontally, which decreases the packing density. r,, as defined in Table 1, is proportional to the conveyor belt speed and inversely proportional to the vertical speed. Therefore, increasing r3 will decrease the overall packing density, as shown in Fig. 3. As the size of a heap, i.e. the height of the heap, increases, the relative dropping height (= H-h), i.e. the difference between the heights of disengagement point and the heap, will decrease, so that the effect
(D = 1600, h = 74 mm):
(0)
sampling
points;
(-)
iso-packing
density
line.
190
0.56
o’55 5
0.56
0.53 -
0
q
11~0.565
.
k0.764
0.49 -
a
0.50
0.47 -
0.0
0.2
0.1
0.3
0.3
0.4
X3
Fig. 3. The effect density.
of dimensionless
number
rj on overall
packing
Fig. 5. The effect density.
0.5 E 4
of dimensionless
0.6
number
0.7
r4 on overall
0.6
packing
coal heap is clearly shown in Fig. 5. Actually, the good reproducibility of the present experiment may be exemplified by the results in Fig. 5, where each line resulted from a number of measurements. The dimensionless number rr5 can be written as:
0.66 -
where 0.64 -
0.62 ' 10
?T,=
'
I 20
Fig. 4. Overall packing packing (h/H = 1).
h density
I
I
I
30
40
50
vs.
heap
height
under
cascade
of the dropping compaction on overall packing density becomes smaller and smaller. On the other hand, increasing the size of a heap may increase the ‘internal’ compaction force and hence the overall packing density simply because of the force of gravity. This effect can be observed under cascading packing conditions as shown in Fig. 4, which was obtained when the height of the disengagement point was kept the same as the height of the coal heap. Therefore, increasing r4 may have two opposite effects. As the size of a heap increases, the decrease in the dropping compaction plays a main role so that the overall packing density decreases; after the size of the heap has increased to a certain value, the increase in the ‘gravity compaction’ becomes more important, so that the overall packing density increases. The effect of rd on the overall packing density of a
H5’=PPdn W
It is obvious that an increase in r5 can be obtained by increasing the values of either r3 or n-8. Increasing r3 decreases overall packing density (see Fig. 3). However, in the experiment, the effect of each dimensionless number on packing density was studied while other dimensionless numbers were kept constant. Therefore increasing r5 can only be obtained by increasing rr8. The latter can be realized by increasing the height of the disengagement point, H, or decreasing the flow rate, W. Increasing the height will increase the compaction force referred to earlier, and a decrease in the flow rate implies a decrease in the loss of the compaction force, as the interactions among the particles in a stream may be reduced. As a result, the overall packing density will increase with increasing T, (or 7r8 as noted above), which can be seen in Fig. 6. The packing density in a confined packing is affected by particle size distribution [2, 31. Theoretically, the packing density of particles with the Rosin-Rammler size distribution is dependent on the value of n only, and the smaller the value of n, the higher the packing density [7,8]. However, in practice, due to the existence
191
0
100
200 K
Fig. 6. The effect density.
300
of dimensionless
number
r5 on overall
packing
0.56
0.54 A .r 0.52
f a
0.50
-
0.46
0.46
0.44 0.0
Fig. 7. The effect density.
0.5
1.0 It 6
of dimensionless
4
8
12
16
Moisture Content,%
0.56
g
0
5
1.5
number
rb on overall
2.0
packing
of the sub-size distributions, usually there is an intermediate value of n giving maximum packing density, as discussed in [9, 131. Figure 7 shows the effect of distribution parameter n on the overall packing density. It is evident from Fig. 7 that the overall packing density increases and then, after a certain value, decreases with increasing II. This result is similar to that obtained under confined packing conditions [13]. Therefore, there may exist a general agreement between the confined and unconfined packings. This agreement can be further examined in the discussion of the effect of moisture content on packing density. As shown in Fig. 8, the overall packing density of a coal heap is strongly affected by the moisture content of coal. The packing density decreases as mois-
Fig. 8. The effect density.
of dimensionless
number
QT,on overall
packing
ture content increases to -9%, and then increases. This result is very similar to the results reported in [lo] for confined packing. The effect of moisture content on packing density results from the formation of agglomerates and the change of friction force among the particles, as demonstrated in [3, lo]. However, another factor which should be considered here is the mechanism of the formation of a coal heap. It was observed in the present study that as the size of the heap increases, the avalanching of particles on the heap surface [ll] plays a more and more important role in the formation of a heap. Similar to the increase in conveyor belt speed, the avalanche may loosen the coal heap. Increasing the moisture content can increase the cohesive force among the particles, which results in an increase in avalanche size so that the overall packing density decreases. However, if the moisture content is higher than a certain value, the cohesive force among particles is so high that the failure zone and avalanche can not be easily formed, and the overall packing density increases. This consideration, though obtained from unconfined packing, may also be applicable to confined packing. However, this should be examined with further experiments. By inspection of all the above figures, it is evident that the most significant factor affecting the overall packing density is moisture content. This result is clearly demonstrated in Fig. 9, in which all the experimental results are included. As mentioned above, another parameter examined in the present work is the repose angle of a coal heap. It has been reported that the angle of repose of a coal heap is mainly affected by moisture content [12]. The present results are in good agreement with the previous results. As shown in Fig. 10, for any given particle size
192
Conclusions
0.4 1 0
I 4
6
12
16
Moisture Content, % Fig. 9. The effect of moisture content on overall packing density.
55 -
8 kil .$j 50 P 3 P
45 -
& !z.
The overall packing density and angle of repose of a conical heap of coal is affected by a number of factors, such as the charging method, the heap size, the material properties and the moisture content. Among the parameters considered in this investigation, the most significant is the moisture content. Although the packing of a coal heap is a case of unconfined packing, similarities between confined and unconfined packings can be observed, e.g. the effects of particle size distribution and moisture content on packing density are similar to each other. This similarity suggests that in both packings the overall packing density is governed by the same mechanisms, such as the compaction, deposition, size segregation etc., although the relative roles played by each mechanism in the two packings may differ. This consideration should be further investigated, since the present investigation is limited to the relatively simple packing phenomena of a stockpile. The effects of the packing parameters represented by some dimensionless numbers on the overall packing density and the angle of repose of a conical coal heap have been established in this investigation. In principle, the results presented in this paper should be generally applicable to stockpile systems, irrespective of the granular materials involved. In fact, these results have been formulated as given in [14]. Based on these formulae, it may be possible to develop a general empirical method for the estimation of the overall packing density of an industrial stockpile.
40 -
Acknowledgement 35 1
I
I
I
I
0
5
10
15
20
Moisture Content,% Fig. 10. The effect of moisture content different particle size distributions.
on repose
angle for
distribution, increasing the moisture content increases the angle of repose to a maximum value, and any further increase in moisture content may decrease the angle of repose. However, it appears that the effect of particle size distribution on repose angle should be considered, as Fig. 10 indicates that the increase in the angle of repose with the moisture content depends on the particle size distribution involved. Other dimensionless numbers may also have some effects on the repose angle, but compared with the strong effects of moisture content and particle size distribution, all of them can be ignored without much error.
The assistance of the Department of Primaty Industries and Energy in providing funds through a NERDDP grant is gratefully acknowledged. One of the authors (A. B. Yu) is also grateful to CSIRO for providing a postdoctoral fellowship.
References N. Standish, 7Jre Bulk Density of Australian Export Coal, Final Research Report to NERDDP, 1990. W. A. Gray, The Packing of Solid Particles, Chapman and Hall, London, 1968. R. M. German, Particle Packing Characteristics, Metal Powder Industries Federation, Princeton, NJ, 1989. M. H. Elfick, J. G. Fryer, R. C. Brinker and P. R. Wolf, Elementaty Surveying, 7th edn., Harper and Row, Sydney, 1987. G. Herdan, Small Particle Statistics, 2nd edn., Buttenvorths, London, 1960. T. Allen, Particle Size Measurement, 3rd edn., Chapman and Hall, London, 1981.
193 7 T. Itoh, Y. Wanibe and H. Sakao, J. Jpn. Insr. Metals, 50 (1986) 740. 8 A. B. Yu and N. Standish, Proc. 2nd World Congr. Particle Technol., Sept. 19-22, 1990, Kyoto, Japan, Vol. 1, pp. 95-101. 9 A. B. Yu and N. Standish, A Study of the Packing of Panicles with a Mimre Size Distribution: I & II, Research Report, Dept. of Mat. Eng., Univ. of Wollongong, 1990. 10 Y. Lu, M. Met. Thesis, Dept. of Materials Engineering, University of Wollongong, 1989.
11 J. A. Drahun
and
J. Bridgwater,
Powder
TechnoL,
36 (1983)
39. 12 E. F. Wolf and H. L. Hohenleiten, Trans. Am. Sot. Mech. Engm, 67 (1945) 585. 13 N. Standish, A. B. Yu and R. P. Zou, Powder Technol., 68 (1991) 175. 14 A. B. Yu and (1991).
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Bulk Solids
Handling,
II, No. 3