The porosity of systems consisting of layers of different particles

PowderTechnology. (1977) 123-138 @ Elsevier Sequoia S-A., Lausanne - Printed in the Netherlands

The Porosity

of Systems

Consisting

123

of Layers of Different

Particles

MARK PROPSTER* Department of Chemical Engineering BuffaIo. Buffalo. NY 14214 (US-A.)

JULIAN

and Center for Process

Metallurgy.

State

Uniuersity

of New

York

at

SZEKELY

Department of Materials Science and Engineering. Auenue, Cambridge. Mass_ 02I39 (US_A_)

Massachusetts

Institute

of Technology.

77 Massachusetts

(Received September 2’7, 19’76; in revised form January 4, 19’7’7)

SUMMARY

q

Experimental measurements are reported on the spatial dependence of the local void fraction for systems where particles of different size form horizontal layers in packed

Cl

ORE

COKE

beds_ This problem is of practical importance in estimating the flow resistance of blast furnace burdens_ It was found that marked local minima in porosity occur in the interfacial region when a layer of smaller particles is placed upon a bed of larger spheres. In contrast, the local

minima in porosity are much less marked when larger particles are placed on a bed of smaller spheres. From a technological viewpoint, the most important finding of the work is that the penetration of smaller particles into the interstices of the larger spheres occurs readily when the particle size ratio exceeds about

two. Under these conditions the interfacial regions will contribute appreciably to the overall flow resistance_

1. INTRODUCTION

In recent years there has been a growing interest in systems in which particulate solids contained in packed beds are contacted with moving gas streams. As a result of work by Jeschar et at. [l], Szekely et al. [Z - 41 and others [5,6], it has been realized that the gas

flow through these systems is generally nonuniform and that the gas flow distribution is *Present address: Owens Coming Fiberglas, Technical Center, GranviIle, Ohio 43023.

CENTER

WZLL

Fig. 1. Sketch of the layered particle distribution the stack region of the iron blast furnace.

in

markedly affected by local variations in the porosity of the bed. A particularly interesting and important example of these systems is the iron blast furnace, the stack region of which, sketched in Fig_ 1, contains alternating layers of coke, iron ore (pellets) and other charge materials, which in general differ in size, shape and porosity. It has been shown that the regions which separate these adjacent layers may pIay an important role in affecting both the overall resistance to flow and the detailed flow pattern through the system [7] _ The main motivation for the work which is described in this paper has been to obtain a better cnderstanding of the structure of this interfacial region, located between adjacent layers of particles, so that a rational representation may be developed for the flow resistance of these systems. While a great deal of work has been done on the structure of homogeneous particle

assemblies, the particular topic described above has received very little attention up to the present.

124 X good general review of the literature on the structure of packed beds was presented by Haughey and Beveridge [S] , which covers both systems composed of regularly packed uniformly sized spheres and the more general case of randomly packed beds containing particles of various sizes and shapes. Much of the effort aimed at studying packed beds has been devoted to randomly packed spheres [9 - 13]In recent years the interest has been focused on the local variations in the void fraction of packed beds, which are of particular interest in the development of correlations for transfer coefficients for flow through randomly packed beds [14] _ Local ordering in the orientation of the particles which make up the packed bed is generally thought to be the cause of local differences in bed propertiesWall and end effects have been shown to cause local variation in voidage of packed bedsThe radial distribution of porosity has been investigated for uniformly sized spheres [ 15, 161 and other shaped material 11’7, X3] _ These local variations in porosity mere found to estend to distances up to say 5 particle diameters from the boundary surface depending on the co!umn to particle diameter ratio and the particle size and shape. _A further complication in determining the voidage of a packed bed is introduced when the particle assemblage is composed of differently sized particles. The fmt attempt at quantifying this effect was made by Furnas [ 191, who studied the mixture of particles of two clifferent sizes. In this now classical paper, the overall bed voidage was found to be less for the mixture than for the individual components; moreover, the overall voidage eshibited minima, for particular compositions, depending on the particle size ratio- As expected, the larger the disparity in sizes, the lower will the numerical values of these minima_ These considerations were recently extended to th me-component systems, with qualitatively similar results [20] _ While this previously cited work of Fumas and of Jeschar et ai.dealing with the bulk properties of particle mistures is helpful in indicating that local porosity minima may e_xist in the regions that separate adjacent layers of different particles, these earlier measurements do not provide a quantitative basis for tackling this problem_

Fig. 2. Sketch of the appa=tus.

OBSCm __

Fig. 3. Sketch of the mold unit.

A program of research was then undertaken in order to characterize the local porosity variations in systems, containing layers of different particles, motivated by the relevance of this problem to a broad range of materials processing operations, where these effects may have a marked influence on spatially distributed resistance to gas flow and hence on the performance of the processing unit.

2. EXPERIMENTAL

PROGRAM

The principle of the experimental technique was adopted from that developed by Benenati and Brosilow [ 153 _ 'The void spaces between the lead spheres of a (non-uniformly) packed bed contained in a mold were filled with a resin, which was then allowed to cure. By the sectioning of the solid matrix obtained

125

and by the weighing of the appropriate sections, the local porosities could be obtained. A schematic sketch of the apparatus is shown in Fig_ 2, which is seen to consist of a belljar, enclosing a mold unit_ The belljar can be evacuated by the use of a vacuum pump and the resin may be drawn into the evacuated mold unit, through a suitable connection from the resin reservoir_ The

detailed

layout

of the mold

unit

is

shown in Fig 3, where it is seen that this consisted of a cylindrical vessel, some 25 cm high and 14 cm id. The lower section of the mold unit, which contained the packing support and the flow straightening section, was fitted with two screw clamps to the upper column. The actual esperimental procedure consisted of pouring uniformly sized solid particles through a tube 5 cm in diameter in order to minimize bridging, so that the mold was filled to a given height. The charge was then carefully levelled by means of a lid or a heavy screen. This was then followed by placing another layer of solid particles, of different size, above the initial charge. The thickness of each individual layer ranged from about 15 to 30 particle diameters_ Once the mold was filled with the solids, the system was evacuated and then the resin was allowed to flow from the reservoir through the flow straightening chamber, into the mold unit. The flow of the resin was so regulated that only the air was displaced, and that the packing arrangement itself was not disturbed_ Once the system was filled with the resin, the valves were closed and the resin was allowed to cure for 24 hours. After curing, the resin-particulate composite was removed from the system and prepared for machining in a standard latheIn all the esperiments, except for those where the wall effect was studied, preliminary cuts were made to eliminate the wall and the end effects. This amounted to machining off material corresponding to at least 5 particle diameters from the outer, radial surface and material corresponding to some 5 particle diameters distance from the base support and the free surface_ The actual experiment entailed taking axial slices off the solid lead-resin composite cylinder in stages. The weight and length of the cylinder, of constant known diameter, was measured after each machining cut. In this

manner the average density phi of each slice removed by the machining operation could be determined_ By simple material balance, the average density may be shown to be related to the average voidage of the slice removed by the following: PL -PM

E c-c vR

_

%I The

PL

depth

-PR

of each

slice

or cut

was main-

tained as small as possible in order to get as close to the point or local porosity as possible, without sacrificing accuracy of the readings. The length and diameter of the remaining cylinder were measured on a micrometer table capable of reading to + 0.00025 mm and the mold was weighed on a balance with a 5 mg sensitivity. In preparing the uniformly sized spherical lead shot for the experiment, it was thoroughly cleansed to improve the adherence of the resin. The lead shot was purchased from National Lead Company, and had a density of 11.33 g/cm3; the particle sizes used in the investigation were O-13, 0.38, 0.48 and 0.76 cm, which provided a six-fold range in particle size difference in the layered system.

3. RESULTS

In the following Figs. 4 - 20 we shall present a-selection of the esperimental results. 3.1 Homogeneous systems Figure 4 shows a plot of the radial variation of the void fraction for a uniformly packed cylindrical bed. It is seen that very marked local changes occur in the void fraction in the vicinity of the wall for distances up about 3 - 5 particle diameters. The findings reported in Fig. 4 are almost identical to those described by Benenati and Brosilow [ 15 ] , whose results are shown in the continuous curve, which also appears on this graph. The very close agreement between these two sets of independent measurements may be regarded as proof of the validity of the experimental technique employed here. The behavior shown in Fig. 4 is of some practical importance in describing the flow of gas through packed bed reactors, where the column diameter is not large compared with the particle diameter; as shown in recent

125 '0,

Fig_ 4_ Radia! porosity diameters_

of a uniform

bed as a function

of distance from the container

Fig_5. Local porosity of a horizontally and in particIe diameters composing

layered packed bed as a function the base layer (I? = 3.0).

articles, under these conditicns tions in bed porosity may give

the local variarise to appreciable flow maldistribution, even for seemingly uniformly packed beds_ 3.2 Horizontally layered system Figures 56 and 7 show the behavior of systems where a layer of smaller particles is placed upon a layer of larger particles, for a progressively increasing dispariw in particle

wall. expressed

in particle

of distance expressed in miliimeters

size. In all these plots the ordinates denote the local porosity, while the abscissae are both the absolute values of the vertical distance in millimeters, and these distances expressed as fractions of the particle diameter, composing the base layer, D&,e. Figures 8 and 9 show photographs of the sections that correspckd to the appropriately numbered positions in Figs. 5 and 6, respectively. Inspection of these figures indicates that

127

==3*0 0

too

25

50

75

Go

I25 L :nm,

150

175

200

225

Fig. 6. Local porosity of a horizontally layered packed bed as a function and in particle diameters composing the base layers (R = 3.80).

there exist very marked local variations in the porosity of the interfacial regions, the depth of which, for most of the cases studied, ranged from about 2 to 6 particle diameters (of the base layer)_ It is seen that for all the cases studied there exist sharp Iocal minima in the local porosity, which in a physical sense are attributable to the penetration of the smaller particles into the void space of the lower layer, composed of the larger particles. It is noted, moreover, that the plot of the local void fraction against distance from the “interface” exhibits an oscillating behavior, with a progressively decreasing amplitude, not unlike the behavior of a Bessel function. As perhaps expected, the larger the disparity in the size of the particles from which the two layers are composed, the greater is tile depth of penetration, and the lower is the absolute value of the local minimum in the void fraction_ A large number of measurements have been made, using lead spheres of various sizes; a detailed description of these is available in the thesis upon which this work is based [22]_ Figures 10,ll and 12 depict the behavior of systems where a layer of larger particles is pIaced upon a layer of smaller lead spheres, ie_ just the reverse of the arrangement that was employed for obtaining the data previously given in Figs. 5 - 7. In comparing these two

i

0

of distance expressed in millimeters

sets of graphs, it is seen that in both cases there exist local minima in the void fraction in the vicinity of the interface. The substantial difference in the behavior of these two systems is manifested by the fact that the local minima in porosity are much less pronounced; moreover, the extent of penetration is also greatly reduced when larger particles are placed upon a layer of smaller spheres, than for the reverse case. Inspection of Figs. 10 - 12 shows that this penetration distance corres>onds to less than about 1.5 particle diameters, measured in units of the larger particles, which composed the upper layer. It follows that the principal difference between these two cases may be described by stating that when smaller particles are placed on a layer of larger particles, penetration will occur; in contrast, for the reverse case only-a surface disturbance will take place. 3.3 Core and shell arrangement of particles Figures 13 and 14 show the profiles of the local void fraction in a cylindrical system, when an axi-symmetrically placed core of particles is surrounded by a shell composed of particles or‘ different size_ This particular arrangement has been employed in previous studies concerned with ffow maIdistribution in packed bed systems. These plots show the local varzations in the void fraction in the vicinity of the zone where particles of

Fig. ‘7. Local porosit_i- of a horizontally layered packed bed as a function in particle diameters composing the base layer (R = 6.00).

different size are in contact with each other; the “wall effect” which was depicted in Fig. 4 has been deliberately eliminated from these data (by machining off the outer region in contact with the wall). Figures 13 and 14 refer to systems where smaller particles constitute the central core and progressively larger particIes make up the outer shell. It is seen that while there exists a small local decrease in the void fraction in the vicinity of the “interface”, these local minima are much less pronounced than those previously shown for horizontal layered sys-

of distance expressed

in millimetes

and

tems. Upon inspection of these figures it is also readily apparent that the depth of penetration is also greatly reduced, compared &th the previously shown cases. 3-4 Non-spherical particles All the previous measurements were carried out with spherical particles, which had a shape factor of at least 0.95*. Since most materials *In this context the shape factor was defined as: (surface area of a sphere of equivalent volume of the particle)/(surface area of the particle).

129

Fig. 8. Photographs

of the sectioned

face of the mold;

encountered in practical materials processing operations are non-spherical, it was of interest to conduct some preliminary measurements with non-spherical particles. In order to use the same materials, these particles were generated by mechanically deforming the lead spheres. Figure 15 shows photographs of these deformed spheres, together with those of the original material. The shape factors of the deformed spheres were about 0.65 and the ratio of the smallest/largest axis was about 0.40. Figure 16 shows the local variation in the void fraction for a system where smaller spher-

the numbers correspond

to the position

indicated

in Fig_ 6.

ical particles are placed on top of a layer consisting of larger, deformed particles_ An important practical system that could exhibit similar behavior is the placing of iron ore pellets upon coke layers in blast furnace practiceIt is of interest to compare the trends seen in Fig. 16 with that previously shown in Fig. 6, this latter depicting the behavior of spherical particles having approximately the same size ratios. It is seen that with the deformed particles the local minimum in void fraction is less pronounced; moreover. the periodicity observed in Fig. 6 is hardly discernible. It has

Fig. 9. Photographs

of the sectioned

face

of the mold;

to be stressed that Fig. 16 represents preliminary measurements with non-spherical systems, and that one cannot draw general conclusions from the trends seen there. One could readily envision non-spherical systems where very marked local minima are quite apparent_ Figure 17 shows photographs of selected cutaway sections of the system, which correspond to those marked in the previous graph. 3.5 OveraIl system behavior The behavior regarding the local minima

in

the numbers

correspond

to the position

indicated

in Fig.

6_

void fraction, shown in the previous Figs. 5 - 12, is conveniently summarized in the following Figs. 18 through 20. Figure 18 shows the plots of the integral mean value of the void fraction, for horizontal layered systems as a function of distance from the interface, measured in units of the particle diameter from which the base layer is composed. The param eter ip_ these curves is the ratio:particle diameter in the base layer/ particle diameter in the upper layer. Here z, the integral mean vah~e of the void fraction, was defined as

131

Fig. lo_ Local porosity of a horizontal!y layered packed

bed of spheres

Fig.

bed of spheres as a function

+=

11.

Local

porosity

of a horizontally

layered

packed

2 AXE*

0

&L

(2)

The minima in the values of E are readily apparent in this plot; it is seen, furthermore, that the larger the ratio of the particle diameters, the greater is the penetration and the lower is the value of E.

as a function

of axial

distance

(R = 0.33).

of asial distance (11 = 0.26).

An alternative way of summarizing these results is shown in Fig. 19, where the local value of the porosity is plotted against the distance from the interface. As espected, these local values of the porosity exhibit much sharper local minima than the mean, integral values that were previously given. Yet another way of summarizing these resuits is presented in Fig. 20, where the depth of penetration, again expressed in units of

133

O.So

25

5.3

15

25

!CC

150

175

23s

225

250

: eL-,

Fig.

1%

Local

porosity

of a horizontally

layered

packed

bed of spheres as a function of axial distance (R = 0.1’7).

0

Fig. 13. function

Radial porosity for a bed of the position_

packed

with

spheres

the particles composing the base layer, is plotted agtist the particle size ratio, defined as R = d,

(lower layer)

dP (upper layer)

(3)

Here the depth of penetration was obtained from the visual observation of the cuts that were made in the machining operation_ Inspec-

in P shell

(d,

= 0.35

cm)

and core (dp = 0.13 cm) ils a

tion of Fig. 20 is very instructive, because it indicates that marked penetration occurs once the ratio R exceeds 2. It was seen earlier that penetration of the particles forming the upper layer resulted in local porosity minima; it follows that such an arrangement would produce appreciably enhanced interfacial resistance to gas flow.

133

Fig. 1-Z. Radial porosity for ZIbed packed with spheres in a shell (dp = 0-4s function of the position.

Fig. 15. Photographs of uniform ed shown on the left-hand side_

cm) and core (dp = 0.13

cm) as a

spheres shown on the rigt t-hand side, and the same spheres mechanically

4. DISCUSSION

In the paper experiment& measurements are reported describing the local porosity profiles in packed beds formed by combining two differently sized particles in various geometric arrangements such that an interface is formed between the bulk regions of the two different species.

deform-

The following principal points arose in the interpretation of the measurements. (1) 1Measurements conducted with uniformly sized spherical particles, in the wall region, were almost identical to those reported previously by Benenati and Brosilow. (2) The measurements have shown that local minima in the porosity occur in the interfacial regions, Le. in the zones that sepa-

Fig. 16. Loczd porosity of a horizontally layered bed packed with uniform particles ti a function of distance composing the base layer (R = 3.60).

rate the bulk portions of differently sized particles_ These local minima in porosity are much more pronounced when smaller particles are placed on top of larger particles than for the reverse case. This finding, which is consistent with physical reasoning, is supported by previously reported flow resistance measurements on similar systems [ 7]_ (3) The following physical explanations may be advanced for this behavior_ When small particles are placed on top of a layer composed of large particles, the smaller particles penetrate the interstices of the iarge spheres, thus causing local minima in porosity_ This penetration has been observed esperimentally_ it has been found that this penetration is markedly affected by the disparity in the size of particles_ When the R ratio (defined in eqn. (3)) is less than 2. relatively little penetration occurs, while R = 6 allows ready penetration of the smaller particles through the matris composed of the larger spheres_ (4) As illustrated in Table 1, the mean values of the porosities found in the interfacial regions, when larger particles are placed upon a base of smaller particles, R < 1, correlate remarkably well with earlier measurements reported by Furnas on the bulk porosity of packed beds formed by the uniform mixing of lead spheres of two distinct sizes. (5) Upon considering the details of these

TABLE

spheres on a base layer of deformed

1

Values of the experimentally measured mean porosity and porosities

predicted

from

Furnas’ measurements, as a function of the particIe size ratio R

E

&

0_50

0.33

0.370 0.335

0.366 0.330

0.26

0.331

0.324

0.1’7

0.299

0.307

*Furnas data for a 5050 mixture of two different size materials_

interfacial regions, the following observations may be made: (a) The penetration of the smaller particles into the interstices of iarger spheres is defrnitely directional in that vertical penetration occurs much more readily than radial penetration, as seen on comparing Figs. 4, 5 and 13,14. (b) The local variations in porosity in the vicinity of the interfacial regions exhibit a periodicity corresponding to approximately one (large) particle diameter. (c) The estent of penetration that took place was consistent with the assumption that the packing of the larger particles was

135

Fig. 17. Photographs in Fig. 16.

of the sectioned

face

of the mo:d

between close packed hesagonal and body center cubic. (d) The preliminary esperiments conducted with the deformed (as opposed to spherical) particles indicated markedly altered behavior, so that this area would be a very fruitful field for further study. The oscillations of the point values of porosity in the interfacial region can be explained by considering the directional nature of the penetration and hence the local voidage- The decreasing amplitude at the same wave number (cycles per unit length) can be associated was

where

the numbers

corresponded

to the position

indicated

with the sieve-like or filtering nature of the solid matrix There is a masimum contact between the upper layer of spheres and the base layer at approximately one half particle diameter, measured from the interface. A number of these particles may penetrate to the next layer of spheres, the probability of which increases as the ratio, R, increases, resulting in another minimum in porosity. The increase in voidage at apprcsimately one particle diameter is due to the fact that the entire void space is not filled by the spheres penetrating from the upper layer_ As the

136

OlOf

,

Cl

*

3

4

5

6

7

@&SE Fig. 1% Integral mean voidage for beds packed with horizontal !apes distance from the interface expressed in particle diameters composing

of spheres of different the base layer.

size ratio (R) against

0 13 I

0

I

2

3

;

I

5

6

I

GUE Fig. 19. Local porosity of horizontal layers of spheres of diffenznt size, with R as a parameter, distance from the interface expressed in ball diameters composing the base layer.

distance from the interface increases, there are progressively fewer particles “ffltered” to the lower layer, thus the damping of the variation of the local voidage. The equation relating the standard deviation of the local voidage and the measured parameters is given by (4)W _

*The derivation of eqn. (4) is available in the thesis (211 on which this work is based_

as a function

of

Assuming average values for the measured quantities in eqn. (4), at a 95% confidence level, the local voidage is known within f 0.008 for any given experiment. Duplicate experiments were performed for a number of systems with excellent agreement. Reproducibility was not exact, as expected, due to the randomness inherent in the system; however, the depth of penetration and trends in the local voidage profiles were practically identical.

13-i ACKNOWLEDGEMENTS

The authors wish to thank the Bethlehem Steel Corporation for partial support of this investigation. Thanks are also due to Mr. Norman Wagner and Mr. William Berent for help in the construction of the apparatus and instructions on the operation of the lathe.

LIST OF SYMBOLS

I

2

4

3

5

6

R

Fig. 20. Extent of the interfacial region or the depth of penetration both expressed in particle diameters of the base layer, as a function of the parameter R. for horizontally layered packed beds.

CONCLUSION

Experimental measurements, conducted with spherical particles, indicate that marked local minima in porosity occur when a layer of smaller particles is placed upon a layer of larger particles. Local minima in porosity are much less marked for other geometric arrangements, the layering of larger particles on smaller spheres, or having a shell-core arrangement where the interface is vertical_ These local minima in porosity, which are directional in nature, are due to the penetration of the smaller particles into the interstices of the larger spheres. From a technological viewpoint, the most important finding of the work is the fact that, for spherical particles, appreciable penetration will occur when the particle size ratio exceeds about two. Under these conditions the interfacial regions could offer a very appreciable resistance to gas flow through the system.

cross-sectional area diameter of spheres composing the base layer diameter of spheres composing the upper layer particle diameter length thickness of slice cut from mold ratio of the diameters of the particles in the base layer to those contained in the upper layer, defined in eqn. (3) radial distance measured from the periphery inwards total volume of the mixture of lead and resin volume of the resin axial distance local voidage integral mean porosity porosity of a mixture given by Furnas mean local voidage density of lead shot density of slice removed from the mold density of cured epoxy resin standard deviation of the void fraction standard deviation of the length measurement penetration distance into base layer/ diameter of the particles contained in the base layer penetration distance into the base layer/diameter of the particles contained in the upper layer radial penetration/diameter of the particles contained in the shell

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11

12

13

14 15 16 17

18 19 20

21

Technol-. 4 (1970171) 56_ F_ A_ Rocke, The cylindrically ordered packing of equal spheres, Powder Technol., 4 (19’10171) 180. S. Debbas and H. Rumpf, On the randomness of beds packed with spheres or irreguIar shaped particles. Chem. Eng_ Sci.. 21 (1966) 583. D- Haughey and G. Beveridge. Local property variation in randomly packed bed of equal sized spheres, Chem- Eng. Sci., 22 (1967) 715 E. Tory, B. Church, M. Tam and hl. Ratner, Simulated random packing of equal spheres. Can_ J. Chem Eng., 51(1973) 484. J. Barker, Heat transfer in packed beds, Ind. Eng. Chere. 57 (1965) 43_ R. Benenati and C. Brosilow, Void fraction distribution in a bed of spheres, AIChE J., 8 (1962) 359. hl_ Shaffer. Radial variation of void space in packed beds, MS. Thesis, Purdue Univ., 1952. M_ Kimura. K Nono and T_ Keneda, Distribution of voidage in packed tube, Chem_ Eng_ Jpn.. 19 (1955) 397. L Roblee, R Baird and J_ Tierney. Radial porosity variation in packed bed, AIChE J., 4 (1958) 460. C. Furnas, Flow of gases through beds of broken solids, U.S. Bur. Mines Bull. 307, 1929. R. Jeschar, W. Potke. V. Petersen and K. Polthier, Blast furnace aerodynamics, B!ast Furnace Aerodynamics Symposium. Wollongong, Australia, 1975 h1. Ptopster, Fluid flow phenomena in the blast furnace stack, Ph.D. Diss., State Univ. of New York at Buffalo, 1977_