- Email: [email protected]
Gas spouting characteristics of fine particles
Shorter
Communications
From these considerations, we conclude that the procedure of the used by Rizzuti et al. (1976) for the determination OJ-OHreaction rate constant, with the revision reported in this paper, leads to the correct value of the kinetic constant. L. RIZZUTI V. AUGUGLIARO istituto di Ingegneria Universith di Palermo Viale delle Scienze 90128 Palermo, Italy
Chimica
G. MARRUCCI Dipartimento di lngegneria Universitic di Napoli Piazzale Tecchio 80125 Napoli, Italy
Chimica
REFERENCES
Augugliaro, V. and Rizzuti, L., 1987, Kinetics of carbon dioxide absorption into catalyzed potassium carbonate solutions. Chem. Engng Sci. 42, 2339-2343. Czapski, G., Samuni, A. and Yelin, R., 1968, The disappearI_ ante of ozone in alkaline solution. Isr. J. Chem. 6,969-97
Chemical
Engineering
Science,
Vol.
2977
Joosten, G. E. H. and Danckwerts, P. V., 1973, Chemical reaction and effective interfacial areas in gas absorption. Chem. Engng Sci. 28, 453461. Patwardhan, V. S., 1978, Effective interfacial area in packed beds for absorption with chemical reaction. Can. J. Chem. Engng 56,5&64. Patwardhan, V. S., 1979, On gas-liquid mass transfer in packed trickle beds. Chem. Engng S>i. 34, 436437. Richards, G. M., Ratcliff, G. A. and Danckwerts, P. V., 1964, Kinetics of COz absorption-III. First-order reaction in a packed column. Chem. Engng Sci. 19, 325328. Rizzuti, L., Augugliaro, V. and Lo Cascio, G., 1981, The influence of the liquid viscosity on the effective interfacial area in packed columns. Chem. Engng Sci. 36, 973-978. Rizzuti, L., Augugliaro, V. and Marrucci, G., 1976, Ozone absorption in alkaline solutions. Chem. Engng Sci. 31, 877-880. Roberts, D. and Danckwerts, P. V., 1962, Kinetics of CO2 absorption in alkaline solutions-I. Transient absorption rates and catalysis by arsenite. Chem. Engng Sci. 17, 961-969. Shulman, H. L., Ullrich, C. k. and Wells, N., 1955, Performance of packed columns-I. Total, static and operating holdups. A.1.Ch.E. J. 1, 247-253.
42. No. 12,pp. 2977-298I, 1987.
OIXK-2509j87 $3.00+ 0.00 0 1987Pergamon Journals Ltd.
Printed in Great Britain.
Gas (Received
spouting 23 February
characteristics 1987; accepted
INTRODUCTION
In an earlier paper (Chandnani and Epstein, 1986), flow regimes were mapped for cold gas spouting of fine particles (d, < 1 mm) and it was shown that termination of stable gas spouting occurs for such particles due to choking of the spout rather than fluidization of the upper annulus as in the case of coarse particles (dp 3 1 mm). The cold gas spoutability criterion d,/dp < 25 was found to be applicable to both fine and coarse particles. In the present communication other observed properties of gas-spouted beds of fine particles are reported. EXPERIMENTAL
Most runs were carried out in a 60” included cone angle, 152 mm diameter plexiglass half column with solids ranging in size from 98 to 1OOO~m and in density from 900 to 8900 kg/m3, and with gas inlet orifice diameters varying from 2.8 to 28 mm. Some runs were also performed with a 36.4” included angle cone. The spouting gas was always atmospheric air, pre-conditioned to 80’y0 relative humidity to eliminate electrostatic effects. Bed heights were varied from approximately one column diameter to the maximum spoutable value, H,, and spouting air velocities from the minimum, CJ,,, to well above the maximum for coherent spouting (Chandnani and Epstein, 1986). The spout diameter at various bed levels was measured by taking photographs through the glass flat face of the half
of tine particles in revised
form
10 July
1987)
while the fountain height was observed and column, measured both through this face and through the semicylindrical plexiglass wall. Gas velocity in the annulus at various bed levels was measured by locating a precalibrated differential pressure probe, similar to one used in an earlier study (Epstein ef al., 1978), midway between the spout and the centre (i.e. the vertical bisector) of the curved wall. Bed pressure drop (with atmospheric outlet) was determined by means of a pressure tap located immediately upstream of the inlet orifice, appropriate correction being made for the corresponding empty column pressure drop (Mathur and Epstein, 1974). The solids flow rate at various bed levels was estimated by timing the motion of colored tracer particles in the annulus at different marked locations on the flat wall and at the centre of the curved wall. Dead solids zones were delineated. For every particle species used, the minimum fluidization velocity was determined by admitting air into a large number of evenly distributed auxiliary gas flow lines in the halfconical base of the column (Sutanto et al., 1985) using bed heights in excess of 800 mm to ensure uniform fluidization. PRESSURE
DROP
To start with, an attempt was made to replicate the work of Heschel and Klose (1981), who reported spouting polyvinfl chloride powder having a mean diameter of 91.5 pm with a gas inlet diameter of 25.4 mm, i.e. di/d,, = 278, which is far in
2978
Shorter
Communications
excess of the number 25 given by the above-mentioned criterion. Their results for pressure drop vs flow rate were also unusual in that they exhibited two peaks, as exemplified by Fig. 1. The first peak corresponds to a gas jet breaking through the bed in an unsteady manner. The foot of the second peak, which corresponds to the minimum fluidization velocity of the particles involved, is attributed to the onset of steady spouting, after which the pressure drop remains constant. In a conventional spouted bed of coarse particles, however, steady spouting sets in when AP first drops, and there is no second peak (Mathur and Epstein, 1974). Runs were made in a 152 mm diameter conical-cylindrical plexiglass half column having a 36.4” included cone angle, as also used by Heschel and Klose in their 300 mm diameter full column, with particles which were also similar to theirs. The half-column dimensions and other conditions of operation are compared with those of Heschel and Klose in Table 1. Even when the conditions of Heschel and Klose were closely matched, by using similar solids and maintaining geometrical similarity in the equipment, the pressure drop vs flow rate characteristics displayed in Fig. 2 were typical. The jet broke through and discharged as bubbles at the foot of the pressure drop peak (point A). Further increase in flow led to a fluctuating pressure drop with an increasing bubble frequency, which in turn eventually led to slugging. Thus the second peak shown in Fig. 1 did not appear at all and steady spouting was never observed ford, = 12.7 mm nor for the two other inlet diameters of Table 1, and with H ranging from 150 to 800 mm, which amply brackets H = -750 mm covered
by Heschel and Klose. Some trials in a full column confirmed our half-column observations. Just before sending this communication to press we received a draft paper from Passos ef al. (1987) reporting two pressure drop peaks, but only in a two-dimensional spouted bed. Such a bed is, however, considerably less representative of a fully round threedimensional bed than is a half-round three-dimensional bed (Whiting and Geldart, 1980; Geldart et al., 1981). We thus have no satisfactory explanation for the observations reported by Heschel and Klose. Typical pressure drop vs flow rate curves for the transition from a fixed packed bed to a steadily spouted bed are shown in Fig. 3 for three different particle sizes at the same bed height. The shape of the transition curves, the hysteresis effect and the trend with particle size are all similar to those observed with coarse particles. However, once steady spouting has set in, the pressure drop increases with gas flow at a steadily decreasing rate, unlike the case of coarse particles, for which the spouting pressure drop remains constant with gas flow. This difference can be explained by the presence of a large stagnant zone of fine solids in the lower outer periphery of the annulus, and by the fact that this stagnant zone decreases as the spouting velocity is increased, thus engaging more particles in the spouting action. Both the stagnant zone volume and the initial rate of change of the spouting pressure drop decrease as the particle size increases. The regime characterization parameter, C, % AP,,,,/AP,, , of Morgan et al. (1985) varied in the present work from 0.4 to 0.7, the latter figure occurring at H = H,. It thus fell in the range predicted and observed by Morgan et al. for coarse particles, but failed to confirm their speculation that Co for air spouting of fine particles at H = H, might fall between 0.785 and unity (as it does for water spouting of fine particles) due to the fact that the spout voidage at Z = 0 would fall significantly short of unity (as for water spouting of fine particles). In fact, the voidage at the bottom of the spout appeared visually to be close to unity, as for coarse particles. GAS FLOW
I
I
t 3.6
I .8
Superf ictal
54
air velocity
DISTRIBUTION
As in the case of coarse particle spouting (Epstein et al., 1978), the superficial gas velocity in the annulus, U,, was found to increase with vertical distance from the gas inlet, to be fairly constant radially above the cone region and to be independent of bed height. However, unlike the case of coarse particle spouting, where (I, at the maximum spoutable bed height is typically about 0.85-1.00 times U,, (Epstein et al., 1978), U,(HM) in the present study was consistently found to be in the range 0.55-0.70 times U,,. If one then uses the measured value of U,(H& instead of U,, in the well known Mamuro-Hattori (1968, 1970) and Lefroy-Davidson (1969) velocity distribution equations for coarse particles, one arrives at uY=
( cm 1s)
U,(H,)C1-_(1-_(Z/H,)}~l
(1)
and Fig. 1. Typical results of Heschel and Klose (1981). Full column: D, = 300 mm, di = 25.4 mm, 0 = 36.4”. PVC: d, = 91.5 pm, H = 550 mm. Air: relative humidity = 80 “/,.
Table Heschel
1.
and Klose
Conditions
CJ,= U,(H,) respectively.
sin (nZ/ZH,,,,)
The flow regime index (Epstein
used in this work vs those of Heschel and Klose
(1981)
(1) Column diameter = 300 mm (full column) Inlet diameter = 25.4 mm (no contraction of the fluid inlet) Cone included angle = 36.4” (2) Solid used: PVC (d, = 91.5 pm) (3) Fluid: air (relative humidity = 800/o) (4) Bed heights = 400, 550 and 750 mm
(2) et al., 1978) has
(1981)
This work (1) Column diameter = 152 mm (half column) Inlet diameters = 25.4, 12.7 and 10.1 mm (no contraction of the fluid inlet) Cone included angle = 36.4” (2) Solid used: PVC (dp = 98 pm) (3) Fluid: air (relative humidity = 80%) (4) Bed heights = 15&800 mm
Shorter Communications
9 0
2979
Increasing Decleashg
flow flow
In
‘B i? 6) rnf I 0.2
0’
I 0.4
I 0.6
Cl
I 0.6
I 1
(std. l/s)
Fig. 2. Typical results obtained on matching the conditions of Heschel and Klose (198 1). Half column: D, = 152 mm, di = 12.7 mm, 0 = 36.4”. PVC: dp = 98 pm, H = 375 mm. Air: relative humidity = 80 “/,.
,dp=0.401
mm
6
2 55
4
%I
2
0
/
I
I
I
2 6)
1
I
3
4
(std.l/s)
Fig. 3. Pressure drop transition from fixed packed bed to spouted bed (and vice versa) for sand of three different particle sizes. DC = 152 mm, di = 6.0 mm, 8 = 60”, H = 410 mm. Solid lines represent increasing flow, dashed lines decreasing flow.
been taken as unity in eq. (2) because, for fine particle spouting, Darcy’s law always governs the flow in the annulus. Whereas there is little to choose between eqs (1) and (2) for prediction of gas distribution in the case of coarse particle spouting, Fig. 4 (which is typical) shows that eq. (2) is unambiguously better for fine particles.
SPOUT
DIAMETER
Except near the gas inlet (approximately within the cone region), where a net expansion of the spout occurred, the spout diameter was in most cases nearly uniform with 2. The longitudinally averaged spout diameter, 0,. as given by the McNab (1972) empirical correlation for coarse particle
Shorter
2980
I8
I6
Communications
c L
c-u,-
I
0’
IO
I
I 30
20
I
I
40
50
Z (cm) Fig. 4. Longitudinal annular air velocity distribution for 401 pm sand, DC = 152 mm, di = 6.0 mm, 9 = 60”, = 468mm, U/U_ = 1.18. Broken line is eq. (l), solid line eq. (2). M-H: Mamuro-Hattori H = H, (1968, 1970), L-D: Lefroy-Davidson (1969).
spouting, D , = 2.t)OG0.49Dco.68/pb‘..+’ (SI units)
(3)
though it underpredicted the measured value of D, on the average by about 25 ‘yO,nevertheless correctly predicted the observed trends of D,, especially with respect to spouting velocity U (= G/pi) for a given bed (p,,, D, and H constant) or even for a given particle species (varying H). FOUNTAIN
HEIGHT
The height, H.F. and development of the approximately parabolic fountain for a given bed increased with spouting velocity, U. An underdeveloped fountain accompanied by a bed surface which sloped downward towards the column wall could become a developed or over developed fountain accompanied by a bed surface which sloped downward towards the spout by increasing~l_J sufficiently above V,,. For a given value of U/U,, the value of H, decreased as H increased for a fixed particle species (constant d, and pP). while H, increased as d, increased for a given particle density. These trends and their explanation are similar to those for spouting of coarse particles (Grace and Mathur, 1978). PARTICLE
CIRCULATION
Except for. the presence of a large stagnant zone of solids at the lower outer periphery of the annulus, especially for the finest particles at the lower spouting velocities using the larger cone angle, particle circulation patterns were similar to those observed for coarse particle spouting (Mathur and Epstein, 1974; Lim and Mathur, 1978). The downward particle velocity in the annulus decreased in the downward direction within the cylindrical region above the stagnant zone and increased in the downward direction for the movie? solids within the conical region surrounded by the stagnant solids. The stagnant zone often extended into the cylindrical parts of the
column when the 60” conical base was used, but disappeared completely with the 36.4” cone, at least for particles larger than 400 Wm. Both the downward particle velocities and the gradients of downward particle velocity were considerably higher near the spout-annulus interface than at the curved wall. The total downward solids flow rate in the annulus (which at any level equals the total upward solids flow rate in the spout at the same level) increased with increasing gas velocity, U, for a given bed. For a given value of U/U,,, the volumetric solids flow rate increased both as H increased for a fixed particle species, and as d, increased for a fixed particle density, but decreased as the cone included angle was enlarged from 36.4 to 60”. Except for the last effect, which is caused by the development of a stagnant zone of fine solids for the 60” cone angle, these trends and their explanation are again similar to those for coarse particles (Mathur and Epstein, 1974). CONCLUSION Aside from a difference in the steady spouting termination mechanism (overloading of the spout rather than fluidization of the annulus) for fine as opposed to coarse particle spouting, the most obvious other difference displayed by fine particle spouting is the presence of a large stagnant solids zone at the lower outer periphery of the annulus, even with a 60” conical (rather than a flat) base. Other observed differences from coarse particle spouting can be related either to the different termination mechanism [which accounts, for example, for the lowering of V. (HM )/U,,,r (Chandnani and Epstein, 1986)j or to the presence of the stagnant solids zone and its changing size. Acknowledgement-Continuing financial support from Natural Sciences and Engineering Research Council Canada is gratefully acknowledged.
the of
Shorter
PRATAP of Chemical Engineering of British Columbia B.C., Canada V6T 1 W5
Department University Vancouver,
Communications
NORMAN EPSTEIN P. CHANDNANIt
lAPma, + PJ [~~:s)~Dc/(Dshd4 =
HF H.&f AP AP,, AP,,
u UH U,(H,,,) U m/
u ms US,
Z
Greek ‘m/
e
-
~2,,&,~
I/M’,,
IAPm,
cylindrical or semi-cylindrical column diameter, mm or m longitudinally averaged spout diameter, m D, at minimum spouting velocity, m gas orifice inlet diameter, mm mean particle diameter, mm mass velocity of fluid [ = pI U, kg/m2. s] acceleration of gravity, m/s loose-packed static bed height = height of annulus, mmorm fountain height, mm maximum spoutable bed height, mm bed pressure drop, Pa or kPa AP at minimum spouting velocity, Pa AP at minimum fluidization [ = (1 -E,,)(& -
U,
APms
pI-
PJ PP
bulk density of loose-packed gas density, kg/m3 particle density, kg/m’
bed, kg/m3
REFERENCES
NOTATION
CO
pb
298 1
Wfl, Pa
volumetric Row rate of gas, l/s at STP Q at minimum Ruidization, l/s at STP superficial gas velocity based on cylinder crosssection, cm/s superficial gas velocity in annulus at a given value of 2, cm/s U, at top of annulus, cm/s cm/s us, for bed of height H, superficial minimum fluidization velocity, cm/s or
m/s
superficial minimum spouting velocity, cm/s or m/s superficial gas velocity at top of spout, m/s vertical distance from gas inlet orifice, cm fetters minimum fluidization, loose-packed voidage included angle of conical base, o
and annulus
‘Present address: The Rampur Distillery & Chemical Co. Ltd, 305/312, Deepali Building, 92, Nehru Place, New Delhi 110019, India.
Chandnani. P. P. and Epstein, N., 1986, Spoutability and spout destabilization of fine particles with a gas, in Proceedings of Fluidization V (Edited by Ostergaard, K. and Sorensen, A.), pp. 233-240. Engineering Foundation. Epstein, N., Lim, C. J. and Mathur, K. B., 1978, Data and models for flow distribution and pressure drop in spouted beds. Can. J. them. Engng 56, 436447. Geldart, D., Hemsworth, A., Sundavadra, R. and Whiting, K. J., 1981, A comparison of spoutinaand iettina in roundand 59.638-639. half-round Auidized beds. can. J.:hem.vEngn> Grace, J. R. and Mathur, K. B., 1978. Height and structure of the fountain region above .spouted beds. Can. J. them. Engng 56, 533-537. Heschel, W. and Klose, E., 1981, Zum stromungstechnischen verhalten feinstkorniger guter in der sprudelschicht. C&m. Tech. Leipzig 33 (3), 122-125. Lefroy, G. A. and Davidson, J. F., 1969, The mechanics of spouted beds. Trans. Instn them. Engrs 47, T120-T128. Lim, C. J. and Mathur, K. B., 1978, Modelling of particle movement in spouted beds, in Fluidization (Edited by Davidson, J. F. and Keairns, D. L.), pp. 104-109. Cambridge University Press, Cambridge. Mamuro, T. and Hattori. H., 1968, Flow pattern of fluid in svouted beds. J. them. Enana Jaoan 1.1-5. Mamuro. T. and Hattori, H., 1970, CorrecTion. 1: them. Engng Japan 3, 119. Mathur, K. B. and Epstein, N., 1974, Spouted Beds. Academic _. _. . rress, New York. McNab, G. S., 1972, Prediction of spout diameter. Br. them. Engng Process Technol. 17, 532. Morgan, M. H., III, Day, J. Y. and Littman, H., 1985, Spout voidage distribution, stability and particle circulation rates in spouted beds of coarse particles-l. Theory. Chem. Engng Sci. 40, 1367-1377. Passos, M. L., Mujumdar, A. S. and Raghavan, V. G. S., 1987, Aerodynamics and solids circulation-rates in a two dimensional spouted bed. Paper presented at Powder and Bulk Solids Conference, Rosemont, Illinois, May 1987. Sutanto, W., Epstein, N. and Grace. J. R.. 1985. Hydrodynami& of spout-fluid beds. Powder Technol. 44; 205-212. Whiting, K. 1. and Geldart, D., 1980, A comparison of cyclindrical and semi-cylindrical spouted beds of coarse particles. Chem. Engng Sci. 35, 1499-1501.
Communications
From these considerations, we conclude that the procedure of the used by Rizzuti et al. (1976) for the determination OJ-OHreaction rate constant, with the revision reported in this paper, leads to the correct value of the kinetic constant. L. RIZZUTI V. AUGUGLIARO istituto di Ingegneria Universith di Palermo Viale delle Scienze 90128 Palermo, Italy
Chimica
G. MARRUCCI Dipartimento di lngegneria Universitic di Napoli Piazzale Tecchio 80125 Napoli, Italy
Chimica
REFERENCES
Augugliaro, V. and Rizzuti, L., 1987, Kinetics of carbon dioxide absorption into catalyzed potassium carbonate solutions. Chem. Engng Sci. 42, 2339-2343. Czapski, G., Samuni, A. and Yelin, R., 1968, The disappearI_ ante of ozone in alkaline solution. Isr. J. Chem. 6,969-97
Chemical
Engineering
Science,
Vol.
2977
Joosten, G. E. H. and Danckwerts, P. V., 1973, Chemical reaction and effective interfacial areas in gas absorption. Chem. Engng Sci. 28, 453461. Patwardhan, V. S., 1978, Effective interfacial area in packed beds for absorption with chemical reaction. Can. J. Chem. Engng 56,5&64. Patwardhan, V. S., 1979, On gas-liquid mass transfer in packed trickle beds. Chem. Engng S>i. 34, 436437. Richards, G. M., Ratcliff, G. A. and Danckwerts, P. V., 1964, Kinetics of COz absorption-III. First-order reaction in a packed column. Chem. Engng Sci. 19, 325328. Rizzuti, L., Augugliaro, V. and Lo Cascio, G., 1981, The influence of the liquid viscosity on the effective interfacial area in packed columns. Chem. Engng Sci. 36, 973-978. Rizzuti, L., Augugliaro, V. and Marrucci, G., 1976, Ozone absorption in alkaline solutions. Chem. Engng Sci. 31, 877-880. Roberts, D. and Danckwerts, P. V., 1962, Kinetics of CO2 absorption in alkaline solutions-I. Transient absorption rates and catalysis by arsenite. Chem. Engng Sci. 17, 961-969. Shulman, H. L., Ullrich, C. k. and Wells, N., 1955, Performance of packed columns-I. Total, static and operating holdups. A.1.Ch.E. J. 1, 247-253.
42. No. 12,pp. 2977-298I, 1987.
OIXK-2509j87 $3.00+ 0.00 0 1987Pergamon Journals Ltd.
Printed in Great Britain.
Gas (Received
spouting 23 February
characteristics 1987; accepted
INTRODUCTION
In an earlier paper (Chandnani and Epstein, 1986), flow regimes were mapped for cold gas spouting of fine particles (d, < 1 mm) and it was shown that termination of stable gas spouting occurs for such particles due to choking of the spout rather than fluidization of the upper annulus as in the case of coarse particles (dp 3 1 mm). The cold gas spoutability criterion d,/dp < 25 was found to be applicable to both fine and coarse particles. In the present communication other observed properties of gas-spouted beds of fine particles are reported. EXPERIMENTAL
Most runs were carried out in a 60” included cone angle, 152 mm diameter plexiglass half column with solids ranging in size from 98 to 1OOO~m and in density from 900 to 8900 kg/m3, and with gas inlet orifice diameters varying from 2.8 to 28 mm. Some runs were also performed with a 36.4” included angle cone. The spouting gas was always atmospheric air, pre-conditioned to 80’y0 relative humidity to eliminate electrostatic effects. Bed heights were varied from approximately one column diameter to the maximum spoutable value, H,, and spouting air velocities from the minimum, CJ,,, to well above the maximum for coherent spouting (Chandnani and Epstein, 1986). The spout diameter at various bed levels was measured by taking photographs through the glass flat face of the half
of tine particles in revised
form
10 July
1987)
while the fountain height was observed and column, measured both through this face and through the semicylindrical plexiglass wall. Gas velocity in the annulus at various bed levels was measured by locating a precalibrated differential pressure probe, similar to one used in an earlier study (Epstein ef al., 1978), midway between the spout and the centre (i.e. the vertical bisector) of the curved wall. Bed pressure drop (with atmospheric outlet) was determined by means of a pressure tap located immediately upstream of the inlet orifice, appropriate correction being made for the corresponding empty column pressure drop (Mathur and Epstein, 1974). The solids flow rate at various bed levels was estimated by timing the motion of colored tracer particles in the annulus at different marked locations on the flat wall and at the centre of the curved wall. Dead solids zones were delineated. For every particle species used, the minimum fluidization velocity was determined by admitting air into a large number of evenly distributed auxiliary gas flow lines in the halfconical base of the column (Sutanto et al., 1985) using bed heights in excess of 800 mm to ensure uniform fluidization. PRESSURE
DROP
To start with, an attempt was made to replicate the work of Heschel and Klose (1981), who reported spouting polyvinfl chloride powder having a mean diameter of 91.5 pm with a gas inlet diameter of 25.4 mm, i.e. di/d,, = 278, which is far in
2978
Shorter
Communications
excess of the number 25 given by the above-mentioned criterion. Their results for pressure drop vs flow rate were also unusual in that they exhibited two peaks, as exemplified by Fig. 1. The first peak corresponds to a gas jet breaking through the bed in an unsteady manner. The foot of the second peak, which corresponds to the minimum fluidization velocity of the particles involved, is attributed to the onset of steady spouting, after which the pressure drop remains constant. In a conventional spouted bed of coarse particles, however, steady spouting sets in when AP first drops, and there is no second peak (Mathur and Epstein, 1974). Runs were made in a 152 mm diameter conical-cylindrical plexiglass half column having a 36.4” included cone angle, as also used by Heschel and Klose in their 300 mm diameter full column, with particles which were also similar to theirs. The half-column dimensions and other conditions of operation are compared with those of Heschel and Klose in Table 1. Even when the conditions of Heschel and Klose were closely matched, by using similar solids and maintaining geometrical similarity in the equipment, the pressure drop vs flow rate characteristics displayed in Fig. 2 were typical. The jet broke through and discharged as bubbles at the foot of the pressure drop peak (point A). Further increase in flow led to a fluctuating pressure drop with an increasing bubble frequency, which in turn eventually led to slugging. Thus the second peak shown in Fig. 1 did not appear at all and steady spouting was never observed ford, = 12.7 mm nor for the two other inlet diameters of Table 1, and with H ranging from 150 to 800 mm, which amply brackets H = -750 mm covered
by Heschel and Klose. Some trials in a full column confirmed our half-column observations. Just before sending this communication to press we received a draft paper from Passos ef al. (1987) reporting two pressure drop peaks, but only in a two-dimensional spouted bed. Such a bed is, however, considerably less representative of a fully round threedimensional bed than is a half-round three-dimensional bed (Whiting and Geldart, 1980; Geldart et al., 1981). We thus have no satisfactory explanation for the observations reported by Heschel and Klose. Typical pressure drop vs flow rate curves for the transition from a fixed packed bed to a steadily spouted bed are shown in Fig. 3 for three different particle sizes at the same bed height. The shape of the transition curves, the hysteresis effect and the trend with particle size are all similar to those observed with coarse particles. However, once steady spouting has set in, the pressure drop increases with gas flow at a steadily decreasing rate, unlike the case of coarse particles, for which the spouting pressure drop remains constant with gas flow. This difference can be explained by the presence of a large stagnant zone of fine solids in the lower outer periphery of the annulus, and by the fact that this stagnant zone decreases as the spouting velocity is increased, thus engaging more particles in the spouting action. Both the stagnant zone volume and the initial rate of change of the spouting pressure drop decrease as the particle size increases. The regime characterization parameter, C, % AP,,,,/AP,, , of Morgan et al. (1985) varied in the present work from 0.4 to 0.7, the latter figure occurring at H = H,. It thus fell in the range predicted and observed by Morgan et al. for coarse particles, but failed to confirm their speculation that Co for air spouting of fine particles at H = H, might fall between 0.785 and unity (as it does for water spouting of fine particles) due to the fact that the spout voidage at Z = 0 would fall significantly short of unity (as for water spouting of fine particles). In fact, the voidage at the bottom of the spout appeared visually to be close to unity, as for coarse particles. GAS FLOW
I
I
t 3.6
I .8
Superf ictal
54
air velocity
DISTRIBUTION
As in the case of coarse particle spouting (Epstein et al., 1978), the superficial gas velocity in the annulus, U,, was found to increase with vertical distance from the gas inlet, to be fairly constant radially above the cone region and to be independent of bed height. However, unlike the case of coarse particle spouting, where (I, at the maximum spoutable bed height is typically about 0.85-1.00 times U,, (Epstein et al., 1978), U,(HM) in the present study was consistently found to be in the range 0.55-0.70 times U,,. If one then uses the measured value of U,(H& instead of U,, in the well known Mamuro-Hattori (1968, 1970) and Lefroy-Davidson (1969) velocity distribution equations for coarse particles, one arrives at uY=
( cm 1s)
U,(H,)C1-_(1-_(Z/H,)}~l
(1)
and Fig. 1. Typical results of Heschel and Klose (1981). Full column: D, = 300 mm, di = 25.4 mm, 0 = 36.4”. PVC: d, = 91.5 pm, H = 550 mm. Air: relative humidity = 80 “/,.
Table Heschel
1.
and Klose
Conditions
CJ,= U,(H,) respectively.
sin (nZ/ZH,,,,)
The flow regime index (Epstein
used in this work vs those of Heschel and Klose
(1981)
(1) Column diameter = 300 mm (full column) Inlet diameter = 25.4 mm (no contraction of the fluid inlet) Cone included angle = 36.4” (2) Solid used: PVC (d, = 91.5 pm) (3) Fluid: air (relative humidity = 800/o) (4) Bed heights = 400, 550 and 750 mm
(2) et al., 1978) has
(1981)
This work (1) Column diameter = 152 mm (half column) Inlet diameters = 25.4, 12.7 and 10.1 mm (no contraction of the fluid inlet) Cone included angle = 36.4” (2) Solid used: PVC (dp = 98 pm) (3) Fluid: air (relative humidity = 80%) (4) Bed heights = 15&800 mm
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9 0
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Increasing Decleashg
flow flow
In
‘B i? 6) rnf I 0.2
0’
I 0.4
I 0.6
Cl
I 0.6
I 1
(std. l/s)
Fig. 2. Typical results obtained on matching the conditions of Heschel and Klose (198 1). Half column: D, = 152 mm, di = 12.7 mm, 0 = 36.4”. PVC: dp = 98 pm, H = 375 mm. Air: relative humidity = 80 “/,.
,dp=0.401
mm
6
2 55
4
%I
2
0
/
I
I
I
2 6)
1
I
3
4
(std.l/s)
Fig. 3. Pressure drop transition from fixed packed bed to spouted bed (and vice versa) for sand of three different particle sizes. DC = 152 mm, di = 6.0 mm, 8 = 60”, H = 410 mm. Solid lines represent increasing flow, dashed lines decreasing flow.
been taken as unity in eq. (2) because, for fine particle spouting, Darcy’s law always governs the flow in the annulus. Whereas there is little to choose between eqs (1) and (2) for prediction of gas distribution in the case of coarse particle spouting, Fig. 4 (which is typical) shows that eq. (2) is unambiguously better for fine particles.
SPOUT
DIAMETER
Except near the gas inlet (approximately within the cone region), where a net expansion of the spout occurred, the spout diameter was in most cases nearly uniform with 2. The longitudinally averaged spout diameter, 0,. as given by the McNab (1972) empirical correlation for coarse particle
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I8
I6
Communications
c L
c-u,-
I
0’
IO
I
I 30
20
I
I
40
50
Z (cm) Fig. 4. Longitudinal annular air velocity distribution for 401 pm sand, DC = 152 mm, di = 6.0 mm, 9 = 60”, = 468mm, U/U_ = 1.18. Broken line is eq. (l), solid line eq. (2). M-H: Mamuro-Hattori H = H, (1968, 1970), L-D: Lefroy-Davidson (1969).
spouting, D , = 2.t)OG0.49Dco.68/pb‘..+’ (SI units)
(3)
though it underpredicted the measured value of D, on the average by about 25 ‘yO,nevertheless correctly predicted the observed trends of D,, especially with respect to spouting velocity U (= G/pi) for a given bed (p,,, D, and H constant) or even for a given particle species (varying H). FOUNTAIN
HEIGHT
The height, H.F. and development of the approximately parabolic fountain for a given bed increased with spouting velocity, U. An underdeveloped fountain accompanied by a bed surface which sloped downward towards the column wall could become a developed or over developed fountain accompanied by a bed surface which sloped downward towards the spout by increasing~l_J sufficiently above V,,. For a given value of U/U,, the value of H, decreased as H increased for a fixed particle species (constant d, and pP). while H, increased as d, increased for a given particle density. These trends and their explanation are similar to those for spouting of coarse particles (Grace and Mathur, 1978). PARTICLE
CIRCULATION
Except for. the presence of a large stagnant zone of solids at the lower outer periphery of the annulus, especially for the finest particles at the lower spouting velocities using the larger cone angle, particle circulation patterns were similar to those observed for coarse particle spouting (Mathur and Epstein, 1974; Lim and Mathur, 1978). The downward particle velocity in the annulus decreased in the downward direction within the cylindrical region above the stagnant zone and increased in the downward direction for the movie? solids within the conical region surrounded by the stagnant solids. The stagnant zone often extended into the cylindrical parts of the
column when the 60” conical base was used, but disappeared completely with the 36.4” cone, at least for particles larger than 400 Wm. Both the downward particle velocities and the gradients of downward particle velocity were considerably higher near the spout-annulus interface than at the curved wall. The total downward solids flow rate in the annulus (which at any level equals the total upward solids flow rate in the spout at the same level) increased with increasing gas velocity, U, for a given bed. For a given value of U/U,,, the volumetric solids flow rate increased both as H increased for a fixed particle species, and as d, increased for a fixed particle density, but decreased as the cone included angle was enlarged from 36.4 to 60”. Except for the last effect, which is caused by the development of a stagnant zone of fine solids for the 60” cone angle, these trends and their explanation are again similar to those for coarse particles (Mathur and Epstein, 1974). CONCLUSION Aside from a difference in the steady spouting termination mechanism (overloading of the spout rather than fluidization of the annulus) for fine as opposed to coarse particle spouting, the most obvious other difference displayed by fine particle spouting is the presence of a large stagnant solids zone at the lower outer periphery of the annulus, even with a 60” conical (rather than a flat) base. Other observed differences from coarse particle spouting can be related either to the different termination mechanism [which accounts, for example, for the lowering of V. (HM )/U,,,r (Chandnani and Epstein, 1986)j or to the presence of the stagnant solids zone and its changing size. Acknowledgement-Continuing financial support from Natural Sciences and Engineering Research Council Canada is gratefully acknowledged.
the of
Shorter
PRATAP of Chemical Engineering of British Columbia B.C., Canada V6T 1 W5
Department University Vancouver,
Communications
NORMAN EPSTEIN P. CHANDNANIt
lAPma, + PJ [~~:s)~Dc/(Dshd4 =
HF H.&f AP AP,, AP,,
u UH U,(H,,,) U m/
u ms US,
Z
Greek ‘m/
e
-
~2,,&,~
I/M’,,
IAPm,
cylindrical or semi-cylindrical column diameter, mm or m longitudinally averaged spout diameter, m D, at minimum spouting velocity, m gas orifice inlet diameter, mm mean particle diameter, mm mass velocity of fluid [ = pI U, kg/m2. s] acceleration of gravity, m/s loose-packed static bed height = height of annulus, mmorm fountain height, mm maximum spoutable bed height, mm bed pressure drop, Pa or kPa AP at minimum spouting velocity, Pa AP at minimum fluidization [ = (1 -E,,)(& -
U,
APms
pI-
PJ PP
bulk density of loose-packed gas density, kg/m3 particle density, kg/m’
bed, kg/m3
REFERENCES
NOTATION
CO
pb
298 1
Wfl, Pa
volumetric Row rate of gas, l/s at STP Q at minimum Ruidization, l/s at STP superficial gas velocity based on cylinder crosssection, cm/s superficial gas velocity in annulus at a given value of 2, cm/s U, at top of annulus, cm/s cm/s us, for bed of height H, superficial minimum fluidization velocity, cm/s or
m/s
superficial minimum spouting velocity, cm/s or m/s superficial gas velocity at top of spout, m/s vertical distance from gas inlet orifice, cm fetters minimum fluidization, loose-packed voidage included angle of conical base, o
and annulus
‘Present address: The Rampur Distillery & Chemical Co. Ltd, 305/312, Deepali Building, 92, Nehru Place, New Delhi 110019, India.
Chandnani. P. P. and Epstein, N., 1986, Spoutability and spout destabilization of fine particles with a gas, in Proceedings of Fluidization V (Edited by Ostergaard, K. and Sorensen, A.), pp. 233-240. Engineering Foundation. Epstein, N., Lim, C. J. and Mathur, K. B., 1978, Data and models for flow distribution and pressure drop in spouted beds. Can. J. them. Engng 56, 436447. Geldart, D., Hemsworth, A., Sundavadra, R. and Whiting, K. J., 1981, A comparison of spoutinaand iettina in roundand 59.638-639. half-round Auidized beds. can. J.:hem.vEngn> Grace, J. R. and Mathur, K. B., 1978. Height and structure of the fountain region above .spouted beds. Can. J. them. Engng 56, 533-537. Heschel, W. and Klose, E., 1981, Zum stromungstechnischen verhalten feinstkorniger guter in der sprudelschicht. C&m. Tech. Leipzig 33 (3), 122-125. Lefroy, G. A. and Davidson, J. F., 1969, The mechanics of spouted beds. Trans. Instn them. Engrs 47, T120-T128. Lim, C. J. and Mathur, K. B., 1978, Modelling of particle movement in spouted beds, in Fluidization (Edited by Davidson, J. F. and Keairns, D. L.), pp. 104-109. Cambridge University Press, Cambridge. Mamuro, T. and Hattori. H., 1968, Flow pattern of fluid in svouted beds. J. them. Enana Jaoan 1.1-5. Mamuro. T. and Hattori, H., 1970, CorrecTion. 1: them. Engng Japan 3, 119. Mathur, K. B. and Epstein, N., 1974, Spouted Beds. Academic _. _. . rress, New York. McNab, G. S., 1972, Prediction of spout diameter. Br. them. Engng Process Technol. 17, 532. Morgan, M. H., III, Day, J. Y. and Littman, H., 1985, Spout voidage distribution, stability and particle circulation rates in spouted beds of coarse particles-l. Theory. Chem. Engng Sci. 40, 1367-1377. Passos, M. L., Mujumdar, A. S. and Raghavan, V. G. S., 1987, Aerodynamics and solids circulation-rates in a two dimensional spouted bed. Paper presented at Powder and Bulk Solids Conference, Rosemont, Illinois, May 1987. Sutanto, W., Epstein, N. and Grace. J. R.. 1985. Hydrodynami& of spout-fluid beds. Powder Technol. 44; 205-212. Whiting, K. 1. and Geldart, D., 1980, A comparison of cyclindrical and semi-cylindrical spouted beds of coarse particles. Chem. Engng Sci. 35, 1499-1501.