Effects of Draft Tubes on Particle Velocity Profiles in Spouted Beds

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Effects of Draft Tubes on Particle VelocityProfiles in Spouted Beds

The vertical particle velocity profiles in a full-column cylindrical conical spoutedbed, with or without a draft tube, are measured using a fibre optic probe system.The profiles have different characteristics for a draft tube spouted bed (DTSB)than for a conventional spouted bed (CSB). The spout of a CSB consists of a cen-tral flow where particle velocities fit exponential distributions, and a boundarylayer where particle velocities are nearly uniform. The spout of a DTSB has noboundary layer and its radial particle velocity profiles are approximately linear.The particle velocities in the spout of a DTSB increase when superficial gasvelocity increases, draft tube diameter decreases, or when entrainment heightdecreases. A kinematic model has been used to simulate the granular flow in theannulus of a CSB and DTSB, and they are compared with the experiments. Theparticle velocities in the annulus of a DTSB are much lower than that of a CSB.Their radial profiles are also different with a CSB. The dependence of particlevelocities in the annulus of a DTSB on superficial gas velocity, draft tube dia-meter, and entrainment height are also discussed. One concludes that the drafttube diameter and entrainment height are two key factors for the solid circulationrate of a DTSB.

Keywords: Particles, Spouted beds, Tubes, Velocity profiles

Received: March 5, 2006; revised: April 6, 2006; accepted: May 4, 2006

DOI: 10.1002/ceat.200600087

1 Introduction

Spouted beds are used as efficient fluid-particle contactors forvarious physical and chemical processes involving coarse parti-cles (dp > 1 mm) [1]. In a conventional spouted bed (CSB)without an internal tube, the spout has direct contact with theannular solids over the entire height of the bed. At the sametime, a continuous percolation of gas from the spout region tothe annular region exists. If the operational bed height is largerthan the maximum spoutable bed depth Hm, the spout cannotsupport the bed, and a transition from spout to collapse occurs[2–3]. In addition, it is also reported that the elevated temper-ature causes a decrease in Hm and the stable spout eventuallydisappears at temperatures above 420 °C despite the changingoperating variables [4].

However, if a draft tube – which is a vertically aligned tubecontaining the spout – is included in the solid bed, the spoutof the CSB efficiently becomes a vertical transport riser. Its Hm

becomes limited only by the energy of the gas stream enteringthe bottom of the draft tube [5, 6]. Besides overcoming thebed height limitation, a draft tube spouted bed (DTSB) hasseveral other advantages. For example, the cases with small-sized fine particles, or at high temperature, etc., which is diffi-cult for a CSB to handle, can be used safely in a DTSB. In addi-tion, the use of a draft tube offers accurate control of gas andsolid residence times and a greater design flexibility, which arevaluable in some specific applications. The DTSB has beenrapidly developed and used in a wide variety of industrial pro-cesses, e.g., drying [7], coal gasification [8], combustion [9],pyrolysis [10], fuel cell [11], coating [12], pharmaceuticals[13], and mixing [14].

There are quite a few studies on particle velocity profiles ina CSB by using various measuring techniques. The optic fiberprobe is one of the most commonplace methods, which hasbeen attempted by Benkrid and Caram, He et al., and Olazar etal., respectively, to measure the vertical particle velocities inboth the annulus and spout of a CSB [15–17]. Some othertechniques, such as the radioactive tracer technique [18], mag-netized marker particle with search coils [19], and the X-ray

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim http://www.cet-journal.com

Xiang-Long Zhao1

Qiang Yao1

Shui-Qing Li1

1 Department of ThermalEngineering, TsinghuaUniversity, Beijing, China.

–Correspondence: Dr. S.-Q. Li ([email protected]), KeyLaboratory for Thermal Science and Power Engineering of the Ministryof Education, Department of Thermal Engineering, Tsinghua University,Beijing, 100084, China.

1) List of symbols at the end of the paper.

Chem. Eng. Technol. 2006, 29, No. 7, 875–881 875

emitting particle tracking technique [20], have also been em-ployed in full CSBs to measure particle velocities. Day et al.measured particle velocity in the spout with a high-speed cam-era, by tracking the motion of colored tracers and also in theannulus by directly using colored particles [21]. His techniqueis only valid for the semi-circular spouted bed system.

However, the studies on DTSBs are relatively limited com-pared with CSBs. Those existing studies mainly focused on thedependence of solid circulation rate on operating variablessuch as draft tube diameter, particle size, length of entrainmentregion, gas velocity, etc. [22–27]. It is also impossible to extendempirical correlations and theoretical analyses developed fromthe experiments of conventional systems to the applications ofDTSBs. The only available literature on the particle velocityprofiles of a DTSB, are reported by Saadevandi and Turton,who used a computer-based video imaging technique in asemicircular DTSB [28]. However, they only investigated parti-cle velocity profiles in the region of the draft tube, instead ofthose in the annulus. As usual, the annulus of a DTSB is con-sidered as a loosely uniform moving bed. The present workinvestigates the flow in both the spout and annulus in a DTSB,tries to find the differences between a DTSB and CSB, and ana-lyzes the effects of gas velocity, draft tube diameter, and en-trainment height on a DTSB.

2 Experiments

A schematic diagram of the experimental apparatus is shownin Fig. 1. The spouted bed unit, made of plexiglass, is a columnwith an inner diameter of 0.196 m and a length of 1.2 m,

joined to a conical base with an included angle of 60° and aninlet diameter of 0.0257 m. Eight holes are drilled along thecolumn wall for the probes. Four are in the cone at 30 mm ver-tical intervals and the other four are in the cylinder at 75 mmvertical intervals. Two tubes with inner diameters of 30 mmand 40 mm, respectively, are used as draft tubes. Millets with amean diameter of 1.34 mm and density of 1.43 g/cm3 are usedas particles. All runs are conducted with a static bed depth of0.42 m, at ambient temperature and pressure. Since the mini-mum spout velocity Ums of a DTSB is much lower than that ofa CSB, the comparisons of CSBs and DTSBs are conducted attheir 1.1 Ums, respectively.

Particle velocities are measured using a fibre optic system,Particle Velometer PV4A, developed by the Institute of ProcessEngineering of the Chinese Academy of Sciences. The probehas an outer diameter of 4 mm and a length of 400 mm. Twocontiguous fibre assemblies, with their centres at a distance of1.92 mm, are contained in the probe. As shown in Fig. 1, lightsfrom an LED are injected into the particles and then reflected.If a particle passes through the probe tip, a signal jump willtransfer through the two fibre assemblies, in sequence. The de-lay between the two signals is then calculated to determine theparticle velocity. More details of the fibre optic probe can befound in [16].

3 A Kinematic Model of Annulus Flow

For slow dense granular flow, there are three types of models:potential, kinematic, and plastic, which lead to partial differen-tial equations that are elliptic, parabolic, and hyperbolic, re-

spectively [29]. It is observed in theexperiments that the flow field at anylevel in the spouted bed does notdepend on the bed height above thatlevel. Therefore, the kinematic modelwhose solution propagates from thebottom up is selected here.

The approach of the kinematic mod-el of annulus flow is based on theresearch of Savage [29] and Sullivan[30]. Assuming that the particle flowin the annulus is a continuous, single,pseudo-phase of constant density, thecontinuity equation takes the form:

1

�r

∂��r �Va�r�∂�r

� ∂�Va�z

∂�z� 0 (1)

All the variables with bars are di-mensionless with the reference lengthlref = rc,where rc is the radius of bedcolumn and reference velocity Vref �Va�z�H� � rc�2Hm in CSB and Vref �Va�z�H� � rc�2He in DTSB. The selec-tion of reference is to simplify theboundary conditions.

The kinematic model assumes thatvacancies arising from radial changesin axial velocity initiate radial move-


Dd

rc

ri

He

H

Figure 1. Schematic diagram of the experimental set-up: (1) Blast blower, (2) Control valve,(3) Flow meter, (4) Spouted bed unit, (5) Fibre probe measuring system

876 X.-L. Zhao et al. Chem. Eng. Technol. 2006, 29, No. 7, 875–881

ment of the particles, which can be described as:

�Va�z � �B∂�Va�r

∂�r(2)

It is convenient to introduce the Stokes stream function WP

as an alternative to Eq. (1).

�Va�r �1

�r

∂wp

∂�z, �Va�z � � 1

�r

∂wp

∂�r(3)

Substituting Eq. (3) into Eq. (2), the governing equation forthe problem is given as:

∂wp

∂�z� B�∂

2wp

∂�r2� 1

�r

∂wp

∂�r� (4)

According to Sullivan [30], the boundary conditions of aCSB are:

wp � 0 at �r � 1 or �z � ��r � �ri� tan a (5)

wp � �z�1 � �r2s � at �r � �rs (6)

A uniform solid entrainment is assumed in Eq. (6). How-ever, the rate of solid entrainment decreases with height, in thepraxis. To obtain a more accurate simulation, it is assumedthat the rate of solid entrainment is in terms of the exponentialfunction, partially, in a CSB with the expression as:

wp � c0 � �z�1 � �r2s � � �1 � c0� � �H�1 � �r2

s ��1 � exp��c1�z��

at �r � �rs (7)

The c0 and c1 in Eq. (7) can be obtained from the experi-ments. The boundary conditions of a DTSB are similar to thatof a CSB, except that the boundary condition of Eq. (6)changes to:

wp � �z�1 � �r2s � at �r � �rs � �z � He�

wp � �z�1 � �H2e � at �r � �rs � �z � He�

(8)

4 Results and Discussions

4.1 Particle Velocities in The Spout

The profiles of Vs, vertical particle velocity in the spout, of aCSB with a superficial gas velocity Us = 0.454 m/s are shownin Fig. 2. The profiles are similar in shape to and resemble pre-vious literature [16, 31]. It is noted that the spout can bedivided into a central flow where Vs profiles fit exponentialdistributions and a boundary layer where Vs are approximatelyuniform due to a high cross flow from the interface. The phe-nomenon of a boundary layer can also be found in other ex-periments [16], but was not pointed out clearly. As far as theradial Vs profiles are concerned, Epstein and Grace have pre-sented a general expression as below [1]:

Vs

Vsc� 1 � r

rs

� �m

(9)

where Vsc is the particle velocity in the centreline.The fitting curves of experimental points in the central flow,

based on Eq. (9), are plotted in Fig. 2. The parameters at dif-ferent levels are listed in Tab.1.

It can be seen that the exponential factor m of all curves arein the range of 1.2–1.4. However, the rs given in Tab. 1 is lowerthan the actual spout radius due to the existence of the bound-ary layer, and thus is different from the original meaning inEq. (9). It can be inferred that the Vsc can reach the maximumvalue at z = 0.115mm, which is about 30 % of the bed height.This distance (z) to achieve a maximum velocity is longer thanthat reported by He et al. [16].

© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

0 5 10 15 200

1

2

3

4

5

z (m)

0.025

0.055

0.085

0.115

V (

m/s

)

r (mm)

0 5 10 15 200

1

2

3

4

5

z(m)

0.190

0.265

0.340

0.415

V (

m/s

)

r (mm)

a)

b)

Figure 2. Profiles of Vs in the CSB. (a) In the cone. (b) In the cy-linder.

Table 1. Fitting parameters corresponding to Fig. 2.

z [m] 0.025 0.055 0.085 0.115 0.19 0.265 0.34 0.415

Vsc [m/s] 3.38 3.82 4.19 4.32 3.79 3.32 2.73 2.52

m [–] 1.39 1.33 1.22 1.39 1.35 1.36 1.25 1.21

rs [m] 12.18 12.32 12.62 12.83 15.37 14.33 12.82 11.21

Chem. Eng. Technol. 2006, 29, No. 7, 875–881 Spouted beds 877

The profiles of Vs for a DTSB with Dd = 30 mm, He =50 mm, and Us = 0.285 m/s are shown in Fig. 3. Since the par-ticle flow is confined in the draft tube and has no cross flow,the boundary layer as in the CSB doesn’t appear. The radialprofiles of Vs are nearly linear, and the exponential factor mapproximately equals 1.0 at all levels. The particle is acceleratedthroughout its entire journey within the tube, which also dif-fers from that in a CSB.

The effects of Us, Dd, and He on the Vs profiles at z = 0.34 mof a DTSB, are shown in Figs. 4 and 5. When Us increases byabout 9 %, the average Vs increases by near 17 %. The largechange in Vs can be attributed to the fact that most of the in-cremental gas enters the tube rather than the annulus. Thevariation of Dd and He both cause the change in the gas distri-bution between the spout and annulus. With He increasing,the area of the entrainment zone will increase and more gaswill diffuse to the annulus, which will cause Vs to decrease.With Dd increasing, the cross-sectional area of the spout willincrease and more gas will enter the tube. Clearly, increasingthe cross-sectional area causes the Vs to decrease greatly, asshown in Fig. 5.

4.2 Particle Velocities in The Annulus

The kinematic model described in the previous section is usedto obtain a prediction of the annulus flow. The stream func-tion WP in a CSB is determined by Eqs. (4), (5), and (7). TheWP in a DTSB is determined by Eqs. (4), (5), and (8). The con-tours of WP in a CSB and DTSB are shown in Fig. 6.

The experimental results of Va of a CSB, together with thesimulation, are presented in Fig. 7. The experiments are con-sistent with the results of He et al. [16] except that the gradientof the profiles is a bit higher due to the material property. Thekinematic model does not agree well with the experimentaldata in the lowest level, where particle entrainment is notproperly estimated. It still delivers a good prediction of theaverage particle velocity in the rest levels. However, there aresudden velocity declines near the spout boundary in the upperpart of the CSB in the experiments and they are not predictedby the model.

The profiles Va in the DTSB are shown in Fig. 8. The averageVa in the cylinder of the DTSB is only 30 % of that in the CSB,


0 5 10 150

1

2

3

4

5

z (m)

0.025

0.055

0.085

0.115

V (

m/s

)

r (mm)

0 5 10 150

1

2

3

4

5

z(m)

0.190

0.265

0.340

0.415

V (

m/s

)

r (mm)

a)

b)

Figure 3. Profiles of Vs in the DTSB. (a) In the cone. (b) In the cy-linder.

0 5 10 150

1

2

3

4

5

Us=0.285 m/s

Us=0.311 m/s

Us=0.337 m/s

V (

m/s

)

r (mm)

Figure 4. Effects of Us on Vs in the DTSB.

0 5 10 15 201

2

3

4

5

Dd=30, H

e=50

Dd=30, H

e=75

Dd=40, H

e=50

V (

m/s

)

r (mm)

Figure 5. Effects of Dd and He, respectively, on Vs in the DTSB.


but the velocities at the lowest two levels of theDTSB are almost as high as that of the CSB.Thus, one can say that the draft tube has lim-ited effects on the particle flow below it. Thedraft tube not only prevents the particle en-trainment, but also changes the state of granu-lar flow in the annulus. The particle velocity,which decreases with radial distance in theCSB, increases slightly with radial distance inthe DTSB. This is probably due to the resis-tance to the flow, caused by friction with thedraft tube being a little higher than the frictionnear the outer cylinder wall. It is noted that thekinematic model predicts that the particle flowin the cylindrical part is a slow, dense, uniformflow. Obviously, this is an ideal prediction de-spite the variation of the particle concentra-tions. According to Fig. 7, the reason for thekinematic model’s success at predicting parti-cle velocities in the annulus of the CSB can beattributed to the fact that the solid entrain-ment at the spout-annulus interface is success-fully described by the exponential function,i.e., Eq. (7). However, the complex stress dis-


0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Radial

Axi

al

0.38225

0.38

225

0.38

225

0.76928

0.76

928

1.15

63

1.15

63

1.5433

1.54

33

1.93

04

1.93

04

2.31

74

2.70

44

3.09

15

3.47

85

0 0.2 0.4 0.6 0.8 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Radial

Axi

al

0.15749

0.15

74 9

0.19

159

0.19

15 9

0.22

568

0.22

56 8

0.25

978

0.25

97 8

0.29

387

0.29

38 7

0.32

797

0.3 2

79 7

0.36

206

0.36

206

0.39

616

0.39

616

0.43

025

0.4 3

02 5

0.46

435

0.4 6

43 5

Figure 6. The contour of the stream function.

0 20 40 60 80

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

z (m)

0.025

0.055

0.085

0.115

V (

m/s

)

r (mm)

0 20 40 60 80

0.005

0.010

0.015

0.020

z(m)

0.190

0.265

0.340

0.415

V (

m/s

)

r (mm)

a)

b)

Figure 7. Profiles of Va in the CSB. (a) In the cone. (b) In thecylinder.

0 20 40 60 800.00

0.01

0.02

0.03

z (m)

0.025

0.055

0.085

0.115

V (

m/s

)

r (mm)

0 20 40 60 800.001

0.002

0.003

0.004

z(m)

0.190

0.265

0.340

0.415

V (

m/s

)

r (mm)

a)

b)

Figure 8. Profiles of Va in the DTSB. (a) In the cone. (b) In the cy-linder.


continuity due to the asymmetric wall frictions and the conicalgeometry, cannot be described within the simplified kinematicmodel and its given boundary conditions [32]. This also im-plies that the flow rule related to plastic potential instead ofthe simplified kinematic model should be considered to pre-dict the relatively slight difference of velocities within the an-nulus of the DTSB, which we discussed in another article [33].

The solid circulation rates Ws in the DTSB and CSB, at dif-ferent levels, are shown in Fig. 9. The Ws is calculated from theparticle velocity in the annulus, Ws = qpVaAa (1–ea). The voi-dage ea is assumed to be a constant value of 0.4. This assump-tion may cause an allowance error since the voidage slightlyvaries around the packing value. As shown in Fig. 9, the Ws be-low the draft tube in the DTSB is almost the same as that inthe CSB. This means that the draft tube does not affect the en-trainment below the tube where the entrainment is most in-tensive. Because the particle entrainment is the highest in thelowest levels, the decline in the circulation rate is secondarycompared to its stability and energy-saving. Thus, the sacrificeof upper entrainment is worthwhile in many cases, and theDTSB has its advantages in the applications where high circu-lation rate is not a requirement.

The effects of Us, Dd, and He on the profiles of Va at z =0.34 m of the DTSB are shown in Figs. 10 and 11. The increas-ing gas velocity in the spout may accelerate the solid’s circula-tion but at the same time, the gas entering the annulus willpull the particle back, decelerating the solid’s circulation rate.As a consequence, the particle velocity in the annulus showslittle change with increment of Us. Both the tube diameter andthe entrainment height have great influences on Va, as shownin Fig. 11. The average Va increases by 28 % as Dd increasesfrom 30 mm to 40 mm, and by 27 % as He increases from50 mm to 75 mm. The particles are entrained in the entrain-ment zone, which can be considered as a column with a diam-eter of Dd and length of He. Since the entrainment area is theproduct of pDd and He, the increments of Dd or He exert greatinfluences on solid circulation rate. However, if Dd and He aretoo large, the spouting of the bed will become unstable.

5 Conclusions

The differences between the particle velocity profiles of theDTSB and CSB are measured and discussed. The spout of theCSB consists of a central flow and a boundary layer. The cen-tral flow varies like the exponential function, and the bound-ary layer has a uniform velocity due to the existence of crossflow. The particle velocity profiles in the spout of the DTSBare flatter and their variations along the radial position areapproximately linear. In the spout of the DTSB, the particlevelocities will increase as superficial gas velocity increases,entrainment height decreases, or the draft tube diameter de-creases.

In the annulus, it is found that the particle velocity in theDTSB increases slightly with the radial distance, which has anopposite trend to that in the CSB. A kinematic granular model,agreeing well with particle velocity in the annulus of the CSB,only predicts the mean value of particle velocity in the DTSB,but not the trend. The superficial gas velocity has little influ-


0.0 0.1 0.2 0.3 0.40.00

0.05

0.10

0.15

0.20

0.25

WS (

kg

/s)

z (m)

CSB

DTSB

Figure 9. The comparison of solid circulation rate between theDTSB and CSB.

0 20 40 60 800.0020

0.0025

0.0030

0.0035

Us=0.285 m/s

Us=0.311 m/s

Us=0.337 m/s

V (

m/s

)

r (mm)

Figure 10. Effects of Us on Va in the DTSB.

20 40 60 800.0020

0.0025

0.0030

0.0035

0.0040

Dd=30, H

e=50

Dd=30, H

e=75

Dd=40, H

e=50

V (

m/s

)

r (mm)

Figure 11. Effects of Dd and He, respectively, on Va in the DTSB.


ence on the particle velocity in the annulus, while the incre-ments of both the tube diameter and entrainment height causethe particle velocity to increase immensely.

The average particle velocities in the DTSB are much lowerthan in the CSB, but they are almost equivalent below the drafttube. That is, the DTSB holds the most efficient entrainmentzone as it sacrifices entrainment to obtain stability. The tubediameter and entrainment height are two effective factors tooptimize solid circulation rate in the DTSB.

Acknowledgement

This work is supported by the Nation Natural Science Founda-tion of China (No. No50306012) and National Key Fundamen-tal Research Project (No.2002CB211600). Part of the revisionwas carried out during a visit to University of Iowa. I am grate-ful to Professors Albert Ratner and Jeffery Marshall for theirhospitality and encouragement.

Symbols used

Aa [m2] cross area of the annulusDd [mm] draft tube diameterH [m] spouted bed heightHe [mm] entrainment heightHm [m] maximum spoutable bed depthUs [m/s] superficial gas velocityUms [m/s] minimum spout velocityrc [m] the radius of bed columnri [m] inlet radiusrs [m] spout radiusVa [m/s] particle velocity in the annulusVs [m/s] particle velocity in the spoutWs [kg/s] solid circulation ratea [°] half-angle of coneea [–] voidage of annulusWp [–] stream function

Reference

[1] N. Epstein, J. R. Grace, in Handbook of Powder Science andTechnology, 2nd ed., Chapman & Hall, New York 1997, Ch.10, pp. 532–567.

[2] J. R. Muir, F. Berruti, L. A. Behie, Chem. Eng. Comm. 1990,88, 153.

[3] M. L. Passos, A. S. Mujumdar, V. S. G. Raghaven, PowderTechnol. 1993, 94, 97.

[4] S. W. M. Wu, C. J. Lim, N. Epstein, Chem. Eng. Comm. 1987,62, 251.

[5] H. Hattori et al., J. Chem. Eng. Japan 2004, 37, 1085.[6] F. Berruti, J. F. Muir, L. A. Behie, Can. J. Chem. Eng. 1988,

66, 91.[7] Z. L. Arsenijevic et al., Can. J. Chem. Eng. 2004, 82, 450.[8] A. Adegoroye et al., Fuel 2004, 83, 1949.[9] J. P. Lucas, C. J. Lim, A. P. Watkinson, Fuel, 1998, 77, 683.

[10] R. K. Konduri, E. R. Altwicker, M. H. Morgan,Chem. Eng.Sci. 1999, 54,185.

[11] M. Olazar, R. Aguado, A. Barona, J. Bilbao, AIChE J. 2000,46, 1025.

[12] B. A. Saadevandi, R. Turon, Chem. Eng. Comm. 2004, 191,1379.

[13] K. Jono, H. Ichikawa, M. Miyamoto, Y. Fukumori, PowderTechnol. 2000, 113, 269.

[14] M. Chen et al., Proc. of the 2003 5th International Symposiumon Coal Combustion, Nanjing, China 2003.

[15] A. Benkrid, H. S. Caram, AIChE J. 1989, 35, 1328.[16] Y. L. He, S. Z. Qin, C. J. Lim, J. R. Grace, Can. J. Chem. Eng.

1994, 72, 561.[17] M. Olazar et al., Chem. Eng. Sci. 2001, 56, 3585.[18] D. Van Velzen, H. J. Flamn, H. Langenkamp, A. Casile, Can

J. of Chem. Eng. 1974, 52, 156.[19] B. Waldie, D. Wilkinson, Can J. of Chem. Eng. 1986, 64, 944.[20] D. Roy, F. Larachi, R. Legros, J. Chaouki, Can J. of Chem.

Eng. 1994, 72, 945.[21] J. Y. Day, M. H. Morgan, H. Littman, Chem. Eng. Sci. 1987,

42, 1461.[22] J. R. Muir, F. Berruti, L. A. Behie, Chem. Eng. Commun.

1990, 88, 153.[23] H. Hattori et al., J. Chem. Eng. Japan 1998, 31, 633.[24] H. Hattori et al., J. Chem. Eng. Japan 2004, 37, 1085.[25] K. Ijichi, M. Miyauchi, Y. Uemura, Y. Hatate, J. Chem. Eng.

Japan 1998, 31, 677.[26] H. Ji, A. Tsutsumi, K. Yoshida, J. Chem. Eng. Japan 1998, 31,

842.[27] T. Ishikura, H. Nagashima, M. Ide, Powder Technol. 2003,

131, 56.[28] B. A. Saadevandi, R. Turton, Chem. Eng. Comm. 2004, 191,

1379.[29] U. Tuzun, G. T. Houlsby, R. M. Nedderman, S. B. Savage,

Chem. Eng. Sci. 1982, 37, 1691.[30] C. Sullivan, A. Benkrid, H. Caram, Powder Technol. 1987, 53,

257.[31] M. Olazar et al., Ind. Eng. Chem. Res. 1998, 37, 4520.[32] S. B. M. Moreea, R. M. Nedderman, Chem. Eng. Sci. 1996,

51, 3931.[33] X.-L. Zhao, Q. Yao, S.-Q. Li, Fifth World Congress on Particle

Technology, Orlando, FL, USA, April 2006.



Effects of Draft Tubes on Particle Velocity Profiles in Spouted Beds

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