nonconventional fluidized beds

20

Other Nonconventional Fluidized Beds

Wen-Ching Yang

Siemens Westinghouse Power Corporation, Pittsburgh, Pennsylvania, U.S.A.

1 INTRODUCTION

In a conventional fluidized bed, fluid is passed througha bed of solids via a distributor plate. At a fluid velo-city beyond the minimum fluidization or minimumbubbling velocity, visible bubbles appear. The fluidthus passes through the bed in two phases, the bubbleand the emulsion phases. The bubble-induced solidsmixing and circulation provide the liquidlike behaviorof a bed of otherwise immobile solids. The liquidlikebehavior of a fluidized bed allows continuous feedingand withdrawal of bed material. The vigorous mixingof solids in the bed gives rise to a uniform bed tem-perature even for a highly exothermic or endothermicreaction. This leads to easier control and operation.The advantages of a fluidized bed, compared to othermodes of contacting such as a packed bed, are numer-ous, and they are described in detail in Chapter 3,‘‘Bubbling Fluidized Beds,’’ and Chapter 26,‘‘Liquid–Solids Fluidization.’’ Because of the inherentadvantages of fluidized beds, they are widely employedin various industries for both physical and chemicaloperations.

The conventional fluidized beds also possess someserious deficiencies, however. The bubbles that areresponsible for many benefits of a fluidized bed repre-sent the fluid bypassing and reduction of fluid–solidscontacting. The rapid mixing of solids in the bed leadsto nonuniform solids residence time distribution in thebed. The rigorous solids mixing in the bed also leads toattrition of bed material and increases the bed material

loss from elutriation and entrainment. Thus for manyindustrial applications, the conventional fluidized bedshave been modified to overcome those disadvantages.Those modifications, in many ways, alter substantiallythe operational characteristics of the fluidized beds andalso change the design and engineering of the beds. It isthe intent of this chapter to document four of the non-conventional fluidized beds in detail: the spouted bed,the recirculating fluidized bed with a draft tube, thejetting fluidized bed, and the centrifugal fluidized bed.

2 SPOUTED BED

The words spouted bed and spouting were first coinedby Mathur and Gishler (1955) at the NationalResearch Council of Canada during the developmentof a technique for drying wheat. The first extensiveassimilation of the literature came from the publicationof Spouted Beds by Mathur and Epstein (1974). Amore recent review can be found in Epstein andGrace (1997).

A classical and conventional spouted bed is shownin Fig. 1. The fluid is supplied only through a centrallylocated jet. If the fluid velocity is high and the bed islow enough, the fluid stream will punch through thebed as a spout as shown in Fig. 1. The spout fluid willentrain solid particles at the spout–annulus interfaceand form a fountain above the bed. The spout fluidwill also leak through the spout–annulus interface intothe annulus to provide aeration for the particles in the

Copyright © 2003 by Taylor & Francis Group LLC

annulus. The spouted bed is usually constructed as acylindrical vessel with a conical bottom as shown inFig. 1 to eliminate the stagnant region. Spouting in aconical vessel has also been employed. Solid particlescan be continuously fed into a spouted bed through theconcentric jet or into the annulus region and continu-ously withdrawn from the annulus region, just as in afluidized bed.

Not all beds are spoutable. For beds with the ratioof nozzle diameter to column diameter Di=D, above acertain critical value, there is no spouting regime. Thebed transfers from the fixed bed directly into the flui-dized state with increasing gas velocity. To achieve astable nonpulsating spouted bed, the nozzle-to-parti-cle-diameter ratio, Di=dp, should be less than 25 or30. There are also the so-called minimum spouting

velocity and the maximum spoutable bed heightrequirements.

2.1 Minimum Spouting Velocity

According to Epstein and Grace (1997), the Mathur–Gishler equation shown below remains the simplestequation to estimate the minimum spouting velocity,good to�15% for cylindrical vessels up to about 0.5 m.

For D 0:5m

ðUmsÞ0:5 ¼dp

D

� �Di

D

� �1=3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2gHð�p � �f Þ

�f

sð1Þ

For nonspherical particles, the diameter, dp, to be usedin Eq. (1) should be the diameter of a sphere with equalvolume. For closely sized near-spherical particles, thevolume–surface mean diameter should be employed.For prolate spheroids, the smaller of the two principaldimensions is best used as the particle diameter inEq (1).

For D > 0:5m

Ums ¼ 2:0DðUmsÞ0:5 D in meters ð2ÞThe maximum value of the minimum spouting velo-city, Um, occurs when the bed height is at the maxi-mum spoutable bed depth or

Um ¼ dpD

� �Di

D

� �1=3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2gHmð�p � �f Þ

�f

sð3Þ

The Um is closely related to the minimum fluidizationvelocity, Umf , of the particles by

Um

Umf

¼ b ¼ 0:9 to 1:5 ð4Þ

A comprehensive review of correlations proposedfor the minimum spouting velocity can be found inMathur and Epstein (1974). A general correlation forthe minimum spouting velocity was also suggested byLittman and Morgan (1983).

The minimum spouting velocity has been shown byKing and Harrison (1980) to decrease markedly withincreasing pressure up to 20 bar. A modified version ofthe Mathus and Gishler correlation, shown in Eq. (1),was proposed by King and Harrison (1980) as

ðUmsÞ0:5 ¼�f

�airðp¼1Þ

� �0:2 dp

D

� �Di

D

� �1=3ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2gHð�p � �f Þ

�f

sð5Þ

where �airðp¼1Þ is the density of air at one atmosphereand room temperature.

Figure 1 A classical and conventional spouted bed.


For single particle size in a rectangular spouted bed,Anabtawi et al. (1992) showed that the minimumspouting velocity had little difference compared tothat in cylindrical beds predictable within the varia-tions from different correlations available for cylindri-cal beds. A dimensionless correlation for predicting theminimum spouting velocity in a rectangular spoutedbed with a mixture of binary particle sizes was recentlyproposed by Anabtawi (1998).

For a given bed height, the minimum spouting velo-city decreases with increasing pressure following theMathur and Gishler equation shown in Eq. (1).Experimental data obtained by He et al. (1988b) indi-cated that Mathur and Gishler equation under-pre-dicted the Ums by about 50% for the heavy steelballs and about 39.5% for the large glass beads. Thedeviation is smaller, about 26%, for the small glassbeads. This corresponds to a Ums dependence of gasdensity of ��0:36

f for the steel balls and large glass beadsand of ��0:22

f for the small glass beads. Thus for correctprediction of the pressure effect on Ums, the exponenton �f in the Mathur and Gishler equation should havedifferent values depending on the particle Reynoldsnumber.

2.2 Maximum Spoutable Bed Height

The maximum spoutable bed height, Hm, can be solvedby combining Eqs. (3) and (4) with the Wen and Yu(1966) equation

ðReÞmf ¼dpUmf�f

�¼ 33:7

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 35:9� 10�6Ar

p� 1

�ð6Þ

to give (Epstein and Grace, 1997)

Hm ¼ D2

dp

D

Di

� �2=3568b2

Ar

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 35:9� 10�6Ar

p� 1

�2 ð7Þ

McNab and Bridgwater (1977) found that Eq. (7) withb ¼ 1:11 fitted the experimental data best. For high-temperature applications, take b ¼ 0:9 to be conserva-tive (Ye et al., 1992; Li, 1992). More correlations werereviewed in Mathur and Epstein (1974) and Littman etal. (1979).

By differentiating Eq. (7) with respect to Ar,dHm=dAr, we can find that there is critical particlesize at Ar ¼ 223,000, calculatable as

ðdpÞcrit ¼ 60:6�2

gð�p � �f Þ�f

!1=3

ð8Þ

For particles larger than the critical particle shown inEq. (8), the maximum spoutable bed height, Hm,decreases with increases in particle size, and with par-ticles smaller than the critical particle, Hm increaseswith increasing dp. Equation (8) is only good forgas–solids spouting and is not applicable to liquid–solids spouting. For liquid–solids spouting, the maxi-mum spoutable bed height decreases with increases inparticle size for all cases. For gas–solids spouting, thecritical Archimedes number Ar ¼ 223,000 correspondsto a critical Reynolds number of (ReÞmf ¼ 67, obtain-able from the Wen and Yu equation, Eq. (6). Thus forgas–solids spouting, the critical particle diameter isusually in the range of 1.0 to 1.5 mm.

The maximum spoutable bed height, Hm, increaseswith increasing pressure based on Eq. (7). Thus theregion of spoutability is greater at higher pressure.Recent experimental data obtained by He et al.(1998b) provided the evidence for the trend.However, it was found that the McNab andBridgwater (1977) modification of Eq. (7) over-pre-dicted the Hm up to 36.5% for the steel balls and thesmaller glass beads and under-predicted the Hm for thelarge glass beads by �10:3%.

2.3 Spout Diameter

The average spout diameter has been correlatedempirically by McNab (1972) with the equation

Ds ¼2:00G0:49D0:68

�0:41b

ð9Þ

Equation (9) is a dimensional equation where SI unitsshould be used. Equation (9) is good to �5:6% atroom temperature. He et al. (1998a) employed afiber-optic probe to measure the spout diameter in asemicylindrical and a full cylindrical spouted bed andfound that the presence of the flat front plate in thesemicylindrical bed considerably distorted the spoutshape. They found that the McNab equation under-estimated the spout diameter in a full cylindrical bedby an average of 35.5%. Under pressure, the McNabequation can also introduce error up to 65.5% at apressure of 343 kPa (He et al., 1998b). Spout diametertends to increase with increasing pressure.

For elevated temperatures, Wu et al. (1987) sug-gested the dimensionally consistent semiempiricalequation


Ds ¼ 5:61G0:433D0:583�0:133

ð�f�bgÞ0:283" #

ð10Þ

2.4 Voidage Distribution

The voidage at the annulus at minimum spouting, "a,can be expected to be close to the voidage at minimumfluidization, "mf . For narrowly sized spherical particles,this voidage is usually around 0.42. For nonsphericalparticles, the voidage will be slightly higher. He et al.(1994) found that the voidage in the annulus was some-what higher than the loose-packed voidage of a packedbed and increased with increasing spouting gas flow.

The voidage in the spout decreases from 1 at thespout inlet almost linearly with height until it reachesaround 0.7 at the top of the spout. Models are avail-able for prediction of the voidage distribution for boththe annulus and spout (Lim and Mathur, 1978).

2.5 Fluid Flow Distribution

By applying Darcy’s law in the annulus of the spoutedbed, Mamuro and Hattori (1968) proposed the follow-ing equation for the calculation of the superficial fluidvelocity, Ua, in the annulus of the spouted bed atheight z.

Ua

Umf

¼ 1� 1� z

Hm

� �3

ð11Þ

Equation (11) is expected to apply even for H Hm

(Grbravcic et al., 1976) and for annulus Reynoldsnumber one or two orders of magnitude larger thanthe upper limit of Darcy’s law (Epstein et al., 1978).

By continuity at any level of the bed, the gas flowbalance can be written as

UszD2s þUaðD2 �D2

s Þ ¼ UD2 ð12ÞThus at any level, the fraction of the total fluid flowpassing through the annulus region can be calculatedfrom Eq. (12) if the spout diameter is known. Thesuperficial velocity at minimum spouting, U ¼ Ums,can be calculated from Eq. (1). In practice, the operat-ing velocity of a spouted bed is typically 10 to 50%higher than Ums. Under those conditions, the excessgas above that required for minimum spouting canbe assumed to pass through the spout as a first approx-imation.

Typical gas streamlines in the annulus are deter-mined by Epstein and Grace (1997) to be like thatshown in Fig. 2. A gas recirculation zone was also

observed immediately adjacent to the gas inlet due tothe venturi effect above the jet nozzle. The gas flow inthe spout is essentially in plug flow and in the annulus,in dispersed plug flow similar to that in a packed bed.Because of the extensive communication of gasbetween the spout and the annulus regions, the gasresidence time distribution deviates substantially fromboth plug flow and perfect mixing.

2.6 Particle Movement and Fountain Height

Solids continuity dictates that, at any bed level, theparticle flowing up in the spout has to be balancedby the particles moving down in the annulus, or

W ¼ �pAsð1� "sÞvs ¼ �pAað1� "aÞvw ð13Þ

Equation (13) neglects the radial variation of particlevelocities in the spout and in the annulus. The particle

Figure 2 Typical gas streamlines in the annulus of a spouted

bed.


velocity in the annulus is further assumed to equal tothe particle velocity observed at the wall, vw.

He et al. (1994) applied a fiber-optic probe system tomeasure the vertical particle velocities in the spout, thefountain, and the annulus of a full-column spoutedbed. They found that radial profiles of vertical particlevelocities in the spout were of near Gaussian distribu-tion rather than parabolic as reported by earlierresearchers. In the annulus, vertical particle velocitiesdecreased with decreasing height because of cross-flowof particles from the annulus to the spout. On thecontrary, vertical particle velocities increased withdecreasing height owing to the reduction of annularcross-sectional area. In the fountain core region, theparticles decelerated, attained zero velocity at top ofthe fountain, and then rained down around the sur-rounding region. In the radial direction, the particlevelocities decreased with increasing radial distancefrom the axis. The semitheoretical model proposedby Grace and Mathur (1978) as shown in Eq. (14)was found to predict the fountain height quite well.

HF ¼ "1:46bs

v20max

2g

�p�p � �f

ð14Þ

2.7 Pressure Gradient in the Annulus

Experimental data obtained by He et al. (1998b)showed that the longitudinal pressure profile in theannulus was independent of pressure with steel ballsand large and small glass beads as bed materials.

2.8 Conical Spouted Beds

Olazar and his associates (1992, 1993a–c, 1995, 1998)studied the design, operation, and performance of aconical spouted bed and found that the conicalspouted bed is especially useful for hard-to-handlesolids that are irregular in texture or sticky. A conicalspouted bed is depicted in Fig. 3. The conical spoutedbed exhibits pronounced axial and radial voidage pro-files that are quite different from the cylindricalspouted beds.

2.8.1 Minimum Spouting Velocity

ðReÞDo;ms ¼ 0:126Ar0:5Db

Do

� �1:68

tan�

2

� �� 0:57

ð15Þ

where Db =upper diameter of the stagnant bedDi =diameter of the bed bottomDo =diameter of the inlet

ðReÞDo;ms=Reynolds number at minimumspouting base of Do

� =included angle of the cone

2.8.2 Bed Voidage Along the Spout Axis

The bed voidage along the spout axis at r ¼ 0 wasfound to be parabolic and dependent on the systemvariables employing an optical fiber probe (San Joseet al., 1998). It can be calculated from

"ð0Þ ¼ 1� Ez

H

�2ð16Þ

where E is an empirical parameter varying between 0.3and 0.6 and is empirically correlated as follows

E ¼ 1:20Db

Do

� ��0:12Ho

Di

� ��0:97U

Ums

� ��0:7

��0:25 ð17Þ

Figure 3 Conical spouted bed.


where Ho is the height of the stagnant bed

and Db ¼ Di þ 2Ho tan�

2

� �ð18Þ

2.8.3 Bed Voidage at the Wall

The bed voidage was found by San Jose et al. (1998) todecrease radially toward a minimum at the wall. Thebed voidage at the wall can be calculated from theequation

"ðwÞ ¼ "o 1þH � z

H

� �0:5

ð19Þ

where "o =loose bed voidage"ðwÞ =bed voidage at the wallH =height of the developed bed

2.8.4 Bed Voidage Correlation

The general bed voidage correlation can be expressedas

" ¼ "ð0Þ � "ðwÞ1þ exp ðr� rsÞ=27:81r2:41s

� þ "ðwÞ ð20Þ

where rs is the radius of the spout.

3 RECIRCULATING FLUIDIZED BEDS WITH

A DRAFT TUBE

The recirculating fluidized bed with a draft tube con-cept is illustrated in Fig. 4. This concept was first calleda recirculating fluidized bed by Yang and Keairns(1974). Several other names have also been used todescribe the same concept: the fluid-lift solids recircu-lator (Buchanan and Wilson, 1965), the spouted fluidbed with a draft tube (Yang and Keairns, 1983;Hadzismajlovic et al., 1992), the internally circulatingfluidized bed (Milne et al., 1992; Lee and Kim, 1992);or simply a circulating fluidized bed (LaNauze, 1976).The addition of a tubular insert, a draft tube, in aspouted fluid bed changes the operational and designcharacteristics of an ordinary spouted bed. Notably,there is no limitation on the so-called ‘‘maximum spou-table bed height.’’ Theoretically, a recirculating flui-dized bed with a draft tube can have any bed heightdesirable. The so-called ‘‘minimum spouting velocity’’will also be less for a recirculating fluidized bed with adraft tube because the gas in the draft tube is confinedand does not leak out along the spout height as in anordinary spouted bed.

There is considerably more operation and designflexibility for a recirculating fluidized bed with adraft tube. The downcomer region can be separatelyaerated. The gas distribution between the draft tubeand the downcomer can be adjusted by changing thedesign parameters at the draft tube inlet. Because thedraft tube velocity and the downcomer aeration can beindividually adjusted, the solid circulation rate andparticle residence time in the bed can be easily con-trolled. Stable operation over a wide range of operat-ing conditions, solids circulation rates up to 100 metrictons per hour, and a solids loading of 50 (weight ofsolids/weight of air) in the draft tube have recentlybeen reported by Hadzismajlovic et al. (1992). Theyused a 95.3 cm diameter bed with a 25 cm diameterdraft tube using 3.6 mm polyethylene particles. Adetailed discussion of the recirculating fluidized bedwith a draft tube is recently published by Yang (1999).

Operating conditions for a recirculating fluidizedbed can be flexible as well. The bed height can belower than the draft tube top or just cover the draft

Figure 4 Recirculating fluidized bed with draft tube oper-

ated as a pneumatic transport tube.


tube top so that a spout can penetrate the bed as in aspouted bed. The bed height can also be substantiallyhigher than the draft tube top, so that a separate flui-dized bed exists above the draft tube. Rather thanoperating the draft tube as a dilute-phase pneumatictransport tube, one can fluidize the solids inside thedraft tube at lower velocities to induce the necessaryrecirculation of the solids. Several studies were con-ducted in this fashion (Ishida and Shirai, 1975;LaNauze, 1976; LaNauze and Davidson, 1976). Thedraft tube wall can also be solid or porous, althoughmost of the studies in the literature employ a solid-walldraft tube. Claflin and Fane (1983) reported that aporous draft tube was suitable for applications in ther-mal disinfestation of wheat where control of particlemovement and good gas/solid contacting could beaccomplished at a modest pressure drop. The conceptcan also be employed as a liquid–solids and liquid–gas–solids contacting device (Oguchi and Kubo,1973). The design and operation of a recirculating flui-dized bed with a draft tube are discussed below.

3.1 Draft Tube Operated as a Fluidized Bed

The schematic for this system, where the draft tube isoperated as a fluidized bed rather than a dilute phasepneumatic transport tube, is shown in Fig. 5. A math-ematical model for the system was developed byLaNauze (1976). The driving force for solids circula-tion in this case was found to be the density differencebetween draft tube and downcomer. The solids circu-lation rate was also found to be affected only by thedistance between the distributor and the draft tube andnot by the draft tube length or height of bed above it.Because of the lower velocity in the draft tube, the

draft tube diameter tends to be larger compared towhen the draft tube is operated in a dilute phase pneu-matic transport mode. One disadvantage of operatingthe draft tube as a fluidized bed is that if the draft tubediameter is too small or the draft tube is too high, thedraft tube tends to operate in a slugging bed mode. Infact, the mathematical model developed by LaNauze(1976) described below assumes that the draft tube is aslugging fluidized bed.

The pressure balance for the dense phase in thedowncomer in the circulating fluidized system shownin Fig. 5 can be expressed as

�P1-4 ¼ �bgHmf ð1� "bdÞ ��dSd

Ad

ð21Þ

A similar expression can be written for the pressurebalance in the draft tube as

��P2-3 ¼ �bgHmf 1� "bfð Þ þ �rSr

Ar

ð22Þ

Combining Eqs. (21) and (22), we have

�bgHmf "br � "bdð Þ ¼ �dSd

Ad

þ �rSr

Ar

ð23Þ

Experimental evidence indicates that the voidage of thesolids flow down the downcomer is close to that ofminimum fluidization, thus "bd ¼ 0.

The bubble voidage in the draft tube, "br, was cal-culated on the basis of the velocity of a rising gas slugin a slugging bed relative to its surrounding solids. Thetotal gas superficial velocity in the draft tube, Ufr, canbe derived as

Ufr ¼ Uslug"br þUmf þVsr"mf

1� "mf

ð24Þ

The slug velocity Uslug, is defined as the rising velocityof the slug relative to the particle velocity at its noseand can be expressed as

Uslug ¼ vp þ 0:35ffiffiffiffiffiffiffigD

pð25Þ

and

vp ¼ ðUfr �Umf Þ þ Vsr ð26ÞSubstituting Eq. (25) into (24), we have

"br ¼Ufr �Umfð Þ � Vsr"mf= 1� "mfð ÞUfr �Umfð Þ þ Vsr þ 0:35

ffiffiffiffiffiffiffigD

p ð27Þ

The flow rate of particles in the downcomer and thedraft tube are related by a mass balance as

Vsr�pAr ¼ Vsd�pAd ¼ WsdAd ¼ WsrAr ð28ÞFigure 5 Recirculating fluidized bed with draft tube oper-

ated as a fluidized bed.


By solving Eqs. (24) and (27) simultaneously, the massflux can be calculated, provided the wall shear stress isknown as a function of particle superficial volume flowrate. Botterill and Bessant (1973) have proposed sev-eral relationships for shear stress, but these are notgeneral. LaNauze (1976) also proposed a method ofmeasuring this shear stress experimentally.

A similar application of the concept as a slugginglifter of solids was studied by Singh (1978) based on thetwo-phase theory of fluidization and the properties ofslugs.

3.2 Draft Tube Operated as a Pneumatic Transport

Tube

Most of the applications for the recirculating fluidizedbed with a draft tube operate the draft tube as a dilutephase pneumatic transport tube. Typical experimentalpressure drops across the downcomer, �P1-4, and thedraft tube, �P2-3, show that they are essentially simi-lar. Thus successful design of a recirculating fluidizedbed with a draft tube requires development of mathe-matical models for both downcomer and draft tube.

An applicable model is described below for generalapplication.

3.2.1 Downcomer and Draft Tube Pressure Drop

Downcomer Pressure Drop When the downcomeris fluidized, the downcomer pressure drop can be cal-culated as in an ordinary fluidized bed as

�P1-4 ¼ Lð1� "dÞ�p ð29ÞWhen the downcomer is less than minimally fluidized,the pressure drop can be estimated with a modifiedErgun equation substituting gas–solid slip velocitiesfor gas velocities (Yoon and Kunii, 1970), as shownin Eq. (30).

�P1-4 ¼L

g150

�ðUgd þUpdÞð1� "dÞ2d2p�

2s"

2d

"

þ1:75�f ðUgd þUpdÞ2ð1� "dÞ

dp�s"d

# ð30Þ

The voidage in the downcomer, ", can be assumed tobe the same as the voidage at minimum fluidization,"mf , which can be determined in a separate fluidizedbed. The agreement between the calculated and theexperimental values is usually better than �10%(Yang and Keairns, 1978a). When the downcomer isnot minimally fluidized, the bed voidage depends onthe amount of aeration and solid velocity. Use of the

voidage at minimum fluidization is only a first approx-imation.

Draft Tube Pressure Drop The pressure dropacross the draft tube, �P2-3, is usually similar to thatacross the downcomer, �P1-4, in magnitude. Thusfor a practical design basis, the total pressure dropacross the draft tube and across the downcomer canbe assumed to be equal. In most operating condi-tions, the pressure drop at the bottom section of thedraft tube has a steep pressure gradient due primarilyto the acceleration of solid particles from essentiallyzero vertical velocity. The acceleration term is espe-cially significant when the solid circulation rate ishigh or when the draft tube is short.

The model suggested by Yang (1977) for calculatingthe pressure drop in vertical pneumatic conveying linescan be applied here to estimate the acceleration pres-sure drop. The acceleration length can be calculatedfrom numerical integration of the equation

�L ¼ðUpr2

Upr1

UprdUpr

34CDS"

�4:7r

�f ðUgr �UprÞ2ð�p � �f Þdp � gþ fpU

2pr

2D

� �ð31Þ

The solid friction factor, fp, can be evaluated with theequation proposed by Yang (1978):

fp ¼ 0:0126ð1� "rÞ"3r

ð1� "rÞðReÞtðReÞp

" #�0:979

ð32Þ

The lower limit of integration, Upr1, is derived from

Wsr ¼ Upr�pð1� "rÞ ð33Þwith "r ¼ 0:5, and the upper limit, Upr2, by the equa-tion

Upr ¼ Ugr �Ut

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ fpU

2pr

2gD

� �� "4:7r

sð34Þ

The total pressure drop in the acceleration region canthen be calculated as

�P2-3 ¼ðL0

�pð1� "rÞ dLþðL0

2fg�fU2gr

gDdL

þðL0

fp�pð1� "rÞU2pr

2gDdL

þ �pð1� "rÞU2pr

g

" #atL

ð35Þ


If the draft tube height is less than the accelerationlength, the integration of Eq. (35) is carried outthrough the whole length of the draft tube. If thedraft tube height is larger than the acceleration length,the integration of Eq. (35) is carried out for the totalacceleration length, and the extra pressure drop for therest of the draft tube can then be included to give thetotal pressure drop in the draft tube. The suggestedequations have been applied to actual experimentaldata satisfactorily (Yang and Keairns, 1978a).

3.2.2 Gas Bypassing Phenomenon

Because of different design and operating parameters,the distribution of the total flow between the draft tubeside and the downcomer side can be very different.According to Yang (1999), the important design para-meters are the area ratio between the downcomer andthe draft tube, the diameter ratio between the drafttube and the draft tube gas supply or the diameter ofthe solid feeding tube, the distance between the distri-butor plate and the draft tube inlet, the area ratio ofthe draft tube gas supply and the concentric solidsfeeder, and the design of the downcomer gas supplynozzle. In addition to the design parameter, the oper-ating parameters will also affect gas bypassing. Therelative strength of the concentric jets of the drafttube gas supply and the solids feeder determines thehalf-angle of the combined jet, and the jet velocitydetermines the jet penetration. The jet velocity of thedowncomer gas supply nozzles is also important if thejets are horizontal and directed toward the draft tube.

The gas bypassing phenomenon was studied byStocker et al. (1989) by measuring the differential pres-sure drops between the draft tube and the downcomer.A more rigorous investigation was conducted by Yangand Keairns (1978a) by injecting gas tracer, carbondioxide or helium, continuously at different locationsand taking gas samples from both the draft tube sideand the downcomer side. The actual amounts of gaspassing through the draft tube and the downcomerwere then obtained by solving mass conservation equa-tions for tracer gas.

Except for the conical distributor plate, no simplegas bypassing relationship exists. No rigorous theore-tical model has thus far been proposed. The quanti-tative gas bypassing information is usually determinedexperimentally. Qualitatively, the gas bypasses fromthe draft tube side into the downcomer side forsmall draft-tube-to-downcomer area ratios and viceversa. Gas bypasses exclusively from the downcomerside to the draft tube side when the distance between

the distributor plate and the draft tube inlet is small.For a conical distributor plate, the angle of the con-ical plate (¼ 45� and 60�) does not seem to affect thegas bypassing characteristics. A more detailed dis-cussion of gas bypassing phenomena is presented inYang (1999).

3.2.3 Solids Circulation Mechanisms and the SolidsCirculation Rate

Both solids circulation mechanisms and the solids cir-culation rate are important in designing and operatinga recirculating fluidized bed with a draft tube. Forcommercial applications in the area of coating andencapsulation of solid particles, such as in coating ofpharmaceutical tablets and in coating seeds for delayedgermination and controlling the release rate of fertili-zers, the particle residence time and cycle time areimportant considerations. The performance based oncycle time distribution analysis for coating and granu-lation was studied by Mann and Crosby (1973, 1975),Mann (1983), and Turton et al. (1999).

Two mechanisms for solids circulation have beenobserved experimentally (Yang and Keairns, 1978a).High-speed movies (1000 to 1500 frames per second)taken at the inlet and the midsection of the draft tubewith a sand bed revealed that solids transport insidethe draft tube was not a conventional pneumatic trans-port, where uniform solid suspension prevailed, but aslugging type transport. The high-speed movies takenat the outlet of a 23 m/s air jet showed that the air jetissuing from the jet nozzle supplying air to the drafttube was composed of bubbles rather than a steady jet.The bubble grew from the mouth of the nozzle until itsroof reached the draft tube; then the sudden suctionfrom the draft tube punctured the roof. A continuousstream of dilute solids suspension passed through theroof into the draft tube. Simultaneously, another bub-ble was initiated. As this bubble grew, it pushed a slugof solids into the draft tube. The high-speed moviestaken at the midsection of the draft tube exhibitedalternate sections of dilute suspension and solids slugoccupying the total cross section of the draft tube.

A steady jet without bubbling can be maintained ina sand bed between the jet nozzle and the draft tubeinlet with high jet velocities of the order of 60 m/s andwithout downcomer aeration. Once the downcomer isaerated, the solids circulation rate increases dramati-cally and the steady jet becomes a bubbling jet.Apparently, the inward-flowing solids have enoughmomentum to shear the gas jet periodically intobubbles.


When the polyethylene beads (density ¼ 907 kg=m3,average size ¼ 2800�m) and the hollow epoxy spheres(density ¼ 210 kg=m3, average size ¼ 2800�m) wereused as the bed material, a steady jet between the jetnozzle and the draft tube was always observed for allexperiments conducted.

Solids circulation rate was found to be stronglyaffected by the design configuration at the bottom ofthe draft tube and the downcomer owing to changes ingas bypassing characteristics (Yang and Keairns,1983). This coupling effect indicates that an under-standing of the gas bypassing characteristics is essen-tial. Except for simple cases, the dependency of the gasbypassing characteristics on design and operatingparameters are still not amenable to theoretical treat-ment as discussed earlier. A recent study by Alappatand Rane (1995) on the effects of various design andoperational parameters on solids circulation rate essen-tially affirms the above conclusions.

When only the draft tube gas flow is employed with-out downcomer aeration, the solid circulation ratedepends primarily on the entrainment rate of the jets.Aeration of the downcomer can be provided withgreatly increased solid circulation rate. At lower down-comer aeration, the solid circulation rate is essentiallysimilar to that without downcomer aeration. At higherdowncomer aeration, however, a substantial increasein solid circulation rate can be realized. Apparently, aminimum aeration in the downcomer is required inorder to increase substantially the solid circulationrate.

As expected, the closer the distance between thedistributor plate and the draft tube inlet, the lowerthe solids circulation rate. This is not only because ofthe physical constriction created by locating the distri-butor plate too close to the draft tube inlet but alsobecause of the different gas bypassing characteristicsobserved at different distributor plate locations as dis-cussed earlier. When the distance between the distribu-tor plate and the draft tube inlet becomes large, it cancreate start-up problems discussed in Yang et al.(1978).

3.3 Design Procedure for a Recirculating Fluidized

Bed with a Draft Tube

From the experimental evidence, the design of a recir-culating fluidized bed with a draft tube involves thespecification of a number of design parameters andan understanding of the coupling effects between thedesign and the operating variables. A procedure is pre-sented here for the design of a bed to give a specified

solids circulation rate. This design procedure assumesthat the solids and gas characteristics, feed rates, andoperating temperature and pressure are given. Thedesign parameters to be specified include the vesseldiameter, draft tube diameter, draft tube height, gasdistributor, and distributor position. These parameterscan be specified using the solids circulation rate model,experimental data on gas bypassing, and processrequirements (e.g., selection of gas velocity in the bedabove the draft tube).

Experience indicates that a simple theoretical modelto predict gas bypassing that takes into account all thedesign and operating variables cannot be developed.Empirical correlation, however, can be obtained byconducting experiments with tracer gas injection fora given distributor plate design at different operatingconditions and at different distances from the drafttube inlet.

It is also assumed that the total gas flow into thebed is known. When the operating fluidizing velocityis selected for the fluidized bed above the draft tube,the diameter of the vessel is determined. The finaldesign decisions include selection of the draft tubediameter, the distributor plate design, the separationbetween the draft tube and the distributor plate, andthe draft tube height. Selection of the draft tubeheight may be determined by other considerations,such as solids residence time, though it also affectsthe solids circulation rate. A gas distributor is selectedto be compatible with the process and to maintain thegas velocity in the downcomer near Umf . The drafttube diameter is then selected by using the solids cir-culation rate model to obtain the desired circulationrate.

The design procedures are thus:

1. Assume a solid circulation rate per unit drafttube area, Wsr, and calculate the particle velocity inthe downcomer, Upd, from the equation

Wsr ¼ Upd 1� "mfð Þ�pAd

Ar

ð36Þ

2. If the two-phase theory applies, the slip velocitybetween the gas and the particles in the downcomermust equal the interstitial minimum fluidizing velocityas

Ufd þUpd ¼ Umf

"mf

ð37Þ

where Ufd and Umf are positive in the upward directionand Upd is positive in the downward direction.


Calculate Ufd from Eq. (37) and the pressure dropacross the downcomer, �P1-4, from Eq. (30) assuming"d ¼ "mf .

3. Use trial and error with Eqs. (32), (33), and (34)to evaluate Upr, "r, and fp.

4. Numerically integrate Eq. (31) to obtain theparticle acceleration length and Eq. (35) to obtain thepressure drop across the draft tube, �P2-3.

5. Compare the pressure drop across the down-comer, �P1-4, and that across the draft tube, �P2-3.If they are not equal, repeat procedures 1 through 5until �P1-4 ffi �P2-3.

3.4 Startup and Shutdown Considerations

Both cold flow experiments and actual pilot-plantexperience show that, if operating conditions anddesign parameters are not selected carefully, start-up(initiating solids circulation) might be a problem (Yanget al., 1978). The primary design parameters that willaffect the start-up are the distance between the grid andthe draft tube inlet (Ld) and the diameter ratio betweenthe draft tube and the draft tube gas supply nozzle(D=dD). The maximum allowable distance, Ld, can bedetermined by applying the jet penetration equationsuggested by Yang and Keairns (1978b):

Lj

dD¼ 6:5

�f�p � �f

U2j

gdD

!1=2

ð38Þ

where Uj is the gas velocity issuing from the draft tubegas supply. For high-temperature and high-pressureoperations, Eq. (41), to be discussed later, should beused for calculating Lj. Another consideration is thatthe jet boundary at the end of jet penetration shouldcorrespond to the physical boundary of the draft tubeinlet. Merry’s expression (1975) for jet half-angle canbe used for this purpose:

cotð�Þ ¼ 10:4�fdD�pdp

� �0:3ð39Þ

or

Ld ¼ ðD� dDÞ2 tanð�Þ ð40Þ

The distance between the distributor plate and thedraft tube inlet, Ld, selected for the design should bethe smaller one of those estimated from Eqs. (38) and(40).

A start-up technique described by Hadzismajlovic etal. (1992) is also worthy of consideration if the drafttube gas supply is retractable. The draft tube gas sup-

ply nozzle can be inserted into the draft tube duringstart-up and shutdown. This will reduce the difficultydescribed here during start-up. After start-up, the sup-ply nozzle can be lower to below the draft tube inlet ata predetermined height to provide the normal opera-tion configuration. This will prevent solids from drain-ing into the gas supply nozzle during shutdown. Ofcourse, if the draft tube gas supply nozzle is not mova-ble due to hostile operating conditions, the techniquecannot be used. Then the design precautions discussedabove during start-up should be followed.

3.5 Multiple Draft Tubes

Studies in the past always concentrate on beds with asingle draft tube. A literature survey failed to uncoverany reference on the operation of multiple draft tubes.Even in the area of conventional spouted beds, thereferences on multiple spouted beds are rare. Foonget al. (1975) reported that the multiple spouted bedwas inherently unstable owing to pulsation and regres-sion of the spouts. Similar instability was also observedby Peterson (1966), who found that vertical bafflescovering at least one-half of the bed height were neces-sary to stabilize the operation. In an industrial envir-onment where solids are processed in large vessels,multiple draft tubes may be both necessary and bene-ficial. Exploratory tests in a 2D bed with three drafttubes were reported by Yang and Keairns (1989). Thedesign methodology proposed earlier for beds with asingle draft tube is still applicable here for beds withmultiple draft tubes.

3.6 Industrial Applications

The application of the recirculating fluidized bed witha draft tube was probably first described by Taskaevand Kozhina (1956) for a coal devolatilizer. Dry coal isintroduced into the devolatilizer below the bottom ofthe draft tube through a coal feeding tube concentricwith the draft tube gas supply. The coal feed andrecycled char at up to 100 times the coal feed rateare mixed inside the draft tube and carried upwardpneumatically in dilute phase at velocities greaterthan 4.6 m/s. The solids disengage in a fluidized bedabove the top of the draft tube and then descend in anannular downcomer surrounding the draft tube as apacked bed at close to minimum fluidization velocity.Gas is introduced at the base of the downcomer at arate permitting the downward flow of the solids. Therecirculating solids effectively prevent agglomeration


of the caking coal as it devolatilizes and passes throughthe plastic stage.

A ‘‘seeded coal process’’ was later developed byCurran et al. (1973) using the same concept to smearthe ‘‘liquid’’ raw coal undergoing the plastic transitiononto the seed char and the recirculating char duringlow-temperature pyrolysis. Westinghouse successfullydemonstrated a first stage coal devolatilizer with cak-ing coals in a pilot-scale Process Development Unitemploying a similar concept where the downcomerwas fluidized and the jet issuing from the draft tubewas immersed in a fluidized bed above the draft tube(Westinghouse, 1977). The same concept was also pro-posed for extending fluidized bed combustion technol-ogy for steam and power generation (Keairns, et al.,1978). The British Gas Council has also developed theconcept for oil and coal gasification (Horsler andThompson, 1968; Horsler et al., 1969). The develop-ment eventually resulted in a large-scale recirculatingfluidized bed hydrogenator gasifying heavy hydrocar-bon oils (Ohoka and Conway, 1973). McMahon (1972)also described a reactor design for oil gasification usinga multiplicity of draft tubes. The Dynacracking processdeveloped by Hydrocarbon Research Inc. in the 1950s(Rakow and Calderon, 1981) for processing heavycrude oil also utilized an internal draft tube. Morerecently, coal gasification in a recirculating fluidizedbed with a draft tube was described by Judd et al.(1984) and a coal–water mixture combustion by Leeand Kim (1992).

Other industrial applications of the concept includethat for coating tablets in the pharmaceutical industry(Wurster et al., 1965), for drying of dilute solutionscontaining solids (Hadzismajlovic, 1989), and for mix-ing and blending (Decamps et al., 1971/1972;Matweecha, 1973; Solt, 1972; Krambrock, 1976).Both Conair Waeschle Systems and Fuller Companysupply commercial blenders based on the concept. Theconcept was also proposed as a controllable solids fee-der to a pneumatic transport tube (Decamps et al.,1971/1972; Silva et al., 1996).

Although most of the experimental data reportedhere were obtained with large particles, Geldart classB and D powders, it is believed that the concept canequally be applicable for any fine aeratable and free-flowing solids, Geldart’s class A powders.

A similar concept has also been used for liquid–solids and liquid–gas–solids contacting devices(Oguchi and Kubo, 1973; Fan et al., 1984) and bio-reactors (Chisti, 1989). Bubble columns fitted withdraft tubes have also been employed in the chemicalprocess industries as airlift reactors for gas–liquid con-

tacting operations. Examples are the low-waste conver-sion of ethylene and chlorine to dichloroethane,biological treatment of high-strength municipal andindustrial effluent, and bioreactors. Critical aspects ofthe design and operation of bubble columns with drafttubes have recently been reviewed by Chisti and Moo-Young (1993). Freedman and Davidson (1964) alsocarried out a fundamental analysis for gas holdupand liquid circulation in a bubble column with adraft tube. Extensive experimentation in a bubble col-umn with a draft tube was conducted by Miyahara etal. (1986), and an in-depth analysis by Siegel et al.(1986). The effects of geometrical design on perfor-mance for concentric-tube airlift reactors were studiedby Merchuk et al. (1994).

4 JETTING FLUIDIZED BEDS

In a gas fluidized bed, the introduction of gas is usuallyaccomplished through distributors of various designs.Any time the gas is distributed through orifices or noz-zles, a jetting region appears immediately above thegrid. A large fluctuation of bed density occurs in thiszone, indicating extensive mixing and contacting ofsolids and gas. If the chemical reactions between gasand solids are fast, much of the conversion may occurin this jetting region.

Another type of fluidized bed, where the jetting phe-nomenon is an important consideration, is the spoutedfluid bed, where a large portion of gas goes through afairly large nozzle. Because of the dominant effect ofthis jetting action provided by the large nozzle, thistype of fluidized bed can be more appropriately calleda ‘‘jetting fluidized bed,’’ especially when the jet doesnot penetrate through the bed like that in a spoutedbed. A schematic of a typical jetting fluidized bed isshown in Fig. 6. Jetting, bubbling dynamics, and solidcirculation are important hydrodynamic phenomenagoverning the performance and operation of large-scale jetting fluidized beds. They are the focus of ourattention in this section. A more extensive discussioncan be found in Yang (1999).

4.1 Jet Penetration and Bubble Dynamics

Gas jets in fluidized beds were critically reviewed inSec. 11 of Chapter 3, ‘‘Bubbling Fluidized Beds.’’Most of the data available now are from jets smallerthan 25 mm. The discussion here will emphasize pri-marily the large jets, up to 0.4 m in diameter, andoperation at high temperatures and high pressures.


The gas jets can also carry solids and are referred to asgas–solid two-phase jets in this discussion.

4.1.1 Momentum Dissipation of a Gas-SolidTwo-Phase Jet

Gas velocity profiles in a gas–solid two-phase jet insidea fluidized bed were determined using a pitot tube byYang and Keairns (1980). The velocity profiles wereintegrated graphically, and gas entrainment into a jetwas found to occur primarily at the base of the jet. Areasonably consistent universal velocity profile can beobtained by plotting ðUjr �UjbÞ=ðUjm �UjbÞ vs. r=r1=2,comparable with the Tollmien solution for a circularhomogeneous jet in an infinite medium (Abramovich,1963; Rajaratnam, 1976).

4.1.2 Jet Penetration and Jet Half Angle

Jet Penetration Jetting phenomena were studiedby Yang and Keairns (1978b) in a semicircular col-umn 30 cm in diameter using hollow epoxy spheres(rp ¼ 210 kg/m3) as the bed material and air as thefluidizing medium to simulate the particle/gas densityratio in actual operating conditions at 1520 kPa and1280�K. A two-phase Froude number, defined as�fU

2j =ð�p � �f Þgd0 and derived from both the momen-

tum balance and the dimensionless analysis, wasfound to correlate jet penetration data well. The cor-relation was extended to cover the high-pressure jetpenetration data of Knowlton and Hirsan (1980) atpressures up to 5300 kPa for fluidized beds of sand(�p ¼ 2629 kg/m3), FMC char (�p ¼ 1158 kg/m3),and siderite (�p ¼ 3988 kg/m3). A subsequent analysisby Yang (1981) indicated that the two-phase Froudenumber originally suggested could be modifiedslightly to account for the pressure effect.

Lj

do¼ 7:65

1

Rcf

�fð�p � �f Þ

U2j

gdo

" #0:472

ð41Þ

where

Rcf ¼ ðUcf Þp=ðUcf Þatm ð42ÞIn the absence of (Ucf Þp and (Ucf Þatm, (Umf Þp and(Umf Þatm can be employed.

The limiting form of Eq. (41) at atmospheric pres-sure (101 kPa), where the correction factor Rcf ¼ 1,approaches the correlation originally proposed foratmospheric conditions shown in Eq (38):

Jet Half-Angle The jet half-angle can be calcu-lated from the experimentally measured bubble sizeand jet penetration depth as follows:

� ¼ tan�1 DB � d02Lj

� �ð43Þ

Experimentally observed jet half-angles range from 8�

to 12� for the experimental data mentioned above.These compare to 10� suggested by Anagbo (1980)for a bubbling jet in liquid.

4.1.3 Bubble Dynamics

To describe the jet adequately, the bubble size gener-ated by the jet needs to be studied. A substantialamount of gas leaks from the bubble to the emulsionphase during the bubble formation stage, particularlywhen the bed is less than minimally fluidized. A modeldeveloped on the basis of this mechanism predicted the

Figure 6 Schematic of a jetting fluidized bed.


experimental bubble diameter well when the experi-mental bubble frequency was used as an input. Theexperimentally observed bubble frequency is smallerby a factor of 3 to 5 than that calculated from theDavidson and Harrison model (1963), which assumedno net gas interchange between the bubble and theemulsion phase. This discrepancy is due primarily tothe extensive bubble coalescence above the jet nozzleand the assumption that no gas leaks from the bubblephase.

High-speed movies were used to document the phe-nomena above a 0.4 m diameter jet in a 3 meter dia-meter transparent semicircular jetting fluidized bed(Yang et al., 1984b). The movies were then analyzedframe by frame to extract information on bubble fre-quency, bubble diameter, and jet penetration depth.The process of bubble formation is very similar tothat described in Kececioglu et al. (1984), but it wasmuch more irregular in the large 3 m bed. A model wasdeveloped to describe this phenomenon by assumingthat the gas leaks out through the bubble boundary ata superficial velocity equivalent to the superficial mini-mum fluidization velocity. For a hemispherical bubblein a semicircular bed, the rate of change of bubblevolume can be expressed as

dVB

dt¼ Gj �Umf

�D2B

2ð44Þ

where VB ¼ �D3B=12 for a hemispherical bubble.

Equation (44) can be reduced to show the changesof bubble diameter with respect to time in Eq. (45):

D2BdDB

ð4Gj � 2�UmfD2BÞ

¼ dt

�ð45Þ

Integrating Eq. (45) with the boundary condition thatDB ¼ 0 at t ¼ 0 gives

t ¼ 1

2Umf

Gjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�GjUmf

p"

ln2Gj þDB

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�GjUmf

p2Gj �DB


p !�DB

# ð46Þ

The maximum bubble size, where the total gas leakagethrough the bubble boundary equals the total jet flow,can be obtained from either Eq. (44) or Eq. (45):

ðDBÞmax ¼ffiffiffiffiffiffiffiffiffiffiffi2Gj

�Umf

sð47Þ

The total amount of gas leakage from the bubble at abubble size DB is then

F ¼ Gj

2Umf

Gjffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�GjUmf

p"

ln2Gj þDB


p2Gj �DB


p �DB

#� �D

3B

12

ð48Þ

Equation (46) and the experimental bubble frequency,n ¼ 1=t, were used to predict the expected bubble dia-meter. The predicted bubble diameters are very close tothose actually observed. Theoretically, Eqs. (46) and(48) can be solved to obtain both the bubble frequencyand the bubble diameter if the total gas leakage at themoment of bubble detachment, F , is known. The bub-ble growth equations can be similarly derived for acircular jet in a three-dimensional bed. The sameexperimental observation and conclusions describedabove for a semicircular bed are expected to hold aswell. Bubble frequency from the jet was also studiedusing a force probe in the same bed. The results werepublished in Ettehadieh et al. (1988).

The validity of extrapolating the data obtained in asemicircular model to a circular one is also of concern.Not much research has been carried out in this area.Preliminary research results by Whiting and Geldart(1980) indicated that, for coarse, spoutable solids(Geldart’s group D powders), semicircular columnscould provide information very similar to that fromthe circular ones.

4.2 Gas Mixing Around the Jetting Region

4.2.1 Gas Mixing Around Single Jets

Gas exchange between the jet and the outside emulsionphase was studied by tracer gas injection and by inte-gration of gas velocity profiles in the jet at variousheights above the jet nozzle in a 28.6 cm diameterbed with a 3.5 cm jet using polyethylene beads as bedmaterial (Yang et al., 1984a). The concentration pro-files obtained at different elevations were found to beapproximately similar if the local tracer concentrationis normalized with the maximum tracer concentrationat the axis, C=Cm, and plotted against a normalizedradial distance, r=ðr1=2Þc, where ðr1=2Þc is the radial posi-tion where the tracer concentration is just half themaximum tracer concentration at the axis. Thus in apermanent flamelike jet in a fluidized bed, not only thevelocity profiles in the jet but also the gas concentra-tion profiles are similar.

The gas mixing between the jetting region and theemulsion phase and the gas flow pattern around the jetwere determined by solving the tracer gas conservation


equation numerically along with the axial velocity pro-files in the jet obtained with a pitot tube. It is con-cluded that the gas mixing in a jetting fluidized bedwith a permanent flamelike jet is due primarily to con-vection and that diffusion plays a negligible role.

The resulting velocity profiles and the flow patterninside and around the jet indicated that the gas flowdirection is predominantly from the emulsion phaseinto the jet at distances close to the jet nozzle. Thisflow can be from the aeration flow in the emulsionphase, as in the cases of high jet velocity or high aera-tion flow, or from the flow recirculated from the upperpart of the jet. The entrainment of gas into the jetoccurs immediately above the jet nozzle. The extentof this region depends on both the aeration flow out-side the jet and the jet velocity. Increases in aerationflow and jet velocity tend to increase the height of thisregion. Beyond this gas entrainment region, the gas inthe jet is then expelled from the jet along the jet height.The gas expelled at the lower part of the jet is recircu-lated back into the jet, setting up a gas recirculationpattern at the lower part of the jet. The extent of thisrecirculation pattern increases with increases in jetvelocity and with decreases in aeration flow outsidethe jet.

The axial velocity profiles, calculated on the basis ofTollmien similarity and experimental measurement inYang and Keairns (1980), were integrated across thejet cross section at different elevations to obtain thetotal jet flow across the respective jet cross sections.The total jet flows at different jet cross sections arecompared with the original jet nozzle flow, as shownin Fig. 7. Up to about 50% of the original jet flow canbe entrained from the emulsion phase at the lower partof the jet close to the jet nozzle. This distance canextend up to about 4 times the nozzle diameter. Thegas is then expelled from the jet along the jet height.

4.2.2 Gas Mixing Around Concentric Jets

Gas mixing phenomena around a concentric jet wereinvestigated by Yang et al. (1988) in a large semicircu-lar cold flow model, 3 meters in diameter and 10 metershigh, with a triple concentric jet nozzle assembly of 25cm in diameter (see also Yang, 1998). A dividing gasstreamline was observed experimentally that preventsthe gas mixing between the jetting region and the emul-sion phase until at higher bed heights. This dividinggas streamline corresponds roughly to the boundaryof down-flowing solids close to the walls, to be dis-cussed later. Several observations were made basedon this study. Regardless of the incoming jet flow

rate, the gases that are injected through the concentricjets essentially remain in the core of the reactor and donot fully mix with the gas in the dense solid down-flowregion of the bed. Similarly, the gas injected throughthe conical grid sections is not entrained by the incom-ing jets. Partial entrainment and mixing of these gasesoccur at locations where bubble formation and bubblecoalescence take place. On the contrary, the mixingamong the concentric jets occurs quite fast and isusually completed within the jet penetration length.

4.3 Solids Circulation in Jetting Fluidized Beds

The solids circulation pattern and solids circulationrate are important hydrodynamic characteristics ofan operating jetting fluidized bed. They dictate directlythe solids mixing and the heat and mass transferbetween different regions of the bed.

In many applications the performance of fluidizedbeds is frequently controlled by the hydrodynamicsphenomena occurring in the beds. Applications suchas the fluidized bed combustion and gasification offossil fuels are the cases in point. In those applications,the rates of fuel devolatilization and fines combustionare of the same order of magnitude as the mixing phe-nomena in a fluidized bed. The mixing and contactingof the gases and solids very often are the controllingfactors in reactor performance. This is especially truein large commercial fluidized beds where only a limitednumber of discrete feed points for reactants is allowedbecause of economic considerations. Unfortunately,solids mixing in a fluidized bed has not been studiedextensively, especially in large commercial fluidizedbeds, because of experimental difficulties.

4.3.1 Solids Circulation Pattern

Yang et al. (1986) have shown that, based on the tra-versing force probe responses, three separate axialsolids flow patterns can be identified. In the centralcore of the bed, the solid flow direction is all upward,induced primarily by the action of the jets and therising bubbles. In the outer regions, close to the vesselwalls, the solid flow is all downward. A transition zone,in which the solids move alternately upward anddownward, depending on the approach and departureof the large bubbles, was detected in between these tworegions.

The solids circulation patterns were investigatedwith a force probe. Since the force probe is directional,the upward solids movement will produce a positiveresponse from the probe and vice versa, the magnitude


of the response being an indication of the magnitude ofthe solids circulation rate. The number of major peaksper unit time is closely related to the actual bubblefrequency in the bed. The force probe data allow theidentification of three major solids flow regions in the3 m model as shown in Fig. 8. At the central portion ofthe bed, the solids flow is induced upward primarily byjetting action at the lower bed height and by largebubbles at the higher bed height. At the outer regionnext to the vessel wall, the solids flow is all downward.

The region has a thickness of approximately 0.25 m.Between these two regions the solids flow is alterna-tively upward and downward, depending on theapproach and departure of large bubbles. No stagnantregion was evident anywhere in the bed.

In addition to the three solids circulation regionsreadily identifiable, the approximate jet penetrationdepth and bubble size can also be obtained from Fig.8. The jetting region can be taken to be the maximumaverage value of jet penetration depth. From the jet

Figure 7 Gas entrainment into a 3.5 cm semicircular jet. (Adapted from Yang, 1998.)


boundary at the end of the jetting region, an initialbubble diameter can be estimated. This value can betaken to be the minimum value of the initial bubblediameter. The diameter of a fully developed bubble canbe obtained from the bubble boundary in the devel-oped-bubble region, as shown in Fig. 8. The centralregion is thus divided further into three separateregions axially: the jetting region, the bubble-develop-

ing region, and the developed-bubble region. Bubbleswere observed to coalesce in the bubble-developingregion during analysis of the motion pictures takenthrough the transparent front plate.

4.3.2 Solids Circulation Rate

The results of the force probe measurement indicatethat the solid circulation rates increase with increasingjet flow rates. A simple mechanistic model was devel-oped to correlate the solids circulation data. The modelassumes that solids circulation inside the bed isinduced primarily by bubble motion. The solids circu-lation pattern inside the bed can be divided into twomajor regions radially. In the center of the bed, theparticle movement is predominantly upward and isinduced by bubbles disengaged from the central jet.This region has a radius similar to the radius of theaverage bubble size. In the outer region, the particlesmove primarily downward. In the meantime, the par-ticles in both regions exchange with each other acrossthe neighboring boundary at a constant rate ofWz g=cm

2-s. This mechanistic model is shown schema-tically in Fig. 9. Material balance in a differential ele-ment dz as shown in Fig. 9 gives,

in the bubble street region,

K@X 0

J

@zþ �R2

i 1� "mfð Þ�p@X 0

J

@tþ 2�RiWz

ðX 0J � XJÞ ¼ 0

ð49Þ

and in the annular region,

K@XJ

@zþ � R2

0 � R2i

� �1� "mfð Þ�p

@XJ

@t

þ 2�RiWz XJ � X 0J

� � ¼ 0

ð50Þ

where

K ¼ nVBfwð1� "wÞ�p ð51ÞThe data do not show any clear dependence on theaxial position, z. The axial dependence is thus assumedto be negligible. Equations (49) and (50) are reducedfrom partial differential equations to ordinary differ-ential equations. If we consider only the annularregion, Eq. (50) reduces to

dXJ

dtþ 2�RiWz

�ðR2o � R2

i Þð1� "mf Þ�pXJ � X 0

J Þ ¼ 0� ð52Þ

Since both XJ and X 0J are independent of z, the rela-

tionship between XJ and X 0J can be approximated by

the material balance of the coarse particles injectedinto the bed to serve as the tracer.

Figure 8 Solids circulating pattern in a jetting fluidized bed.


Solving for X 0J we have

X 0J ¼

Wt

�R2iHð1� "mf Þ�p

� Ro

Ri

� �2

�1

" #1� "mf

1� "i

� �XJ

ð53ÞSubstituting Eq. (53) into Eq. (52), after some mathe-matical manipulation we get

dXJ

dtþ PXJ �Q ¼ 0 ð54Þ

where

P ¼ 2RiWz

ðR2o � R2

i Þð1� "mf Þ�pþ 2Wz

Rið1� "iÞ�pð55Þ

Q ¼ 2WzWi

�RiðR2o � R2

i ÞHð1� "mf Þð1� "iÞ�2pð56Þ

Equation (54) can be integrated with the boundarycondition that XJ ¼ 0 at t ¼ 0 to give

XJ

XoJ

¼ 1

twPPt� 1� expð�PtÞ½ �� ð57Þ

The equilibrium tracer concentration in the bed aftercomplete mixing can be expressed as

X0J ¼ Wt

�H�p R2i ð1� "iÞ þ ðR2

o � R2i Þð1� "mf Þ

� ð58Þ

The voidage inside the bubble street, "i, can be calcu-lated as

"i ¼ "mf þ fBð1� "mf Þ ¼ "mf þnVB

�R2iUA

ð1� "mf Þ

ð59Þwhere fB is the volumetric fraction of bubbles occupy-ing the bubble street region at any instant; it can beevaluated from

fB ¼ nVB

�R2iUA

ð60Þ

If the bubble frequency, bubble diameter, and bubblevelocity are known, the solids mixing rate can be cal-culated.

In correlating the data, the solid exchange ratebetween the two regions, Wz, was assumed to be con-stant. Comparison of the calculated and the experi-mentally observed tracer concentration profiles wasgood.

The solids mixing study by injection of tracer par-ticles indicated that the axial mixing of solids in thebubble street is apparently very fast. Radial mixingflux depends primarily on the bubble size, bubble velo-city, and bubble frequency, which in turn depend onthe size of the jet nozzle employed and the operating jetvelocity.

4.4 Solid Entrainment Rate into Gas and Gas–Solid

Two-Phase Jets

A mathematical model for solid entrainment into apermanent flamelike jet in a fluidized bed was pro-posed by Yang and Keairns (1982). The model wassupplemented by particle velocity data obtained byfollowing movies frame by frame in a motion analyzer.The particle entrainment velocity into the jet wasfound to increase with increases in distance from thejet nozzle, to increase with increases in jet velocity, andto decrease with increases in solid loading in the gas–solid two-phase jet.

High-speed movies indicated that the entrained par-ticles tended to bounce back to the jet boundary morereadily under high solid loading conditions. This may

Figure 9 Schematic of a mathematical model for solids cir-

culation in a jetting fluidized bed.


explain why the entrainment rate decreases withincreases in solid loading in a two-phase jet. A readyanalogy is the relative difficulty in merging into a rush-hour traffic as compared to merging into a light traffic.

A simple model for solid entrainment into a perma-nent flamelike jet was described in Sec. 11.5.1 ofChapter 3 ‘‘Bubbling Fluidized Beds.’’

4.5 Scale-up Considerations

The development of commercial fluidized bed proces-sors generally requires intermediate stages of testing onphysical models simulating commercial equipment.Simulation (or scale-up) criteria derived from fluidizedbed momentum-conservation relations may be appliedto determine the design and operating conditions forphysical models discussed in Chapter 13 ‘‘FluidizedBed Scale-up.’’ Such criteria, while not totally estab-lished at this time, have been applied to simulate apressurized fluidized bed gasifier having a large verticalcentral jet for fuel feeding, combustion, and gasifica-tion (Yang et al., 1995).

Physical models of commercial fluidized bed equip-ment provide an important source of design informa-tion for process development. A physical model of acommercial fluidized bed processor provides a small-scale simulation of the fluid dynamics of a commercialprocess.While commercial processes will typically oper-ate at conditions making direct observation of bed fluiddynamics difficult (high temperature, high pressure,corrosive environment), a physical model is designedto allow easy observation (room temperature and pres-sure, nonreactive atmosphere, transparent vessel).

Cold flow studies have several advantages.Operation at ambient temperature allows constructionof the experimental units with transparent plasticmaterial that provides full visibility of the unit duringoperation. In addition, the experimental unit is mucheasier to instrument because of operating conditionsless severe than those of a hot model. The coldmodel can also be constructed at a lower cost in ashorter time and requires less manpower to operate.Larger experimental units, closer to commercial size,can thus be constructed at a reasonable cost and withinan affordable time frame. If the simulation criteria areknown, the results of cold flow model studies can thenbe combined with the kinetic models and the intrinsicrate equations generated from the bench-scale hotmodels to construct a realistic mathematical modelfor scale-up.

The need for physical modeling of fluidized bedprocessors is dictated by the state of the art of fluidized

bed scale-up technology. In general, no rational proce-dure exists for scaling up a new fluidized bed processorconcept that precludes the need for physical modeling.Many empirically developed rules of thumb for flui-dized bed scale-up exist in specific areas of fluidizedbed application that are not generally applicable.Existing mathematical modeling approaches are them-selves based heavily on empirical descriptions of flui-dized bed fluid dynamics. These bubbling bed modelscan be applied only where confidence exists for theempirical bubble flow description built into themodel. Fluidized bed processors operate over such abroad range of fluid dynamic regimes that this confi-dence rarely exists for new concepts.

Yang et al. (1995) described the application of thisscale-up approach. Comprehensive testing programswere performed on two relatively large-scale simula-tion units for a period of several years: both a 30 cmdiameter (semicircular) Plexiglas cold model and a 3 mdiameter (semicircular) Plexiglas cold model operatedat atmospheric pressure.

The results are highly significant to the developmentof fluidized bed technology because they represent acase study of a rational fluidized bed developmentapproach. The extensive data generated are unique intheir equipment dimensions, pushing existing modelsand correlations to new extremes and offering newinsights into large-scale equipment behavior. Theunderstanding of the hydrodynamic phenomena devel-oped from the cold flow model studies, and the analy-tical modeling reported was integrated with parallelstudies that investigated coal gasification kinetics, ashagglomeration, char–ash separation, and fines recycleto develop an integrated process design procedure.

4.6 Applications

The primary applications for large-scale jetting flui-dized beds are in the area of coal gasification asdescribed by Yang et al. (1995), Kojima et al. (1995),and Tsuji and Uemaki (1994). Smaller scale applica-tions are for fluidized bed coating and granulation dis-cussed in Chapter 17, ‘‘Applications for Coating andGranulation.’’

5 ROTATING FLUIDIZED BEDS

Rotating fluidized beds make use of the centrifugalforce, which can reach many times the gravitationalforce, to increase the minimum fluidizing velocity ofthe particles and minimize the formation of bubbles


even at a very high gas flow rate. This can make therotating fluidized beds very compact compared to con-ventional fluidized beds so that they can be utilized inspecial applications. Pfeffer et al. (1986) described anapplication using a rotating fluidized bed as a high-efficiency dust filter. Tsutsumi et al. (1994) investigatedthe reduction of nitrogen oxides with soot emittedfrom diesel engines using a centrifugal fluidized bed.The fundamental governing equations have been stu-died by Kao et al. (1987), Chen (1987), Fan et al.(1985), and Chevray et al. (1980). A schematic of arotating fluidized bed is presented in Fig. 10.

5.1 Minimum Fluidization Velocity

Because both the centrifugal force and the drag forceon the particles in the centrifugal fluidized bed varywith radial position, there are three minimum fluidiza-tion velocities that can be defined (Qian et al., 1998).The surface minimum fluidization velocity is defined asthe point when the inner surface of the bed is fluidized.The pressure drop across the bed can be calculated onthe basis of a fixed bed because the bed is essentially afixed bed except at the surface. The point where thewhole bed is fluidized (at the distributor plate) is calledthe critical minimum fluidization velocity. In this case,the pressure drop can be determined as in a fluidized

bed. Then there is the average minimum fluidizationvelocity calculated from these two extremes.

When we make use of the Wen and Yu modificationof the Ergun equation (1966), the surface minimumfluidization velocity, Umfi, can be derived as

Umfi�f dp�

rori

¼ ð33:7Þ2 þ 0:0408�f ð�p � �f Þd3

p!2ri

�2

" #0:5

�33:7

ð61Þ

Similarly, the critical minimum fluidization velocity,Umfc, can be expressed as

Umfc�f dp�

¼ ð33:7Þ2 þ 0:0408�f ð�p � �f Þd3

p!2ro

�2

" #0:5

�33:7

ð62Þ

The average minimum fluidization velocity can then becalculated from

Umf�fdp�

¼ 33:7C2

C1

� �� 2

þ 0:0408�f ð�p � �f Þd3

p!2

�2

C3

C1

�0:5� 33:7

C2

C1

ð63Þ

Figure 10 Schematic of horizontal and vertical rotating fluidized beds.


where

C1 ¼ r2o1

ri� 1

ro

� �C2 ¼ ro ln

ror1

� �

C3 ¼ðr2o � r2i Þ

2

ð64Þ

5.2 Pressure Drop

For Ug Umfi, the bed is a packed bed and thepressure drop can be calculated from the packed bedequation

dP

dr¼ �

Ugro

r

� �þ � Ugro

r

� �2

ð65Þ

or

�P ¼ �Ugro lnrori

� �þ �U2

g r2o

1

ri� 1

ro

� �ð66Þ

where

� ¼ 1650ð1� "Þ�d2p

� ¼ 24:5ð1� "Þ�fdp

ð67Þ

When Ug � Umfc, the bed is completely fluidized andthe pressure drop can be calculated from the fluidizedbed equation.

dP

dr¼ ð�p � �f Þð1� "Þr!2 ð68Þ

or

�P ¼ ð�p � �f Þð1� "Þ!2 ðr2o � r2i Þ2

ð69Þ

With Umfi < Ug < Umfc, the bed is partially fluidized,and the pressure drop can be calculated by summingthe pressure drop across the fluidized bed and thepacked bed:

�P ¼ ð�p � �f Þð1� "Þ!2 ðr2pf � r2i Þ2

þ �Ugro lnrorpf

� �þ �U2

gr2o

1

rpf� 1

ro

� �ð70Þ

Qian et al. (1998) found that when a sintered metaldistributor plate was used for gas distribution, theexperimental pressure drop could be predicted fairlywell with the theoretical equation mentioned above.However, when a distributor with slotted openings

was used, the experimental pressure drop is justabout 70% of that calculated from the theoreticalequation. Apparently, with a slotted distributor plate,the bed was not completely fluidized. The bed abovethe webs was not fluidized. Chen (1987) also reportedtwo different types of pressure drop in the literature.One shows a pressure drop curve similar to that of aconventional fluidized bed, while the other one exhibitsa maximum pressure drop in the fluidized region.

NOTATION

Aa = cross-sectional area of annulus at any level

Ad = cross-sectional area of the downcomer

Ar = cross-sectional area of the draft tube

Ar = Archimedes number, �f ð�p � �f Þd3pg=�

2

As = cross-sectional area of spout at any level

C = tracer gas concentration

CDS = drag coefficient of a single particle

Cm = maximum tracer gas concentration at the

jet axis

D = draft tube diameter

= fluidized bed or spouted bed diameter

Db = upper diameter of the stagnant bed in

conical spouted bed

DB = bubble diameter

ðDBÞmax = maximum bubble diameter

dD = diameter of draft tube gas supply

Di = diameter of spout nozzle in spouted beds

= diameter of the bed bottom in conical

spouted bed

do = diameter of jet nozzle

Do = diameter of the inlet in conical spouted bed

dp = mean solid particle diameter

ðdpÞcrit = critical particle size in spouted bed

Ds = spout diameter

Ds = average spout diameter

F = total amount of gas leakage during bubble

formation from a jet

fB = volumetric fraction of bubble in bubble

street

fp = solid friction factor

fw = wake fraction of the bubble

g = gravitational acceleration

G = superficial mass flux of spouting fluid

Gj = total gas flow rate through the jet

Gr = total gas flow rate in the draft tube

H = bed height of a fluidized bed or a spouted

bed

= height of the developed bed in the conical

spouted bed

HF = fountain height, m

Hm = maximum spoutable bed height

Hmf = bed height at minimum fluidization


Ho = height of stagnant bed in conical spouted

bed

L = height of draft tube or height of

downcomer

Ld = distance between the distributor plate and

the draft tube inlet

Lj = jet penetration length

�L = distance required for acceleration of

particles

n = bubble frequency

�P = pressure drop

�P1-2 = pressure drop between 1 and 2 (see Fig. 5)




r = radial distance from the jet axis or from

the spout axis

ri = radius of inner surface of granule bed

ro = radius of rotating fluidized bed

rpf = radius of interface of fluidized and packed

beds

rs = radius of the spout

r1=2 = radial distance where gas velocity is one-

half the maximum gas velocity at the jet

axis

ðr1=2Þc = radial distance where tracer gas

concentration is one-half the maximum at

the jet axis

Ri = radius of bubble street, Ri ¼ DB=2Ro = bed radius

ðReÞDo;ms = Reynolds number at minimum spouting

based on Do

ðReÞmf = Reynolds number at minimum fluidization,

¼ dpUmf�f=�ðReÞp = Reynolds number based on the slip

velocity, ¼ dpðUgr �UprÞ�f=�ðReÞt = Reynolds number based on the terminal

velocity, ¼ dpUt�f=�Sd = total wall area in the downcomer

Sr = total wall area in the draft tube

t = time

tw = total time required to inject all tracer

particles

U = superficial fluid velocity

Ua = superficial fluid velocity in annulus of a

spouted bed at any level

UA = absolute bubble velocity

ðUcf Þatm = complete fluidization velocity at

atmospheric pressure

ðUcf Þp = complete fluidization velocity at pressure P

Ufr = superficial fluid velocity in the draft tube

Ug = superficial gas velocity

Ugd = superficial gas velocity in the downcomer

Ugr = superficial gas velocity in the draft tube

Uj = superficial jet nozzle velocity

Ujb = gas velocity at jet boundary

Ujm = maximum gas velocity at the jet axis

Ujr = gas velocity at radial distance r from the

jet axis

Um = maximum value of the minimum spouting

velocity at the maximum spoutable bed

height

Umf = superficial minimum fluidization velocity

Umfc = critical minimum fluidization velocity

Umfi = surface minimum fluidization velocity

ðUmf Þatm = superficial minimum fluidization velocity at

atmospheric pressure

Umf Þp = superficial minimum fluidization velocity at

pressure P

Ums = minimum spouting velocity

ðUmsÞ0:5 = minimum spouting velocity for vessel

diameter less than 0.5 meters

Upd = solid particle downward velocity in the

downcomer

Upt = solid particle velocity in the draft tube

Uslug = rising velocity of the gas slug relative to

the particle velocity at its nose

Usz = superficial upward fluid velocity in spout

or fountain core at any level

Ut = terminal velocity of a single solid particle

VB = volume of a gas bubble

V0max = particle velocity along axis at bed surface

vs = local upward particle velocity in spout or

fountain core at any level

Vsd = net upward superficial volumetric flow rate

of particles in the downcomer

Vsr = net upward superficial volumetric flow rate

of particles in the draft tube

vw = downward particle velocity at column wall

W = mass downflow rate of solids in annulus at

any level ¼ mass upflow rate of solids in

spout at same level

Wsd = mass flux of particles in the downcomer,

Wsd ¼ Vsd�pWsr = mass flux of particles in the draft tube,

Wsr ¼ Vsr�pWt = cumulative weight of tracer particles

injected after time t

Wz = radial solids mixing flux

Xoj = tracer particle weight fraction in the bed

after complete mixing

Xj;X0j = tracer particle weight fractions in annulus

and in bubble street, respectively

z = axial coordinate

Greek Letters

" = bed voidage

"ð0Þ = bed voidage at r ¼ 0

"ðwÞ = bed voidage at the wall in conical spouted

bed


"a = annulus voidage at minimum spouting

"bd = bubble voidage in the downcomer

"br = bubble voidage in the draft tube

"bs = spout voidage at bed surface

"d = voidage in the downcomer

"i = voidage in bubble street

"mf = voidage at minimum fluidization

"r = voidage in the draft tube

"o = loose bed voidage in conical spouted bed

"s = voidage in spout or fountain core at any

level

"w = voidage in bubble wake

� = viscosity of the fluid

�airðp¼1Þ = density of air at one atmosphere and room

temperature

�b = bed density or bulk density

�f = density of the fluid

�p = solid particle density

�s = sphericity of the solid particle

! = rotating speed

� = jet half angle

= included angle of the cone in conical

spouted bed

�d = particle–wall shear stress in the downcomer

�r = particle–wall shear stress in the draft tube

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