Geldart - Types of Gas Fluidization

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2owd er Techn ology, 7 (1973) 285-2920 Elsevier equoia SA, Lausanne- Printedn t h e NetheriandsTypes of Gas FhidizationD. GELDARTPost g r a dua t e Schoo l of Powder Techno l ogy . Un i ue r s i t y of B r ad f o r d , Yor k s. (G t . B r i t a i n )(ReceivedMay 22, 1972; in revised ormNovember1, 1972)

S umm a r y

T h e b eh a v i o u r o f s ol i d r f l u i d i z e d b y g a s es f a l l s i n t of o u r c l ea r l y r e cogn i z ab l e g roup s , cha r a c t e r i z ed bydens i t y d z y f e r en ce p , - p r ) an dm eanpa r t i c l e s i z e. Themos t eas i l y r e cogn i z ab l e f ea t u r e s o f t h e g roup s a re :po , v der s i n g roup A exh i b i t dense pha se expa ns i o na f t e r m i ? l ~ ? l w ? r j l u i d i ~ a t i o ~ l a n d p r i o r t o t h e commen -men t o f bubb l i n g ; t h o se i n g roup B bubb l e a t t h em i n i mw n f l u i d i z a t i o n v el o c i t y : t h o s e i n g r o u p C a r ed y f i c u u l t t o f l u i d i z e a t aN a n d t h o s e i n g r o u p D c a nf o rm s t a b l e s p ou t e d b ed s . A n um e r i c a l c r i t e r i o n, v h i c h isti z g u i s h es bet l v een g roup s A a nd B ha s beendev i s ed an d ag r ees i v e t i l v i t h pub l i s hed da ta . Gener -a l i z a t i o n s c on c er n i n g p o k v d e r s Gt h k z a g r o u p c a n b ema de k t h reasonab l e con f i d ence bu t conc l u s i o ?=d r a b v n f r om o bs er v a t i o n s mad e o n a p o ? vd e r i n o n eg r o u p s h o u l d n o t i n g en e r a l b e u s ed t o p r e d i c t t h eb eh a v i o u r o f a p o l v d er t i l a n o t h e r g r o u p .

I . INTRODUCTIONIt is impractical for most research workers partic-ularly those wishing to work on a reasonably largescale to test a wide variety of powders as this is only

one of the variables to be studied_ There i s thereforea tendency to assume that conclusions drawn fromdata on the fluidization of one powder, e.g. crackingcatalyst, are applicable to other powders havingquite different particle sizes and densities. This cancause confusion, and as has been shown in a recentpaper I, it is responsible for some of the apparentcontradictions and differences of opinion whichappear in published papers.In this paper an attempt is made to group togetherthose powders having broadly similar propertieswhen fluidized by a gas, so that generalizations con-cerning powders within a group can be made withreasonable confidence.Althou& a few of the characteristics of fluidized

solids are common to all groups. many are not aintergroup predictions should therefore be avoidor made only with considerable caution. A simpcriterion, which differentiates between the twlargest groups of powders, is presented.

2. PREvIOUS WORKVarious attempts have been made to devise

criterion which would distinguish between bubblin(aggregative. heterogeneous) and non-bubbling (paticulate, homogeneo-s) fluidization.Some criteria are based on the concept of intparticle forces in the vicinity of bubbles and lead dimensionless groups such as the Froude numbeor combinations of Fr with Re and other groupsWhilst having the advantage of simplicity, thecriteria do little more than distinguish correcbetween liquid and gas tluidization. Zenz4 presentan empirical graphical plot of bed voidage againp s / p r with partide size as a parameter which indcates that bubbling and slugging become less likeas p , / p t decreases.Other criteria5- are based on a consideration the stability or rate of growth of disturbanceDespite being much more complicated_ they mapredictions which are no more accurate than tsimple Froude criterion. Two other groups. workers have assumed that bubbles are alwapresent but are not observable below a certabubble-particle ratio. Simpson and Rodgersg aproach offers a way of estimating the size of bubbllik-ly to be present in a given system at differe.voidages. If the calculated bubble size is very smthe system is said to be particulate. Unfortunatethe correlations are rather cor,lplex and have belittle used. Harrison, Davidson and de Kocktheory is based on the max i n :w n s i z e of bubblikely to be stable in a fluidized system. The mechnism of bubble co lapse on which the theory


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286 D GELDARTbased is almost certainly incorrect but it does,like the other theories, differentiate correctly be-tween gas and liquid fluidization. Unlike the cor-relation of Simpson and Rodger, which predictsthat a given system can exhibit both homo- andheterogeneous behaviour depending on the voidage(and therefore on the fluid velocity), the theory ofHarrison et al. merely classifies systems into bub-bling, transition and non-bubbling systems. In itspresent form it is not able to say whether a givensystem can exhibit more than one type of behaviour.The most recent approach has been that ofVerloop and Heertjes. who use the occurrence ofshock waves ia the bed s riterion for the transitionbetween bubbling and non-bubbling. Their criterionshows that some systems can behave homogeneouslyat low voidages and heterogeneously at highvoidages. It appears to give reasonable agreementwith experimental data for liquid systems but, aswill be shown later. its accuracy is poor in makingpredictions concerning gas-solid fluidization.

It is evident from this brief survey that as yet thereis no easy and accurate method for predicting how agiven powder will behave when fluidized by gas.3 DESCRIPTION OF POWDER GROUPS

Before attempting to develop a numerical cri-terion which can be used to predict how a givenpowder is likely to behave when fluidized by gas, adescription of the properties of three clearlyrecognizable groups. and one other. -will be given.This is based both on the published literature andon the present experimental work.3.1 Gr o u p A

Materials having a small mean size and/or a lowparticl- density (less than about 1.4 g/cm3) generallyexhibit the type of behaviour described below. somecracking catalysts being typical examples.

Beds of powders in this group expand consider-ably before bubbling commences. When the gassupply& suddenly cut off the bed collapses slo~ly~,typically at a rate of 0.3-O-6 cm/s, this being similarto the superficial velocity of the gas in the densephase. Gross circulation of the powder (akin toconvection currents in liquids) occurs even whenfew bubbles are present, producing rapid mixing.Bubbles in a two-dimensional bed appear to splitand recoalesce very frequently. All bubbles rise morerapidly than the interstitial gas velocity, but in freelybubbling beds the velocity of small bubbles (-z 4 cm)

appears to be about 3r 40 cm/s regardless of bubbsizei5, suggesting that the gross circulation referrto controls the rise velocity. There is some evidencthat the mean size of bubbles may be reduced in twways, i .e. by having a wide particle size distributioand/or a small mean particle size16. A maximububble size does appear to exist. Considerablback-mixing of gas in the dense phase occurs and gexchange between bubble and dense phase generally high * ; however, the ratio (volume cloud/volume of bubble) is negligibleg. When tsuperficial gas velocity is sufftciently high to cauthe formation of slugging conditions. the sluproduced are axi-symmetric: as the superficial gvelocity is further increased slug flow breaks dowinto a turbulent regimewith tongues of fluid dartinzig-zag fashion up the bed . The velocity at whithis occurs appears to decrease with particle si3.2 Gr o u p B

Group B contains most materials in the mean sand density ranges 40 ,um < d,, -c 500 pm, 4 g/cm p, > 1.4 g/cm3, sand being the most typical powde

In contrast with group A powders, naturaloccurring bubbles start to form in this type of powdeat or only slightly above minimum fluidizatiovelocity. Bed expansion is small and the bcollapses very rapidly when the gas supply is cut oThere is little or no powder circulation in the absenof bubbles and bubbles burst at the surface of tbed as discrete entities. Most bubbles rise moquickly than the interstitial gas velocity and bubbsize increases linearly with both bed height aexcess gas velocity (U - U,) ; coalescence is the pdominant phenomenon r There is no evidence omaximum bubble size, although few studies2 hainvolved beds sufliciently deep or large enough allow bubbles to reach the maximum size predicteby theory. It has been shown recently that whcomparisons are made at equal values of bed heigand U - U,, bubble sizes are independent of bomean particle size and size distribution. Bacmixing of dense phase gas is relatively low as is gexchange between bubbles and dense. phase; tcloud volume/bubble volume ratio is generally nnegligible. When the gas velocity is so high thslugging commences, the slugs are initially asymmetric, but with further increase in gas velocian increasing proportion become asymmetrimoving up the bed wall with an enhanced velocirather than up the tube axis. There is no evidence the breakdown of slugging into turbulent flowZo


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TYPESOFGASFLUIDIZATION 2A numerical method for distinguishing powder

groups will be discussed later. in Section 4.3.3.3 Gr o u p C

Powders which are in any way cohesive belong inthis category_ Normal fhridization of such powdersis extremely difficult; the powder lifts as a plug insmall diameter tubes, or channels (rat-holes) badly.i x_ the gas passes up voids extending from distri-butor to bed surface. This difftculty arises becausethe inter-particle fcrces are greater than those whichthe fluid can exert on the particle. and these aregenerally the result of very small particle size. strongelectrostatic charges or the presence in the bed ofvery wet or sticky material. Particle mixing andconsequent y heat transfer between a surface andthe bed is much poorerZ3 than with powders ofgroups A or B.Fluidization can generally be made possible orimproved by the use of mechanical stirrers orvibrators which break up the stable channels, or. inthe case of some powders. by the addition of a fumedsilica of sub-micron size. Where agglomerationoccurs due to excessive electrostatic charging someimprovement can generally be effected by humidi-fication of the incoming gas, or by making the equip-ment walls conducting, for example. by coating glasswith a very thin layer of tin oxide. An equallyeffective but less permanent technique is to coat theparticles with a conducting substance such asgraphiteZ6.3.4 Gr o u p D

The justification for this further category of pow-ders, confined to large and/or very dense particles.is not so readily apparent as in the other three casessince relatively little published information isavailable7-8.

Certainly all but the largest bubbles rise moreslowly than the interstitial fluidizing gas. so that gasflows into the base of the bubble and out of the top,providing a mode of gas exchange and by-passingdifferent from that observed with group A or Bpowders. The gas velocity in the dense phase is high,solids mixing relatively poor; consequently back-mixing of the dense phase gas is small. The flowregime around particles in this group may beturbulent, causing some particle attrition with rapid-ehrtriation of the fines producedZq. Relatively stickymaterials can be ffuidized since the high particlemomentum and fewer particle-particle contactsminimize agglomeration. There is some evidence

that bubble sizes may be similar to those in group powdersat equal values of bed height and U - fY, bthat bubble formation does not commence unabout 5 cm above the distributor3. Hcwever, it doappear that ifgas is admitted only through a centraly positioned hole. group D powders can be mato spout.

3 CRITERIA FOR CLASSIFYING POWDERS INTGROUPS

4.1 Th e bubb l e po i n ihe most easily observed difference betweepowders in groups A and B is whether or not the b

bubbles at or very close to minimum fluidizationIf there is an appreciable bed expansion befobubbling commences, then the powder belongs group A and is likely to have the other propertieassociated with that group. Calling the superficigas velocity at which the first bubble appears U,the minimum bubbling point, we can define grouA powders as those in which U&U, > 1. Corrlations for U , are well established, but the only simpand accurate correlation for Us


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2ss D. GELDARTTABLE 1Experimental results on Group A powders

Dialron - 105 78 0 52 0.85 0.542 1 095p,= 1.18 g cm- 105-325 118 0.82 1.17 0.496 1.065

125-150 141 0.96 1.34 0.48 1 1.04015S180 155 1.43 1.60 0.465 1.012180-210 190 1.67 1.76 0.452 1.003210-250 220 2.44 7.5 0.44 1.001250-300 263 3.11 3.11 0.444 1.000300-350 318 4.11 4.11 0.444 1.000

Fresh catalystp.21 gcme3

1O-20 2520-30 3945-53 5553-63 6863-75 7575-90 loo90-105 108as received 65

0.080.090.230.290.330.460.44

0.25 0.645 1.430.35 0.629 1.370.59 0.645 1.280.68 0.645 1.210.73 0.638 1.200.90 0.627 1.160.93 0.630 1.190.64 0.630 1.25

Spent catalyst -45 45 0.13 0.51 0.675 1.41p= 1.5 g cm-3 45-53 62 0.18 0.60 0.630 I.355343 75 0.22 0.68 0.635 1.31

63-75 87 0.26 0.73 0.600 1.2575-90 95 0.35 0.82 0.610 I.1890-105 115 0.4 0.84 0.610 1.14

4 .3 C r i t er i o n f o r g r oups A and BIt is interesting to note that the two largest sizesof Diakon bubbled at the incipient fluidizationvelocity and the 21&250-pm fraction at a velocity

very close to U,,. According to the criterion (U,,,/U, > 1 for group A powders) these largest fractionsshould be classified as belonging to group B.When the minimum bubbling velocities of all theother fractions, as well as that of the wide size range

fresh catalyst (i.e. all the group A powders), areplotted against mean particle size a,( = l/Xx/d,)it can be seen (Fig 1) that a very simple relationshipexists between lJ ,, and d,,, namely

%r = K,&v (1)K MB7which has units of s- , has a value of 100 whenU,,, is in cm s- and d , in cm. Thus

U,, = 100 d,, (2)Some data of Davies i_ Godardi5, de J ong35 andlZietema3 are also represented well by eqn. (2).Data fit equally well whether derived from narrowcuts or wide size range material.

100 200Meanparticle size dSv (urn1Fig. 1. Minimum tubblizg velocity us. mean particle size.

It is curious that the bubble point can be correlated by means of an equation which involves a term( Km ) having units of frequency. Hibyx3 has note


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TYPES OF GAS FLUIDIZATION 28that gas-fluidized beds of low height show a ten-dency to spontaneous vertical oscillation of theparticles with frequencies in the range 7-25 s- l_ Hesuggested that this might act as a triggering me-chanism for bubble formation, and at first sight thisseems a plausible explanation for the frequencyterm in the bubble point equation. However, asHibys experimentally measured frequencies wereconsiderably lower than 100, we shall not pursuethis line of thought further. We are pleased that sucha simpie equation describes the experimental dataso well and shall proceed to use it.

0.1 0.2 0.5 1 2 5Velocity u,, or uo cm/sFig. 2 Minimum fluidization velocity (for air) arsd minimumbubbling velocity cs. mean particle size.

Let us replot eqn. (2) on log-log paper (line MB,Fig. 2) together with C;I equation for the minimumfluidization velocity

u0

= 8 x 10-4g~:v(P,--Pr)c1 (3)

using two selected values of ps-pr, and ,u for air atroom temperature.Consider particles of density difference 1 g cme3

and mean particle size 100 ,nm. Entering the graphat the left along the 100-m line we strike first thetheoretical minimum~fluidization velocity for theseparticles at 0.43 cm s-r and then the minimumbubbling point velocity at 1 cm s-i, giving a value ofU,,a/Ue = 2.33 indicating a bubble-free expansion

region and a group A powder. In contrast lOO-psand (p,= 2.7 g/cme3) has a U, of 1-2 cm s- I. whicis larger thar, the bubbling velocity of 1 cm s-i. will therefore bubble at minimum fluidization anfall into group B as will particles of density differenc1 g cmm3 larger than about 25G pm_

Thus for a powder to belong to group A,uB>lTI0

Substituting in this equation from eqns. (1) and (we have the following criterion :

For a powder to belong to group A.8 x lw4 g dsv(p,--PPr)

&*a lu


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290 D. GELDARTKey

Grou~C$rm &ertiezA eaerns0 Brekken et alP de J ong et al

Group A propertiesreportedd Baems

Davies et alD RietemaI de Jong et al0 Go&u-d et a,0 Cltmgged Kehoe0 deGruot0 This work

Group D propertiesrepwtedX Mathur50 100 200 500 1000Mean particle size d,, (pm)

Fig. 3. Powder classification diagram for flu%ization by air (ambient conditions).

cult to envisage a transition within a large deepfluidized bed in which, near the distributor, smallbubbles travel more slowly than the interstitial gasand faster than the interstitial gas velocity higher upthe bed.Bubble sizes greater than 25 cm have rarely beenreported, so let us choose da = 25 cm. The choice isnot critical since in eqn. (7) we-are considering ,/da_For large-particle systems s0 z 0.4 and for air J L=1.8x 10e4 g cm- s-i. If we insert these numericalvalues and substitute d (pm) for .dsv (cm) we obtain,for group D,

(P,--r)(d) 3 lo6 (8)The use of eqn. (3) on the ri,:ht-hand side of eqn. (7)is not strictly justified for these large particles sincethe flow regime is transitional, not iaminar. How-ever, the arbitrary (though reasonable) choice of daand the nature of the other assumptions do notwarrant the adoption ofa more complicated (thoughmore accurate) equation for U,.

The second possible criterion is based on a recentsuggestion from Baeyens37 that group D powdersare capable of maintaining a stable spout in a bedmore than 30 cm deep. Experimental investigationsare in progress on this and will be reported in duecourse, but for the present, the density-size combi-nations of powders which have been reported asspoutable3* are shown on Fig. 3 as crosses It can be

seen that, with the exception of the 350-pm powde(reported to be the smallest size ever spouted), tcrosses fall near or to the right of the line. This dogive some validity to eqn. (8).

5. COMMENTS ON THE CRITERIA

It can be seen from Fig. 3 that eqn. (6) does reprsent a realistic boundary between groups A and for ambient conditions_ However, further data arequired in selected areas-notably high-densitsmall particles and low-density large particles. Itparticularly desirable to choose series of size frations which cross ovex the line representing eqn. (6This was achieved with Diakon and it was possibto demonstrate that, depending on mean size, tmaterial could behave either as group A or B (Tab1). There is probably also a gradual change properties across group A. For example, expermental evidence (Table 1 and refs. 11 and 1suggests that as we move diagonally away from Xtowards the left, the maximum dense phase epansion sMa increases.5.1 E i x ts o f gas dens i t y an d v i scosi t yGodard and Richardson showed that an icrease in pressure, and therefore of gas density, icreased the minimum bubbling velocity_ Althoug


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TYPES OF GAS FLUIDIZATION 2there are too few results available to correlate theirdata, the overall effect must be to increase the magni-tude of &a in eqn. (5). This increases the size of theconstant on the right-hand side of eqn. (6) and thusmoves XY (Fig. 3) to the right. An increase in pres-sure could therefore have two effects :(a) Some powders which have group B propertiesin air at aknbient pressure and temperature may nowbehave as members of group A.

(b) Those already in group A could now behave asthough they have a smaller size and density sincetheir distance from XY has been increased, i .e. theymay exhibit increased bed expansion and the tran-sition from slug flow to turbulent fluidization couldnow occur at a lower velocity, giving the appearanceof smoother fluidization.It has been reported by several workers34,Q*4 thatoperation at higher pressure on an industrial scaleproduces smoother fluidization and less slugging.It may be significant that the powder used by Leeet aL3 (240 pm, ps=0.9 g cm-) falls very close tothe line XY at ambient conditions.

Equation (5) predicts that an increase in viscosityalone should also moveXY to the right and producesimilar improvements in fluidization. However,some caution is needed before this is accepted at itsface value, because the effect of changing onlyviscosity is not easy to study. The viscosity of a gascan be changed in two ways-by using a different gasand/or by increasing the temperature-but bothmethods normally also involve changing the gasdensity-As far as is known, the effect on the minimumbubbling velocity of changing viscosity alone has notbeen studied nor has the effect of operating at lowgas densities ( i.e. reduced pressure). It is thereforedifficult to decide whether or not operation at hightemperature would produce a net movement of XYto the right, since although the gas viscosity wouldincrease, we do not know the effect on K,,, ofsimultaneously reducing the gas density, this beinganother area for further research.5.2 Compa r i s on w i t h o t her c r i t er i a

It is possible to compare two other criteria withthe one already presented and expressed as eqn. (5).Verloop and HeertjesO suggest that heterogeneous( i.e. bubbling) fluidization will occur ilmmediately if

W)f h-PA > 5m 9)POltrogge36 finds that his data correlate with thesame group on the left-hand side of eqn. (9) but that

for bubbling at U,,W3) @s-P,) > 4m

P 1Using the nomenclature of powder groups giveearlier, it is apparent that eqns. (9) and (10) could als

be used to identify group B powders. Obviously botcannot be correct, and in fact that of Verloop anHeertjes lies much too far to the right and is nshown on Fig. 3. Equation (lo), however, (line O-Oon Fig. 3) agrees with published results about as weas eqn. (5) and this is most interesting since ththinking behind eqn. (5) is quite different from thleading to eqn. (10).

CONCLUSIONS

(1) The behaviour of powders fluidized by gasefalls into four categories characterized by densitdifference (p, - pr) and mean size. Powders in grouA exhibit dense phase expansion after minimumfluidization and prior to the commencement bubbling; those in group B bubble at the minimumfluidization velocity; those in group C are difficulto fluidize at all and those in group D are of largsize and/or density and spout readily.

(2)A criterion which distinguishes between groupA and B has been devised and is shown to agree wewith published data. It also predicts that a change ipressure and/or gas viscosity may cause a change the behaviour of particles. _4 tentative criterion also suggested for group D.

LIST OF SYMBOLS

d particle size in microns (cm x 1G)d v surface/volume diameter of particle (cm)de frontal diameter of bubble (cm)9 gravitation constant (981 cm s-)K MB constant in eqn. (1) (s- )UO superficial velocity of gas at minimum fluidi

zation (cm s- )uMB superficial velocity of gas at minimum bubbling condition (cm s- )x weight fraction of particles in each size rangso bed voidage at minimum fluidization velocityp viscosity of lluidizing gas (g cm- s-r)Pf density of fluidizing gas (g cm-)Ps density of particle (including any internaporosity) (g cme3)


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292 D. GELDARTREFERENCES

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Geldart - Types of Gas Fluidization