An investigation into slugging fluidized beds

Chemical Enwwermg

Scmce,

1974, Vol

AN

29, pp 255-265

Pe&?mon Press

Prmted I” Great Bntam

INVESTIGATION INTO SLUGGING FLUIDIZED BEDS J

BAEYENS

and D

GELDART

Postgraduate School of Powder Technology, Umverslty of Bradford, Bradford, YorkshIre, England (Frrst received

11 January 1973, m revuedform

9 Aprd 1973)

Abstract-A study of sluggmg flmdlzed beds has been camed out m four tubes ranging m size from 5-30 cm I d usmg particles havmg mean sizes 55-3380 pm and densities 0 85-2 8 gm crne3 For all but the smallest column neither particle size nor size dlstnbutlon had any effect on slugging Equations are presented which enable us to calculate (a) The height and gas velocity at which sluggmg commences, (b) The distance above the dlstnbutor at which further slug coalescence ceases, and (c)The numerical value of the stable slugging frequency which 1s thereafter attained

1 INTRODUCTION

t EXPERIMENTALDETAILS

If we take a bed of powder held at incipient flmdlzatlon and gradually increase the gas velocity, bubbles form and nse upwards through the bed growing m size as they do so (Fig la) As the velocity 1s increased further, the average bubble size increases and may reach a size comparable with the size of the tube, when this happens the bed 1s said to be slugging The commencement of sluggmg 1s dependent pnmanly upon the tube diameter and the difference between the total superficial gas velocity and that reqmred to Just fluldlze the bed This ddference, U - UO, is called the excess gas velocity In beds of fine low density particles, and at low excess slugging velocltles m most powders < 700 pm, slugs are axl-symmetnc (Fig lb), but with high slugging velocities and m large and/or dense powders slugs may be asymmetnc (wall slugs) (Fig lc) or may be initiated as honzontal voids before transforming to wall slugs (Fig Id) Slugs of gas nse upwards more slowly than bubbles of the same volume nsmg m a larger bed Moreover the posslblhty of the gas by-passing solids 1s mmlmlsed m a sluggmg bed, and since chemical conversion efficiencies are affected by both these effects, scale-up can become d&cult Although m the last 5 years or so some expenmental and theoretical efforts[9, 11, 18,261 have been directed towards investigating the sluggmg phenomenon, numerous problems remain This present study was directed towards measunng and understanding the effects of bed geometry, particle size and size dlstnbutlon on the onset of sluggmg Equations are presented which help m the scahngup of hydro dynamic data

Full data concerning the powders are given m Table 1 and complete expenmental details are avadable elsewhere [2] 2 1 Equrpment Four cyhndncal columns with perspex or glass walls were used (5 O&7 62, 15 24 and 30 8 cm 1d ) The supply of air was controlled and metered by four rotameters calibrated using a wet gas meter and a bellows dry-type gas meter, gvmg a range of O-5 X lo5 cm3 set-’ The dlstnbutor plate consisted of a sandwich of low pressure drop filter paper (Whatman No 4) between two sheets of perforated zinc (12 holes per cm*, each 2 mm dla) 2 2 Measurmg techmques The behavlour of beds at the onset of slugging was assessed by two different methods The first method involved observing the bed surface visually Before slugging commences the bed surface has a turbulent appearance due to erupting bubbles, when sluggmg commences the surface remains relatively flat and nses and falls m regular ‘piston-like’ fluctuations The frequency of these fluctuations was timed and used to interpret results from the second method which involved using a pressure probe posltloned Just above the distributor The probe, which was made from 0 635 cm I d copper tube with a suitable gauze on the tip, was connected to a pressure transducer and the signal from this was amplified and recorded on a Honeywell vlslcorder oscdlograph Large pressure fluctuations near the dlstnbutor are caused by the bursting of bubbles or slugs at the

255

J BAEYENS and D GELDART

256

0

00 0.0 _---_

00 .-A-

n

0

l I

I t

b Axl-symmetnc

a Freely bubbling bed

A- symmetric

slugs

slug

Fig 1 Modes of slugging

surface, as powder 1s flung upwards by a slug or large bubble a well defined reduction m pressure 1s recorded, and as the powder falls back an increase m pressure is recorded This increase is generally not so clearly defined since it may be masked by the effect of the next bursting bubble or slug The number of negative peaks on a chart taken when a bed was fully slugging was compared with those counted visually It was thus possible to specify the followmg cntenon a slug or large bubble was counted as such If a negative peak was followed by a trace which crossed to the positive side of the datum line The magnitude of the pressure fluctuations mcreased with gas flow rate and when it rose above .--the operating range of the transducer, a metered air bleed was taken from the line connectmg the l rl t probe to the transducer and the gas flow rate to the Hor&tal voidstransform bed increased accordmgly The maxlmum flowrate to wall- slug adJustment which has to be made amounted to only 6 per cent The tir bleed was successful in reducing Table 1 Powder charactenstlcs

No

Powder

1 Glass spheres 2 Alkahzed alumma catalyst 3 Crackmg catalyst 4 Moloclute sand 5 Dmkon spheres 6 Southport sand 7 Moloctite sand 8 Dlakon spheres 9 Southport sand 10 Molochlte sand 11 Molochlte sand 12 Nltram fertlhzer 13 Glass spheres 14 Nltram fertlhzer 15 Flson’s granular fetihzer 16 Millet seed 17 Bakehte cubes

a(pm)t

&m)

Size dlstnbutlonS classification

55

14

W

58 64 15 105 195 252 270 435 470 778 993 1060 1520

16 20 16 36 75 90 85 65 70 83 107 38 230

1790 1848 3380

280 180 520

Shapes

pa(g crnms)

U,, Unbll (cm set-I)

s

2 80

0 34/o 53

W VW W VW VW VW VW N N N N VN VN

A A A S R A S R 2 S S S

1 63 0 85 2 54 1 18 2 65 2 54 1 18 2 65 2 54 2 54 1 80 2 80 1 80

0 23/O 60 0 12/O 60 11 066/l 1 39 51 29 10 8 19 2 50 1 34 0 51 3 63 2

N VN N

A S Cubes

1 72 1 17 0 92

73 0 54 1 86 6

tThe mean sizes were calculated from BX

d8u = Z (x/d,) where x IS the weight fraction collected between sieves of mean aperture da or between the mean microscope count range d, _tThe particle size dlstnbutlon is classified accordmg to an arbitrary crltenon based on the ratio u/d,, A dlstnbutlon IS called (VN) very narrow, if a/& 1s less than 0 1 (N) narrow, dcr/d,, IS less than 0 2 (W) wide, If a/& ISless than 0 3 (VW) very wide, If u/&, exceeds 0 3 OThe particle shapes were classified as A- angular (sphenaty J, = 0 67), R-rounded ($ = 0 85), S - spherical (I/J= 1) “UOand U,b are slmdar for all powders other than numbers l-3 and 5

An rnvesugation into slugging flurdlzed beds the size of the fluctuattons frequency

without affecting their

2 3 Expenmental on results

and general comments

procedure

The column was filled to a suitable height with a powder The velocity at mmlmum flutdlzatlon, U,,, was determined m the usual way (AP vs U graph) and the mmtmum bubbling veloctty, LIti, was taken as the gas velocity at which the first bubbles broke the surface For small sized and/or low density materials Uti can ddfer markedly from UO The bed height at minimum flmdtzatton or minimum bubbling velocity was also noted The gas velocity was increased until the bed was well into the slugging regime, and then gradually reduced to zero Flow rate readings, visual observations and osctllograph recordings were made at appropriate intervals Generally speaking the rule of thumb proposed by Leva et al [14] that at the onset of slugging pressure fluctuations constitute 5-10 per cent of the pressure drop through the bed at that gas flow rate, was m agreement with our observations Figure 3, Chart A shows the trace obtained m a

257

Coarse matenals gave higher wind-box pressure fluctuations than finer matenals and thts may be due to the higher terminal veloctty of coarse matenals resulting m htgher kmeuc energy when the slug bursts through the surface of the bed and 1

IIIO-

osOB-

o-r-

Fig 3 Pressure fluctuations m bubbhng and sluggmg beds of powder No 2 DL = datum he, H, = 78 cm, D = 7 62cm

Inclplent

06-

sluggmg

OS

_k

CT

I 2

I 4

u-u,,,

I 6

cm

I

I 8

I IO

sac-

Fig 2 Slug and bubble frequency vs excess gas velocity Powder No 2 H,, = 78 cm, D = 7 62 cm

bed operating below the mciptent slugging velocity The large bubbles or occasional slugs, mdlcated by the dots, have an trregular frequency, whereas m a fully sluggmg bed (Chart B) the frequency is higher and more regular Figure 2 shows how the measured frequency varies with mcreasmg values of the excess gas velocity It IS clear that the slug frequency becomes independent of excess gas flow rate once the bed is slugging. Similar graphs were obtamed for all powders and geometries tested

CES-Vol

29,No

1-Q

powder falls back For example, powder 11 gave AP vanabons up to 30 cm w.g , powder 10 up to 22 cm w g and powder 7 up to 15 cm w.g. at similar values of excess gas flow rate and bed hetght. In powders 15 and 17 slugs occurred as horizontal voids throughout the bed At excess gas flow rates exceedmg the value at incipient sluggmg and m the larger beds, the axrsymmetnc slugs transform raptdly to wall-slugs In the 7 62 cm I d column we observed that for powders larger than No 9 (Table 1) the transformation to asymmetnc slugs often passed through a transttlonal state whtch took the form of honzontal voids. Complete tabulated experimental data are avatlable elsewhere [21 and are presented here m graphlcal form at appropnate stages in the discussion

J BAEYENS and D

258 3 DISCUSSION 3

1 Mmrmum sluggzng-

and height, partwle

ie

5 cm column were anomalous in many respects and showed a wide scatter (Fig 6) they have been omitted from the subsequent analyses This demonstrates the hnutatlons of work camed out m such small columns The vanatlon of excess gas velocity at the onset of sluggmg (U - U,), shows the same trend m all the geometnes tested and consists of two parts (I) For beds deeper than a cntlcal height, HL, which at fn-st sight appears to be about 100 cm, the excess gas velocity has a constant value which will be called hereafter UL, the hmltmg excess gas velocity UL corresponds to Stewart’s slugging cntenon for the 7 62, 15 24 and 30 8 cm 1d columns, as shown m Fig 6 By calculatmg average values of (U-U,), for each 5 cm increment m H,, and plotting the results m Fig 7, rt can be shown that HL depends on D The equation

the effect of bed dzameter and stze dlstnbutlon

we

Stewart[26] first put forward a cntenon excess gas velocity at mclplent sluggmg

for the

(U-Uuo)s=oo7(go)“2

GELDART

(1)

This equation lmphes an absence of effect due to particle size, size dlstnbutlon and bed height However it IS widely beheved (a) that coarse matenals slug more readily than fine and (b) that slugging does not occur m beds in which HID < 1 The first belief was questioned recently[7] and our results show clearly (Figs 4 and 5) that particle size and size dlstnbutlon have no effect on (U - ILJ,,)~,bed height on the other hand, IS an important vanable up to a cntlcal height HL Because results from the

.

19 -

0 *

17-

T f

*

.

*

le-

E, -:

151413-

a”

IZ-

i

II-

b _*

IO-

a0

9-

&

67l

6s-

0

-1

d

I 40

20

I 60

I 60

I 100 H o,

Fig 4

120 I

140 I

160 I

I60I

200 I

I

cm

Influence of bed height on the excess gas velocity at umplent sluggmg

Powder

No

:‘6

60

Fig 5

I 20

I

40

I

60

I

60

I

I loo

120

H o.

cm

I 140

I

I

I

160

I60

200

I 220

Influence of bed height on the excess gas velocity at mclplent sluggmg

An mvestlgatlon mto sluggmg fhudlzed beds HL = 60 Do 175

(2)

259

3 2 Slug frequencies An equation for slug frequency, fs, and slug length, h,, can be denved from conslderatlons [ 183 of bed expansion and a matenal balance on the slugs and slug wake W,, which IS assumed to be proportional to the slug diameter, d,, and therefore to the bed diameter D Consldermg the solids and gas present between the noses of consecutive slugs yields

fits the results and allows us to interpolate the hmltmg height for other values of D (11) For beds shallower than HL a decrease in bed height produces an increase m the gas tlow rate needed to cause slugging Our data for bed heights greater than 30 cm and the literature data are fitted well by the equation (U-U~),-007(gD)“Z=16x10-3(HL-H0)2

%l=~=H

H-Ho

h,

(3)

=- U--U0 UA

(4)

Now the slug frequency

UA

&=h,+W,

(5)

and, substituting for UA from (4), gives

Now it has been shown that [ 19,201 H-Ho -= Ho

u-u0 UB

(6)

The total height of all the wakes of n slugs = n W, = Ho, and the total height of all the slugs = nh, = H-Ho Substltutmg m (6) gives h s-u-uo _W,

0

I

2

3

4

5

6

Assuming

W, = kD, and UB = 0 35 (gD)“* h = (U - U,) kD1’2 s 0 35 g”Z

Fig 6 Comparison of Stewart’s cntenon with the expenmental hmltmg values of the excess gas velocltles

0 306 cm l 1524cm n 762cm

D=

.

. .a: 50

I I 20

I 40

I 60

.

_.

.

.***

.

.

.=m

I 80

I IO0 H o.

UB

. . .

.

.

l

.

*

. ==m

I 120

.-.

I I40

n

I 160

-

n

I I60

I 200

-

. I 220

cm

Fig 7 Average values of the excess gas velocltles at mclplent sluggmg vs bed height

(7)

BAEYENS and D

J

260

and substltutmg

From this figure it IS clear that there is a levelhng off for bed heights exceeding 1 lo-120 cm for all the bed diameters Plotting the results obtamed m different columns at vanous mean bed heights on log-log graph paper gave a dependance ofxwlth D according to

m (5a) for h, gives

5 =

0 35 g”2 kD’l2

GELDART

(5b)

This means that the slug frequency is independent of the gas velocity, as is often observed The constant k, the only unknown parameter m the equation, must be expenmentally determined Before startmg the dlscusslon of our results, it must be pointed out that the observations for low bed depths (< 25 cm) are difficult to interpret, and because no reliance could be attached to them they were discarded from the analyses The variation of slug frequency with bed height IS illustrated m Fig 8 for the results obtained m the

x = Kfn (If,) D-O lm

(8)

For deep beds, however, one might expect coalescence to be complete, and d this IS so, j$ should be Independent of Ho above the cntlcal bed height Figure 9 seems to confirm this, and the value of this hmltmg frequency fL for the different column diameters 1s expressed by the equation fL =

1

17 D-O

(

143

(9)

12

J

II IO 09

.

08 L

1

0

20

40

60

v

8

0

I

I

I

I

I

I

1

80

100

120

140

160

180

200

H,, cm Fig

8 Slug frequencies

IS-

v

vs bed height for sluggmg

expenments

m the 7 62 cm

1d

column

.

17-

‘I $

IS-

“,’

IS-

l

l4-

.v

l

o

l3-

. 0

12I3

.

. 5 08

.

0.;

&62z4

v l

IIIOos-

cm

0 30 8 y

.

0

y o$

.

. iavt

.

.

.

.

.

.

0m.=.;..

ir:.;

oe-

SO@.

do

07I 20

0

Fig

9

I 40

I 60

I 80

I 100

I 120

I 140

I 160

Vanatlon of the average slug frequency

7 62 cm 1d column As the slug frequency appears to be independent of particle propertles m all of the columns, It IS reasonable to calculate average values of the frequencies for each 10 cm of bed height. The average values,& are shown m Fig 9

I I80

I 200

. I 220

with bed height

For beds deeper than HL Eq. (Sb) becomes O-35 g”2

h = kLDll2

(5c)

where kL IS the height of powder between conse-

261

An mvestigatlon mto sluggmg fluldlzed beds

cutlve slugs m a bed m which coalescence is complete - bed diameter From Eq (5~) and (9) kL = 9 38/D” 357(D m cm) and values are gven m Table 2 Table 2 Calculated values for slug spacmg coefficient k, - height of matenal between consecutive slugs bed dmmeter

D (cm) 508 762 1524 30 8

kL 53 46 35 27

We did not find m the hterature any values of k slrmlar to these Using an expenmental value for fs(= 1 2 set-I) obtamed m a 14 cm I d bed, Matsen and Tarmy [ 181 calculated k to be 2 44 However, then value for fs is high compared with the predlctlon from Eq (9) perhaps suggesting that the value may have been taken for a bed less deep than HL 3 3 Apphcatron of a bubble growth equation It now seems reasonable to postulate the exlstence of three zones m a slugging bed In the top portion (Zone III) coalescence 1s complete and there 1s a constant spacing between slugs Below this the slugs are still coalescmg (Zone II), and m the lowest portion there 1s a freely bubbling region (Zone I) In Sectlon 3 1 we calculated the bed height, HL, at which coalescence 1s complete. To predict the height of the freely bubbling zone of the bed, we could use the bubble growth equation [71 d

El

+0027H

(U-Uo)Og4

(10)

which 1s a generahzed semi-empmcal form of the equation obtamed for fluldlzatlon of sand-like powders In a column fitted with a porous plate dlstnbutor d,=O915

(U-Uo)04+0027H

(U-Uo)Og4 (11)

To apply this equation, the smallest bubble size affected by the walls must be known Several dlfferent approaches are possible By comparmg the velocity of an isolated slug with the velocity of a single nsmg bubble, one might expect wall effects to become slgmficant If

& > (0 35YD - (071) ’ 1 e 0 25 D Davidson and Hamson suggest a value of D/3 Some recent work of ours[2] on sohds mlxmg caused by bubbles suggests that the walls mhlblt motion d C&> 0 5 D and these results agree with data given by Dons1 et al [4] Applying equation (11) to deep beds at incipient slugging (Ho > HL, (U - U,), = 0 07 (go) l’*), and assuming the transition from bubbhng mto sluggmg to start when dB = D/2, we obtam the value for the maxlmum height below which the bed 1s freely bubbling, Hfl, as H

fb

=D-251D02 0 13 Do4?

(12)

The values of Hfl and H,,, for dflerent column sizes and operation at mclplent slugging are plotted m Fig 10 From Fig 10 it IS clear that, although one 150-

0

20

40

60

100

60 D.

120

140

160

160

200

cm

Fig 10 Influence of column diameter on the freelybubbling bed height, HB, and the bed height of stable sluggmg, HL,for operation at mclplent slugging

can with almost total confidence apply slugging models to deep beds m small diameter columns, the effect of the freely bubbhng zone becomes more important with mcreasmg bed duuneter and hence, predlctmg conversions m these large units ought to be done m two steps for the fraction of the bed below Hm, 1 e Zone I, a bubbling bed model (e g combmation of the Kato-Wen[ 101 or KunuLevensplel[ 121 model equations with the bubble growth equation) ought to be used Further up the bed, a sluggmg model (Hovmand-Davidson [9]) wdl allow prediction of the conversion It 1s important to appreciate that operation at

262

J

BAEYENS and

D

GELDART

Data of Lewis et al [ 151 and Wilhelm and Kwauk higher excess gas flow rates than 0 07 (@)1’2 ~111 yield a bubble size 0 5 D at lower values of Hfb, as [281 are also presented m range-form because of the fact that then results include only a hmlted number can be calculated from Eq (11) Figure 10 applies of bed height fluctuations AHb, with gas flow rate stnctly only to porous plate dlstnbutors but Eq We assumed slugging to start between those two (10) shows that a different dlstnbutor design will successive expenmental gas flow rates whereby the reduce the height of the freely bubbling zone (see lower limit corresponds to a fluctuation of k 5- 10 also Ref 18) per cent of the average bed height at that flow rate Although the validity of some of our assumptions 3 4 Analyses of lrterature data concerning these earher investigations 1s open to Sluggmg data are widely aviulable m the hteradlscusslon, It seems more reasonable to include ture, but few precise values of the gas velocity at incipient slugging are included Table 3 reviews their results than to ignore them It can be seen from Fig 11 that Eq (3) 1s relathe papers which were examined for mformatlon on tively successful m descnbmg the results of other bed geometry, particle charactenstlcs, relevant workers conclusions for slugging and presentation of data Few expenments appear to have been carned out using beds deeper than 70 cm and smce from 4 CONCLUSIONS Eq (2) HL > 70 cm for all the beds described,, Eq (3) should be vahd Sluggmg expenments were carned out m vanous Nearly all conclusions mentioned agree with our bed geometnes and, together with visual observaobservations tions, vanatlons m pressure drop over the fluldlzed

-70

Fig

11

-60

-50

-40 -30 -20 tfO_ffL,cm

-10

0

IO

Companson of literature data with Eq (3)

In most cases, however, data on mclplent sluggmg conditions were not given m terms of the excess gas flow rates, but rather as comments or data on fluctuations of pressure, bed densltles or bed height As already discussed, a vanatlon of 5-10 per cent of the pressure drop or the bed density 1s often a strong mdlcatlon of slugging Avadable data on vanatlons of bed density, Afb, with gas velocity were analysed according to these limits Hence, no single pomt could be assigned to these data but rather a range of velocltles

bed were recorded usmg a pressure transducer and a Honeywell 2 106 vlslcorder Bed height has a marked effect on the excess gas velocltles required to cause a powder to slug We have shown that It 1s possible to predict the bed height which no further coalescence of slugs occurs (HL) usmg Eq (2) For bed heights exceeding HL, Stewart’s cntenon 1s vahd For lower bed heights, however, Eq (3) satisfies both the hterature data and our expenmental results reasonably well for bed depths exceeding i= 30 cm For the three larger columns tested, neither mean

263

An mvestlgation mto sluggmg flmdlzed beds Table 3 Review of papers relevant to this study Authors

Cunler [3]

Dotson [5]

Gerald [8]

Kehoe and Davldson [ 1 l]

1 07 1 27 1 65 3 10 10 2 10 2 61 6

Leans era1 [15]

6 35 114

Molstedt [taken from Ref 181 Orcutt et al [22] Romero et al [24]

Shuster et al [25] Volk et al [27] Wilhelm et al [28]

The graphs show that deep beds slug more readily For beds 153 and 272 cm high, there IS no longer a marked dtierence No effect of parhcle size The slug frequency 1s independent of excess gas velocity for slugging

-

6 35

Morse et al [2 11

Slhcon powder

-

Leva et al [ 141

Mathls et al [ 171

The slug height exceeds D at incipient sluggmg

-

7 62

154 1 89 7 62

Fme catalyst

Glass spheres, Aerocat nucrospheres, puffed nce Fluid hydroformmg catalyst Crackmg catalyst, Fe, sand

5 08 7 62 10 2 10 2

Catalyst

30 8

Fluid coke

15 2 10 2

Catalyst Sand, lead shot, Feoxlde ohvme glass beads

4 45 95 5 08 14 0 27 9 7 62 15 24

Conclusions relevant to this work

Mg

-

Lanneau[l3]

May [taken from Ref 181 Matheson et al [ 161

Powder

D(cm)

Catalyst

Glass beads

Data presentation

beds

Wall sluggmg occurs often with coarse matenals (> 70 pm) at high values of U - II, No influence of gas properties (different pressures) on the excess gas flow rate at mcipient slugging Tall beds slug more readily Pressure drop fluctuations amount 5- 10% of bed pressure No influence of gas properties (illr, C0.J All results refer to very shallow beds

-

APb

-

u

u

-

If bubbles are larger m coarse mater&, these should slug more readily No such difference was found for particles of d,, > 156 pm Fme catalyst slugs m deeper beds For very low bed heights, one often gets channelhng instead of slugging Deeper beds slug more readily than shallow beds

-

Applying Yasm’s Eq (29) for bubble heights, the authors calculated that at the onset of slugging the slug height exceeds D No effect of particle size Deeper beds slug more readily than shallow beds

APb -

u

U APP~

U U

-

Hematite

APPa

Glass beads, Socony beads sea sand

AHb

264

J

BAEYENS

and D

partrcle size nor size drstnbutron had any effect on slugging and data obtamed from the smallest column (5 08 cm 1 d ) were found to be anomalous According to our analyses, there are three zones m a deep bed operatmg at high excess gas velocttres m Zone I the bed 1s freely bubbling, m Zone II the bed 1s slugging but slug growth occurs, and m Zone III slugs no longer coalesce and stable spacing 1s achteved This approach suggests a more reahsttc scale-up procedure for large umts based on applymg a combmatron of freely bubbhng and slugging models to the appropnate regtons m the bed

NOTATION

dB frontal diameter of bubble, cm D

column diameter, cm

4 frontal dtameter of slug, cm dnn mean microscope count range, cm da anthmetlc mean of apertures of adJacent

fL

sieves, cm surface/volume mean diameter (= l/X (x/d,) cm expenmental values of slug frequenctes, set-’ average values offs for narrow consecutive ranges of H,,, set-’ limiting value of x for deep beds (Eq 1 l), see-’ gravrtatronal constant, 98 1 cm set-* bed height, cm bed height at minimum flmdrzatlon, cm bed height at mmlmum bubbling, cm slug hetght, cm hmrtmg bed herght where coalescence 1s complete and a stable slug spacmg achieved (Eq 8), cm height of the freely-bubbhng zone m a flmdrzed bed, cm coefficient for slug wake, coefficient for slug wake for Ho > HL, number of holes per unit area of gas dtstnbutor, cm-* pressure drop, g cm+ superficial velocity of gas entenng flmdrzed bed, cm set-1 absolute nse velocny of slugs at any level, cm set-1 nse velocity of an isolated slug, cm see-l superficial velocity of gas at minimum fltudrzatton, cm see-1 supertictal velocity of gas at minimum bubbling velocny, cm set-’

ITi HO Hmb h, HL

HRl k

kr. Nd AP V

VA UB

UO

GELDART

VL

hmrtmg value of the excess gas velocrty for deep beds, cm set-’ x weight fractton of parttcles collected between two sieves of mean aperture d, height of slug wake, cm W, Greek

symbols

lg

fraction of total bed volume occupted by bubbles pb bulk denstty of flutdtzed bed, g cm-3 ps density of parttcle (mcludmg any Internal porosny), g cm-3 o standard devlatton for sieve analyses, cm REFERENCES

111 BAEYENS J and GELDART D , Paper submttted to the Conference on Fhudrzatton, Toulouse, October 1973 121 BAEYENS J , Ph D theses, Umverslty of Bradford (m preparation) [31 CIMLER E , M Ch E thesis, Polytechmc Institute of Brooklyn 1949 141 DONS1 G , M-ASSIMILLA L , CRESTICELLI S and VOLPICELLI G . Powder Tech 1972 6 216 151 DOTSON J M , A I Ch ii JZ 1959 5 169 161GELDART D , Chem Engr 1970 No 239 CE 147 171 GELDART D , Powder Technol 1972 6 201 181 GERALD C F , Chem Engng Prog 195 1 47 483 191HOVMAND S and DAVIDSON J F , Trans Instn Chem

Engrs 1968 46 190

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