Liquid dispersion in gas—liquid fluidized beds

The Chemrcal Engrneerzng Journal, 18 (1979) 151 - 159 0 Elsevler Sequoia S A , Lausanne - Prmted m the Netherlands

151

Liquid Dispersion in Gas-Liquid Fluidized Beds Part I: Axial Dispersion. The Axially Dispersed Plug-Flow Model

SEHAM A EL-TEMTAMY*, Pilot Plant Laboratory,

YOUSEF

0 EL-SHARNOUBI

and MOHAMMED M EL-HALWAGI

N R C Dokkl, Cairo (Egypt)

(Received 28 Aprd 1977, m final form 25 January 1979)

Abstract Axial dlsperslon coeffwrents m the hquld phase of gas-bquld (three-phase) flurdlzed beds have been determmed from tracer concen tra tlon measurements upstream of the mlectlon plane by using the steady state mlectlon technique and applymg the axially dispersed plug-flow model Water, arr and glass beads of 0 45, 0 96, 2 and 3 mm diameter particles were used as the laquld, gas and solid phases, respectwely The superficial velocl ties ranged from 1 15 to 12 8 cm/s for the llquld phase and from 1 3 to 7 cm/s for the gas phase The calculated daspersaon coefflclents increased with mcreasmggas flow rate and their vanatlon wath the llquld flow rate depended on particle sze These coefficients were higher for three-phase fluldlzed beds than those for the correspondmg two-phase part&e-free systems The mixrng length decreased wlth mcreasmg particle size

INTRODUCTION

Gas-hquld flmdlzatlon 1sone of a number of chemrcal engmeermg operations that can be used to establish simultaneous contact between a gas, a hqurd, and a bed of solid particles. Qstergaard [l] ongmally defined such systems as those m which the solid particles are flmdlzed by an upward flowmg liquid while the gas flows as discrete bubbles. However, owing to contmued developments m chemical engineermg technology, different types of gas-liquid or three-phase flmdlzatlon *Correspondance should be addressed to S A. El-Temtamy, 3 El Tawfic St Hehopohs, Cairo, Egypt

are now known [ 21. The present operation could be more speclflcally identified as cocurrent, liquid-supported, gas-liquid fluidlzatlon, an important mdustnal apphcation of which 1sheterogeneous catalysis. As an operation gas-liquid flurdlzatlon is currently gammg ground for future competltlon wrth more conventional reactors. However, gas-hqmd flmdized beds have been reported to suffer from an unfavourably low ratio of gas to hqmd flow rate, and substantial muting m the fluid phases. The purpose of this paper 1sto investigate the magnitude of axial mixing m the liquid phase of such a system. Prior work Qstergaard and Mlchelsen [3] used the imperfect tracer injectron technique to study axial murmg m the gas and liquid phases of 21.59 cm diameter flurdized beds of 0.25,l.O and 6 mm diameter glass beads. They extended then studies [4] to 15.24 cm diameter beds of 1,3 and 6 mm glass beads. The intensity of mixing was found to depend strongly on the particle size and on the flow rates of the fluid phases. While beds of 1 mm beads were characterized by a high degree of mrxmg, 6 mm particle beds on the other hand showed neghgrble mixing. These investigators developed a new method for processmg the data [5, 61 which proved superior to the conventional moments method. Liquid-phase mrxmg m a 22.86 cm diameter three-phase flmdlzed bed IS more recently reported by Qstergaard [7], glass ballotml of 1.1, 3 and 6 mm diameter being used. An increase in the axial mrxing coefficients of 50 - 100% over those obtamed m the 15.24 cm diameter beds was reported

152

Val et al [El] employed the steady state tracer mlectlon technique and the diffusiontype equation to study mlxmg m the liquid phase of 14 7 cm diameter beds of 0.87 mm sand particles. Then longitudmal mixing results were m complete agreement urlth those reported by Qstergaard and Michelsen [3]. Kim et al [9] used the pulse and step mJection techniques to study mixing m the liquid phase of 6 mm glass beads and 2 5 mm irregular gravel fluidlzed m a 66 cm wide by 2.5 cm thick two-dimensional column Axial mixing increased with an increase m either gas or hquid flow rates. The height of a mixing unit (HMU) was correlated m terms of hquidand gas-phase Reynolds and Froude numbers and the ratio of solid to fluid density.

EXPERIMENTAL

The fluidization column (Fig 1) was constructed of three Plexiglass sections each 5 cm m internal diameter and 41 cm high. Longitudinal slabs having several threaded holes were welded to the test section to house the necessary array of sampling tubes and pressure taps. The uppermost member of the column served to mamtam a constant

Fig 1 Experimental setup 1, liquid, 2, gas, 3, tracer, 4, pressure taps, 5, axial sampling probes, 6, radial samplmg probes

dynamic liquid level m the system. Its comcally enlarged cross-section prevented the escape of particles m the outlet liquid stream. The liquid was pumped through a conical inlet and a calming section, 50 cm m height (filled with % m. Raschig rmgs), and entered the experimental section through several flowredistributmg screens and a reinforced wire screen that supports the bed of particles. Compressed an was admitted to the system 5 cm above the bottom of the calming section through a rmg-shaped 8 mm diameter brass tube punctured with six equid@ant 2 mm holes (bubble dispersions were @ore uniform when the holes were downwardly’&rected). The tracer, a one molar ammonium chloride solution, was inJected into the fluidized bed axis at 54 cm above the support screen through a hypodermic needle with a feed rate precalculated to produce a ducharge velocity equivalent to that of the hquid phase m the column. This ehmmates any likelihood of disturbance caused by the mtroduction of the tracer. When equllibnum distribution was attamed, as affirmed by successive samples from the dram pipe displaying constant tracer concentration values, backmixmg was analysed. Samples of the liquid phase upstream of the mlection plane were withdrawn through 2 mm diameter stamless steel tubes mserted through the slab openmgs and the column walls. The tubes were packed with fine wires to prevent particle clogging and thar sampling points could be varied accurately to probe any radial position of the column. The sampling tubes were introduced to the column axis, one at a time Before collecting the desired number of samples m carefully cleaned 15 ml test tubes, the first 10 - 20 ml of the liquid were used solely to purge the sampling tubes. Prehmmary experiments have shown that samplmg rates less than 2.0 ml/ mm had no noticeable effect on the column operation. Glass beads of 0.45 mm, 0 96 mm, 2 mm and 3 mm average diameter were fluidized with tap water and an. The physical properties of the particles together with the range of the fluid flow rates are given m Table 1. Settled bed height was 55 cm m all the experiments The gas and liquid flow rates were adJusted to produce bed voidages ranging between 0.5 and 0.7.

TABLE 1 Process variables

4

Range of fluzd uelocrtres

Ps

(mm)

Wcm3)

0 0 2 3

2 2 2 2

45 96 00 00

599 930 936 926

Ul (cm/s)

Us (cm/s)

115 - 3 25 25-70 53-120 53-137

00-60 00-60 00-70 00-70

DATA PROCESSING

The analysis of axial mixmg in the present mvestigation is based on the assumption, previously adopted by ostergaard and Michelsen [3], that flow of the gaseous and liquid phases may be described by the axially dispersed plug-flow model. The flow of the fluid phases through the column is described by a constant linear velocity and a constant dispersion coefficient. When the system is under steady state conditions, and no reaction takes place, the model can be represented by the diffusiontype equation ,d2C -=---dZ2

V, dC DzdZ

(1)

with the boundary conditions C=Ce

at

Z=O

(2)

c=o

at

Z==

(3)

The standard solution of eqn. (1) upstream of the mjection plane has been given [lo] as

-= C

Co

(4)

A semilogarithmic plot of the reduced axial concentration uersus the axial distance would be expected to produce a straight line of slope -Vl/Dz if the system can be represented by the model. Typical sample plots are illustrated in Fig. 2, from which it can be concluded that the resulting straight lines justify the use of the above-mentioned model m cases where backmixmg is manifested. The best slopes of these lines were determmed by the leastsquares method usmg a digital computer. The axial dispersion coefficients are obtained by multiplymg the reciprocal of the slope by the actual prevailing liquid-phase velocity

0 01

I

0

I

10

I

20 z,

I

30

cm

Fig 2 Typicalsemdogarlthmx plot of axial concentratlon profile below qectlon plane d, = 0 96 mm, &=25cm/s oAlx Symbol l Us (cm/s) 1 3 2 3 4 5

calculated from holdup data reported elsewhere [ 111. However, these straight lines do not meet the vertical axis at C/Co = 1, as would be expected from the boundary condition eqn. (2). An explanation for this situation could be the following. According to Wehner and Wilhelm [ 121 the general contmuity conditions at the boundary m a steady state reactor are C(0’) = C(O_)

(5)

and 0;;

dC(O+)

c(o+)-vI~=c(o-)

Dz dC(O-)

- v,

- dz

(6)

In the present case 2 IS considered to be positive m the downward direction. The tracer concentration C IS taken as the bulk average across any horizontal plane. Therefore, by continuity, dC/dZ above the injection plane is equal to zero and dC(O-)/dZ just above the injection plane is also equal to zero. There is thus a step change in concentration at the injection plane and eqn. (6) reduces to D; idC(O+) C(O’)-= C(O_) Vl

dz

154 RESULTS

At the mjection plane eqn. (2) implies that C( 0’) = C( o-) = c,

(2a)

Equations (7) and (2a) therefore cannot be satisfied simultaneously unless the term (Di/V,) X dC(O’)/dZ disappears, z.e either Di/V, = 0 (the case of molecular diffusion) or dC(O’)/dZ = 0, which may not be the general case. Equation (7) m fact is equivalent to Danckwerts’ boundary condition at the reactor entry [13] Since dC(O’)/dZ is negative, eqn (7) therefore predicts the concentration just below the mjection plane to be less than the concentration above it, a situation which is found m the present work as well as m the work of others [8,14], but no explanation for this situation has so far been offered. The apphcation of this boundary condition of Danckwerts would also account for the absence of any back-flow under certam conditions [ 151. Equation (7) can give a separate estimate of the dispersion coefficient provided that the value of the denvative dC(O’)/dZ and C(0’) are known. Differentiation of eqn. (4) once (or alternatively integration of eqn. (l)), now with C,-, = C(O’), and evaluation of the derivative at 2 = 0 gives dC( 0’) ~ = - -! C( 0’) dZ Dz

(8)

Solvmg (7) and (8) simultaneously results m C(0’) = $C(O_)

The results are discussed m terms of the two mlxmg parameters. (a) the axial murmg coefficient Dz and (b) the mixing length Dz/Vl. The effect of gas-phase and liquid-phase flow rates on the murmg parameters is shown m Figs 3 - 8 for the 0 45,0.96 and 2 mm particle beds. No backmurmg was detected m the 3 mm particle beds. The mixing charactenstics m such beds are studied from the downstream radial concentration profiles m I

1

I

I

100 -

/p F .

80 VI .

“5

60-

0” LO -

/’

0

I 1

/’

I 2

I 3

ug,

I

I

4

5

I 6

I

7

cm /5

Fig 3 Axial mlxmg coefflclents m 0.45 mm particle beds Symbol l 0 A v x 115 178 2 18 273 3 25 ul(cm/s) Broken curve, air-water system at VI = 3 25 cm/s

(9)

On comparing C( O’)/C( O-) calculated via eqn. (9) with the expenmental values of the mtercepts (e g m Fig. 2), we find that the latter exhibited different values rangmg between one and zero for the whole set of experimental results. Also when calculatmg the derivative from (8) and (9) (with VI/D; = -slope m Fig. 2), then using this calculated denvative m estimatmg the dispersion coefficient from (7), we find that the dispersion coefficients so calculated are different from those determined from the experimental results. It seems, therefore, that Danckwerts’ eqn. (7), though it offers an explanation for the observed concentration jump, still leaves the vahdity of the diffusion equation in the close vicinity of the source questionable [ 161. However, this argument does not affect the value of the calculated dispersion coefficient.

I

I

/

I

I

I

,

I

I

100,

80.

e WE

60.

u

‘N P

40

20

Fig 4 Ax& mixmg coefficients m 0 96 mm particle beds oAVx Symbol l Ul (cm/s) 2 5 4 5 6 7 0 Broken curve, rur-water system at VI= 5 cm/s

155

Fig 7 Variation of mixing length m 0 96 mm particle beds U, as for VI m Fig 2

ug, cm15 Fig 5 Axial nuxmg coefficients m 2 mm particle beds Symbol l 0 A v x UI(cm/s) 53 75 88 105 120 Broken curve, iur-water system at VI = 8 8 cm/s

I

I

I

I

32 t

I

ZB-

I

6

I

7

I

8

1

I

9

10

I

11

I

12

UL ,cm/s

Fig 8 Variation of mtxmg length m 2 mm particle beds Arxo Symbol U, (cm/s) 3 4 5 7

2L-

20-

16 -

0.96 mm particle beds, and increases and passes through a maximum m beds of 2 mm particles.

12 -

8-

4 1

I

I

2

3

I

UL, cm IS

Fig 6 Vanatlon of mlxmg length m 0 45 mm particle beds U, as for VI m Wg 2

Part II of this series [ 171. The mixmg parameters are observed to increase with increasmg gas velocity m all systems under mvestigation. The effect of liquid velocity on the different parameters may be differentiated as follows: Axtal daspemron coefficrent (Figs 3 - 5) With increasing liquid velocity, this parameter decreases in 0.45 mm particle beds, increases and approaches an asymptotic value m

Maxmg length (Figs 6 - 8) This parameter decreases with increasing hquid flow rate in 0.45 mm particle beds, as well as in 0.96 mm particle beds at the higher gas rates. In beds of 2 mm and 0.96 mm particles at low gas flow rates, the mixing length primarily increases with liquid velocity, reaches a maximum, and then decreases with further mcrease in the water velocity. It 1sevident that while the range of vanation of the axial dispersion coefficients with the fluid flow rates is approximately the same in the different particle beds, the other mixing parameter decreases with mcreasmg particle size. Comparison of the axial dispersion coefficients with the values obtamed for the corresponding solid-free systems signifies that the presence of the solids intensifies axial mixing.

156 TABLE 2 Companson

of mlxmg length data

Mzchelsen and Qstergaard [4] d, = 1 25 mm, ps = 2 67 g/cm3

Present work d, = 0 96 mm, ps = 2 93 g/cm3

VI (cm/s)

vi% (cm/s)

DzIV (cm)

s (cm/s)

42

15 30 60

24 27 2 35 3

40

13 30 60

7 019 8 59 947

56

15 30

20 0 21 0

60

13 30

5 917 7 489

68

15 30

18 0 20 5

70

13 30

5 388 6 787

COMPARISON

WITH PRIOR WORK

The dependence of the mixing parameters on fluid flow rates m 0.45 mm particle beds is charactenstic of small particle beds and cocurrent two-phase flow. Similar trends for the variation of the mixmg length have been reported by Michelsen and Qstergaard [4] and Vail et al [8] for three-phase fluidized beds of 1 mm and 0.87 mm particles, respectively, by Michelsen and Qstergaard [4] for cocurrent gas-liquid flow and by Kato et al [18] for three-phase flow. Afschar and Schugerl [ 191, however, reported opposite trends for three-phase fluidized beds of 0.25 mm particles and for gas-liquid systems. An increase of axial mixmg coefficient with liquid flow rate, similar to that observed in 0.96 and 2 mm particle beds, has been reported by Kim et al. [9] for three-phase fluidized beds of 2.5 mm irregular gravel and 6 mm glass ballotml, and by Mlchelsen and @stergaard [4] for 6 mm particle beds. A comparison between some of the mixing length values of this work and those calculated from the results of Mlchelsen and @&ergaard [4] under approximately similar conditions in a 15.2 cm diameter column is given in Table 2. The higher mixing length values corresponding to ref. 4 may be attnbuted to the effect of column diameter. An increase in axial mixing with increasing column diameter is observed in the work of Michelson and Qstergaard [4 ] , Kato et al. [ 181 and Aoyama et al. [ 201.

DzIV (cm)

DISCUSSION

Before attemptmg to discuss the effect of the different operating variables on the mlxmg parameters it is relevant to give a bnef analysis of the flow dynamics m three-phase fluidized beds. The main factors that may cause axial mixing in the liquid phase of a gas-liquid fluidlzed bed are* (a) the presence of bubbles and particles, (b) the motion of bubbles and particles, (c) the contmuous formation and separation of bubble and particle wakes, (d) the radial velocity profile. Assummg the bubbles and particles exlstmg m a fluidized bed to be stationary, mixing m the liquid phase would be induced by the continuous splitting and recombmation of the liquid streams around such bubbles and particles. Increasing their size or concentration would increase the effective magnitude of the resultmg turbulence and thereby intensify axial mixing. When the bubbles are m motion they are trailed by turbulent wakes which recurrently form and separate during then rise. These faster moving liquid elements will snnultaneously cause axial mixing in the direction of flow, and a downflow of the displaced liquid fluldized phase in other parts of the bed. The extent to which such downflow, or “backmixmg” as it is commonly called, takes place depends upon the bubble relative velocity V, - V, and bubble and wake sizes.

Liquid flmdized particles are essentially in a state of continuous oscillation, and their amplitude of oscillation in the vertical dlrection increases with increasing liquid velocity. Ruckenstein [ 211 stated that m addition to the turbulence mduced by the sphttmg and recombmation of the fluid streams this mode of particle motion 1s responsible for fluid murmg m liquid flurdized beds. Recently, evrdence for the existence of particle wakes and their importance m effecting axial mixing was presented by Letan and Elgm [22]. The wake formed on the roof of a particle was assumed to embody highly mixed zones which multiply with an increase in either particle size or liquid rate. Axial mixing m the direction of flow was claimed to be mamly generated by the continuous formation and detachment of these wakes. In view of the above representation, it is to be expected that increasing the gas flow rate, z e mcreasmg the gas holdup and bubble size, would under all conditions lead to an increase m the mixmg parameters. An increase m liquid flow rate will normally cause finer bubble dispersion (with no great effect on gas holdup), lower particle concentration, and increased particle oscillations. While the first two consequences contribute to decreasing the magnitude of the mixing parameters, the third acts to increase the axial dispersion coefficient. The gross effect of these opposmg factors will depend greatly on particle charactenstrcs. Letan and Elgm [22] argued that m small particle beds (Re < 30) dampening of fluid turbulence on the solid particles would be expected. In beds of relatively large or high inertia particles, interaction between the above-mentioned countereffects could lead to an mcrease m the dispersion coefficients with hquld velocity, and to the observed maxima m the mixing length DZ /VI. However, mcreasmg Vi and hence V, will always tend to counteract any increase of Dz in the mutmg length Dz /VI. That is why &/VI is more prone to a maximum with Vi than is Dz. The increase of dispersion coefficient m three-phase fluldlzed beds over those measured m solid-free systems 1s a result of the additional mechanisms offered by the presence of the solid particle phase. The results are plotted m Fig. 9 accordmg to the correlation presented by Gunn [23]

10

0” . 8 F

2

01

0011 ‘..I

’ 10

.

100

1000

Re,,dJv’p/~I Fig 9 Correlation of axud mlxmg coeffxlents ,( 1) present data, (2) data of Mlchelsen and Qstergaard

[41 for hquid fluidized beds. The loganthmrc plot clearly reveals the effect of different varrables grouped round a particle Reynolds number (Uipid,/~i) and a particle Peclet number (V&,/D, ). The data of Michelsen and Qstergaard [4] for 15.24 cm gas-liquid flurdized beds of 1, 3 and 6 mm particles are included for comparison. The Peclet group m both cases increases with mcreasmg Reynolds number and decreasing tube to particle diameter ratio. It can also be observed that for particles of the same Reynolds number, the Peclet mixing group appears to vary with the reciprocal of the tube diameter raised to a power m excess of one. This suggested a correlation of the type Pe=aRe P“0” where a, b and c are the correlation constants. A least-squares fit of the two forementroned sets of data together with Cpstergaard’sdata on mrxing in a 22.86 cm diameter column [ 71 (a total number of 209 data points) to the suggested equation resulted m Pe = 0.0012 Rei lssDml 156

(1’0)

The predictions of eqn. (10) are shown in Fig. 9 as straight lines. It is clear from that Figure that the deviation of the experimental pomts from eqn. (16) is high (an average

158

devratron of 75%). Also the multiple correlation coeffrclent 1s low (0 8) which lndlcates that other factors that may affect axial mlxmg are not accounted for by the present correlation (e g the effect of gas velocity) The dependence of the axral mrxmg coefficient on tube dnuneter for three-phase fluldlzed beds is comparable with that for two-phase gas-hqmd systems, an exponent of 1 25 and 1.5 has been reported for the latter [24,251

CONCLUSION

The steady state tracer mJectron technique 1s an appropnate tool m drsclosmg the axral mrxmg characterrstrcs of systems where backmrxmg can be detected upstream of the inJectron plane The axial mrxmg parameters, namely the axial drspersron coeffrcrent and mrxmg length, were found to Increase with increasing gas flow rate The axial dispersion coefflclents did not vary greatly wrth particle size, and were higher for three-phase flurdrzed beds than for solid-free systems. The effect of hqmd flow rate on the mlxmg parameters depended on the relative contnbutlon of the bubbles and particles m each system The particle Peclet number increased w&h mcreasmg partrcle Reynolds number and decreasing tube to particle dmmeter ratio Equation (lo), though rt has a high devlatlon, can be used at least for estlmatmg the order of magnitude of axial mlxmg m gas-hqmd flmdlzed beds until a more elaborate expression 1savarlable

ACKNOWLEDGMENTS

We are grateful to Professor Norman Epstein who kindly read the draft of this paper and offered many helpful comments We should also like to thank the N.R.C of Egypt for provldmg the expenmental faculties and the N R C of Canada for fmancurl support to one of us whrle wntmg this paper.

NOMENCLATURE c

Co

absolute tracer concentratron expenmental absolute average tracer concentration

absolute tracer concentration Just below the mJectlon plane absolute tracer concentration Just above the mJectron plane particle diameter, mm or cm 4 D column diameter, cm axial dlsperslon coeffrcrent, cm’/s Dz Pi, DZ axial drspersron coefficrent below and above the mJectlon plane, cm2/s Pe = V,d, /Dz , particle Peclet number Re = U,pld,/p,, particle Reynolds number superfrcral liquid velocrty, cm/s Q superficial gas velocity, cm/s *, = Ur/el, actual liquid velocity, cm/s VI = U, /fg , actual gas velocity, cm/s VlZ Z axial positron, cm

W’)

Greek symbols El

eg 12 P

hqurd holdup gas holdup viscosity, poise density, g/cm2

Subscrapts

1 g S

hqmd gas sohd

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