characterization of bubble column hydrodynamics with local measurements

* Correspondence author. Tel.: #1-514-3404711x4526; fax: #1-514-3404159.

E-mail address: [email protected] (C. Guy)

Chemical Engineering Science 54 (1999) 4895}4902

Characterization of bubble column hydrodynamics with localmeasurements

Sylvain Lefebvre, Christophe Guy*Department of Chemical Engineering, Ecole Polytechnique, P.O. Box 6079, Station Centre-Ville. Montreal, Que., Canada H3C 3A7.

Abstract

The objective of this work is to study the hydrodynamics of the liquid phase and its interaction with the gas-phase hydrodynamics.The local liquid #ow is investigated by means of thermal pulse anemometry. That is, local residence time distributions and localvelocity distributions are experimentally measured. The study is carried out in the liquid up#ow region and through the homogenousand heterogeneous #ow regimes. Liquid mixing is analysed separately on the basis of two di!erent assumptions: as a dispersivemechanism or as a convective mechanism. Moreover, the liquid velocity distributions are compared with global absolute bubblevelocity distributions. ( 1999 Elsevier Science Ltd. All rights reserved.

Keywords: Bubble columns; Liquid velocity distribution; Liquid mixing

1. Introduction

Bubble columns are widely used as gas}liquid contac-tors. They have applications in chemical, petrochemicaland biological industries. Knowledge about hydrodyn-amics of bubble columns is necessary for design purposes.Although a lot of information is found in the literature,bubble columns are still not, however, well understoodand the work is often oriented on only one phase, i.e.liquid or gas. Because the hydrodynamics of each phaseare intimately linked, the study of their interaction is ofinterest. This work aims at studying this interaction withthe help of local measurements.

This interaction generates #ow characteristics whichpossibly change with position in the bubble column,super"cial gas velocity and #ow regime. In order to studythat, a measurement technique "rst elaborated by LuK b-bert and Larson (1987) is further developed and used tomeasure local liquid #ow behaviour. Results concerningthe gas-phase hydrodynamics obtained previously(Hyndman & Guy, 1995a,b; Hyndman, Larachi & Guy,1997) with the same bubble column as used here are

compared with the local liquid results obtained in thiswork.

2. Literature review

2.1. Liquid-phase hydrodynamics

The mixing of the liquid phase may be caused bya di!usion mechanism (stochastic mixing process), bya turbulent mechanism (eddy di!usion), by a convectivemechanism (mass transport at di!erent velocities) or bya combination of these. Each type is used in the literaturefor interpreting the #ow behaviour of the liquid phase inbubble columns.

Because of its simplicity, the dispersion model is oftenused to describe the non-ideal #ow of a #uid (Riquarts,1981; Ulbrecht & Baykara, 1981; Ityokumbul, Kosaric& Bulani, 1994; Herbrard, Bastoul & Roustan, 1996).Mass transport is in plug #ow and mixing is a di!usion-like process represented by a dispersion coe$cient.

In the eddy di!usion model (Dudukovic, Devanathan& Holub, 1991; Kawase & Tokunaga, 1991; Degaleesan,Roy, Kumar & Dudukovic, 1996), the mixing process iscaused by mass transport between eddies. In other words,if particles were injected at one point in a #uid theywould pass from one eddy to another and spread in thismanner in the #uid.

0009-2509/99/$ - see front matter ( 1999 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 9 - 2 5 0 9 ( 9 9 ) 0 0 2 1 0 - 9

Fig. 1. Schematics of the thermal pulsed anemometry (TPA) probes.The distance between the electrodes and the anemometer is 7.0 mm.

Zahradnik and Fialova (1996) concluded, based onglobal mixing measurements, that mixing of the liquidphase is a convective mechanism. This type of mixing ischaracterised by a velocity distribution of the liquid.Using the same analogy as before, segregation of par-ticles would occur, caused by transport at di!erentvelocities.

It is also possible that a combination of these mixingmechanisms represents better the #ow behaviour. Indeed,for gas}liquid #ow, LuK bbert and Larson (1990) con-cluded that liquid mixing is caused by a superposition oftwo mechanisms, di!usion and convective-mixing mech-anisms. A model based on this conclusion was proposedby Nassar, Schmidt and LuK bbert (1992), Schmidt, Nassarand LuK bbert (1992a,b). They stipulated that an elementof #uid is attached to the bubble in its wake and has thebubble velocity. This liquid bubble wake may detach andpass to the bulk liquid surrounding it. A small CSTRreactor may approximate the bubble wake. Moreover,the bulk liquid is entrained by the rising bubbles andfollows a stochastic behaviour.

2.2. Gas phase hydrodynamics

Hyndman and Guy (1995a) have recently shown thatthe axial dispersion model is not able to describe thegas-phase hydrodynamics in bubble columns. A fullyconvective model based on an absolute bubble velocitydistribution was proposed. This model was later simpli"-ed (Hyndman et al., 1997) to represent the #ow of bubblesas a superposition of large bubbles with an averagevelocity on a population of smaller homogeneous bub-bles with a velocity distribution. This model based onkinetic theory was also able to predict gas hold-up,transition from homogeneous to churn-turbulent #owand ratio of the two bubble populations. It was in agree-ment with the observations of Kawagoe, Octakeand Robinson (1989) which proposed a two bubblepopulation model and Krishna, De Swart, Hennephof,Ellenberger and Hoefsloot (1994), who underlined thissuperposition of each bubble population on the gashold-up.

The mixing of one phase is certainly in#uenced by themixing of the other. The mixing of each phase and theirinteraction is thus an important "eld of study for theunderstanding of bubble column hydrodynamics.

3. Experimental

The Plexiglas bubble column studied is a batch liquidsystem. The liquid is tap water and the gas is compressedair. The column diameter is 0.20 m and the height is1.90 m. The gas-free water level is 1.40 m. The system isused at ambient temperature and atmospheric pressure.The distributor is a perforated plate with 69.1 mm

diameter ori"ces arranged in a square pattern. Moredetail of the experimental set-up can be found inHyndman and Guy (1995a).

The study is carried out for a super"cial gas velocityrange of 0.9}7.8 cm/s. This covers both homogenous(bubbly) #ow and heterogeneous (churn-turbulent)#ow regimes. The transition point is experimentallydetermined for the system studied at 3.75 cm/s. Dimen-sionless radial positions (r/R) investigated are 0.00,0.20, 0.41 and 0.58. These positions are located in theliquid up#ow region. This is the region where the interac-tions between the bubbles and liquid are more direct.Moreover, only the ascendant velocity component ismeasured.

The thermal pulse anemometry (TPA) technique isused to measure local liquid residence time distributionsand local liquid velocity distributions. This technique"rst proposed by LuK bbert and Larson (1987) is an intru-sive technique but there is no regime limit as long as theliquid is the continuous phase. TPA is a tracer technique.A pseudo-stochastic thermal signal is transmitted toa #uid element by a "rst probe that consists of twoelectrodes. The #uid element transports the thermal sig-nal with its velocity to a second probe a few millimetresaway; it consists of a hot-"lm anemometer that is used tomeasure continuously the #uid temperature. A cross-correlation calculation is performed between the knowninput signal ("rst probe) and the measured signal (secondprobe) in order to obtain the delay between emission andreception. In this way, only the axial upward velocitycomponent is measured. Fig. 1 details the measuringsystem.

4. Results and discussion

4.1. Mean local liquid velocity

Fig. 2 presents the mean local liquid velocity as a func-tion of super"cial gas velocity for di!erent radial posi-tions. The relative axial position of the measurement is

4896 S. Lefebvre, C. Guy / Chemical Engineering Science 54 (1999) 4895}4902

Fig. 2. Local mean liquid velocity at di!erent super"cial gas velocities and di!erent radial positions in the up#ow region.

h/D"4.3 above the distributor, far from sparger e!ects.As any other tracer technique, TPA measures the velocityin only one direction. The experimental data are between0.12 and 0.55 m/s; this range is in agreement with theliterature. Moreover, the relative error in the mean liquidvelocity is less than 6%.

No change in the increase of the local liquid velocity isapparent when the super"cial gas velocity crosses fromthe homogenous #ow regime to the heterogeneous #owregime. However, a change of the velocity radial pro"le ismore obvious. Indeed, in the heterogeneous regime,a strongly radial pro"le of liquid velocities is observed.This is not the case in homogeneous #ow where thevalues of the liquid velocities are the same fromr/R"0.00 to 0.20 and from r/R"0.41 to 0.58 for a givensuper"cial gas velocity. The experimental error does notexplain this surprising pro"le. However, the reportedvelocities are only upward vertical velocities and it can beexpected that the downward velocities show a steeperradial pro"le. The velocity pro"le is then di!erent fromthe velocity pro"le found by Mudde, Groen and VanDen Akker (1997), and Franz, BoK rner, Kantorek andBuchholz (1984), who reported averaged overall (upwardand downward) velocities. Moreover, the radial gradientof the velocity is larger in magnitude in heterogeneous#ow than in homogeneous one. This is explained by thefact that, in homogenous #ow, the radial pro"le of gashold-up is #at (Hills, 1974; Hebrard et al., 1996) and thebubble velocity pro"le is less parabolic than in hetero-geneous #ow, especially close to the central axis (Yao,Zheng, Gasche & Hofmann, 1990). In churn-turbulent#ow, large bubbles appear and induce parabolic pro"lesof bubble velocity and gas hold-up because they movepreferentially at the centre of the column (Yao et al.,1990).

4.2. Considering mixing as a dispersion mechanism

The time distributions obtained with the TPA tech-nique allow for the measurement of local mixing in liquid(LuK bbert & Larson, 1987). However, this mixing informa-tion neither accounts for micromixing, i.e. at very smallscales between the electrodes and the anemometer, nordoes it include the large #ow patterns representative ofmacromixing that is usually identi"ed in the literature.This mixing measurement represents thus a mesomixingand it is di!erent from the dispersive mixing e!ects foundin the literature. Moreover, this does not measure lateralliquid #ow.

The axial dispersion model is used to describe the dataand its parameters (local mean residence time and Pecletnumber) are obtained from the experimental data. Thewell known residence time distribution function for anopen}open system was used for "tting the residence timedistribution data. A least-square method was used foroptimizing the values of the parameters. Several initialparameters were used to insure the method robustness.The local mean velocities found with the local meanresidence times are in agreement with the local meanvelocities calculated above (plug #ow was then assumed)and presented previously in Fig. 2. Here, the local Pecletnumber is de"ned as the ratio of local convective masstransport to dispersive mixing transport at the meso-scale.

A plot of local Peclet number (Pe( ) as a function ofsuper"cial gas velocity at di!erent radial positions ispresented in Fig. 3. The relative error in the local Pecletnumber is less than 5%. It shows that local di!usiontransport increases (P

e(decreases) more than local con-

vective transport when super"cial gas velocity increases.This behaviour is more obvious at the centre of the

S. Lefebvre, C. Guy / Chemical Engineering Science 54 (1999) 4895}4902 4897

Fig. 3. Local Peclet number evolution with super"cial gas velocity atdi!erent radial positions.

Fig. 4. Local dispersion coe$cient evolution with super"cial gas velo-city at di!erent radial positions.

column. Indeed, the liquid turbulence is higher awayfrom the central axis (Yao et al., 1991; Dudukovic et al.,1991) and the mixing more vigorous. Then, in homo-genous #ow, the increase of bubble frequency passageinduces more local mixing than higher local liquid velo-city and that in the whole liquid up#ow region investi-gated. But, this is more pronounced near the central axiswhere the liquid phase is entrained by higher velocitybubbles. The evolution between the #ow regime observedin Fig. 3 shows that the appearance of large bubblesinduces a marked increase of liquid mixing relative to theliquid velocity (a marked decrease of Pe( ). Furthermore,increasing super"cial velocity increases radial homogen-eity of the local Peclet number (see at ;

g"7.8 cm/s).

Then the increase of bubble passage and bubble velocityinduces more mixing mass transport than convectivemass transport.

Fig. 4 shows the evolution of the local dispersioncoe$cient (D

a( x) with the super"cial gas velocity for di!er-

ent radial positions. The characteristic distance in thede"nition of the local Peclet number as measured byTPA is the distance between the two probes. The relativeerror in D

a( xis estimated to be less than 11%. Values of all

dispersion coe$cients shown in this "gure are two ordersof magnitude lower than the values found in the litera-ture. This is caused by the nature of the mixing scaleinvestigated. As expected, mesomixing is not of the sameorder of magnitude than macromixing. LuK bbert andLarson (1987) reported local Peclet numbers (calledBodenstein number in their case) with the TPA techniquewhich give dispersion coe$cient values of the same orderof magnitude than those in Fig. 4: D

a( x"1.7 to 2.7 cm2/s

for ;g"1.1 to 5.4 cm/s.

Even if this mesomixing dispersion coe$cient isa measure at a smaller scale, its evolution is likely to bethe same as the one found in literature for macromixing.

In the homogenous #ow, the dispersion coe$cient doesnot increase much with super"cial gas velocity as shownby Ityokumbul et al. (1994), but increases more thanliquid velocity as mentioned above. Moreover, in theheterogeneous #ow, the dispersion coe$cient increasesas shown by Dudukovic et al. (1991), Ityokumbul et al.(1994) and Hebrard et al. (1996). Mixing is thus moresensitive to the presence of large bubbles (Riquarts, 1981).

Although it is not obvious in Fig. 4 and contrary to theradial pro"le of liquid velocities, the radial gradient oflocal dispersion coe$cient is steeper at low super"cialgas velocities than at large super"cial gas velocities. Thisis in accordance with reported data by Rustemeyer,Pauli, Menzel, Buchholz and Onken (1989). Because theradial pro"le of liquid velocity changes less with super"-cial gas velocity than the pro"le of dispersion coe$cient,the pro"le of the Peclet number becomes more #at withincreasing super"cial gas velocities (see Fig. 3 and re-member that Pe( (r)Ju(

L(r)/D

a( x(r)).

However, the dispersion model is possibly too simplefor the mixing mechanism of the liquid phase in theup#ow region of the bubble column. Indeed, the "tting ofthis model was not always perfect. In homogenous #ow,"tting of the tail of the time distributions was not goodenough, especially away from the central axis. Underthese conditions the liquid #ow is more intermittentbecause of the less frequent passage of bubbles and thedispersion model represents a continuous #ow.

4.3. Considering the distribution of local liquid velocity(convective mixing)

The local instantaneous liquid velocity is obtained byinverting the instantaneous time delay and multiplyingit by the distance of the two TPA probes. A localliquid velocity distribution is then obtained. Fig. 5 shows


Fig. 5. Local liquid velocity distributions in the homogenous #ow(;

g"0.0090 and 0.0197 m/s), transition point (;

g"0.0369 m/s) and

churn-turbulent #ow regimes (;g"0.0499 and 0.0779 m/s) at the

centre of the column (r/R"0.00).

Fig. 6. Comparison of averaged liquid velocity distribution atr/R"0.00 to 0.58 and global absolute bubble velocity distribution* ;

g"0.037 m/s.

local liquid velocity distributions at di!erent super"cialgas velocity in the centre of the column (r/R"0.00).The distributions shown are obtained by averaginga minimum of two di!erent distributions (with 1000or 1500 samples for each) measured under the sameconditions.

As mentioned above, TPA measures only upwardliquid velocities. Although it could be possible to obtainthe distributions of the downward liquid by reversingthe probes, it is nevertheless interesting to discussupward liquid #ow distributions as they relate to therising mechanism of the liquid and the mixing of therising liquid.

As noticed by Franz et al. (1984) and Yao et al. (1991),the local liquid velocity distribution is small and nar-rower under homogenous #ow than in churn-turbulent#ow. Indeed, in the homogenous #ow, bubbles are smalland homogenous in size. Thus, their range of rise velocityis also small and narrow. A tail in the distributionsappears with the appearance of large bubbles. The areaunder this tail increases with the fraction of large bubbles.Indeed, the fraction of large bubbles is 0.14 and 0.24 atsuper"cial gas velocity of respectively 0.050 and0.078 m/s. These values were found with the simpli"edequations developed by Krishna et al. (1994). Thismeans that the bubble velocity has a direct in#uence onliquid velocity. In other words, liquid velocity followsthe bubble velocity as well. This con"rms the hypothesisthat part of the liquid moves in the bubble wakes at thesame velocity as the bubbles which follow a convective#ow (Hyndman & Guy, 1995a; Zahradnik & Fialova,1996).

Schmidt et al. (1992) have reached a similar conclusionin an air-lift reactor but through a di!erent analysis

based on the signal standard deviation and time delay.They found that #ow is a superposition of convectiveand dispersive #ow. However, in the centre, i.e. in thezone of upward #ow, they indicated that #ow is mainlyconvective.

4.4. Comparison of local liquid velocity distribution andglobal absolute bubble velocity distributions

Hyndman and Guy (1995a) and Hyndman et al. (1997)measured global absolute bubble velocity distributionsfor the same bubble column as studied in this work. Theymade RTD measurements with argon radioactive tracer.A bubble velocity distribution is shown in Fig. 6 with thesection averaged liquid velocity distribution. Both distri-butions are at the transition point. The distribution ofliquid velocity is averaged between r/R"0.00 to 0.58 inorder to represent the up#ow region with the followingequation:

f (u(Li)"

2

R20P

R0

0

f (u(Li)Drr dr, (1)

where R0

value is 5.8 cm.Fig. 6 shows that the form of the two distributions is

similar. This con"rms that the liquid is in part entrainedat the bubble velocity in the bubble wake. However, thedistributions are more di!erent for large liquid velocities.That is, the average liquid velocity distributions have anhigher average value than the global bubble velocitydistribution. This is explained by the fact that the liquidvelocity distribution is averaged on only the up#owregion and the global bubble velocity distributionwas measured over the whole bubble column section. If


Fig. 7. Comparison of dimensionless distributions of global absolute bubble velocities and liquid velocities in the up#ow region at the transition point(;

g"0.037 m/s) and in the churn-turbulent #ow regime (;

g"0.050 and 0.078 m/s). The symbols are the same as in Fig. 6.

integrated on the whole section, the averaged liquid velo-city distribution would translate toward the smallerliquid velocities. Moreover, the liquid velocity distribu-tion is measured along a small axial distance (betweenthe two probes) unlike the global bubble velocity distri-bution which is measured along the whole height of thebubble column: instantaneous bubble velocities may bemuch higher than averaged bubble velocities.

For a mixing mechanism comparison purpose, thedistributions of both phases are presented in Fig. 7 ina dimensionless form. The dimensionless velocity isthe ratio of the liquid velocity to the mean velocity andthe dimensionless distribution is the distribution ofdimensionless velocities. This allows comparing therespective mixing mechanism in relation to the super"-cial gas velocity. Fig. 7 presents thus the global bubbleand averaged liquid dimensionless velocity distributionsat the transition point and in the churn-turbulent #owregime.

Since gas-phase hydrodynamics are essentially thesame for di!erent super"cial gas velocity (convective#ow, Hyndman & Guy, 1995a), the dimensionless bubblevelocity distribution remains almost identical althoughthe dimensional distribution shows a shift to the rightdue to higher velocity bubbles. For all super"cial gasvelocities investigated, a fair superposition of the two-phase dimensionless velocity distributions is observed.This means that the liquid mixing mechanism in theliquid up#ow region is nearly the same as the bubble #owmechanism. A di!erence is observed principally aboutthe tail. This would be caused by the contribution of anadditional dispersive mixing. This explains why the di-mensionless liquid velocity distribution widens with theincrease of super"cial gas velocity: dispersion mixing

becomes more important as the large bubble fraction andvelocity increase which results in larger wakes and higherrenewal of the liquid in the wake.

5. Conclusion

The main objective of this work was to study theinteraction of liquid and bubbles with the help of localmeasurements. The local liquid #ow was investigated bymeans of a thermal pulse anemometry technique. Thelocal residence time distribution and local velocity distri-bution were thus measured. The study was carried out inthe up#ow region and through the homogenous andheterogeneous #ow regimes.

The liquid velocity pro"le changes with the appear-ance of large bubbles in the heterogeneous #ow regime,but no change appears in the evolution of the local meanliquid velocity when the super"cial gas velocity crossesfrom the homogenous #ow regime to the heterogeneous#ow regime. Liquid mixing is investigated at the meso-scale because the measurement technique does not ac-count for the very small scales between the probes, nordoes it include the large #ow patterns representative ofmacromixing. If liquid mixing mechanism is assumed tobe dispersive, the in#uence of large bubbles on localmixing appears to be large. The Peclet number (de"nedas the ratio of local convective mass transport to localdispersive transport) decreases with super"cial gas velo-city. If mixing is assumed to be due to convective #ow,local liquid velocity distributions are narrower underhomogeneous #ow than in churn-turbulent #ow. Indeed,the appearance of a long tail on the distribution (high-liquid velocities) coincides with the appearance of large


bubbles. That is, mesomixing is more vigorous whenlarge bubbles are present. Moreover, the area under thistail increases with the fraction of large bubbles. It is alsoshown that the global bubble velocity distribution andthe average up#ow section liquid velocity distributionare similar. The liquid seems thus intimately linked withthe bubbles (bubble wake). As gas phase mixing is con-vective, it is expected to "nd that liquid mixing is at leastpartially convective too. That is, although the convectivemodel is able to quantify the liquid-phase #ow and itsevolution, its does not represent alone the liquid mixingmechanism in the up#ow region of the bubble column,nor the dispersion model. Furthermore, the comparisonof the dimensionless velocity distributions of the twophases shows that the liquid mixing mechanism seems tochange with super"cial gas velocity unlike the gas-phase#ow mechanism. It will be important to con"rm this inthe future with the help of local bubble velocity distribu-tion data.

Notations

b fraction of large bubble (EgL

/Eg)

D bubble column diameter, mD

a( xlocal liquid dispersion coe$cient, m2/s

Eg

global gas hold-upEgL

global gas hold-up of large bubbles(E

g!E

gs)

Egs

global gas hold-up of small bubbles(E

gtrans)

Egtrans

global gas hold-up at transition pointf(u(

Li)Dr

local liquid velocity distribution at radialposition r, s/m

f(u(Li) section average liquid velocity distribution,

s/mh axial position, mH bubble column height, m¸ distance between electrodes and anemom-

eter, mPe( local liquid Peclet number (u(

L¸/D

a( x)

R bubble column radius, mR

0radial position limit of the liquid up#owregion, m

r radial position, m;

gsuper"cial gas velocity, m/s

;gtrans

super"cial gas velocity at transition point,m/s

u(L

interstitial mean local liquid velocity, m/su(Li

interstitial instantaneous local liquidvelocity, m/s

Acknowledgements

The authors want to thank Richard-Francois Caronfor the construction and his help in the operation of

Thermal Pulsed Anemometry probes. Financial supportfrom NSERC (Canada) and FCAR (Quebec) is alsoacknowledged.

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characterization of bubble column hydrodynamics with local measurements

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