Chemical Engineering Science 61 (2006) 1300–1311www.elsevier.com/locate/ces

Solid effects on hydrodynamics and heat transfer in an externalloop airlift reactor

H. Dhaouadia,∗, S. Poncinb, J.M. Hornutb,c, G. Wildb

aFaculté des Sciences, Dpt. de Chimie, Laboratoire de Chimie Appliquée et Environnement, Bvd. de l’Environnement, 5000 Monastir, TunisiabLaboratoire des Sciences du Génie Chimique, CNRS ENSIC/INPL Nancy, France

cUniversité Henri Poincaré de Nancy I, IUT Le Montet, France

Received 19 November 2004; received in revised form 25 June 2005; accepted 18 August 2005Available online 6 October 2005

Abstract

The effect of a solid presence on global hydrodynamic parameters and heat transfer in an external loop airlift reactor has been experimentallyinvestigated. Results obtained in both two- and three-phase flow are presented in this study. Two different external loop airlift reactor sizeshave been used and local hydrodynamic characteristics including local gas hold-up and bubble velocity have been obtained in two-phase flow.Optical and ultrasound probes have been used to obtain this information, respectively. It was found that an increase of solid hold-up leadsto a decrease of liquid velocity and heat transfer coefficient. Measured in a two- and three-phase reactor using a horizontal-heating probe,a correlation of the average gas hold-up and heat transfer coefficient is proposed. Correlation parameters are identified in homogeneous andheterogeneous flow regimes, which have been derived from the gas slip velocity concept. The experimental liquid velocity and gas hold-up inthe riser have been represented in a satisfactory way by a hydrodynamic model, either in the absence or in the presence of solid particles.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Airlift reactor; Hydrodynamics; Heat transfer; Two-phase; Three-phase

1. Introduction

Airlift reactors present the same advantages as conventionalbubble columns; they are characterised by a simple construc-tion, good mixing and low shear rate as compared with stirredtanks. They are particularly well suited for processes with de-mands for rapid and uniform distribution of the reaction com-ponents, and for multiphase systems for which high mass andheat transfer are necessary.

Many installations employ this type of reactor in varioussectors of industrial activities. They are mainly used as bioreac-tors in fermentation processes (Al-Qodah and Lafi, 2001) andin the biotransformation of many substances (Sánchez Mirónet al., 2002; Klein et al., 2002; Shu and Yang, 1996; Siegeland Robinson, 1992). Some particular applications to the

∗ Corresponding author. Tel.: +216 73 500 276; fax: +216 73 500 278.E-mail address: Hatem.Dhaouadi@fsm.rnu.tn (H. Dhaouadi).

0009-2509/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.08.024

wastewater treatment process are increasingly being developed(Beun et al., 2002; Van Benthum et al., 1997, 2000; Frijterset al., 1997; Heijnen et al., 1997).

Airlift reactors also have several chemical applications. Theyare used in ore leaching, high tonnage heterogeneous cata-lyst industries as well as in the ethylene chlorination process(Orejas, 1999).

Several works describe globally and locally the fluid dy-namic in external loop airlift reactors (Freitas et al., 1999, 2000;Dhaouadi et al., 1996; Douek et al., 1994). Many models, gener-ally derived from energy balances, are used to predict hydrody-namics and mass transfer in these reactors (García-Calvo et al.,1999; Livingston and Zhang, 1993; Kochbeck et al., 1992). Inmost published papers the three-phase hydrodynamic behaviouris an extension of the two-phase behaviour. Glass beads severalmillimetres in diameter are often used as the solid phase. Someworks are conducted with marine sediments (Tobajas et al.,1999) or active biomass (Schügerl, 1997) as the solid phase.Few works are conducted with very small diameter particles(Oey et al., 2001).

H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311 1301

In all these applications, the heat exchange aspect is impor-tant. However, works that describe the heat transfer in airliftreactors are very rare (Kawase and Kumagai, 1991). In a reviewpaper Kim and Kang (1997) studied the effect of gas velocityand density and also that of the solid and liquid properties onthe heat transfer coefficients in three-phase fluidised beds anddiscussed the analogy between the heat and mass transfer in thistype of reactor. Indeed, many gas–liquid and gas–liquid–solidreactions in chemistry or biochemistry are either endothermi-cal or exothermical. The removal or the supply of the heat byan indirect way is an important aspect in the design of thesereactors in order to ensure safe process operation or to main-tain optimal conditions for reaction. In order to design the heattransfer surfaces, information is required on heat transfer co-efficients between the two- or three-phase bed and heating orcooling surfaces. It is well known now that the heat transfer co-efficient is highly influenced by the hydrodynamic behaviour.Several published papers have focused on hydrodynamics ofthese reactors but only a few of them have studied heat transfer,especially in three-phase airlift reactors.

2. Theoretical aspect

Airlift reactors may be operated in homogeneous and hetero-geneous regimes. Under the usual operating conditions of anairlift reactor, the heterogeneous regime would prevail in theriser and the homogeneous regime would prevail in the down-comer. While some qualitative observations have been made onflow regimes in such reactors, the correlations of the hydrody-namic parameter (mean gas hold-up and liquid velocity) usu-ally do not take into account differences in flow regime. Here,we shall consider the gas slip velocity based on the classicalapproach of Wallis (1969):

Vgl = Ug

�g− Ul

1 − �g. (1)

For the slurry system, considered here as a pseudo-homogeneousphase, the same concept for gas slip velocity will be used.

Many hydrodynamic models have been developed for air-lift reactors. Experimental results obtained in this work willbe compared to the García-Calvo et al. (1999) model, based,like almost all published papers in this field, on an energybalance. For induced liquid velocity in the downcomer thefitting parameters are the friction coefficient in both riser anddowncomer parts of the external loop airlift reactor and the� parameter. As proposed by the authors the value of thenumber N (liquid profile parameter) is taken to be equal to2. For slip velocity calculation, the Zuber and Findlay modelis used rather than the fixed value (0.25 m s−1) proposed byGarcia-Calvo. From the application of the mass conserva-tion principle between the downcomer and the riser, liquidvelocity in the riser is easily deduced from the one in thedowncomer.

The basic equations of the model used are the following:

pmUg,m ln

(1 + �sl,r

gH

Pat

)

= 1

2

[�Kf,r�sl,r

(Ad

Ar

)2

+ Kf,d�sl,d

]Ad

Ar

(1 − �s,d )3

× V 3l,d + 0.64(2)3N/2�sl,rH(Vl,o − V l,r )

3

Dr

×(

1

2(3N − 1)+ 1

(3N + 1)− 21/2

(3N)

)+ �gVgl�sl,rgH, (2)

�g = Ugm

Vgl + 0.5Vl,c + Vl,r

, (3)

where

Vlc = (Vlo − V lr )

(1 − �g − �sr )

(N

N + 2

). (4)

It has to be kept in mind that the model used does assume thatthere is no gas present in the downcomer, which is the mainweakness especially for slurry-gas systems, where, experimen-tally, it has been observed that the presence of gas in the down-comer is relatively important.

3. Experimental

The investigation of global hydrodynamics (regime transi-tions, overall gas hold-up, liquid circulation velocity and theeffect of small particle with volume fractions up to 7% vol.) hasbeen conducted in two external loop airlift reactors of 10 cmID, 3 m height (EL1) and 15 cm ID, 6 m height (EL2). The heattransfer measurements have been conducted only on an EL1 re-actor. The experimental set-up is shown in Fig. 1. The spargerused represented in Fig. 1 consists of perforated tubes: 60 holesof 1 mm for the EL1 reactor and 64 holes of 1 mm for the EL2reactor.

Glass beads of 90 �m mean diameter (measured by aMALVERN laser granulometer) having a density of 2.537have been used as solid particles, and water and air as liquidand gas phases. Pressure probes as well as sampling taps aremounted at different axial positions of the riser and the down-comer. The velocity of the samplings was chosen to ensureisokinetic conditions in the sampling taps and the riser (or thedowncomer) so that the flow pattern will not be disturbed. Anultrasound probe based on the Doppler effect has been used tomeasure both the bubble rising velocity and frequency at dif-ferent axial and radial positions of the riser. Volume-averagedgas hold-ups have been measured using the usual manometricmethod in two-phase flow, which has been combined to thesampling of slurry suspension through the sampling taps inthree-phase flow; both measurements are performed at differ-ent axial positions in the riser. The solid hold-up distributionin different sections of the riser has also been determined us-ing the Wenge method (see Fig. 2). This method is as follows:after shutting off the gas feeding, the pressure measured at the

1302 H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311

sparger

gas – liquidseparator

downcomer toriser junction

1st floorri

ser

dow

ncom

er

2nd floorLegend:

1 Conductivity probe2 Pressure probe3 Ultrasonic probe4 Monofiber probe5 Heat probe6 Septum for tracer injection7 Sampling tap

Acquisitioncard

ground level

1, 2, 3, 4

1, 2, 3, 4

1, 2, 3, 4

1, 2, 3,4

1, 2, 3,4

1, 2, 3, 4

5

5

2

7

7

7

7

7

7

6

6

1, 2

1, 2

7

3, 4

3, 4

1, 2, 3 & 4probe

Fig. 1. Experimental set-up.

6

6.1

6.2

6.3

6.4

6.5

6.6

6.7

6.8

6.9

7

0 20 40 60 80 100 120 140

Time (s)

Pres

sure

dat

a ac

quis

ition

Sig

nal (

volt)

measuring time

Pressure

Time

2 phases

gas desengagement

gasing off

gasing on

Fig. 2. Wenge method application: sample of pressure data acquisition.

H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311 1303

Fig. 3. Home-made heat probe used in this work.

bottom of the studied section will increase within the air dis-engagement period. According to the Wenge method (Wengeet al., 1995), we have nearly 10–20 s (for the particles used inthis study) of stabilised pressure within which measurementscould be done. Pressure Measurements then enable solid andgas hold-up calculations using the following relationships:

�s = �l

�l − �s

(1 − �p

�p0

), (5)

�g = 1 − �p

�p0+ �s

(�s − �l

�l

). (6)

Superficial gas supply rates were varied up to 0.1 m s−1. Theglobal liquid circulation velocity in the downcomer is deter-mined using a tracer technique. More details concerning thehydrodynamic measurement techniques and calculations can befound elsewhere (Dhaouadi, 1997).

For heat transfer measurements, the probe used (see Fig. 3)allows to estimate the transfer coefficient between the probe andthe bulk at various superficial gas, and by consequent liquid,velocities. The probe is constituted of a brass cylinder of 15 mmexternal diameter.

This cylinder is electrically heated by the interior with aresistance rolled on a central brass core of 5 mm diameter. Thelength of the resistance is 1 m, its diameter 1 mm and the power12–500 W under 12–80 V.

The probe is provided with six thermocouples installed indifferent positions on the external surface of the brass tube.Two other thermocouples are installed in the column: one tomeasure the temperature of the heated volume element near theprobe and the other, installed at the bottom of the column, tocontrol the average temperature of the liquid.

The heat transfer from the resistance to the external probecylinder is ensured by an interstitial mixture which has topresent a high thermal conductivity and be as homogeneous aspossible to avoid hot points on the resistance. A mix of 50 �mdiameter copper particles with water and a wetting agent wasselected.

During the experimentation, the probe is implanted horizon-tally in the column and a chosen temperature difference is ad-justed by varying the electrical power. The probe can be placedat different axial positions. The heat probe temperatures is usu-ally between 24 and 29 ◦C for liquid temperatures of 23 to26 ◦C. This difference reduces the free thermal convection ef-fects and variations of fluid properties in the heat transfer film.

Tests showed that an increase of the probe temperature by afew degrees has no effect on the measured heat transfer coeffi-cient. Also, it is verified that a steady-state value of the probetemperature is reached within 2 s of the application of heatingcurrent.

4. Results and discussion

A transition from the homogeneous to the heterogeneousflow regime is observed in the three-phase airlift reactor (seeFig. 4). Compared to the gas–liquid–solid system, and for theEL2 reactor, the transition in flow regime for an air–water sys-tem is delayed to higher velocities because of the relatively highliquid velocity in the riser. For the EL1 reactor, and in com-parison to the air–water system case, this transition is observedfor lower velocities with the GLS system; this shift towardssmaller transition velocities increases slightly with an increaseof the solid quantity present in the reactor (see Fig. 5). A solidpresence would favour the formation of larger bubbles even ina homogeneous regime. The extension of the slip velocity con-cept to the three-phase systems clearly shows that the presenceof a solid leads to bubble coalescence by increasing the turbu-lence. In the airlift reactor case, liquid and gas velocities areinterdependent and the liquid movement in the riser delays theflow regime transition. Also, It appears that a plot of the slipvelocity vs. the overall gas+liquid velocity (or vs. the liquidvelocity) yields a clear distinction between flow regimes. Fi-nally, in a homogeneous flow, the slip velocity decreases withincreasing liquid velocity UL while in a heterogeneous regimeit is an increasing function of UL.

Within the range of solid concentrations investigated, onlythe initial solid addition has an influence on liquid velocity,which has also been reported by Lu et al. (1994). Indeed, theliquid velocity decreases rapidly when changing from a waterto a slurry system with 3% vol solid content; it decreases veryfeebly when the solid passes from 3 to 5 and 7% vol (see Fig. 6).By itself, the slurry viscosity variation (not important within thesolid content range studied) does not seem to justify the liquidvelocity variations. This slowing can be linked to the upwardflow driving force variation as follows:

Compared to the water system, the riser gas hold-up in athree-phase reactor is slightly lower. Simultaneously, the down-comer gas hold-up is somewhat higher in the three-phase sys-tem than in the two-phase system (see Figs. 7 and 8). Addingsolid to water therefore leads to a decrease in the driving forceand consequently to a decrease in the liquid circulation veloc-ity. It was experimentally found that the supplementary solidaddition does not induce any change in gas hold-up in thereactor. The solid phase is homogeneously distributed in thereactor and does not affect the driving force any more. This has

1304 H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

0.7

0 0.02 0.04 0.06 0.08 0.1 0.12

Ug,r (m/s)

Vgl

(m/s

)

water

water + 3% vol. solidwater + 5% vol. solidwater + 7% vol. solid

EL2

Fig. 4. Solid effect on slip velocity and flow regime transition (EL2).

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0 0.03 0.06 0.09 0.12 0.15

Ug,r (m/s)

Vgl

(m

/s)

heterogeneous regime(coalesced bubbles)

water + 4% vol. solidwater + 7% vol. solid

water

EL1

homogeneous regime(dispersed bubbles)

Fig. 5. Solid effect on slip velocity and flow regime transition (EL1).

been experimentally verified for all solid hold-ups studied andeven for low gas superficial gas velocities in an EL2 reactor andfrom superficial gas velocities of about 0.02 m s−1 in EL1. Re-sults obtained for a solid hold-up of 5% and for the EL2 reactorhave been reported in Fig. 9 which shows the uniformity of thesolid hold-up in the downcomer and at different axial positionsof the riser. This figure also compares results obtained by bothWenge and sampling methods in the riser. Experimental dataare well described using the model of Calvo-Garcia. For theliquid velocity, the fitting parameters are the friction loss coef-ficients and the � parameter (see theoretical aspect paragraphand Figs. 6 and 7).

A change in gas hold-up reflects a change in bubble velocityand often a change in bubble size. An increase of bubble ve-locity corresponds to a decrease of the gas hold-up. Variationsof bubble velocity are often related to their size change.

Liquid velocity in the riser is more affected by a solid pres-ence than the gas hold-up. The increase of solid hold-up in-creases the system turbulence, which leads to a decrease of thevelocity of the rising bubbles (see Fig. 10) and therefore thatof the bubble size. Indeed, the bubble frequency increases withincreasing solid hold-up (see Fig. 11 ).The wider frequencyspectra obtained in a three-phase system as compared to thetwo-phase one indicates a larger bubble size distribution.

H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311 1305

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0 0.02 0.04 0.06 0.08 0.1 0.12

Ug,r (m/s)

Ul,r

(m/s

)

water

water + 3% vol solid

water + 5% vol solid

water + 7% vol solid

E. Garcia-Calvo model

EL2

Fig. 6. Solid effect on liquid velocity in the riser—E. Garcia-Calvo model application (EL2).

0

2

4

6

8

10

12

14

0 0.02 0.04 0.06 0.08 0.1 0.12

Ug,r (m/s)

ε g,r

(%)

WaterWater + 3% vol. solidWater + 5% vol. solidWater + 7% vol. solidE. Garcia-Calvo model

EL2

Fig. 7. Solid effect on gas hold-up in the riser—E. Garcia-Calvo model application (EL2).

Variations in global and local hydrodynamic parameters inthree-phase airlift reactors can be the consequence of one, orof a combination of the following mechanisms:

• bubble coalescence producing larger and faster bubbles,• turbulence generating smaller bubbles with lower rising

velocity,• changes in physico-chemical slurry properties. In fact, when

particles are distinctly smaller than bubbles, and their termi-nal velocity is lower than the liquid velocity, the slurry canbe considered as a pseudo-homogeneous phase. The solidpresence increases both the density and the slurry viscos-ity. The resulting effect is a decrease in the liquid veloc-ity, even though it has the opposite effect on bubble risevelocity, and

• the presence of a solid in the bubble wakes, stabilises trailsof bubbles which increase their upward velocity and reducethe gas hold-up.

The hydrodynamic behaviour of airlift reactors dependsstrongly on the reactor geometry, dimension, shape andriser to downcomer junction (and vice versa). On the otherhand, the hydrodynamic behaviour is also strongly depen-dent on the flow regime. Thus, correlating the mean hydro-dynamic parameters according to the flow regime will behelpful.

Within the range of solid concentrations investigated a cor-relation is proposed which takes into account the slurry viscos-ity rather than the solid concentration (the slurry is supposedto be a pseudo-homogeneous phase) for the estimation of both

1306 H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311

0

1

2

3

4

5

6

0 0.02 0.04 0.06 0.08 0.1 0.12

ε g ,d

(%)

Ug,r (m.s-1)

EL2

water3% vol. solid

5% vol. solid7% vol. solid

Fig. 8. Solid effect on gas hold-up in the downcomer (EL2).

0

1

2

3

4

5

6

0 0.02 0.04 0.06 0.08 0.1 0.12

Ug,r (m/s)

ε s,r

,d

Z=0.25 mZ=1.35 mZ=3.80 mmean solid holdup (wenge method)downcomer

EL2 ; εS = 5 %

Fig. 9. Solid hold-up in the riser and the downcomer (EL2).

superficial liquid velocity and gas hold-up in the riser. The pro-posed interpolation correlations are available for EL1 reactorconfiguration. The solid presence modifies the slurry viscos-ity which can be easily estimated by Thomas’ formula (1965)(�(cP ) = 1 + 2.5�s + 10.05�2

s + 2.73 × 10−3e16.6�s ).The correlations proposed for both gas hold-up and liquid

velocity are of the following type:

Ulr or �gr = aUbgr

(�sl

�water

)c

. (7)

In the same way, the external heat transfer coefficient to a tubewill be linked to the superficial gas velocity in the riser, Ugr ,according to the corresponding flow regime.

The parameters of the proposed correlations differ accordingto the flow regime; the correlations yield a good agreementwith experiments (see Figs. 12 and 13).

The values of the parameters of these correlation devel-oped here for both a three-phase system and viscous media(ranging between 0.001 and 0.033 Pa s) for the estimation ofboth liquid velocity and gas hold-up in the riser and taking

H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311 1307

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

r/R (-)

Vb,

r(m

/s)

water3% vol. solid5% vol. solid7% vol. solid

EL2

Fig. 10. Solid effect on radial profile of rising bubble velocity in the riser.

0

50

100

150

200

250

300

-100 -80 -60 -40 -20 0 20 40 60 80 100

Vb,r (cm/s)

Freq

uenc

y

water3% vol.solid

Fig. 11. Solid effect on bubble size distribution.

into account the flow regime can be found in the followingtables.

For superficial liquid velocity in the riser

Parameter Homogeneous Incertitude Heterogeneous Incertitude

a 0.71 0.057 0.42 0.021b 0.44 0.022 0.26 0.021c −0.12 0.009 −0.12 0.006

And for the gas hold-up in the

Parameter Homogeneous Incertitude Heterogeneous Incertitude

a 1.59 0.146 0.45 0.034b 0.90 0.026 0.46 0.032c −0.05 0.007 −0.08 0.008

Concerning the heat transfer, measurements in EL1 were con-ducted in both a two- and three-phase flow system. It was found

1308 H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311

0.01

0.1

1

0.001 0.01 0.1 1

Ug,r (m/s)

Ul,r

(m/s

)

Fig. 12. Riser liquid velocity experimental data correlation with regard to the flow regime.

0.001

0.01

0.1

1

0.001 0.01 0.1 1

Ug,r (m/s)

ε g,r

Fig. 13. Riser gas hold-up experimental data correlation with regard to the flow regime.

that the heat transfer coefficient, measured with the home-made probe, increases with the gas flowrate augmentation (seeFig. 14). From the data obtained from the two-phase system,and taking into account the flow regime, we propose the fol-lowing correlation relating the external heat transfer coefficientand the superficial gas velocity in the riser:

he(W/m2 K) = 26.09 × 103U0.48gr , Ugr expressed in

(m s−1), for the homogeneous regime.

hc(W/m2 K) = 15.95 × 103U0.33gr , Ugr expressed in

(m s−1), for the heterogeneous regime.

Tests conducted with two different values of solid hold-up (1%and 3% vol) in the EL1 reactor clearly show that the increaseof solid concentration induces a decrease of the heat transferperformance of the reactor (see Fig. 15). For superficial gasvelocities less than 0.018 m s−1 (1% solid content case) and0.036 m s−1 (3% solid content case) a negligible effect on he

is observed so that the results are quite similar to the watercase. This is due to the fact that for small gas velocities solidhold-up is lower in the EL1 reactor as previously indicated andthe presence of particles has a negligible effect. This effectis furthermore reinforced by the negligible effect of the gasvelocity on the liquid velocity and by the higher imprecision of

H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311 1309

1000

10000

0.001 0.01 0.1 1

Ug,r (m/s)

h ce

(W/m

2 .k)

hce = 15.95.103Ug,r0.33

heterogeneous regimehce = 26.09.103Ug,r

0.48

homogeneous regime

EL1 reactor

Fig. 14. External heat transfer coefficient correlation with regard to the flow regime.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 0.02 0.04 0.06 0.08 0.1 0.12

Ug,r (m/s)

h ce

(W/m

2 .K)

water1% vol. solid3% vol. solid

EL1Ug,r=0.018 m/s

Ug,r=0.036 m/s

Fig. 15. Solid effect on the external heat transfer coefficient.

measurement in these gas velocity ranges. Complex phenomenaoccur when particles, gas and liquid are in contact. Especially,the heat amount transferred in each phase is still difficult toevaluate.

5. Conclusion

The effect of the presence of a solid on hydrodynamics andheat transfer characteristics has been investigated. It is experi-mentally shown that transition in a flow regime occurs at smallervelocities in a three-phase system than in a two-phase system.Measurements of global and local hydrodynamic parametersshow that the presence of a solid phase leads to many changesin bubble size and velocity distribution, liquid velocity andgas hold-up. Within the riser section of the reactor, the liq-uid velocity decreases notably, compared to gas hold-up,

with increasing solid hold-up. The upward force acting onliquid circulation decreases with increasing gas hold-up inthe downcomer. The increase of solid hold-up increases thesystem turbulence; thus, the bubble size and rising velocitydecrease. Because of the relatively high liquid circulationrate in airlift reactors, bubble coalescence also occurs, butis counter-balanced by the system turbulence, the gas hold-up in the riser is less affected by the presence of solid thanliquid velocity. External heat transfer coefficients measuredin the airlift reactor show that increasing the solid hold-updecreases the heat transfer. Correlations of global hydrody-namic parameters with operating variables and taking intoaccount the flow regime transition are proposed. Up to nowthese correlations are, however, only valid for the geome-try and size of the airlift reactor on which they have beenbased.

1310 H. Dhaouadi et al. / Chemical Engineering Science 61 (2006) 1300–1311

Notation

a, b, c correlation parameterA cross-sectional area, m2

D diameter, mg gravitational constant, m s−2

h heat transfer coefficient, w m−2 KH height of the reactor, mKf friction coefficient, dimensionlessN liquid profile parameterp pressure, PaP power, Wr radius, mR column radius, mS surface, m2

T temperature, KU superficial velocity, m s−1

V interstitial (linear) velocity, m s−1

Vgl gas slip velocity, m s−1

Vlo interstitial velocity on the axis of column,m s−1

Vlc mean interstitial velocity in the core region,m s−1

V mean linear velocity, m s−1

Greek letters

� parameter related to two-phase flow, dimen-sionless

� difference� hold-up, dimensionless� viscosity, Pa s� density, kg m−3

Subscripts

at atmosphericb bubblec columnd downcomere externalg gash heatl liquidm middler risers solidsl slurry0 time zero

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