2006--studies in multiple impeller agitated gas liquid cont actors 2006

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Chemical Engineering Science 61 (2006) 489–504

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Studies in multiple impeller agitated gas–liquid contactors

Satish D. Shewale, Aniruddha B. Pandit∗

Chemical Engineering Division, Institute of Chemical Technology, University of Mumbai, Matunga, Mumbai 400 019, India

Received 16 October 2004; received in revised form 27 April 2005; accepted 29 April 2005

Abstract

Experiments have been performed to study the effect of the density and the volume of the tracer pulse on the mixing time for twoimpeller combinations in the presence of gas in a 0.3 m diameter and 1 m tall cylindrical acrylic vessel. The tall multi-impeller aerobicfermenters, which require periodic dosing of nutrients that are in the form of aqueous solution, is a classic case under consideration.Conductivity measuring method was used to measure the mixing time. Two triple impeller combinations; one containing two pitchedblade downflow turbines as upper impellers and disc turbine as the lowermost impeller (2 PBTD–DT) and another containing all pitchedblade downflow turbines (3 PBTD) have been used. Other variables covered during experiments were the density and the amount of thetracer pulse, the impeller rotational speed and the gas superficial velocity. Fractional gas hold-up, Power consumption and mass transfercoefficient have also been measured for both the impeller combinations. Influence of aeration and impeller speed on the mixing time hasbeen explained by the interaction of air induced and impeller generated liquid flows. Three different flow regimes have been distinguishedto explain the hydrodynamics of the overall vessel (i.e., multiple impeller system). A compartment model with the number of compartmentsvarying with the flow regimes have been used to model liquid phase mixing in these flow regimes. A correlation for the prediction of thedimensionless mixing time in the loading regime has been proposed in order to account the effect of the density and the amount of thetracer pulse on the mixing time. Correlations have also been proposed to predict fractional gas hold-up andkLa.� 2005 Elsevier Ltd. All rights reserved.

Keywords:Gas–liquid contactor; Multiple impeller system; Flow patterns; Mixing time; Compartment model; Exchange flow rate

1. Introduction

The multiple impeller-agitated systems are used in severalindustrial applications namely; fermentations, gas–liquid re-actions such as hydrogenation, dissolution and crystalliza-tion, polymerization reactors, waste water treatment, etc.Multiple impellers are preferred over a single impeller asmultiple impellers provide better gas utilization in gas–liquidsystem due to the higher gas phase residence time, narrowerspread in the residence time distribution in the flow sys-tems and higher surface area per unit liquid volume for heattransfer. Also, multiple impellers are preferred over a sin-gle impeller where shear sensitivity to micro-organisms isan important criteria for the design, as multiple impellers

∗ Corresponding author. Tel.: +91 22 24145616; fax: +91 22 24145614.E-mail address:[email protected](A.B. Pandit).

0009-2509/ - see front matter� 2005 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2005.04.078

offer lower average shear as compared to a single impellersystem due to overall lower operational speeds (Gogate etal., 2000) at equivalent power dissipation rate and allow thefreedom of controlling the dispersed phase hold-up and theresidence time over a wide range. Multiple impeller biore-actors are now becoming important due to their efficientgas-distribution and better oxygen utilization characteris-tics, higher gas phase residence time, increased gas hold-upand superior liquid flow (plug flow) characteristics (Gogateet al., 2000).

The study of the liquid phase homogenization processin a stirred tank (single or multiple impellers) has of-ten been approached through the study of ‘mixing time’.Mixing time is the time necessary for attaining the pre-defined state of homogeneity of the liquid bulk after theaddition of a tracer pulse or a second liquid, which is tobe homogenized. It is the main parameter used to definetime scale of the macroscopic convective processes in the

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490 S.D. Shewale, A.B. Pandit / Chemical Engineering Science 61 (2006) 489–504

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liquid mixing in the stirred reactor when liquid used isbatch-wise.

Smith et al. (1987), Nocentini et al. (1988), Hudcova etal. (1989), Abrardi et al. (1988, 1990)and Bouaifi et al.(1997) have investigated flow patterns for gas–liquid con-tactor agitated by different multiple impeller combinations.Abardi et al. (1988)have identified different flow regimesfor the lowermost impeller and upper impellers.Abrardi etal. (1990), Vasconcelos et al. (1995), Vasconcelos and Alves(1995), Vrabel et al. (1999)andMachon and Jahoda (2000)have studied the effect of the impeller speed and the gasvelocity on the mixing time.Hristov et al. (2001)have an-alyzed the gas–liquid mixing accompanied by bioreactionusing a 3-D network-of-zones and have reported that thesimulations can provide detailed predictions of the local gashold-up distribution, the local mass transfer area, the par-tial segregation of both the dissolved gas and the nutrientand the extent of oxygen depletion of bubbles.Hristov etal. (2001)have demonstrated these theoretical predictionsusing colour-augmented 3D contour maps and solid-bodyisosurface images. The analysis reported byHristov et al.(2001) is for a real case and they have shown that variousgradients (dissolved gas, nutrient, etc.) were well matchedby the predictions of the 3D model.Alves et al. (1997)have compared compartment model of mixing, with differentnumber of compartments per agitation stage with exchangeflow between the adjacent compartments. This compartmentmodel resembles fluid plug flow model when the number ofcompartments are more.Machon and Jahoda (2000)haveused both plug flow model and compartment model success-fully. In the present study, a compartment model with a sin-gle compartment per agitation stage has been used. Similarmodel has been successfully used byJahoda and Machon(1994), Otomo et al. (1995)and Kasat and Pandit (2004)for unaerated system and byMachon and Jahoda (2000)andMoucha et al. (2003), for aerated system. Several studieshave been reported (Ahmad et al., 1985; Rielly and Pan-dit, 1988; Burmester et al., 1991; Bouwmans et al., 1997;Gogate and Pandit, 1999; Pandit et al., 2000) to account forthe effect of the density difference between the tracer fluidand the bulk fluid, the type and geometry of the impeller andthe amount of the tracer fluid on the mixing time in a sin-gle impeller system.Kasat and Pandit (2004)have reportedfor the first time the effect of the density and the volumeof the added tracer pulse on the mixing time for unaeratedmultiple impeller system.

Maximum cell growth and optimum product yield in theseed fermenter; and optimum cell growth and maximumproduct yield in the production fermenter, are ensured bycontrolling the nutrient concentration and other fermenterparameters precisely. The tall multi-impeller aerobic fer-menters, which require periodic dosing of nutrients (that arein the form of aqueous solutions) to maintain desired nutrientconcentration in the fermenter, is a classic case under consid-eration. In addition to periodic dosing of nutrients, the con-centration of nutrients in the dose (i.e., density of dose) and

the dose volume are also important parameters. The avail-ability and the distribution of these nutrients, throughout thefermenters can significantly affect the metabolic pathwaysand the biological product distribution. However, no studieshave been reported to characterize the effect of the tracerproperties (the tracer density and the tracer volume) on themixing time in the multiple impeller system in the presenceof gas. The motion of the rising bubbles affects the inter-action (exchange flows) between the adjacent impellers andhence acquiring the knowledge of the different flow patternsunder different operating conditions is essential. Hence ob-jectives of the present work are to identify different flowregimes, to study the effect of these flow regimes on themixing time, if the tracer of different densities is used andis added in the different quantities, and to getkLa data forthe gas–liquid operation in the multiple impeller system.

2. Experimental

The experiments have been performed in a cylindricalacrylic vessel of 0.3 m i.d. and 1 m height, with three im-pellers mounted on the shaft. Four perpendicular baffles hav-ing width 0.1 T were fitted along the height of the liquid. Thevessel has several apertures for the incorporation of the con-ductivity measuring probes, having diameters of 26 mm. Theimpeller spacing (S) has been maintained at 3D, with a lower-most impeller located at a distance of 0.5 T from the bottomof vessel, which was chosen on the basis of the assumptionthat each impeller forms its own circulation loop when theimpeller spacing(S)�2D (Hudcova et al., 1989). Air wassparged through a ring sparger having diameter, same as thatof impeller. The ring sparger with eight symmetrically drilledholes of 1 mm diameter was located at a distance of 0.25 Tfrom the bottom of vessel. The ring sparger was designed byusing a criterion reported byRewatkar and Joshi (1991)forensuring that all the holes of the sparger should be effectiveover the range of superficial gas velocities covered in thiswork. Fig. 1 schematically shows the experimental set upused in the present study. Two different types of impellers;six bladed pitched (blade angle,� = 45◦) downflow turbine(D=T/3, blade height(h)=0.3D), PBDT and six bladedrushton disc turbine(D = T/3, h = 0.2D, blade length=0.25D), DT were used to form two triple impeller com-binations. Power numbers of DT and PBTD were 5 and1.3, respectively (Kasat and Pandit, 2004). One impellercombination was comprised of three Pitched Blade down-flow turbines, while other was containing Disc turbine as thelowermost impeller and Pitched Blade downflow turbinesas upper two impellers. First and second impeller combina-tions are denoted as 3 PBTD and 2 PBTD–DT respectivelyin the later text. Experiments have been performed with tapwater at 30◦C. The vessel was filled with tap water up to theheight of 2.9 T. Superficial velocities(VG) of the sparged airwere 5, 10, 15 and 20 mm/s. The impeller rotational speed(N) was varied in the range of 0–8 rps.

ARTICLE IN PRESSS.D. Shewale, A.B. Pandit / Chemical Engineering Science 61 (2006) 489–504 491

×P4

⋅P3

×P2

⋅* P1

P2

P1

P4

P3

H

S

S

0.5T 0.25T

D

T

× Conductivity probe P1, P2, P3, P4

* Tracer injection point

0.1T

Tracer Addition Tube

Rubber Cork

Aluminum Rod

Acrylic tube

Fig. 1. Experimental set-up.

The fractional gas hold-up was determined by visuallyobserving the dispersion heights between the two baffles inthe absence and presence of the aeration. Power consump-tion was measured using electrical method. Electrical powerconsumed by the impeller was determined by using a Tongtester or Clamp-on meter. Following equation has been uti-lized for calculating the impeller power consumption,

P = (VRIR + VBIB + VY IY ) cos�, (1)

where the value of power factor, ‘cos�’ is 0.8. Due to thevariation of the power factor, it was independently estimatedbefore the start of the experimental run on each day. Thepower factor varied only within a narrow range of±3%. Theeffective power consumed in the bulk liquid is the differencebetween impeller power consumption measured at the exper-imental conditions and that measured at the same impellerspeed, but in the absence of water. The total power dissipatedin the bulk fluid can be calculated by summing the effectiveimpeller power(PG) and gassed power(=QGHD�LGg).Flow regimes for the multiple impeller agitated gas–liquidcontactors were identified by visual observations and by tak-ing images of the vessel at a time interval of 0.5 s using adigital camera. Also by giving a pulse of KMnO4 solutionnear the free surface of the gas–liquid dispersion, liquid flowbehavior in the vessel was observed and recorded. Based onthese observations, Flow regimes have been distinguished

0

1

2

3

0 20 40 60 80time, s

Dim

ensi

onle

ss c

once

ntra

tion

C1

C2

C3

Fig. 2. Experimental conductivity response curve, for 2 PBTD–DT,VG = 5 mm/s, N = 8 rps, tracer density= 1054 kg/m3, Vt /Vb = 0.0025where,C1, C2 andC3 are concentrations in the 1st, 2nd and 3rd com-partments, using probesP2, P3 andP4, respectively.

for the lowermost impeller, upper impellers and overall ves-sel as such.

Conductivity measurement method with NaCl solution asa tracer fluid has been used to measure the mixing time.The density of the tracer fluid was varied from 1054 to1178 kg/m3 by dissolving an appropriate quantity of sodiumchloride in water. The amount of the tracer pulse was variedin the range of 0.25–1.75% of the bulk liquid volume, i.e.,160–1120 ml. A tracer pulse of known density and volumewas dumped on the surface of the bulk liquid with the helpof an acrylic tube of diameter 0.05 m (Fig. 1), having pulland push type of an arrangement (an aluminum rod withrubber cork at one end). With the help of this arrangementit was also possible to add the high volume tracer almost in-stantaneously (maximum addition time of 1 s for the largestvolume). The change in the conductivity of the bulk liquidalong the height of the vessel was recorded with the help ofthe four conductivity probes. One of the conductivity probeswas located near the surface of the bulk liquid to get the cor-rect estimate of the time at which the tracer was added. Theremaining three conductivity probes were located just be-low each impeller plane, which gives an accurate estimationof the mixing time in each impeller zone and also the over-all mixing process. Each of the three probes was separatedfrom its adjacent probe by a vertical distance of 0.3 m andby an azimuthal angle of 90◦ (Fig. 1). Fig. 2shows a typicalexperimental conductivity response. From the conductivityvs. time data, the mixing time was calculated for 95% ho-mogeneity. Details of the calculation of 95% mixing timeare described byKasat and Pandit (2004). The values of theexperimental mixing time (i.e., the mixing time for slow-est responding probe which is the lowermost probe) with


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respect to the different parameters, reported later in the textare typically an average of 3–4 such experiments. Mixingtime measurement was found to be reproducible within theaccuracy limits of±5%.Bujalski et al. (2001)have stronglyrecommended that unshielded probes should not be usedfor measuring the mixing time in the presence of gas phasebecause the contact of the gas bubbles with the electrodemakes local conductivity signal too noisy to measure themixing time accurately. In the present study, each conductiv-ity probe was covered with the fine mesh screen to preventthe contact of the gas bubbles with the electrode and to geta smooth conductivity response curve. No significant differ-ence in the values of the mixing time was observed whenthe experiments were performed for unaerated liquid usingconductivity probes with and without the fine mesh screencovering. This indicates that the fine mesh screen did not in-troduce any significant delay in the response to the changesin the conductivity and also did not affect the liquid flow atthe electrodes significantly.

A dissolved oxygen (DO) probe was located at a distanceof T/4 from the bottom of the vessel in a separate set ofexperiments. Experiments have been performed to measurekLa for both of the impeller combinations, for two valuesof VG; 5 and 10 mm/s and at impeller speed ranging from 0to 8 rps. DO of the tap water was eliminated by the additionof the stoichiometrically required quantity of the sodiumsulfite. Once the DO of the bulk liquid reached the rangeof 0–0.3 mg/l, i.e., initial DO for the experiment(Ci), airflow and impeller action were started simultaneously and thechange in the DO level of bulk liquid (C) was recorded withrespect to the time (t), until C reached the saturation con-centration(C∗). Data ofC varying in the range of 20–60%of the saturation concentration vs. respective values of thetime was considered for the calculation ofkLa. kLa is theslope of the curve ln((C∗ − Ci)/(C

∗ − C)) plotted againsttime, t. The values ofkLa, reported later in the text are typ-ically an average of 2–3 such experiments. Measurement ofkLa was reproducible within accuracy limits of±7%.

3. Results and discussion

3.1. Flow patterns

Flow patterns observed in the vessel depend uponVG,N and impeller combination. Different flow patterns wereobserved for the lower and upper impellers.Fig. 3 showssome typical flow patterns observed in the vessel; with im-peller combination of 2 PBTD–DT forVG = 10 mm/s andwith 3 PBTD forVG=5 mm/s, at different impeller speeds.Mainly two flow regimes have been identified for the low-ermost impeller; one Flooding (F) regime and second beingthe Loading (L) regime. For upper impellers also mainly twoflow regimes were observed; in the first one, upper impellerswere not able to divert gas bubbles in radial or downwarddirection, but due to rotating action of the upper impellers,

diameter of the central gas plume increases and gas bubblesare poorly dispersed (radially) in the region above the upperimpellers. While in the second one, upper impellers divertgas bubbles in the radial or in the vertically downwards di-rection and gas bubbles get well dispersed in the region un-derneath each of the impeller and/or radially outward. Usingthe same terminology as used byAbrardi et al. (1990), thefirst regime is defined as Ineffective dispersion (DI) whilethe second one is defined as Effective dispersion (DE). Theimpeller speed at which the transition occurs from DI to DEregime for upper impellers is defined asNU , while the im-peller speed at which the transition occurs from the F to Lregime for the lowermost impeller is defined asNF . Threehydrodynamic regimes can be distinguished to explain hy-drodynamics of the overall vessel (i.e., multiple impellersystem); DI–F, DE–F, DE–L for both of the impeller combi-nations. Shortcut notations used to define hydrodynamics ofthe overall vessel are straightforward, e.g. DI–F means up-per impellers are in the DI regime and lowermost impelleris in the flooding (F) regime while DE–L means upper im-pellers are in the DE regime and the lowermost impeller isin the loading (L) regime. Similarly DE–F means upper im-pellers are in the DE regime and the lowermost impeller isin the flooding (F) regime.

It can be seen fromTable 1that the values ofNF for 2PBTD–DT are lower by 6–35% than predictedNF for singleDT using the correlation proposed byNienow et al. (1985);whereas the values ofNF for 3 PBTD are also lower (devia-tion of 20–26%) than predictedNF values for single PBTDusing the correlation proposed byMedek and Fort (1997).Thus it can be concluded fromTable 1that the values ofNFfor multiple impeller (actually lowermost impeller in mul-tiple impeller system) system are lower than that for a sin-gle impeller. It can be also seen that the difference betweenNU andNF is higher, i.e., DE–F regime gets extended overa wider impeller speed range, for 3 PBTD than that for 2PBTD–DT. This could be attributed to the difference in thepower dissipation level as discussed later.

3.2. Power consumption studies

Gassed power consumption(PG) values in the DE–Lregime has been given in the following correlation form,originally proposed byMichel and Miller (1962), rather thanreporting these values individually for the brevity of the text,

PG = �

(P 2

oND3

Q0.56G

)n. (2)

Values of� andn, required to fit the gassed power consump-tion data for both of the impeller combinations are given inthe Table 2along with the values reported byMichel andMiller (1962)which are for a single DT. It can be seen fromthe Table 2that the values of ‘n’ obtained for both of theimpeller combinations are much closer to the value of ‘n’reported byMichel and Miller (1962), i.e., 0.45; while the


Fig. 3. Flow patterns for 2 PBTD–DT (A,B,C) and for 3 PBTD (D,E,F) atVG = 10 mm/s and 5 mm/s respectively. (A, D) DI–F regime; (B, E) DE–Fregime; (C, F) DE–L regime. (A) N= 1.67 rps; (D) N= 0 rps; (B,E) N = 3.75 rps; (C,F) N= 5.08 rps.

Table 1Values ofNU andNF for 2 PBTD–DT and 3 PBTD, with predicted values ofNF for single DT and single PBTD

VG (mm/s) 2 PBTD–DT 3 PBTD DT (Nienow et al., 1985) PBTD (Medek and Fort, 1997)

NU (rps) NF (rps) NU (rps) NF (rps) NF (rps) using NF (rps)QGND3 = 30(D/T )3.5N

2Dg =854.5Q0.558

Gn−0.542b

(sin�)−0.58

5 <1.67 2.42 <1.67 3.75 3.76 4.6710 1.67 3.75 <1.67 5.08 4.75 6.8715 2.42 5.08 1.67 6.5 5.4 8.6120 2.42 6.5 2.42 8 6 10.1

Table 2Values of� andn for PG correlation, Eq. (2)

Impeller combination PG correlation, Eq. (2)

� n Std. dev. (%)

DT (Michel and Miller, 1962) 0.812 0.45 —2 PBTD–DT 1.501 0.425 93 PBTD 1.52 0.427 4

values of ‘�’ obtained for both of the impeller combinationsare approximately same(�1.52 ± 0.05) but significantlyhigher (nearly two times) than the value of ‘�’ reported byMichel and Miller (1962), i.e., 0.812. This also shows thatthe lowermost impeller follows the classical gassed impellerflow regimes and gets affected by the gas even in multi-impeller system as if it was the only impeller present in thesystem. The variation in the value of ‘�’ shows that ‘�’ in-creases essentially due to an additive effect (addition of theindividual impeller power number) of the upper impellers,but remains approximately constant irrespective of the im-peller combination indicating the relative insensitivity of theupper impellers to the gassed conditions.

3.3. Fractional gas hold-up

It can be seen fromFig. 4 that for any value ofVG,at equivalentPG/V , both impeller combinations gives ap-proximately the same (within±10%) fractional gas hold-up. Our gas hold-up data for the DE–L regime is comparedwith the correlation reported byMoucha et al. (2003)asshown in Fig. 5. It can be observed fromFig. 5 that for2 PBTD–DT, deviation in the gas hold-up values observedby Moucha et al. (2003)and our experimental gas hold-up values is large (Moucha et al. (2003)reported 40–200%higher �G values), while for 3 PBTD, it is low (anywherebetween 10% and 90%). This can be attributed to the factthat tap water has been used as the experimental liquid inthe present work while 0.5 M Na2SO4 aqueous solution wasused byMoucha et al. (2003). The effect of the solutes onthe fractional gas hold-up is mainly through the property ofthe coalescence and the presence of coalescence inhibitingsolutes results into an increase in the fractional gas hold-up. This is in accordance with the results ofPinelli et al.(1994)who have reported that for triple impeller configura-tions containing all DTs, the coalescence inhibiting solutionsof sodium sulphate and polyvinyl-pyrrolidone (PVP) exhibit


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0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 2

log (PG/V, W/m3)

εG

2 PBTD-DT

3 PBTD

VG =

20 mm/s

VG = 15 mm/s

VG =

10 mm/s

VG = 5 mm/s

1 3

Fig. 4. Effect of PG/V on �G with VG as a parameter (emptypoints= DI– F regime; shadowed empty points= DE– F regime; filledpoints= DE– L regime).

0

0.04

0.08

0.12

0.16

0 0.04 0.08 0.12 0.16Experimental εG

Pre

dict

ed εG

2PBTD-DT and

3PBTD, Moucha et al. (2003)

2PBTD-DT and

3PBTD, Eq. 3

Fig. 5. The comparison of experimental�G in the DE–L regime with theliterature data.

80–150% and 130–300% higher hold-up, respectively, thanwater. Nevertheless, near parallel lines to the 45◦ line indi-cate that the type of the parameter dependence proposed byMoucha et al. (2003)is still valid for the impeller combina-tions explored in this work.Rushton and Bimbinet (1968)had correlated fractional gas hold-up as a function of thetotal power consumption per unit volume(Ptot/V ) and thesuperficial gas velocity (VG) with exponent overPtot/V as0.37 and exponent overVG as 0.61 for disc turbine. Since

correlating gas hold-up with impeller power consumptionper unit volume(PG/V ) instead ofPtot/V gave better datafitting in this work, fractional gas hold-up was correlated asa function ofPG/V andVG using the following type of anempirical equation:

�G = A

(PG

V

)BV CG . (3)

Values of constantsA,B,C obtained by the regression ofthe experimental data in the DE–L regime for both of theimpeller combinations are given in theTable 3along withthe values ofA,B,C given byMoucha et al. (2003)whoreported correlation for�G in similar form as that of Eq.(3). It can be seen fromTable 3that values of the constantsA,B,C for 2 PBTD–DT are higher than that for 3 PBTD.It can be also seen fromTable 3that for both of the impellercombinations, the value ofB (exponent overPG/V ) reportedby Moucha et al. (2003)is higher than that reported here;while the value ofC (exponent overVG) reported byMouchaet al. (2003)is lower than that obtained in this work. Thiscould be also attributed to the difference in the type of thegas sparger used in this work.

3.4. Mixing time studies

3.4.1. Effect of impeller rotational speedFig. 6 shows a typical variation in the mixing time for 2

PBTD–DT with impeller speed at aVG of 10 mm/s. Similartrend was observed for all values ofVG for both impellercombinations (2PBTD–DT and 3 PBTD). It can be seenfrom Fig. 6 that lowest values of the mixing time (whichare changing marginally with an increase in the impellerspeed) are observed in the DI–F regime. This is due to thefact that the liquid mixing is controlled by the liquid flowinduced by the gas bubbles (Fig. 3A). When impeller speedreaches just beyondNU , the liquid flow generated by themiddle impeller, PBTD in the vertically downward directionincreases and becomes comparable to the air-induced liquidflow in the vertically upward direction. Due to these equaland opposite flows, local turbulence is generated. Since en-ergy gets dissipated in this local turbulence, less energy isavailable towards the overall liquid circulation and convec-tive mixing and the mixing time increases due to the transi-tion from DI to DE regime for the upper impellers as seen inFig. 6. The role of the convective and turbulent mixing hasbeen discussed byPatwardhan and Gaikwad (2003)and thisobservation is consistent with their conclusion. If the im-peller speed is further increased to reach the DE–F regime,the middle impeller starts diverting gas bubbles in the radi-ally outwards and/or the downward direction (referFig. 3B).These gas bubbles rise near the wall region and continue totravel along the wall region due to the uppermost impeller.In the DE–F regime, in the upper compartment of the ves-sel, liquid flow induced by the motion of the gas bubblesis in the vertically upward direction in the wall region and


Table 3Values ofA, B andC for gas hold-up correlation, Eq. (3) andkLa correlation, Eq. (8)

Impeller combination Gas hold-up correlation, Eq. (3) kLa correlation, Eq. (8)

A B C Std. dev. (%) A B C Std. dev. (%)

2 PBTD–DT 1.544 0.263 1.156 7 0.0191 0.57 0.7 6.53 PBTD 1.504 0.2 1.079 6 0.0057 0.701 0.59 5

Moucha et al. (2003)2 PBTDT–DT 0.101 0.518 0.707 6.2 9.577e−4 1.138 0.462 11.73 PBTD 0.347 0.288 0.795 3.7 1.133e−3 1.154 0.508 8.6

in the vertically downward direction in the central region(Fig. 3B). This vertically downward liquid flow in the centralregion gets supplementary action of the liquid flow generatedby the PBTDs in the downwards direction and the overallliquid circulation flow rate in the upper compartment of thevessel increases improving the interaction between the upperand lower compartments of the vessel and hence the mixingtime decreases with an increase in the impeller speed in theDE–F regime as can be seen in theFig. 6. If the impellerspeed is further increased, aboveNF , transition from flood-ing to loading regime occurs for the lowermost impeller.In this DE–L regime, each impeller is having its own flowpattern, i.e., it forms a circulation cell around itself (referFig. 3C). In the DE–L regime, mixing performance of theentire vessel is dominated by the exchange flow rate betweenthe adjacent circulation cells (compartments) instead of theoverall circulation flow rate generated by each impeller andhence the mixing time increases sharply (referFig. 6). Ifimpeller speed is further increased in the DE–L regime, ex-change flow rate between circulation cells further increasesand the mixing time decreases again (referFig. 6). Abrardiet al. (1990)have reported similar observation (decreasingmixing time with an increasingN) in the DE–L regime fora dual impeller system.

3.4.2. Effect of impeller rotational speed and gassuperficial velocity

Fig. 7 shows that for both of the impeller combinations,in the DI–F and DE–F regimes, mixing time decreases withan increase inVG at any impeller speed, because the liquidflow induced by the gas bubbles obviously increases withan increase inVG and hence improves the mixing; while inthe DE–L regime, ifVG is increased at a constantN, mix-ing time increases because increase inVG at constantN de-creases the impeller power consumption reducing the liquidcirculation velocity generated by impeller and hence the ex-change flow rate between adjacent circulation cells.Panditand Joshi (1983)have reported similar behavior for a sin-gle impeller system.Pandit and Joshi (1983)have assumedtwo different regimes separated by a critical impeller speedfor gas-phase dispersion(NCD) for a specific gas flow rate(QG) and have reported that the mixing time decreases withan increase in theQG at any impeller speed which is less

0

10

20

30

40

50

60

0 2 4 6 8Impeller speed, N, rps

Mix

ing

time,

sec

DE-L

DE-FDI -F

Transition from DE-F

to DE-L regime

Transition from DI-F

to DE-F regime

NUNF

Fig. 6. Effect of Impeller speed on mixing time, for 2 PBTD–DT,VG = 10 mm/s, tracer density= 1054 kg/m3, Vt /Vb = 0.0025 (emptypoints= DI– F regime; shadowed empty points= DE– F regime; filledpoints= DE– L regime).

thanNCD and the mixing time increases with an increase intheQG at any impeller speed which is greater thanNCD.

Fig. 8 shows that at same values ofPtot/V , mixing timefor 3 PBTD is always less than that for 2 PBTD–DT. Thiscould be because of better axial dispersion efficiency of theaxial impellers as compared to that of radial one. This alsoconfirms the conclusion from the past literature (Prajitno etal., 1998; Vrabel et al., 2000; Moucha et al., 2003) that theimpeller combinations having axial liquid flow give bettermixing efficiency as compared to others at the same powerconsumption per unit volume in the case of multiple impellersystem.

3.4.3. Effect of tracer propertiesIt has been observed that in the DE–L flow regime, for

low tracer volume (i.e.,Vt/Vb = 0.0025),NTmix marginallychanges (Fig. 9A) and for higher tracer volume (i.e.,Vt/Vb=0.0175),NTmix increases (Fig. 9B) significantly, with anincrease in��/�LG or tracer density at a constantNandVG.This could be attributed to the reason that though increasein the��/�LG is significant due to an increase in the tracerdensity and decrease in the bulk density from�L to �LG,increase in the buoyancy force exerted on the tracer packet


ARTICLE IN PRESS

0

20

40

60

80

100

120

0 2 4 6 8

05101520

VG, mm/s

VG

VG

0

20

40

60

80

100

120

0 2 4 6 8

05101520

VG, mm/s

VG

VG

Impeller speed, rps

Mix

ing

time,

s

(a) (b)

Fig. 7. Mixing time vs.N, with VG as a parameter, tracer density= 1054 kg/m3, Vt /Vb = 0.0025 (empty points= DI– F regime; shadowed emptypoints= DE– F regime; filled points= DE– L regime) (a) 2 PBTD–DT and (b) 3 PBTD.

20

25

30

35

40

45

50

55

60

0 200 400 600

Ptot/V, W/m3

Mix

ing

time,

s

3 PBTD

2 PBTD-DT

Fig. 8. Mixing time vs.Ptot/V with impeller combination as parameter,VG = 10 mm/s, tracer density= 1054 kg/m3, Vt /Vb = 0.0025 (emptypoints= DI– F and DE–F regime; filled points= DE– L regime).

(FB = ��Vtg) is significant, at higherVt than that at lowerVt . It can be seen from theFig. 9C and D thatNTmix in-creases with an increase in the tracer volume (Vt ) for all thevalues of tracer densities covered in this work. This couldbe attributed to the fact that the lower volume of the tracerpulse added loses its identity very soon against the liquidturbulence generated by the impeller, while higher volumeof the tracer pulse retains its identity for some more timedue to relatively large size and lower rate of turbulent ero-sion of its identity. Also for higher tracer volumes, gravitycontrolled liquid flow exists for unaerated case (Kasat andPandit, 2004) that results into lower mixing time, but in theaerated case, gassing effect opposes gravity controlled liq-uid flow significantly and results into higher mixing time.

Similar effect of tracer properties was also observed for DI–Fand DE–F regimes (Fig. 10). It can be also observed thatthe extent of increase inNTmix, with an increase in��/�LGat higherVt/Vb (Fig. 9B) and with an increase inVt/Vb atany value of the tracer density (Fig. 9C and D), is lower atlow impeller speed and higher at high impeller speeds in theDE–L regime at constantVG. Fig. 10depicts that the effectof tracer properties on the mixing time is more pronouncedat higherVG in the DI–F and DE–F regimes. This is be-cause at higher speeds (for a constant value ofVG) in theDE–L regime and at higherVG (for a constant value ofN)in the DI–F and DE–F regime, high values of gas hold-upexists. This decreases average bulk density (�LG), increas-ing the buoyancy force exerted on the tracer packet(FB)

significantly at higherVt and resulting in an increase in themixing time.

3.4.4. Richardson numberThe Richardson number is the ratio of the static head of

liquid to the dynamic head of the flowing liquid generatedby the impeller action. Since the buoyancy forces exertedon the tracer packet also depends on the density and thevolume of the tracer packet.Pandit et al. (2000)have mul-tiplied Richardson number (Ri) by Vt/Vb and modified theconventional definition of it (which is valid in the range ofVt/Vb from 0.0025 to 0.08), as follows:

Modified Richardson number(Rio)= ��gHD�LGN2D2

Vt

Vb. (4)

It can be observed from theFig. 11 for DE–L regimethat they-intercepts of the lines,NTmix vs.Rio, for differentimpeller speeds atVG = 5 mm/s are approximately same(average= 241.1); while they-intercept increases with anincrease inVG (for VG=20 mm/s,y-intercept is 314.2) andthe slope of the lines ofNTmix againstRio at low N like3.75 rps is low (224) while at highN like 8 rps it is muchhigher (4212). The increase in the slope with an increase inthe impeller speed at constantVG and the increase in the


100

150

200

250

300

350

0 0.1 0.2 0.3

5-3.75 5-5.085-6.5 5-8.015- 6.5 15- 8.0

VG, mm/s-N, rps

(A)

100

150

200

250

300

350

400

450

500

0 0.1 0.2 0.3

5-3.75 5-5.085-6.5 5-8.015- 6.5 15- 8.0

VG, mm/s-N, rps

(B)

0

50

100

150

200

250

300

350

400

0 0.005 0.01 0.015 0.02

10- 5.0810- 6.510- 8.0

VG, mm/s-N, rps

(C)

0

50

100

150

200

250

300

350

400

450

500

0 0.005 0.01 0.015 0.02

10- 5.0810- 6.510- 8.0

VG, mm/s-N, rps

(D)

∆ρ/ρLG

Vt/Vb

N×

Tm

ix

Fig. 9. Effect of the tracer properties onNTmix in the DE–L regime for 2 PBTD–DT: (A)Vt /Vb = 0.0025, (B) Vt /Vb = 0.0175, (C) tracerdensity= 1054 kg/m3 and (D) tracer density= 1178 kg/m3.

y-intercept with an increase in theVG are probably due to thefact that due to the better distribution of the gas, the gassingeffect needs to be overcome to bring the tracer down firstafter its addition at the top (relative increase in the��/�LGvalue) and then mix with the liquid bulk. This gassing effectis high when high gas hold-up exists in the vessel, i.e., lowQG and highN or highQG and lowN in the DE–L regime.Another reason that can be put forward to explain this is that,at low impeller speeds in the DE–L regime, existence of thegravity controlled regime improves the mixing performanceby bringing the tracer down in the impeller zone quickly andlow dependency on theRio was thus found; while at highimpeller speeds in the DE–L regime, existence of the stirrercontrolled regime results in the delayed entrainment of theadded tracer in the impeller stream giving high dependencyof the mixing time on theRio which is an effect undesirablein the normal operation, but has been observed in this study,mainly attributed to the fractional gas hold-up values.

Fig. 12A, which is constructed for 2 PBTD–DT in theDE–L regime, indicates that the slopes of the lines (NTmixvs.Rio) for a typicalN at different values ofVG are approx-imately the same (atN=8 rps, slopes are 4212, 3524, 2239,3309 forVG = 5,10,15,20 mm/s respectively.).Fig. 12B,which is constructed for 3 PBTD in the DE–L regime, also

shows similar behavior. This indicates that the mixing timemainly depends upon the inertial forces generated by theimpeller in the DE–L regime, as the role of the gas spargingis much lower but the value of the fractional gas hold-upcontributes significantly. This observation is consistent withthe observed variation in the mixing time.

For unaerated single impeller system,Ahmad et al. (1985)have reported thatNTmix is proportional toRi0.8. Pandit et al.(2000)have reported existence of criticalRio for unaeratedsingle impeller system.Pandit et al. (2000)also reported thatat lowRio (i.e., less than criticalRio), NTmix is independentof Rio and at higherRio (i.e., higher than criticalRio), itis proportional toRino where the value ofn is 0.58 for DTand 0.76 for PBTD. It can be observed fromFig. 12 thatat low values ofRio (which exists forVt/Vb = 0.0025),the values ofNTmix are approximately the same (nearly thesame intercept), regardless ofN (in the DE–L regime) atconstantVG. This is because though fractional gas hold-upincreases with an increase inN, due to lowVt/Vb increasein the FB is not significant. At high values ofRio (whichexists forVt/Vb=0.01 and 0.0175), higher values ofNTmixhas been observed at higher speeds (Fig. 12). This could beattributed to the higher values of fractional gas hold-up andhigher tracer volume as discussed earlier in this section.


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0

10

20

30

40

50

0 0.1 0.2 0.3

5-0.0 5-1.675-2.42 15- 015- 1.67 15- 3.7515- 5.08

VG, mm/s-N, rps

(A)

0

10

20

30

40

50

60

70

80

0 0.1 0.2 0.3

5-0.0 5-1.675-2.42 15- 015- 1.67 15- 3.7515- 5.08

VG, mm/s-N, rps

(B)

10

15

20

25

30

35

40

45

50

0 0.005 0.01 0.015 0.02

10- 0.010- 1.6710- 2.4210- 3.75

VG, mm/s-N, rps

(C)

0

10

20

30

40

50

60

0 0.005 0.01 0.015 0.02

10- 0.010- 1.6710- 2.4210- 3.75

VG, mm/s-N, rps

(D)

∆ρ/ρLG

Vt/Vb

Mix

ing

time,

s

Fig. 10. Effect of tracer properties onTmix in flooding regime for 2 PBTD–DT: (A)Vt /Vb=0.0025, (B)Vt /Vb=0.0175, (C) tracer density=1054 kg/m3

and (D) tracer density= 1178 kg/m3.

3.4.5. Development of correlationSince as discussed earlier for the plots ofNTmix vs.Rio,

y-intercept is a function ofVG while the slope is mainlya function of impeller speed, it was decided to correlateNTmix in the similar format. The correlation ofNTmix con-tains two terms; first term being dimensional and a functionof VG, while second term being dimensionless, with inclu-sion of dimensionless numbers. The following correlationhas been developed to predictNTmix in the DE–L regimefor 2 PBTD–DT,

NTmix = 453.7V 0.127G + 583.95

(HD�GT

)−0.496

×(PG

PO

)−1.297

(N2D/g)1.756(Rio)0.711. (5)

Eq. (5) has correlation coefficient= 0.89 and std. dev.=6.85%, where all the variables are in MKS units. Correlationfor theNTmix in the DE–L regime for 3 PBTD having similarform as that of Eq. (5) is as follows:

NTmix = 333.82V 0.184G + 553.63

(HD�GT

)−0.286

×(PG

PO

)−0.39

(N2D/g)0.858(Rio)0.294. (6)

0

100

200

300

400

500

600

0 0.05 0.1 0.15 0.2 0.25Modified Richardson number, Rio

N×

Tm

ix

5-3.75 5-5.08 5-6.55-8.0 20-8

VG, mm/s - N, rps

y = 3308.7x + 314.2

y = 4211.9x + 242.4

y = 1973.6x + 244

y = 900.4x + 231.6

y = 224.2x + 246.5

Fig. 11. Variation in the slope of curveNTmix vs. Rio, with VG–N as aparameter in the DE–L regime, for 2 PBTD–DT.

Eq. (6) has correlation coefficient=0.9 and std. dev.=6.7%,where all the variables are in MKS units. Parity plots forcorrelations, i.e., Eqs. (5) and (6) are shown inFig. 13A andB, respectively, and it can be seen that the agreement is rea-sonable. From the Eq. (5) for 2 PBTD–DT and Eq. (6) for3 PBTD, it can be seen that proportionality constant in the


0

100

200

300

400

500

600

0 0.1 0.2

5- 3.75 5- 5.08 5- 6.55- 8.0 10- 5.08 10- 6.510- 8.0 15- 6.5 15- 8.020- 8.0

VG, mm/s - N, rps

(A)

0

100

200

300

400

500

600

700

0 0.05 0.1 0.15

5- 5.08 5- 6.55- 8.0 10- 6.510- 8.0 15- 8.0

VG, mm/s - N, rps

(B)

Modified Richardson number, Rio

N×

Tm

ix

Fig. 12.NTmix vs. Rio, in the DE–L regime: (A) 2 PBTD–DT and (B) 3 PBTD.

0

100

200

300

400

500

600

0 100 200 300 400 500 600

(A)

0

100

200

300

400

500

600

0 100 200 300 400 500 600

(B)

Experimental N×Tmix

Pre

dict

ed N

×T m

ix

Fig. 13. Comparison of predictedNTmix with experimentalNTmix, in the DE–L regime: (A) using Eq. (5) for 2 PBTD–DT and (B) using Eq. (6) for 3PBTD.

first term for 2 PBTD–DT (453.7) is higher than that for 3PBTD (333.82) and proportionality constant in the secondterm for 2 PBTD–DT (583.95) is also higher than that for 3PBTD (553.63), which indicates that the mixing efficiencyof 3 PBTD is better than that of 2PBTD–DT. Exponent overVG in the first term for 2 PBTD–DT (0.127) is lower than thatfor 3 PBTD (0.184) indicating that effect ofVG over the mix-ing time is more pronounced for 3 PBTD as compared to 2PBTD–DT. Exponent over(HD�G/T ) for 3 PBTD (−0.286)is higher than that for 2 PBTD–DT (−0.496); which indi-cates that the gassing effect is more pronounced for 3 PBTDthan 2 PBTD–DT which also results into a relatively differ-ent bubble size distribution (and hence different variation init’s rise velocity) and is consistent with the observed varia-tion in thekLa as discussed later. Exponent over(N2D/g)for 2 PBTD–DT (1.756) is higher than that for 3 PBTD(0.858). This again indicates that for 2 PBTD–DT, mixingtime is a strong function ofN as compared to 3 PBTD. Theexponent overRio for 2 PBTD–DT (0.711) is higher thanthat for 3 PBTD (0.294), indicating that the effect of tracerproperties onNTmix is more pronounced for 2 PBTD–DTthan that for 3 PBTD, i.e., 2 PBTD–DT is more suscepti-

ble to the variation in the tracer density andVt/Vb than 3PBTD. This could be attributed to the fact that at equiva-lent values ofPtot/V , due to lower value of impeller speedfor 2 PBTD–DT, it produces lower hydrostatic head (whichis proportional to�N2D2) than that produced by 3 PBTDwhich at equivalent power values operate at higher rotationalspeeds and also at same values ofN andVG, due to highervalues of�G and hence lower�LG, though 2 PBTD–DT isrequired to produce higher hydrostatic head as compared to3 PBTD. This also indicates that though 2 PBTD–DT drawshigher power, it produces lower hydrostatic head as com-pared to that produced by 3 PBTD and hence the depen-dency as observed on theRio (in terms of it’s exponent) iscontrary to the expection (based on the power dissipation).

3.5. Compartment model

A single circulation cell (or compartment) model is shownin theFig. 14A for DI–F regime based upon the visual obser-vation (Fig. 3A and D).Joshi et al. (1982)have discussed atheoretical procedure for the calculation of the mixing time,which is based on the knowledge of the circulation velocity


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QEQE

QEQE

D

QE

(A) (B) (C)

Fig. 14. Physical representation of the compartmental model for flowregimes: (A) DI–F, (B) DE–F and (C) DE–L.

(VC) and the length the flow path (L). They assumed that themixing time is five times the circulation time(=L/VC). Lis the length of longest loop. Average liquid circulation ve-locity (VC), which is responsible for the overall mixing inthe DI–F regime, is calculated using the above definition ofthe mixing time and experimentally measured mixing times.Visual observation (Fig. 3B and E) depicts the presence oftwo compartments in the vessel for DE–F regime. Locationof an imaginary boundary (indicated by dotted line in theFig. 14B) between the two compartments vary from distanceof H/2 (whenN is just aboveNU ) to H/3 (whenN is justbelowNF ) from the bottom of the vessel. Liquid exchangeflow rate between the adjacent compartments was estimatedby least-square fitting the conductivity responses utilizingthe model of cascade of two perfectly mixed compartmentsfor DE–F regime. Model of three perfectly mixed circulationcells with exchange flow rateQE between adjacent cells forDE–L regime is shown in theFig. 14C. The numbers of com-partments are taken to be equal to the number of impellers;since in the present work the impeller spacing is equal to3D(=T ) and for such a spacing it has been proved previ-ously (Hudcova et al., 1989; Mishra and Joshi, 1994) thatthe impellers are hydro-dynamically independent of eachother. All the compartments have the same volume (Vcell).Exchange flow rate (QE) was estimated by least-square fit-ting the conductivity responses using the triple compartmentmodel for DE–L regime.

It can be observed fromFig. 15 that the exchange flowrate(QE) increases with an increase in the impeller speed(QE ∝ N�) at a constantVG in the DE–L regime. ExponentoverN is approximately equal to unity (i.e., 1.02 and 0.95,for VG = 5 and 10 mm/s, respectively), indicating thatQEis some constant fraction of the impeller discharge flow rate(which is directly proportional toN). Similar behavior was

0

0.5

1

1.5

2

2.5

3

0 3 6 9N, rps

QE, 1

0-3 m

3 /s

0 5

10 15

20

VG, mm/s

Fig. 15. Exchange flow rate vs.N in the DE–L regime, for 2 PBTD–DT,tracer density= 1054 kg/m3, Vt /Vb = 0.0025.

observed for other sets of the tracer density andVt/Vb inthe DE–L regime. Another observation which can be madefrom Fig. 15 that contrary to the expectation of increasedexchange flow rate due to the vertical motion of the bubblesthrough all the cells sequentially, the exchange flow rateswere found to decrease with an increase in the gas flow rateat any specific impeller rotational speed in the DE–L regime.This also suggests that the decrease in the impeller powerdissipation rate due to the gas sparging and its net effect onthe reduction in the overall circulation velocities is far moresignificant as compared to the additional liquid circulationgenerated by the gas sparging. The observed increase in theoverall mixing time is also consistent with the above argu-ment and the observation.Kasat and Pandit (2004)have re-ported that for unaerated multiple impeller system, exchangeflow rate increases with an increase in the impeller speedfor both of the impeller combinations (2 PBTD–DT and 3PBTD). Similar observation has been made for aerated mul-tiple impeller system in the DE–L regime at a constant gasflow rate. However the exchange flow rate (QE) was foundto decrease with an increase in the gas flow rate (Fig. 15)due to a reduced impeller power as discussed earlier.

Effective liquid velocity (Vl) responsible for the liquidmixing in the vessel is equal to the liquid circulation velocitywhich was calculated using a single circulation cell modelfor DI–F regime, while for DE–F and DE–L regimesVl isequal toQE/(�T 2/4). Vl has been plotted againstPtot/V

in Fig. 16 for both of the impeller combinations. It can beseen fromFig. 16 that Vl in the DI–F regime is high ascompared toVl in the DE–F and DE–L regimes. It has beenalso observed that at a constantVG in the DI–F regime, thevalues ofVl are approximately same (Fig. 16) and are nearlyequal (within±5%) to the liquid circulation velocity in thecase of only sparging (i.e.,VCS=1.31{gT (VG−�GVb∞)}1/3,


-2.5

-2

-1.5

-1

-0.5

0

0 200 400 600 800

0 510 1520

VG, mm/s

(A)

-2.5

-2

-1.5

-1

-0.5

0

0 100 200 300 400

0 510 1520

VG, mm/s

(B)

Ptot/V, W/m3

log

(Vl,

m/s

)

Fig. 16. Effect ofPtot/V on effective liquid velocity responsible for the liquid mixing(Vl): (A) 2 PBTD–DT and (B) 3 PBTD.

Table 4Average values ofQE/QCG w.r.t. tracer properties

Vt /Vb QE/QCG

2 PBTD–DT 3 PBTDTracer density (kg/m3) Tracer density (kg/m3)

1054 1114 1178 1054 1114 1178

0.0025 0.293 0.308 0.298 0.333 0.336 0.3410.01 0.277 0.257 0.244 0.281 0.242 0.2330.0175 0.26 0.235 0.21 0.241 0.233 0.218

Joshi, 1980), which is calculated usingVb∞ = 0.3 m/s, i.e.,system essentially behaves like a bubble column in DI–Fregime.

The flow pattern generated by the impeller is characterizedby a circulation loop, involving a liquid circulation flow rate(QCO = NCOND

3) in un-gassed condition. For DT withD = T/3, NCO�2NQ�1.5 (Mahouast et al., 1991); whilefor PBTD,NCO�NQ�0.8. NCO andNQ are circulationnumber and flow number, respectively. The liquid circulationflow rate under gassed conditions can be easily obtained by

QCG =QCO(PG/PO)1/3. (7)

Average values of the ratio,QE/QCG, for all the sets of thetracer density andVt/Vb are given in theTable 4. It was ob-served that for 2 PBTD–DT, average values of theQE/QCGare 0.30, 0.259 and 0.235 and for 3 PBTD, they are 0.337,0.252 and 0.23, for the values ofVt/Vb; 0.0025, 0.01 and0.0175, respectively. It can be seen from theTable 4thatfor both of the impeller combinations, forVt/Vb = 0.0025,the ratio,QE/QCG, is approximately constant irrespectiveof the change in the tracer density; while forVt/Vb = 0.01and 0.0175, the ratio decreases with an increase in the tracerdensity. These results are consistent with the results ob-tained from the circulation cell model (Joshi and Sharma,1979) used to explain the behavior of the gas–liquid bub-ble column (similar to the compartment model) that theinter-cell exchange velocity is 0.31–0.33 times the average

circulation velocity.Kasat and Pandit (2004)have reportedthatQE/QCO varies from 0.34 to 0.44 for unaerated systemfor the same impeller combinations.

Vasconcelos et al. (1995)reported thatvax is a scale inde-pendent, characteristic velocity of liquid flow induced by airhaving average value of 0.066 m/s.Vasconcelos et al. (1998)have confirmed the scale independency ofvax with an in-variant value of 0.07 m/s for gassed tank stirred by multi-ple Rushton turbines.Vrabel et al. (1999)also reported thatthe value ofvax is 0.054 m/s. By using the methodology ofVasconcelos et al. (1995), value ofvax has been calculatedin the present work. The values ofvax for 2 PBTD–DT and3 PBTD were found to be 0.032 and 0.015 m/s, respectively.These values are lesser (but of the same order of magni-tude) as compared to the value ofvax (0.066 m/s) reportedby Vasconcelos et al. (1995)for impeller combination com-prising Rushton turbines.

3.6. Mass transfer studies

Fig. 17 depicts that at same value ofPtot/V , both theimpeller combinations gives approximately same (within±7%) values of thekLa (MTC) in all regimes. This is in ac-cordance with the conclusion ofMoucha et al. (2003)whostudied the effect of the impeller configuration onkLa at con-stantPtot/V and reported that at lowerPtot/V (300W/m3)the kLa values are approximately independent of impeller


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0

0.005

0.01

0.015

0.02

0.025

0.03

0 200 400 600

Ptot /V, W/m3

k La,

s-1

2 PBTD-DT

3 PBTD

VG = 10 mm/s

VG = 5 mm/s

Fig. 17. kLa vs. Ptot/V , for both of the impeller combinations (emptypoints= DI– F and DE–F regime; filled points= DE– L regime).

configuration, while at higherPtot/V (800W/m3), theimpeller configurations with high power number providesignificantly higher mass transfer coefficients.Linek et al.(1987)have shownkLa to be independent of reactor size andonly dependent upon power consumption per unit volumeandVG.

Mass transfer coefficient (kLa) is correlated as a functionof total power consumption per unit volume(Ptot/V ) andgas superficial velocity (VG) by the following equation:

kLa = A

(Ptot

V

)BV CG . (8)

The values ofA,B,C were obtained by regression of theexperimental data in the DE–L regime for both of the im-peller combinations and are given inTable 3along with thevalues ofA,B,C reported byMoucha et al. (2003), whoproposed correlation forkLa in the similar form. Our ex-perimentalkLa data are compared with the correlation ofMoucha et al. (2003)in theFig. 18. Values predicted by thecorrelation ofMoucha et al. (2003)are much higher as com-pared to our experimental data. This can be explained onthe basis of the reason thatMoucha et al. (2003)have used0.5 M Na2SO4 aqueous solution as an experimental fluid,i.e., the presence of coalescence inhibiting solutes increasesthe fractional gas hold-up (as explained earlier) and subse-quently the MTC. It can be also seen fromTable 3that expo-nent overPtot/V reported byMoucha et al. (2003)is higherthan that observed in the present work; while exponent overVG reported byMoucha et al. (2003)is lower than that inthe present work. These results are in accordance with thefindings ofLinek et al. (1987)who reported that exponentover power dissipation per unit liquid volume increases with

0

0.04

0.08

0.12

0.16

0 0.04 0.08 0.12 0.16

Experimental kLa, s-1

Pre

dic

ted

k La

, s-1

□ 2PBTD-DT and

◊ 3PBTD, Eq. 8

� 2PBTD-DT and

♦ 3PBTD, Moucha et al. (2003)

Fig. 18. The comparison of experimentalkLa in the DE–L regime withliterature data.

an increase in the concentration of coalescence inhibitingsolutes in the liquid.

4. Conclusions

Three hydrodynamic flow regimes have been identifiedfor the vessel having multiple impeller gas–liquid system,namely; DI–F, DE–F and DE–L. DI–F means upper im-pellers are in the ineffective dispersion (DI) regime and low-ermost impeller is in the flooding (F) regime; while DE–Lmeans upper impellers are in the effective dispersion (DE)regime and the lowermost impeller is in the loading (L)regime. Similarly DE–F means upper impellers are in theeffective dispersion (DE) regime and the lowermost im-peller is in the flooding (F) regime. Lowest values of mix-ing times were observed at zero and low impeller speeds(DI–F regime) with only gas sparging. If the impeller speedis increased at a constantVG, aboveNU mixing time in-creases due to transition from DI–F to DE–F regime andthen decreases in the DE–F regime. With further increasein the impeller speed, aboveNF , mixing time increases dueto transition from DE–F to DE–L regime and decreases inthe DE–L regime with an increase in impeller speed. In theDI–F and DE–F regimes, mixing time decreases while it in-creases with an increase in the gas flow rate in the DE–Lregime. At equivalent values ofPtot/V , mixing efficiencyof 3 PBTD was observed to be better than 2 PBTD–DT,whereas comparable values ofkLa were observed for bothof the impeller combinations. At low impeller speed in theDE–L regime, low dependency ofRio is observed on the di-mensionless mixing time because mixing phenomenon getsa supplement from the buoyancy generated liquid flow by


naturally distributing the tracer packet. Whereas at higherimpeller speed in the DE–L regime, high dependency onRiohas been observed probably due to the fact that gassing ef-fect needs to be overcome to bring tracer down (when addedat the top). Mixing under these conditions is totally gov-erned by the stirrer generated flow and the power drawn bythese impellers in the presence of gas.

Notation

C concentration, mg/lD impeller diameter, mFB buoyancy forces exerted on the tracer packet

(��Vtg), Ng gravitational constant, m/s2

HD dispersion height in the vessel, mIR, IY , IB electric current flowing throughR, Y,B

phases, respectively, AkLa volumetric mass transfer coefficient,s−1

nb number of bladesN impeller rotational speed, rpsNF impeller speed required for transition from F

to L regime, rpsNU impeller speed required for transition from

DI to DE regime, rpsPG gassed impeller power consumption, WPO unaerated impeller power consumption, WPtot total power consumption

(PG + gassed power(=QGHD�LGg)), WQG gas flow rate, m3/s

Ri Richardson number(

��gHD�LGN2D2

)Rio modified Richardson number(RiV t/Vb)T tank diameter, mTmix mixing time, sV, Vb bulk volume, m3

VG superficial gas velocity, m/sVl effective liquid velocity responsible for liquid

mixing, m/sVR, VY , VB voltage across phasesR, Y,B, respectively,

VVt volume of the tracer added, m3

Greek letters

�� difference between the densities of tracerfluid and gas–liquid dispersion

�L density of the liquid, kg/m3

�LG density of the gas–liquid dispersion, kg/m3

Acknowledgements

Authors would like to thank to University Grant commis-sion for providing research fellowship to SDS.

References

Abardi, V., Rovero, G., Sicardi, S., Baldi, G., Conti, R., 1988. Spargedvessels agitated by multiple turbines. Proceedings of the Sixth EuropeanConference on Mixing, pp. 329–336.

Abrardi, V., Rovero, G., Sicardi, S., Baldi, G., Conti, R., 1990.Hydrodynamics of gas–liquid dispersion with a multi impeller system.Transactions of the Institution of Chemical Engineers 68 (A), 516–522.

Ahmad, S.W., Latto, B., Baird, M.H.I., 1985. Mixing of stratified liquids.Chemical Engineering Research Design 63, 157–167.

Alves, S.S., Vasconcelos, J.M.T., Barata, J., 1997. Alternative compartmentmodels of mixing in tall tanks agitated by multi-Rushton turbines.Transactions of the Institution of Chemical Engineers 75 (A), 334–338.

Bouaifi, M., Roustan, M., Djebbar, R., 1997. Hydrodynamics of multi-stage agitated gas–liquid reactors. Proceedings of the Ninth EuropeanConference on Mixing, pp. 137–144.

Bouwmans, I., Bakker, A., Van den Akker, H.E.A., 1997. Blending liquidsof differing viscosities and densities in stirred tank vessels. Transactionsof the Institution of Chemical Engineers 75 (A), 777–783.

Bujalski, W., Pinelli, D., Nienow, A.W., Magelli, F., 2001. Comparisonof experimental techniques for the measurement of mixing time ingas–liquid system. Chemical Engineering Technology 24 (9), 919–923.

Burmester, S.S.H., Rielly, C.D., Edwards, M.F., 1991. The mixingof miscible liquids with large difference in density and viscosity.Proceedings of the Seventh European Conference on Mixing, pp. 9–16.

Gogate, P.R., Pandit, A.B., 1999. Mixing of miscible liquids with densitydifference: effect of volume and density of the tracer fluid. CanadianJournal of Chemical Engineering 77, 988–996.

Gogate, P.R., Beenackers, A., Pandit, A.B., 2000. Multiple impellersystems with a special emphasis on bioreactors: a critical review.Biochemical Engineering Journal 6, 109–144.

Hristov, H., Mann, R., Lossev, V., Vlaev, S.D., Seichter, P., 2001. A 3-Danalysis of gas–liquid mixing, mass transfer and bioreaction in a stirredbio-reactor. Transactions of the Institution of Chemical Engineers 79(C), 232–241.

Hudcova, V., Machon, V., Nienow, K.C.A.M., 1989. Gas–liquid dispersionwith dual Rushton turbine impellers. Biotechnology and Bioengineering34, 617.

Jahoda, M., Machon, V., 1994. Homogenization of liquids in tanks stirredby multiple impellers. Chemical Engineering Technology 17, 95–101.

Joshi, J.B., 1980. Axial mixing in multiphase contactors — A unifiedcorrelation. Transactions of the Institution of Chemical Engineers 58,155–165.

Joshi, J.B., Sharma, M.M., 1979. Some design features of radial bafflesin sectionalized bubble columns. Canadian Journal of ChemicalEngineering 57, 375–377.

Joshi, J.B., Pandit, A.B., Sharma, M.M., 1982. Mechanically agitatedgas–liquid reactors. Chemical Engineering Science 37, 813–844.

Kasat, G.R., Pandit, A.B., 2004. Mixing time studies in multiple impelleragitated reactors. Canadian Journal of Chemical Engineering 82,892–904.

Linek, V., Vacek, V., Benes, P., 1987. A critical review and experimentalverification of correct use of dynamic method for the determinationof oxygen transfer in aerated agitated vessels to water, electrolyticsolutions and viscous liquids. Chemical Engineering Journal 34, 11.

Machon, V., Jahoda, M., 2000. Liquid homogenization in aerated multi-impeller stirred vessel. Chemical Engineering Technology 23 (10), 869–876.

Mahouast, M., Fontaine, P., Mallet, J., 1991. A two-component LDV benchfor automated determination of flowrates and energy transfers generatedby agitators. Proceedings of the Seventh European Conference onMixing, pp. 181–185.

Medek, J., Fort, I., 1997. Dispersion effect of pitched blade impellers.Proceedings of the Ninth European Conference on Mixing, pp.107–114.

Michel, B.J., Miller, S.A., 1962. Power requirements of gas–liquid agitatedsystems. A.I.Ch.E. Journal 8 (2), 262–266.


ARTICLE IN PRESS

Mishra, V.P., Joshi, J.B., 1994. Flow generated by disc turbine. PartIV: multiple impellers. Chemical Engineering Research Design 73,657–668.

Moucha, T., Linek, V., Prokopova, E., 2003. Gas hold-up, mixing timeand gas–liquid mass transfer coefficient of various multiple-impellerconfigurations: rushton turbine, pitched blade and techmix impeller andtheir combinations. Chemical Engineering Science 58, 1839–1846.

Nienow, A., Warmoeskerken, M., Smith, J., Konno, M., 1985. On theflooding loading transitions and the complete dispersion dispersedcondition in aerated vessels agitated by a Rushton turbine. Proceedingsof the Fifth European Conference on Mixing, pp. 143–154.

Nocentini, M., Fajner, D., Pasquali, G., Majeli, F., 1988. A fluid dynamicstudy of gas–liquid, non standard vessel stirred by multiple-impellers.Chemical Engineering Journal 37, 53.

Otomo, N., Bujalski, W., Nienow, A.W., 1995. The application of acompartment model to a vessel stirred with either dual radial or dualaxial flow impellers. The 1995 IChemE Research Event, The Universityof Birmingham, vol. 2, pp. 829–831.

Pandit, A.B., Joshi, J.B., 1983. Mixing in mechanically agitated gas–liquidcontactors, bubble columns and modified bubble columns. ChemicalEngineering Science 38, 1189–1215.

Pandit, A.B., Gogate, P.R., Dindore V.Y., 2000. Effect of tracer properties(volume, density and viscosity) on mixing time in mechanically agitatedcontactors. Proceedings of the 10th European Conference on Mixing,pp. 385–393.

Patwardhan, A.W., Gaikwad, S.G., 2003. Mixing in tanks agitated by jets.Transactions of the Institution of Chemical Engineers 81 (A), 211–220.

Pinelli, D., Nocentini, M., Magelli, F., 1994. Hold-up in low viscositygas–liquid systems stirred with multiple impellers: comparison ofdifferent agitator types and sets. Proceedings of the Eighth EuropeanConference in Mixing, pp. 81–84.

Prajitno, D.H., Mishra, V.P., Takenaka, K., Bujalski, W., Nienow, A.W.,McKeemie, J., 1998. Gas–liquid mixing studies with multiple up- and

down-pumping hydrofoil impellers: power characteristics and mixingtime. Canadian Journal of Chemical Engineering 76, 1056–1068.

Rewatkar, V.B., Joshi, J.B., 1991. Role of sparger design in mechanicallyagitated gas–liquid reactors. Part I: power consumption. ChemicalEngineering and Technology 14, 333–347.

Rielly, C.D., Pandit, A.B., 1988. The mixing of Newtonian liquidswith large density and viscosity differences in mechanically agitatedcontactors. Proceedings of the Sixth European Conference on Mixing,pp. 69–77.

Rushton, J.H., Bimbinet, J., 1968. Holdup and flooding in air liquidmixing. Canadian Journal of Chemical Engineering 46, 16–21.

Smith, J.M., Warmoeskerken, M., Zeef, E., 1987. Flow conditionsin vessels dispersing gases in liquids with multiple impellers.Biotechnology Processes, A.I.Ch.E. Journal 107–115.

Vasconcelos, J.M.T., Alves, S.S., 1995. Mixing in gas–liquid contactorsagitated by multiple turbines in the flooding regime. ChemicalEngineering Science 50, 2355–2357.

Vasconcelos, J.M.T., Alves, S.S., Barata, J.M., 1995. Mixing in gas–liquidcontactors agitated by multiple turbines. Chemical Engineering Science50, 2343.

Vasconcelos, J.M.T., Alves, S.S., Nienow, A.W., Bujalski, W., 1998. Scale-up of mixing in gassed multi-turbine agitated vessels. Canadian Journalof Chemical Engineering 76, 398–404.

Vrabel, P., Van der lans, R., Cui, Y.Q., Luyben, K., 1999. Compartmentalmodel approach: mixing in large scale aerated reactors with multipleimpellers. Transactions of the Institution of Chemical Engineers 77(A), 291–302.

Vrabel, P., Van der lans, R., Luyben, K., Boon, L., Nienow, A.W., 2000.Mixing in large-scale vessels stirred with multiple radial or radial andaxial up-pumping impellers: modeling and measurements. ChemicalEngineering Science 55, 5881–5896.

2006--studies in multiple impeller agitated gas liquid cont actors 2006

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