The effect of aspect ratio in counter-current gas-liquid bubble columns: Experimental results and gas holdup correlations

The effect of aspect ratio in counter-current gas-liquid bubble

columns: Experimental results and gas holdup correlations

Giorgio

Besagni

∗

_,

_Alessandro

_Di

_Pasquali,

_Lorenzo

_Gallazzini,

_Elia

_Gottardi,

_Luigi

_Pietro

_Maria

_Colombo,

_Fabio

_Inzoli

Politecnico di Milano, Department of Energy, Via Lambruschini 4a, 20156, Milano

Article history:

Received 19 September 2016 Revised 2 March 2017 Accepted 19 April 2017 Available online 21 April 2017

Keywords: Bubble column, Gas holdup, Flow regime transitions, Counter-current mode, Electrolyte, Gas holdup correlation

It is generally admitted that the gas holdup is independent of the column dimensions and gas sparger design if three criteria are

satisfied: the diameter of the bubble column is larger than 0.15 m, gas sparger openings are larger than 1–2 mm and the aspect ratio

is larger than 5. This paper contributes to the ex- isting discussion; in particular, the effect of the aspect ratio (within the range 1–

15) in a counter-current gas-liquid bubble column has been experimentally studied and a new gas holdup correlation to estimate

the influence of aspect ratio, operation mode and working fluid on the gas holdup has been proposed. The bubble column,

equipped with a spider gas sparger, is 5.3 m in height, has an inner diameter of 0.24 m; gas superficial velocities in the range of

0.004–0.23 m/s have been considered, and, for the runs with water moving counter-currently to the gas phase, the liquid has been

recirculated at a superficial velocity of −0.0846 m/s. Filtered air has been used as the gaseous phase in all the experiments, while the

liquid phase has included tap water and different aqueous solutions of sodium chloride as electrolyte. Gas holdup measurements have

been used to investigate the flow regime transitions and the global bubble column hydrodynamics. The counter-current mode has

turned out to increase the gas holdup and destabi- lize the homogeneous flow regime; the presence of electrolytes has resulted in

increasing the gas holdup and stabilizing the homogeneous flow regime; the aspect ratio, up to a critical value, has turned out to

decrease the gas holdup and destabilize the homogeneous flow regime. The critical value of the aspect ratio ranged between 5 and

10, depending on the bubble column operation (i.e., batch or counter-current modes) and liquid phase properties. Since no

correlation has been found in the literature that can cor- rectly predict the gas holdup under the investigated conditions, a new

scheme of gas holdup correlation has been proposed. Starting from considerations concerning the flow regime transition,

corrective param- eters are included in the gas holdup correlation to account for the effect of the changes introduced by the aspect

ratio, operation mode and working fluid. The proposed correlation has been found to predict fairly well the present experimental

data as well as previously published gas holdup data.

1. Introduction

Bubblecolumns are multiphasereactors where agas phase is dispersedintoacontinuousphase(i.e.,aliquidphase—two-phase bubblecolumn:thesubjectofthisstudy—ora suspension—slurry bubblecolumn) inthe formof“non-coalescence-induced”/disperse bubbles or of “coalescence-induced” bubbles. The two-phases are separated by an interface between the dispersed phase and the continuousphase; atthisinterface, interfacialtransport phenom-ena (i.e., heat and mass transfer) may occur. Two-phase bubble columnsarewidelyusedinchemical,petrochemicaland biochem-icalindustriesthankstothemanyadvantagestheyprovideinboth

∗_{Corresponding author.}

E-mail address: giorgio.besagni@polimi.it (G. Besagni).

designandoperation.Onthepracticalpointofview,thesimplicity of construction, the lack ofany mechanically operatedparts, the lowenergyinputrequirements,thelargecontactareabetweenthe liquidandgasphases,andthegoodmixingwithintheliquidphase are some of the practical advantages in bubble column technol-ogy.Thesimplestbubblecolumnconfigurationconsistsina verti-calcylinderwithnointernals,inwhichthegasphaseentersatthe bottom—through a gas sparger—and the liquid phase is supplied inbatch modeoritmaybe ledineitherco-currentlyor counter-currently to the upward gas stream. Eventually, internal devices maybeaddedtocontroltheheattransfer,tolimittheliquidphase back-mixingortofoster thebubblebreak-uprate(asreviewedin ref. Youssef Ahmed etal., 2013). These elementshave significant effects on the fluid dynamics inside the reactor and the predic-tion oftheseeffects isstill hardly possible without

experimenta-© 2017. This manuscript version is made available under the CC-BY-NC-ND 4.0 license

http://creativecommons.org/licenses/by-nc-nd/4.0/

Published Journal Article available at:

http://dx.doi.org/10.1016/j.ijmultiphaseflow.2017.04.015

54 G. Besagni et al. / International Journal of Multiphase Flow 94 (2017) 53–78

Nomenclature

Symbols

a Yardstickresolution[m]

A c Cross-sectionalareaofthebubblecolumn

[m2_]

A i(i =1,2) Parameters inthe gasholdup correlation

(Eq.(21))[-]

B RetardedHamakerconstant(Eq.(2))[Jm]

C 0 Distributionparameter(Eq.(15))[-]

C _i(i ₌1,2,3,4,5,6,7) Parametersinthegasholdupcorrelations (Eqs.(24)and(33))[-]

d o Gasspargerholesdiameter[mm]

d c Diameterofthecolumn[m]

D H Hydraulicdiameter[m]

D ∗H Non-dimensionaldiameter(Eq.(1))[-]

error Relativeerror(Eq.(25))[-]

g Accelerationduetogravity[m/s2_] H c Heightofthecolumn[m]

H D Height of the free-surface after aeration

[m]

H 0 Heightofthefree-surfacebeforeaeration

[m]

l Number of additional measurements in uncertaintyevaluation[-]

J Drift-flux[m/s]

n MolarconcentrationofNaCl[mol/l]

n t Molar transition concentration of NaCl

(Eq.(2))[mol/l]

n ∗ Dimensionlessconcentration(Eq.(2))[-]

Ndata Total number of data in the dataset, in MPE and MAPE evaluation (Eqs.(27) and

(28))[-]

o Exponent in the drift-flux method (Eqs. (13)and(14))[m/s]

Q Volumetricflowrate[m3_/s] r _b Bubbleradius(Eq.(2))[mm]

R g Gasconstant(Eq.(2))[J/Kmol]

s H Samplestandard deviationofa

measure-ment[m]

S i(i =1,2,3) Parametersintheswarmvelocitymethod

(Eq.(8))[-]

T Temperature[K]

u d Weighted mean drift velocity (Eq. (15))

[m/s]

u g Meanrisevelocityofthegasphase[m/s]

U _b Parameter in the drift-flux method (Eq. (11))[m/s]

U _∞ Terminal velocity of an isolated bubble (Eqs.(13)and(14))[m/s]

U Superficialvelocity[m/s]

U ∗ Dimensionlessvelocity(Eq.(24))[-]

u Meanrisevelocityofthegasphase[m/s]

ν

Bubbleterminalvelocity[m/s]

V Volume[m3_]

w Localphasevelocity[m/s]

w G-L relative velocity betweenthephases(Eq.

(B.12))[m/s]

w G->L drift velocities (Eqs. (B.13) and (B.14))

[m/s] GreekSymbols

μ Viscosity[Ns/m2_]

β

Exponent(Eq.(18))[-]

γ

Parameterinthecounter-currentgasholdup corre-lation(Eq.(29))[-]

ε

Holdup[-]

ρ

Density[kg/m3_]

σ

Surfacetension[N/m]

ξ

H0 Uncertainty related to the evaluation of H0 (Eq.

(A.1))[m] Subscripts

Batch Batchmode

c Bubblecolumnparameter

Correlation Valueobtainedfromcorrelation

Counter-current Counter-currentmode

Cr Criticalvalue

Experimental Experimentalvalue

G Gasphase

Homogeneous Homogeneousflowregime

i Data considered inthe dataset,in MPEand MAPEevaluation(Eqs.(27)and(28))

I Firstflowregimetransitionpoint

II Secondflowregimetransitionpoint

L Liquidphase

Slug-bubble Slug-bubbleparameter

Swarm Swarmvelocity

T, E Subscriptsinthedrift-flux formulation(Eqs. (10)–(12),(14))

Trans Flowregimetransitionpoint

Transition Transitionflowregime

Wallis Wallisplotmethod

Wt Massconcentration

Zuber-Finley Zuber-Finleymethod Superscripts

R1 Homogeneousflowregime(Eq.(22)) R2 Heterogeneousflowregime(Eq.(22)) Acronyms

MPE meanpercentageerror(Eq.(27))

MAPE Meanabsolutepercentageerror(Eq.(28))

AR Aspectratio(AR =H 0/d c)

BSD Bubblesizedistribution

Fr Froudenumber(Fr ₌U G/(gH 0))

NaCl Sodiumchloride Other

Batchmode UL=0

Counter-currentmode UL < 0

|| Consider only the numerical value

withoutunits Meanvalue

tion.It isworth notingthatthe masstransferthat takesplaceat the interface does not necessarily involve reactions between gas andliquidcomponents,evenifthisoccursinmanypracticalcases (i.e.,oxidation,hydrogenation,chlorination,phosgenationand alky-lationprocesses).Despitethesimple bubblecolumndesign, com-plexfluiddynamicsinteractionsandcouplingbetweenthephases (whichmanifestsintheprevailingflowregimes(Majumder,2016)) exist; please note the fluid dynamics in bubble columns is sim-ilar to the ones observed in nuclear and energy conversion sys-tems.Therefore,correctdesignandoperationofbubblecolumn re-actors rely onthe proper predictionof the globalandlocal fluid dynamicproperties:a typicalapproachisapplyscale-up methods toestimatethefluiddynamicsof“industrial-reactor-scale” reactors from “laboratory-reactor-scale” experimental facilities (Shaikh and Al-Dahhan, 2013). Subsequently, models for the interfacial mass

transfer (Rzehak, 2016) and, eventually, to take into account the multi-phasereactions,areapplied.Amongthemanyfluiddynamic properties, the gas holdup (

ε

G)—a dimensionless parameter

de-finedasthevolumeofthegasphasedividedbythetotalvolumeof thesystem—isaglobalfluiddynamicpropertyoffundamentaland practical importance. The gas holdup determines the mean resi-dence time ofthe dispersed phase and, in combinationwiththe sizedistributionofthedispersedphase,theinterfacialareaforthe rate ofinterfacialheat and masstransfer. The global andthe lo-cal fluiddynamicpropertiesdependon themanyvariablesofthe systems (i.e., the operation mode, the physical properties of the phases, the propertiesat the gas-liquidinterface, …) andare re-latedtotheprevailingflowregime,whichcanbedistinguished— in alarge-diametercolumn—in(a)thehomogeneousflowregime,(b) thetransitionflowregime and(c)theheterogeneousflow regime (see thediscussionsinref.Besagni andInzoli., 2016candBesagni etal.,2016b,2017).Thescale-upapproachesfromthe

“laboratory-reactor-scale ” towardsthe “industrial-reactor-scale” relyon similar-itycriteriathatwouldresultinsimilarmixingandfluiddynamics and,hence,transportandperformanceinthetwodifferentscales. Many approaches were proposed and, in this respect,a pioneer-ingstudywasproposed byWilkinsonetal.(1992),after perform-ing experimentsintwo differentcolumndiameters(d c=0.15and

d c=0.23m), at different operating pressures and using different

liquidphases(n-heptane, monoethyleneglycol, andwater).Based ontheir ownresultsaswell asonliteraturedata,theyconcluded thatthegasholdupisindependentofthecolumndimensionsand thegasspargerdesignifthefollowingcriteria(the“Wilkisonetal.

scale-up criteria ”)aresatisfied1_:

1. criterion 1. The diameter of the bubble column, d c, is larger

than0.15m;

2. criterion 2.Theaspectratio, AR (theratiobetweentheheight andthediameterofthecolumn),islargerthan5;

3. criterion 3. The gas sparger openings diameter, d o, is larger

than1–2mm(“coarse” gasspargers).

The discussionconcerning the large-diametereffects(criterion 1) was proposed in our previous papers (i.e., Besagni and Inzoli, 2016b,c; Besagni et al., 2017 – see Section 2.1.1) and the influ-ence of the gassparger design (criterion2) a matter of ongoing research activities (and isto be presentedelsewhere). Thispaper contributes to the existing discussion and mainly focuseson the influenceoftheaspectratio, AR ,ingas-liquidlarge-diameter bub-blecolumns(criterion3).Itisworthnotingthat,despitesome au-thors definedthe aspect ratioin termsof the columnheight H c,

thecorrectdefinitionof AR strictlyreliesontheinitialliquidlevel (AR =H 0/d c), ratherthe column height, as discussed by Sasaki et

al. (2016,2017) and demonstrated in thisstudy. Generally speak-ing, inthe systemswherethe bubblesizesare notat their max-imum equilibrium size2 _{(and where coalescence may occur),the}

liquid height willinfluence theextent ofthe coalescence.

Conse-1 These three criteria are the rule of the thumb in bubble column scale-up. To the authors’ opinion, all these criteria can be expressed in term of non-dimensional groups: (a) non-dimensional diameter (i.e., Eq. (1) ); (b) non-dimensional dimension of the bubble column (i.e., the aspect ratio, AR); (c) non-dimensional sparger open- ing. This concept is a matter of ongoing research and it will be formalized in future works. The present paper is intended as a first step towards the study of these cri- teria, with a major focus on the aspect ratio.

2 This situation is typical of bubble columns with “coarse ” spargers (i.e., ring or spider spargers, d o > 1–1.5 mm): large sparger openings generally produce a non-

stable bubble size distribution at the inlet, which evolves, in the axial direction of the bubble column, towards an equilibrium. Conversely, when using “fine ” gas spargers (having small gas sparger openings d o < 0.5–1 mm), the bubble bed pro-

duced by the gas sparger may be stable from the beginning. A stable bubble bed at the inlet may change the relationship between the gas holdup and superficial gas velocity (i.e., the gas holdup curve is “S-shaped ”) and may stabilize the homo- geneous flow regime.

quently,thegasholdupwoulddecreasewiththeliquidheight, be-causethehigherthecolumnthelongerthetimethebubbleshave to coalesceand, thus, thelower the meanresidence time of the gasphase.Furthermore,inshorterbubblecolumns,theliquid cir-culationpatterns(that tends todecrease thegas holdup) arenot fullydevelopedandtheend-effects(i.e.,neargasspargerand top-columneffects)aremoreevident;actually,Xueetal.(2008)found a stronginfluence ofthe gassparger propertiesin thelocal void fractionsupto AR =5.Allthesephenomena(namely, coalescence, local flow phenomena and gas sparger effects) tend to destabi-lizethehomogeneousflowregimeinshorterbubblecolumns.The number of studies dealing withthe influence of the liquid level (AR ) on the bubble column fluid dynamics is quite limited and, inthefollowing,aliteraturesurvey isproposed.Allthedetails of thestudies listed below(i.e., bubblecolumnandgas sparger de-sign),along withotherstudies that willbe usedinthe following tocompareourexperimentaldata,aresummarizedinTable1(refs.

AkitaandYoshida,1973;Patiletal.,1984;Reillyetal.,1986; Roll-buschetal.,2015a;Ruzickaetal.,2001a;Sarrafi etal.,1999;Sasaki etal., 2016; Sasaki etal., 2017; Schumpeand Grund,1986; Tho-rat et al., 1998; Wilkinson et al., 1992; Yoshida andAkita, 1965; Zahradnı ´ketal.,1997).Inoneoftheveryfirststudy,Yoshidaand Akita(1965)didnotobservedanyremarkableeffectsof AR onthe gasholdupandmasstransferintheirexperiments;itisworth not-ing that they also studied a small-diameter bubble column. Patil etal. (1984),using a “very coarse ” gas sparger (apure heteroge-neousflowregime isexpected),didnot observedanyremarkable effectof AR onthegasholdup.Later,Wilkinsonetal.(1992)—when presentingthe“Wilkisonetal. scale-up criteria ” —discussedthe re-sults obtained by Kastanek et al. (1984): the influence of AR is negligible for H C greater than 1–3m and with AR larger than 5.

(Zahradnı ´k etal., 1997) foundthat the gas holdupdecreases and thehomogeneous flowregimeisdestabilizedwhileincreasing the initial liquid level up to a critical aspect ratio, AR Cr; the authors

concludedthat their results supportthe assumptionof a negligi-bleinfluenceof AR ongasholdupandflow regimetransitionsfor

AR larger than 5. These assumption has been also confirmed by

Thoratet al.(1998),which found a negligible influenceof AR on thegasholdupfor AR largerthan5(air-watersystem)or8

(“non-coalescing ” system).Sarrafi etal.(1999)comparedtheir experimen-talresultswithotherexperimentaldataandexcludedanyeffectof theinitialliquidlevelontheflow regimetransition, forH0>3m.

Ruzickaetal.(2001a)foundthatanincreaseinliquidheight desta-bilizesthehomogeneousflowregimeanddecreasesthegasholdup uptocriticalvalues.Sasakietal.(2016)foundthatan increasein liquid height destabilizesthe homogeneous flow regime and de-creasesthegasholdupup(AR upto5);inaddition,theyproposed theveryfirstgasholdupcorrelationtakingintoaccount H 0.More

recently,Sasakietal.(2017)furtherdevelopedtheirpreviouswork (Sasakietal.,2016)andstudiedlarge-diameterbubblecolumnsat low-intermediate AR (d Cintherangeof0.16–0.3m- AR upto6.5)

andvery-large-diameterbubble columnatlow AR (d C=2m - AR

up to 2). Theyconcluded that the gas holdup is independent of thecolumndesign inlarge-diameterandhigh AR bubblecolumn; inparticular,theystatedasfollows:“the effects of d c and H0on

ε

G

are negligible when scaling up from small to large bubble columns, provided that

α

Gin the small columns are obtained for d C200 mm

and H0࣡2200mm. The height-to-diameter ratio is useless in evalu- ation of the critical height, above which

ε

G does not depend on H 0. ”

(Pleasenoticethatthenomenclaturehasbeenchangedaccordingly withournotationlist). Thisconclusionisquiteinteresting and,at present,thisistheonlystudywithtends todisagreeonthe con-ceptof AR asscale-upcriterion.Thistopicisfurtherconsideredin thefollowingofthepaperandourpointofviewisstatedin out-looksections.Fromtheliteraturesurvey,itisclearthat thereisa lackofstudiesconcerning:

1. theinfluenceof AR for (a)the differentoperation modesofa bubblecolumn(i.e.,batchandcounter-current)and(b)the dif-ferentliquidphaseproperties(i.e.,non-coalescingsystems); 2. the influence of AR on (a) the gas holdup and (b) the two

flowregimetransitionsexistinginlarge-diametercolumns(the homogeneous/transition andthetransition/heterogeneousflow regimetransitions);

3. gas holdup correlations taking into account (a) AR , (b) the operation mode and (c) the liquid phase properties (i.e., the only correlation taking into account H0 is the one proposed

by Sasaki et al., 2016 andone of the few attempts to obtain counter-current correlationshas beenpreviously presented by theauthorsDeGuidoetal.,2016).

Takingintoaccounttheabove-mentionedgapsintheliterature, the goalof this study is to understand the influence of the col-umnaspect ratioand to contribute to theexisting discussion on thescale-up criteriafor multiphase reactors. In thisrespect, this papermaypropose anoriginal point ofviewon thescale-up cri-teria,which isin linewiththe goals ofa very recentstudy pro-posedby Sasaki et al. (2017) concerning the role of bubble col-umndiameterandinitial liquidlevel. Inparticular, inthis paper, we have studied the effect of AR in a counter-current gas-liquid bubblecolumnandwehaveproposedagasholdupcorrelationto estimatethe influenceofaspect ratio,operationmode and work-ing fluid on the gas holdup. The bubble column, equipped with aspider gassparger, is5.3m inheight, hasan inner diameterof 0.24m, wehaveconsidered gassuperficial velocitiesinthe range of0.004–0.23m/s, and, for theruns withwater moving counter-currentlyto the gas phase, the liquid has been recirculated ata superficial velocity of −0.0846m/s. Filtered air hasbeen used as thegaseous phase in all theexperiments, whilethe liquidphase hasincludedtapwateranddifferentaqueoussolutions ofsodium chloride(NaCl)inthe“coalescent flow regime ” and“non-coalescent

flow regime ”,asdiscussedbyBesagniandInzoli(2015,2016c).The experimental investigation has consisted ingas holdup measure-ments,which hasbeenused to investigatetheflow regime tran-sitionsandtheglobalbubblecolumnfluiddynamics.Moreover,a newcorrelationforthegasholduphasbeendevelopedreachinga satisfactoryaccuracyinanextendedrangeofconditions:the pro-posedcorrelationtakesintoaccounttheoperationmode,theliquid phasepropertiesandtheaspectratio.

The paperisorganizedasfollows.Theexperimental setupand methodsare describedinSection 2.The experimental resultsare presentedand discussed in Section 3 and are used to develop a correlationforthegasholdupinSection4.Finally,themain con-clusions,outcomesandoutlooksofthisstudyarediscussed.

2. Theexperimentalsetupandmethods 2.1. Experimental setup and liquid phases 2.1.1. Experimental setup

The experimental facility (Fig. 1a), available at the Depart-ment of Energy of Politecnico di Milano, is a non-pressurized verticalpipe madeof Plexiglas® with d c=0.24m and H c=5.3m.

The column diameter classifies this facility as a large-diameter bubble column. The classification of large-diameter bubble col-umn, is related to the fluid dynamic properties of the bubble columns itself and, in particular, it is related to the absence of the slugflow regime because ofthe Rayleigh–Taylorinstabilities (seeref.KitschaandKocamustafaogullari,1989).Thequantification ofthe Rayleigh–Taylorinstabilities at the “reactor-scale” is quan-tified through the dimensionless diameter D ∗H, which is related

to the Eötvös number of the slug bubbles as follows (See ref.

BesagniandInzoli,2016b;Besagnietal.,2017): D∗_H=√ DH

σ/g(ρL−ρG)

Circularbubblecolumn

−−−−−−−−−−−−−→ √ dc σ/g(ρL−ρG)= =_√ 1 σ/d2 cg(ρL−ρG)= 1 √ 1/Eoc = √ Eoc=



Eoslug−bubble (1)

In Eq. (1), D His the hydraulic diameter, d cis the bubble

col-umn (inner) diameter,

σ

is the surface tension,g is the accelera-tionduetogravity,

ρ

L -

ρ

Gisthedensitydifferencebetweenthe

twophases, and Eo c=Eo slug-bubble is theEötvösnumbercomputed

usingthe bubblecolumn diameter,whichis alsothe characteris-tic length of the slugbubbles. Bubble columns with D ∗H greater

than thecritical value D ∗H, cr=52(accordingly withBrookset al.,

2012)—corresponding to Eo slug-bubble=7.21 (i.e., d c ࣡ 0.13–0.15m;

ambient temperature and pressure)—are considered to be large-diameterbubblecolumns.When the d c > D ∗H, cr,the capbubbles

can no morebe sustained, and“coalescence-induced” bubbles (or, cluster of bubbles) appear instead of the slugflow regime.3 _The

presentbubble columnhasa dimensionless diameter D ∗H=88.13

(Besagni andInzoli,2016b). When thecolumn diameteris larger thanthecriticalvalue,thestabilizingeffectofthechannelwallon theinterfaceoftheTaylorbubblesdecreases,andslugflowcannot besustainedanymore becauseoftheRayleigh–Taylorinstabilities. Thefluiddynamicpropertiesinlarge-diametercolumnsdifferfrom theflowinsmall-diametercolumnsandtheflowregimemapsand flowregimetransitioncriteriausedtopredictthebehaviorof two-phaseflowinsmall-diametercolumnsmaynotbescaledupto un-derstandandpredict the flow inlarge ones(ShawkatandChing, 2011), inagreementwiththe scale-upcriteriaof Wilkinsonetal. (1992)andtheflowmapofShahetal.(1982).Thelargediameter effectsweredescribedinourprevious paper,towhom thereader mayrefer(forexample,refs.Besagnietal.,2016a;Besagniand In-zoli,2016b,c)

In the experimental facility(Fig. 1a), a pressure reducer con-trolsthepressureupstreamfromtherotameters(1)and(2),used tomeasurethegasflowrate(accuracy± 2%f.s.v.,E5-2600/h, man-ufacturedbyASA,Italy).Apump,controlledbyabypassvalve, pro-videswaterrecirculation,anda rotameter(3)measurestheliquid flowrate(accuracy± 1.5% f.s.v.,G6-3100/39,manufactured by ASA, Italy): in the present experimental investigation, the bubble col-umnhasbeentestedinthebatch(U L=0m/s)andinthe

counter-current(U L=−0.0846m/s)modes. Thevalueoftheliquidvelocity

hasbeenselectedtakingintoaccountourpreviousresultsandthe literature.Indeed,lowliquidvelocitiesdonotaffectthegasholdup (see, for example,refs. Akita andYoshida, 1973; de Bruijn et al., 1988; Lau et al., 2004; Rollbusch et al., 2015a; Sangnimnuan et al., 1984;Shahetal.,1982;Shawaqfeh,2003; VoigtandSchügerl, 1979;YangandFan,2003)because,if U Lislowcomparedwiththe

bubblerisevelocities,theaccelerationofthebubblesisnegligible (Hills,1976).Onthecontrary,athigherliquidvelocities(astheone selectedinthepresentstudy),thecolumnoperationinfluencesthe gasholdup:theco-currentmodereducesthegasholdup,andthe counter-currentmode increasesthegasholdupasbubblesare ei-ther acceleratedor decelerated by liquidmotion (Baawain et al., 2007;Besagni etal., 2014;Besagni etal., 2016a;Bi´netal., 2001; Jinetal.,2010;Otakeetal.,1981).Thevaluesofgasdensity(used tocompute U G) are basedupon theoperatingconditions existing

at the column midpoint (computed by using the ideal gas law) (Reilly et al., 1994). The midpoint column pressure has been as-sumedequaltothecolumnoutletpressureplusone-halfthetotal experimentalhydrostaticpressurehead.Withinthisstudy,gas su-perficialvelocitiesintherangebetween0.004(± 0.0005)and0.23

3 It is worth noting that this concept provides rational basis for the scale—up criterion 1 of Wilkinson et al. (1992) .

57 Table 1

Literature survey.

Ref. d c [m] H c [m] H 0 [m] AR [-] Sparger type d o [mm] U G [m/s] Working fluids

This study 0.24, circular 5.3 0.24 up to 3.6 1 up to 15 Spider 2 up to 4 up to 0.2 Air/Water

Sasaki et al. (2016) 0.2, circular and square 2 0.3 up to 1 1.5 up to 5 Perforated plate 1.4 0.025 - 0.4 Air/Water

Rollbusch et al (2015a) 0.16, circular 1.8 1.8 11.25 Perforated Plate 1 up to 0.1 Nitrogen/Water, aqueous

solutions of cumene and acetone

0.30, circular 2.63 2.63 8.75

0.33, circular and under pressure up to 3.6 MPa

3.88 3.88 11.25

Ruzicka et al. (2001a) 0.14/0.29/0.4, circular – 0.1 up to 1.2 0.25 up to 8.5 Perforated plate 0.5 up to 0.175 Air/Water

Sarrafi et al. (1999) 0.155, circular – 1.5/1.8 around 10 Perforated plate 1 up to 0.12 Air/Water

Thorat et al. (1998) 0.385, circular 3.2 0.385 up to 2.695 1 up to 7 Perforated plate 1 up to 0.3 Air/Water, Aqueous solution of

electrolytes and Carboxymethyl cellulose

Zahradnı ´k et al. (1997) 0.14/0.15/0.29, cicular 2.6 0.25 up to 10 1 up to 29 Perforated plate 0.5/1.6 up to 0.15 Air/Water, Aqueous solution of

ethanol, saccharose and electrolytes

Wilkinson et al. (1992) 0.158/0.23, circular – 1.5/1.2 5 up to 10 Ring 2 up to 7 up to 0.28 Nitrogen/n-Heptane, MEG,

water

Reilly et al. (1986) 0.30, circular 5.0 3 10 ∗ _{Single orifice 25.4}

Schumpe and Grund (1986) 0.30, circular 4.4 – 10 ∗ _{Ring plate (perforated plate sparger}

is not considered here)

1 up to 0.20 Air/Water

up to 0.16 Air/Water

Patil et al. (1984) 0.38, sectionalized bubble

column

0.684/1.026/1406 1.8/2.7 and 3.7 Perforated plate (single point sparger is not considered here)

3.57 up to 0.16 Air/Water, CMC, NAOH and acid

dichromate solutions

Akita (1973) 0.152, circular 4 2 up to 3 13.2 up to 19.7 single-hole nozzle 5 0.006 up

to 0.42

Various gas/liquid mix Yoshida and Akita (1965) 0.077/0.152/0.301/0.6,

circular

– 0.9 up to 3.5 2.1 up to 22.9 Single-hole nozzle 2.25 up to 40 up to 0.25 Air or pure Oxygen/Sodium

sulfite solution

(± 0.01)m/shave beenconsidered, wherethe uncertaintieswere evaluatedat95%confidence.

The gasdistributor,is aspider-gas sparger distributor(Fig. 1b, c) withholediameters d o=2–4mm,whichclassifythisgassparger

as“coarse” gas spargertype. The spider gasspargerhas sixarms madeof0.12mdiameterstainlesssteeltubessolderedtothe cen-ter cylinderofthegassparger.Thegasspargerhasbeeninstalled withthesixholeslocatedonthesideofeacharmfacingupward. The holes aredistributed asshowninFig. 1c,withan increasing diametermoving toward thecolumn wall.Additional images and flowvisualizationsofthespidergasspargerwereproposedinrefs.

BesagniandInzoli(2016b,c)andBesagnietal.(2016b).

2.1.2. Gas and liquid phases

Thegasandliquidtemperatureshavebeencheckedand main-tained constant at room temperature during all the experiments (T ₌295_{± 1}K); a survey onthe influenceof theoperating condi-tions has beenproposed by recent reviews(Leonard et al., 2015; Rollbuschetal.,2015b) andisnotrepeatedhere.Inthefollowing, adiscussionconcerningliquidandgasphasesisgiven.

Filteredairfromlaboratorylineshasbeenusedasthegaseous phaseinalltheexperiments;theair-cleaninglineconsistsinfilters (mechanical and activated carbon) andcondensation drying unit, in order to clean the gas phase properly and, thus, to avoidthe presenceofcontaminantsinformof(i)solid particlesand(ii) or-ganicsubstances.

The liquid phase has included deionized water and different aqueoussolutionsofsodiumchlorideaselectrolyte(kitchen qual-ity, NaCl 98.52% in mass). During the experimentation, care has been taken to ensure that the bubble column has been always cleantominimizeanycontaminationthatmightaffecttheresults (the systemhas beenpreviously flushedto remove contaminants andtoavoidthepresenceofadditionalsurfactants).Theinclusion ofNaCltotheliquidphasechanges(a)theinterfacialbubble prop-erties and (b)the physical properties ofthe mixture. Both these aspectsarediscussedinthefollowing.

EffectofNacloninterfacialbubbleproperties.Totheauthors’ opinion, to understand the influence of NaCl on bubble column fluid dynamics, the mainconcept is the bubble coalescence sup-pressioninducedbytheelectrolytes(i.e.,seerefs.Craigetal.,1993; Deschenesetal.,1998;Firouzietal.,2015;KeitelandOnken,1982; Marrucci and Nicodemo, 1967; Weissenborn andPugh, 1996). In this respect, the transitionmolar concentration, n t, is defined as

the concentration, n , of the non-coalescent media above which bubble coalescence is drastically reduced. This concentration has been quantitatively evaluated in the pioneeringstudy of Lessard and Zieminski (1971) by studying coalescence on bubble pairs: they havefound that n t isuniqueforeachsalt.Later,theconcept

of transition concentration has been extended to swarm of bub-blesbyCraigetal.(1993),byconsideringNaClaqueoussolutions: theyhavefoundthat n tdoesnotdependon U G.Theseresultshave

been further extended by Nguyen etal.(2012) fordifferentsalts in bubblecolumn: they have found that—exceptfor NaI—nt does

not depend on U G. Therefore, itis reasonable andcorrect touse

the concept of transition concentration to characterize the bub-blecolumnfluid dynamicsandto relate the“bubble-scale” tothe “reactor-scale” (the importance ofthe relations betweenthe bub-ble and the reactor scale has been clearly demonstrated in one ofourpreviousstudy,ref.Besagnietal.,2016b).Inparticular, de-pendingontheelectrolyte concentration, n ,wemaydefinea

“co-alescent flow regime ” (n ∗≤ 1) and a “non-coalescent flow regime ” (n ∗>1), through the dimensionless concentration, n ∗—following theformulationof n tproposedbyPrinceandBlanch(1990)(which

is a modified version of the first formulation of Marrucci

(MarrucciandNicodemo,1967)):

n∗=n/nt (

PrinceandBlanch,1990)

−−−−−−−−−−−−−−−→n/



1.18

μ

L

ρ

L



_B

_σ

rb



0.5 RgT



∂σ

∂

n



−2



(2)

Where B is the retarded Hamaker constant (B =1.5× 10− 28

Jm), R g is the gas constant, T is the temperatureof the system,

r _bisthe bubbleradius,and

σ

and

∂

σ

/

∂

n arethesurfacetension andthesurfacetensiongradientwithelectrolyteconcentration, re-spectively. In the case of NaCl, different values of n t have been

reportedin the literature, based on different measurement tech-niques (i.e. adjacent capillaries, light intensity inbubble column, size distributions in bubble column and micro-interferometry, as reviewedbyFirouzietal.,2015) and,inthisstudy,weselected n t

=0.145mol/l, following the study ofZahradnı ´k etal. (1999). No-ticethat n t=0.145mol/lisinagreementwiththepredictionofEq.

(2).Thisvaluehasbeenobtainedbyconsideringadjacent capillar-iesandis,therefore,apropertyrelatedtothe“bubble-scale” ; the readershouldrefertoBesagniandInzoli(2015,2016c)forthe dis-cussion concerning the effect of the electrolytes on the

“reactor-scale ” (i.e., gas holdup and flow regime transitions). It is worth notingthat Ribeiro andMewes(2007),have obtainedsimilar gas holdup curves regardless of the electrolyte forgiven dimension-lessconcentration, n ∗:therefore,Eq.(2)isa promisingmodelling parameterto account for thechemical nature of electrolytesand wouldbe useful toextend ourexperimental results (Section 4.3) toothersystems.FutureresearchersmightuseEq.(2)toobtain n t

foragenericelectrolyteand,byusingourexperimentaldata,they mighteasilyinterpretourresultsbyusingdifferentdefinition.

Effect of Nacl on the physical properties. When including NaClinthe liquidphase, not onlythe propertiesat theinterface change,butalsothephysicalpropertiesofthe binarymixture.In thisrespect,thepropertiesof thebinarymixturewere estimated based on the information provided in ref. Hai-Lang and Shi-Jun (1996) and are summarized in Fig. 2, for the sake of clarity. It isworth notingthat salt-quality NaClhasalmost identical physi-cal propertiesofpure NaCl,within the errorofdetermination,as deeplydiscussedbyOrvalho etal.(2009).Inthediscussionofthe resultswedemonstratethatthefluiddynamicsinbubblecolumns can not be entirely explained and modelled by using the bulk physical properties of the liquid phase (i.e., the surface tension, densityandliquidphaseviscosity). Thispointwasalso discussed intheremarkablestudybyShahetal.(1985)andcanbeconcluded alsobasedonourprevious worksconcerningthe influenceof or-ganicactive compounds(Besagni etal.,2016b)andviscous liquid phase(Besagnietal.,2017).

2.2. Gas holdup measurements

Thegasholdup(

ε

G),whichisconsideredaglobalfluiddynamic

parameter(atthe“reactor-scale”),isadimensionlessparameter de-finedasthevolumeofthegasphasedividedbythetotalvolume. Measurementsofthebedexpansionallowedtheevaluationof

ε

G:

theprocedureinvolvesmeasuringthelocation (height)ofthe liq-uidfree surfacewhen airflowsin thecolumn. Thegasholdup is thenobtainedusingEq.(3):

ε

G=

VG

VL+G

Constantcross−section−area

−−−−−−−−−−−−−−−−→

(

HD− H0

)

HD

(3)

Where V G is the volume of the dispersed phase, V L+G is the

total volume, H D is the height of the free-surface after aeration

andH0 istheheightofthefree-surfacebeforeaeration.H0 is

var-ied in orderto studythe influence of different AR (in the range 1≤ AR≤ 15).Itisworth notingthatheight measurementsare per-formedfromgassparger openingasreferencelocation. The

com-Fig. 2. Physical properties of the water-NaCl binary mixture.

pleteuncertainty analysisin the estimation of the gas holdup is proposedinAppendixA.

The gas holdup curve (the relationship between ɛG−UG)

pro-videsinformationoftheglobalbubblecolumnfluiddynamicsand canbeused tostudytheflowregime transitions(asdescribedin

Section 2.3). Indeed, applying the mass conservation to the gas

phase,thegasholdupiscomputedas:

ε

G =UG/Uswarm→Uswarm =UG/

ε

G

α

tG (4)

Where U Swarms isthemeanrisevelocityofthegasphase(itcan

becomputedbytheexperimentalmeasurementsobtainedthrough

Eq.(4))and t Gisthemeanresidencetimeofthegasphase. U Swarms

isstrictlyrelatedtothecouplingbetweenthephasesandthemain parameters (i.e.,bubblesizes, risevelocities, …)and, thus,to the mean residence time of the gas phase, t G (Orvalho et al., 2009;

Ruzickaetal.,2008).

2.3. Analysis of the flow regime transitions

Inthissection,theflowregimesinalarge-diameterbubble col-umnaredescribedandthemethods(bythe interpretationofthe

ɛG−UGcurve)todetecttheflowregime transitionpointsare

pre-sented.Althoughtheflowregimetransitionsdonotoccur instanta-neously,thedefinitionofanapproximatetransitionpointis help-fultounderstandandmodelthehydrodynamicbehaviorofbubble columns,asdeeplydiscussed byKrishna etal.(1991),andto de-velopgasholdupcorrelations,asdiscussedinSection4.

2.3.1. Flow regimes in large-diameter bubble columns

The global and the local fluid dynamic parameters of a bub-blecolumn are relatedto theprevailing flow regimes.In the lit-erature,different definitionsof flowregimes havebeenproposed andthereisnot agreement: forexample,manydefinitions ofthe homogeneousflowregimewereproposed,asreviewedbyBesagni etal. (2016b,2017). The goalof thissection is toclearly present and describe the flow regimes, and extend the discussion pro-posedinourpreviouspapers.Generally,thefluiddynamicsin bub-blecolumns isdetermined by the momentum exchangebetween theliquid andthegasphases. In thisrespect,thefluid dynamics ina bubble columnisgoverned by the samemechanisms asthe other vertical pipe flows (i.e., momentum exchange, …). In ver-tical pipe flows, with non-foamingsystems (see ref. Shah et al., 1985),fourmaintypesofflowpatternscanbeobservedwhen in-creasingthe gasflow rate(and, thus,the superficial gasvelocity,

U G),atfixedsystemdesignandphaseproperties:(a)the

homoge-neousflowregime,(b)theheterogeneousflowregime;(c)theslug flowregime;(d)theannularflowregime.Inindustrialapplications, large-diameter(definedbyEq.(1))andlarge-scalebubblecolumns are used:inthissituation,two mainflow regimes(andthe tran-sitionflowregimein-between)areobserved(see,forexample,the well-knownflowmapsinref.Shahetal.,1982):

(i) thehomogeneousflowregime; (ii) thetransitionflowregime; (iii) theheterogeneousflowregime.

Indeed,inpracticalapplications,theannularflowregimeisnot observedbecauseoftheveryhighgasvelocitiesrequested(seethe methodinref.Paganetal.,2017).Conversely,theslugflowregime is not observed because of the fluid dynamics phenomena and, in particular, becauseof the Rayleigh–Taylorinstabilities (Kitscha andKocamustafaogullari,1989).ThequantificationoftheRayleigh– Taylor instabilitiesat the “reactor-scale” is quantified through Eq. (1).Therefore,twomaintransitionsexistinlarge-diameterbubble columns:

(i) the transitionbetweenthehomogeneousandthetransition flowregimes(

ε

G,trans,I, U G,trans,I);

(ii) thetransitionbetweenthetransitionandtheheterogeneous flowregimes(

ε

G,trans,II, U G,trans,II).

Themainfeaturesoftheseflowregimesasdiscussedinthe fol-lowing.

Homogeneous flow regime.The homogeneous flow regime— generally associated with small gas superficial velocities—is re-ferredastheflowregimewhere“non-coalescence-induced” bubbles exist (as detected by the gas disengagement technique (Besagni andInzoli, 2016b) and visualized by Sasaki etal., 2016).The ho-mogeneous flow regime can be further distinguished into

“pure-homogeneous ” (or“mono-dispersed homogeneous ”)flowregime and “pseudo-homogeneous” (or “poly-dispersed homogeneous ” or “gas

maldistribution ”) flow regime: the former is characterized by a mono-dispersedBSD(astheoneobservedbyMuddeetal.(2009), by usinga “fine” gassparger), whereas thelatter ischaracterized by a poly-dispersed BSD (if large bubbles are aerated (Besagni and Inzoli, 2016a, b), by using a “coarse” gas sparger). We de-finethemono-dispersedandpoly-dispersedBSDsaccordinglywith thechangeofsignintheliftforce coefficient(Besagni andInzoli, 2016b; Besagni et al., 2016b, 2017; Lucas et al., 2015; Zahradnı ´k etal.,1997;Ziegenheinetal.,2015).

Transitionflow regime.Thetransitionfromthehomogeneous flow regime to the heterogeneous flow regime is a gradual pro-cess, in which a transitionflow regime occurs. Thisflow regime is characterized by large flow macro-structureswithlarge eddies and a widened bubble size distribution (BSD) due to the on-set of bubble coalescence; it is identified by the appearance of “coalescence-induced” bubbles,asdefinedandobservedbyBesagni et al.(2016b),and visualized by Sasaki et al.Sasaki etal. (2016, 2017) when “coalescing” solutions are employed. Conversely, if “non-coalescing” solutionsareemployed,thetransitionflowregime is identified by the appearance of “clusters of bubbles ”, as de-fined in refs. Takagi and Matsumoto (2011) and Takagi et al. (2008)andobservedbyBesagniandInzoli(2016b)andBesagniet al. (2016b). Besagni et al. (2017) demonstrated that

“coalescence-induced ” bubbles (and, thus, the destabilization of the homoge-neousflowregime)arecausedby theliftforcepushingthelarger bubblestowardthecenterofthebubblecolumn(seeSection3.4in

Besagnietal.,2017).Similarly,Takagietal.(TakagiandMatsumoto, 2011; Takagi etal., 2008) discussed how the“clusters of bubbles ” are formed because ofthe lift force acting on a mono-dispersed BSD. Beinhauer (1971) found that the first “coalescence induced”

bubble appeared at about U G=0.02m/s and, increasing the gas

superficial velocities, both “non-coalescence-induced” and

“coales-cence induced” increase till the non-coalescence-induced” bubbles

reachedamaximumand, then,decreasetowardaconstant value. Conversely, Schumpe and Grund (1986), Krishna and co-workers (Krishnaetal., 2000a; Krishna etal., 2000b)andBesagni and In-zoli(2016b)reportedthatthe non-coalescence-induced” bubbles in-creasetilltheflowregimetransitionpointand,then,only

“coales-cence induced” bubbles increase.Thedifferenceisprobablycaused bythedifferentgasspargerdesign(“fine-gas sparger ” and

“coarse-gas sparger ”).

Heterogeneousflow regime.At highgassuperficialvelocities, afullyheterogeneousflowregime isreached(Sharafetal.,2015); it is associated with high coalescence and breakage rates and a wide varietyof bubblesizes.A recent,andinteresting,review on themechanismsgoverningtheflowregime transitiontowardsthe heterogeneous flow regime hasbeen proposed by Montoyaet al. (2016).

The transitionsbetweenthe differentflowregimesdepend on the operationmode,design parametersandworkingfluidsofthe bubble column. For example, considering the effect of the gas sparger,a“fine” gasspargerthat producesmainlyverysmall bub-bles the homogeneous flow regime is stabilized (Mudde et al., 2009), whereas the mono-dispersed homogeneous flow regime may not exist if large bubbles are aerated (Besagni and Inzoli, 2016a,b)uptoa“pure heterogeneous flow regime ” fromthe begin-ning (Ruzicka et al., 2001b). Concerningthe influence ofthe liq-uid phase properties,ethanol andelectrolyte stabilize the

homo-geneousflowregimeandsuppressthe“coalescence-induced” bub-bles(Besagni andInzoli,2015; Besagni etal., 2016b) andviscous solutionsexhibiteda“dual effect ” dependingonthe natureofthe prevailingBSD.

In the present bubble column, the “mono-dispersed homoge- neous ” doesnotexist (asobservedinour previousstudy,Besagni andInzoli,2016b) andtheexisting flow regimesare: (i)

“pseudo-homogeneous flow regime ”,(ii)transitionflowregimeand(iii) het-erogeneousflowregime.

2.3.2. First flow regime transition point

Inourpreviouspapersweshowedhowtheswarmvelocityand the drift-flux/Wallisplot methods havebeen able to identify the first flow regime transition point (Besagni and Inzoli, 2016b). In particular, the first flow regime transition point (in terms of the transitiongasvelocity andtransition gasholdup) is computedas theaverageofthevaluesobtainedbythetwomethods:

U_G,trans,I=UG,trans,swarm+UG,trans,Wallis

2 (5)

ε

G,trans,I=

ε

G,trans,swarm+₂

ε

G,trans,Wallis (6)

Thedetailsconcerningthetwomethodsareprovidedbelow.

2.3.2.1. Swarm velocity method. The swarm velocity method has beendevelopedby ZuberandFindlay(1965)andisbasedon the swarm velocity, U swarm, (Eq. (4)). The swarm velocity is plotted

against the gas superficial velocity: U swarm is almost constant in

thehomogeneousflowregime(or,insomecases,itcanbeslightly decreasing),butitstartstoincreaseasthesystementersthe tran-sitionflowregimeatatransitionsuperficialvelocity, U G,trans,I.The

appearanceofthefirst“coalescence-induced” bubbleisresponsible forthis sudden increase in theswarm velocity andis an indica-tion ofthe flow regime transition. Inthis study,the quantitative evaluationof U G,trans,swarmhasbeendeterminedbytheintersection

betweenthetrendsof U swarminthetwoflowregimes.

Thus, U swarm has been takenas constant inthe homogeneous

flowregime(Eq.(7)):

Uswarm,homogeneous=constant (7)

Whereas,inthetransitionflowregime ithasbeendetermined byaleastsquaresfittingofthefollowingfunction:

Uswarm,transition=S1

(

UG

)

S2+S3 (8)

Where S 1, S 2and S 3arefittingparameters.

Thetransitionpoint(U G,trans,swarm,

ε

G,trans,swarm)isthusevaluated

bysolvingthefollowingEq.(9):

U_swarm,homogeneous=Uswarm,transition (9)

2.3.2.2. Drift-flux/Wallis plot method. The drift-flux method has been proposed by Wallis (1969)and has beenwidely applied in theliterature.Thismethodisbasedonthedrift-flux,which repre-sentsthegasfluxthroughasurfacemovingwiththespeedofthe two-phasemixtureandisexperimentallyobtainedasfollows: JT=UG

(

1−

ε

G

)

± UL

ε

G (10)

ThecompletederivationofEq.(10)hasbeendescribedand de-tailed by Besagni and Inzoli (2016c) and is further discussed in

AppendixB,forthesakeofclaritywithinthisresearch.InEq.(10), the sign on the rightside of the equations dependson the op-erationmode ofthebubble column:(a)the co-currentmode (+) or(b)the counter-current mode (-).Inthiswork, only thebatch modeandthecounter-currentmodewereconsidered.

Theoretically, the drift-flux is written in terms of the bubble swarm velocity, whosedependenceupon

ε

G varieswiththe

pre-vailingflowregime:

JE=Ub

(

1−

ε

G

)

(11)

The idea in thismethod is to employ a model for U b that is

validforthehomogeneousflowregime,plot J Eand J Tinthesame

graphasafunctionof

ε

G.Sincetheformulationisvalidforthe

ho-mogeneousflowregime,byplotting J Eand J Tagainstthegas

hold-up on the same graph,it is possible to determine the transition pointfromone flow regime tothe other one asthepoint where thecurve of J E deviatesfromthe curve of J T.Thus, thetransition

pointisdefinedwhen:

JT=JE (12)

Theevaluationof U _binEq.(11)isamatterofdiscussioninthe literature and differentmodels havebeen proposed andapplied. Inthisstudy,theapproachofKrishnaetal.(2000b)hasbeen fol-lowed,which isbased ontheempirical modelofRichardson and Zaki(1997):

Ub=u∞

ε

G

(

1−

ε

G

)

o−1 (13)

Where o isfluid-dependent and u _∞ istheterminalvelocity of an isolatedbubble. Thesevaluesshould be fitted withtheaid of theexperimentaldatainthedeterminationofthetransitionpoint. CombiningEqs.(11)and(13),thefollowingequationisderived:

JE=u∞

ε

G

(

1−

ε

G

)

o (14)

2.3.3. Second flow regime transition point

The second flow regime transition is estimated following the proposal of Sharaf et al. (2015), which relies on the drift-flux method for multiphase systems proposed (Zuber and Findlay, 1965).Withinthisapproach,

ε

Giscomputedasfollows(thereader

should refer to thepaper of Zuber andFindlay for the complete derivationofthismethod):

ε

G,Zuber−Finley=

UG/

(

UG+UL

)

C0+[ud/

(

UG+UL

)

]

(15)

Where C 0 is the distribution parameter (to account for radial

profile effects in the cross-section of the column) and u _d is the weightedmeandrift velocity.Theseparameters canbe computed byusingeitheralocaloraglobalapproach:(i)thelocalapproach reliesonlocalflow(liquidphasevelocityandlocalvoidfractions) measurements, whereas (ii) the global approach relies on fitting thegasholdupcurve.Inthebatchmode(U L=0m/s),Eq.(15)reads

as:

ε

G,Zuber−Finley = UG/

(

UG+UL

)

C0+[ud/

(

UG+UL

)

] UL=0 −−−→ 1 C0+[ud/UG] = UG UGC0+ud (16)

In this study C 0 and u d have been determined by a least

squaresfittingwiththeexperimentaldata(theglobalapproach)at

U G>0.15,asthesecond flow regime transitionis expectedabout

0.1m/saccordinglytoNedeltchev(2015)andSharafetal.(2015). The transition point (

ε

G,trans,II, U G,trans,II) is, thus, evaluated by

solvingthefollowingEq.(17):

ε

G,Experimental=

ε

G,Zuber−Finley (17)

3. Theexperimentalresults

Herein the experimental results (the gas holdup and flow regime transitionpoints)havebeen presented.At first,the effect of AR (onthegasholdupandflowregimetransitions)incoalescing

Fig. 3. Gas holdup measurements: air-water system.

systems(air-water) inthebatchmode andinthecounter-current mode hasbeendiscussed. Atsecond, the influenceof AR (on the gasholdupandflowregimetransitions)innon-coalescingsystems (air-water-NaCl)hasbeendiscussed.Theseexperimentaldatahave beenusedtoassessnovelgasholdupcorrelations(Section4).

3.1. The effect of aspect ratio in coalescing (air-water) systems: batch mode

3.1.1. Gas holdup

Fig.3adisplaysthegasholdupcurvesinthebatchmodeforthe different ARs (in therange1≤ AR≤ 15).All thegasholdupcurves are similar inshape andthe relation between

ε

G and U G can be

interpretedbytheproportionality:

ε

G∼ UGβ (18)

Wheretheexponent

β

dependsonthebubblecolumnfluid dy-namics (i.e., the flow regimes, the coupling between the phases, …).At low gassuperficial velocities—inthe pseudo-homogeneous flowregime—therelationshipbetween

ε

Gand U Gislinear(

β

> 1),

followed by a change in tendency, caused by the appearance of “coalescence-induced” bubbles, at the first flow regime transition. After the flow regime transition, the appearance of

dis-persedphaseandreducesthemeangasresidencetimeinthe bub-blecolumn(BesagniandInzoli,2016b;Yangetal., 2010),thus re-ducing the gas holdupversus gas velocity slope (

β

<1).The val-ues of

β

in Eq. (18) have been already discussed by De Guido et al. (2016) and are in agreement with the theoretical expecta-tions: applying the mass conservation to the gas phase, the gas holdup iscomputedas

ε

G=UG/u G, where u G isthemeanrise

ve-locityofthegasphase.Ifthebubbleswouldtravelattheir termi-nal velocity, the gasholdup wouldincrease linearlywith thegas flowrate;however,thecouplingbetweenthephasescauses devi-ationsfromlinearity(see, refs.Besagni andInzoli,2016c; Ruzicka et al., 2003):(i) in thehomogeneous flow regime, the hindrance reduces the bubble velocity, thus increasing

ε

G; (ii) in the

tran-sition/heterogeneous flow regime the “coalescence-induced” bub-blesandtheenhancedcirculationscause

ε

G todecreaselessthan

proportionally to U G. The shape of the gas holdup curves is the

onetypicallyfoundforsimilargasspargergeometries;indeed,the shape of the gas holdup curve is mainly relatedthe gas sparger design (if large-diameter columns are considered, see, for exam-ple, ref. Sharaf et al., 2015): (a) “fine gas spargers ” (d 0 <1mm;

see,forexample,ref.Muddeetal.,2009)producemono-dispersed BSBs, leading to the hindrance effect, which is physically mani-fested by the peak on the gas holdup curve (please notice that the reversed S-shaped curve can be interpreted on the basis of the Ledinegg instability); (b) “coarse gas spargers ” (d 0 >1–2mm,

assuggestedbythescale-upcriteriaofWilkinsonetal.(1992),as theone employed inthisstudy,lead tomonotonic increasinggas holdupcurves,whichisdescribedbytheproportionality,Eq.(18).

Thegas holdupdecreasescontinuously whileincreasing AR up to the criticalaspect ratio, AR Cr =5.Above AR Cr, there is no

re-markable difference in the gas holdup curves: our experimental observationsconfirm theexistenceofa criticalaspectratioabove which the gas holdup does not depend anymore from AR . The value of the critical aspect ratio, AR Cr =5, is in agreement with

the scale-up criteria of Wilkinson et al. (1992) and the experi-mentalobservationofother authors(i.e.,refs.Thorat etal., 1998; Zahradnı ´ketal., 1997). Moreover,the decreaseinthe gasholdup whileincreasing AR isinagreementwiththeexperimental obser-vationsofdifferentauthors(Sasakietal.,2016;Thoratetal.,1998; Zahradnı ´k etal., 1997) andis probablybe causedby the coales-cence phenomena. In systemswhere the bubble sizesare not at theirmaximumequilibriumsize,

ε

Gwoulddecreasewhile

increas-ing H 0: the higherthe column, the longer the time available for

bubble coalescence. This concept is further explainedwhen con-sideringtheinfluenceoftheliquidvelocity(Section3.2)and non-coalescingliquidphases(Section3.3).

Wehavecomparedourresultswithasetofexperimental stud-ieswithsimilarcolumndiametersandgasspargerdesigns:Fig.4

displaysthe gasholdup dataconsidered andTable 1summarizes thedetailsofthestudiesconsidered(AkitaandYoshida,1973;Patil etal., 1984;Reillyetal.,1986; Rollbuschetal., 2015a;Ruzicka et al., 2001a; Sasaki et al., 2016; Sasaki et al., 2017; Schumpe and Grund, 1986; Thorat etal., 1998; Wilkinson etal., 1992;Yoshida andAkita,1965).Afurthercomparisonwiththeliterature is pro-vided in our previous paper (Besagni and Inzoli, 2016b). When gas holdupdata are compared betweendifferentconfigurations— atthesameoperatingconditionsforgivengasandliquidphases— thefollowingdesignparametersmustbeconsidered(Rollbusch et al., 2015a), following the criteria of Wilkinson et al. (1992): (i)

d c, (ii) d o and (iii) AR . All the studies considered in Fig. 3 are

large-diameter(d c࣡0.15m)and,thus,thewalleffectscanbe

ne-glected. The shape of the gas holdup curves can be easily inter-preted basedon considerations concerningthe gassparger open-ing, d o. As previously stated (Section 2.3.1), “coarse” gas spargers

(d o ࣡ 1mm)ensure a “poly-dispersed” homogeneous flow regime

(BesagniandInzoli,2016a,b)orapure-heterogeneousflowregime

(Ruzicka etal.,2001b);onthe otherhand,“fine” gas spargers(d o

࣡ $?> 0.5-1mm)ensurea “mono-dispersed” homogeneous flow regime (Mudde et al., 2009). Taking into account this consider-ation, the shapes of the gas holdup curves obtained by Ruzicka et al. (2001a) are not surprisingly; they have used a “fine” gas sparger (d o=0.5mm), which leads to a “mono-dispersed”

homo-geneous flow regime: the real uniformity leadsto the hindrance effect that physically manifestsby the peak on the gas holdup graph(Ruzicka etal., 2001a;Zahradnı ´k etal.,1997). Thoratetal. (1998) and Schumpe and Grund (1986) have used a sieve plate gassparger(d o=1mm)andaring plategassparger(d o =1mm),

respectively: these gas spargers lead to a gas holdup curve in-termediate betweena peakedcurve andamonotonically increas-ing curve. On the contrary, Sasaki et al.(2016, 2017), Patil etal. (1984),YoshidaandAkita(1965)andWilkinsonetal.(1992)have used“coarse” and“very-coarse” gasspargersand,therefore,thegas holdupcurveismonotonicallyincreasing,similarlytotheshapeof ourexperimentalresults(Fig.3a).Rollbuschetal.(2015a)have ob-tainedamonotonicallyincreasinggasholdupcurveusinga perfo-ratedplategasspargerwith d o =1mm,however,itisworth

not-ing that Rollbusch et al. (2015a)used Nitrogen asgas phase. As far as AR is concerned, Sasaki et al. (2016, 2017), Ruzicka et al. (2001a)andThoratetal.(1998)havefoundthatanincreaseinH0

decreasesthegasholdup.Patil etal.(1984)haveobserveda very loweffectof AR onthegasholdup,whichcanbeexplainedbythe “very-coarse” gasspargerused,whichcausesapure-heterogeneous flow regime. It is well known that the effect of the bubble col-umn design is lower in the heterogeneous flow regime. Finally,

Sasakietal.(2017)further developedtheir previouswork (Sasaki et al., 2016) and studied large-diameter bubble columns at low-intermediate AR (d Cintherangeof0.16– 0.3m-ARupto6.5,Fig.

4a)andvery-large-diameterbubblecolumnatlow AR (d C=2m

-ARup to2,Fig.4b);they concludedthat thegasholdup is inde-pendentofthecolumndesigninlarge-diameterandhigh AR bub-blecolumn. Itseemsthat,invery-large-diameterbubblecolumns, the effect of the initial liquid level is lower. In particular, they statedthattheeffectsofthebubblecolumndesignparameters be-comenegligiblefor d C200mmand H 0࣡2200mm,regardlessof

AR.Theconclusionofthisstudyisquiteinterestingand,atpresent, this is the only studywith tends to disagree on the concept of

AR asscale-upcriterion;unfortunately,nodatawere availablefor very-large-diameterbubblecolumnsathigh AR .

3.1.2. Flow regime transitions

Thefirstandthesecond flowregimetransitions(asdefinedin

Section 2.3.1) have been analyzed by applying the methods pre-sentedin Sections2.3.2 and2.3.3.Fig. 5a andc display the first andthesecond transitionpointsandshowthe boundariesofthe homogeneous,thetransitionandtheheterogeneousflowregimes. InparticularFig.5adisplaystheinfluenceof AR onthetransition gasvelocities(U G,trans,Iand U G,trans,II)andFig.5cdisplaysthe

influ-enceof AR onthetransitiongasholdups(ɛ G,trans,Iand ɛ G,trans,II).

The homogeneous flow regime is destabilized (decrease in

U G,trans,I andɛG,trans,I)whileincreasing AR ,upto thecriticalaspect

ratio, AR Cr=5, in agreement with some of the previous studies

(Ruzicka etal., 2001a;Sasaki etal., 2016;Zahradnı ´ketal., 1997). Indeed,inshortbubble columns(low AR ) three phenomenatend to destabilize the homogeneous flow regime: (i) the coalescence phenomenaaremoreimportant(asdescribedinSection3.1.1),(ii) theliquidcirculationpatternsarenotfullydevelopedand(iii)the end-effects(i.e.,thegasspargerandtop-column)aremore impor-tant(Xueetal.,2008).Adualeffecthasbeenobservedforsecond flowregimetransition:thetransitionflowregimeisstabilized (in-creasein U G,trans,IIandɛG,trans,II) upto AR =8anditisdestabilized

(decreasein U G,trans,IIand ɛ G,trans,II)forhigher AR .Therangeof

Fig. 5. Flow regime transitions: air-water system.

ofthepreviousstudiesdealingwiththesecondflowregime transi-tion(Nedeltchev,2015;Sharafetal.,2015)(pleasenoticethatthere isalackofstudyconcerningthesecondflowregimetransition).It isworth notingthatthe secondflow regimetransitionpointsare morescattered, becauseofthe complexphenomenainvolvingthe secondtransition(Montoyaetal.,2016).

Thereisalackofstudiesconcerningtheinfluenceof AR onthe first and(mainly,asalreadystated)the secondflow regime tran-sitions. In order to fill thisgap, we have interpreted the ɛG−UG

curvestakenfromtheliterature(Fig.3)bythemethodspresented in the Sections 2.3 obtaining quantitative data on the first and the second flow regime transitions. It should be noticed that, by using this procedure, the flow regime transition pointsobtained are coherent,asthey rely onthe samedefinition.Only the stud-ies havingmonotonically increasing gasholdup curveshavebeen considered(asdescribedinSection3.1.1).Theresultsaredisplayed in Fig.6; inparticular, Fig.6a (U G,trans,I) andFig. 6c(ɛG,trans,I)

dis-play the firstflow regime transition pointsandFig.6b (U G,trans,II)

and Fig. 6d (ɛG,trans,II) display the second flow regime transition

points. From these results four considerations are drawn: (i) the second flow regime transitions are more scattered than the first

flowregimetransitions(aspreviouslyobserved);(ii)arelation be-tweenthetransitionpointsand AR clearlyexist:thehomogeneous flowregime isdestabilized whileincreasing AR , upto thecritical aspectratio;(iii)thevalueof AR Cr forthegasholdupisobserved

alsoforthe flow regime transitions: above AR Cr, theflow regime

transitions (in particular, the first transition)do not change any-more;(iv)theflowregimetransitionpoints(inparticular,thefirst transition)betweenthedifferentstudiesareinagreements,which isexplainedbythebubblecolumnssimilarindesign(i.e.,onlythe studies having monotonically increasing gas holdup curves have beenconsidered).Itisworthnotingthat,owingtothe“large” gas spargeropeningsconsidered,theflowregimetransitionsoccur ear-liercomparedwithotherliteraturestudies(asreviewedbyBesagni andInzoli,2016b). Thisis because,inthe batch mode,the larger bubblesgenerated atthegassparger (havinga negativelift coef-ficient,see refs. Lucas et al., 2005; Tomiyama et al., 2002), tend to migratetoward the centerof the column, thus promoting the appearanceofthe“coalescence-induced” bubblesand,subsequently, theflowregimetransition.Onthecontrary,thesmallbubbles, hav-ingpositiveliftcoefficient,stabilizethehomogeneousflowregime.

Fig. 6. Flow regime transitions: comparison against data from the literature (air-water system).

3.2. The effect of aspect ratio in coalescing (air-water) systems: counter-current mode

3.2.1. Gas holdup

Fig. 3b displays the gas holdup curves in the counter-current mode (U L=−0.0846m/s) for the different ARs (in the range

5≤ AR≤ 15).Comparedwiththebatch mode,upon increasingthe liquidflowrate, a fasterincrease in the gas holdup hasbeen ob-servedatlow U G,andthefirsttransitionpointmovestowardlower

gassuperficial velocities.Thischangeisexplainedbytheeffectof theliquid flow, which slows down therise of the bubbles, lead-ing to higher gas holdup: the reader should refer to our previ-ous papers (Besagni and Inzoli, 2016b, c) for a complete discus-sionconcerningtheinfluenceoftheliquidvelocityonbubble col-umnhydrodynamics (globalandlocalflow properties).The influ-enceof U L onthe gas holdup is probablycaused by the

compa-rableorderofmagnitudeoftheliquidandgasvelocities.Actually,

Hills(1976)mentioned that if U L is low comparedwiththe

bub-blerisevelocities(representedintermsof U swarm(Rollbuschetal.,

2015a)),no impactof U L on

ε

G isexpectedbecause the

accelera-tionofthebubblesisnegligibleandvice-versa.Theinfluenceof U L

onthegasholdupisalsoinagreementwiththefindingsofOtake etal.(1981),Baawain etal.(2007),Bi´n etal.(2001)andJinetal.

(2010),asdescribedinourpreviouspapersaswell.Thegasholdup decreases continuously whileincreasing AR up to the critical as-pectratio, AR Cr=10.Above AR Cr,thereisnoremarkabledifference

inthegasholdupcurves.Thisobservationsuggeststhat thevalue of AR Crdependson theoperation modes. The increase in AR Cr in

counter-currentmodecanbe explainedby theincreaseinthe co-alescence phenomena. Indeed, in the counter-current mode, the lower bubble rising velocity causes higher gasholdup and, thus, themorecompactarrangementofbubblesleadstohigher coales-cence rate (Besagni and Inzoli,2016b, c). It is,therefore, easy to understand that thecounter-current mode causesthe increase in thecriticalvalueoftheaspectratio, AR Cr.

3.2.2. Flow regime transitions

Thefirstandthesecondflowregime transitions(asdefinedin

Section 2.3.1) have been analyzed by applying the methods pre-sentedin Sections2.3.2 and2.3.3.Fig. 5band ddisplay the first andthesecond transitionpointsandshow theboundariesofthe homogeneous,thetransitionandtheheterogeneousflowregimes. InparticularFig.5bdisplaystheinfluenceof AR onthetransition gasvelocities(U G,trans,Iand U G,trans,II)andFig.5dtheinfluenceof AR

Fig. 7. Relation between NaCl concentration and gas holdup (U G = 0.065 m/s).

The counter-current mode destabilizes the homogenous flow regime, comparedwiththebatchmode, asthe morecompact ar-rangement of the bubbles leads to an earlier appearance of the “coalescence-induced” bubbles and, thus, the flow regime transi-tion; the comprehensive discussion concerning the effect of the counter-current mode on thedestabilization ofthe homogeneous flow regime can be found in Besagni andInzoli (2016b, c). This observationisinagreementwiththepreviousliterature.Jinetal. (2010)havereportedthatthetransitionpointisthesameif U L is

lower than 0.04m/s, whereas forhigher U L, thetransition

veloc-itydecreaseswithincreasing U L.Otakeetal.(1981)haveobserved

an earlierflow regime transitionincreasing theliquidflowratein thecounter-currentmode(U Lupto-0.15m/s).Similarconclusions

havebeendrawnby YamaguchiandYamazaki (1982)(d c=0.04m

and 0.08m) and in our previous research (Besagni et al., 2014; Besagni et al., 2016a; Besagni and Inzoli, 2016b, c). As expected from our experimental results in the batch mode, the homoge-neousflowregimehasbeendestabilized(decreasein U G,trans,I and

ɛG,trans,I)while increasing AR ,upto AR Cr, inagreementwithsome

ofthe previous studies(Ruzicka etal., 2001a;Sasaki etal., 2016; Zahradnı ´ketal.,1997).Thereasonsarethesameasstatedbefore: inshortbubblecolumnsthecoalescencephenomenaaremore im-portant,theliquidcirculationpatternsarenotfullydevelopedand theend-effectsaremoreimportant.Similarly,thesystemsislikely to becomefullyheterogeneous (decrease in U G,trans,II andɛG,trans,II)

decreasing AR .

3.3. The effect of aspect ratio in non-coalescing (air-water-NaCl) systems

First, we have tested the effect of NaCl concentration on the gasholdupforfixedgassuperficialvelocity (Fig.7)and, secondly, we haveanalyzed theinfluence of AR andNaClconcentration on thegasholdupcurves(Figs.7and8).Finally,thegasholdup mea-surementshavebeneusedtoevaluatetheflowregimetransitions (Fig.10). It isworth noting that nocrystallization inside the ori-ficesontheplatehasbeenobserved(seeref.Orvalhoetal.,2009)).

3.3.1. Gas holdup

Fig. 7displays theinfluence ofNaCl concentration on thegas holdup forfixed gas superficial velocity (U G=0.065m/s) atthree

aspectratios (AR =5,7.5and10).InFig.7we haveclearly distin-guishedbetweenthe“coalescent flow regime ” (n ∗<1)andthe

“non-coalescent flow regime ” (n ∗> 1),throughthedimensionless concen-tration, n ∗,as definedin Eq. (2)and considering n t=0.145mol/l,

accordingtotheexperimentalstudyofZahradnı ´ketal.(1999)(as we have discussed in Section 2.1.2). In the “non-coalescent flow regime ”, a continuous increase of

ε

G while increasing the

elec-trolyte concentration has been observed: indeed, in this region, bubble coalescence is progressivelyreduced while increasing the electrolyte concentration. For better understanding this concept, the readershould refer to the previous literature concerning the effectsofelectrolyteson thebubbleproperties(i.e.,theliterature survey in Section 2.1.2) and, in particular,to the work of Firouzi etal.(2015),whohavesummarizedtheexperimentaldatarelating the percentageof coalescence to the concentration of NaCl. Tak-ingintoaccounttheliteratureconcerningtheeffectsofelectrolytes onbubblecoalescence(i.e.,thecoalescencebetweenbubblepairs) andinterfacialproperties(i.e., the liquidfilm drainage),the rela-tions between the bubbleproperties (the “bubble-scale”)and the gasholdup(the“reactor-scale”)canbeunderstood.Indeed,the re-ducedcoalescence rateshiftsthebubblesizedistributiontowards smallerbubbles:thesmallbubbles,havingapositiveliftcoefficient (Tomiyamaetal.,2002),spreadinthecross-sectionofthecolumn andreduce theliquid phase recirculation(Lucas et al., 2006; Lu-casetal.,2005)sothatnolargervorticitiesareexpected,thus in-creasing

ε

G.This concept is inagreement with ourexperimental

observations concerning ethanolnon-coalescing solution (Besagni etal., 2016b). Onthe contrary, inthe “coalescent flow regime ”, a plateauhasbeenobservedand,subsequently,anincreaseuntilthe maximumconcentration,atapproximately n ∗_{≈ 4,}wherethethree differentcurvesconvergetothesamevalueofthegasholdup, be-causeofthelimitin saltsolubility(see, forexample,ref. Haynes, 2014).Thisresultsupportstheexistenceofthedualeffectof inor-ganicactive compoundsonbubblecolumnfluid dynamics,as de-scribed by Orvalho et al. (2009). For a more detailed discussion concerningthe dualeffects inbubblecolumns,the readershould refertoref.Besagnietal.(2017).

Fig.7displaysthegasholdupcurvesforthedifferentaspect ra-tios(intherange5≤ AR ≤ 12.5)andthedifferentNaCl concentra-tions(in therange0.14< n ∗_{< 3.64,dependingonthe AR ). Fig.7a}

displaysthe experimental data (AR =12.5) presented in our pre-viouspaper (Besagni andInzoli,2015), whereas Fig.7b–ddisplay theexperimental dataobtainedin thisexperimental campaign.It isworth notingthat thedata obtainedinourprevious paper are slightlybelowtheactualmeasurements. Indeed,despitethegreat carein the experimentations, some factors may, ofcourse, affect the experimental results, especially in a large-scale experimental facility:(i) the quality ofwater may differ from day to day; (ii) minorresiduesofusedliquids;(iii)minorchangesinthe tempera-ture(thetemperatureiscontrolledwithintherangeof1K,Section 2.1.1), (iii). The gasholdup growscontinuously (and non linearly) whileincreasing theelectrolyte concentration(in agreementwith

RibeiroandMewes,2007;Zahradnı ´ketal., 1997),up toacertain value of the NaCl concentration (as also observed by Zahradnı ´k etal.,1999):thisvalueoftheNaClconcentration,isinagreement withthecriticalvalueof n t=0.145mol/l,previouslydefinedinthis

work. Please note that n t=0.145mol/l has been selected

follow-ingthestudyofZahradnı ´ketal.(1999)andhasbeenobtained us-ingconsideration fromcoalescencebehavior ofbubblepairs; cur-rently,thereisnoagreementofthegeneralvalueof n tanda

cer-tain variabilityaround thisvalue islikely tobe expected(Firouzi et al., 2015). However, it is clear that, the “bubble-scale” can be relatedto the bubble columnscale (the “reactor-scale”)by using the transitionconcentration, i.e., by using a theoretical approach asinEq.(2).Thenon-linearityoftheelectrolyteseffectupon the gasholdup,asdiscussedbyRibeiroandMewes(2007)andinour previouspaper(BesagniandInzoli,2015).Thenon-linearityofthe electrolyteseffectupon thegasholdup suggest thatthe fluid dy-namicsinbubblecolumnshavingabinaryliquidphasecannotbe