Generation and evaluation of an artificial optical signal based on X-ray measurements for bubble characterization in fluidized beds with vertical internals

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Delft University of Technology

Generation and evaluation of an artificial optical signal based on X-ray measurements for

bubble characterization in fluidized beds with vertical internals

Schillinger, F.; Schildhauer, T. J.; Maurer, S.; Wagner, E.; Mudde, R. F.; van Ommen, J. R.

DOI

10.1016/j.ijmultiphaseflow.2018.03.002

Publication date

2018

Document Version

Final published version

Published in

International Journal of Multiphase Flow

Citation (APA)

Schillinger, F., Schildhauer, T. J., Maurer, S., Wagner, E., Mudde, R. F., & van Ommen, J. R. (2018).

Generation and evaluation of an artificial optical signal based on X-ray measurements for bubble

characterization in fluidized beds with vertical internals. International Journal of Multiphase Flow, 107,

16-32. https://doi.org/10.1016/j.ijmultiphaseflow.2018.03.002

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International Journal of Multiphase Flow 107 (2018) 16–32

ContentslistsavailableatScienceDirect

International

Journal

of

Multiphase

Flow

journalhomepage:www.elsevier.com/locate/ijmulflow

Generation

and

evaluation

of

an

artiﬁcial

optical

signal

based

on

X-ray

measurements

for

bubble

characterization

in

ﬂuidize

d

b

e

ds

with

vertical

internals

F. Schillinger

a

_,

_T.J.

_Schildhauer

a,∗

_,

_S.

_Maurer

a

_,

_E.

_Wagner

b

_,

_R.F.

_Mudde

b

_,

_J.R.

_van

_Ommen

b

a Paul Scherrer Institut, PSI, 5232 Villigen, Switzerland

b Delft University of Technology, Van der Maasweg 9, 2629 HZ Delft, The Netherlands

a

r

t

i

c

l

e

i

n

f

o

Article history:

Received 22 October 2017 Revised 25 February 2018 Accepted 3 March 2018 Available online 6 March 2018

Keywords:

Bubbling ﬂuidized bed Measurement methods X-ray

Optical Bubble properties Monte Carlo simulation

a

b

s

t

r

a

c

t

The performanceoffluidizedbedreactorsstronglydependsonthe bubblebehavior,for whichreason knowledgeconcerningthebubblepropertiesisimportantformodelingand reactoroptimization.X-ray measurementscanbeusedtocharacterizebubbleswithinthecross-sectionofafluidizedbedona labo-ratoryscale,butcannoteasilybeextendedtohot,pressurizedlargescaleplants.Forfuturemeasurements athot conditionsinafluidizedbedmethanationreactor,wehavedevelopedanopticalprobingsystem thatcanbeemployedundertheseconditions.However,opticalsensorsareonlyabletoinvestigatethe localfluidizationpatternsatadefinedpositioninthebed.Theobjectiveofthisstudyistocharacterize differencesinbubblepropertiesbetweenlocalopticalmeasurementsandanX-raytomographymethod thatisabletodetectbubblesovertheentirecross-section.Therefore,anartificialopticalsignaliscreated outofexistinghydrodynamicX-raymeasurementdataobtainedatacoldflowmodel ofapilotscale methanationreactor.Thedeterminedbubblepropertiesofbothmethods (i.e.evaluationofthederived artificialopticalprobesignalandimagereconstructionbasedontheevaluationoforiginalX-ray tomo-graphicdata) arecomparedwithregardtothebubblerisevelocityand thebubblesize(forthe X-ray method)orpiercedchordlength(fortheopticalevaluationmethod),respectively.Thecomparisonshows thatfortheevaluationoftheopticalprobedata,statisticaleffects havetobeconsideredcarefully.The detectedmeanchordlengthoftheopticalmethoddoesnotimmediatelycorrespondtothemeanbubble sizedeterminedbytheX-raymethod.Moreover,alsodifferencesregardingthebubblerisevelocitywere detectedforsomefluidizationstates.Thereasonforthediscrepanciesbetweenbothmethodscouldbe identifiedandcorrected,amongstothersbymeansofaMonteCarlosimulationinwhichrisingbubbles inafluidizedbedweresimulatedandcharacterizedbyalocalvirtualopticalsensor.

1. Introduction

Thehydrodynamicsofaﬂuidizedbedhavetobeunderstoodfor aproperdesignandscale-upofﬂuidizedbedreactors.Forthis pur-pose, hydrodynamicpropertieslike the bubblehold-up, the bub-ble size or the bubble rise velocity (BRV) have to be measured. Awide rangeof different measurement techniques are available. Whichonesarepreferred,stronglydependsontheapplicationand therequired informationthat becomes accessibleby the individ-ualmeasurement techniques(Asegehegn etal., 2011; Rautenbach etal., 2013;van Ommen and Mudde,2007; Verma et al., 2014). Themeasurementtechniquescanbesubdividedintointrusiveand non-intrusive methods. Optical sensors are often used as

intru-∗ _{Corresponding author.}

E-mail address: tilman.schildhauer@psi.ch (T.J. Schildhauer).

sive probes since they are easy to construct, have a reasonable priceandtheirapplicationhasalreadybeenprovenforalongtime (Acosta-Iborra et al., 2011;Glicksman etal., 1987; Rüdisüliet al., 2012a; Whitehead et al., 1967). Due to their intrusive character, itcannot beexcluded that theflowpatterngetsdisturbed bythe sensor. To deal with thisissue, the influence of intrusive probes on the flow structure in fluidized bedsystems is investigated in Baietal.(2010),Maureretal.(2015a),Tebianianetal.(2015,2016), Whitemarshetal.(2016).Thepossibilitytodesignanoptical sen-sor ina way that the flow structure isalmost not influenced by the intrusive character ofthe sensor is shown in Maurer (2015), Maureretal.(2015a),andWhitemarshetal.(2016).

A significant drawback of optical probes is the fact that they only deliver local information of the fluidization state like the piercedchord length ofa bubbleinstead oftheentirebubble di-ameter. Expensive, non-intrusive methods,such asX-ray or elec-tricalcapacitancetomography,mayprovideinformationofthe flu-https://doi.org/10.1016/j.ijmultiphaseflow.2018.03.002

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idizationstateovertheentirecrosssectionandgather thebubble diameter, the hydraulic bubble diameter and the position of the center ofgravity(Maurer etal., 2015a).However, these measure-ment methods cannot be easily implemented at industrial scale (Liuetal.,2010).

If heat has to be removed out of the reactor in the case of exothermicreactions ortosupplyendothermicreactions withthe requiredamountofheat,aheat transfersystemwhichconsistsof averticalheatexchangertubeshastobeintegratedinsidethe re-actor.Forthecaseofhydrodynamicinvestigationsofcold-flow flu-idizedbeds,theverticalheatexchangertubesarereplacedby ver-ticalinternalswiththesamegeometry.Investigationsonthe influ-enceofverticalheatexchangertubesonthehydrodynamic behav-ior have already been conductedin (Maurer etal., 2016,2015b,c) andsimulationsbasedonatwofluidmodelinVermaetal.(2016). A new correlation for the bubble size and bubble rise velocity which considers the presence of vertical internalswas published inMaureretal.(2016).Thesestudieshaveshownthatvertical in-ternals stronglyinfluencethe bubbleproperties.Oneof themain findings wasthe fact that the bubble shape deviates to a larger extentfromasphericalshapeifverticalinternalsarepresent com-paredtoaconfigurationwithoutinternals.

If the geometry of the bubbles is known and can be de-scribed mathematically,methods toconvertthechord length dis-tribution of the pierced bubbles into a bubble size distribution of all bubbles exist in literature (Clark and Turton,1988; Rüdis-üli et al., 2012b; Santana and Macias-Machin, 2000). Moreover, Sobrinoetal.(2015) showedfora two fluid modelsimulationof a three-dimensionalbubblingfluidizedbed(BFB) withoutvertical internals thatthe pierced chord length distributioncan be confi-dentlytransferredintoanequivalentbubblevolumediameter dis-tributionbymeansofmathematicmethods.

However, thesemethods arenot suitableforsystemsinwhich the bubble shape cannot be describedby a simple mathematical equation as it isthe casefor the investigatedﬂuidized bed with verticalinternals.Inthescope ofthisstudy,the relationbetween thepiercedchordlengthandthevolumeequivalentbubble diam-eterbasedonexperimentaldataisinvestigatedfortheﬁrsttime.

At the Paul Scherrer Institute (PSI), an intrusive optical mea-surement systemwas developed todetect bubbles ina bubbling ﬂuidized bed reactor under hot, pressurized and reactive condi-tions for thecaseof a methanationreactor. It should be pointed out thatno X-raymeasurementswillbe available tomeasurethe hydrodynamicsundertheseconditions.

Themeasurementprincipleofanopticalsensorisbasedonthe reflectionof light by thebedmaterial. Laserlight is fed intothe opticalsensorwhichiscomposedofopticalfibers.Thelightenters the fluidizedbedattheprobe tip.Forthecasethat nobubbleis infrontoftheprobetip,lightisreflectedtoalargeextentbythe whitebedmaterial(Al2O3).Ifthereisabubbleinfrontofthe

sen-sorsignificantlylesslightisreflected.Theamountofreflectedlight is analyzedby a phototransistorthat generatesthevoltage signal whichisusedforfurtherevaluation.Themeasurementprincipleis schematicallydepictedinFig.1.

Theintentionofthepresentstudyistoworkout a methodol-ogytodescribetherelationofthebubblepropertiesthatare deter-minedbymeansofopticalmeasurementstothebubbleproperties that aredeterminedwithX-raymeasurementsforafluidized bed withverticalinternals.Basedontheseresults,futureoptical mea-surementscanbeinterpreted moreprecisely. Inordertocompare thebubble propertiesdeterminedby bothmethods,the datasets ofthe X-raymeasurementsare usedasbasis togeneratean arti-ficialopticalsignal. Bygeneratingafictitiousopticalsignal outof X-raydata,onecanensurethatthedatabasefortheevaluationof theopticalsignal isidenticaltothedatabasethatisusedforthe evaluationoftheX-raysignal.Asequentialperformanceofoptical

andX-raymeasurementscouldnotguaranteetheconditionof an-alyzingthesamefluidizationstate.AparallelperformanceofX-ray measurementsandopticalmeasurementsisnotpossiblesincethe opticalsensorwhichismadeoutofsteelinfluencestheX-ray sig-nal.Moreover,ifwe usedarealopticalprobeforthiscomparison, othereffects likethedisturbanceoftheflow patternby the opti-cal sensorcould notbe quantified. Hence,the generatedartificial opticaldatasetcorrespondstothesignalofavirtualandperfectly workingoptical sensorthat islocated atdefined positionsin the columnthathasnoinfluenceontheactualflowstructure.

Systematic differences between both methods concerning the determinedbubblesizeandthebubblerisevelocityweredetected inthescopeofthiswork. Byapplyingtheconclusionsofthis pa-per, it is possible to assess future results of hydrodynamic mea-surementsinbubblingfluidizedbedsforwhichonlyintrusive op-ticalmeasurements areavailable. Theunderlyingrawdatasets of X-raymeasurementswhichareusedforthisstudyareavailableas partofapreviousworkinacold-flowbubblingfluidizedbedthat hasbeenconductedinthescopeofMaurer(2015).Insummary,it canbestatedthattheexplicitgoalofthismethodologicalpaperis tocomparethe optical evaluationmethodwiththeX-ray evalua-tionmethodtodeterminethebubblepropertieswiththe particu-laritythatbothdatasetsoriginatefromtheidenticalmeasurement campaign. A detailed hydrodynamic characterization of bubbling fluidized beds withvertical internalsis shown inMaurer (2015), Maurer et al. (2016,2015b,2014), Schillinger et al. (2017) and is thereforenotinthefocusofthisstudy.

2. Theoreticalbackgroundofthetwo-phasemodel

The classical approach to describe the behavior of a bubbling fluidizedbedisthe twophasemodel whichisdepictedinFig.2. Theideaofthismodelistoseparatethetotalgasflowenteringthe column(u)intoapartthatflowsthroughthebubblephase(u_bub.)

andapartthatﬂowsthroughthedensephase(ud)(Davidsonand

Harrison,1966). Thelocal bubblehold-up

ε

B iscalculated by the

areathatiscoveredbybubblesdividedbythefreecross-sectionof thecolumn.

A more detailed theory was proposed by Grace and Clift (1974) who stated that the gas flow in the bubble phase can be further divided into the superficial gas velocity through the bubble phase (vb) which corresponds to the volume flow of

gas that rises in the form of bubbles with regard to the entire cross-sectionat onemeasurement height (seeEq. (1)) andinto a bubblethroughﬂow (utf). Abalance ofthe gasphase leadstoEq.

(2)(Gogolek andGrace, 1995). However, the bubblethroughﬂow isusuallynegligible.

v

b= ˙ Vb A (1) u=

v

b+

ε

but f+

(

1−

ε

b

)

ud (2)

Adimensionless parameter

ψ

(see Eq.(3)) was introduced in HilligardtandWerther(1985)todescribethedeviationofthe su-perficialgasvelocity through thebubblephase fromtheclassical two-phasetheory whichstatesthattheentiregasflowabove the minimumfluidization flowsthrough the bedintheform of bub-bles.

v

b=

ψ

·

u− um f

(3)

Theparameter

ψ

canbedeterminedbasedonacorrelation(see Eq.(4)) independenceofthe columndiameterdt andtheheight

abovethedistributorplatehforparticleswithGeldartB classiﬁca-tion.

ψ

=

₀_.₆₇ _h/_d t < 1.7 0.51·

h/dt 1.7< h/dt < 4 1 h/dt > 4 (4)

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18 F. Schillinger et al. / International Journal of Multiphase Flow 107 (2018) 16–32

Fig. 1. Measurement principle of the optical sensor.

Combination of Eqs. (2)and (3)and the informationgiven in Fig.2leadstoEq.(5)whichcanbeusedtocalculatethesuperﬁcial gasvelocitythroughthedensephase.Thebubblethroughﬂow(utf)

isneglected. ud= u−

ψ

u − um f

1−

ε

b (5) 3. Experimentalsetup

The experimentswere conductedinacold ﬂowmodelat am-bienttemperature andpressure.

γ

-Alumina inthe rangeof Gel-dartA/B (Werther, 2007) withaSautermeandiameterof289μm andaparticledensityof1350kg/m3_was_used_as_bed_material._Gas

distributionwasachievedbya poroussinteredmetalplatewitha thicknessof3mm andameanporesize of10μmsincethistype canalsobeusedathightemperaturesandunderpressure.The col-umnwasfilledwithbedmaterialuptoaheightof60cm.The min-imumfluidizationvelocityumfwhichcorrespondstosuperficialgas

velocityatwhichthebedbeginstoﬂuidizewasdeterminedtobe 3cm/sinRüdisüli(2012).Theﬂuidizationnumberu/umf standsfor

the ratio between the total gas velocity and the gas velocity at incipientﬂuidization.Round,square-arrangedinternalsareplaced insidethecolumnwithan inner diameterof22.4cmasdepicted inFig.3(a).Theseinternalsmimictheheatexchangertubesinthe investigatedcold-ﬂow model since they will be required for up-comingexperimentsina methanationreactor.The largerinternal tubeshaveadiameterof2cm,thesmalleroneswhicharecloseto themarginofthecolumnhaveadiameterof1cm.

Fig. 4 depicts a schematic drawing of the applied X-ray de-viceforhydrodynamicmeasurementsatthe column.The appara-tusis composed of three stationary X-raysources. The measure-ments were conducted at a X-ray energy of 150keV and a cur-rentof1mA.ThedetectionoftheX-raybeamstakesplacesattwo heightswithaverticaldistanceof4cm.At eachheight,three

de-tector sets are arranged in a circle around the column. Each de-tector setconsistsof 32detectorsthat are arrangedside by side. The average vertical distance betweenthe X-raybeams reaching thelower andtheupperdetectorset is18.2mm(15.5mmatthe inletof thecolumnand21mm attheoutletofthe column).The distancebetweenthesourceandthecolumncenterwas714mm. Thedistancebetweenthedetectorsetandthecolumncenterwas 532mm. The signal strength of each measurement point is con-vertedintoapathlengthoccupiedby airwithacalibrationfactor that wasdetermined by a seven point calibration.Adetailed de-scriptionoftheexperimental setupandthemeasuring devicehas alreadybeengiveninMudde(2011).

All X-raymeasurements were conducted for120s with a fre-quency of 2500Hz. X-ray measurements were completed at ﬂu-idizationnumbers (u/umf) of3, 4 and6 at two differentbed

lo-cationsofH=36cmandH=56cm. 4. Methodology

4.1. DeterminationofbubblepropertiesbasedontheX-ray evaluationalgorithm

TheprincipleoftheX-raymeasurementsisbasedonmeasuring theattenuation oftheX-raybeamsthrough thebedmaterial be-forethey reach thesingle detectorarrays. Theattenuation which ismeasuredateachdetectorarrayisconvertedintoapathlength occupiedbyairforeach detectorarray.The conversionfactor be-tweentheattenuationandthepathlengthoccupiedbyairisbased on a 7-pointcalibration. A detaileddescription ofthe calibration processisgiveninMaureretal.(2015c).

Themathematicalreconstructionoftheﬂuidizationstatebased on the X-ray measurements is conducted with a simultaneous algebraic image reconstruction technique (SART) (Andersen and Kak, 1984) that has already been applied to reconstruct images for the same measurement setup in Maurer et al. (2015c). The

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Fig. 2. Schematic view on the classical two-phase model.

presentmeasurementsetup enablesa resolutionof55× 55pixels for thereconstructed images. Three exemplary reconstructed im-ages of the non-threshold ﬁltered ﬂuidization state are given in Fig. 5 in which the location of bubbles is indicated by the grey areas.

TheapplicationoftheSARTalgorithmenablesasigniﬁcant re-ductionofthesaltandpeppernoisewiththedrawbackofahigher computational effort(Mudde, 2011). Fig. 6 shows the raw signal obtainedatonerandompixelinthe55× 55pixelpatterninwhich thebubbleeventscanbeclearlyseparatedbythedensephase.

Based on thisresolutionand thecolumndiameter of22.4cm, the dimension of a pixel is 0.4cm x 0.4cm. A variable pixel sizecannot beimplementedintheSARTimagereconstruction for which reasonthepositionofthe internalsandthemargin ofthe columnhavetobeapproximatedbypixelsofthesamesize.In to-tal,internalswithadiameterof2cmareapproximatedby21

pix-elsandinternals withadiameterof 1cmare approximatedby 5 pixelsintotal(seeFig.7).

The round column lies centrically in the quadratic array of 55_{× 55}pixelsasdepictedinFig.3(c).Ithastobementionedthat thepositioning of thesquare arranged internals istwisted by an angleof 4.9° towardsthe principal axis dueto geometrical con-straints in the measurement setup. To reduce the computational effort,themeanoftensucceedingmeasurementpointswastaken resultinginaneffectivemeasurementfrequencyof250Hz.

Theoutputoftheimagereconstructionprocessisamatrixwith thesizeof[55× 55× 30,000]elementsineachcasefortheupper and lower detector. The matricesinclude the information of the solidfractionforeachpixelasagreyscalebetweenzeroandone forall ofthe30,000timeincrementsatthecertain measurement height.

Forthefurtherdataprocessing,thethresholdofthesolid frac-tion wasset to 75%, a value that has alreadybeen used for the evaluationofX-raymeasurements inthescope ofMaurer (2015). Above this value, the matrix element is assigned to the dense phase,belowthethresholditisassignedtothebubblephase.This leadstoabinarymatrixfilledwithzerosandoneswhichincludes thecompleteinformationofthefluidizationstateduringthe mea-surementperiod.Anexamplepictureofthereconstructed fluidiza-tionstatewitharesolutionof55× 55pixelsforarandommoment intimeisshowninFig.3(b).Allwhitepixels(zeros)otherthanthe positionoftheinternalsare relatedtothebubblephase; allblack pixels(ones) to thedense phase.The positionof theinternalsas well asthe area outsidethe columnis set tozero per definition andexcluded from locating bubbles in the evaluation algorithm. It should be noted that the reconstructed fluidization state (see Fig.3(b)) is derived after applying a thresholdfilterto the grey-scaleimages(seeFig.5)inordertoobtaina binarysignal. Subse-quently,thebinarysignal oftheareainside thecolumninwhich nointernalsarelocatedisinverted.

Afterapplyingthethreshold,thebubblelinkingalgorithmscans thematrixofallconnectedstructuresforwhichtheelementshave thevalueofzero(bubblephase).Theoutershellofevery indepen-dent structure is assignedto a bubble. The shape of a bubble is notinﬂuencedbysomeelementsinsidewhichmaybeassignedto thevalue ofone (emulsionphase) since,forexample,ifparticles arepresentinsidethebubble.Therisevelocityofabubbleis cal-culatedbythe timespan,the centerofgravityneeds topass the lowerandupperdetectorarray.

Bymeansof thisprocedure,thevolume equivalentbubble di-ameterandthehydraulicbubblediametercanbedetermined.The smallest bubble size that can be reconstructed by means of the X-rayevaluationmethodisinﬂuenced bythe numberofdetector arraysand the diameterof the investigated column. The relative

Fig. 3. (a) Cross-section of the column, (b) exemplary reconstructed ﬂuidization state determined by X-ray measurements with overlayed internals, (c) overlayed 55 × 55 pixel pattern for generation of ﬁctitious optical signal (with evaluation path along the centerline of the column).

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Fig. 4. Top view and side view of the X-ray tomographic setup adapted from ( Maurer et al., 2015c ).

Fig. 5. Exemplary reconstructed and non-threshold ﬁltered images of the ﬂuidization state.

Fig. 6. Signal of grey scale plotted over time for a random pixel in the 55 × 55 patter.

accuracy of the SART reconstruction algorithm to determine the bubblesizereducestowardssmallerbubbles.Forexample,a bub-blewithadiameterof2cmcouldbedeterminedwithamaximum

Fig. 7. Approximation of the internals’ location by pixels with a size of 0.4 cm × 0.4 cm.

accuracy of± 25% and a bubble with a diameter of 10cm could bedetermined withamaximumaccuracyof_{± 5%}inMaurer etal. (2015c). The void fraction of smaller bubbles might be added to thevoidfractionoflargerbubblesinthebubblereconstructionfor which reason the average void fraction over the cross-section of thecolumnisquitepreciseafterthereconstructionalgorithmhas reachedconvergence.

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The image reconstruction based on the SART algorithm may also lead to artefacts that occur asapparent small bubbles since onlythreeX-raysourcesareused(Mudde,2010).Theoccurrenceof artefactscouldbe reducedbytheapplicationofafivepointX-ray source asinvestigatedinMudde etal.(2005).Toensure thatthe reconstructed bubbles do not originate froman artefact,all bub-bles witha chord length smaller than 1.5cm are excluded from further investigations. Although,it is evident that not every sin-gle bubblewith a chord length smallerthan 1.5cm is the result of an artefact,small bubbles are uncriticalconcerning the break-throughofreactants.Onegeneralpurposeofthisworkistofeeda two-phasecomputermodelwithexperimentaldataonthebubble behaviortopredict theconversionofa bubblingfluidized bed re-actor.Neglectingsmallerbubblesinatwo-phase computermodel of a bubblingfluidized bedreactor decreases the calculated con-version. Hence, the calculated conversion describes a worst case scenarioofabubblingfluidizedbedreactorwithoutsmallbubbles. Expectedly,theconversionofarealfluidizedbedreactorshouldbe higherthanthecalculatedconversion.

Higherresolutionscanbeachievedbyanincreasingnumberof detector arrayswhich also enablesthe detection ofsmaller bub-bles.FirstresultsgeneratedbyX-raymeasurements ataplate de-tector witharesolutionof roughly1500_{× 1500}pixelsinthe ver-ticaldirectionare presentedinGomez-Hernandezetal.(2016).A furtherinstallationofadditionalplatedetectorswouldenablea di-rect 3-dimensionalimagingof thebubbles.An algorithm to eval-uatethebubblepropertiesresultingfrom3-dimensional hydrody-namicmeasurementsispresentedinBakshietal.(2016).This algo-rithmshowstheadvantagethatbubblescanbetrackedalongtheir trajectories and smaller bubbles are detected with an increased likelihood.

4.2. Determinationofbubblepropertiesbasedontheoptical evaluationalgorithm

The matrix obtained by the X-ray tomographic reconstruction algorithm (SART)is thebasis to createan artificialoptical signal. The entire information on the fluidization state at the measure-ment height is storedin thismatrix. Therefore, trackingone po-sitioninthe matrixovertime correspondstoa perfectlyworking virtualopticalsensorwhichisinsertedintothecolumnwithout in-fluencingtheflowstructure.Theopticalsignalsequencewas sam-pled ateach pixelalong theevaluationpath separately asshown inFig.3(c).

Togain the bubbleproperties,itis necessarytoevaluate both the signal ofthe lower andupper measurementplane. The eval-uation stepto assigna signalpeak ofabubblewhich isdetected atthelower sensortothecorrespondingsignalpeakoftheupper sensor isnamed thebubble linkingstep. The averagedistanceof 18.2mmfortheX-raybeamsthat reachthe lowerandupper de-tectorarraysisusedasverticaldistance_࢞sinEq.(6).Bymeansof thetimedifference࢞tbetweentheexceedanceofthethresholdat thelowerandtheuppersensor,thebubblerisevelocityubcanbe

calculatedaccordingtoEq.(6).Sincetherangeofthevertical sep-aration forX-raybeams that reach thelower andupper detector arraysisbetween15.4mmand21mm(seeFig.4),theuncertainty concerningthedetermined bubblerisevelocity maybe upto18%

ub=

s

t (6)

Thechordlengthofabubbleiscalculatedastheproductofub

and thegapless time periodbelow thethreshold t_b asshownin Eq.(7).

dchord= ub· tb (7)

Fig. 8. Effect of filter application on signal for an exemplary time interval at the lower measurement plane for a fluidization number of 6 and a measurement height of 36 cm. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Adetailedproceduretocharacterizebubblesonthebasisof op-ticaldataisshowninMaurer(2015),Rüdisülietal.(2012a).Fig.8 showsan excerpt of a binarysignal (thin black line) which was acquiredby placing the fictitiousprobe tip on a certain pixel of the reconstructed X-ray signal and scanning its value over time. Usually,optical measurements donot provide a binarysignal for whichreasonathresholdmustbedefinedtodeterminewhenthe passageofabubblestartsandends.Theadjustmentofa represen-tative thresholdfor optical signals was investigated inthe scope ofRüdisülietal.(2012a).However, thegeneratedfictitiousoptical signal is binarysince the selected thresholdof 0.75 wasalready appliedduringthe reconstructionof theX-rayimages.Again, the valueofone isassignedto theemulsionphase;the valueofzero representsabubble.

The excerptshows severalevents of a signal rise back to the valueofoneforonlyafewtimeincrementsduringaperiodofzero values.Hence, itmightbeassumedthatthissignalchangeshows twoseparaterisingbubblesinaveryshortdistancetoeachother. However,itshouldbeconsideredthatthemeasurementfrequency is250Hzsoonetimeincrementonlycoversfourmilliseconds.

Forcomparableexperimentalconditions,atypicaltimegap be-tweentwobubblesthataredetectedbyanopticalsensorisinthe rangeof one and two seconds which corresponds to bubble fre-quencyof 30–60 bubbles per minute depending on the ﬂuidiza-tionnumberandthemeasurementheight (Rüdisüli etal., 2012a). Hence,it seemsvery unlikelythat twobubbles followeachother in a time period of only a few milliseconds without having co-alescedbefore. It can therefore be assumedthat a signal change fromzerotooneforatimeperiodofonlyafewmilliseconds be-longs to the same bubble. This signal change may be causedby alocallyhigherparticleconcentrationinsidethebubbleordueto artefactsthataregeneratedinthebubblereconstructionprocess.

Sudden changes of the signal for a few time increments like theyareshowninFig.8haveagreatinﬂuenceonthebubble prop-ertiesdetermined with theoptical evaluation. Theyinterrupt the gapless timeperiod tb below thethresholdand thereforelead to

muchshortereffectivechord lengths.Toobtainrepresentative re-sults,a filter hasto be applied to smooth the misleadingevents forwhichthesignalswitchesitsvaluefromzerotooneforonlya fewtime increments.Thefiltercanbe adjustedby themaximum numberofconsecutivetimeincrementsthat canbesmoothedfor thecasethatthebinarysignalswitchesitsvaluefromzerotoone. Onetimeincrementcorrespondstoatimeperiodof1/250s. Sub-sequently,the maximumnumber ofconsecutive time increments thatcan besmoothed bythe filtercorresponds to thenumberin bracketse.g.filter(5)orfilter(10).InFig.8,thethick yellowline (filter(5))andthickgreenline(filter(10))showtheeffectofa fil-terwhichisabletofilteroutsuddenchangesinthesignalofupto

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Fig. 9. Data processing scheme.

fiveorrespectivelytenincrementsoftime.Itshouldbementioned thatthemaximumtimegapthatcanbefilteredoutwithfilter(10) correspondsto40ms,hence,atooseverefilteringisnotexpected. A flowdiagram that showsthe singlestepsto generatean ar-tificialopticalsignaloutoftheX-raymeasurements isdepictedin Fig. 9. The determined bubble propertiesby the optical and the X-rayevaluationalgorithmcannowbecomparedandpossible de-viationsofthebubblepropertiesbediscussed.

5. Resultsanddiscussion

In this chapter, the artificial optical signal is used to deter-minethebubblerisevelocityandthepiercedchordlengthateach pixelalongtheevaluationpathpresentedinFig.3(c).Theobtained resultsare compared with available results from X-ray measure-ments in order to elaborate andfind the reasons for the differ-encesinthe determinedbubble propertiesby bothmeasurement methods.The impactoffilteringthefictitiousoptical datais eval-uatedandan annulusweighting ofthebubblepropertiesthatare determinedbythefictitiousopticalsignalisintroducedinorderto obtainastatisticallypropermean.

5.1.Inﬂuenceofﬁlterapplicationonopticaldataevaluation

Tolinkabubblesignalofthelowersensortothecorresponding signaloftheuppersensor,thethresholdexceedance atboth sen-sorshastobewithinadefinednumberoftimeincrementswhich dependson the measurement frequency, the vertical distance of thelower andupper optical sensorandthe minimumdetectable bubblerise velocity. A detaileddescription of the bubble linking algorithmis giveninRüdisüli etal. (2012a). Arepresentative ex-cerpt ofthe binaryartificial optical signal is shown inFig. 10 in whichsomecharacteristiclinkableandnon-linkablebubbleevents arevisibleforafilteredsignal.

As discussedintheprevious section,singlesuddenchanges of thesignalhaveaninfluenceonthe bubblepropertiesdetermined by the optical evaluationmethod. In the following,filters of dif-ferentstrengths are compared withtheoriginal, unfiltered signal toquantify theeffectof thefilteron thefractionand numberof linkedbubbles aswell asits influenceon themeanchord length and the mean bubble rise velocity. A description how the filter worksisgivenintheprevioussection.Theevaluationofeachpixel

Fig. 10. Characteristics of bubble linking for a ﬁltered signal.

Fig. 11. Inﬂuence of ﬁlter strength on annulus weighted (see Section 5.2 ) fraction of linked bubbles for a measurement height of 56 cm.

alongthecenterline (seeFig.3(c))provides thedatabasisforthe opticalevaluationthatispresentedinthesubsequentﬁgures.The depictedpointscorrespondtothemeanvalueofalldetected bub-blesalongtheevaluationpath.

Theinfluenceofthefilterapplicationonthefractionoflinked bubbles isshowninFig.11.The fractionoflinked bubblesis de-finedbythetotalnumberoflinkedbubblesdividedbytheamount of all threshold exceedances for the lower sensor. Hence, it de-creaseswithan increasing numberofsudden changesinthe

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sig-Fig. 12. Influence of filter application on mean chord length (a) and mean bubble rise velocity (b) for different fluidization numbers at a measurement height of 56 cm.

nalofthelowersensor.Thisisduetothefactthat inmostcases, sudden changes appear inonly one ofthe two signals,since, for example,abubbleshowsatemporarilyandpartiallyhighfraction of densematerial whichis onlydetected by one ofthe two sen-sors.Bytheuseofaﬁlterthatscansaminimumofsixsuccessive time incrementswhich corresponds toa time spanof24ms ata frequency of 250Hz, a fraction of atleast 60% linked bubbles is reachedforallﬂuidizationstates.

The increase can be attributed to the fact that some sudden changes ofthesignalastheyare showninFig.8areﬁlteredout. Hydrodynamicinvestigationsonabubblingﬂuidizedbedwith ver-tical internals have shown that bubbles do not rise exactly in a verticalline(Schillingeretal.,2017). Duetobubblesrisingwitha lateralmovementcomponent,itmayhappenthatthesamebubble isnotpiercedbyboththelowerandtheuppersensor.Asa conse-quence ofrising bubbleswitha lateraldisplacement,thefraction oflinkedbubblescannotreach100%.

The influence ofthe filterstrength on themean chord length fora measurementheight of56cm isshowninFig.12(a).As ex-pected,themeanchordlengthriseswiththeapplicationofafilter. Ifafilterisapplied,thefilterstrengthhasaminorinfluenceonthe chordlengthexceptforthehighestfluidizationnumber.Thiscould beexplainedbythefactthatthesignaldurationoflargerbubbles isingenerallongerforwhichreasonalsolongertimeperiodswith asignalrisefromzerotoonemayoccur.Hence,thelongersudden signalchangescanonlybeflattenedwithastrongerfilter.

Fig.12(b)depictsthe influenceofthefilteronthebubblerise velocity. It becomes apparent that the effect ofthe filteron the BRVatlowerfluidizationnumbersisingeneralnotaspronounced as it is the case forthe chord length. This can be explained by the fact that in general, the time difference betweenthe bubble detectionattheloweranduppersensorwhichdeterminestheBRV isnot influencedby thefilter.However,forafluidizationnumber of six, the application ofa filterleads to a decrease ofthe BRV. Thisimpliesthat filteringout “wrongly” linkedbubbles decreases the determined bubble rise velocity since the bubblelink of the filtered signal is switched to the next eventresulting in a lower BRV.

5.2. Weightingofdatageneratedbyopticalevaluationmethodbased onannulusarea

Forlocalopticalmeasurements,itshouldbenotedthat the re-sultofameasurementposition closeto thecenterofthecolumn hasa muchlower contributiontothe overallmeanvalue (dueto thesmallerarea oftheannulusthatcorresponds tothe measure-mentposition)comparedtomeasurementpositionsthatareclose tothewallofthecolumn(seeFig.13).Itisthereforenecessaryto

Fig. 13. Schematic principle to weight the single optical measurement position to a mean value.

weight the singlemeasurement pointsto get a reasonable mean valuefortheentirecross-section.

Thecontribution ofthe determined meanbubble risevelocity ofevery singlemeasurement point (represented by the blue cir-clesinFig.14)tothemeanweightedchordlengthofall measure-mentpositions (dashedbluelineinFig.14) dependsontheratio betweentheareaoftheannuluswherethemeasurementposition islocatedtothetotalcross-sectionalarea.Althoughthevertical in-ternalsdisrupttheannulusuniformity,thismethodwasselectedto weightthesinglemeasurement pointssince itﬁllsout theentire column. A weighting of the single measurement pointsby areas ofrectangularringscouldnotcompletelycoverthecircular cross-sectionofthecolumn.Asaﬁrstapproximation,itisassumedthat thefractionoftheareawhichiscoveredbyinternalsisthesamein eachannulus.Largerdeviationstothisapproximationapplytothe innermostannuli.However,their contributiontothe overall aver-ageis negligible due to the smallarea ofthe innermost circular rings.

Sincethere arealways two measurement positionsin one an-nulus, the averageof both measurement positions isrelevant for thecalculationofthemeanvalueovertheentirecross-section.For example,todeterminethecontributionofthethirdinnermost an-nulusinFig.13tothemeanvalue,theaverageofthemeasurement positions C1 and C2 is calculated and in the next step weighted

bythe area ofannulus“C” relative tothe totalcross-section.The principleofthe“annulus” weightingisappliedinSections5.3and 5.4for theoptical evaluation method tocalculate the meanBRV andthemeanchordlengthdepictedinFigs.14and18.Forthe in-vestigatedsystemwitharesolutionof55× 55pixels, the weight-ing is conducted over 27 circular rings. Unlike the data analysis withanartiﬁcialopticalsignal,theX-raymethoddirectlyprovides bubblepropertiesforthe entirecrosssection ofthebubbling ﬂu-idizedbedforwhichreasonanannulusweightingisinappropriate.

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Fig. 14. Mean BRV from X-ray evaluation (solid line) and mean annulus weighted BRV from optical evaluation (dashed lines). Each radial measurement point matches with the mean BRV of the corresponding pixel on the evaluation path in Fig. 3 (c). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

5.3.ComparisonofbubblerisevelocitybetweenopticalandX-ray evaluationmethod

Iftheshapeofabubbledoesnotchangebetweenthelowerand upperdetectorarray,itisexpectedthatboth theX-rayevaluation methodaswell asthe evaluationby means ofthe artiﬁcial opti-calsignal resultinthe samebubblerise velocity.Thishypothesis isbasedonthefact thatthe timedifference ࢞twhichisused to calculatethebubblerisevelocityisthesame,irrespectivewhether thebeginning of the bubble(optical evaluation) orthe center of gravity(X-rayevaluation)istakenasreferencepoint(seeEq.(6)). However,itturnedoutthatstatisticaleffectshavetobeconsidered carefullyif X-ray results are compared with results from optical measurementsasitwillbeshowninthissection.

For a measurement height of 56cm andfluidization numbers ofthreeandsix,Fig.14showstheBRVcalculatedonbasis ofthe filteredand unfiltered optical signal in dependence of the radial measurement positions along the evaluation path (see Fig. 3(c)). Furthermore,themeanannulusweightedBRVoftheoptical eval-uation and the mean BRV of the X-ray evaluation are depicted. Toobtain comparable results,the BRV whichis based on the X-rayevaluationonlyincludestheverticalvelocitycomponentsince thefictitiousopticalsensorcannot detectthelateralvelocity com-ponent ofrising bubbles. For a fluidization numberof three,the meanbubblerisevelocityoftheopticalfilteredsignalalmost cor-respondstothemeanbubblerisevelocitydeterminedbytheX-ray evaluation.Fora fluidizationnumberofsix, itisnotable that the X-rayevaluationresultsinahighermeanBRVcomparedtothe op-ticalevaluationofthedata.Asmentionedabove,asignificant dif-ferencebetweenthemeanvelocitiesdeterminedbybothmethods wasnot expectedforwhichreasonthe interpretationofthe data ischallenging.

Anexplanationforpossiblediscrepanciescouldbethefactthat bubblesofvarioussizesmayhaveadifferentmeanbubblerise

ve-locity dependingon the ﬂuidization numberu/umf and the

mea-surementheight.Fig.15(a)showsthenumberofbubblesclassiﬁed by their volume equivalent bubble diameter (db.vol.eq.) and their

bubble rise velocity determined by the X-ray evaluation method fora measurement height of56cmanda ﬂuidization numberof three.Fig.15(e)showsthemeanhorizontalcross-sectionalareaof thebubblesinthecorrespondingsizeintervalofthevolume equiv-alentdiameter.The largerthebubbles areextendedinto the hor-izontal directions,the morelikely they are pierced by an optical sensor.Fig. 15(g)showstheprobability ofa piercedbubbleto lie within a certain interval of the volume equivalent diameter. The probability iscalculatedastheproductofthe meancross-section andthe number ofbubbles in the corresponding size interval of the volume equivalent diameterdivided by the absolutenumber ofdetectedbubbles.

Forameasurementheight of56cmandaﬂuidizationnumber of three, the BRV determined by the optical evaluation method almost corresponds to the BRV determined by the X-ray evalua-tion method as presentedin Fig. 14(a) since the meanBRV (see Fig.15(c))inthesizeintervalswithahighpiercingprobability(see Fig.15(g))doesnotvarytoalargeextent.

However,forameasurementheightof56cmandafluidization numberofsix,theopticalevaluationresultedinalowerBRV com-paredtotheX-rayevaluation(seeFig.14(b)).Thisfindingcannot only been explained by the results shown in Fig. 15(b) and (d) since thenumber basedmean BRVin each interval isnot signif-icantly belowthenumber basedmeanBRV ofall bubbles. Hence thequestionariseshowtheopticalmeasurement methodcan re-sultinalowerbubblerisevelocitycomparedtotheX-raymethod? Inordertofindanexplanation,therelationbetweenthe probabil-itytopierceabubbleinacertainsizeintervalandthe correspond-ingbubblerisevelocityhastobeinvestigated.

Sincethelargerbubblesaremorelikelytobepiercedbyan op-ticalsensor(see Fig.15(h)),the lowermeanBRV ofbubbleswith

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Fig. 15. Classiﬁcation of the number of bubbles by their volume equivalent diameter and their velocity (color) based on the X-ray evaluation method at a height of 56 cm for ﬂuidization numbers of three and six.

a larger size showsa disproportionately high contributionto the mean BRV determined by the optical sensor. Hence, the optical evaluationmayresultinalowermeanBRVthantheX-ray evalua-tionforameasurementheightof56cmandaﬂuidizationnumber ofsix.

This discrepancy can be further explained by a scatter plot of the bubble rise velocity and the mean cross-section of each detected bubble shown in Fig. 16 for a ﬂuidization number of six anda measurement height of56cm.The cross-section is de-ﬁned by a horizontal cut through the bubbles. The bubbles with a high BRV tend to havea lower cross-sectional area and there-fore a lower probability to be pierced. Inversely, bubbles with a

largecross-sectionalarea(highpiercingprobability)tendtoshow alowerBRV.Hence,itcanbeexplainedwhytheoptical measure-mentmethodleadstoalowernumberbasedmeanbubblerise ve-locitycompared to the X-ray evaluationmethod (see Fig. 14(b)). Thetrendtowardslower bubblerisevelocitiesforbubbleswitha largerhorizontal cross-sectionalarea could be explainedby their increasedﬂow resistance compared to slender bubbles that have topushasidelessbedmaterialwhileascending.

Forfuturemeasurementcampaignsthat are basedonlyon lo-cal optical measurements, itshould be considered forwhich set-tingsthe determined bubblerise velocityhas tobe corrected.As ageneraltrendtowardshigherﬂuidizationnumbers,itturnedout

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Fig. 16. Scatter plot of BRV and the corresponding mean cross-sectional area for all detected bubbles at a measurement height of 56 cm and a ﬂuidization number of six.

Fig. 17. Ratio of bubble rise velocity determined by optical evaluation method to X-ray evaluation method for measurement heights of 36 cm and 56 cm and ﬂuidiza- tion numbers of 3, 4 and 6.

thatthebubblerisevelocitydeterminedby theopticalevaluation islowerthan therise velocityofall bubbles thatis measuredby theX-rayevaluationasdepictedinFig. 17whichshowstheratio ofthe mean bubble rise velocity determined by both evaluation methods.Thisismostprobablyduetothefactthatthenumberof slugsincreasestowards higherﬂuidizationnumberwiththe con-sequencethat theslugswhichhavealargecross-sectionalarea in thehorizontaldirectionandatthesametimealowbubblerise ve-locityarepiercedmorelikely.Fig.17canbeusedasanassistance tocorrectthebubblerisevelocityoffutureopticalmeasurements inacolumnwithverticalinternalsforsimilarconﬁgurations.

5.4.ComparisonofthebubblesizebetweenopticalandX-ray evaluationmethod

Fig. 18 showsthe chord length ofthe optical evaluation with andwithout applicationof a ﬁlterforall pixels along the evalu-ation path (see Fig.3(c)) at a measurement height of 56cm and ﬂuidization numbers of four and six. It emerges that the chord lengthatanysinglepixelissmallerthanthemeanvolume equiv-alentbubblesize ofthe X-rayevaluation. Ingeneral, the annulus weightedchordlengthisupto25%smallerthanthemeanvolume

equivalentbubblesizedeterminedbytheX-rayevaluation.Atﬁrst glance,thisﬁndingseemsnottobeinaccordancewiththeresults that are presented in the study of Rüdisüli et al. (2012b) which statedthatthemeanchordlengthalmostcorrespondstothemean bubblediameterforthecaseofsphericalbubblessincetheerrorof piercinglargerbubblesiscompensatedbythefactthatabubbleis oftennotpiercedclosetoitsvolumeequivalentdiameter.

However, forthe presentstudy, there maybe different expla-nations forthis apparent discrepancy to the resultspresented in the scope of Rüdisüli etal. (2012b). Due tothe evaluation along thecenterlineasshowninFig.3(c),thesamebubbleispiercedat severalradialpositionsbytheﬁctitiousopticalprobeasvisualized schematicallyforasphericalbubbleinFig.19.Therefore,the ﬁcti-tious opticalsensordoesnotpiercea lotofbubbles nextto their volumeequivalentdiameterbutratherapartfromtheir centerline resulting in a lower mean chord length compared to the actual volumeequivalentbubblediameterwhichisdeterminedbythe X-ray method.The statistical meanexpectation value for thechord lengthofarandomlypiercedbubbleatvariouspositionsis2/3of thebubblediameterifthebubblehasaperfectlyroundshape.This valueisbasedontheratiobetweenthevolumeofaspheretoits projectedarea(Sjöstrand,2003).

InFig.20,thedeterminedchord lengthdistributionforthe ar-tificial optical signal along the centerline of the columnis com-paredwiththedistributionofthevolumeequivalentdiameterover theentirecross-sectionatameasurementheightof56cmfor flu-idizationnumbersoffourandsix.Thevolumeequivalentdiameter distributionforafluidizationnumberofsix(seeFig.20(b))shows a second peak atadiameter between10and17cm,whereas, no second peak isdetectable forthe samedistribution ata fluidiza-tionnumberoffourasdepictedinFig.20(a).Forbothfluidization numbers,thechordlengthdistributiondecreasesmonotonically to-wardslargersizes.

The different shape of the chord length distribution and the bubble volume equivalentdiameterdistribution for a fluidization numberofsix(seeFig.20(b))canbeexplainedduetothe forma-tionofslugswhicharevisibleinFig.21(b).Thepresentedbubble images are a quasi-3-dimensional reconstruction of the fluidiza-tionstate sincetheverticalaxiscorresponds tothetime. Bubbles rising with the mean bubble rise velocity are neither elongated norshrunkeninthisillustration.However,bubblesthatareslower thanthemeanrisevelocityappearasapparentlyelongatedinthe vertical directioninthe graphicalpresentation ofthe fluidization statedepictedinFig.21,although,theiractualshapeismuch flat-ter.An apparent elongation especiallyapplies to slugs since they areslowerthanthemeanbubblerise velocity(see.Fig.15(b)and (d)) forwhichreason some bubblespresented inFig.21(b)seem tobeelongatedintheverticaldirection.

Aslugthat covers the majorityofthe cross-sectionexhibits a high volume that is determined with the X-ray evaluation, and thereforeresultsinalargevolumeequivalentdiameter.Conversely, piercingaslugthatisshrunkintheverticaldirectionwiththe fic-titious optical sensor does not necessarily lead to a large chord length, for which reason there is no second peak in the chord lengthdistribution.Forafluidizationnumberofthree,thebubbles are significantly smaller as depicted inFig. 21(a).Hence, no fur-therpeakforbubbleswithasizebetween13and19cmispresent for the volume equivalent diameter distribution. For the reasons mentioned above, great caution should be exercised in draw-ing conclusions on bubble propertiesif the bubble size is deter-mined with differentmeasurement respectively evaluation meth-ods.Hence,statisticalmethodslikeaMonteCarlo(MC)simulation couldbeanoptiontorevealthereasonsforthediscrepancyinthe bubblepropertiesderivedby theoptical andtheX-rayevaluation method.

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Fig. 18. Mean bubble size from X-ray evaluation (green dashed line) and mean annulus weighted chord lengths from optical evaluation (red and blue dashed lines). Each radial measurement point matches with the mean chord length of the corresponding pixel on the evaluation path in Fig. 3 (c). (For interpretation of the references to color in this ﬁgure legend, the reader is referred to the web version of this article.)

6. MonteCarlosimulation

In this section, the results of a Monte Carlo (MC) simulation are presented inorder toinvestigate thequestion: “Which chord length distribution does a perfectly working local optical sensor determinecomparedtothevolumeequivalentdiameterofall bub-blesinthecolumn?” Moreover,theMC-simulationisusedto iden-tifythereasonsforthegapbetweenthebubblepropertiesderived bytheopticalandtheX-rayevaluationmethod.Theprocedureand the results of the MC-simulation are described in the following sections.

Rising bubbles in a ﬂuidized bed are simulated withthe aim togenerateanundisturbedsignalofanartiﬁciallocaloptical sen-sor. This signal is used to determine the bubble properties with

thestandardalgorithmtoevaluateanopticalsignal(Rüdisülietal., 2012a).Thederivedbubblepropertiesarecomparedtothe proper-tiesofallbubblesthatweregeneratedintheMonteCarlo simula-tion.

6.1. PrincipleandprocedureoftheMonteCarlosimulation

Fig.22showstheschematicprocedureoftheconductedMonte Carlosimulation.Inthefirststep,alogarithmicnormaldistribution isfittedbothonthebubblerisevelocityandthevolumeequivalent bubblediameterdistributionofthebubblesthatweredetermined byX-raymeasurementsinthescopeofMaurer (2015).The distri-butionswerefittedforallsixcombinationsbetweenthe measure-mentheightsof36and56cmandthefluidization numbersof3,

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Fig. 19. Visualization of mean chord length for a bubble pierced at various positions by the ﬁctitious optical sensor and the volume equivalent bubble diameter (X-ray method).

4and6.Hence,eachrunoftheMonteCarlosimulationwas con-ductedseparatelybasedonthecorrespondingrandomparameters forthesimulatedmeasurementheightandﬂuidizationnumber.

In a bubbling fluidized bed with vertical internals, the bub-blesmay be restricted in their shape dueto the presence of in-ternals in the column. This leads to a broad spectrum for the shape of the bubbles as pointed out in Maurer et al. (2015b), Schillingeretal.(2017).Anexemplaryexcerptofthereconstructed bubblesisdepictedinFig.23whichshowsthat thebubbleshape can be manifold. Hence, in the scope of the Monte Carlo simu-lation, the geometry of the bubbles has to be approximated by a shape that may cover the broad range of possible shapesthat are present in a real bubbling fluidized bed. Ellipsoidal bubbles werechosensincetheirgeometrycanbedescribedmathematically andtheir shape ismostlikelyrepresentingbubbles inafluidized bedwithverticalinternals.The bubbleellipsoidsweredefinedby thediameterd1inbothhorizontaldirectionsofthesimulated

col-umnandtheindependentdiameterd2intotheverticaldirectionof

thecolumnDuetotheindependentdeterminationoftherandom numbersfor thevertical andhorizontal diameters ofthe bubble, the ellipsoidalbubble shape maybe pronounced to a greater or lesserextent.Nexttothesimulationofellipsoidalbubbles,a

sepa-Fig. 21. Reconstructed bubbles at H = 56 cm for ﬂuidization numbers of 3 and 6 based on X-ray measurements.

rateMonteCarlosimulationwasconductedforperfectlyspherical bubbleswhichshouldrepresentthetheoreticalcase.

Intotal,theriseof5000individualbubbleswithafrequencyof 10bubblespersecondwassimulatedforeachsetting.Thestarting point ofabubble wasselectedrandomly acrossthe cross-section of the column. After a bubble is generated atthe bottom of the simulatedcolumn, thevelocityandthesize ofthisbubblestayed constant along the height of the column. The simulated column hasadiameterof22cmandaresolutionof5pixelsper cminall dimensions.

The volume of a rising bubble in the simulation is described bythevalue ofone,whereas,thecellswherenobubbleislocated havethevalue ofzero.The ﬁctitioussensorsamplesthevalue of thecellthatislocatedinthecenterofthecolumnatheightsof15 and16cm.Ifabubblereachesthecellswherethesamplingtakes place,the value of thiscell changes fromzero toone aslong as thebubbleispresentinthecorrespondingcell.

Fig. 20. Histograms of the chord length distribution for the ﬁltered artiﬁcial optical signal and the volume equivalent diameter (above the entire cross-section) for the X-ray evaluation at H = 56 cm and u/u mf = 4 and 6.

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Fig. 22. Schematic procedure of the Monte Carlo simulation.

Fig. 23. Quasi 3-dimensional reconstruction of the bubble shape for a ﬂuidization number of 3 at a measurement height of 36 cm by means of X-ray measurements. The vertical internals are not visualized. Picture adapted from ( Maurer, 2015 ).

In the next step, the chord length andthe bubble rise veloc-ityare determined by means ofthe optical evaluationalgorithm. These properties can now be compared to the properties of all bubblesthatweregeneratedinthescopeofthesimulation.

6.2. ResultsofMC-simulationforsphericalbubbles

For spherical bubbles, Fig. 24 shows the bubble size and the bubble rise velocity distribution of all simulated bubbles (input) compared to the distributions determined by the optical evalua-tion.The resultsforthe sphericalbubblesareingoodaccordance withtheworkofRüdisülietal.(2012b)whostatedthatthemean chordlengthdeterminedbyanopticalsensorroughlycorresponds to the meandiameter ofthe underlying bubblesize distribution. Thisisduetothefactthatalocalopticalsensorpiercesmorelikely largerbubblescomparedtosmallerbubbles,whereas,thebubbles areoftennotpiercedwithachordlengththatisclosetothe diam-eter.However,theworkofRüdisülietal.hasfocused onthe sim-ulationofsmallerbubbles forwhichreasontheremightbe slight deviationsto thepresentwork.As expected,the BRVdistribution determinedbytheopticalevaluationcorrespondsalmostexactlyto theBRVdistributionofallsimulatedbubbles.

6.3. ResultsofMC-simulationforellipsoidalbubbles

Forbubbleswithanellipsoidalgeometry,Fig.25(a)presentsthe distribution of the volume equivalent diameter for all simulated bubblescompared tothechordlengthdistribution determinedby the local optical measurement. In contrast to the simulation of spherical bubbles, it turns out that thechord length distribution isshiftedtowards asmallersizecompared tothevolume equiva-lentdiameterdistributionofall simulatedbubbles.Thisresultsin ameanchordlengthwhichisroughly25%smallerthanthemean inputdiameterofallbubbles.

The emerging gap between the mean chord length and the mean volume equivalent bubble diameter may be explained by the ellipsoidalbubblegeometry.If thebubblediameterd1 inthe

horizontaldirectionis largerthan thediameter d2 in thevertical

direction, the pierced chord length of an ellipsoidal shaped bub-ble issmaller than thevolume equivalentdiameter ofthe

corre-Table. 1

Factor X to correct the mean chord length for ellipsoidal shaped bubbles. Height [cm] 36 36 36 56 56 56 u/umf [-] 3 4 6 3 4 6 X = d¯Chord,optical ¯ dVol.eq.,input 0.73 0.7 0.71 0.73 0.77 0.74

sponding bubble.On the other hand,if an ellipsoid is elongated in the z-direction, the chord length maybe larger than the vol-umeequivalentdiameter.However,bubblesofacertainvolumeV

thatareelongatedinthehorizontaldirectionaremorelikelytobe piercedthanbubbles ofthe samevolumeV thatareelongated in thevertical direction. The differentpiercing probabilities of hori-zontallyandverticallyelongatedbubblesexplainthegapbetween themeanchordlength oftheopticalevaluationtothemean vol-umeequivalentdiameterthatarebothmarkedinFig.25(a).

Fig.25(b)showsthebubblerisevelocitydistributionforthe in-putandtheopticalevaluation.Asexpected,thebubblerise veloc-itydistribution thatisdeterminedby theopticalsensorisalmost identicaltotheBRVdistributionofallsimulatedbubbles.

Basedonthe resultsoftheMonteCarlosimulation,a factorX isdefinedthatdescribestheratiobetweenthemeanchordlength determinedbyan opticalsensorandthemeanvolumeequivalent diameter of all bubbles withan ellipsoidal geometry. The deter-minedfactorsaregiveninTable1forallinvestigatedsettings.This factormay now be applied to correctthe chord length which is generatedbythefictitiousopticalsignalbasedonthe X-ray mea-surements(see Fig. 18) aswell asthe chord length of upcoming opticalmeasurements underthe assumptionthatthebubblescan beregardedasellipsoidsinafirstapproximation.

6.4.Correctionofthemeanchordlength

In thissection, the results of the Monte Carlo simulation are appliedtocorrectthemeanchord lengththat iscalculatedbased onafictitiousopticalsignalwhichgeneratedonthebasisofX-ray measurements.The uncorrectedmeanchord lengthshavealready beenpresentedinSection5.4.Fig.26depictsthemeancorrected chordlengthbasedonthefactorsshowninTable1foreach mea-surementpositionalongtheevaluationpathandthemeanvolume equivalent bubble diameter determined by the X-ray evaluation. Fora measurement height of36cm, the gap between the mean bubble sizes which are determined by both evaluation methods could be reduced significantly in comparison to the uncorrected chord lengths (see Fig. 18). For a measurement height of 56cm, themeanchordlengthoverestimatesthemeanvolumeequivalent bubblediameterbyamaximumof15−20%. However,withregard to the applicationof thefactor, it should be mentioned that the correctionfactorisbasedonaMonteCarlosimulationofperfectly ellipsoidalshaped bubbles.This shapewasselected since the ge-ometry can be described mathematically and since this geome-trycanberegardedasafirstapproximationfortheactualbubble shapeinafluidizedbedwithverticalinternals.Morespecific cor-rectionfactorscouldbederivedbysimulatingabubblingfluidized bedwithverticalinternalsinthescopeofcomputationalfluid dy-namicstudies.Hence,a transferofthesefindings toother bubble

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Fig. 24. Comparison of diameter (a) and bubble rise velocity (b) distribution for the input into the MC-simulation with the results generated by the optical evaluation for spherical bubbles.

Fig. 25. Comparison of diameter vs. chord length (a) and bubble rise velocity (b) distribution for the input into the MC-simulation with the results generated by the optical evaluation for ellipsoidal bubbles.

shapesthatmay appearina BFBwitha differentcolumndesign cannotbeconductedwithoutfurtherinvestigations.

7.Conclusions

Opticalmeasurementsarecommonlyusedtodeterminethe hy-drodynamicsindifferentkindsofbubblingﬂuidizedbeds(van Om-menandMudde,2007).It couldbe shownthat thebubble prop-ertieswhich are obtainedby local optical measurements haveto beconsidered cautiouslyduetostatisticaleffects.Thisconclusion isnot onlylimited to the geometrythat wasinvestigated in the scopeofthisstudy,butshouldbetakenintoaccountforthe inter-pretationofanykindofdatasetsthatarebasedonopticalprobes. Explicit intention ofthiswork wasnot todescribe the hydro-dynamicbehaviorofabubblingﬂuidizedbedasitisconductedin Maureret al.(2015b,c)andSchillinger etal.(2017), but, topoint out possible differencesconcerning the determined bubble prop-ertiesbetween the evaluationmethod of an X-ray signal andan opticalsignal.

Thisinvestigation wasconductedsince inlarge scale fluidized bedreactors athot andreactive conditions, itis not always pos-sibleto performX-raymeasurements that provideinformationof thefluidizationstateovertheentirecrosssection.AtPSI,an opti-cal sensor wasdevelopedin orderto enablehydrodynamic mea-surements in a bubbling fluidized bed reactor under these con-ditions.Optical probingisacomparatively easy methodto exam-inethe localstate offluidization.However, opticalmeasurements have the drawback that only the chord length and not the vol-umeequivalent diameterof the bubbles are accessiblesince this methodislimitedtoacertainpositioninthecolumn.Hence, eval-uatingthedifferencebetweenbothmethodsisinevitabletojudge futuremeasurements withalocaloptical sensor.Toachieve a di-rect comparisonbetweentheresults obtainedby bothevaluation methods, existing hydrodynamic X-ray measurements on a bub-blingfluidized bed withvertical internalswere forthe first time usedassourcetogenerateanartificialopticalsignalatdefined po-sitionsinthecolumn.

Concerningthebubblerisevelocity,itturnedoutthatforlarger ﬂuidizationnumbers,themeanBRVthatisdeterminedbythe

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op-Fig. 26. Corrected mean chord lengths by results of MC simulation in comparison to bubble size determined by X-ray evaluation for H = 56 cm and ﬂuidization numbers of 4 and 6.

ticalevaluationmethodtendstobesmallerthantheBRVwhichis obtained bythe X-rayevaluation method.Thisdiscrepancy could be explained by the fact that bubbles with a larger horizontal cross-sectional area showa tendencyto rise withaslowermean BRV compared to bubbles with a smaller cross-sectional area. Hence, the higherprobability to piercetheselarger bubbles with anopticalsensorreﬂectsinthelowernumberbasedmeanrise ve-locitythatisdeterminedbythismethod.Themeanbubblerise ve-locityoffuturemeasurementcampaignswithlocal,opticalsensors cannowbecorrectedbyafactor(seeFig.17)thatdescribesthe ra-tiobetweenthemean BRVdetermined bylocalmeasurements to themeanBRVdeterminedbymeasurementsovertheentire cross-section (X-ray). It should be pointed out that this factor is only valid inthe scope ofthe investigated settingsfor bedswith ver-tical internalsconcerning the ﬂuidization numbers and measure-mentheightsforwhichitcanbeappliedtocorrectthebubblerise velocityatreactiveconditions.

Severalindependentfactshavetobeconsideredinorderto ex-plain the finding that the mean chord length resulting fromthe opticalevaluationissmallerthanthemeanvolumeequivalent di-ameterresultingfromtheX-rayevaluation.Theanalysisofthe flu-idizationstate by the fictitiousoptical probe along theentire di-ameter of the column has the effect that the same bubble may be pierced at several radial positions. For the case of spherical

bubbles,thisleadstoamean chordlength whichissmaller than the mean volume equivalent diameter determined by the X-ray method.Incaseofasufficientlyhighfluidizationnumber,the for-mationofslugsthatcovertheentirecross-sectionmaybeafurther reasonwhythemeanchord lengthissmallerthanthemean vol-umeequivalentdiameter.Thisis duetothe factthat the pierced chordlengthofaslugisoftensignificantlysmallerthanthe corre-spondingvolumeequivalentdiameter.

In order to investigate the relation between the mean chord lengthwhichisdeterminedbyalocallylimitedopticalsensorand themeanbubblesizeofallsimulatedbubbles,aMonteCarlo sim-ulationofrising bubbleswasconducted.The simulationwas per-formedbothforbubbleswithasphericalandanellipsoidal geome-trysincethebubbleshapeinaﬂuidizedbedwithverticalinternals can be regarded asellipsoidalas a ﬁrst approximation.It turned out that the mean chord length that is determined by the opti-calevaluationintheMC-simulationisingeneralsmallerthanthe mean volume equivalent diameter of all simulated bubbles with an ellipsoidal shape. Based on these results, a factor was intro-ducedwhich describestheratio betweenthe meanchord length oftheopticalevaluationandthe meanvolumeequivalent diame-terofallbubblesforthecaseofanidealellipsoidalgeometry.The meanchord lengthincreasesifthefactorisappliedontheresults of the optical measurements. For the most settings, the relative

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deviationbetween both values could be reduced, although, after applicationof thefactor,themean chordlength slightly overesti-mates the meanvolume equivalentbubble diameter. Hence, cor-rectingthe meanchord lengthdetermined infutureoptical mea-surementcampaigns bythe factorspresentedinTable 1isuseful intermsofreducingthemaximumerroroflocalmeasurements.

In general, the knowledge obtained within the scope of this study allows a judgement and correction of the bubble proper-tiesresultingfromfuturemeasurementcampaignsatbubbling ﬂu-idizedbedreactorsunderhotandpressurizedconditionsforwhich onlyopticalprobeswillbeavailable.

Acknowledgment

This research projectis ﬁnancially supported by theSwiss In-novationAgency lnnosuisse andispart ofthe SwissCompetence CenterforEnergy ResearchSCCERBIOSWEET.Further, supportby theEnergySystemIntegrationplatform(ESI)isgratefully acknowl-edged.

References

Acosta-Iborra, A., Sobrino, C., Hernández-Jiménez, F., de Vega, M., 2011. Experimen- tal and computational study on the bubble behavior in a 3-D ﬂuidized bed. Chem. Eng. Sci. 66, 3499–3512. doi: 10.1016/j.ces.2011.04.009 .

Andersen, A.H., Kak, A.C., 1984. Simultaneous Algebraic Reconstruction Technique (SART): a superior implementation of the art algorithm. Ultrason. Imaging 6, 81–94. doi: 10.1177/01617346840 060 0107 .

Asegehegn, T.W., Schreiber, M., Krautz, H.J., 2011. Investigation of bubble behavior in ﬂuidized beds with and without immersed horizontal tubes using a digital image analysis technique. Powder Technol. 210, 248–260. doi: 10.1016/j.powtec. 2011.03.025 .

Bai, W. , Deen, N.G. , Kuipers, J.A.M. , 2010. Bubble properties of heterogeneous bub- bly ﬂows in a square bubble column. In: Proceedings of the Sixth International Symposium on Multiphase Flow, Heat Mass Transfer and Energy Conversion, pp. 563–568 .

Bakshi, A., Altantzis, C., Bates, R.B., Ghoniem, A.F., 2016. Multiphase-ﬂow Statistics using 3D Detection and Tracking Algorithm (MS3DATA): methodology and application to large-scale ﬂuidized beds. Chem. Eng. J. 293, 355–364. doi: 10.1016/ j.cej.2016.02.058 .

Clark, N.N., Turton, R., 1988. Chord length distributions related to bubble size distributions in multiphase ﬂows. Int. J. Multiph. Flow 14, 413–424. doi: 10.1016/ 0301-9322(88)90019-5 .

Davidson, J.F., Harrison, D., 1966. The behaviour of a continuously bubbling ﬂuidised bed. Chem. Eng. Sci. 21, 731–738. doi: 10.1016/0 0 09-2509(66)870 01-X .

Glicksman, L.R., Lord, W.K., Sakagami, M., 1987. Bubble properties in large-particle ﬂuidized beds. Chem. Eng. Sci. 42, 479–491. doi: 10.1016/0 0 09-2509(87)80 010-6 .

Gogolek, P.E.G., Grace, J.R., 1995. Fundamental hydrodynamics related to pressurized ﬂuidized bed combustion. Prog. Energy Combust. Sci. 21, 419–451. doi: 10.1016/ 0360-1285(95)0 0 010-0 .

Gomez-Hernandez, J. , van Ommen, R. , Mudde, R.F. , Wagner, E. , 2016. "Pressure and X-ray tomography characterization of the ﬂuidization behavior of TiO2 nanopar- ticles. In: Proceedings of the Fluidization XV .

Grace, J.R., Clift, R., 1974. On the two-phase theory of ﬂuidization. Chem. Eng. Sci. 29, 327–334. doi: 10.1016/0 0 09-2509(74)80 039-4 .

Hilligardt, K., Werther, J., 1985. Lokaler Blasengas–Holdup und expansionsverhalten von gas/feststoff-wirbelschichten. Chemie Ing. Tech. 57, 622–623. doi: 10.1002/ cite.330570713 .

Liu, M., Zhang, Y., Bi, H., Grace, J.R., Zhu, Y., 2010. Non-intrusive determination of bubble size in a gas-solid ﬂuidized bed: An evaluation. Chem. Eng. Sci. 65, 3485–3493. doi: 10.1016/j.ces.2010.02.049 .

Maurer, S., 2015. Hydrodynamic characterization and scale-up of bubbling ﬂuidized beds for catalytic conversion. ETH Zürich, Diss., ETH Zürich, Nr. 22722, Eid- genössische Technische Hochschule. doi: 10.3929/ethz- a- 010453120 .

Maurer, S., Gschwend, D., Wagner, E.C., Schildhauer, T.J., van Ommen, J.R., Biol- laz, S.M.A., Mudde, R.F., 2016. Correlating bubble size and velocity distribution in bubbling ﬂuidized bed based on X-ray tomography. Chem. Eng. J. doi: 10.1016/ j.cej.2016.02.012 .

Maurer, S., Schildhauer, T.J., van Ommen, J.R., Biollaz, S.M.A ., Wokaun, A ., 2014. Scale-up of ﬂuidized beds with vertical internals: Studying the sectoral approach by means of optical probes. Chem. Eng. J. 252, 131–140. doi: 10.1016/j. cej.2014.04.083 .

Maurer, S. , Wagner, E.C. , Schildhauer, T.J. , van Ommen, J.R. , Biollaz, S.M.A. , Mudde, R.F. , 2015a. X-ray measurements on the inﬂuence of optical probes on gas–solid ﬂuidized beds. Int. J. Multiph. Flow 74, 143–147 .

Maurer, S., Wagner, E.C., Schildhauer, T.J., van Ommen, J.R., Biollaz, S.M.A., Mudde, R.F., 2015b. X-ray measurements of bubble hold-up in ﬂuidized beds with and without vertical internals. Int. J. Multiph. Flow 74, 118–124. doi: 10. 1016/j.ijmultiphaseﬂow.2015.03.009 .

Maurer, S., Wagner, E.C., van Ommen, J.R., Schildhauer, T.J., Teske, S.L., Biollaz, S.M.A., Wokaun, A., Mudde, R.F., 2015c. Influence of vertical internals on a bubbling fluidized bed characterized by X-ray tomography. Int. J. Multiph. Flow 75, 237– 249. doi: 10.1016/j.ijmultiphaseflow.2015.06.001 .

Mudde, R.F., 2011. Bubbles in a ﬂuidized bed: a fast X-ray scanner. AIChE J. 57, 2684– 2690. doi: 10.1002/aic.12469 .

Mudde, R.F., 2010. Time-resolved X-ray tomography of a ﬂuidized bed. Powder Tech- nol. 199, 55–59. doi: 10.1016/j.powtec.2009.04.021 .

Mudde, R.F., Bruneau, P.R.P., van der Hagen, T., 2005. Time-resolved gamma- densitometry imaging within ﬂuidized beds. Ind. Eng. Chem. Res. 44, 6181–6187. doi: 10.1021/ie049091p .

Rautenbach, C., Mudde, R.F., Yang, X., Melaaen, M.C., Halvorsen, B.M., 2013. A com- parative study between electrical capacitance tomography and time-resolved X-ray tomography. Flow Meas. Instrum. 30, 34–44. doi: 10.1016/j.ﬂowmeasinst. 2012.11.005 .

Rüdisüli, M., 2012. Characterization of rising gas bubbles in uidized beds by means of statistical tools. ETH/PSI. doi: 10.3929/ethz- a- 007089625 .

Rüdisüli, M., Schildhauer, T.J., Biollaz, S.M.A., Ruud van Ommen, J., 2012a. Bubble characterization in a ﬂuidized bed by means of optical probes. Int. J. Multiph. Flow 41, 56–67. doi: 10.1016/j.ijmultiphaseﬂow.2012.01.001 .

Rüdisüli, M., Schildhauer, T.J., Biollaz, S.M.A., van Ommen, J.R., 2012b. Monte Carlo simulation of the bubble size distribution in a ﬂuidized bed with intrusive probes. Int. J. Multiph. Flow 44, 1–14. doi: 10.1016/j.ijmultiphaseﬂow.2012.03. 009 .

Santana, D., Macias-Machin, A., 20 0 0. Local bubble-size distribution in ﬂuidized beds. AIChE J. 46, 1340–1347. doi: 10.1002/aic.690460708 .

Schillinger, F., Maurer, S., Wagner, E.C., van Ommen, J.R., Mudde, R.F., Schild- hauer, T.J., 2017. Influence of vertical heat exchanger tubes, their arrangement and the column diameter on the hydrodynamics in a gas–solid bubbling fluidized bed. Int. J. Multiph. Flow. doi: 10.1016/j.ijmultiphaseflow.2017.07.013 .

Sjöstrand, N.G., 2003. On the average chord length. VTT Symp. (Valtion Tek. Tutkimuskeskus) 30, 7–9. doi: 10.1016/j.anucene.2004.04.007 .

Sobrino, C., Acosta-Iborra, A., Izquierdo-Barrientos, M.A., de Vega, M., 2015. Three- dimensional two-ﬂuid modeling of a cylindrical ﬂuidized bed and validation of the Maximum Entropy method to determine bubble properties. Chem. Eng. J. 262, 628–639. doi: 10.1016/j.cej.2014.10.014 .

Tebianian, S., Dubrawski, K., Ellis, N., Cocco, R.A., Hays, R., Reddy Karri, S.B., Lead- beater, T.W., Parker, D.J., Chaouki, J., Jafari, R., Garcia-Trinanes, P., Seville, J.P.K., Grace, J.R., 2016. Comparison of particle velocity measurement techniques in a ﬂuidized bed operating in the square-nosed slugging ﬂow regime. Powder Tech- nol. 296, 45–52. doi: 10.1016/j.powtec.2015.08.040 .

Tebianian, S., Ellis, N., Lettieri, P., Grace, J.R., 2015. X-ray imaging for flow characterization and investigation of invasive probe interference in travelling fluidized bed. Chem. Eng. Res. Des. 104, 191–202. doi: 10.1016/j.cherd.2015.08.006 . van Ommen, J.R. , Mudde, R.F. , 2007. Measuring the gas–solids distribution in flu-

idized beds – a review. In: Proceedings of the Twelfth International Conference on Fluidization – New Horizons in Fluidization Engineering .

Verma, V., Li, T., Dietiker, J.-F., Rogers, W.A., 2016. Hydrodynamics of gas–solids ﬂow in a bubbling ﬂuidized bed with immersed vertical U-tube banks. Chem. Eng. J. 287, 727–743. doi: 10.1016/j.cej.2015.11.049 .

Verma, V., Padding, J.T., Deen, N.G., Kuipers, J.A.M.H., Barthel, F., Bieberle, M., Wag- ner, M., Hampel, U., 2014. Bubble dynamics in a 3-D gas-solid ﬂuidized bed using ultrafast electron beam X-ray tomography and two-ﬂuid model. AIChE J. 60, 1632–1644. doi: 10.1002/aic.14393 .

Werther, J., 2007. Fluidized-bed reactors. In: Ullmann’s Encyclopedia of Industrial Chemistry, Wiley 723–725. doi: 10.10 02/143560 07.b04 _ 239.pub2 .

Whitehead, A.B., Dent, D.C., Bhat, G.N., 1967. Fluidisation studies in large gas-solid systems Part I: bubble rise rates. Powder Technol. 1, 143–148. doi: 10.1016/ 0 032-5910(67)80 025-1 .

Whitemarsh, E.A., Escudero, D.R., Heindel, T.J., 2016. Probe effects on the local gas holdup conditions in a ﬂuidized bed. Powder Technol. 294, 191–201. doi: 10. 1016/j.powtec.2016.02.035 .