Pressure drop and axial dispersion in industrial millistructured heat exchange reactors

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Pressure drop and axial dispersion in industrial

millistructured heat exchange reactors

Maxime Moreau, Nathalie Di Miceli Raimondi, Nathalie Le Sauze, Michel

Cabassud, Christophe Gourdon

To cite this version:

Maxime Moreau, Nathalie Di Miceli Raimondi, Nathalie Le Sauze, Michel Cabassud, Christophe

Gourdon.

Pressure drop and axial dispersion in industrial millistructured heat exchange

reac-tors. Chemical Engineering and Processing: Process Intensification, Elsevier, 2015, 95, pp.54-62.

�10.1016/j.cep.2015.05.009�. �hal-01338169�

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rchive

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Eprints ID : 15850

To link to this article : DOI : 10.1016/j.cep.2015.05.009

URL :

http://dx.doi.org/10.1016/j.cep.2015.05.009

To cite this version :

Moreau, Maxime and Di Miceli Raimondi,

Nathalie and Le Sauze, Nathalie and Cabassud, Michel and

Gourdon, Christophe Pressure drop and axial dispersion in

industrial millistructured heat exchange reactors. (2015) Chemical

Engineering and Processing: Process Intensification, vol. 95. pp.

54-62. ISSN 0255-2701

Any correspondence concerning this service should be sent to the repository

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Pressure

drop

and

axial

dispersion

in

industrial

millistructured

heat

exchange

reactors

Maxime

Moreau

,

Nathalie

Di

Miceli

Raimondi

*

,

Nathalie

Le

Sauze

,

Michel

Cabassud

,

Christophe

Gourdon

a_{UniversitédeToulouse,INP,UPS,LGC(LaboratoiredeGénieChimique),4alléeEmileMonso,F-31432Toulouse,Cedex04France} b_{CNRS,LGC(LaboratoiredeGénieChimique),F-31432Toulouse,Cedex04France}

Keywords:

Heatexchangereactors Pressuredrop Axialdispersion Modelling

ABSTRACT

Hydrodynamic characterizationby meansof pressure drop and residence time distribution (RTD) experimentsisperformedinthreemillistructuredheatexchangereactors:twoCorningreactors(further referredtoasCorningHPandCorningRT)andaChartreactor.Pressuredropismeasuredfordifferent flowratesandfluids.FanningfrictionfactoristhencalculatedanditsevolutionversusReynoldsnumber isplottedforeachreactor,showingtheinfluenceofthegeometricalcharacteristicsofthereactorsonthis parameter.FromRTDexperiments,axialdispersioncoefficientsthatallowcalculatingPécletnumbersare identifiedbysolvingtheconvection-dispersionequation.Theresultshighlightplugflowbehaviorof thesereactorsfortherangeofflowratesstudied.PécletnumberinCorningHPremainsconstantinthe rangeofReynoldsnumberstudied.Itsspecificpatternisdesignedtogeneratemixingstructuresthat allowhomogenizationofthetraceroverthecross-section.Itexplainstheplugflowbehaviorofthis reactorevenatlowReynoldsnumberbutgenerateshighpressuredrop.PécletnumberinCorningRTand ChartShimTec1_{increaseswithReynoldsnumber.Thisevolutionisencounteredforstraightcircular}

pipesinturbulentregimeandconfirmsthepressuredropanalysis.

1.Introduction

The need to develop safer, more effective and less energy

consuming processes while respecting environmental

require-mentscausedsinceafewyearstheinterestoftheindustryforthe

intensifiedtechnologies.Inthiscontext,heatexchangereactorsare

promising technologies [1]. Indeed it is difficult to control

temperatureinbatchorsemi-batchreactorswhenreactionsare

highly exothermic. Heat exchange reactors may offer a better

thermalcontrolofthereactionsincreasingsafetyandselectivity

while reducing by-products generation. Continuous

millistruc-turedheatexchangereactorsprovideheattransferattheclosestof

thereaction.Theycombinetheadvantagesofmillireactors(fast

mixing,reactivevolumeconfinement)andcompactheat

exchang-ers(hightransferareaandlargematerialmassperunitofreactive

volume).

However, the miniaturization of the devices leads to low

Reynoldsnumberfortheprocess_fluid.Toavoidpurelaminar_flow,

instabilitieshavetobegeneratedformixingandtransferissues.

Thereforemillistructureddevicesaregenerallycharacterizedbya

complexgeometry of theprocess channelsto promotemixing,

providing specific hydrodynamicbehaviors notably in terms of

pressure dropand Residence TimeDistribution (RTD). Pressure

dropisakeyparametertodesignaprocesssincethecostofthe

pumpsdrivingthe_fluidthroughtheinstallationisgenerallyagreat

partofthewholecapitalcost.RTDgivespreciousinformationon

thehydrodynamics of the reactorand particularlyon theaxial

dispersion generated. Axial dispersion is responsible of the

spreading of the reactants and the products along the device

which can lead to selectivity and conversion issues. This

hydrodynamicparametermustthus bedeterminedtocorrectly

modelthereaction[2].

The aim of this study is to provide and analyze the

hydrodynamicbehaviorof threeindustrial millistructured

reac-tors:twoCorningfluidicmodulesandaChartreactor.Elgueetal.

[3] demonstrated the performances of these devices for the

implementationofachemicalreaction.Theauthorscarriedouta

two-phaseesterificationandobservedhigherconversionwiththe

intensifiedmillireactorsthaninbatchconditions.Brauneetal.[4]

*Correspondingauthor.Tel.:+33562258920;fax.:+33562258891.

E-mailaddresses:mmoreau3@ensiacet.fr(M.Moreau),

nathalie.raimondi@iut-tlse3.fr(N.DiMiceliRaimondi),

nathalie.lesauze@iut-tlse3.fr(N.LeSauze),michel.cabassud@ensiacet.fr

(M.Cabassud),christophe.gourdon@ensiacet.fr(C.Gourdon).

thenBuissonetal.[5]alsodemonstratedtheefficiencyofmass

transfer in Corning mixing module by performing selective

reactions.PressuredropandresidencetimedistributioninCorning

reactorshavealreadybeeninvestigated[6,7]andresidencetime

distribution have also been studied in Chart ShimTec1 based

technologybyCantu-Perezet al.[8].However, theexperiments

werecarriedoutwithwaterforpressuredropmeasurementsand

generic correlations are missing toestimate thehydrodynamic

behaviorusingquantitativeparameters.

In thepresentwork,pressuredropandRTDexperimentsare

carriedout.Theyareanalyzedinordertosuggestcorrelationsfor

the estimation of dimensionless numbers characteristic of the

hydrodynamics of reactors such as Fanning friction factor and

Pécletnumber.Theimpactofthegeometryofthethreedeviceson

thepressuredropandtheRTDresultsisalsodiscussed.The_first

part of this paper presents the reactors design and the

experimentalsetup.Thepressuredropresultsarepresentedina

secondpart.Then,theRTDexperimentsandthemethodologyto

identifythePécletnumberaredescribed.Theresultsarecompared

tomodelsavailableinliterature.

2.Experimentalmethod

2.1.Descriptionofthereactors

ThedevicestestedaretwoCorningfluidicmodulesG1basedon

theCorningAdvanced-FlowTM_{technology[9]andaChartreactor}

basedontheShimTec1_{technology[10](Fig.1).}

Corningmodulesaremadeofthreeglassparts.ThefirstCorning

module (hereinafter called Corning RT for Residence Time) is

composedofoneplatecarvedbyasinglerectangularchannelwith

180!_{bends.Thesecondmodule(hereinaftercalledCorningHPfor}

HeartPattern)isbasedonaHeartPatterndesigned togenerate

mixing structures (51 hearts by plate). Each process plate is

combined with two utility plates that allow to control the

temperatureofthereaction.Thesemodulescanbeusedinseries

to form a complete reactor. The Chart ShimTec1 _{reactor is}

composed of thin plates (also called shims) that include the

channelsofthereactor.Theyarebonded togethertocreatethe

wholestructure.Itiscomposedofthreeparallelprocesschannels.

Thereactorcanbefedbyautilityfluidforheatexchangepurpose.

Thesethreereactorsaredesignedforspecificapplications.Corning

RTismadetopre-heatreactantsbeforeareactionplateortoadd

residencetimeattheendofthesetup.CorningHPislikelyusedfor

two-phase reactions that need intensified mass transfer. Chart

ShimTec1 _{reactoris designed to producelow pressure dropto}

performreactionswithviscous_fluids.Theircharacteristic

dimen-sionsaregiveninTable1.Itisdifficulttoestimatethelengthof

CorningHPreactorsinceitssectionisnotconstant.However,the

RTDresultsareusedtoidentifytheequivalentcrosssectionand

length of the reactor. Indeed, these parameters are fitted by

comparingtheshapesoftheexperimentalandcalculatedoutlet

RTDcurvesandtheexperimentalandtheoreticalresidencetimes

(seeAppendixA).Nevertheless,eveniftheseequivalent

character-isticsarenotperfectlyreliable,theydonotaffecttheidentification

ofhydrodynamicbehaviorsasfunctionofthereactorgeometry.For

theChartShimTec1_{reactor,theequivalentlengthistheaverage}

lengthofthe3channels.FortheRTDexperiments,itisconsidered

thattheoutputRTDcurvescanbedecomposedintothreedistinct

curvesrepresentingthepathofthetracerinthethreechannelsof

Nomenclature

c Concentrationoftracer(molm"3₎

Dax Axialdispersioncoefficient(m2s"1)

Dh Hydraulicdiameterofthetube(m)

Dm Molecular diffusion coefficient of tracer in solvent

(m2_s"1₎

E Distributionfunction(s"1₎

f Fanningfrictionfactor_(")

J Numberofstirredtanks_(")

L Lengthofthereactor(m)

P Perimeterofthecrosssection(m)

Pe Pécletnumber_(")

Q Flowrate(m3_s"1₎

Reh HydraulicReynoldsnumber(")

Re ffiffip_S SquaresectionReynoldsnumber_(")

S Crosssectionofthechannel(m2₎

s Minimizationfunction(mol2_sm"6₎

t Time(s)

tr,exp Experimentalresidencetime(s)

u0 Averagevelocity(ms"1)

V Volume(m3₎

x Longitudinalcoordinate(m)

Greekletters

m

r

D

Subscripts

calc Calculated

exp Experimental

in Inletofthereactor

out Outletofthereactor

square Squaresection

Fig.1.Millistructuredreactors:(a)CorningRT,(b)CorningHPand(c)ChartShimTec1

[9,10]. Table1 Reactorsdimensions. Corning RT Corning HP ChartShimTec1 EquivalentcrosssectionS

(10"6_m2₎

3.8 4.6 4.0$3

channels

differentlength.However,itisassumedthatthetracer

concentra-tionattheentranceofeachchannelisthesameastheaverage

velocityand theaxial dispersioncoefficientcharacterizingeach

channel.

2.2.Experimentalsetup

TheexperimentalsetupisillustratedonFig.2.Itiscomposedof

an external gearpump connectedto a feedingtank.A by-pass

systemallowsabettercontroloftheflowrate.AT-shapeinjectoris

usedtoinjectthetracerwithasyringerightbeforetheinletofthe

reactortocarryouttheRTDexperiments.Theoutletofthereactor

islinkedtoastoragetank.ACoriolis-effectflowmetermeasures

the mass flow rate and the density of the process fluid. A

Rosemountdifferentialpressuretransducerconnectedtotheinlet

andtheoutletofthereactorisusedtomeasurethepressuredrop

generated.UVsensorsmeasuretheabsorbanceofthefluidatthe

inletandtheoutletofthereactortofollowtheconcentrationofthe

tracerasafunctionoftime.

2.3.Pressuredropmeasurement

Thepressuredropismeasuredfordifferentflowrates.Water

(

m

r

Silicon oils (

m

r

_m

_r

and a glycerol-water mixture with 75%wt glycerol (

m

r

flowratesandReynoldsnumbersusedforeachreactor.Hydraulic

diameterDhisgenerallyusedasthecharacteristiclengthscalefor

non-circularchannels.HoweverBahramietal.[11]showedthatit

ismoreappropriatetousethesquarerootofthecrosssectionSfor

pressuredropconsiderations.Therefore,thecharacteristiclength

is equivalenttothewidthof asquarechannel.AnewReynolds

number is definedand basedonS, theaveragevelocity u0,the

density

r

m

Re ffiffip_S¼

r

ffiffiffi

S

p

m

Theaveragevelocityiscalculatedfromtheexperimentalflowrate

oftheprocess_fluidQfromEq.(2).

u0¼

Q

S (2)

Re ffiffip_ScanberelatedtotheclassicalhydraulicReynoldsnumberReh

usingEq.(3),wherePisthechannelperimeter.

Re ffiffip_S¼ P

4 ffiffiffi

S

p Reh (3)

WiththehydraulicReynoldsnumberdefinedasafunctionofthe

hydraulicdiameterDhfollowingEq.(4).

Re_h¼

r

m

ThehydraulicdiameterDhisderivedfrom:

Dh¼

4S

P (5)

2.4.RTDexperiments

Residence Time Distribution (RTD) is determined by the

injectionofamethylenebluetracerintheprocessfluid(water)

atdifferent_flowrates.Itsmoleculardiffusioncoefficientinwateris

Dm=3.10"10m2s"1[12,13].UVsensorsmeasuretheabsorbanceof

thefluidpassingthroughthereactorasafunctionoftime.Both

sensors are calibrated and the linear relationship between

absorbanceand thetracerconcentrationis establishedinorder

tocalculatetheaverageconcentrationatthemeasurementpoints.

The RTD response to a Dirac-like injection is given by the

distributionfunctionE(t)which isa normalizedfunctionof the

concentrationc(t).

EðtÞ¼R1cðtÞ

0 cðtÞdt

(6)

Fig.3isanexampleofexperimentalinjections.Thecontinuousline

correspondstothereactorentrance.Thecurve’strailisduetothe

syringe-injection method. The dashed line corresponds to the

outletofthereactor.Thespreadingofthecurveisduetotheaxial

dispersion generated by the hydrodynamic conditions in the

reactor.Table3showstherangeof_flowrateandReynoldsnumber

studiedforeachreactor.

Fig.2. Experimentalsetup. Table2

Experimental range of flow rates and Reynolds numbers for pressure drop measurement.

CorningRT CorningHP ChartShimTec1

Water Q(Lh"1_{) 0.5–15 1–15 2–78} Re ffiffip_{S 85–2000 350–1850 200–3600} Siliconoils Q(Lh"1_{) 2–12 3–14 3–15} Re ffiffipS 25–170 40–180 4–130 Glycerol Q(Lh"1_{) – 4–14.5 –} Re ffiffipS – 15–63 –

3.Resultsanddiscussion

3.1.Pressuredrop

Fig.4showstheevolutionofpressuredropversusflowratefor

eachreactorandeachprocessfluidused.Foragivenfluid,Chart

ShimTec1_{reactorgenerateslesspressuredropthantheotherones.}

Reactor

Q

=

6 L.

h

Q

= 10 L.

h

Corning

RT

Experimental inlet Experimental outlet

0 0.5 1 1.5 2 2.5 15 10 5 0 E(t) (s-1₎ Time (s)

Experimental inlet Experimental outlet

Corning

HP

Experimental inlet Experimental outlet

0 0.5 1 1.5 2 15 10 5 0 E(t) (s-1₎ Time (s)

Experimental inlet Experimental outlet

Chart

ShimTec

®

Experimental inlet Experimental outlet

0 0.5 1 1.5 2 2.5 15 10 5 0 E(t) (s-1) Time (s)

Experimental inlet Experimental outlet

Fig.3.DistributionfunctionsE(t)obtainedinthethreereactorsforQ=6Lh"1_andQ=10Lh"1_.

Table3

RangeofflowratesandReynoldsnumbersforRTDexperiments.

Flowrate(Lh"1₎ Re ffiffip_S

CorningRT 6–12 850–1700

CorningHP 3–11 380–1420

ChartShimTec1

Thedivisionoftheflowinthreeparallelchannelsallowstoreduce

the averagevelocity per channelcompared to a single-channel

configurationwiththesamehydraulicdiameterwhilemaintaining

thesameglobalflowrate.Itconfirmsitscapabilitytodealwith

viscous_fluidsorhigh_flowrates.Asexpected,CorningHPreactor

generatesmorepressuredropthantheotherreactors.Itspattern,

designedtoimprovemixingandtwo-phasetransferperformances

leads to larger energy dissipation into the fluid producing

significantpressuredrop.

ThepressuredropgeneratedinachannelisfunctionofFanning

frictionfactorf,density

r

L,its crosssectionareaSand itsperimeterPfollowing Eq.(7).

Therefore, it is possible to determine f from a pressure drop

measurement(Eq.(8)).

D

r

D

r

Fanningfrictionfactordependsonthegeometryofthechannel.

Forastraightsquarechannelithasdifferentempiricalexpressions

have been established depending on the flow regime [14]. In

laminarconditions(Re ffiffip_S<2100):

f_square¼ k1

Re ffiffip_S (9)

Intransitional_flowforsmoothducts(2100<Re ffiffip_S<10000):

fsquare¼k2Re ffiffip "0:25S (10)

(Blasiusequation)

Infullyturbulentflow(Re ffiffip_S>10000):

fsquare¼k3 (11)

kiareconstantvaluesdependingontheshapeofthechannelcross

section.Fig.5representsFanningfactorversusReynoldsnumber.

Fromthis_figure,correlationsareproposedtopredictthepressure

dropinthethreereactorsstudied(Table4).

TheevolutionoftheFanningfrictionfactorforallthereactors

canbecomparedtotheoneinastraightsquarechannel.Forlow

Reynoldsnumber(Re ffiffip_S<1000forCorningRTandChartShimTec1 Fig.4. Experimentalpressuredropversusflowrate.

0.001 0.01 0.1 1 10 10000 1000 100 10 1 f √ Corning RT Corning HP Chart ShimTec®

Straight square channel, laminar flow

Straight square channel (smooth), transitionnal flow

reactor and Re ffiffip_S<50 for Corning HP) the trend observed

correspondstoEq.(9)associatedtoalaminarbehavior.

AnevolutiontothetransitionalregimeisobservedatRe ffiffip_S¼

1000respectivelyforChartShimTec1_{andCorningRTandatRe ffiffi}

S p

around 50 for Corning HP. Above these values, Fanning factor

valuesseemtofollowtheBlasiusequationtrend.Thedifference

betweenReynolds number values correspondingto theregime

changeforstraightpipeandforthereactorsstudiedmustbedueto

theparticulargeometriesofthereactors.Indeed,theChartreactor

iscomposed ofthreechannelswitha fewbends;CorningRTis

composedofarectangularchannelwithnumerous180!_bendsthat

generate energy dissipation at lower Reynolds than straight

channels.The trend observed for Corning HP canbe explained

by the specific geometry of the channel which is designed to

generatemicromixingstructuresevenatlowReynoldsnumber.

ThelaminarregimeisonlyobservedforReynoldsnumberlower

than 50. Fanning factor seems to reach a constant value,

characteristic of a turbulent regime for Reynolds higher than

1000insteadof10000inastraightpipe.

3.2.RTDexperiments

Theglobalhydrodynamicbehaviorofchemicalreactorsisoften

characterizedbytheRTD.Itcorrespondstothetimenecessaryfor

different elements of fluid to pass through the reactor. It

determines if the reactorbehavior is closeto a perfect stirred

tankortoaplugflowreactor.RTDprovidesinformationaboutthe

Table4

TendenciesofFanningfrictionfactordependingontheflowregime.

CorningRT ChartShimTec1

CorningHP Re ffiffipS<1000:f¼ 16 Re ffiffip_S Re ffiffipS<1000:f¼ 25 Re ffiffip_S Re ffiffipS<50:f¼ 25 Re ffiffip_S Re ffiffip_S>1000:f0:08 Re0:25 ffiffi S p Re ffiffipS>1000:f¼ 0:33 Re0:25 ffiffi S p Re ffiffip_S>1000:f¼0:2

Reactor

Q

=

6 L.

h

Q

= 10 L.

h

Corning

RT

Experimental inlet Experimental outlet Calculated outlet 0 0.5 1 1.5 2 2.5 0 5 10 15 E(t) (s-1₎ Time (s)

Experimental inlet Experimental outlet Calculated outlet

Corning

HP

Experimental inlet Experimental outlet Calculated outlet 0 0.5 1 1.5 2 0 5 10 15 E(t) (s-1) Time (s)

Experimental inlet Experimental outlet Calculated outlet

Chart

ShimTec

®

Experimental inlet Experimental outlet Calculated outlet 0 0.5 1 1.5 2 2.5 0 5 10 15 E(t) (s-1) Time (s)

Experimental inlet Experimental outlet Calculated outlet

mixingefficiencyanddefectssuchasstagnantregionsorshortcuts

thatcanlowertheperformancesofthereactor.RTD

characteriza-tionisthennecessarytomodelappropriatelyreactivesystems.

In a plug flow reactor, each element of fluid has the same

residence time. RTD experiments in a tubular reactor allowto

highlight a deviationfrom this idealbehavior. Thedeviation is

generally quantified by the Péclet number Pe. It comparesthe

convectivetransportandthediffusivetransportoverthelengthof

adeviceandisdefinedasfollows:

Pe_¼u0L Dax

(12)

Peisdirectlyrelatedtotheaxialdispersioncoefficientthattakes

intoaccountallthephenomenainducingdispersioninareactor.

Axialdispersionisduetomoleculardiffusion,turbulenceand

non-uniformity of the velocityprofile. It is thus a key factor when

reactions with selectivity issues are considered [15,16]. This

dimensionlessnumberquantifiesthedifferencebetweenaperfect

stirredreactorandaplugflowreactor.Theplugflowbehavioris

assumedwhenPe>100[15].

Current methodologies for the characterization of axial

dispersionarebasedontheidentificationoftheaxialdispersion

coefficient fromRTDexperiments. It consistsin comparingthe

outletsignalwithananalyticalsolutionprovidedbyaconvection–

dispersionmodel[8,17,18]orasuccessionofperfectlymixedtanks

model[19].ThesemodelsimplyaperfectDiracinjectionthatis

experimentallydifficulttoperform.Totakeintoaccountthereal

injection, a deconvolution method is often used to treat the

entrancesignal[8,17].Butthismathematicaltreatmentcanleadto

alossofinformation,especiallyalossconcerningthetrailofthe

injection.

Another method is proposed in this work totreat the RTD

experimentswithoutdeconvolutionstep.Itconsistsinsolvingthe

one dimension convection–dispersion equation (Eq.(13))using

thecommercialsoftwareComsolMultiphysics.

@

@

@

@

@

@

WithInitialcondition:

t_¼0:cðxÞ¼0 (14)

AndBoundaryconditions:

x¼0:cðtÞ¼cin;expðtÞ (15)

x_¼L:

@

@

cistheaverageconcentrationoftraceroverthecrosssection.tis

timeandxthelongitudinalcoordinatealongthereactor(0_*x_*L).

At t=0, notraceris present in thereactor(Eq. (14)).The inlet

concentrationissetequaltotheexperimentalconcentrationcin,

exp(t) (Eq. (15)). At the outlet of the reactor the gradient of

concentrationissupposedtobezero(Eq.(16)).

Firstly, an initial value of Dax is chosen and the calculated

concentrationatx=L,cout,calc(t),iscomparedtotheexperimental

concentrationcout,exp(t).ThevalueofDaxisthenadjustedfollowing

the least squares method in order to minimize the s function

definedasfollows:

s¼

Z 1

0 ðcout;calcðtÞ"

cout;expðtÞÞ2$dt (17)

Fig.6givesexamplesofcalculatedE(t)curvewithidentifiedDaxby

minimization of the s function. This method is applied to

characterizethethree reactors.Daxisrepresentedasa function

of flow rate onFig. 7.The axial dispersioncoefficient remains

constantforbothCorningRTandChartShimTec1_{reactorswhile}

the flow rate increases. For the Corning HP, this coefficient

increaseswiththeflowrate.Table5summarizesthesetendencies

andproposesacorrelationtocalculateDaxinthestudiedrangeof

flowratefortheCorningHP.

Fig. 8 shows the results of Péclet numbers as function of

Reynoldsnumberforeachindustrialreactor.Eachofthesethree

devicescanbeconsideredasaplug_flowreactorforRe ffiffip_S>400

sinceallthevaluesofPécletarerathercloseto100.InFigs.7and8,

theirregularity of thecurves is due tothe uncertainty on the

experimentalaxialdispersioncoefficients.Itisrelatedtothenoise

ontheabsorbancesignalswhichgeneratesanuncertaintyofabout

+0.05s"1_{onE(t)functions.ExtremevaluesofD}

axareidentifiedby

adding and subtracting this uncertainty on RTD curves. The

resultinguncertaintyonDaxisaround+20%.

In Corning RTand Chart ShimTec1 _{reactors, Péclet number}

increaseswithReynoldsnumber.Theplug_flowbehaviorofthese

reactorsresultsofthevelocityofthefluid.Pécletnumberofthe

CorningHPreactorisquiteconstantaroundthevalue100inthe

studiedrangeofReynoldsnumber.Thiscanbeexplainedobserving

thegeometryofthechannel.TheHeartPatternhadbeendesigned

to generate mixing structures at low velocity. These mixing

structuresimplythehomogenizationofthetracer’sconcentration

across the section of the channel. In fact, each heart can be

consideredasindividualperfectmixedvolume.Thewholereactor

issocomposedofa successionof51equivalentstirredtanks.It

resultsinatheoreticalPécletnumberof100usingEq.(18)whereJ

correspondstothenumberofstirredtanksinseries[20].

Pe_¼2ðJ"1Þ (18)

Therefore,theplug_flowofthisreactorisduetothegeometryofits

channel, instead of being due to the velocity of the incoming

processfluidasitisforthetwootherreactors.

3.4.Discussion

Theaxialdispersioncoefficientsobtainedfromtheexperiments

arecomparedtomodelsavailableinliteratureforcircularpipes:(i)

themodelsuggestedbyTaylor[21]forlaminarflowand(ii)the

modelproposedbyLevenspiel[15]forturbulentflow.

For laminar _flow in tubular pipes (Re<2100), Taylor model

givesarelationshipbetweentheaxialdispersioncoefficientDax,

themoleculardiffusioncoefficientDm,thehydraulicdiameterand

theaveragevelocity[21].

Dax¼Dmþu0 2_D

h2

192Dm

(19)

Eq.(19)wasdemonstratedbyTaylor[21]inthecaseofsteady

flow.Thisequationgivesveryaccurateapproximationconsidering

0 0.005 0.01 0.015 0.02 0.025 0 2 4 6 8 10 12 14 Dax(m2.s-1) Q(L.h-1₎ Corning HP Corning RT Chart ShimTec® Trend Corning HP Trend Corning RT Trend Chart ShimTec®

that Daxonly depends on geometricaland physicalparameters

[22,23].

Inturbulentregime(Reh>2100)andforstraightcircularpipes

the relationship between the axial dispersion coefficient and

Reynoldsnumberiswrittenasfollows[15,24]:

Dax u0Dh¼ 3_,107 Reh2:1 þ 1:35 Reh0:125 (20)

Fig.9 showstheevolutionofPéclet numberasafunctionof

Reynoldsnumber forastraight circularpipeusingbothmodels

(Eqs.(19)and(20)).ThelengthofthereactorissetatL=2mand

Dh=2mmwhich roughlycorresponds tothedimensions ofthe

Corning and Chart reactors studied.The experimental data are

added to the graph.The models predict that Péclet number

decreaseswhen Reynoldsnumber increasesin laminar_flow.At

higher Reynolds number, Péclet number first increases with

Reynoldsnumber(2100<Reh<10000)andthentendstoreacha

constantvalue.

TheevolutionofPécletversusReynoldsobtainedforCorningRT

andChart ShimTec1 _{reactors in therange ofReynolds number}

exploredissimilartotheevolutionobtainedinastraightpipein

thetransitionalregime.Itisconsistentwiththeinterpretationof

thepressuredropresults(Section3.1).TheconstantvalueofPe

experimentallyobtainedfortheCorningHPreactorcorrespondsto

the tendency observed in turbulent regime at high Reynolds

numbersin a straight pipe. This is still in agreement withthe

pressuredropcharacterizationdescribedinSection3.1.

4.Conclusion

Thisworkdescribesandcomparesthehydrodynamicsofthree

millistructured reactors. Pressuredrop is measuredin order to

estimatetheFanningfrictionfactor.RTDexperimentsarecarried

outinordertostudythe_flowbehaviorofthesethreedevices.The

methodology usedin this work toidentifytheaxial dispersion

coefficientfromtheRTDcurvesisbasedonthecomputationofthe

convection–dispersionequation.Itallowstotakeintoaccountthe

realsignalshapeofthetracerinjectiontoavoidanytreatmentof

theexperimentaldatasuchasdeconvolutionthatcouldleadtoa

lossofinformation.

Thethreereactorshavedifferentgeometriesinaccordanceto

theapplicationtheyaredesignedfor.CorningHPreactorcanbe

consideredasamixer-exchanger.CorningRTislikelyusedto

pre-heatreactantbeforeareactionortoaddresidencetimeafterthe

reaction occurred. Chart ShimTec1 _{is used toperform reaction}

withviscousfluids.Thesecharacteristicshaveanobviousimpact

onthehydrodynamicsofthereactors.Plug_flowbehaviorofthese

threereactorsishighlightedbytheRTDanalysis.TheHeartPattern

particular geometrygeneratesmixing structures thatinduces a

plug _flow behavior independently of the _flow rate but is also

responsibleforthehighpressuredropobservedinthismodule.

Pressuredropmeasurementsshowthatthetransitiontoturbulent

regime is observed for Re ffiffip_S¼50. In Corning RT and Chart

ShimTec1_{, the RTD experiments show that Péclet number}

increaseswithReynoldsnumber.Thevelocityofthe_fluidenhances

plug flow behavior for these reactors. This last result is in

accordance with literature data for straight circular pipes in

turbulentregimeandcorroboratespressuredropresultswherethe

transitiontoturbulentregimeoccursaroundRe ffiffip_S¼1000.

In ordertocomplete the hydrauliccharacterizationof these

reactors,furtherstudywillbeperformedintermsofmixingtime

asfunctionof_flowrateand_fluidproperties.

Acknowledgements

ThisworkhasbeensupportedbytheANR(AgenceNationalede

laRecherche),France:ProjectANRPROCIP,

ANR-2010-CD2I-013-01.Theexperimentalfacilitywassupportedby:theFNADT,Grand

Toulouse,PrefectureMidi-PyreneesandFEDERfundings.

AppendixA.

CorningHPreactor:estimationoftheequivalentcrosssection

andlength

EquivalentlengthandcrosssectionforCorningHPreactorare

identifiedbyusingtheRTDresults(8experiments).Indeed,these

parameters are fitted by comparing the experimental and

theoretical residence times (Eq. (A.1)) and the shapes of the

experimentalandcalculatedoutletcurvesE(t)wheretheaverage

velocityu0intheonedimensionconvection-dispersionequation

givenbyEq.(13)isobtainedfromthecrosssection(Eq.(A.2)).

tr;exp¼ LS Q (A.1) u0¼ Q S (A.2)

TheresultsintermsofcrosssectionandlengtharegiveninTable1.

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