Modeling of lead (II) biosorption by residue of allspice in a fixed-bed column

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Modelingoflead(II)biosorptionbyresidueofallspiceina?xed-bed

column

J.Cruz-Olivaresa,C.Pérez-Alonsoa,C.Barrera-Díazb,?,FernandoUreña-Nuñezc,M.C.Chaparro-Mercadod,BryanBilyeue

a

UniversidadAutónomadelEstadodeMéxico,FacultaddeQuímica,PaseoColónintersecciónPaseoTollocanS/N,CP50120Toluca,EstadodeMéxico,Mexico

CentroConjuntodeInvestigaciónenQuímicaSustentableUAEM–UNAM,CarreteraToluca-Atlacomulco,km14.5,UnidadElRosedal,CP50200Toluca,EstadodeMéxico,Mexicoc

InstitutoNacionaldeInvestigacionesNucleares,A.P.18-1027,Col.Escandón,DelegaciónMiguelHidalgo,CP11801México,DF,Mexicod

DepartamentodeIngenierías,UniversidadIberoamericana,Prol.PaseodelaReforma880,LomasdeSantaFe,ÁlvaroObregón,CP01219México,DF,Mexicoe

DepartmentofChemistry,XavierUniversityofLouisiana,NewOrleans,LA70125,UnitedStates

b

highlights

??Pb(II)ionscanbesuccessfullyadsorbed(99%)byacontinuouscolumnofallspiceresidue.

??Columnservicetimeis272minata?owof20mL/min,columnlengthof15cm,andC0=15mgPb(II)/L.??Traditionalmodelsonlyprovideinformationonmaximumsorptioncapacityandkineticcoef?cients.??MassTransfermodelprovidesinformationonthesorptionmechanism.

articleinfoabstract

Residueofallspice(PimentadioicaL.Merrill)obtainedasaby-productfromtheessentialoilsupercriticalextractionprocess,hasbeenevaluatedasabiosorbentforremovinglead(II)fromaqueoussolutionsinbatchstudies,butnotinapracticalsystemlikea?xedbedcolumn[12,13].Inthispaper,theeffectsof?owrate(20and40mL/min),beddepth(8and15cm)andin?uentleadconcentration(15and25mg/L)ontheadsorptioncapacityoftheresidueofallspiceina?xed-bedcolumnwereinvestigated.Thehighestadsorptioncapacity(99.2%)ona15mg/LPb(II)solutionwasachievedwithina?owrateof20mL/minandabeddepthof15cm.TheexperimentaldataobtainedfromtheadsorptionprocesswassuccessfullycorrelatedwiththeThomas,Adams–Bohart,Yoon–Nelson,BedDepthServiceTime(BDST),andDoseResponsemodels.Arigorousmodelbasedonthedifferentialbalancemasstransferwasalsousedtodescribetheadsorptionprocessinthecolumn.Theresultsoftheparameterszonemasstransfer,diffusionandmasstransfercoef?cientsobtainedwithmodelingthecontinuousprocesscouldbeappliedtoscaleuptheprocesstoanactualindustrialcolumn.

Ó2013ElsevierB.V.Allrightsreserved.

Articlehistory:

Received18February2013

Receivedinrevisedform25April2013Accepted28April2013

Availableonline7May2013Keywords:BiosorptionLeadAllspice

Fixed-bedcolumnBreakthroughcurve

1.Introduction

Indevelopingcountries,thefactoriesoflargeinternationalcom-panieshaveappropriatewastewatertreatmentfacilities,http://wendang.chazidian.comrgecompa-nieshavesophisticatedwatertreatmentsystems,butsmallbusi-nessesdonothavetheeconomiccapacityforthat.Thereforesmallindustriesrequirecheapandeffectivetechnologiestoremovetoxicmetalsfromwastewater.Althoughtheconcentrationofheavymetalsintheindustrialwastewaterissmall,thiscontaminatedwaterhasanadverseimpactontheenvironmentandaquaticlifeCorrespondingauthor.Tel.:+52(722)2965514;fax:+52(722)2965541.

E-mailaddress:cbd0044@http://wendang.chazidian.com(C.Barrera-Díaz).

1385-8947/$-seefrontmatterÓ2013ElsevierB.V.Allrightsreserved.http://wendang.chazidian.com/10.1016/j.cej.2013.04.101

[1].Manyofthesesmallbusinesseswouldtreattheirwastewateriftheyhadaninexpensiveandeasilyimplementedtechnique.Bio-sorptionusingagriculturalwaste[2–10]isinexpensiveandtheequipmentiseasytoimplementandoperate.

Amongheavymetals,leadhasbeenrecognizedasoneofthemosttoxicmetals,mainlyinitsionicstate.Duetoitshightoxicity,leadisharmfulwhenitaccumulatesinthetissuesoflivingspecies.Leadactsasanenzymeinhibitorincelltissuesand,therefore,isconsideredametabolicpoison.Damagetokidneys,nervoussys-tem,reproductivesystem,liver,andbrainarethemajoreffectsonthehumanbody[11].Theresidueofallspiceisaby-productintheallspiceoilextractionprocess.Thisbiomaterialhasbeenuti-lizedasalow-costadsorbentfortheremovalofleadions,butonlyinbatchexperiments[12,13].

22J.Cruz-Olivaresetal./ChemicalEngineeringJournal228(2013)21–27

Thesorptioncapacityparametersobtainedfrombatchexperi-mentsareusefulinprovidinginformationabouteffectivenessofmetal-biosorbentsystems.However,thedataobtainedunderbatchconditionsaregenerallynotapplicabletomosttreatmentsystems(suchascolumnoperations)wherecontacttimeisnotlongenoughtoreachequilibrium[14].Thus,itisnecessarytoascertainthepracticalapplicabilityofthebiosorbentinacontinu-ouscolumnprocess[15].Theeffectivenessofabiosorbentcanbeevaluatedfromthebreakthroughcurveoftheef?uentconcentra-tionwhereatypicalS-shapedbreakthroughcurveiscommonlyob-served[16,17].

Theaimofthepresentworkistoinvestigatetheeffectsof?owrate,beddepthandtheleadconcentrationonadsorptioncapacitybyresidueofallspiceina?xed-bedcolumn.Thomas,Adams–Bo-hart,Yoon–Nelson,BedDepthServiceTime(BDST),DoseResponse,andMassTransfermodelswereusedto?ttheexperimentaladsorptionresults.Theresultsoftheparametersmasstransferzone,diffusionandmasstransfercoef?cientsobtainedwithmod-elingthecontinuousprocesscanbescaledtoanactualindustrialcolumn.

2.Materialsandmethods2.1.Adsorbentpreparation

Thecrushedde-oiledresidueofallspicewasobtainedasaby-productfromtheessentialoilsupercriticalextractionprocess.Thiswastewasrinsedwithdilutenitricacid(0.1M)andthenwitheth-anol(99.9%purity)inordertoeliminatecolor.Itwasthendriedat60°Cfor24hinanoven.Itwassievedthrougha20meshscreentoobtainparticlessmallerthan0.836mmandstoredinadesiccator.Theresidueofallspicewasanalyzedtoestablishthepresenceofcellulose,hemi-cellulose?bercontent,particlesize,densityandmoisture[8].2.2.Pbdetection

LeadconcentrationwasdeterminedbyFastSequentialAtomicAbsorptionSpectroscopy(AAS)usingaVARIANAA240FSequippedwithanacetyleneburnerandahollowcathodelampsource.Thetransmittedlightwasanalyzedattwowavelengths:217.0nmwithaslitwidthof1.0mm(optimumrange0.1–30lg/mL)and283.3nmwithaslitwidthof0.2mm(optimumrange0.5–50lg/mL).Reportedconcentrationsweretheaverageoftripli-catemeasurementswitharelativeerroroflessthan5%.2.3.Characterization

TheEDSspectraofthesamplesbeforeandafteroftheadsorp-tionaswellaselementalanalysisweretakenonaScanningelec-tronmicroscopy(SEM)JEOLJSM-6510LVequippedwithanOxfordPentaFetx5energydispersiveX-rayspectrometer(EDS)forelementalanalysis.Thesampleswerecoatedwithgold(10–15nm)onaDentonVacuumDeskIV.

ThesurfaceareaofthebiosorbentwasmeasuredusingtheBrunauer–Emmett–Teller(BET)method(Brunaueretal.1938)onaBELSORP-max(BELJapanInc.)instrumentusingtheincludedBELMastersoftware(v.6.1.04),usingnitrogenastheadsorbate.2.4.Metalsolutions

AllsolutionswerepreparedusingARgradereagentsanddeion-izedwater.The1000mgLÀ1Pb(II)stocksolutionwaspreparedfromPb(NO3)2(Merck,99.5%).Theworkingsolutionswerepre-paredfromdilutionsmadefreshfromthestocksolution.Theinitial

pHofeachworkingsolutionwasadjustedbyadditionof0.1MHNO3(Fermont).

2.5.Columndesignandexperimentalprocedure

Fixedbedbiosorptionstudieswereconductedtoevaluatedy-namicbehaviorforPb(II)removalonresidueofallspice.Theexper-imentalset-upconsistedofadown?owglasscolumn(17.8mmID,30cmlength)packedwithvaryingamountsofbiosorbent.Thepackingdensity(qb=436g/L)andvoidfraction(e=0.46)ofeachcolumnbedweredeterminedpriortotheexperiment[15].Thecol-umnwaspreconditionedtopH5byelutingthecolumnwith0.1MHNO3.In?uentfeed?owratewasvariedandmaintainedthrough-outtheexperiments.TheinitialPb(II)concentrationsintheaque-oussolutionswere15and25mg/L.Inalltheexperimentsthetemperaturewasmaintainedat25°C.Attheexitofthecolumn,?owratewasalsomeasuredsoastogetsteadystate?owcondi-tionsinthecolumn.Samplingofcolumnef?uentwasdoneatspec-i?edtimeintervalsinordertoinvestigatethebreakthroughpointorcolumnservicetimeandshapeofbreakthroughcurve.Theef?u-entsampleswereanalyzedusingAtomicAbsorptionSpectroscopy(AAS).Theexperimentswerecontinueduntilaconstantconcentra-tionofPb(II)wasobtained.Theeffectsofinletfeed?owrate(20and40mL/min),initialsorbateconcentration(15and25mg/L)andadsorbentbedheight(8and15cm)wereevaluatedbythebreakthroughcurves.Fortheanalysisofmasstransferzoneandbreakthroughcurve,thedatawasappliedtotheThomas,Adams–Bohart,Yoon–Nelson,BDST,DoseResponseandMassTransfermodels.

2.6.Fixedbedbiosorptionprocessanalysisandmodeling

Thecolumncapacity,qc(mg),foragiveninletconcentrationand?owrateisequaltotheareaundertheplotoftheadsorbedPb(II)concentrationCads(Cads=C0ÀCe),whereC0andCe(mg/L)arethein?uentandef?uentmetalionconcentrations,respectively,versustime(min)andiscalculatedasfollows[15,18]:

qQÁAQZ

t¼t

c¼1000¼

1000

Cadsdtð1Þ

t¼0

whereQisthe?owrate(mL/min),Aistheareaunderthebreak-throughcurveandt(min)couldbettotal,tsatortbthatrepresentthetotal?owtime,thesaturationtimeorthebreakthroughtime,respectively.

Theamountofmetalionssenttothecolumnatdifferenttime,inmg,canbecalculatedfromthefollowingexpression,

m¼

C0ÁQÁtð2Þ

Andthemetalremoval(%)canbecalculatedfromtheratioofcolumncapacitytotheamountofmetalionssenttothecolumnas,

%R¼

qc

m

Á100ð3Þ

Thebiosorptioncapacityq,theweightofPb(II)adsorbedperunitdryweightofadsorbent(mg/g)canbedeterminedasfollowing:

q¼

qcX

ð4Þ

whereXisthetotalmassoftheadsorbentinthecolumn(g).

Ineachexperimentthemasstransferzone,MTZ(cm)wascal-culatedby[19]:

MTZ¼L??1À

tb

tð5Þ

sat

J.Cruz-Olivaresetal./ChemicalEngineeringJournal228(2013)21–2723

whereListhebedheight(cm).

Experimentalevaluationoftheperformanceofa?xed-bedcol-umninbiosorptionisgenerallypossibleonlywithsmalllaboratorycolumns.Thedatacollectedduringlaboratoryexperimentscanbeusedforpredictingandevaluatingtheperformanceofpracticalsizecolumnsbyapplyingsuitablemathematicalmodelsdevelopedforsuchpurposes[15].Severalmodelshavebeenappliedtopre-dictthebreakthroughperformanceandalsotocalculatethecol-umnkineticconstantsandadsorptioncapacityofthe?xed-bedcolumns[20,21].

2.6.1.Thomasmodel(Th)

TheThomasmodel[22]isoneofthemostwidelyusedindescribingthecolumnperformanceandpredictionofbreak-throughcurves.ThemodelfollowstheLangmuirkineticsofadsorption.Itassumesnegligibleaxialdispersioninthecolumnadsorptionsincetheratedrivingforceobeysthesecond-orderreversiblereactionkinetics[23].Itisgivenbytheequationbelow:

CC¼

01þexpkTh1

ðqXÀCð6Þ

00QtÞ

wherekThistheThomasrateconstantinmL/minmgandq0isthemaximumconcentrationofthePb(II)inthesolidphaseinmg/g.2.6.2.Adams–Bohartmodel(AB)

TheAdams–Bohartmodel[24]assumesthattheadsorptionrateisproportionaltoboththeresidualcapacityoftheadsorbentandtheconcentrationoftheadsorbingspecies.Thismodelisusedonlyforthedescriptionoftheinitialpartofthebreakthroughcurve,i.e.uptothebreakpointor10–50%ofthesaturationpoint[25].Theequationis:

CexpðkABCC¼

0expk0tÞ

ð7Þ

ABN0LÀ1þexpðkABC0tÞ

wherekABistheAdams–BohartkineticsconstantinL/mgmin,N0isthemaximumvolumetricsorptioncapacityinmg/Landvisthelin-ear?owrateincm/min.

2.6.3.Yoon–Nelsonmodel(YN)

TheYoon–Nelsonmodel[26]isarelativelysimplemodelbasedontheadsorptionofgasesonactivatedcharcoal.Thismodelas-sumesthattherateofdecreaseintheprobabilityofadsorptionforeachadsorbatemoleculeisproportionaltotheprobabilityofsorbatesorptionandtheprobabilityofsorbatebreakthroughonthesorbent[27].Theequationforthismodelis:

CexpðkYNtÀskYN¼

Þð8Þ

0YNYNwherekYNistheYoon–NelsonproportionalityconstantinminÀ1

andsisthetimerequiredforretaining50%oftheinitialadsorbateinmin.

2.6.4.BedDepthServiceTime(BDST)model

TheBDSTmodelwasderivedfromtheequationdescribedbyAdams–Bohart,butwasmodi?edbyHutchins[28].Itisoneofthemostwidelyusedmodelsthatdescribeheavymetaladsorptionusinga?xed-bedcolumn.BDSTisasimplemodelforpredictingtherelationshipbetweenthedepthandservicetimeintermsofprocessconcentrationandbiosorptionparameters.Themodelisbasedonphysicallymeasuringthecapacityofthebedatdifferentbreakthroughvalues.Itignorestheintraparticlemasstransferresistanceandexternal?lmresistancesuchthattheadsorbateisadsorbedontothebiosorbentsurfacedirectly[29].TheBDSTmod-

elcanbeusedtoestimatetherequiredbeddepthforagivenser-vicetime.Itisgivenbyequation:

CC¼

01þexp1

kð9Þ

BDSTC0NC0LÀt

whereN0isthebiosorptioncapacityofthebed(mg/L),visthelin-ear?owvelocityofmetalsolutionthroughthebed(cm/min),kBDSTistheadsorptionrateconstantthatdescribesthemasstransferfromtheliquidtothesolidphase(L/mgmin)andListhebedheight(cm).

2.6.5.DoseResponsemodel(DR)

TheDRmodelhasbeencommonlyusedinpharmacologytode-scribedifferenttypesofprocesses,canalsobeappliedtodescribebiosorptionincolumns[20,27,30].TheDRmodelisrepresentedbytheequation:

CC¼1À1

1þCð10Þ

Qt

0whereaisaconstant.

2.6.6.MassTransfermodel(MT)

Thesimplemodelsforadsorptioninthecolumns(BDST,Tho-mas,Yoon–Nelson,etc.)?texperimentalresultsfairlywell.How-ever,inordertoobtainthetransportparameters,anothermodelbasedonthemasstransferhasbeendeveloped.Undertheassump-tionsthatthediffusionoccursintheaxialdirections,thereisnointraparticlediffusion,themassdiffusivitydoesnotdependoftheconcentrationofthesolute,andthetemperature,densityandvelocityareconstants,thefollowingmodelisappliedforadiffer-entialmassbalance:

@C@t¼D@2C@z2Àu@Cð1ÀeÞ@zÀkcaðCÀCeÞð11Þ

whereaisthespeci?careaoftheparticles,Disthecoef?cientofdispersionofleadions,eistheporosityofthepackedbed,kcisthemasstransfercoef?cient,uisthespeedsurfaceoftheliquid,tistime,zistheaxialdistanceinthecolumn,Cistheconcentrationofleadwithintheliquid,andCeistheequilibriumconcentrationbe-tweentheliquidandthesurfaceoftheparticlesobtainedfromtheFreundlichorLangmuirequilibriumisotherms.KcisestimatedbyacorrelationfactorbasedJDdimensionlessReynolds(NRe)andSchmidt(NSc)numbers.

J0:25

D¼

NÀ0:31Re

ð12Þ

kcN2=3

whereJD¼

.

3.Resultsanddiscussion3.1.Characterization

AccordingtotheBETanalysistheresidueofallspicehasaspe-ci?csurfaceareaof1.3m2gÀ1withanaverageporediameterof5.55nm.Theatomicradiusofleadis0.181nmso,thesorptionpro-cesscantakeplaceonthesurfaceandinthepores.ThisresultislatercorroboratedwiththeMassTransfermodels(Section3.3).TheEDSspectraofthesorbentbeforeandaftertheleadadsorp-tionareshowninFig.1.Leadisdetectedonthesurfaceofthesor-bentaftertheprocess,verifyingthatleadisadsorbedonthesurface.

3.2.Parametersofthebreakthroughcurves

Thecontinuousleadbiosorptionprocesswascontinuedthroughthesaturationpointofthecolumn,i.e.untiltheoutletconcentra-tionwasatleast0.9C0.Fromthebreakthroughcurvesconstructedfromtheexperimentaldata,theperformancecouldbeevaluatedfromthebreakthroughtime(tb),biosorptioncapacityinthebreak-throughpoint(qb),percentageofmetalremovalinthebreak-throughpoint(%Rb),saturationtime(tsat),biosorptioncapacityinthesaturationtime(qsat),percentageofmetalremovalinthesatu-rationtime(%Rsat),masstransferzone(MTZ)andvolumetreatedinthesaturationtime(Vsat).

Theresultsofthebreakthroughcurvesatbreakthroughtimes(tb)andatsaturationtimes(tsat)forthe?owrates(Q)of20and40mL/min,bedheights(L)of8and15cm,andinitialleadconcen-trations(C0)of15and25mg/L,arepresentedinTable1.

Table1

ParametersofbreakthroughcurvesofthepackedbedcolumnforPb(II)biosorptionbyresidueofallspice.Q(mL/min)2020404020204040

LC0tbqb(cm)(mg/L)(min)(mg/

g)888815151515

1525152515251525

11762522627212212141

11.68.810.07.513.19.911.38.3

Rb(%)99.699.199.098.899.799.199.398.6

tsatqsatRsat(min)(mg/g)(%)18811211070339200199121

15.615.215.415.116.215.916.015.8

MTZ(cm)

Vsat(mL)37602248440127906770400479584856

3.2.1.Effectof?owrate(Q)

Thebreakthroughcurvesattwodifferent?owrates(20and40mL/min)areshowninFig.2.

Theslower?owrateprovidesmoretimeformasstransferintotheporesofthematerial,whichallowstheleadionsaccesstomorebindingsiteswithintheadsorbent.

Fig.2indicatesthatbreakthroughpointsgenerallyoccurredfas-terwithhigher?owrate.Theeffectofthe?owrateatthebreak-throughtime(tb),isthatat20mL/mintheadsorptioncapacityisincreased16–19%comparedwith40mL/min.Thiseffectalsooc-cursatthesaturationtime(tsat).

ThevariationintheslopesofthebreakthroughcurvesandtheadsorptioncapacitiesisduetotherapidmasstransferofPb(II)frombulksolutiontothesolidsurface,sothattheactivesitesofRAwereoccupiedinstantaneouslybythePb(II)ions.However,athigher?owrate,therateofmasstransfertendstoincreaseandtheamountofPb(II)adsorbedontotheunitbedheight(MTZ)in-creasedwithincreasing?owrate,leadingtofastersaturationatahigher?owrate[31,32].

3.2.2.Effectof?xedbedcolumnheight

Thesteepnessofallthebreakthroughcurvesisastrongfunc-tionofbedheight.Theperformanceofbreakthroughcurvesatbedheightsof8and15cmisshowninFig.3.

Fig.3showsthatanincreaseincolumndepthincreasedthethroughputvolumetreatedduetohighercontacttime.ForPb(II)removalthetreatedvolumevariedfrom2790mLto4856mLasthebedheightwasincreasedfrom8cmto15cmat40mL/min.Furthermore,theadsorptioncapacityisraised12%atthebreak-throughpointand4%atthepointof

saturation.

85.93.082.73.672.34.267.35.099.22.998.45.883.15.980.610.0

J.Cruz-Olivaresetal./ChemicalEngineeringJournal228(2013)21–2725

3.2.3.Effectofinletconcentration

TheEffectofinitialconcentrationonthebreakthroughcurvesisshowninFigs.2and4,usingabeddepthof15cmat?owrateof40mL/min.WhenthePb(II)concentrationofthesolutionsin-

creasedfrom15mg/Lto25mg/Ltheadsorptioncapacityde-creased25%atthebreakthroughpointandonly2%atthepointofsaturation.

Inmanycasesthediffusionprocessisconcentrationdependent[18,33,34].Inthiscase,decreasingtheinletPb(II)concentrationin-creasesthetreatedvolumethatcanbeprocessedandshiftsthebreakthroughcurvetotheright.Alowin?uentconcentrationcausestheslowtransportofPb(II)ionsfromthe?lmlayertothesurfaceofadsorbentduetothelowerconcentrationgradient,whichimpliesadecreaseddiffusioncoef?cientanddecreasedmasstransferdrivingforce[35].

TakingintoconsiderationtheresultsfromTable1andtheeffectdiscussedpreviously(Sections3.2.1–3.2.3),theoptimalconditionsareQ=20mL/min,L=15cmandC0=15mg/L.Underthesecondi-tions,theservicetimeis272min,theremovalpercentageis99.7%andtheeffectiveMTZis2.9cmforatreatedvolumeof6770mL.3.3.Modelingofthebreakthroughcurves

Table2listedthecalculatedThomas,DoseResponse,Adams–Bohart,BDST,Yoon–Nelson,andMassTransfermodelsparametersfromtheexperimentalcolumndatawheninitialin?u-entconcentrationwasvaried.Theseparameterscorrespondtothebestresultsofadsorptioncapacityobtainedata?owrateof20mL/minandaheightofthebedof15cm.

TheThomas,Adams–Bohart,Yoon–Nelson,BedDepthServiceTime(BDST)and,DoseResponsemodelsweremodeledusingPolymath5.1andtheMassTransfermodelusingCOMSOL4.2withMATLABsoftware,asshowninFigs.5and6.

Thecorrelationcoef?cientvaluesrangedfrom0.987to0.999,indicatingagoodagreementbetweentheexperimentaldataandthecolumndatageneratedusingthemodels.Thisisfurthervali-datedbyFigs.5and6,wherethepredictedbreakthroughcurvesandexperimentalpointsatdifferentinletconcentrationareshown.ForThomasandDoseResponsemodelsthevaluesoftheinitialadsorptioncapacity,q0,decreaseswithincreasinginitialconcen-tration.Thisisbecauseatlowerconcentration,masstransferisslower,andenhancestheadsorptioncapacity[36].ThomasandDoseResponsemodelsaresuitableforadsorptionprocesseswhere

Table2

Thomas,Adams–Bohart,Yoon–Nelson,BDST,DoseResponseandMassTransfermodelparametersatdifferentinletPb(II)concentrationforQ=20mL/minandL=15cm.Model

Parameters

C0(mg/L)15

25Thomas

kTh(L/mgmin)5.9Â10À33.0Â10À3q0(mg/g)14.313.4r2

0.9970.997Adams–Bohart

kAB(L/mgmin)5.7Â10À33.0Â10À3N0(mg/L)2434.12252.1r2

0.9990.998Yoon–Nelson

kYN(minÀ1)0.0890.075scal(min)295.1166.4sexp(min)303.3166.2r2

0.9970.997BDST

kBDST(L/mgmin)6.0Â10À33.0Â10À3N0(mg/L)2435.42222.4r2

0.9990.999DoseResponse

a

27.212.4q0(mg/g)14.613r2

0.9990.999MassTransfer

D(m2/s)3.02Â10À83.01Â10À8kc(m/s)1.56Â10À51.61Â10À5u(m/s)2.65Â10À32.65Â10À3a(m2/m3)250250r2

0.989

0.987