Dynamic interfacial tension measurement method using axisymmetric drop shape analysis

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Method Article

Dynamic interfacial tension measurement

method using axisymmetric drop shape analysis

Nikhil Bagalkot, Aly A. Hamouda*, Ole Morten Isdahl

DepartmentofEnergyandPetroleumEngineering,UniversityofStavanger,Norway

ABSTRACT

Thecurrentmethoddescribesasimplemodiﬁcationtothedynamicandequilibriuminterfacialtension(IFT) measurementinamultiphasesystem(gas-liquid/liquid-liquid)bytheAxisymmetricDropShapeAnalysis(ADSA) pendantdroptechnique.TheprimarydifﬁcultyassociatedwithdynamicIFTmeasurementbyADSAisproviding theappropriatephasedensities,especiallyinasystemconsistingofgas(CO2,methane,andpropane)andliquids (waterandhydrocarbon).Thedensityofthephasesiscalculatedusinga,consideringthesolubilityoggasesin liquids,asafunctionoftime.Thecalculateddensitiesofthephasesarethenusedasinputsintheexperimentto measuretheIFTathighpressureandtemperaturePVT-cell.

Themethodoffersbeneﬁtsuchas:

Straightforwardandcosteffectiveasitdoesnotrequireadditionalexperimentalsetup(likedensitymeter)ora complicatedequationofstate.

^Thecompositionofthebinarymixtures(moleandmass)andthedensitychangesofthebinarymixturedueto masstransfermaybeobtainedasafunctionoftimeatﬁxedpressureandtemperature.

ÎFTâsâ^functionôf^timeîs^measured^by^takingîntoconsiderationofcorrectphasedensity.

creativecommons.org/licenses/by/4.0/).

ARTICLE INFO

Methodname:DynamicIFTmeasurement

Keywords:DynamicIFT,Pendantdropmethod,Multiphase,Dynamicdensity Articlehistory:Received13June2018;Accepted21June2018;Availableonline23June2018

*Correspondingauthor.

E-mailaddress:aly.hamouda@uis.no(A.A. Hamouda).

https://doi.org/10.1016/j.mex.2018.06.012

creativecommons.org/licenses/by/4.0/).

ContentslistsavailableatScienceDirect

MethodsX

journalhomepage: www.elsevier.com/locate/mex

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SpeciﬁcationsTable

Subjectarea Selectoneofthefollowingsubjectareas:

ChemicalEngineering Engineering Mathematics

Morespeciﬁcsubjectarea Masstransferandinterfacialscience Methodname DynamicIFTmeasurement Nameandreferenceof

originalmethod

Bagalkot,Nikhil,andAlyA.Hamouda.“Experimentalandnumericalmethodforestimating diffusioncoefﬁcientofthecarbondioxideintolightcomponents.”Industrial&Engineering ChemistryResearch56.9(2017):2359–2374.

Zolghadr,Ali,MehdiEscrochi,andShahabAyatollahi.“Temperatureandcompositioneffect onCO2miscibilitybyinterfacialtensionmeasurement.”JournalofChemical&Engineering Data58.5(2013):1168–1175.

Resourceavailability Equipmenttheory:https://www.kruss-scientiﬁc.com/services/education-theory/glossary/

pendant-drop/

Equipment:https://www.kruss-scientiﬁc.com/products/contact-angle/dsa100/drop- shape-analyzer-dsa100/

Software:https://www.kruss-scientiﬁc.com/products/advance-software/overview/

Methodbackgroundanddescription

Interfacialtensionplaysasigniﬁcantroleinnumerousengineeringapplicationsinvolvingmultiphase ﬂow.MeasuringtheIFTisacrucialpartofmultiphasesystems,thereareseveralmethodsavailablelikering method,dropvolumemethod,spinningdropmethod,bubblepressuremethodandpendantdropmethod.

Inrecentyears,thependantdropmethodhasbeenwidelyusedasaneffectivemethodwithhighaccuracy (0.05mN/m²) [1,2],especially at elevatedpressure andtemperature.There are severaltypes ofequipment available that rely onpendant drop method to estimate the IFT, few ofthem are IFT-700 (Vinci Technologies), IFT-10-P(Corelaboratories),DSA-00(KRÜSS),andModel-190(ramé-hartinstrument).Mostoftheseuse imageprocessingcombinedwithYoung-LaplaceequationtoestimatetheIFT.

TheprimarydifﬁcultyassociatedwithIFTmeasurementbypendantdropmechanismisprovidingthe appropriatedensitiesofthetwophases,especiallyinasystemconsistingofgas(likeCO2,methane,and propane)andliquids(waterandhydrocarbon).MultiphasesystemslikeCO2-hydrocarbon,CO2-water/brine, andcarbonatedwater-hydrocarbonareofincreasinginterestduetotheirapplicationin petroleum(CO2EOR), environmental (CO₂ sequestration) and renewable energy (geothermal). When CO₂ contact liquid (hydrocarbon)itdiffusesanddissolvesintotheliquids,formingabinarymixture.Thediffusionofgases intoliquidsaltersthecompositionoftheresultingbinarymixture,hencealterthepropertieslikedensity.

Obtaining thedensity of the binarymixture is complex,especially atelevated pressures and temperaturesandasafunctionoftime.Mostofthestudieshaveneglectedthedensitychangesdueto thesolubilityeffectsofdissolvedgasesinbulkliquidsandhaveusedthedensityofpureﬂuidsinstead ofthebinarymixture[3,4].Whilesomestudieshaveusedseparatehighpressureandtemperature densitymeasuringequipmentatequilibriumcondition(notdynamic),whichcomplicatesthesystem [5,6],asitrequirestwodifferentsetups.Somestudieshaveevenusedacomplexequationofstate model(GERGequationofstate(EOS))[7].

Inthepresentstudy,asimpleandeffectivemethodisusedtomeasurethedynamicandequilibrium IFToftheﬂuid-ﬂuidsystem withamasstransferacrosstheinterface.InsteadofacomplicatedEOSmodel or expensive additional instrument, in the presentmethod, the density of changes in the hydrocarbon due toCO₂masstrasferismeasuredfromacombinationofexperimentalandanalyticalapproach,andthe obtaineddensityisthenusedtoestimatetheIFTbypendantdroptechnique.

PrincipleofIFTmeasurement

Thependantdropmethodisaneffectiveandpopularmeanstomeasuretheinterfacialtensionof liquid-liquidorliquid-gassystem.Inthependantdropmethod,thedropiscreatedfromaneedle

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(capillarytube)inabulkphase(liquidorgas)insideaPVT-cell.Theshapeofthependantdropis governedbygravityandthesurface/interfacialtension.TheIFTiscalculatedfromtheshadowofthe digitalimagecapturedbythecamerausingthedropshapeanalysis.Thedropshapeanalysisrelieson Young-Laplaceequation(Eq.(1))forcalculationofIFT[8,9].

D

^P¼

s

1 r1þ1

r2

; ð1Þ

where

D

^Pîs^the^pressureâcross^theînterface;^r¹ând^r²âre^the^principal^radiiôf^the^pendant^drop,ând

s

^is^theinterfacial/surfacetension.

WhilecarryingoutanIFTmeasurement,thescaleofthedigitalimageismeasuredﬁrsttogetthe actualdimensionofthependantdrop.Oncethescaleisobtained,usinggreyscaleanalysis,theshape ofthedropisthendetermined.Ashapeparameter(B)isthenadjustedinanumericalmethoduntilthe calculateddropshaperesembleswiththeactualshape.Theinterfacialtensionmaythenbecalculated fromEq.(2)fromthedensitydifferencebetweenthePgandPd(

Dr

^=P^d–Pg)andthemodiﬁedshape parameter(B)[8,10].

s

¼

Dr

^gd²

B ; ð2Þ

where

Dr

îs^the^density^difference^between^the^phases;^gîs^theaccelerationduetogravity,anddisthe maximumhorizontaldiameteroftheunmagnifiedpendantdrop.

FromEqs.(1)and(2)itmaybeobservedthatexceptfordensitydifference(

Dr

^),^the^rest^of^the

parametersarecalculatedbytheimageprocessingsoftware.Thedensityofthephasesgoesasinput thattheuserhastoprovide.Therefore,evenifthesoftwareishighlyaccurate,aninaccuratedensity inputwouldresultinanincorrectIFT.Therefore,theactualdensityofthephasesplayacrucialrolein estimationoftheIFT.

Materials

Inthepresentstudy,CO₂(PRAXAIRwithpuritygreaterthan99%)andn-decane(MerckKGaAwith purity99%)wereusedastheexperimentalﬂuids.NISTChemistryWebBook[11]wasthesourceof densityandviscositymeasurementsforpuresubstances(n-decane,andCO2).

Experimentalsetup

Fig.1Ashowstheschematicsoftheexperimentalsetup.ThecriticalpartofthesetupistheHigh- PressurePendantDropApparatus(PD-E1700LL-H)(PVT-cell)builtbyEUROTHECHNICAandKRUSS[12], whichhasbeenusedtomeasuretheinterfacialtension.InFig.1A,PVT-celliscorrosionresistant,high-

Fig.1.(1A)Schematicsoftheexperimentalsetup;(1B)ArrangementofthependantdropinthePVT-cell.

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pressurecylindricalchamber(25mlcapacity)havingalimitingpressureandtemperatureof690barand 180C respectively. The PVT-cell is a see-through chamber, inwhich the pendant drop will be created.Fig.1B showsthearrangementofdropphase(pendantdrop,Pd)andthesurroundingenvironmentalphase(gas orliquid,Pg)inthePVT-cell.ThetemperatureofthePVT-celliscontrolledbyaNiCr-Nithermocouple ﬁttedwithadigitalindicator.Thepressureofthesystemismaintainedexternallythroughapump (maximumpressureof32MPa,GILSON)connectedtothegascylinder.ThePVT-cellhasasee-through windowandisplacedbetweenahigh-resolutioncamera(CF03),andalightsource.KRUSSDSA100 (ADVANCE)[13]softwareisusedtoanalysetheacquiredimagesandcomputethePdvolume,and interfacialtension(IFT)atpre-settimesteps.Further,detailsoftheexperimentalsetupmaybefoundin BagalkotandHamouda[14].Thepressuresensorhasanaccuracyof0.1MPa,whilethetemperature sensorhasaccuracyof0.1Cat0Cto0.8Cat400C,respectively.

ProcedureformeasurementofIFT

InthecurrentworktheCO2-decanesystemhasbeentakenasthereferencesystem,withCO2being theenvironmentalphase/ﬂuid(Pg)andn-decanethedropphase/ﬂuid(Pd).Fig.2showstheschematic representationoftheprocessinvolvedinthemeasurementofIFT.

1ThePVT-cellisﬁlled withtheenvironmentalﬂuidatrequiredpressureusingtheCO2cylinder connectedtothepump,whichissetattherequiredpressureasshownintheFig. 1A.Therefore,atall timesthepressureinsidethePVT-cellismaintained.Further,thetemperatureofthePVT-cellisset, whichismaintainedbyaNiCr-Nithermocouple.

2Once the PVT-cell consisting of environmental ﬂuid achieves the required pressure and temperature,ann-decanependantdrop(Pd)iscreatedattheendofthecapillarytubeasshown intheFig.1B.

3Assoonasthependantdropiscreated,thecameraandtheADVANCEsoftwarestartstocapturethe high-resolutiondigitalimagesofthependantdropfortheanalysis.

4DiffusionofCO2(Pg)intothen-decane(Pd)startswhentheﬂuidscomeincontactwitheachother, resultinginabinarymixtureofCO₂+decane.ThediffusionofCO₂wouldresultinincreasedvolume ofPd.Theexperimentwillcontinueuntilthevolumeofthependantdrophasreachedequilibrium

Fig.2.SchematicrepresentationoftheprocessinvolvedinthemeasurementofIFT.

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(pointabovewhichthereisnoorminimalincrementinthevolumeofthependantdrop)(Fig.3at 50bar25C).

5 Fromtheimagescaptured,withtheaidoftheimageanalysissoftware,thevolumeofthePdat differenttimestepswillbeobtained(Fig.3).

Atthestartoftheexperiment(timet=0),theP_dconsistssolelyofn-decane(100%hydrocarbon).

WiththeinitiationoftheCO2diffusion(t>0s),thevolumeofthePdincreasesduetotheadditional volumeofCO2.Hence,thevolumeofthependantdrop(VPd)wouldbeasummationofthevolumeof hydrocarbon(VHC)andtheincreaseinvolumecausedbythediffusionofCO2(VCO2)inthePd,as givenbyEq.(3).

VPdðtÞ¼VCO2ðtÞþVHC ð3Þ

Foraﬁxedtemperatureandpressurethevolumeofthen-decanewouldbesameasthatduringthe startoftheexperiment(sincethePVT-cellisclosedforanyadditionaldecanemasstocomein).

Hence, in Eq. (3) VPd (obtained from the experiment (step 5) and VHC are known,therefore rearrangingEq.(3)wouldgivethevolumeofCO2inthependantdropasgivenbyEq.(4).

VCO2ðtÞ¼VPdðtÞVHC ð4Þ

6 FromtheacquiredvolumeofCO2(VCO2)anddecane(VHC)inPdateverytimestep(step5),themassand moles,andhence, themole fraction ofCO2(xCO2), andn-decane (xHC) may beobtained atalltime steps.

7 ThecalculateddynamicmolefractionofCO₂(x_CO2)andmolefractionofn-decane(x_HC)wasfurther beusedtoobtainthedensityofthePdconsistingofabinarymixture(

r

^Pd⁾^at^everyexperimental timestepbyEq.(5)[15–17].

r

ðtÞPd¼ðxðtÞCO₂

r

CO2ÞþðxðtÞHC

r

HCÞ

P;T; ð5Þ

where

r

CO2and

r

HCarethedensitiesofCO₂andhydrocarboninthedrop,respectively(obtained fromNISTwebbook[11]).

8 ThedensitydataoftheCO2anddensityofpendantdropconsistingofCO2+n-decanefromEq.(5) wasusedasaninputtothesoftwaretoobtainthedynamicandequilibriumIFToftheCO2-decane system.

Validation

AsdescribedinSection1.1,forthependantdropmethodtheIFTmeasurementisafunctionofthe densityofphases.Therefore,tovalidatethepresentmethod,itwouldbesufﬁcienttovalidatethe

Fig.3.Volumeofthependantdropasafunctionoftime.

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densityvaluescalculatedfromtheEq.(5),withthatobtainedinliterature.DensitydataofCO2+decane binarymixtureat34barand40CobtainedbyKandiletal.[16]wasusedtovalidatethepresent method.ThedensityofthepresentworkandthatformKandil,etal.[16]werebeinputintothe software for theexperiments carried out at 35bar,and 40C withthe CO2-decane system. The obtainedIFT’swerethencomparedforbothofthedensityinputs(Table1).Itmaybeobservedthat bothdensityandobtainedIFTofthepresentmethodarecomparablewithKandiletal.[16],therefore, validatingthepresentmethodofcalculatingthedensityandhence,theIFT.

Methodresultsandcomparison

Todemonstratetheimportanceofcorrectphasedensities(PgandPd)intheestimationofIFT,two differentmethodsondensityinputfromtheliteraturewereusedandcomparedwiththemethod presentedinthecurrentarticle.Allthreemethodsareanalysedusingthesameexperimentcarriedout at50bar,25CforaCO2-decanesystem.Thedetailsofeachofthesemethodsaredescribedbelow:

Case1(initialdensity)[3,4]:This method usesthepurephase density(CO2and decane) andneglecting thedensitychangesduetothediffusedgases(CO2+decane)inbulkliquidstoestimatetheIFT.

Case2(equilibriumdensity)[2,6]:Inthismethod,theIFTismeasuredusingtheequilibriumphase density.Thedensitychangeduetothesolubilityofgaseswasthenconsidered,however,itisdoneonly atequilibrium(ﬁnalpoint),andthisequilibriumdensityisusedtoestimateIFTforthewholeprocess (atalltimes).

Case3(dynamicdensity,presentmethod):HeretheIFTismeasuredusingthecorrecteddensityof thephases(Pg(CO2)andPd(CO2+decane))ateverytimestepcalculatedfromEq.(5),thenfollowing theprocedure described in section2.0. The present methodimproves case-2 asit is capable of calculatingthedensitychangeofthedropphase(CO2+decane)causebythesolubilityofthegas,asa function of time. This is unlike in case-2 where only the density of equilibrium is considered.

Therefore,thepresentmethodreﬂectsthereal-timechangesindensityonIFT,withoutrequiring additionalsetupasincase-2.

Fig.4showsthedensityofthependantdropphaseobtainedfromthethreecases1–3asafunction oftimeat50barand25CfortheCO2-decanesystem.Thedifferenceinthedensityvstimeproﬁle Table1

ValidationofdensityandIFTofthepresentmodelatequilibriumcondition.

Study DensityofCO2-decanependantdrop(g/ml) DensityofCO2[11](g/ml) IFT(mN/m)

Kandiletal.[16] 0.720 0.07087 12.85

Presentmethod 0.711 0.07087 12.53

Fig.4.Densityofthependantdropasafunctionoftimeforcase-1,case-2andcase-3at50barand25C.

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amongthecases(1–3)isevident.Thedensityforcase-1(initialdensity)andcase-2(equilibrium density)remainconstantwithtime,whilethedensityforcase-3(dynamicdensity)whichrepresent theactualscenariovaries(decreases)withtime,depictingchangesindensityofthedropphase(P_d) duetothesolubilityofCO2indecane.

Fig.5showstheIFToftheCO2-decanesystemforcase1,case-2,andcase-3at50barand25C.Itis clearfrom the Fig. 5 that different IFT vs time proﬁles are obtained for the same experiment, emphasising,thedependencyoftheIFTmeasurementonthedensity.Since,bothcase-1andcase-3do notconsiderthedynamicchangeinthedensityofpendantdropduetothesolubilityofagasina liquid,thedynamicIFTmeasuredbythesemethodsaredifferentfromtheonewherethesolubility effectisconsidered(case-3).TheerrorintheestimationofIFTvariesfromamaxof13.4%tominof0.2%

forcase-1andmaximumof14.7%toaminimumof0.2%forcase-2whencomparedtocase-3.However, theequilibriumIFTforcase-2andcase-3seemstobesameorneartoeachother.IfequilibriumIFTis thefocusofthestudyandnotthedynamicnatureoftheIFT,thenapplyingthecase-2wouldbeﬁne,as thedensitiesofthephasesrepresenttheequilibriumconditions.However,ifthedynamicchangesin theIFT,aswellastheequilibriumIFT,istobeanalysed,thencase-3wouldbethebestoption(followed inthepresentstudy),asthedensitiesofthephasesarecalculatedatdifferenttimeintervalsuntil equilibriumisreached.ObtainingIFTusingthecase1approachwouldleadtoanerror,asthedensity representonlytheinitialstateofthesystem,nottheequilibriumorthedynamic.

Drawbacksandrecommendations

Althoughthemethodpresentedissimple,reliable,andfreefromhumaninterference,themajor setbackwouldbemanuallyenteringthedensityofphasesinthesoftware.Thetaskmayseemsimple, buttoobtainhighresolutiondynamicdata,itrequiresalotofentries.Further,ifexperimentsare carriedoutwithsensitivityforbothtemperatureandpressure,thenumberofentriesismultiplied accordingly.Anexample,a4-hexperimentwithdynamicIFTdataforevery5minandsensitivityfor two temperatures and three pressuresresults inn 576manual inputs (two for each time-step).

However,sincetheprocessisrepetitive,itisstraightforwardtoletcomputer-scriptsperformthetask.

Moreimportantly,theproblemcanbeeliminatedifthesoftware-developers allowedforinputof densityofphasesobtainedfromthemodelaseitherafunctionoftimeorasatablewithtimeand densityofthephases.

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Fig.5.DynamicIFTCO2-decanesystemasafunctionoftimeforcase-1,case-2andcase-3at50barand25C.

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