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Gas-Liquid Separation for Direct Methanol Fuel Cells

Permanent Link: http://ufdc.ufl.edu/UFE0045010/00001

Material Information

Title: Gas-Liquid Separation for Direct Methanol Fuel Cells
Physical Description: 1 online resource (98 p.)
Language: english
Creator: Credle, Sydni S
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: carbon -- component -- design -- dioxide -- experimental -- hydrophobic -- membrane -- model -- porous -- portable -- ptfe -- transport -- vent -- vle
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A portable direct methanol fuel cell (DMFC) system rated at 20W (nominal) has been successfully implemented at University of North Florida and University of Florida. The novel DMFC system utilizes an open-cathode design that allows for passive water recovery within the membrane electrode assembly of the fuel cell stack. In the anode loop, product CO$_2$ resulting from the fuel cell oxidation reaction is vented from the system through a gas-liquid separation (GLS) device which utilizes hydrophobic porous membranes. A software model has been developed to simulate the bulk transport of CO$_2$ and the water/methanol loss rate through the membrane. Two loss modes are considered 1) saturated CO$_2$  vent stream through the 'active' membrane area directly in contact with the carbon dioxide bubble, and 2) evaporation from the 'idle' membrane portion that is solely in contact with the liquid phase. A properties model that includes vapor liquid equilibrium (VLE) for the ternary system composed of methanol, water, and carbon dioxide is presented. Membrane morphology was observed using scanning electron microscopy (SEM) and contact angle measurements analyzed with ImageJ software. Single-phase (CO$_2$ only) and two-phase (CO$_2$ + H$_2$O) experiments were conducted to observe CO$_2$ mass flux to vent pressure relationship via hydraulic conductance parameter. The magnitude of the hydraulic conductance is influenced by the wet/dry condition of the membrane. A 'wet' membrane in contact with liquid exhibits a hydraulic conductance that is an order of magnitude lower than that of a dry membrane suggesting a higher vent pressure requirement for the wet case to achieve the same mass flux. Experiments were performed to determine the rate of water loss for GLS membrane under various active and idle conditions. It was concluded that vent pressure range 0 - 6895 Pa (gage) has no significant influence on the evaporation loss rate. Model results for total water loss rate correlated with experimental data within 6.5\%. Lastly, a new GLS design configuration that utilizes membrane technology, Pandora, is introduced. Design, fabrication, and testing of the prototype device illustrates proof of concept and feasibility for the component.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sydni S Credle.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Lear, William E, Jr.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045010:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045010/00001

Material Information

Title: Gas-Liquid Separation for Direct Methanol Fuel Cells
Physical Description: 1 online resource (98 p.)
Language: english
Creator: Credle, Sydni S
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2013

Subjects

Subjects / Keywords: carbon -- component -- design -- dioxide -- experimental -- hydrophobic -- membrane -- model -- porous -- portable -- ptfe -- transport -- vent -- vle
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: A portable direct methanol fuel cell (DMFC) system rated at 20W (nominal) has been successfully implemented at University of North Florida and University of Florida. The novel DMFC system utilizes an open-cathode design that allows for passive water recovery within the membrane electrode assembly of the fuel cell stack. In the anode loop, product CO$_2$ resulting from the fuel cell oxidation reaction is vented from the system through a gas-liquid separation (GLS) device which utilizes hydrophobic porous membranes. A software model has been developed to simulate the bulk transport of CO$_2$ and the water/methanol loss rate through the membrane. Two loss modes are considered 1) saturated CO$_2$  vent stream through the 'active' membrane area directly in contact with the carbon dioxide bubble, and 2) evaporation from the 'idle' membrane portion that is solely in contact with the liquid phase. A properties model that includes vapor liquid equilibrium (VLE) for the ternary system composed of methanol, water, and carbon dioxide is presented. Membrane morphology was observed using scanning electron microscopy (SEM) and contact angle measurements analyzed with ImageJ software. Single-phase (CO$_2$ only) and two-phase (CO$_2$ + H$_2$O) experiments were conducted to observe CO$_2$ mass flux to vent pressure relationship via hydraulic conductance parameter. The magnitude of the hydraulic conductance is influenced by the wet/dry condition of the membrane. A 'wet' membrane in contact with liquid exhibits a hydraulic conductance that is an order of magnitude lower than that of a dry membrane suggesting a higher vent pressure requirement for the wet case to achieve the same mass flux. Experiments were performed to determine the rate of water loss for GLS membrane under various active and idle conditions. It was concluded that vent pressure range 0 - 6895 Pa (gage) has no significant influence on the evaporation loss rate. Model results for total water loss rate correlated with experimental data within 6.5\%. Lastly, a new GLS design configuration that utilizes membrane technology, Pandora, is introduced. Design, fabrication, and testing of the prototype device illustrates proof of concept and feasibility for the component.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Sydni S Credle.
Thesis: Thesis (Ph.D.)--University of Florida, 2013.
Local: Adviser: Lear, William E, Jr.
Electronic Access: RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-05-31

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2013
System ID: UFE0045010:00001


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GAS-LIQUIDSEPARATIONFORDIRECTMETHANOLFUELCELLSBySYDNISTEVENSCREDLEADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013SydniStevensCredle 2

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Andwillyousucceed?Yes!Youwill,indeed.(98and3=4percentguaranteed)-Dr.Seuss,OhthePlacesYou'llGo 3

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ACKNOWLEDGMENTS ThroughthecourseofmytimehereattheUniversityofFlorida,Ihavebeenfortunatetocrosspathswithsometrulyremarkablepeople.Firstandforemost,I'dliketothankmyadvisorDr.Learforthecountlesshoursspentmentoringmethroughmyacademiccareer.It'sbeenanabsolutepleasureworkingforyouoverthepastfewyears.ThelessonsI'velearnedfrombothyouandDr.JamesFletcherareimmeasurable.Thankyou.Ialsowanttothankthemembersofmycommittee:Dr.JamesFletcher,Dr.OscarCrisalle,Dr.Mikolaitis,andDr.HerbertIngley.Thankyouforyourservice.MyworkonthisprojecthasbeensupportedthroughvariousfundingagenciesincludingtheCommunications-ElectronicsResearch,DevelopmentandEngineeringCenter(CERDEC)oftheUnitedStatesArmy[ContractNumber:W909MY-09-C-0052,W909MY-11-C-0005],theSouthEastAllianceforGraduateEducationandtheProfessoriate(SEAGEP),theFlorida-GeorgiaLouisStokesAllianceforMinorityParticipation(FGSLAMP),andtheAlumniProgramintheDepartmentofMechanical&AerospaceEngineeringatUniversityofFlorida.I'dliketoacknowledgemyDMFCresearchgroup:MattInman,RafeBiswas,FennerColson,PhilipBailey,WeiChen,andShyamMudiraj.Also,Dr.LukeNealandJohnCrittendon.ManythankstotheamazingGLSteam:SharunKumar,PalakThakkar,AdamButler,TimGaynor,andGirishSuri.Special'thankyou'totheUniversityofNorthFloridateam:JasonHarrington,BenjaminSwanson,TaylorMaxwell,andAaronMeles.I'dalsoliketoacknowledgetheUNFNWteam:HenryVoss,PhilCox,AlexMossman,SabaRahmani,andRussellBarton.ThefacultyandstaffattheUniversityofFloridaaresimplythebest.AfewstandoutaspeoplethatIadmireandrespectforbeingconscientiousoftheirworkaswellasmakingmylifeasastudentrunsmoothlyfrombothapersonalandadministrativestandpoint.SpecialthankstofacultymembersDr.DavidHahn,Dr.SivaramakrishnanBalachandar,Dr.BenjaminJ.Fregly,andDr.JamesKlausner.Also,asincere 4

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'thank-you'totheMAEstaff:MarkReidy,JanRockey,JeffStudstill,ShirleyRobinson,SalenaRobinson,PamSimon,JaredCarnall,ColeStudstill,MikeBraddock,DavidRockey,ShellyBurleson,andGenevieveBlake.BlessingsandlighttomyfriendsCheng-ChanKuo,I-ChingKuo,SannaMartin,FotouhAl-Ragom,AyyoubMehdizadeh,PraneethPilarisetti,AnupamPatil,VisheshVikas,HectorLeiva,MichaelAsgill,XunJia,AkikoHiramitsu,JamesWang,BhupinderSingh,AmeyBarde,andGabrielEspinosa.Lastly,Isendheartfeltregardstomyfamilyfortheirsupport.Specialthankstomymother,Dr.GaynaStevens-Credle,andgrandmother,BettyeStevens.I'msuretherearecountlessinstanceswereyoumayhavesacricedandmadeawaywheretherewasnoneinordertogivemetheopportunitytobewhereIamtoday.Imaynoteverknowwhatyou'vedonebehindthescenesonmybehalf.JustknowthatIamtrulythankful.IwouldalsoliketothankmysistersTerryMcKeeverandDaynaCredleaswellasmynieces,NatalieandMia.AsInavigatemywaythroughlifeandtheworld,IammotivatedbythehopethatImakeallofyouproud.Thankyousomuch. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 LISTOFSYMBOLS .................................... 11 ABSTRACT ......................................... 16 CHAPTER 1INTRODUCTION ................................... 18 1.1Background ................................... 18 1.2Motivation .................................... 24 1.3ResearchObjective .............................. 25 1.4DissertationOutline .............................. 26 2LITERATUREREVIEW ............................... 27 3MODELINGANDSIMULATION ........................... 33 3.1Introduction ................................... 33 3.2BulkFlowModel ................................ 34 3.2.1HagenPoiseuilleLaw ......................... 34 3.2.2Gas-VaporMixturePropertiesModel ................. 36 3.2.2.1ConstituentPartialPressures ................ 36 3.2.2.2CarbonDioxideSolubility .................. 37 3.2.2.3Vapor-LiquidEquilibrium(VLE) ............... 39 3.2.2.4ViscosityandDensityofGasMixture ........... 40 3.3EvaporationModel ............................... 41 3.3.1Fick'sLawforMolecularDiffusion ................... 44 3.3.2MassTransferbyNaturalConvection ................. 47 4MODELVALIDATIONEXPERIMENTS ....................... 51 4.1Gas-LiquidSeparator(GLS) .......................... 51 4.1.1BriefDesignHistory .......................... 51 4.1.2ExpandedPolytetrauoroethylene(ePTFE)Membrane ....... 55 4.1.3GLSTestCell .............................. 57 4.2ExperimentalSetup .............................. 61 5RESULTSANDDISCUSSION ........................... 66 5.1MassFluxtoVentPressureRelationship .................. 66 6

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5.2WaterLossRate:Evaporation ........................ 71 5.3WaterLossRate:BulkFlow+Evaporation ................. 73 6PANDORAGLSDESIGN:APPLICATIONEXAMPLE ............... 79 7CONCLUSIONS ................................... 86 APPENDIX:UNIVERSALFUNCTIONALACTIVITYCOEFFICIENTMETHOD ... 91 REFERENCES ....................................... 94 BIOGRAPHICALSKETCH ................................ 98 7

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LISTOFTABLES Table page 3-1CO2Solubilityin1Lwateratvarioustemperaturesandpressures. ....... 39 4-1ListofcomponentsandspecicationsfortheGLSexperimentalteststation. .. 64 5-1Hydraulicconductance,inkg/(Pam2s),resultsfortwo-phase(DIwater+CO2)GLSexperiments. .............................. 68 6-1Hydraulicconductanceresultsfortwo-phase(DIwater+CO2)PandoraGLSexperiments. ..................................... 83 A-1Volume(Rk)andsurface(Qk)parametersformethanolandwater[ 1 ]. ..... 92 A-2Group-groupinteractionparameters(aij)formethanolandwater[ 1 ]. ...... 93 8

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LISTOFFIGURES Figure page 1-1GravimetricenergydensityasafunctionofoperationtimeforvariousDMFCsystemsascomparedwiththecurrentstateoftheartforLi-ionbatteries[ 2 ]. .. 19 1-2GravimetricenergydensityversusvolumetricenergydensityforvariousDMFCsystemsandtraditionalbatterytechnology.[ 2 ]. .................. 20 1-3Directmethanolfuelcell(DMFC). .......................... 21 1-4TraditionalDMFCsystem. .............................. 22 1-5Open-cathodeDMFCsystem. ............................ 22 1-6ConceptdrawingoftheDemonstrationPrototype4(DP4)system[ 3 ]. ..... 23 1-7DemonstrationPrototype4(DP4)system[ 3 ]. ................... 24 3-1Illustrationof'active'and'idle'portionsofGLSmembranewithassociatedcharacteristiclengthscales. ............................. 33 3-2Cross-sectionviewofidlemembranearea ..................... 42 3-3Electricalresistancemodelusedforevaporationtransportthroughmembranelayers ......................................... 43 4-1GLSusedinDemonstrationPrototype3(DP3)packagedunit. ......... 52 4-2Rev4GLSdesignconceptdrawing. ........................ 53 4-3GLSconceptdesignthatfeaturesatankwithpleatedmembranestructure. .. 54 4-4PoreontubularGLSconguration. ......................... 55 4-5ePTFElayerofcompositeDonaldsonmembrane. ................ 56 4-6DIwaterdropletonsurfaceofePTFEmembranelayer. .............. 57 4-7ComparisonofliquiddropletsofdifferentuidsincontactwithhydrophobicePTFEmembranesurface-1Mmethanolsolution(left)andDIwater(right). .. 58 4-8Cross-sectionviewofcompositeDonaldsonmembrane. ............. 59 4-9BackinglayerofcompositeDonaldsonmembrane. ................ 60 4-10GLSRev2oweld. ................................. 60 4-11TopviewoffullyassembledGLSRev2testcell. .................. 61 4-12SchematicdiagramofGLStestcell. ........................ 62 9

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4-13SchematicdiagramofGLSexperimentalteststation. ............... 63 4-14GLSexperimentalteststation. ........................... 65 5-1Massuxofcarbondioxideversusventpressurefordrymembranecase. ... 67 5-2Comparisonofthehydraulicconductance,,forvarioussingle-phase(CO2only)andtwo-phase(CO2+H2O)case. ...................... 70 5-3Waterlossrateduetoevaporationforthecaseofnoappliedbackpressure(BP=n/a). ...................................... 75 5-4Evaporationwaterlossrateatventpressure(gage)of3447Pa. ......... 76 5-5Evaporationwaterlossrateatventpressure(gage)of6895Pa. ......... 77 5-6Comparisonofexperimentalandcalculatedvaluesforcombinedbulkow+evaporationatvarioustemperatures. ........................ 78 6-1IllustrationofPandoraGLSdesign. ......................... 79 6-2Pandoraprototype(notshown:coverlidforthetank). .............. 80 6-3Pandoraprototypeduringtesting.Waterlevelshownatv50%oftankcapacity. 81 6-4ComparisonofexperimentalandcalculatedwaterlossrateforPandoraGLSprototype(T=333K). ................................ 85 10

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LISTOFSYMBOLS,NOMENCLATURE,ORABBREVIATIONS AMembranearea,m2AmemMembranearea,m2AporePorearea,m2aij,ajiGroup-groupinteractionconstantDbl,H2O,airDiffusioncoefcientforwaterinairthroughboundarylayer,m2=sDH2O,airDiffusioncoefcientforwaterinairthroughmembranepore,m2=sd(..)=d(1=T)Temperaturedependentempiricalcoefcient,KGEExcessGibbsfreeenergy,JGrLeGrashofnumbergGravity,m=s2gCCombinatorialcontributiontomolarexcessGibbsfreeenergy,J=molgEMolarexcessGibbsfreeenergy,J=molgRResidualcontributiontomolarexcessGibbsfreeenergy,J=molHCO2,H2OHenry'sLawconstant,PaH0CO2,H2OHenry'sLawconstantatT=298.15K,mol=(kgbar)hHHeattransfercoefcient,W=(m2K)hmMasstransfercoefcient,m=skThermalconductivity,W=(mK)LeCharacteristiclengthforevaporation,mlmMembranethickness,mMiMolecularweight,g=mol 11

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MtotalTotalmolecularweightofgasmixture,g=mol_m00airMassuxofair,kg=(m2s)_m00bBulkowgasmixturemassux,kg=(m2s)_m00b,iBulkowmassuxforthei-thgasspecies,kg=(m2s)_m00comp,H2OEvaporationmassuxofwaterthroughcompositemembrane,kg=(m2s)_m00e,H2OEvaporationmassuxofwater,kg=(m2s)NuNusseltnumberniNumberofmolesofspeciesi,molPPressure,PaP(1)H2OPartialpressureofwater,PaP(2)CH3OHPartialpressureofmethanol,PaP(3)CO2Partialpressureofcarbondioxide,PaPamb,H2OVaporpressureofwaterinambient,PaPbinBinary(methanol+water)pressure,PaPgageUpstreammembranegagepressure,PaPH2O,E1Partialpressureofwateratliquid/ePTFEmembranelayerinterface,PaPH2O,E2PartialpressureofwateratePTFE/polyestermembranelayerinterface,PaPH2O,E3PartialpressureofwateratPolyester/boundarylayerinterface,PaPH2O,E4Partialpressureofwateratboundarylayer/ambientinterface,PaPlogMLogmeanpressure,PaPtotalTotalpressure,Pa 12

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Psat,CH3OHSaturatedvaporpressureofmethanol,PaPsat,H2OSaturatedvaporpressureofwater,PaPventVentpressure,PaPrPrandtlnumber_QHeattransferrate,J=sqi,qjSurfaceareaofspeciesi(orj)RUniversalgasconstant,J=(molK)RblBoundarylayerresistance,s=mRcompComposite(membrane+polyesterlayer)resistance,s=mRkVolumeofgroupkRmemMembraneresistance,s=mRtotalTotalresistance,s=mRywPolyesternon-wovenmembranelayerresistance,s=mrjMolecularvolumeofspeciesjScSchmidtnumberShSherwoodnumberTTemperature,KxCH3OHMolefractionofmethanolinliquidphasexCO2MolefractionofcarbondioxideinliquidphasexH2OMolefractionofwaterinliquidphaseyMolefractioningasphase 13

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GreekijGasmixtureviscosityconstantCH3OHActivitycoefcientformethanolH2OActivitycoefcientforwateriActivitycoefcientforspeciesiPorediameter,mPorosityiSurfaceareafractionofspeciesiDynamicviscosity,PasKinematicviscosity,m2=siNumberofkgroupsinmoleculejDensity,kg=m3iVolumefractionofspeciesiTortuosityfactorH2OMassfractionofwateriMassfractionofspeciesijiGroupinteractionparameterHydraulicconductance,kg=(Pam2s)SubscriptsambAmbient 14

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avgAveragebBulkowE1Liquid/ePTFEmembranelayerinterfaceE2ePTFE/polyestermembranelayerinterfaceE3Polyester/boundarylayerinterfaceE4Boundarylayer/ambientinterfaceeEvaporationsSurfaceAbbreviationsBLBoundarylayerDMFCDirectmethanolfuelcellGLSGas-liquidSeparatorMEMePTFEmembranelayerPWPolyesternon-wovenmembranelayerUNFNWUniversityofNorthFloridaNorthwestUNIFACUniversalFunctionalActivityCoefcientVCGLSventchamberVLEVapor-liquidEquilibrium 15

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyGAS-LIQUIDSEPARATIONFORDIRECTMETHANOLFUELCELLSBySydniStevensCredleMay2013Chair:WilliamE.LearMajor:MechanicalEngineeringAportabledirectmethanolfuelcell(DMFC)systemratedat20W(nominal)hasbeensuccessfullyimplementedatUniversityofNorthFloridaandUniversityofFlorida.ThenovelDMFCsystemutilizesanopen-cathodedesignthatallowsforpassivewaterrecoverywithinthemembraneelectrodeassemblyofthefuelcellstack.Intheanodeloop,productCO2resultingfromthefuelcelloxidationreactionisventedfromthesystemthroughagas-liquidseparation(GLS)devicewhichutilizeshydrophobicporousmembranes.AsoftwaremodelhasbeendevelopedtosimulatethebulktransportofCO2andthewater/methanollossratethroughthemembrane.Twolossmodesareconsidered1)saturatedCO2ventstreamthroughthe'active'membraneareadirectlyincontactwiththecarbondioxidebubble,and2)evaporationfromthe'idle'membraneportionthatissolelyincontactwiththeliquidphase.Apropertiesmodelthatincludesvaporliquidequilibrium(VLE)fortheternarysystemcomposedofmethanol,water,andcarbondioxideispresented.Membranemorphologywasobservedusingscanningelectronmicroscopy(SEM)andcontactanglemeasurementsanalyzedwithImageJsoftware.Single-phase(CO2only)andtwo-phase(CO2+H2O)experimentswereconductedtoobserveCO2massuxtoventpressurerelationshipviahydraulicconductanceparameter.Themagnitudeofthehydraulicconductanceisinuencedbythewet/dryconditionofthemembrane.A'wet'membraneincontactwithliquidexhibitsahydraulicconductancethatisanorderofmagnitudelowerthanthatofa 16

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drymembranesuggestingahigherventpressurerequirementforthewetcasetoachievethesamemassux.ExperimentswereperformedtodeterminetherateofwaterlossforGLSmembraneundervariousactiveandidleconditions.Itwasconcludedthatventpressurerange0-6895Pa(gage)hasnosignicantinuenceontheevaporationlossrate.Modelresultsfortotalwaterlossratecorrelatedwithexperimentaldatawithin6.5%.Lastly,anewGLSdesigncongurationthatutilizesmembranetechnology,Pandora,isintroduced.Design,fabrication,andtestingoftheprototypedeviceillustratesproofofconceptandfeasibilityforthecomponent. 17

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CHAPTER1INTRODUCTION 1.1BackgroundPortabledevicescoverawiderangeofenergylevelsdependingontheapplication.Typicalpowerrequirementsinclude2-5Wforcellphones,8-15Wformicroairvehicles,15-30Wforlaptopcomputers,and500-1000Wforsmallvehiclessuchasgolfcartsandforklifts[ 4 5 ].Thepredominantfeatureofportablepowersystemsisthenecessityforhighenergy(andpower)density,lowweight,andcompactness.Forthesesystems,thekeyobjectiveistomaximizetheamountofpowerwhileminimizingthephysicalfootprint(mass,volume)ofthesystem.Traditionally,thisisachievedusingrechargeablebatteriessuchaslithiumion,nickelcadmium,nickelmetalhydride,andlithiummagnesiumoxide.[ 2 ].Themassandvolumeoftraditionalbatterysystemstendtoscalelinearlywiththepowerrequirement.Thisisreasonableforportablesystemsthatoperateforshortdurationslessthan50hours.However,atlongerdurations(>50hrs),traditionalbatteriesarenotfeasibleduetothebulkinessofthesystem[ 2 ].AcomparisonofcommerciallyavailableDMFCsystemstoLi-ionbatteriesonthebasisofgravimetricenergydensityisgiveninFigure 1-1 .Asshowninthegure,astheoperationtimeofthedutycycleforthesystemincreases,theenergydensityforLi-ionbatterytechnologystaysconstant.Thisisduetotheproportionalnatureoftheenergydensityforthistechnologytotheoperationtime.Conversely,theenergydensityforDMFCsystemsincreasesastheoperationincreasesuntilitreachestheasymptoticlimitbasedonthehigherheatingvalueofthemethanolfuelitself[ 2 ].Figure 1-2 showsagraphiccomparisonofgravimetricversusvolumetricenergydensityofcommerciallyavailableDMFCsystemstovarioustraditionalbatterytypes.Asshowninthegure,DMFCsystemsshowhigherpromiseofachievinggreaterenergydensitywhencomparedtotraditionalbatteriesduetotheuntappedpotentialofthemethanolconversionefciency[ 2 ]. 18

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Figure1-1. GravimetricenergydensityasafunctionofoperationtimeforvariousDMFCsystemsascomparedwiththecurrentstateoftheartforLi-ionbatteries[ 2 ]. Directmethanolfuelcellsaredevicesthatproduceelectricityfromelectrochemicalreactionsthattakeplacewhenahydrogen-richfuel(methanol)combineswithoxygenwithinamembraneelectrodeassembly(MEA).Figure 1-3 showsasinglecellDMFC.Asshowninthegure,waterandmethanolaresuppliedtotheanodeowchannel.Byreactionsontheanodecatalystlayer,themethanolisoxidizedtoformhydrogenprotons,electrons,andcarbondioxide.Thehydrogenprotonstravelthroughthemembranelayerstothecathodecatalystwhereasecondelectrochemicalreactiontakesplaceinthepresenceofoxygenandelectronsthattraveltothecathodeviaexternalcircuit.Thesoleproductofthecathodereactioniswater.Theoverallchemicalreactionforadirectmethanolfuelcellis CH3OH+3=2O2)166(!CO2+2H2O(1)Thetwoseparatereactionsthattakeplaceontheanodeandthecathodeareasfollows: 19

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Figure1-2. GravimetricenergydensityversusvolumetricenergydensityforvariousDMFCsystemsandtraditionalbatterytechnology.[ 2 ]. (AnodeReaction) CH3OH+H2O)166(!CO2+6H++6e(1)(CathodeReaction) 6H++6e+3=2O2)166(!3H2O(1)DMFCstacksarecomposedofmultiplecellsarrangedtogetherinseriestoprovidepoweratadesiredvoltageforagivenapplication.AtraditionalDMFCsystemisgiveninFigure 1-4 .Asshowninthegure,thereisahostofperipheralequipmentthatconstitutesacompletesystem.Ontheanodeside,methanolandwatersolutionisstoredinatankandintroducedintothesystemviaadosingpump.Liquidwaterisnormallyrecoveredfromthecathodesideandintroducedasneededintotheanodeloop.ProductCO2isremovedusingagas-liquidseparationdevice.Otherequipment 20

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Figure1-3. Directmethanolfuelcell(DMFC). includesare-circulationpumptocontinuouslytransportthemethanol-watermixturearoundtheanodecircuit.Lastly,aheatexchangermaybeneededtoconditionthereactantstreaminsupportofthetemperaturesetpoint.Thecathodeloopconsistsofair(oxygen)introducedintotheDMFCstackbyuseoffanorblower.Someofthewaterproducedasapartofthecathodereactionisthencondensedoutoftheexitairstreamviaheatexchangerandaknock-outseparationdevice,thenreturnedtothewaterstoragetank.AnoticeablecharacteristicforthetraditionalDMFCsystemshowninFigure 1-4 isthelargenumberofcomponents.Eachcomponentinthesystemrepresentsaparasiticpowerlosswhichcanlowerthenetefciency.Theuseofmanydifferentsubsystemsinthismannerprecludescompactnessandcanleadtoabulky,non-practicalsystemthatisnotsuitableforportabledevices. 21

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Figure1-4. TraditionalDMFCsystem[ 6 ]. ThetraditionalDMFCsystemcanbesimpliedonthebasisofnumberofcomponentsbyusinganopen-cathodedesignasillustratedinFigure 1-5 .Theopen-cathodesystemdiffersfromatraditionalsysteminthattheproductwaterformedatthecathodeisnotrecoveredexternallyfromtheexitingairstreambutrecycledinternallybyusingaliquidbarrierlayer(LBL)withintheMEA.Forthisdesign,thecathodeisessentially'open'toambientandthereactantair(oxygen)streampassesthroughthestackitself.Therefore,peripherycondensationequipmentfoundonthecathodeloopofthetraditionalsystemisdeemedunnecessary.Theendresultisasmallersystemwithlesscomponentsandlowercomplexity. Figure1-5. Open-cathodeDMFCsystem[ 6 ]. 22

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WaterbalanceisacriticalissueforDMFCsystems.Theconcentrationintheanodeloopmustremainwithinacertainbounds,asdoesthetotalliquidinventoryforthesystem.Waterrecoveryusingfromthecathodeplaysanimportantroleinmaintainingoptimalwaterbalance.TheUniversityofNorthFlorida(UNF)andtheUniversityofFlorida(UF)currentlyhavea20W(nominal)hybridDMFCpowersystemthatisusedtopoweralaptopcomputerformilitaryapplication.ThecurrentiterationofthedesignisreferredtoastheDemonstrationPrototype4(DP4).Figure 1-6 showsaconceptdrawingoftheDP4.Areal-worldimageoftheDP4packagedunitisgiveninFigure 1-7 Figure1-6. ConceptdrawingoftheDemonstrationPrototype4(DP4)system[ 3 ]. Fora10-hrruntime,theDP4systemhasaspecicpowerof26.3W/kgandspecicenergyof263(W-hr)/kg.Ithasapowerdensityof28W/Landanenergydensityof280(W-hr/L)[ 3 ].TheDP4packagedunitrepresentsabreakthroughintermsofsizeandweightinitsrespectivepowerclass(portablesystems).Futureversionsofthisdevicewillonlyimproveinallaspectsandonedaybecomeacommerciallyavailablesystem. 23

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Figure1-7. DemonstrationPrototype4(DP4)system[ 3 ]. 1.2MotivationDirectmethanolfuelcells(DMFC)representaviableenergyalternativetoonedaydisplacetraditionalbatterytechnologyforportableapplications.AttheanodeofaDMFC,theoxidationreactionofmethanolproducesonemoleofcarbondioxideforeverymoleofmethanolconsumed.AcriticalissueonthesystemlevelisventingtheproductCO2whileretainingtheliquidphasewaterandmethanolforrecirculationbacktothefuelcellinlet.Carbondioxidethatremainsintheloopcaninterruptsensormeasurements,interferewithpumpingefciencies,andcausecatastrophicburstfailures.AsshowninFigure 1-4 andFigure 1-5 ,thereisagas-liquidseparator(GLS)componentthatistaskedwithcarbondioxideremoval.Traditionally,separationbetweengasandliquidphasesisachievedusinggravitysystemssuchasknockoutdrumsandashseparators.Thesetypesofsystemsprovetobetoobulkyanddonotachievethesoughtafterorientationindependenceandportabilitythatisrequiredforportablesystems.Membranetechnologyoffersthepotentialforasimple,low-costmethodtoventtheCO2gasfromaDMFCsystem.Therearetwotypesofpolymermembranes-porous 24

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andnon-porous.Non-porous,or'dense'membraneshaveamorphousstructurethatreliesonsolution-diffusionmethodtotransportspeciesviaconcentrationgradient.Porousmembranes,asusedinmicroltrationandultraltrationprocesses,transportspeciesthroughtheporesthemselves.Separationforthistypeofmembraneisbasedonthediameterofthetransportingspecieswithrespecttotheporediameter.Thecurrentdissertationstudyanalyzesahydrophobic,porousePTFEmembraneforuseinaGLSforaportabledirectmethanolfuelcellsystem.Themembraneissplitintoan'active'and'idle'region.TheactiveregionisadirectparticipantintheventingoftheCO2bubbles.ThemassuxofCO2thatventsthroughthemembraneisproportionaltothepressuredropacrossthematerial.Thisventpressuretomembranearearelationshipisimportantforthesizingofthemembrane.Theidleregionforthemembranedoesnotparticipateinthegasventingandisindirectcontactwithliquidphase.Waterlossoccursfrombothportionsofthemembrane.Intheactiveregion,waterlossisintheformofasaturatedCO2gasventingstream.Intheidleregion,waterlossisduetoevaporationfromthemembranesurface.Characterizingthemembranetransportprocessesonthebasisofwaterlossrate,ventpressure,andmembraneareawouldbebenecialtoGLSengineersseekingtopredicttheperformanceforthepurposeofcomponentdesign. 1.3ResearchObjectiveTheobjectiveofthisresearchistopredicttheperformanceofaGLSdesignthatusesporousmembranetechnologytoseparateCO2gasfromliquidphasesolutions.AvalidatedmodelwillbecreatedtorelatethekeyperformanceparametersofCO2ventrate,pressuredifference,andtheactivearearelationshipforthemembrane.Themodelwillalsoincludeliquidlossviaadvectionandevaporation.Applicabilityforthemodelincludesanyseparationdevicethatutilizesporoushydrophobicmembranes,servingasadesigntoolforfutureGLScongurations. 25

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1.4DissertationOutlineThisDissertationdocumentgivesasummaryofresearcheffortsforbothmodelingandexperimentationforthegas-liquidseparator(GLS)component.Chapter2givesadetailedliteraturereviewthatputsthecurrentresearchincontextwithotherworkinthesameeld.Chapter3givesafulldescriptionofthemodeldevelopmentforthemasstransportthroughthemembrane.ThetransportmodelissplitintotwodistinctmodesdictatedbywhetherornotthemembraneisactivelyinvolvedintheventingoftheCO2gasstream.The'active'portionofthemembraneisdirectlyinvolvedintheCO2gasventingprocessandgovernedbybulkowviaHagen-Poiseuillelaw.The'idle'portionofthemembraneissubjecttoevaporation.Transportfortheevaporationportionofthemembraneismodeledusinganelectricalresistanceanalogybasedonmoleculardiffusionandnaturalconvectionawayfromthemembranesurface.Chapter4introducestheexperimentsthatwereconductedinordertovalidatethesoftwaremodel.AfulldescriptionofdesignandinstrumentationfortheexperimentaltestrigisgivenaswellasadiscussionoftheexperimentsthatwerecarriedouttoobservetheperformanceoftheePTFEmembranes.ThekeyperformancecharacteristicsaretheCO2ventrate,thewaterlossrate,membranearea,andventpressure.InChapter5,acomparisonofthemodelsimulationsandexperimentalresultsisgivenbasedontheseperformanceparameters.Lastly,inChapter6,anexampleapplicationofthevalidatedmodelasadesigntoolformembrane-basedGLScomponentsisgiven.AnewGLSprototype,namedPandora,isintroduced.ExperimentalanalysisandfurthermodelvalidationisgivenusingPandora.Chapter7willprovideasummaryoftheconclusionsforthisDissertationstudy. 26

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CHAPTER2LITERATUREREVIEWTheeffectiveremovalofproductCO2fromthefuelcellstackaswellasthesystemisacriticalissuethateffectsoverallperformance.WithintheDMFCstack,akeymasstransportissueisdetermininghowtouniformlydistributethemethanolfueltotheanodecatalystlayer[ 7 ].Thepresenceofcarbondioxideinterfereswithachievingthisgoalbycausinglocalizedareasoflowmethanolconcentrationthatlowercellvoltageduetomasstransportlosses[ 7 ].Arelatedissueregardingtheproductionofcarbondioxidewithinthestackisthebubbledynamicsofowthroughthechannels.Dependingonthetypeofbubbleregime(whetherbubbly,slug,orannularow)forthecarbondioxide,theowchannelsmaybecomeblockedandpreventmethanolfromaccessingcatalystsites.Previousresearchershavedeterminedthatowrate,owelddesign,currentdensity,andsurfacetensionalleffectthebubbleregimeforthecarbondioxide[ 7 10 ].Thisphenomenahasbeenstudiedextensivelythroughvariousvisualizationstudies[ 11 ].Oncecarbondioxidehaseffectivelybeenremovedfromthefuelcellstack,theissuestillremainsastohowtoremovetheCO2fromthesystem.Forboththetraditionalandthenovelopen-cathodesystems,thereisagas-liquidseparator(GLS)componentthatistaskedwithremovingtheproductCO2gaswhileretainingtheliquidphasewaterandmethanolforre-circulationbacktotheDMFCstackinlet.ThedisadvantagesofCO2intheanodeloopincludespossiblyover-pressurizingthesystemandcausingcatastrophicburstfailures.Also,anincreasedpressureheadfortheanodecircuitinterfereswiththepumpingefciencyaswellasthelongtermdurabilityofboththere-circulationandmethanoldosingpumps.Additionally,CO2gasbubblescanalsodisruptsensorsintheanodeloop.Oneexampleisthemethanolsensorwhichcontrolsthedosingpumpthatregulatesthemethanolconcentration.FalsemethanolsensorreadingsasaresultofCO2bubblescaninducepoorfuelcontrolwhichcannegativelyaffectDMFCperformance. 27

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Two-phase(liquid,gas)separationistraditionallyconductedvia'knockout'or'ashdrum'-adevicethatutilizesgravitytoseparategasfromliquid.Typicalapplicationforthesesystemsisthepetroleumandoilindustry[ 12 13 ].Sizingfortheseindustrial-sizedsystemsareontheorderofafewsquaremeters[ 14 ].ForportableDMFCsystemsliketheDemonstrationPrototype4(DP4)createdatUniversityofNorthFloridaandUniversityofFlorida,traditionalseparationmethodssuchasthisaretoobigtobeimplemented.MembranetechnologyservesasanidealsolutiontotheCO2ventingproblembecauseitispassivewithnoparasiticpowerdraw.Polymermembranescanbeclassiedintotwocategories-1)porousand2)non-porous.Thedistinctionbetweenthetwotypesisbasedonthestructure(i.e.-theporesize)ofthemembrane.Porousmembraneshaveporediameterof10nmto1mm.Membranesthatexhibitporesizesbelow10nmareconsiderednon-porousor'dense'membranes[ 15 ].Themechanismoftransportdiffersforeachmembranetype.Forporousmembranes,transportoccurswithintheporesthemselvesandseparationiscarriedoutviadifferencesbetweentheparticlesizeandtherepresentativeporediameter[ 16 ].Transportindensemembranesisdrivenbysolution-diffusionmechanismwheremoleculesrstadsorbontothemembranesurface,thenmigratefromonesidetotheotherviadiffusion[ 16 17 ].Separationfordensemembranesisbasedonselectivity,thepreferentialafnityofonemoleculeoveranotherwheninteractingwiththemembrane.Porousmembranesusedasaseparationbarrierhavemanydifferentusesoverawidespanofapplications.Themostcommonprocessesaremicroltration(MF)andultraltration(UF).Eachoftheseprocessesutilizesapolymermembranetosuccessfullyretainthesolventwhilepassingthesolute(orviceversa)[ 18 ].Ultraltrationprocessesdealwithparticlesizesfrom1-20nmrangeandareusedinelectrolyticpaintrecoveryandagriculturalprocessessuchastheseparationofwheyfromcheese.Microltrationisusedinthe0.02-10mrangeandiswidelyusedfordrugsterilization,particleremoval 28

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fromcorrosiveuidsinelectronicsindustry,andtheremovalofbacteriafromdrinkingwater[ 18 19 ].TheGLSdeployedintheDP4utilizesaporous,hydrophobicePTFEmembranetopreferentiallyventthegasphasecarbondioxidefromthesystemwhileretainingtheliquidphasemethanol-watersolution.Historically,thistypeofmembranewasdevelopedinthe1970'sandstandsasthe'mostsolventresistant'microltrationmembrane[ 19 ].TheworkinthisdissertationstudywillbegearedtowardthesuccessfulmodelingandexperimentationofthistypeofmembraneforDMFCapplication.Currentresearchformembrane-basedgas-liquidseparation(GLS)fordirectmethanolfuelcell(DMFC)applicationisverywide.KrausandKrewer[ 20 ]utilizedbothhydrophilicandhydrophobic(EmonRPTFE,manufacturedbyPallCorporation)membranematerialsinsuchawaytocreateaamiablecapillarypressureforcenecessarytoventCO2forDMFCapplication.Bycreatinganoptimalcapillarypressuregradientwithinmilli/microchannels,theresearcherswereabletoachieveorientationindependence(notgravitydependent).AlthoughcompleteventingofCO2wasachieved,experimentsrevealedwaterandmethanollossasafunctionoftheambienttemperatureandtherelativehumidity.Incalculations,theresearchersaccountedforthewaterlossduetosaturationoftheCO2ventstreamthenattributedtheexcesswaterlossthatwasexperimentallyobservedtobeduetoevaporation.Predictionoftheevaporationwaterlossduetomembranepropertiesandambientconditionsisnotconsidered.Mengetal.[ 21 ]utilizedaporousPTFEandporouspolypropylenemembranestoachieveCO2separationforDMFC(andmicrouidicdevice)application.Themajorconcernfortheresearchersistheavoidanceofleakageforthemembrane.Experimentswereconductedtoobservethegasventingratefordifferentmolaritysolutionsupto10Mandpressuresof200kPa.A1-Dmodelofthegasventingratebasedonthegasbubblelengthinthemicrochannelwascreated.Modelsimulationswereveriedusing 29

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transientimageanalysisofgasbubblesastheyshrink(activelybeingvented)insidethemicrochannel.ThesameresearchersdeployedmicroporousmembranetechnologyintoanovelDMFCsystemdesignthatintegratedtheGLSfunctionintotheanodechamberitself[ 22 ].Inthisarticle,theevolutionoftheCO2bubbleasitisproduced,traversesthemicrochannel,andisventedthroughthemicroporousmembraneactivelyservesasthepumpingforceforthemethanolfueltotheanodecatalystlayer.Thewholeunitiscompactandsuitableforportablepowerapplications.Again,thereisnoconsiderationofthewaterbalanceforthesystemandtheamountofwaterandmethanolthroughthemicroporousmembranevent.UtilizingporousmembranesasabubbleventisacontinuationofearlierworkbyMengetal.[ 23 ]thatusedasilicondegassingplatecoatedwithTeonRtocapturegasbubblesviasurfacetension,thenventthemthroughholescreatedusingdeepreactive-ionetching(DRIE)[ 24 ].Asecondcongurationincludedaporouspolypropylenemembrane(ChemplexIndustries)sandwichedinbetweentwodegassingplates.Bothcongurationsservedasproof-of-conceptdesignsthatshowedgassescouldbeventedpassivelyusingporousmedia.PaustandKrumbholz[ 25 ]utilizedasimilarpassivedesignforDMFCwherecapillaryforcesservedasthepumpingmechanismforfuelow.Withtheadditionofataperedchannel,productCO2inthiscongurationisventedfromthesystemusingahydrophobicmembrane.ExperimentswereperformedtoobservetheDMFCperformance(currentvs.voltage)indifferentorientations.CompleteCO2separationwasachievedforoperationtimesof40hrsinvariousorientations.Modeldevelopmentforthisresearchveriedowchanneldesignparameters.VentingratesofCO2throughthehydrophobicmembraneandthemethanol/waterlossratesarenotconsideredinthemodel. 30

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Membrane-baseddegassingunitsareprevalentinmicrouidicsystemsasin[ 26 28 ].Theresearchersin[ 27 ]gavedesigncriteriaforutilizingporoushydrophobicmembranesforgasventingpurpose.Againthemodelisbasedonleakpreventionbyoperatingatpressuresbelowbreakthroughpressureandsuchbubbleparametersaslength,speed,andresidencetimeincontactwiththemembranesurface.Itisalsonotedthattheseresearchersshowedthatporousmembranesarecapableofmassuxesthatwerefourordermagnitudehigherthanpoly(dimethylsiloxane(PDMS)membranesatagiventhicknessandtransmembranepressure.PolymermembranessuchasPDMSareconsidered'nonporous'.Nonporousmembranesrelyonselectivityinordertoachievepreferentialtransportofonespeciesoveranother.Theselectivityisbasedondifferingratesofadsorptionanddiffusionthroughthepolymermembranematrix[ 29 ].Prakash,Mustain,andKohl[ 30 ]studiedtwononporouspolymers:poly(dimethylsiloxane)(PDMS)andpoly(1-trimethylsilylpropyne)(PTMSP).ResearchersmeasuredthepermeationratesofCO2andmethanolindependentlyandtherespectiveselectivityofonetotheotherbasedontheseratesweregivenasanalphavalue.Thehigherthealphavalue,themorepreferentialthetransportofonespeciesovertheother.Researchersfoundthattheuseofadditivessuchas1,6-divinylperourohexaneand1,9-decadieneincreasedtheselectivityofCO2overmethanolwitha50wt%of1,6-divinylperourohexaneinPTMSPmembraneperformingthebest.ThecorrespondingalphavalueforCO2versusmethanolwas9.2.Thisrepresenteda5ximprovementoverpurePTSMPand10ximprovementoverpurePDMSmembranes.In[ 31 ],thesameresearchersalsostudied1,6-divinylperourohexaneinadditiontoPTMSPforpassiveCO2ventingfordirectmethanolfuelcellapplication.BothmethanolandCO2permeabilitiesthroughthemembranewereobservedasafunctionoftemperature.Again,experimentsprovedthatthesemembraneshaveahighselectivity 31

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forCO2overthatofmethanol,makingthemgoodcandidatesforDMFCapplicationwhentheventuxdoesnotneedtobehigh.Asshowninthediscussionabove,previousmodelingeffortsforGLSarefocusedalmostexclusivelyonthepreventionofbreakthroughpressureandwaterleakageasadesignconstraint.Fundamentallymodelsforthetransportoftheconstituentspecies(CO2,methanol,andwater)throughporousGLSmembranesisneeded.TheworkpresentedherewillgiveamorecomprehensivemodelforGLSperformancethatincludespredictivetoolsfortherequiredmembraneareaforagivenpressuredropaswellasthelossratesoftheconstituentspeciesbasedonmembraneproperties.Oncecomplete,theexperimentallyvalidatedmodelwillprovetobeamuchneededtreatmentofmembranetransportandwillmarkastepforwardinGLSresearchforDMFC. 32

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CHAPTER3MODELINGANDSIMULATION 3.1IntroductionThepurposeofthegas-liquidseparator(GLS)istosuccessfullyventproductCO2fromtheanodeloopofaDMFCsysteminvariousorientationswhilepreventingliquidloss.AhydrophobicePTFEmembraneinstalledforthispurposehastwodistinctregionsofmasstransport-1)an'active'regiondirectlyinvolvedinventingthesaturatedcarbondioxidegas,and,2)an'idle'regionthatconsistsofthemembranedirectlyincontactwiththeliquidphasemethanol-watersolution.Figure 3-1 showsagraphicillustrationoftheactiveandidleregionsfortheGLSmembrane.Transportthroughtheactiveregionisbasedonbulkowofcarbondioxidewhichisdirectlyafunctionofpressuredropacrossthemembranelayer.Masstransportthroughtheidleportionofthemembraneissolelyduetoevaporationwhichisgovernedbymoleculardiffusionandnaturalconvectionawayfromthesurface. Figure3-1. Illustrationof'active'and'idle'portionsofGLSmembranewithassociatedcharacteristiclengthscales. Thischapterpresentsthemodeldevelopmentforbulkowandevaporationwhichareconsideredseparately.BulkowisgovernedbyHagen-Poiseuilleforlaminarowincirculartubes.Evaporationisevaluatedusinganelectricalresistanceanalogy 33

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throughthemembranelayers.Bothmodelcodesutilizeapropertiesmodelthatemploysequilibriumargumentstoevaluatethevaporandliquidcompositionsofmethanol-watersolutionsatvarioustemperatureandpressuresetpoints. 3.2BulkFlowModel 3.2.1HagenPoiseuilleLawThebulktransportofcarbondioxidethroughtheporousmembraneismodeledasaseriesofcapillariesusingtheHagen-Poiseuillelawasfollows[ 18 32 33 ]: _m00b="2 32dP dx(3)where_m00b[inkg=(m2s)]isthethebulkowmassuxofthegas-vaporstreamventingoutofthemembrane,istheporosityofthematerial,istheporediameter(m),dP dxisthepressuregradientacrossthemembrane,and,aretheaveragedensity(kg=m3)andviscosity(Pas)ofthegasmixture,respectively.Theparameteristhetortuosityfactor.Thisconstant,greaterthanunity,isascalefactorthatisappliedtothelengthofthemembraneporetobetterrepresentthe'tortuous'pathofagasmoleculethroughanon-idealmembrane.Theuxgiveninequation( 3 )isbasedonthetotalmembranearea,Amem(inm2).Theportionofthetotalmembraneareathatisopenfortransportistheporearea,Apore.Therelationshipbetweenporeareaandthetotalareaofthemembraneisgivenasafunctionoftheporositysuchthat "=Apore Amem(3)TheHagen-PoiseuillelawisvalidforlowReynoldsnumber(Re<2100)andlowKnudsennumber(Kn<1)owconditions[ 18 ].TheporousGLSmembraneunderconsiderationwithinthisworkhasatotalmembraneareaof10cm2andaverageporediameterof1m.Thedesignrequirementforthemembraneis0-270sccmofCO2atatemperaturerangeof313-333K(40-60C).DeterminationoftheReynoldsnumberisbasedon50%membraneporosity(estimated),themaximumCO2owrateof270 34

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sccmequallydistributedovertheporearea,andporediameterastherequisitelengthdimension.ThecomputedresultisRe=9.7x10)]TJ /F5 7.97 Tf 6.59 0 Td[(5whichqualiesascreepingow(Re1)thussatisfyingthelowReynoldsnumbercriteria.TheexpressionfortheKnudsennumberisbasedonthemeanfreepathofagasmolecule,(m),andtheporediameterasfollows: Kn= (3)Theequationforthemeanfreepathisgivenas =kT p 2d2P(3)wherekisBoltzmann'sconstant(=1.38x10)]TJ /F5 7.97 Tf 6.59 0 Td[(23J/K);Tisthetemperature(K);Pisthepressure(Pa);anddisthemoleculediameter(m).ForKn1,thedistanceformolecularcollisionsislargerthantheporediameterandspecialconsiderationforKnudseneffectsneedtobeconsideredinsoftwaremodels[ 16 34 35 ].KnudseneffectscanbeneglectedforthecaseofKn<1.Carbondioxideatatemperatureof333Kandpressureof108.2kPa(15.7psi)yieldsaKnudsennumberofKn=0.05,thusKnudseneffectscanbeneglected.Assumingthedownstreampressureofthemembranetobeatmosphericpressure,thepressuredifferencereducestothegagepressure,Pgage,upstreamofthemembranesurface.Thepressuregradientterminequation( 3 )acrossthemembranethickness,lm,cannowbeexpressedas dP dxvPgage lm(3)Therefore,equation( 3 )cannowbere-writtenasfollows: _m00b="2 32Pgage lm(3) 35

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Themembranegeometryandgasmixturepropertiescanbegroupedintoasinglebulkowresistanceparameter,,asfollows: ="2 32lm(3)Theparameterhastheunitsofkg=(Pam2s).Substitutionofequation( 3 )intoequation( 3 )showsthatthemassuxduetobulkowthroughthemembranemayalsobeexpressedas _m00b=Pgage(3)Theuxesofeachconstituenti-thcomponentgasspecies,_m00b,i,arecalculatedbyusingtherespectivemassfractions,i,inthefollowingmanner: _m00b,i=i_m00b(3)Asshowninequations( 3 )throughequation( 3 ),thebulkowmodelgoverningtheventrateofthegasmixturethroughtheGLSmembraneisafunctionofpropertiessuchasviscosityanddensity.Aseparatepropertiesmodelwascreatedtopredictthesevaluesforthegas-vapormixture.Afulldiscussionispresentedinthenextsection. 3.2.2Gas-VaporMixturePropertiesModelThegas-vapormixtureisamulti-componentsystemcomposedof(1)methanol,(2)water,and(3)carbondioxide.Bothmethanolandwaterarecondensiblevaporsthatsubstantiatedaseparatevapor-liquidequilibrium(VLE)treatmenttodeterminetherelevantproperties.Informationaboutthefullpropertiesmodelisgiveninthesectionsbelow. 3.2.2.1ConstituentPartialPressuresThedrivingforceforbulktransport(venting)ofgasthroughtheGLSmembraneispressuredifferencebetweentheupstreamanddownstreamsides.Theupstream(vent) 36

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pressureofthemembraneisgivenbyDalton'sLawasthesummationofthepartialpressureofeachconstituent. Ptotal=kXi=1Pi(3)Forthecaseofmethanol,water,andcarbondioxide,theexpressionforupstreampressurecanbewrittenexplicitlyas Ptotal=Pvent=P(1)H2O+P(2)CH3OH+P(3)CO2(3)whereP(1)H2O,P(2)CH3OH,andP(3)CO2arethepartialpressuresofwater(vapor),methanol(vapor),andcarbondioxide(idealgas),respectively.Waterandmethanol,bothcondensiblevapors,weretreatedasaseparatebinarysystemwhosepartialpressuresweredeterminedusingvapor-liquidequilibrium(VLE)[seeSection 3.2.2.3 ].Thebinarypressure,composedofthepartialpressuresformethanolandwateronly,isgivenas Pbin=P(1)H2O+P(2)CH3OH(3)Substitutingequation( 3 )intoequation( 3 ),thepartialpressureofcarbondioxidecanbesolvedforalgebraicallyas P(3)CO2=Ptotal)]TJ /F6 11.955 Tf 11.96 0 Td[(Pbin(3) 3.2.2.2CarbonDioxideSolubilityTheextentofCO2solubilityinwaterisgivenasthemolefractionofCO2intheliquidphase,xCO2[ 18 36 37 ]: xCO2=1 HCO2,H2OP(3)CO2(3) 37

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whereHCO2,H2OistheHenry'sLawconstant(Pa).AnempiricalcorrelationpresentedbyNISTChemistryWebBookwasusedtocomputetheHenry'slawconstantforCO2inwater,HCO2,H2O[in(molesofCO2)/(kgofH2OPa)]asfollows[ 38 ]: HCO2,H2O=10)]TJ /F5 7.97 Tf 6.58 0 Td[(5H0CO2,H2Oexpd(lnHCO2,H2O) d(1=T)1 T)]TJ /F3 11.955 Tf 27.44 8.08 Td[(1 298.15(3)whereTisthetemperature(K);H0CO2,H2OisHenry'sLawconstantatT=298.15K[mol=(kgbar)];d(..)=d(1=T)isatemperaturedependentempiricalcoefcient(K).Valuesfortheconstantsusedinequation( 3 )arebasedontheLideandFrederiksecorrelation[ 39 ]: H0CO2,H2O=0.035(3) d(lnHCO2,H2O) d(1=T)=2400(3)ComputedvaluesforHenry'sLawconstantswereveriedwithdatapresentedin[ 37 ]and[ 40 ].Table 3-1 showssimulatedvaluesfortheamountofCO2(inmoles)thatissolublein1literofwaterasafunctionoftemperatureandpressure.Notethatforagiventotalpressuresetting,thepartialpressureofCO2decreasesasthetemperatureincreases.Thisoccurrenceisduetohighervaporpressurecontributionofmethanolandwaterathighertemperatureswhich,accordingtoequation( 3 ),decreasestheCO2partialpressure.AsshowninTable 3-1 ,thereis0.123to0.241molesofCO2perliterofwateratsteady-stateforthegiventemperatureandpressurerange.Thisrangerepresentsapproximately1.70-3.30%whencomparedtothe0.723molesofCO2producedin1hourduringnormalDMFCstack(andGLS)operation.Therefore,theamountofCO2thatissolubleinwaterisnegligibleandnotconsideredintheGLSmodel. 38

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Table3-1. CO2Solubilityin1Lwateratvarioustemperaturesandpressures. TotalPressureTemperaturePCO2Henry'sConstantCO2Solubility[kPa][K][kPa][molCO2=(kgH2OPa)][molCO2=LH2O] 101.331394.00.2390.022532389.10.1880.016833381.50.1510.0123104.731397.40.2390.023332392.50.1880.017433385.00.1510.0128108.2313100.90.2390.024132396.00.1880.018133388.40.1510.0133 3.2.2.3Vapor-LiquidEquilibrium(VLE)Thevaporpressureformethanolandwaterusedtocomputethebinarypressureinequation( 3 )aredeterminedusingmodiedRaoultLawasfollows[ 18 29 36 41 ] P(1)H2O=xH2OH2OPsat,H2O(T)(3) P(2)CH3OH=xCH3OHCH3OHPsat,CH3OH(T)(3)wherexisthemolefractionintheliquidphase(scalar),istheactivitycoefcient(scalar),andPsat,CH3OH(T)isthesaturatedvaporpressure(Pa)whichisafunctionofthetemperature.Theactivitycoefcients,H2OandCH3OH,werecomputedusingtheUniversalFunctionalActivityCoefcient(UNIFAC)methodwhichallowsfornon-idealmolecularinteractionsofliquidphasesolutionstobeconsidered[ 1 18 29 36 ].Equation( 3 )andequation( 3 )showthatthevaporpressureisafunctionoftemperatureandtherespectivemolefractionintheliquidphase.RecallfromtheCO2solubilityvalidation[seeSection 3.2.2.2 ]thattheamountofCO2dissolvedintotheliquidphaseisnegligible.Therefore,thefollowingconstraintholdstruefortheliquid-phasemolefractionsintheisolatedmethanol-waterbinarysystem: 39

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xH2O+xCH3OH=1(3)Oncethemolarityofthesolutionisknown,Therefore,equation( 3 )forPbinisafunctionofthemethanolmolefractionintheliquidphaseandtemperatureasfollows Pbin=Pbin(xCH3OH,T)(3)Thisportionofthemodelcodewasveriedusingreferencedataformethanol-watersolutionsasin[ 42 46 ] 3.2.2.4ViscosityandDensityofGasMixtureTheviscosity,,ofthemixtureisobtainedfromthesemi-empiricalformula[ 47 ]: =kXi=1yii Pkj=1yjij(3)wherekisthenumberofconstituentsinthegasmixture[k=3forcaseof(1)CH3OH,(2)H2O,and(3)CO2].Thesymbolyi(andyj)isthemolefractionofthei-th(andj-th)component;iistheviscosityofspeciesi.Theexpressionforthescalarquantityijisgivenbythefollowingformula[ 47 ]: ij=1 p 81+Mi Mj)]TJ /F5 7.97 Tf 6.59 0 Td[(1=2"1+i j1=2Mi Mj1=4#2(3)whereMi(andMj)isthemolecularweighting=molofthei-th(andj-th),respectively.Thegasmixtureviscositygiveninequation( 3 )isbasedondeterminingthemolefractionsofeachconstituent.Usingequation( 3 )forcomputationofthetotalpressure,itfollowsthatthegasphasemolefractionsforeachspeciesaresimply yi=Pi Ptotal(3)suchthat 40

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kXi=1yi=1(3)Thegasdensityforthegas-vapormixtureisgivenbythefollowingexpression: =kXi=1ii(3)whereiisthemassfraction(scalar)andiisthedensity(kg=m3)ofthei-thspecies,respectively.Computationoftheconstituentmassfractionsisbasedonthetotalmolecularweightofthegasmixture,Mtotal,suchthat Mtotal=kXi=1mi=kXi=1yiMi(3)wheremiisthemolarmass(g=mol),yiisthemolefraction(scalar),andMiisthemolecularweight(g=mol)ofthei-thcomponent,respectively.Themassfractionscannowbefoundusingthetotalmolecularweightasfollows: i=mi Mtotal(3) 3.3EvaporationModelTheidleportionofthemembrane(notinvolvedinthe'active'bulktransportofcarbondioxide)issubjecttoevaporation.ThisportionofthemodelcodeispredominantlybasedontheworkofA.Mourgues,etal[ 48 ]thoughothersourcesincludingC.J.Geankopolis[ 37 ]andS.Turns[ 49 ]areutilizedthroughoutmodeldevelopment.Figure 3-2 showsthecross-sectionoftheidleportionofthemembraneandthenomenclaturethatwillbeusedinthisevaporationdiscussion.Asshowninthegure,themembraneiscomposedoftwo(2)layers-1)ahydrophobicePTFElayer,and2)apolyesternon-wovenlayer.Thehydrophobicmembranesurfaceisdirectlyincontactwiththeliquidwater.Itisthishydrophobiclayer(MEM)thatactsasabarrierandretainstheliquidwaterfromowingthroughtotheothersideviasurfacetension.Thereisamaximum 41

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pressurecalledthe'break-through'pressurethatrepresentsthemaximumpressurethatthemembranewillbeabletowithstandbeforeliquidwaterpiercesthroughandceasestobeaneffectivebarrier.FortheePTFEmembraneunderconsideration,thebreakthroughpressurewasexperimentallydeterminedtobe96530Pa(gage),or14psig.Thepresentmodelschemeisvalidforpressuresbelowthis'breakthrough'pressure. Figure3-2. Cross-sectionviewofidlemembranearea Theporesareidealizedasintheprevioussection[seeSection 3.2.1 ]ascylinderslledwithstagnantair.TherstportionoftheevaporationmodelistocreateanexpressionforwatervapordiffusingfromtheliquidsurfaceatE1interfacethroughtheair-lledporestoE2interface.Thesecondlayer(E2toE3),thepolyesternon-wovenlayer(PW),isacoarselayerwhosesolepurposeistoprovidestructuralsupporttothehydrophobiclayer.Thenallayer,E3toE4),istheboundarylayer(BL)whichisatransitionlayerwheremasstransferoccursfromthecompositemembranelayerstoambientair.Watervaportransportthroughthislayerisgovernedbyconvectionwhichdependsonthevelocityofthebulkowofair.Theambientaircaneitherbequiescent,laminar,orturbulentinnature.Thecaseofnaturalconvectionthroughquiescentairisconsideredhere.Onemajorassumptionisthatthereisnobackdiffusionofairintotheliquidphaseandthattheairisstagnantthroughoutthecompositemembraneaswellastheboundarylayer.Oncethisassumptionismade,thetransportofwatervaporaway 42

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fromtheliquidsurfaceistheonlyconcern.Thislossrateofwatervaporthroughtheidleportionofthemembraneisaccountedforbyusinganelectricalresistanceanalogywhichincludesthemembranelayer(MEM),thepolyesterbackinglayer(PW),andtheboundarylayer(BL).Figure 3-3 showstheelectricalresistancemodelwherethethreerelevanttransportlayersaretranslatedintothreeresistorsinseries.Insteadofelectricalpotentialbeingthedrivingforceforcurrent,the(partial)pressuregradientofwatervaporistheanalogousdriver. Figure3-3. Electricalresistancemodelusedforevaporationtransportthroughmembranelayers UsingFigure 3-3 ,theevaporationmassuxofwatervapor,_m00e,H2O,isafunctionofthetotalresistance,Rtotal,inthefollowingmanner: _m00e,H2O=Rtotal(Psat,H2O)]TJ /F6 11.955 Tf 11.96 0 Td[(Pamb,H2O)(3)Where_m00e,H2Oisinkg=(m2s);Psat,H2Oisthesaturationpressure(Pa)attheliquidinterfaceandPamb,H2Oisthevaporpressure(Pa)ofwaterintheambient.Theunitsfortheresistance,Rtotaliss=m. 43

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UsingthenamingconventionsetforthinFigure 3-2 ,equation( 3 )canbere-writtenusingPsat,H2O=PH2O,E1andPamb,H2O=PH2O,E4as _m00e,H2O=Rtotal(PH2O,E1)]TJ /F6 11.955 Tf 11.96 0 Td[(PH2O,E4)(3)Thetotalresistanceisthesumtotaloftheresistanceforeachofthethreerespectivetransportlayersgivenas: Rtotal=1 Rmem+1 Rpw+1 Rbl)]TJ /F5 7.97 Tf 6.59 0 Td[(1(3)Atthepresenttime,layer-specicmembraneproperties(suchastherelativethicknessofeachlayer,etc)isunknown.Thisinformationiscurrentlybeinginvestigated.However,untilfurtherinformationisknownthemembranelayers(hydrophobiclayerandthebackinglayer)havebeenlumpedtogetheraretreatedasasinglecompositemembranewhoseresistancecanbedescribedas Rcomp=1 Rmem+1 Rpw(3)Substitutingequation( 3 )intoequation( 3 )yields Rtotal=1 Rcomp+1 Rbl)]TJ /F5 7.97 Tf 6.59 0 Td[(1(3)Modeldevelopmentforevaporationthroughthecompositemembraneandboundarylayersinvolvesderivingeachofthetworesistancesgiveninequation( 3 ),RcompandRbl,basedonthephysicalprocessesthatoccurforeachlayer.Forthecompositemembranelayertransportisgovernedbymoleculardiffusion.Withintheboundarylayer,transportisbasedonananalogybetweenconvectiveheatandmasstransfer. 3.3.1Fick'sLawforMolecularDiffusionTheevaporationmassuxforwaterthroughairwithinthemembranelayers,_m00comp,H2O,isgovernedbymoleculardiffusionusingtheFick'slaw.Thevalidityof 44

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moleculardiffusionisbasedonKnudsennumberanalysisrstpresentedinSection 3.2.1 .TheKnudsennumber,calculatedusingequation( 3 ),forwatervaporat333KisKn=0.77whichsatisesthecasewherethemeanfreepathofthemoleculeislessthantheorderofmagnitudeoftheporediameter(=1m).Therefore,thetreatmentoftheevaporationprocessviamoleculardiffusionisconrmedandKnudseneffectsmaybeneglected.ThegoverningequationformoleculardiffusionisgivenviaFick'slaw[ 37 48 49 ]: _m00e,H2O=H2O)]TJ /F3 11.955 Tf 8.72 -9.69 Td[(_m00comp,H2O+_m00e,air)]TJ /F4 11.955 Tf 11.96 0 Td[(eDH2O,airdH2O dx(3)where_m00airisthemassuxofair[kg=(m2s)],DH2O,airisthediffusioncoefcientforwaterinair(m2=s)[ 50 ],H2Oisthemassfractionofwater(scalar),andeisthegasdensity.Thersttermontherighthandsideofequation( 3 )isthebulkowtermofwaterinairandthesecondtermisthecontributionofmoleculardiffusion[ 49 ].AsdiscussedinSection( 3.3 ),akeyassumptionisthatthereisnonettransportofairwithinthesystem.Therefore,themassuxtermforairisequaltozero[_m00e,air=0]andequation( 3 )canbere-writtenas: _m00e,H2O=H2O)]TJ /F3 11.955 Tf 8.72 -9.68 Td[(_m00comp,H2O)]TJ /F4 11.955 Tf 11.95 0 Td[(eDH2O,airdH2O dx(3)Asin[ 49 ],aseparationofvariablesandre-arrangingforequation( 3 )yields: _m00e,H2O eDH2O,airdx=dH2O 1)]TJ /F3 11.955 Tf 11.96 0 Td[(H2O(3)Itfollowsthatbyintegratingbothsidesofequation( 3 ),givesthefollowingresult: _m00e,H2O eDH2O,airx=)]TJ /F3 11.955 Tf 11.29 0 Td[(ln[1)]TJ /F3 11.955 Tf 11.95 0 Td[(H2O]+C(3)Theboundaryconditionsforthemassfractionsoneithersideofthecompositemembraneare 45

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(x=0)=E1(3) (x=lm)=E3(3)Applyingbothconditionsgiveninequation( 3 )andequation( 3 )toequation( 3 )yieldsthefollowingsolutionforthemassuxofwatervapor: _m00e,H2O=eDH2O,air lmln1)]TJ /F3 11.955 Tf 11.96 0 Td[(E3 1)]TJ /F3 11.955 Tf 11.96 0 Td[(E1(3)Itisassumedthatthetotal(ambient)pressure,Pambisconstantthroughoutallmasstransportresistancelayers[ 48 ].Recallthatthemassfractionsareafunctionoftotalpressureasfollows E1=PH2O,E1 Pamb(3) E3=PH2O,E3 Pamb(3)suchthat Pamb=PH2O,E1+Pair,E1(3)and Pamb=PH2O,E3+Pair,E3(3)Equation( 3 )canbenowbere-writtenusingpressurevaluesinsteadofmassfractionsbysubstitutingequation( 3 )andequation( 3 ).Thepressure-basedmassuxofwatervaporisnow 46

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_m00e,H2O=eDH2O,air lmlnPamb)]TJ /F6 11.955 Tf 11.95 0 Td[(PH2O,E3 Pamb)]TJ /F6 11.955 Tf 11.95 0 Td[(PH2O,E1(3)Analstepisneededinordertore-writeequation( 3 )toanotherformsimilartothatofequation( 3 ).Thisisperformedbysolvingequation( 3 )andequation( 3 )fortheairterms,Pair,E1andPair,E3,thentakingthelogmeanvalueasfollows[ 37 48 ]: PlogM=Pair,E3)]TJ /F6 11.955 Tf 11.96 0 Td[(Pair,E1 ln(Pair,E3=Pair,E1)=PH2O,E1)]TJ /F6 11.955 Tf 11.96 0 Td[(PH2O,E3 ln[(Pamb)]TJ /F6 11.955 Tf 11.96 0 Td[(PH2O,E3)=(Pamb)]TJ /F6 11.955 Tf 11.96 0 Td[(PH2O,E1)](3)Themassuxofwatervaporviamoleculardiffusioncannowbedeterminedbysolvingequation( 3 )forthenaturallogarithmtermandsubstitutingintoequation( 3 ).Thenalresultisthen _m00e,H2O=eDH2O,air lmPlogM[PH2O,E1)]TJ /F6 11.955 Tf 11.95 0 Td[(PH2O,E3](3)Inspectionofequation( 3 )yieldsthefollowingrelationshipforthediffusionresistancethroughthecompositemembrane,: Rcomp=eDH2O,air lmPlogM(3) 3.3.2MassTransferbyNaturalConvectionMasstransportthroughtheboundarylayer(sectionE3toE4inFigure 3-2 )istreatedasanaturalconvectionproblem.Heattransferrate,_Q(inJ=s),forthesurfaceisgovernedbyNewton'sLawofcoolingas _Q=hHA(Ts)]TJ /F6 11.955 Tf 11.96 0 Td[(Tamb)(3)whereTambistheambienttemperature(K),Tsisthesurfacetemperature(K),Aisthearea(m2),andhHistheheattransfercoefcient[W/)]TJ /F6 11.955 Tf 5.48 -9.68 Td[(m2K].Forthecaseofaatwet 47

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platewiththehotsurfacefacingup,theheattransfercoefcient,hHisdeterminedusingacorrelationfortheNusseltnumber,Nu,whichstates[ 51 52 ]: Nu=hHLe k=0.54(GrLePr)1=4(3)whereLeisthecharacteristiclengthoftheevaporationportionofthemembrane(m),kisthethermalconductivity[W/(mK)],GrLeistheGrashofnumber(scalar),andPristhePrandtlnumber(scalar).Byanalogy,heatandmasstransferhavethesamemathematicalstructure.However,formasstransferintheboundarylayer(E3toE4inFigure 3-2 ),densityisthedrivingforce.Thereforethewatermassuxthroughtheboundarylayer,_mbl,H2O,isrepresentedasfollows: _mbl,H2O=hmA(H2O,E3)]TJ /F4 11.955 Tf 11.95 0 Td[(H2O,E4)(3)wherehmisthemasstransfercoefcient(m=s);H2O,E3andH2O,E4isthedensityofwatervaporatthemembranesideandtheambientenvironmentsideoftheboundarylayer,respectively(kg=m3).Similartoequation( 3 )fortheNusseltnumber,themasstransfercoefcientisdeterminedusingtheSherwoodnumberinthefollowingmanner: Sh=hmLe Dbl,H2O,air=0.54(GrLeSc)1=4(3)Acomparisonofequation( 3 )andequation( 3 )yieldsasimilaritybetweentheNusseltnumberandtheSherwoodnumberaswellasPrandtlnumber,Sh,andtheSchmidtnumber,Sc,suchthat NuvSh(3)and PrvSc(3) 48

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TheexpressionfortheGrashofnumber(ratioofbuoyancyforcetoviscousforce)isfoundbythefollowingexpression: Gr=g(E4)]TJ /F4 11.955 Tf 11.95 0 Td[(E3)L3e avg2(3)whereE3andE4isthegasdensityatreferencepointsE3andE4oftheboundarylayer,respectively(kg=m3);avgistheaveragedensity=(E3+E4)=2=kg=m3;gisgravity(m=s2);isthegasviscosity(m2=s).TheexpressionfortheSchmidtnumber,Sc,isasfollows: Sc= Dbl,H2O,air(3)Itshouldbenotedthatasarstapproximation,thediffusioncoefcientofwatervaporinairinbothequation( 3 )andequation( 3 )isevaluatedattheaveragetemperaturebetweentheoperatingtemperatureatthemembraneuidinterfaceatE1andtheambienttemperatureatE4.Solvingequation( 3 )forthemasstransfercoefcient,hmandsubstitutingintoequation( 3 )yieldsanupdatedformofthemassowthroughtheboundarylayerduetonaturalconvection: _mbl,H2O=ShDbl,H2O,air LeA(H2O,E3)]TJ /F4 11.955 Tf 11.95 0 Td[(H2O,E4)(3)SimilartoSection( 3.3.1 ),thenalformofthemasstransferequationneedstobepresentedasafunctionofpressuredifferencesimilartoequation( 3 ).Thedensityvaluesofequation( 3 )canbere-writtenasfunctionsofpartialpressureasfollows: H2O,E3=PH2O,E3 RTE3(3) H2O,E4=PH2O,E4 RTE4(3) 49

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whereRistheuniversalgasconstant[J=(molK)]Again,asarstapproximationthetemperaturesusedoneithersideoftheboundarylayerareassumedtobeconstantaveragetemperaturesevaluatedbetweenE1andE4suchthat Tavg=TE3=TE4=TE1+TE4 2(3)Therefore,equation( 3 )formassowofwatervaporintheboundarylayercannowbere-writtenas _mbl,H2O=ShDbl,H2O,air LeRTavgA(PH2O,E3)]TJ /F6 11.955 Tf 11.95 0 Td[(PH2O,E4)(3)Dividingbythearea,theequivalentmassuxis _m00bl,H2O=ShDbl,H2O,air LeRTavg(PH2O,E3)]TJ /F6 11.955 Tf 11.96 0 Td[(PH2O,E4)(3)Thenalboundarylayerresistancefortheresistancenetworkmodelofevaporationisthen Rbl=ShDbl,H2O,air LeRTavg(3)Bothequation( 3 )andequation( 3 )cannowbesubstitutedinto( 3 )tondthetotalmassuxofwatervaporduetoevaporation. 50

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CHAPTER4MODELVALIDATIONEXPERIMENTSAnexperimentalteststationwasdevelopedtoevaluatethepropertiesofcandidateGLScongurations.ForagivenGLSconguration,thefollowingperformancecharacteristicscanbedetermined:CO2ventingrate,waterlossrate,membraneventarea,andventpressure.Afulldescriptionofthetestrigalongwithalistofcomponentsisgiveninthischapter.TheGLStestcellisdescribedalongwithabriefhistoryoftheGLScomponentwhichhighlightsvariousdesignsthathavebeentestedinthepast.AkeyfeatureofthecandidateGLSdesignsistheuseofacompositemembranemadefromhydrophobicePTFEandnon-wovenpolyester(backinglayer).AnoverviewofthemembranestructureaswellasadiscussionofthemorphologyofthemembranesurfacebasedonSEMimagesisgiveninthischapter. 4.1Gas-LiquidSeparator(GLS) 4.1.1BriefDesignHistoryTheGLScomponenthasgonethroughmanyrevisionsoverthepastfewyears.Tothispoint,allthedesignsthathavebeencreatedbyUNFNWandtestedatbothUFandUNFthroughapartnership.AsdiscussedintheChapter 1 ,thesought-aftergoalistocreateaGLSdevicethatispassiveinnaturethatsuccessfullyventsCO2whileretainingtheliquid-phasesolution.Thepreferredsolutionisusingmembranetechnology.ThissectiongivesabriefhistoryoftheGLScomponentandgivescommentaryastowhycertaincongurationswerenotchosenasthenaldesign.Figure 4-1 showsaGLSthatwasusedintheDemonstrationPrototype3(DP3)thatwasmanufacturedbyPolyfuel,Inc.(nowknownasUNFNW).ThisGLSutilizesvemembranelayers(twomembranelayers,twowicklayers,andameshsupportinbetween)sandwichedinbetweentwoUltemplates.EachUltemplatefeaturesasingle-serpentineoweldwherethetwo-phasegas-liquidowwouldcomeincontactwiththeventmembraneandtheventingofthecarbondioxidegasoccursin-plane 51

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towardthemiddleoftheassembly.Carbondioxidethenexitsthedevicelaterallyoutthesides.ThisversionoftheGLSiswhatisreferredtoasRev1(Revision1).OtherrevisionsforthisGLS(Rev1-Rev4)haveincludedvariationsoftheserpentineoweldpropertiesincludingchangesintheowelddimensions(wide,narrow)aswellasdifferentgasketmaterials.Deviationsfromtheserpentineoweldhavebeentested.Figure 4-2 showstheRev4GLSdesignconceptdrawingthatfeaturesadeviationfromtheserpentinestructuretoincludestraightchannels.Thisdesignincludedraisedinsetswhichwereincorporatedasowrestrictionstoproducehigherbackpressure,thuscreatingangreaterpressuredropfortheCO2toventacrossthemembranelayers.TestingofthisdeviceshowedthatthebackpressuredidnotreachhighenoughtoventtheCO2andfailed(CO2attheexitoftheGLScomponent)inrepeatedtests. Figure4-1. GLSusedinDemonstrationPrototype3(DP3)packagedunit. EarlierGLSdesignswererectangulartanksthatfeaturedmembranesasacoverlid.Themembraneforthiscongurationwaseitheraatsurfaceoranarea-maximizing 52

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Figure4-2. Rev4GLSdesignconceptdrawing[ 53 ]. pleatedstructureasinFigure 4-3 .Forbothcases(at,pleated),themembraneareawouldllwithwaterovertimeandceasetoventtheCO2gas.Un-ventedCO2gaswouldthenpressurizethecomponentandmakethemembraneplumeoutwarduntilcatastrophicfailurewherethemembranewouldeventuallyburst.Lastly,aGLSusingtubularcongurationmembraneasadesignchoicewasinvestigatedbytheUNFProjectTeam.Figure 4-4 showstubularmembranesmanufacturedbyPoreon.Two(2)differentdiametertubesweretested(ID=1mmandID=5mm).Structuralsupportwasakeyissueasmuchofthemembranelengthisunsupported.Also,thoughthemembranesufcientlyretainedtheliquidphase,thewaterlossforthiscongurationinvaporformwasunacceptable.WiththeexceptionofthePoreontubularconguration,alltheconceptdesignsthathavebeenmanufacturedandtestedhavefeaturedtheDonaldsonmembraneastheventmembrane.AdetaileddiscussionoftheDonaldsonmembraneincludingphysical 53

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parameterssuchasporosityandmorphologicalstructurebasedonSEMimagesisgiveninthenextsection. Figure4-3. GLSconceptdesignthatfeaturesatankwithpleatedmembranestructure[ 54 ]. 54

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Figure4-4. PoreontubularGLSconguration. 4.1.2ExpandedPolytetrauoroethylene(ePTFE)MembraneTheventmembraneusedthroughoutthemodelvalidationexperimentsisadual-layercompositemembranemanufacturedbyDonaldson,Inc(Laminate,6963,TetratexPTFE).Thecompositemembraneconsistsof1)anePTFElayerthathasbothahydrophobicandoleophobictreatment,and2)apolyesternon-wovenbackinglayer.Figure 4-5 showsanSEMimageoftheePTFEmembranelayer.Asshown,themembranesurfaceisadensebrousweavethathasarepresentativeporesizeontheorderof1m.Theseparationofthecarbondioxidegasfromtheliquidstreamoccursatthislayer.Thislayeralsoservesasabarriertoretaintheliquidphasesolutionandpreventleakageoftheuid.ThehydrophobicnatureoftheePTFEmembranelayerinthepresenceofDIwaterand1Mmethanolsolutionwascharacterizedusingcontactanglemeasurements.Foreachuid,ve(5)contactanglemeasurementsweretakenatdifferentlocationsofa4cmx4cmePTFEmembranesampleandanalyzedusingaRameHart,Inc.Goniometer.Adropletsizeof5Lwasusedforeachmeasurementusinganautomaticdispensingsystem.Figure 4-6 showsadropletofDIwateronthesurfaceoftheePTFEmembraneandanillustrationofthecontactangle,,withrespecttohorizontal. 55

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Figure4-5. ePTFElayerofcompositeDonaldsonmembrane. Contactanglesofliquiddropletsonthemembranesurfacegiveinformationabouttheliquid-membraneafnity(thewettability)forthematerial[ 16 ].Auidthathasalowafnityforamembranewillnotwetthematerial(hydrophobic).Conversely,ahighafnityuid-membraneinteractionwillwetthemembraneandallowuidtopenetratethepores(hydrophilic).Therespectivecontactanglesforthehydrophobicandhydrophiliccasesare>90and<90,respectively.TheaveragecontactangleforDIwaterontheePTFEsurfaceis141.45(hydrophobic).SincetheePTFEmembranewillbedeployedintheanodeloopofadirectmethanolsystem,thequestionarisesastowhetherornotthepresenceofmethanolchangestheuid-membraneafnityobservedforthecaseofpureDIwater.Figure 4-7 showsaside-by-sidecomparisonofadropletof1MmethanolandadropletofDIwateronthemembranesurface.Asshowninthegure,thetwodropletslookalmostidentical.The 56

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Figure4-6. DIwaterdropletonsurfaceofePTFEmembranelayer. averagecontactanglefor1Mmethanolis135.1,aproximately4.5%differencefromDIwaterresult.Therefore,onecanconcludethatformethanolsolutionsupto1M,thereisnosignicantdeviationinuid-membraneinteractionfromthatofDIwater.Figure 4-9 showsanSEMimageofthepolyesternon-wovenbackinglayer.ComparedtotheePTFElayerinFigure 4-5 ,oneobservesthatitalsocontainsabrousmesh.However,thepackingforthislayeristwoordersofmagnitudelargerthanthatoftheePTFElayer(v100mwhencomparedto1m).ThepurposeofthislayeristoprovidestructuralsupporttotheePTFElayer.BothlayersformthecompositeGLSmembranethatisusedthroughoutallvalidationexperiments. 4.1.3GLSTestCellExperimentswereconductedusingaone-sidedRev2GLScongurationproducedatUNFNW.Thiscongurationwaschosentoallowforfundamentaltestingofthemembraneperformanceandprovidedatatovalidatemembranetransportmodels. 57

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Figure4-7. ComparisonofliquiddropletsofdifferentuidsincontactwithhydrophobicePTFEmembranesurface-1Mmethanolsolution(left)andDIwater(right). Figure 4-10 showsanimageoftheGLStestcell.Thetestcellis11.2x4cmx1.4cmblockmadefromaUltem1000whichisapolyetherimide(PEI).Thismaterialwaschosenbecauseofitsexcellentmechanicalstrength,thermalandchemicalresistance,aswellasmachinability[ 55 ].TheGLStestcellconsistsofasingleserpentinepathwhichcarriesthegas/liquidstream.Surroundingtheoweldisa1/16siliconegasketusedtosealthemembraneandpreventleaks.Theventmembranelayer(hydrophobicePTFEsidefacingdown)laysontopofthisoweldindirectcontactwithgas-liquidstreamthatowsintheserpentinechannel.Twonylonmeshlayersarethenusedtoprovidestructuralreinforcementtotheunsupportedregionsofthemembrane.Lastly,aslottedplatemadefromthesameUltemmaterialisusedtosecurethelayers.Theentireassemblyisheldtogetherusingsix(6)socketheadcapscrewsinconcertwithtwo(2)Bellevillewashers,and 58

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Figure4-8. Cross-sectionviewofcompositeDonaldsonmembrane. compressionnuts.Atorquescrewisusedtoapplya80oz-in.compressionforcetoeachscrew/nutpairingtoensureevenloadingproleacrosstheGLStestcell.Figure 4-10 andFigure 4-11 showtheserpentineoweldandtopviewofthefullyassembledone-sidedRev2GLS,respectively.AsshowninFigure 4-11 ,themembraneareathatisavailableforgasventingisthespacebetweenslotsofthetopplatereferredtoas'ventchambers(VC)'.Thereareeight(8)totalventchambersonthetestcell.Duringoperation,informationregardingthetemperatureandpressureforthetestcellisloggedforanalysis.Therearetwo(2)temperaturesprobeslocatedattheGLSinletandext,one(1)differentialpressurereadingacrosstheGLS,andtwo(2)independentgagepressurereadings(GLSinletandexit).ThegagepressurereadingattheGLSinletisusedtosetthe'ventpressure'totherequiredsetpointduringtesting. 59

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Figure4-9. BackinglayerofcompositeDonaldsonmembrane. Figure4-10. GLSRev2oweld. Figure 4-12 showsagraphicillustrationoftheGLStestcellthatshowstheplacementoftheve(5)temperature/pressuresensorsfortheunit.Thenalstepintestcellpreparationistheleaktest.EachGLSisleaktestedbyllingthefully-assembledunit(withtemperaturesensorsinplaceandcapsonthetwo 60

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Figure4-11. TopviewoffullyassembledGLSRev2testcell. pressureports)withwater,thenpressurizingitto5psifor5minutes.Duringthiselapsedtime,thetestcellisobservedforanyleaksinseals,ports,etc.Ifanyleaksarepresent,itisaddressedasneededthentheleaktestisrepeateduntilitpasses. 4.2ExperimentalSetupAsdiscussedinprevioussections,theGLScomponentisevaluatedonthebasisoftheventrateofCO2andtheabilitytoretainwaterinaneffectivemanner.AGLSteststation,originallydesignedbyUNFNWandthenimprovedatbothUNFandUF,wasconstructedtoassesstheperformanceofcandidateGLScongurations.Figure 4-13 showsaschematicdiagramoftheGLSteststation.TheliquidreservoirholdstheDIwaterwhichisthenpumpedtoahottubewhereitreachestherequiredtemperaturesetpoint.Thedesignatedowrateisconrmedusingarotameter(designatedinthegureasagenericmassowmeter'MFM').Theheatedwaterthengoestoahumidiersection.ThehumidierconsistsofashellandtubecongurationwheretheinnertubeisaNaonmaterialthatallowsforthetransferofwatervaportothedryCO2gasstream.CO@gas,whichisstoredinagascylinderissuppliedtothere-circulationloopviaamassowcontroller(MFC).Thehumidiedgasstreamatthehumidier(tube)exitthere-combineswiththeheatedwaterstreamviawyebarb.The 61

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Figure4-12. SchematicdiagramofGLStestcell. twophaseowthenenterstheGLStestcellwhichutilizesmembranetechnologytoachieveseparationofthegasfromtheliquidsolution[seeSection 4.1.2 ].Ideally,theGLSwillventall(100%)oftheCO2thatentersthecomponent.Forthiscase,theexitstreamfortheGLSiscomposedentirelyofwaterthatisthenreturnedtotheliquidreservoir.ForthecasewherealltheCO2isnotvented,thenon-ventedportionoftheCO2gasstreamthenenterstheexhaustloopwhichiscomposedofadesiccantcartridgeandamassowmeter(MFM)beforeventingtoambient.TheCO2thatventsthroughtheGLSisthenthedifferenceinowrateregisteredbetweentheMFCsetpointandtheMFMmeasurementintheexhaustloop.AttheGLSexit,thereisabackpressurevalvelocatedinthere-circulationlinebeforetheuidreturnstotheliquidreservoirthatallowstheGLStooperateathigherpressurelevels.Also,acameraissituatedbelowtheGLSas-neededfortestswhereit 62

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Figure4-13. SchematicdiagramofGLSexperimentalteststation. isnecessarytovisualizetheCO2gasbubbleareaasitenters/leavesthecomponent.Ambienttemperatureandhumidityreadingsarerecordedduringteststhroughahumiditysensor(notshown).AfulllistofcomponentsfortheteststationisgiveninTable 4-1 .Animageofthereal-worldGLSteststationisgiveninFigure 4-14 63

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Table4-1. ListofcomponentsandspecicationsfortheGLSexperimentalteststation. ComponentSpecications BKPrecisionTMDCpowersupply1785B,0-18V,singleoutputClaybornLabhottube6'length,1/4OD,304SS,120VAC,400WDrieritelaboratorygasdryingunitAnhydrousCaSO4Hammond,50gwatercapacityDwyerdifferentialpressuretransmitter616-7,0-200w.c.,0.25%F.S.MKSmassowcontroller1179A,500sccm,+/-1%F.S.NI92038-channel,+/-20mA,200KS/S,16-bitanaloginputNI9211thermocouplemodule4-channel,+/-80mV,14S/S,24-bitthermocoupleanaloginputNIcDAQ-9174(Analoginput)Samplerate:6.4MS/s(system)Timingaccuracy:50ppmofsamplingrate(Analogoutput)Samplerate:1.6MS/s(system)Timingaccuracy:50ppmofsamplingrateNIPS-15powersupply24VDC,5A,100-120/200-240VACinputOmegadifferentialpressuretransmitterPX2300,+/-0.25%RSSF.S.OmegagagepressuretransducerMMG2.5C1P3C0T2A4,0-2.5psi,+/-0.08%Omegahumidity/temperaturemeterHH314A,Humidity:+/-2.5%RHat25C;Temperature:+/-0.7COmegamassowmeterFMA1600A,0.5slpm,+/-(0.8%ofreading+0.2%F.S.)OmegarotameterFL-3665ST,150mmarbitraryscale,+/-2%F.S.SymmetryTMmassbalancePR4200,4200g+/-0.01gWatlowtemperaturecontrollerEZZone,+/-0.1%F.S. 64

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Figure4-14. GLSexperimentalteststation. 65

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CHAPTER5RESULTSANDDISCUSSIONAseriesofexperimentswereconductedtoverifymodelsimulationsforgastransportthroughtheGLSmembrane.Bothsingle-phase(CO2only)andtwo-phase(CO2+H2O)testswereconducted.Observationsofthemassuxtoventpressurerelationshipaswellaswaterlossduetobulkowandevaporationweremade.Themassuxtoventpressurerelationshipisanalyzedviabulkowresistanceparameter,,gleanedbyinspectionofdataresults.Abaselineowresistanceparameterisestablishedforthesingle-phaseCO2case(CO2,dry),thencomparedtotheresistanceparameterforthetwo-phasecase(CO2,H2O).AnalseriesoftestsdeterminedCO2,wetforthecaseofsingle-phaseCO2transportthrougha'wet'membraneimmediatelyaftertwo-phaseusage.Theowresistanceparameterresultsforeachcaseispresentedanddiscussed.WaterlossrateanalysisforGLSbeginswiththeevaporationlossthroughtheidleportionofthemembrane.Thewaterlossrateduetoevaporationforaseriesofventpressurecasesrangingfrom0-6895Pa(gage)isgiven.Lastly,waterlossratetestsresultsforcombinedbulkowandevaporationaregiven.Dataresultsandanalysisforalltestingarepresentedbelow,andthencomparedtocalculatedvaluesusingtheMatlabsimulationcode.Afulldiscussionisgiveninthefollowingsections. 5.1MassFluxtoVentPressureRelationshipExperimentswereconductedtoobservethemassuxtoventpressurerelationshipfortheePTFEmembraneandcharacterizeitbasedonthebulkowresistanceparameter,.Thebaselinevaluefortheconductanceparameterwasgleanedfromsingle-phase(CO2only)tests.Forthisseriesoftests,aone-sided,Rev2GLStestcellwasusedwiththeexitcappedoff,forcingthecarbondioxidetoventthroughthemembranetoambient.ThetestswereconductedatroomtemperatureandtheCO2owratewasvariedfrom100-300sccmat100sccmincrements.Therespectivevent 66

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pressureateachowratesettingwasobservedandrecorded.Thetestwasrepeatedtwotimesforatotalofthreetrials.Figure 5-1 showsthemassuxtoventpressurerelationshipforeachtrialintheseries.Asshowninthegure,asthemassuxincreases,theventpressurealsoincreases.AcomparisonofthedatagiveninFigure 5-1 toequation( 3 )showsthattheconductanceparametercanbedeterminedbyobservingtheslopeofthedatatrendline.Theaverageslopeforthesingle-phaseseriesoftestswasCO2,dry=2x10)]TJ /F5 7.97 Tf 6.59 0 Td[(5kg/(Pam2s). Figure5-1. Massuxofcarbondioxideversusventpressurefordrymembranecase. Recallthatthehydraulicconductance,,rstintroducedinequation( 3 )includesgeometricmembranepropertiessuchasporosity,thickness,averageporesize,etc.Athighertemperatures,theporesizewidensduetothermalexpansion.Also,highconcentrationsofmethanolmaychangethewettingpropertiesofthemembraneduetochangesinthesurfacetensionatthemembrane-liquidinterface.Lastly,thehydraulic 67

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conductancealsoincludesgasmixturepropertiessuchasviscositywhichisafunctionoftemperature.Experimentswereconductedtodeterminewhetherthehydraulicconductance,CO2,dry,gleanedfromsingle-phasetestscouldinfactbeusedtopredictthemassuxtoventpressurerelationshipforthetwo-phase(DIwater+CO2)case.Forthetwophaseexperiments,DIwaterandsaturatedCO2wasusedattemperaturesof313K,323K,and333K.TheDIwaterowratewasheldconstantat33mL/minandthegasowratewasvariedfrom100-300sccm.Threetrialswerecompletedforeachtemperaturesetting.Similartothesingle-phasetests,theventpressurewasrecordedforeachowratesettingandtheslopeoftheCO2massuxtoventpressurecurvewasanalyzedtoextracttheeffectivehydraulicconductanceforthistwo-phasecondition,CO2,H2O.Table1showstheresultingconductanceforeachtrialaswellasaveragevalues.Fromthisinformation,theomegaparameterforthetwo-phasecaseisapproximatelyCO2,H2O=5.3x10)]TJ /F5 7.97 Tf 6.58 0 Td[(6kg/(Pam2s),anorderofmagnitudedifferentfromtheobservedsingle-phaseomegaparameter,CO2,dry=2x10)]TJ /F5 7.97 Tf 6.59 0 Td[(5kg/(Pam2s).Thislowermagnitudeslopeonthemassuxtopressurecurvemeansthatforagivenmassux,thepressurerequirementtoventtheCO2ishigherforthetwo-phasecasewhencomparedtothesingle-phasecase. Table5-1. Hydraulicconductance,inkg/(Pam2s),resultsfortwo-phase(DIwater+CO2)GLSexperiments. T=40CT=50CT=60C Trial16x10)]TJ /F5 7.97 Tf 6.59 0 Td[(63x10)]TJ /F5 7.97 Tf 6.59 0 Td[(67x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6Trial24x10)]TJ /F5 7.97 Tf 6.59 0 Td[(66x10)]TJ /F5 7.97 Tf 6.59 0 Td[(65x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6Trial35x10)]TJ /F5 7.97 Tf 6.59 0 Td[(66x10)]TJ /F5 7.97 Tf 6.59 0 Td[(66x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6(Average)5x10)]TJ /F5 7.97 Tf 6.59 0 Td[(65x10)]TJ /F5 7.97 Tf 6.59 0 Td[(66x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6 Thechangeinthecharacteristicslopeofthemassuxtopressuregraphfromv10)]TJ /F5 7.97 Tf 6.59 0 Td[(5forsinglephaseCO2transporttov10)]TJ /F5 7.97 Tf 6.59 0 Td[(6observedduringthetwo-phasecaseillustrateswhatisknownasapore-blockagestateforthemembrane.TheePTFEmembraneusedforvalidationexperimentshasbeenstudiedextensivelywithv1000hrsworthoftestingexperienceinsupportofotherprojectgoals.Oneobservation 68

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forthistypeofmembraneistheoccurrenceofpore-blockagewhichisdenedhereasamembranestatewheretheeffectiveporeareaisreducedsuchthatahigherpressureisneededtosuccessfullyventthegasow.Thecauseofthispore-blockagephenomenonhasbeenhypothesizedtobeeitherinducedbycondensation(occurringonthedownstreamsideofthemembraneinconjunctionwithatemperaturegradient)orthepresenceofaerosolswhichcauseliquidtoentrainintothemembraneporesandblockpassagesovertime.Furthervericationofthispore-blockagephenomenonwascarriedoutviasinglephasetestsof'wet'membrane-i.e.membraneimmediatelyaftertwo-phaseusagethatstillexhibitsporeclogging.Initially,amembraneinstalledinthesingle-sidedRev2GLSwasputinservicewithatwo-phaseowpassingthroughitforthetemperaturesof313K,323K,and333K.TheDIwaterowratewasthensettozerowiththeCO2gasstillowinginordertopurgethelineandGLSchamber.Then,immediatelyaftertheGLSchamberwasemptied,theexitwascappedoffinamannersimilartothesingle-phaseCO2tests.Thehydraulicconductanceparameter,CO2,wet,whichrelatesmassuxofCO2toventpressureforthis'wet'membranecasewasthenobserved.Threetrialswerecompleted;oneaftereachtwo-phasetemperaturesetting.TheresultinghydraulicconductanceparameterswereCO2,wet(1)=7x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6kg/(Pam2s),CO2,wet(2)=4x10)]TJ /F5 7.97 Tf 6.58 0 Td[(6kg/(Pam2s),andCO2,wet(3)=9x10)]TJ /F5 7.97 Tf 6.58 0 Td[(6kg/(Pam2s)foranaveragevalueofCO2,wet=6x10)]TJ /F5 7.97 Tf 6.58 0 Td[(6kg/(Pam2s).Again,thislowerslopestatesthatforagivenmassux,ahigherventpressurerequirementisnecessaryduringtwo-phaseowasopposedtothedryCO2gascase.Agraphicalillustrationofthechangingmagnitudeforthehydraulicconductance,,foreachofthethreecasesissummarizedinFigure 5-2 .Asshowningure,thehydraulicconductanceisinitiallyv10)]TJ /F5 7.97 Tf 6.59 0 Td[(5forthecaseofdryCO2thendropsbyanorderofmagnitudeforthetwo-phasecaseaswellasthewetmembranecase.Again,the 69

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reasonbehindthisoccurrenceisthattheactiveareaforthemembranehasdecreasedfromnominalconditionperhapsduetoliquidblockageofmembranepores. Figure5-2. Comparisonoftheowhydraulicconductance,,forvarioussingle-phase(CO2only)andtwo-phase(CO2+H2O)case. Thehydraulicconductancegiveninequation 3 wascomputedusingtypicalparametersforGLSoperationandcomparedtovaluesthatwereexperimentallydetermined.Again,theporediameterwas=1x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6mandthemembranethicknesslm=40x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6m.Atatemperatureof323K,thedensityandviscosityofthegasmixturewas1.65kg/m3and1.527kg/(ms),respectively.Thesevaluesyieldacomputedhydraulicconductanceofcalc=4.22kg/(Pam2s).ThiscalculatedvalueisalsoanorderofmagnitudelowerthanthedryCO2case(CO2,dryv10)]TJ /F5 7.97 Tf 6.58 0 Td[(5).Forthecalculatedresulttomatchtheexperimental,theratioofporositytotortuositywouldhavetobeapproximately/=1.185whichisnotpossiblesince<1and>1bydenition.ThisresulthighlightstheshortcomingofHagen-Poiseuillelawwhichusesidealized 70

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straighttubeswithconstantcross-sectionandfullydevelopedowforthemembranemorphologydepictedinFigure 4-5 .Asshowninthegure,theePTFEmembraneusedinthisstudyhaswidelychangingowareasacrossthesurfacewhichwouldleadtorapidaccelerationsanddecelerationsoftheow.TheHagen-Poiseuillelawislimitedwhentryingtoeffectivelydescribesuchaowcasescenario.AnempiricalapproachtodeterminingthehydraulicconductanceisrecommendedforGLSdesigners.Withthisparameter,theventpressuretomassux,or,theventpressuretoarearelationshipisnowknown.ThisportionofthemodelcanbeusedasapredictivetooltodeterminethemembranerequirementforagivenpressureconstraintorCO2owrate. 5.2WaterLossRate:EvaporationIntheprevioussection,analysisofthebulkowmassuxtoventpressurerelationshipwaspresentedfortheactiveportionoftheventmembranedirectlyinvolvedwithventingthecarbondioxidegas.BulktransportofCO2thatventsthroughtheporousmembraneisfacilitatedbypressuredifferenceacrossthemembranelayer.Thedownstreamboundaryconditionforthemembraneisatmosphericpressure.Thereforethepressuredifferenceacrossthemembranelayerisdictatedbythegagepressurerecordedattheupstreammembraneboundary.Theupstream(gage)pressurerangeforthegas-liquidseparatorcomponentinstalledintheanodeloopoftheDP4DMFCsystemiscurrentlyconstrainedto0-6895Pa(0-1psig).ExperimentswereconductedtodetermineifthisventpressurerangehasaninuenceontheevaporationrateofwaterfromtheidleportionoftheGLSmembrane(notinvolvedingasventing;incontactwiththeliquidphase).TestswereconductedataGLSoperationtemperature313K,323K,and333KwithDIwaterataconstantowrateof33mL/min.TheGLScongurationwastheone-sidedRev2design(seeFigure 4-12 )withanidlemembraneareaof10cm2exposedtoroomtemperaturecondition.Three(3)differentventpressurecaseswereobserved-noappliedbackpressure(n/a),3447Pa(0.5psig),and6895Pa(1.0psig).Thevent 71

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pressuresetpointwasvariedusingthebackpressurevalveonthetestapparatus.Thewaterlossratewasdeterminedusingthechangeinmassoftheliquidreservoironthemassbalanceovertheelapsedtime.Eachtestwasrepeatedforaminimumofthree(3)trialsateachtemperaturesetpoint.Theeffectofventpressureonthewaterevaporationratewasevaluatedbycomparingsoftwaremodelsimulationstoexperimentaldata.Asshownin(Section 3.3 ),theevaporationofwaterfromtheporousmembraneismodeledasatwo-partprocessofmoleculardiffusionthroughthemembraneporeandconvectionawayfromthesurface.Masstransportforthisportionofthemodelcodeistemperaturedependentandutilizesthedifferenceinwatervaporpressurebetweenthemembrane/liquidinterfaceandambientasthedrivingforce.Themodeldoesnotaccountforventpressurevariations.Therefore,acloseagreementbetweenexperimentalresultsoverthespeciedpressurerangeof0-6895Pa(0-1psig)andcalculatedresultsbasedsolelyontemperaturewillservetovalidatethisportionofthemodelcodeandverifythattheinuenceofpressurecaninfactbeneglected.Figure 5-3 showsresultsfortheaveragewaterlossrateversusGLSoperationtemperatureforthecaseofnoappliedbackpressure(backpressurevalvecompletelyopen).AthigherGLSoperatingtemperatures,thevaporpressureofwaterattheliquid/membraneinterface,Psat,H2Obecomesincreasinglyhigherthanthatofthevaporpressureofwaterintheambient,Pamb,H2O.Recallfromequation( 3 )thatalargerquantitydifferencebetweenthewatervaporpressureattheliquid/membraneinterfaceandambientresultsinaproportionalincreaseintheevaporationmassuxofwater.TheresultsgiveninFigure 5-3 supportthisobservationwiththewaterlossrateincreasingastheGLSoperationtemperatureincreases.Thistrendisrepeatedforboththesubsequentcasesof3447Paand6895PacasesgiveninFigure 5-4 andFigure 5-5 72

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Modelsimulationssuccessfullypredictexperimentaldataforthecaseofnoappliedbackpressurewithin0.8-5.5%.Atventpressureof3447Pa(gage),themodeltodataresulthasanagreementbetween6.5-19%.Lastly,forthe6895Paventpressurecase,thepredictedresultdeviates16.4%fromexperimentaldataat323K.Howeverat313Kand333K,thedatamatchessimulationswithin7.4%and0.007%,respectfully.Onaverage,themodelcodeisabletocomputethewaterlossratewithin7.8%oftheexperimentaldataresult.ThiscloseagreementveriesthatthemodelcodeissatisfactoryforpredictingtheevaporationwaterlossratethroughporousePTFEmembraneovertheventpressurerangeof0-6895Pa(gage). 5.3WaterLossRate:BulkFlow+EvaporationThenalvalidationforthemodelinvolvedcomparingexperimentallydeterminedwaterlossdatatosimulationresultscomputedusingequation( 3 )forbulkow(i-thconstituentiswater)andequation( 3 )forevaporationlossrate.Experimentswereconductedwithtwo-phase(DIwater+CO2)conditionsinordertoverifythatthecompositemodelthatincludeswaterlosscontributionforbothevaporationandsaturatedcarbondioxidecouldsuccessfullypredictthetotalwaterlossrate.Testswereconductedforasingle-sidedGLScongurationwithanactiveregion(directlyinvolvedinCO2Cventing)composedoffourventchambersandtheremainingfourventchambersleftidle.Twotemperaturesof323Kand333Kwereconsidered.TheDIwaterowratewas33mL/minandtheCO2owratewas162sccm.ThetotalwaterlossratefromthesystemwasdataloggedviaLabVIEWusingtheoutputmeasurementsfromthemassbalance.Threetrialswerecompletedateachtestpointforatotalofsixtests.Figure 5-6 showsacomparisonoftheexperimentalandcalculatedresultsfortheaveragewaterlossratewithcombinedbulkowandevaporation.Theerrorbarsshowthestandarddeviationfromthemeanfortheseries.Forthe323Kcase,thereisadirectcorrelationbetweenthesoftwaremodelandexperimentalresult.Thehighertemperaturesetpointcaseshowsexperimentalresultsthatslightlydeviatefromthemodelprediction 73

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by6.5%,thusverifyingthatthecompositemodelcodeissuccessfulatpredictingthetotalwaterlossratefromboththeactiveandidleportionsoftheGLS. 74

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Figure5-3. Waterlossrateduetoevaporationforthecaseofnoappliedbackpressure(BP=n/a). 75

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Figure5-4. Evaporationwaterlossrateatventpressure(gage)of3447Pa. 76

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Figure5-5. Evaporationwaterlossrateatventpressure(gage)of6895Pa. 77

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Figure5-6. Comparisonofexperimentalandcalculatedvaluesforcombinedbulkow+evaporationatvarioustemperatures 78

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CHAPTER6PANDORAGLSDESIGN:APPLICATIONEXAMPLEAnewmembrane-basedGLSprototype,namedPandora,hasbeendesigned,fabricated,andtestedforfeasibility.ThefundamentalshiftofthisdesignistheintegrationoftheGLSfunctionintothere-circulationtankfortheportableDMFCsystem.AnillustrationofthebasicoperationforPandoraGLSdesignisgiveninFigure 6-1 Figure6-1. IllustrationofPandoraGLSdesign. AsshowninFigure 6-1 ,thePandoraGLSdesignfeaturesarectangulartankwithhydrophobic,porousmembranesintubularcongurationinstalledalongtheinterior. 79

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Theupstreamsideofthemembraneisexposedtotwo-phaseowthatconsistsofliquidphasemethanol-watersolutionandgas-phasecarbondioxide.Thedownstreammembraneboundaryisopentoambientconditionatatmosphericpressure.Pressuredifferenceacrossthemembraneisthedrivingforceforbulktransport(gasventing)ofCO2asdiscussedintheGLSmodeldevelopmentinSection 3.2.1 .Figure 6-2 showstheprototypePandoradevicethatwasfabricatedforfeasibilitytesting. Figure6-2. Pandoraprototype(notshown:coverlidforthetank). ThePandoraprototypewasmanufacturedin-houseusingmanualandcomputernumericcontrol(CNC)millingmachines.ThetankforPandoraismadefromUltem1000materialandhasanominalopenvolumeof40cm3whichiscomparativetotheDP4liquidvolumetankcapacity.Withinthetank,two(2)tubularcongurationhydrophobic,porousmembranesareinstalledandsealedusinghigh-strengthsiliconerubber.ThemembranesaremanufacturedbySumitomoElectricandhavedimensionsofID=2mm;OD=3mm(wallthickness=0.5mm).Eachmembranetubehasanexposedmembrane 80

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lengthof17cm.Four(4)membranesupportswereinstalledtokeepthemembraneinplaceduringoperation.Thevolumedisplacedbythepresenceofmembraneis2.4cm3(basedonmembraneODand34cmtotallength)whichisapproximately6%ofthenominalopentankvolume.AnimageofthecompletedPandoraprototypewhileinserviceisgiveninFigure 6-3 Figure6-3. Pandoraprototypeduringtesting.Waterlevelshownatv50%oftankcapacity. ThesiliconerubberusedtosealthemembraneisSilasticTMT-2manufacturedatDowCorning.Thebaseandcuringagentwasmixedtogetherinaratioof10:1.Thesiliconematerialwasthenplacedinavacuumchamberat-30mmHganddegassedfor30mins.Duringthefabricationoftheprototype,asyringewasusedtoapplythesiliconematerial.Thecuretimeforthesiliconewas24hoursatroomtemperature. 81

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ThePandoraGLSdesignwhichintegratestheGLSfunctionintothere-circulationtankofDMFCsystem,hasmanyfeaturesthatareadvantageouswhencomparedtopreviousstand-aloneGLSdesigns(seeSection 4.1.1 ).First,theremovaloftheGLS(andperipheryequipmentforowpathto/fromthedevice,housingmounts,etc)asaseparatecomponentallowsforadecreaseinthesystemmassandvolume,twokeyparametersinthedeterminationoftheenergydensity.ApreviousGLSdesign,Rev2fortheDP4system(seeFigure 4-10 ),observedahighevaporativewaterlossratefromtheidleportionofthemembraneduringoperation.Asshowninprevioussections,thereisanactiveregionofthemembranethatisdirectlyinvolvedinventingtheCO2gasandanidleportionofthemembraneincontactwiththeliquidsolutionthatispronetowaterlossduetoevaporation.Thisevaporationlosshasbeenanalyzedwithinthisdissertationstudyandhasbeenexperimentallydeterminedtobev0.3g/(hrcm2).Thisrepresentsanon-trivialissueduetotheimportanceofwaterbalanceforopencathodeDMFCsystems.ForthePandoraprototype,thewaterlossduetothiseffectiseliminatedbecausethe'idle'portionsofthetubularmembranelocatedbelowtheliquidlevelinthetankwillhaveasaturatedcarbondioxidegasstreamasthedownstreamboundarycondition.Recallthatthedrivingforceforevaporationisawatervaporpressuredifferenceacrossthemembranelayer.SaturationconditionatboththeupstreamanddownstreamboundaryforthePandoraGLSdesignmitigatesanylossrateduetoevaporation.TheRev2GLSdesignalsohadanissuewherethewaterinventoryleftintheGLSoweldatshutdownwouldevaporatethroughtheporousmembraneduringoffstatetimeperiods.Thisoccurrencecreatedwaterstorageissueswithnothavingenoughwaterinthesystemtosuccessfullystartup.AbenetofthePandoraGLSdesignisthatitreadilyallowsforavalvesystemtobeinstalledonthedownstream(membraneinterior)circuit,thusshuttingoffthemembranefromambientduringoff-statedurationsandeliminatingthisissue. 82

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AnessentialsensormeasurementfortheDP4systemisthewaterlevelwithinthere-circulationtank.Thismeasurementgivescriticalinformationastowhetherornotthesystemiswithinwaterbalance.Thecontrolsystemswitchesintodifferent'waterregeneration'or'waterpurge'modesbasedoffthisinformation.Currently,thewaterlevelmeasurementistakenusingcapacitancesensors.Thereisanaddedcostandcomplexitytousingthesetypesofsensorsforthesystem.Asshownpreviously,thereisamathematicalrelationshipforporousmembranesbetweentheactiveventareaandtheupstreamventpressure.ForthePandoraprototype,itispossibletoinferthewaterlevelwithinthetankwithjustthisonepressuremeasurement.Thismarksasimplicationinthedetectionschemeforthewaterlevel,thussavingmoneyandloweringthecomplexityofthehardware.Single-phaseCO2experimentswereconductedtodeterminethemassuxtoventpressurerelationshipforthehydrophobicPTFEmembraneinstalledinthePandoraprototypeinamannersimilartovalidationexperimentsofChapter 4 .Previously,itwasobservedthatthehydraulicconductanceforthedryCO2casedecreasesbyanorderofmagnitude[twophase=10)]TJ /F5 7.97 Tf 6.58 0 Td[(6kg/(Pam2s)]forthe'wet',two-phasecasewithcombinedDIwaterandCO2.Two-phaseexperimentswereconductedtodetermineifthisphenomenonrepeatsitselfwiththeporousmembraneinstalledinthePandoraconguration.Table 6-1 showsthehydraulicconductanceresultsforthetwo-phasetestsofPandora. Table6-1. Hydraulicconductanceresultsfortwo-phase(DIwater+CO2)PandoraGLSexperiments. T=40CT=50CT=60C Trial12.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(51.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(52.0x10)]TJ /F5 7.97 Tf 6.58 0 Td[(5Trial22.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(52.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(52.0x10)]TJ /F5 7.97 Tf 6.58 0 Td[(5Trial32.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(51.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(52.0x10)]TJ /F5 7.97 Tf 6.58 0 Td[(5(Average)2.0x10)]TJ /F5 7.97 Tf 6.59 0 Td[(51.5x10)]TJ /F5 7.97 Tf 6.59 0 Td[(52.0x10)]TJ /F5 7.97 Tf 6.58 0 Td[(5 AsshowninTable 6-1 noobservableshiftinthehydraulicconductanceisapparentfromthebaselinecaseofsingle-phaseCO2tothatofthetwo-phasecasewithboth 83

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DIwaterandCO2.ThisisdifferentfromwhatwasobservedpreviouslywiththeRev2,one-sidedowchanneldesignusedinvalidationexperiments.Apossiblereasonforthedifferentbehaviorwouldbethecongurationitself.TheRev2,one-sidedchanneldesignusedforthevericationtestshadboththeCO2bubbleandtheliquidincontactwitheachotherinashallowoweldofapproximately1mm.Inthisconguration,aerosolsandperhapscondensationhaveagreaterinteractionwiththemembrane.Thesefactorsprovideanamenableenvironmentforthemembraneporestobecomecloggedandtherespectivemembraneareaavailableforgasventingtodiminish.Incontrast,thePandoraGLSwhichisatankcongurationhasaphaseseparationthatoccursduetogravity.TheCO2withalowerdensitymigratestotheheadspaceofthetankandtheventingoccursattheexposedmembrane.Thegasventinginthiscase,independentoftheliquidphaseinteraction,iscomparativetothenominalbaselinecaseofsingle-phaseCO2.Therefore,asimilarhydraulicconductance(andmassuxtopressurerelationship)isobserved.Thehydraulicconductancevalueswereincorporatedintothemodelcodeandwaterlosstestswereconducted.ThewaterlossforPandorasolelyconsistsofthesaturatedwatervaporthatexitstheGLSintheCO2stream.ThisportionofthemodelcodewasveriedviathevalidationexperimentsofChapter 4 .Noevaporationwaterlossisconsideredforthiscase.TestswereconductedatthehightemperatureofT=333K(60C)fortwoCO2owratecasesof162sccmand270sccm.ForbothcasetheDIwaterowratewasheldconstantat33mL/min.Thetestswererepeatedtwiceforatotalofthree(3)trialsateachsetpoint.Figure 6-4 showsboththeexperimentalandcalculatedwaterlossrateresultsforPandoraprototype.Asshowninthegure,theexperimentalwaterlossrateis30-40%higherthanthatpredictedbythebulkowwaterlossmodel.ApossiblereasonforthisobservationisthatthemembraneinstalledinPandorahasdifferenthydrophobicsurfacecharacteristicsthanthemembraneusedforvericationtesting.ThePandoramembrane 84

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Figure6-4. ComparisonofexperimentalandcalculatedwaterlossrateforPandoraGLSprototype(T=333K). exhibitsacontactangleof109whichis23%lesshydrophobicwhencomparedtothemembraneusedforthevalidationexperiments(contactangle=142).ThelargerwaterlossrateversusthatwhichispredictingviasaturatedCO2shouldbetakenintoconsiderationbeforeintegrationintoaDMFCsystem. 85

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CHAPTER7CONCLUSIONSDirectmethanolfuelcellsareapromisingtechnologytodisplacetraditionalbatteriesforportablepowersystems.Thekeytargetforportableapplicationsistohaveahighpoweroutputwhileminimizingthemassandthevolumeofthesystem(i.e-highenergydensity).Withcurrenttechnologylevel,DMFCsareonparwithtraditionalbatterytechnologyonthebasisofgravimetricandvolumetricenergydensity.However,incontrasttobatterytechnologywhichismoremature(smallchanceoftechnologicalimprovement),DMFCsystemsareearlyintheirdevelopmentpathandhaveahighpossibilityforinnovationthatwillmakethemevenbetterinthefuture.AtUniversityofNorthFloridaandUniversityofFlorida,aportableDMFCsystemreferredtoasthe'DemonstrationPrototype4(DP4)'hasbeendemonstratedtooperateat20W(nominal).TheDP4systemisanovelopen-cathodesystemwhichfeaturesaspecialliquidbarrierlayerwithinthemembraneelectrodeassembly(MEA)thatallowsforinternalrecyclingofwaterproducedatthecathode.Internalwaterrecoveryeliminatesthenecessityforexternalprocessingequipmentonthecathodeloopandresultsinasimpliedsystemwithlesscomponents.Carbondioxideisproducedattheanodeasapartoftheelectrochemicalreactionthattakesplaceattheanodecatalystlayer.AkeyissueforDMFCengineersishowtoremovecarbondioxidefromthestackaswellasthesystem.Atthesystem-level,agas-liquidseparator(GLS)componentistaskedwithventingthecarbondioxidefromtheanodeloopwhileretainingliquidphasemethanolandwater.Hydrophobic,porousmembranesrepresentalowcost,passivemethodtoachievethisgoal.AsoftwarecodewasdevelopedtomodelthemasstransportofcarbondioxidethroughtheporousGLSmembrane.Themodelcodeisseparatedintotwopartsbasedonthe'active'and'idle'regionsofthemembrane.TheactivemembraneareaisdirectlyinvolvedinthetransportofCO2andtheidleportionofthemembraneisnot.Inthe 86

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activeregion,waterlossbasedontheamountofwaterthatissaturatedinthecarbondioxideventstream.Fortheidleregion,thereisnoCO2bubbleandtheliquidphaseisdirectlyincontactwiththemembranesurface.Forthisregion,waterlossisbasedonevaporation.AnexperimentalteststationwasdevelopedandaseriesofmodelvalidationexperimentswereconductedtodeterminethemembraneperformanceonthebasisofCO2massuxtoventpressurerelationshipaswellaswaterlossduetosaturatedCO2andevaporation.Single-phaseCO2testswereperformedtodeterminethebaselinemassuxtoventpressurerelationshipfordrymembranes.Thehydraulicconductance,,isdeterminedbyinspectionofthetrendlineforthisrelationship.Thehydraulicconductanceisagroupingofcoefcienttermsinthebulkowequationthatencompassesinformationaboutthemembranestructure(porosity,thickness,etc).TheobservedhydraulicconductanceforthedryCO2casewasCO2,dry=2x10)]TJ /F5 7.97 Tf 6.59 0 Td[(5kg/(Pam2s).ExperimentswerethenconductedtodetermineifthisCO2,dryvaluesuccessfullydescribedthemassuxtoventpressurerelationshipforthetwo-phase(DIwater+CO2)case.Dataresultsshowedthatforthetwo-phasecase,thehydraulicconductancedecreasedbyanorderofmagnitudefromCO2,dry=2x10)]TJ /F5 7.97 Tf 6.59 0 Td[(5kg/(Pam2s)toCO2,H2O=5.3x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6kg/(Pam2s).Thisorderofmagnitudedifferencemeansthatforagivenmassuxtheventpressurerequirementishigherforthetwo-phasecasethanforthesingle-phaseCO2case.Thephenomenonofmembraneporeblockage-thedecreaseoftheactiveareaavailableforgastransportduetothepresenceofliquidentrainedwithinthepores-ishypothesizedasbeingthecauseforthechangingmagnitudeofthehydraulicconductance.Theonsetofporeblockageoccursinthepresenceofaerosolsimpactingthemembranesurfaceandcondensationviatemperaturegradient.Otherphenomenonsuchasmembraneporesenlargingslightlyduetothermalexpansionandhighconcentrationsofmethanolchangingthewettingpropertiesofthemembrane 87

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mayalsocontributetotheporeblockagephenomenon.Asecondconrmationoftheporeblockagephenomenonisviasingle-phaseCO2testsconductedforthe'wet'membraneconditionimmediatelyaftertwo-phaseusage.TheresultingconductancevalueobservedaftertestsattemperaturesofT=313K,323K,and333KforCO2transportthroughwetmembranecaseisCO2,wet=6.7x10)]TJ /F5 7.97 Tf 6.59 0 Td[(6kg/(Pam2s)whichisthesameorderofmagnitudeforthetwo-phasecase.ThislowermagnitudeconductancevaluewhencomparedtothedryCO2caseshowsthatporeblockagehasaresidualeffectonthestateofthemembraneimmediatelyaftertwo-phaseuse.Atlongertimescalesaftertwo-phaseuse,themembraneisabletodryandreturntotheoriginaldryCO2transportprole.ThischangingmassuxtoventpressurerelationbasedonmembraneinteractionwithliquidphaseiskeytoGLSdesign.ExperimentswereperformedtodeterminetherateofwaterlossforGLSmembraneundervariousactiveandidleconditions.Testswereconductedforidlemembranetoanalyzethewaterlosssolelyduetoevaporation.Duringthesetestsitwasdeterminedthatfortherelevantventpressuresof0-6895Pa(gage),thereisnoobservabledeviationawayfrommodelpredictionsforevaporativewaterloss.Therefore,theinuenceofventpressureforthispressurerangecanbeneglectedinthemodelcode.Overall,thisportionofthecodeeffectivelypredictedtheexperimentalwaterlossratewithinanaveragevalueof7.8%.Combinedactiveandidlemembranetestswerethencompletedtoobservethewaterlossratewhenbothbulkowandevaporationprocesseswererunningsimultaneously.Modelresultsfortotalwaterlossratecorrelatedwithexperimentaldatawithin6.5%.Lastly,anewGLSdesignnamed'Pandora'wasintroduced.ThePandoraprototypedesignintegratestheGLSfunctionintothestoragetankfortheDP4system.Thekeyfeaturesofthedesignincludeorientationindependence,eliminationof'idle'membranewaterloss,valveshut-offcapabilitythatallowsforisolationofthemembraneduringoff-statetimedurations(thuseliminatingoff-statewaterloss),andapossiblewaterlevel 88

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sensingmechanism.ThePandoraprototypewasbuiltandtestedforfeasibility.ItisastrongcandidatetobeusedinfutureversionsoftheportableDP4system.ThePandoraprototypehasshowngreatpromiseforthenextgenerationofGLS.However,itisfarfrombeingoptimized.TheSumitomoelectricmembranethatwasinstalledinPandorasuccessfullyventsalltheCO2,howeveritventsslightlymorewaterthanpredicted.Othermembranecompaniesshouldbeinvestigated.Themodelcodethathasbeendevelopedcanserveasthebasisofsuchamembraneselectionstudy.Foragiventemperature,stacksize,andmethanolconcentration,theoptimalmembranepropertiescanbecomputed.Thisinformationcanbeusedtoevaluateprospectivemembranes.Also,lengthandsizeofthemembraneneedstobeoptimized.Sincethemembraneisintegratedintothemethanol-waterstoragetankforthesystem,thereisaconstraintastohowmuchmembranecanbeinstalledbecauseitdisplacescriticalwaterinventorythatisneededforsystemstart-up.Amethod(costfunction)thatincorporatesthisconstraintintothedesignoffutureversionsofPandoraGLSisnecessary.Additionally,theplacementofthemembranewithinthetankinordertoensuresufcientmembraneisavailabletoventalltheCO2foragivenandorientation(andpressurelevel)isneeded.Ananalysisofthe'deadzones'wherethereisn'tsufcientmembranetodeterminethewaterlevelfortheprototypeneedstobedetermined,thenmitigatingstrategiesneedtobecreated.Determiningthemethanolconcentrationwithintheanodeloopisakeyfactorforthesystem.Asstatedpreviously,methanolisthefuelforDMFCsystemandisthebasisforthechemicalreactionsthattakeplace.Ifthereisaninstancethattoomuchortoolittlemethanolissuppliedtothestack,oodingorstarvationmodescanoccurwhichareadverseoperatingconditionsthatlowertheoverallperformance.Currently,theDP4systemusesadensity-basedmethanolsensorforconcentrationmeasurements.Itisexpensivewithahighmassandrelativelylargevolume.Methodstobypasstheuseofthistypeofsensorarecurrentlybeinginvestigatedincludingthepossibilityofinferring 89

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themethanolconcentrationfromthestackperformanceitself(sensorlesscontrol).ThePandoraprototypemayalsohavethepowertodetectthemethanolconcentrationforthesystembyaddingamethanolsensortotheCO2exhaustforthecomponent.IfthemethanolconcentrationintheCO2exhaustisknown,thenequilibriumargumentscanbemadetobackoutthemethanolconcentrationintheliquidphase.Asuitablemethanolsensorneedstobefoundforthispurpose.TheGLScomponentisanintegralpartofanyDMFCsystem.Forthecasewherehydrophobicporousmembranesareused,asimulationcodehasbeencreatedinordertopredicttheperformance.Themodelwasvalidatedviaexperimentsthatconrmedtheventpressuretoarearelationship,and,thewaterlossduetosaturatedCO2streamandevaporation.TheuseofthemodelasadesigntoolwasillustratedviathePandoraGLSprototype,markingapromisingGLSdesignforfutureDMFCsystems. 90

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APPENDIX:UNIVERSALFUNCTIONALACTIVITYCOEFFICIENTMETHOD ThefollowingisabriefsummaryoftheUniversalFunctionalActivityCoefcient(UNIFAC)methodimplementedforabinarymethanol-watersystemasgivenbyJ.Winnick[ 29 ]andPoling,etal[ 1 ].ThereaderisencouragedtoseekouttheseoriginalsourcesforadetaileddiscussionoftheUNIFACmethod.OthersourcessuchasFredenslund,Jones,andPrausnitz[ 56 ],J.M.Smith,etal.[ 41 ]andSeaderandHenley[ 18 ]arealsoavailableforreference.TheactivitycoefcientcalculatedbasedonthepartialmolalderivativeoftheGibbsfreeenergyasfollows: lni=@GE=RT @ni(A)ThemolalGibbsfreeenergy(chemicalpotential)isexpressedintermsofacombinatorialandresidualportionusingthefollowingequation: gE=gC+gR(A)Thecombinatorialportion,basedonmoleculegeometry,isgivenas: gC=MXi=1xilni xi+z 2MXi=1qixilni i(A)whereiisthevolumefraction,iisthesurfaceareafractionofconstituentmolecules,andxiisthemolefraction.Theseparametersaredeterminedbasedonthemolecularvolume,rj,andsurfacearea,qi,viathefollowingequations: irixi PMj=1rjxj(A) iqixi PMj=1qjxj(A)where 91

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rj=NXk=1jkRk(A)and qj=NXk=1jkQk(A)Inequation( A )andequation( A ),jkisthenumberofkgroupsinmoleculej;Rkisthevolumeofgroupk;qjisthemolecularsurfacearea;Qkisthegroupsurfacearea.ValuesforboththevolumeandsurfaceparamtersformethanolandwateraregiveninTable A-1 TableA-1. Volume(Rk)andsurface(Qk)parametersformethanolandwater[ 1 ]. GroupRkQk CH3OH1.43111.432H2O0.92001.400 Informationaboutthedifferenceininteractionenergiesbetweenmoleculargroupsisgivenintheresidualportionofequation( A ),expressedasfollows: gR=)]TJ /F7 7.97 Tf 15.89 14.94 Td[(MXi=1qixiln MXj=1j ji!(A)where ji=exp)]TJ /F6 11.955 Tf 10.49 8.09 Td[(aji T(A)Inthisequation, jirepresentsthegroupinteractionparametersbasedoninteractionconstantsaijsuchthataij6=aji.Thegroup-groupinteractionparametersformethanolandwateraregiveninTable A-2 92

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TableA-2. Group-groupinteractionparameters(aij)formethanolandwater[ 1 ]. GroupCH3OHH2O CH3OH0-181.0H2O289.60 ThederivativeoftheGibbsfreeenergyequationleadstothenalexpressionfortheactivitycoefcients: lni=lnCi+lnRi(A)Again,theactivitycoefcientisbasedonthecontributionsofthecombinatorial(C)portionandtheresidual(R)portionasfollows: lnCi=lni xi+z 2qilni i+li+i xiMXj=1xjlj(A)and lnRi=NXk=1ikln)]TJ /F7 7.97 Tf 6.78 -1.79 Td[(k)]TJ /F6 11.955 Tf 11.96 0 Td[(ln)]TJ /F7 7.97 Tf 6.77 4.94 Td[(ik(A)where ljz 2(rj)]TJ /F6 11.955 Tf 11.96 0 Td[(qj))]TJ /F3 11.955 Tf 11.95 -.17 Td[((rj)]TJ /F3 11.955 Tf 11.95 0 Td[(1)(A)and ln)]TJ /F7 7.97 Tf 6.78 -1.79 Td[(k=Qk(1)]TJ /F6 11.955 Tf 11.96 0 Td[(ln NXm=1m mk!)]TJ /F7 7.97 Tf 17.69 14.94 Td[(NXm=1"m km PNn=1n nm#)(A)Intheaboveequations,ziscoordinationnumberandNistotalnumberofgroupsinallspecies. 93

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[28] X.S.Zhu,Micro/nanoporousmembranebasedgas-waterseparationinmicrochannel,MicrosystemTechnologies-Micro-andNanosystems-InformationStorageandProcessingSystems,vol.15,pp.1459,2009. [29] J.Winnick,ChemicalEngineringThermodynamics.JohnWiley&Sons,Inc.,1996. [30] S.Prakash,W.Mustain,andP.A.Kohl,Carbondioxideventfordirectmethanolfuelcells,JournalofPowerSources,vol.185,pp.392,2008. [31] S.PrakashandP.A.Kohl,Performanceofcarbondioxideventfordirectmethanolfuelcells,JournalofPowerSources,vol.192,pp.429,2009. [32] A.E.Scheidegger,ThePhysicsofFlowThroughPorousMedia.UniversityofTorontoPress,1974. [33] R.Bird,W.Stewart,andE.Lightfoot,TransportPhenomena.WileyInternationaledition,JohnWiley&Sons,Inc.,2007. [34] G.MarinandG.Yablonsky,KineticsofChemicalReactions.Wiley,2011. [35] E.Cussler,Diffusion:MassTransferinFluidSystems.CambridgeSeriesinChemicalEngineering,CambridgeUniversityPress,1997. [36] P.Argyropoulos,K.Scott,andW.Taama,Modellingpressuredistributionandanode/cathodestreamsvapourliquidequilibriumcompositioninliquidfeeddirectmethanolfuelcells,ChemicalEngineeringJournal,vol.78,no.1,pp.2941,2000. [37] C.J.Geankoplis,TransportProcessesandSeparationProcessPrinciples.Printice-Hall,Inc.,4thed.,2003. [38] P.LinstromandW.Mallard,eds.,NISTChemistryWebBook,NISTStandardReferenceDatabaseNumber69.NationalInstituteofStandardsandTechnology,accessdate:2011. [39] D.LideandH.Frederikse,eds.,CRCHandbookofChemistryandPhysics.BocaRaton,FL:CRCPress,Inc.,76thed.,1995. [40] C.Yaws,YawsHandbookofPropertiesforEnvironmentalandGreenEngineering.GulfPublishingCompany,2008. [41] M.A.J.M.Smith,H.C.VanNess,IntroductiontoChemicalEngineeringThermody-namics.McGraw-Hill,Inc.,5thed.,1996. [42] S.Ohe,Vapor-liquidequilibriumdata.Physicalsciencesdata,Elsevier,1989. [43] M.Hirata,S.Ohe,andK.Nagahama,Computeraideddatabookofvapor-liquidequilibria.Kodanshascienticbooks,KodanshaLimited,1975. 96

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[44] P.Dalager,Vapor-liquidequilibriumsofbinarysystemsofwaterwithmethanolandethanolatextremedilutionofthealcohols,JournalofChemical&EngineeringData,vol.14,no.3,pp.298,1969. [45] M.Kato,H.Konishi,andM.Hirata,Newapparatusforisobaricdewandbubblepointmethod.methanol-water,ethylacetate-ethanol,water-1-butanol,andethylacetate-watersystems,JournalofChemical&EngineeringData,vol.15,no.3,pp.435,1970. [46] M.L.McGlashanandA.G.Williamson,Isothermalliquid-vaporequilibriumsforsystemmethanol-water,JournalofChemical&EngineeringData,vol.21,no.2,pp.196,1976. [47] R.P.O'Hayre,S.-W.Cha,W.G.Colella,andF.B.Prinz,FuelCellFundamentals.JohnWiley&Sons,Inc.,2nded.,2009. [48] A.Mourgues,N.Hengl,M.P.Belleville,D.Paolucci-Jeanjean,andJ.Sanchez,Membranecontactorwithhydrophobicmetallicmembranes:1.modelingofcoupledmassandheattransfersinmembraneevaporation,JournalofMembraneScience,vol.355,pp.112,2010. [49] S.R.Turns,AnIntroductiontoCombustion.McGraw-Hill,Inc.,2nded.,2000. [50] F.Ullmann,Ulmann'sChemicalEngineeringandPlantDesign,vol.1-2.JohnWiley&Sons,Inc.,2005. [51] A.Mills,HeatandMassTransfer.RichardD.Irwin,Inc.,1995. [52] W.Kays,M.Crawford,andB.Weigand,ConvectiveHeatandMassTransfer.McGraw-Hill,Inc.,4thed.,2005. [53] A.Mossman,GlsupdateApril122011.InternalDocument,April2011. [54] A.Mossman,Historyofanodeloopgas-liquidseparatorsrev2.InternalDocument,February2010. [55] D.O.Kipp,ed.,PlasticMaterialDataSheets.MatWeb-DivisionofAutomationCreation,Inc.,2010. [56] A.Fredenslund,R.L.Jones,andJ.M.Prausnitz,Group-contributionestimationofactivitycoefcientsinnonidealliquidmixtures,AIChEJournal,vol.21,no.6,pp.1086,1975. 97

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BIOGRAPHICALSKETCH SydniCredlereceivedherdoctoraldegreeintheeldofmechanicalengineeringattheUniversityofFlorida(UF)inGainesville,Florida.Hereldofexpertiseisingas-liquidseparationsusingmembranetechnologyfordirectmethanolfuelcellapplication.Herresearchalsoincludestwo-phaseow,multi-componenttransport,design/prototyping,andfuelcellsystemmodeling.Ms.CredleisanalumnusofFloridaAgricultural&MechanicalUniversitywhereshereceivedherBachelorofScienceandMasterofSciencedegreesinmechanicalengineering.Sydnipridesherselfonvolunteeringandprofessionalservice.Shehasmentoredoversevenstudentsinaresearchenvironmentatalllevelsofacademicstudy.Ms.CredlealsoservesasareviewerfortheJournalofSolarEnergyandJournalofHydrogenEnergy. 98