FundamentalsofChemicalReactorEngineering
AMulti-ScaleApproach
TimurDoğu ProfessorofChemicalEngineering MiddleEastTechnicalUniversity Çankaya,Ankara
GülşenDoğu
ProfessorofChemicalEngineering GaziUniversity Maltepe,Ankara
Thiseditionfirstpublished2022. ©2022JohnWiley&Sons,Inc.
Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted, inanyformorbyanymeans,electronic,mechanical,photocopying,recordingorotherwise,exceptas permittedbylaw.Adviceonhowtoobtainpermissiontoreusematerialfromthistitleisavailableat http://www.wiley.com/go/permissions.
TherightofTimurDoğuandGülşenDoğutobeidentifiedastheauthorsofthisworkhasbeenassertedinaccordance withlaw.
RegisteredOffice(s)
JohnWiley&Sons,Inc.,111RiverStreet,Hoboken,NJ07030,USA
EditorialOffice 111RiverStreet,Hoboken,NJ07030,USA
Fordetailsofourglobaleditorialoffices,customerservices,andmoreinformationaboutWileyproductsvisitusat www.wiley.com.
Wileyalsopublishesitsbooksinavarietyofelectronicformatsandbyprint-on-demand.Somecontentthatappearsin standardprintversionsofthisbookmaynotbeavailableinotherformats.
LimitofLiability/DisclaimerofWarranty
Inviewofongoingresearch,equipmentmodifications,changesingovernmentalregulations,andtheconstantflowof informationrelatingtotheuseofexperimentalreagents,equipment,anddevices,thereaderisurgedtoreviewand evaluatetheinformationprovidedinthepackageinsertorinstructionsforeachchemical,pieceofequipment,reagent, ordevicefor,amongotherthings,anychangesintheinstructionsorindicationofusageandforaddedwarningsand precautions.Whilethepublisherandauthorshaveusedtheirbesteffortsinpreparingthiswork,theymakeno representationsorwarrantieswithrespecttotheaccuracyorcompletenessofthecontentsofthisworkandspecifically disclaimallwarranties,includingwithoutlimitationanyimpliedwarrantiesofmerchantabilityorfitnessfora particularpurpose.Nowarrantymaybecreatedorextendedbysalesrepresentatives,writtensalesmaterialsor promotionalstatementsforthiswork.Thefactthatanorganization,website,orproductisreferredtointhisworkasa citationand/orpotentialsourceoffurtherinformationdoesnotmeanthatthepublisherandauthorsendorsethe informationorservicestheorganization,website,orproductmayprovideorrecommendationsitmaymake.This workissoldwiththeunderstandingthatthepublisherisnotengagedinrenderingprofessionalservices.Theadvice andstrategiescontainedhereinmaynotbesuitableforyoursituation.Youshouldconsultwithaspecialistwhere appropriate.Further,readersshouldbeawarethatwebsiteslistedinthisworkmayhavechangedordisappeared betweenwhenthisworkwaswrittenandwhenitisread.Neitherthepublishernorauthorsshallbeliableforanyloss ofprofitoranyothercommercialdamages,includingbutnotlimitedtospecial,incidental,consequential,orother damages.
LibraryofCongressCataloging-in-PublicationData:
Names:Doğu,Timur,author.|Doğu,Gülşen,author.
Title:Fundamentalsofchemicalreactorengineering:amulti-scale approach/TimurDoğu&GülşenDoğu,ProfessorsofChemical Engineering,MiddleEastTechnicalUniversity&GaziUniversity.
Description:Hoboken,NJ,USA:Wiley,2022.|Includesindex.
Identifiers:LCCN2021032013(print)|LCCN2021032014(ebook)|ISBN 9781119755890(cloth)|ISBN9781119755906(adobepdf)|ISBN 9781119755913(epub)
Subjects:LCSH:Chemicalreactors.|Chemicalplants.
Classification:LCCTP157.D5952022(print)|LCCTP157(ebook)|DDC 660/.2832–dc23
LCrecordavailableathttps://lccn.loc.gov/2021032013
LCebookrecordavailableathttps://lccn.loc.gov/2021032014
CoverDesign:Wiley
CoverImage:CourtesyofTimurDoğuandGülşenDoğu
Setin9.5/12.5ptSTIXTwoTextbyStraive,Pondicherry,India
10987654321
WearegratefultoourmothersHalideDuralı andMübdiaDoğu,ourfathersHüseyinDuralı andLatif Doğu.Theirmemoriesarestillaliveandsupportive.
OurendlessthankstoourchildrenBurcuBalamandDoruk,andourdaughter-in-lawSerapfor theircontinuingsupportandaffection.
Ourdeepestloveisforourgrandchildren İpek,Emre,andDemir.
Thisbookisdedicatedtoallofyou.
Contents
Preface xiii
ForewordbyMarc-OlivierCoppens xv
ForewordbyUmitS.Ozkan xvii
AbouttheAuthorsandAcknowledgments xix
ListofSymbols xxi
AbouttheCompanionWebsite xxvii
1RateConceptandSpeciesConservationEquationsinReactors 1
1.1ReactionRatesofSpeciesinChemicalConversions 1
1.2RateofaChemicalChange 3
1.3ChemicalReactorsandConservationofSpecies 6
1.4FlowReactorsandtheReactionRateRelations 8
1.5ComparisonofPerfectlyMixedFlowandBatchReactors 9
1.6IdealTubularFlowReactor 10
1.7StoichiometricRelationsBetweenReactingSpecies 13
1.7.1BatchReactorAnalysis 13
1.7.2Steady-FlowAnalysisforaCSTR 13
1.7.3UnsteadyPerfectlyMixed-FlowReactorAnalysis 14 ProblemsandQuestions 15 References 18
2ReversibleReactionsandChemicalEquilibrium 19
2.1EquilibriumandReactionRateRelations 19
2.2ThermodynamicsofChemicalReactions 21
2.3DifferentFormsofEquilibriumConstant 23
2.4TemperatureDependenceofEquilibriumConstantandEquilibriumCalculations 25 ProblemsandQuestions 33 References 34
3ChemicalKineticsandAnalysisofBatchReactors 35
3.1KineticsandMechanismsofHomogeneousReactions 35
3.2BatchReactorDataAnalysis 39
3.2.1IntegralMethodofAnalysis 41
3.2.1.1First-OrderReaction 41
3.2.1.2 nth-OrderReactionandMethodofHalf-Lives 43
3.2.1.3OverallSecond-OrderReactionBetweenReactantsAandB 44
3.2.1.4Second-OrderAutocatalyticReactions 48
3.2.1.5Zeroth-OrderDependenceofReactionRateonConcentrations 50
3.2.1.6DataAnalysisforaReversibleReaction 51
3.2.2DifferentialMethodofDataAnalysis 52
3.3ChangesinTotalPressureorVolumeinGas-PhaseReactions 54 ProblemsandQuestions 56 References 61
4Ideal-FlowReactors:CSTRandPlug-FlowReactorModels 63
4.1CSTRModel 63
4.1.1CSTRDataAnalysis 67
4.2AnalysisofIdealPlug-FlowReactor 69
4.3ComparisonofPerformancesofCSTRandIdealPlug-FlowReactors 71
4.4EquilibriumandRateLimitationsinIdeal-FlowReactors 72
4.5UnsteadyOperationofReactors 76
4.5.1UnsteadyOperationofaConstantVolumeStirred-TankReactor 76
4.5.2Semi-batchReactors 77
4.6AnalysisofaCSTRwithaComplexRateExpression 79 ProblemsandQuestions 81 References 85
5MultipleReactorSystems 87
5.1MultipleCSTRsOperatinginSeries 87
5.1.1GraphicalMethodforMultipleCSTRs 91
5.2MultiplePlug-FlowReactorsOperatinginSeries 93
5.3CSTRandPlug-FlowReactorCombinations 94 ProblemsandQuestions 96 References 98
6MultipleReactionSystems 99
6.1SelectivityandYieldDefinitions 100
6.2SelectivityRelationsforIdealFlowReactors 101
6.3DesignofIdealReactorsandProductDistributionsforMultipleReactionSystems 104
6.3.1ParallelReactions 104
6.3.2ConsecutiveReactions 110 ProblemsandQuestions 113 References 116
7HeatEffectsandNon-isothermalReactorDesign 117
7.1HeatEffectsinaStirred-TankReactor 118
7.2Steady-StateMultiplicityinaCSTR 121
7.3One-DimensionalEnergyBalanceforaTubularReactor 126
7.4HeatEffectsinMultipleReactionSystems 131
7.4.1HeatEffectsinaCSTRwithParallelReactions 131
7.4.2HeatEffectsinaCSTRwithConsecutiveReactions 132
7.4.3EnergyBalanceforaPlug-FlowReactorwithMultipleReactions 133
7.5HeatEffectsinMultipleReactorsandReversibleReactions 133
7.5.1TemperatureSelectionandMultipleReactorCombinations 133
7.5.1.1Endothermic-ReversibleReactionsinaMulti-stageReactorSystem 141
7.5.2ColdInjectionBetweenReactors 147
7.5.3Heat-ExchangerReactors 149 ProblemsandQuestions 150
CaseStudies 154
References 160
8DeviationsfromIdealReactorPerformance 161
8.1ResidenceTimeDistributionsinFlowReactors 161
8.2GeneralSpeciesConservationEquationinaReactor 163
8.3LaminarFlowReactorModel 166
8.4DispersionModelforaTubularReactor 168
8.5PredictionofAxialDispersionCoefficient 172
8.6EvaluationofDispersionCoefficientbyMomentAnalysis 174
8.7RadialTemperatureVariationsinTubularReactors 175
8.8ACriterionfortheNegligibleEffectofRadialTemperatureVariationsontheReaction Rate 177
8.9Effectof L/dt RatioonthePerformanceofaTubularReactorandPressureDrop 179 ProblemsandQuestions 180 Exercises 181 References 182
9Fixed-BedReactorsandInterphaseTransportEffects 185
9.1Solid-CatalyzedReactionsandTransportEffectsWithinReactors 185
9.2ObservedReactionRateandFixed-BedReactors 187
9.3SignificanceofFilmMassTransferResistanceinCatalyticReactions 189
9.4TubularReactorswithCatalyticWalls 191
9.4.1One-DimensionalModel 192
9.4.2Two-DimensionalModel 193
9.5ModelingofaNon-isothermalFixed-BedReactor 194
9.6Steady-StateMultiplicityontheSurfaceofaCatalystPellet 196 Exercises 197 References 198
10TransportEffectsandEffectivenessFactorforReactionsinPorousCatalysts 199
10.1EffectivenessFactorExpressionsinanIsothermalCatalystPellet 199
10.2ObservedActivationEnergyandObservedReactionOrder 205
10.3EffectivenessFactorinthePresenceofPore-DiffusionandFilmMassTransfer Resistances 208
10.4ThermalEffectsinPorousCatalystPellets 210
Contents
10.5InterphaseandIntrapelletTemperatureGradientsforCatalystPellets 215
10.6PoreStructureOptimizationandEffectivenessFactorAnalysisforCatalystswith Bi-modalPore-SizeDistributions 217
10.7CriteriaforNegligibleTransportEffectsinCatalyticReactions 221
10.7.1CriteriaforNegligibleDiffusionandHeatEffectsontheObservedRateofSolid-Catalyzed Reactions 221
10.7.2RelativeImportanceofConcentrationandTemperatureGradientsinCatalyst Pellets 222
10.7.3IntrapelletandExternalFilmTransportLimitations 225
10.7.4ACriterionforNegligibleDiffusionResistanceinBidisperseCatalystPellets 225
10.8TransportEffectsonProductSelectivitiesinCatalyticReactions 226
10.8.1FilmMassTransferEffect 226
10.8.2Pore-DiffusionEffect 227
ProblemsandQuestions 228
Exercises 229 References 233
11IntroductiontoCatalysisandCatalyticReactionMechanisms 235
11.1BasicConceptsinHeterogeneousCatalysis 235
11.2SurfaceReactionMechanisms 237
11.3AdsorptionIsotherms 241
11.4DeactivationofSolidCatalysts 244
Exercises 246 References 246
12DiffusioninPorousCatalysts 247
12.1DiffusioninaCapillary 247
12.2EffectiveDiffusivitiesinPorousSolids 251
12.3SurfaceDiffusion 252
12.4ModelsforthePredictionofEffectiveDiffusivities 253
12.4.1RandomPoreModel 253
12.4.2GrainModel 254
12.5DiffusionandFlowinPorousSolids 254
12.6ExperimentalMethodsfortheEvaluationofEffectiveDiffusionCoefficients 255
12.6.1Steady-StateMethods 255
12.6.2DynamicMethods 256
12.6.3Single-PelletMomentMethod 257
Exercises 259 References 259
13ProcessIntensificationandMultifunctionalReactors 261
13.1MembraneReactors 262
13.1.1ModelingofaMembraneReactor 263
13.1.2GeneralConservationEquationsandHeatEffectsinaMembraneReactor 265
13.2ReactiveDistillation 266
13.2.1Equilibrium-StageModel 267
13.2.2ARate-BasedModelforaContinuousReactiveDistillationColumn 269
13.3Sorption-EnhancedReactionProcess 270
13.4MonolithicandMicrochannelReactors 275
13.4.1MicrochannelReactors 278
13.5ChromatographicReactors 279
13.6AlternativeEnergySourcesforChemicalProcessing 279
13.6.1Microwave-AssistedChemicalConversions 280
13.6.2UltrasoundReactors 282
13.6.3SolarEnergyforChemicalConversion 282
References 283
14MultiphaseReactors 285
14.1SlurryReactors 285
14.2Trickle-BedReactors 289
14.3Fluidized-BedReactors 290 References 294
15KineticsandModelingofNon-catalyticGas–SolidReactions 295
15.1Unreacted-CoreModel 296
15.2DeactivationandStructuralModelsforGas–SolidReactions 299
15.3ChemicalVaporDepositionReactors 302 Exercises 305 References 307
AppendixASomeConstantsofNature 309 AppendixBConversionFactors 311 AppendixCDimensionlessGroupsandParameters 313 Index 315
Preface
Themulti-scalenatureofchemicalreactorengineeringmakesitquitedistinctfrommostofthe othercoursesinachemicalengineeringcurriculum.Itsdiversenatureisquiteuniqueascompared tothecoursesinmanyoftheengineeringfields.Analysisanddesignofchemicalreactorsaregenerallytaughtintheundergraduate-levelChemicalReactionEngineering,ChemicalEngineering Kinetics,orReactorDesigncourses,aswellasinthegraduate-levelAdvancedChemicalReaction EngineeringandCatalysiscourses.Anychemicalengineeringgraduateshouldacquireastrong backgroundinthefundamentalsofkineticsandthermodynamicsofchemicalconversions,aswell ashydrodynamicsandtransportprocessestakingplaceinachemicalreactor.Theinteractionofthe reactingmoleculesonthemolecularscaledeterminesthemechanismandthekineticsofchemical reactions.Comprehensionofthekineticsandthermodynamicsofchemicalconversionsisrequired butnotenoughtoanalyzeanddesignchemicalreactors.Solidcatalyticmaterialscatalyzemanyof thechemicalconversions.Mostofthesecatalystsareporous,havingveryhighsurfaceareavalues, reaching1000m2/gorevenhigher.Inthescaleofacatalystpellet,knowledgeontheadsorption andsurfacereactionmechanismsisneededtodeveloptherateexpressions.Understandingpore diffusionandheattransfereffectsontheobservedratesofthereactionscatalyzedbyporouscatalyticmaterialsarecrucialforanalyzinganddesigningcatalyticreactors.
Observedratesofchemicalconversionsstronglydependuponthetemperatureandconcentration distributions,aswellasthemixingcharacteristicswithinareactor.Designandscale-upofachemicalreactorfrombench-scaletoindustrial-scalerequireastrongknowledgeofhydrodynamicsand transportprocesseswithintheseunits.Understandingheatandmasstransferresistanceswithin suchunitsisrequiredfortherealisticdesignofchemicalreactors.Transportprocessesbetween thephasesshouldbeconsideredintheanalysisanddesignofmultiphasereactionvessels,such asslurry,trickle-bed,fluidized-bed,andfixed-bedreactors.Pseudo-homogeneoustransportequationsareusedtodesignmultiphasereactionsystems.Theseequationsinvolveinterphaseandintraphasetransportrateparametersinsolid-catalyzedreactions.
Designandanalysisofachemicalreactionvesselrequirethesynthesisofbasicknowledgeofthe fundamentalsateachscaleoftheprocessestakingplaceinareactor.Thismulti-scalenatureof chemicalreactorengineeringandthefundamentalsofeachscaleareemphasizedthroughoutthis book.Somenewapproachestoprocessintensificationarealsoincludedinthistext.Thisbookis intendedasatextbookforundergraduate-andgraduate-levelchemicalreactionengineeringand reactordesigncoursestaughtinthechemicalengineeringprograms.AlthoughChapters1–8are designedmainlyforanundergraduate-levelchemicalreactionengineeringcourse,thechoiceof thechapterstobecoveredintheundergraduate-orgraduate-levelcoursesdependsuponthebackgroundofthestudentstakingthesecourses.
Chemicalreactorengineeringisacontinuouslyevolvingareainthechemicalengineeringcurriculum.Thefirstbook,whichtreatskineticsandcatalysis,ispartIIIofthe “ChemicalProcess
Principles” bookseriesofHougenandWatson(1947).Theclassical “ChemicalEngineeringKinetics” bookofJ.M.Smith(1956),andthe “ChemicalReactionEngineering:AnIntroduction” bookof O.Levenspiel(1962)madelastingimpactsontheunderstandingofprinciplesandapplicationsof chemicalreactionengineering.Someoftheotherexcellentbookspublishedinthisareaare “ChemicalReactorTheory” bookbyK.G.DenbighandJ.C.R.Turner(1965), “ChemicalReactionAnalysis” bookbyE.E.Petersen(1965), “ElementaryChemicalReactorAnalysis” bookofR.Aris(1969), “ChemicalandCatalyticReactorEngineering” bookofJ.J.Carberry(1976), “AnIntroductionto ChemicalKineticsandReactorDesign” bookbyC.G.Hill(1977), “ChemicalReactorAnalysis andDesign” bookofG.F.FromentandK.B.Bischoff(1979), “ElementsofChemicalReactionEngineering” bookofH.S.Fogler(1986),and “ChemicalReactionsandChemicalReactors” bookof G.W.Roberts(2009).Multipleeditionsofsomeofthesebookswerepublishedandusedinthe chemicalreactionengineeringcoursesinanumberofchemicalengineeringprograms.Theauthors gratefullyacknowledgealloftheformercontributorswhomadetheirmarkinchemicalreaction engineeringandcatalysis.
Recentadvancesinprocessintensificationcomprisethedevelopmentofmoreefficient,smaller, cleanerprocessesthantheconventionalonesusedinthechemicalindustry.Costandwasteminimization,improvedproductionyieldofthedesiredproduct,lessenergyandreactantconsumption perunitmassoftheproduct,improvedsafety,andenvironmentalcleanlinessaresomeoftheconcepts,whichshouldbeconsideredinthedesignofnewchemicalprocessesandreactors.Fromthe reactorengineeringpointofview,theideaofintegrationofreactionandseparationprocessesintoa singleunitinitiatedthedevelopmentofmultifunctionalreactors.Also,theuseofalternativeenergy sources,likemicrowave,solarenergy,ultrasound,etc.inchemicalprocessinganddesignofnovel reactors,suchasmicrochannelreactors,monolithicreactors,supercriticalreactors,openednew avenuesinreactionengineeringapplications.
Processintensificationconceptsandmodelingofmultifunctionalreactors,suchasmembrane reactors,equilibrium-stageandcontinuouspacked-bedreactivedistillationunits,andsorption enhancedreactors,arecoveredinChapter13.Someotherchemicalreactorengineeringapplicationsinmaterialprocessing(chemicalvapordepositionreactors)arealsoillustratedwithexamples. Effectsofthepore-sizedistributionofthecatalystshavingmicro-,meso-,andmacroporesonthe observedratesofreactions,criteriafortheneglectionoftransporteffectsontheobservedrates,diffusionmechanismswithinporouscatalysts,dynamicmethodsusedfortheevaluationofrateparameters,modelingofgas–solidnon-catalyticreactionsandcatalystdeactivationaresomeofthe othertopicscoveredinthisbook.Severalproblemsareincludedattheendofeachchapter,and alistofopen-endedcasestudiesisgiveninChapter7.Differentsoftwareisavailableintheuniversitiesforthenumericalsolutionandsimulationofengineeringproblems.Studentsareexpected towritedowntheirowncodesoruseanyoneoftheavailablesimulationsoftwareanddesign packagestosolvesomeofthecomplexreactordesignproblemsandimprovetheirproblem-solving abilitieswithoutbeingside-trackedfromthebasicsofchemicalreactorengineering.Hence,the emphasisisgiventothedeepunderstandingofthebasicprinciplesofchemicalreactoranalysis andheterogeneouscatalysisateveryscaleofthissubject,andthesebasicprinciplesareillustrated withexamples.OnlineAppendicesarealsoavailable,coveringareviewofmathematicaltools neededinchemicalreactorengineeringapplicationsandsomecasestudyexamples. TimurDoğu GülşenDoğu AnkaraTurkey
Foreword
Chemicalreactorengineeringisoneofthecoresubjectsofthechemicalengineeringcurriculum. Itisoftensaidthatthereactoristheheartofachemicalplant.Afterall,thisiswherethemagic occurs,turningreactantsintomorevaluableproducts – andthisoughttohappenselectively,reliably,safely,andeconomicallyatthepaceandscalerelevanttopracticalapplications.Hence, properdesignandanalysisofchemicalreactorsareoftheutmostimportance.Aproperly designedandoperatedreactorcanlimitorevenavoidveryexpensiveseparationstepsdownstream,whichmightseverelyaffecttheenvironmentalfootprintaswell.Chemicalreactorengineeringconnectschemistry(moleculartransformations,atnanoscales)withthemacroscopic world,bridgingagapofupto9,10,sometimesevenmoreordersofmagnitudeinlengthscales. Tomakethispossible,transportphenomenaatintermediatemesoscalesneedtobeharnessed, whichiswheremass,heat,andmomentumtransfercomein – conceptslikediffusionandconvection.Toofrequently,thisisneglectedoroversimplified,atacost.Furthermore,acatalyst,and mostoftenaheterogeneousporousone,istypicallyemployedtoacceleratethedesiredreactions, whileundesiredreactionsaresuppressedtorealizeaparticularproductorproductdistribution. Catalyticandreactorengineeringareintimatelyconnected,andanintegralapproachis,therefore,required.
Thistextbookintroducesthereaderstochemicalreactorengineering,emphasizingwaysto bridgethemicro-andthemacroworld.Itsauthorspointouttheneedforarigorous,multi-scale approach.Onlythencanonemovebeyondidealizedpicturesofreactorsthatserveapurposeas limitingcases(andthusshouldbelearntfirst,suchastheclassicbatch,plug-flow,andtheperfectly stirred-tankreactor),butdonotsufficientlyaddresstheinterferenceoftransportphenomenaat mesoscales.Thisiskeytosolvingsomeofthechallengesthatmodernchemicalengineersface.
Theplaygroundforchemicalengineershasbeenconsiderablyexpandedinrecentyears,fromthe traditionalrealmofrefineriesandpetrochemicalstotheproductionofhighvalue-added,finechemicals,pharmaceuticals,andspecialtyproducts,andincludingabroadeningrangeofbiotechnologicalprocesses,electrochemicalandphotocatalyticdevices.Opportunitiesinchemicalreactor engineeringhaveincreasedthankstofastercomputationaltools,advancesinmaterialsofconstruction,catalysis,andprogressonthefundamentals.Butthereisalsoashiftintheuseofresources, design,andoperationalconstraintsimposedbysustainabilitytargetsinthefaceofpressingenvironmentalconcerns.Chemicalreactorengineeringisafascinatingsubject,becauseitallowsusto manipulatethedesignandoperationalspacetoaddresssuchchallenges.However,todoso,amasteryofthefundamentalconceptsisessential.Asystematicpedagogicalapproachisrequiredto makethesubjectapproachable,graduallymovingfromthebasicstobuildamorecomplextoolbox thatallowsformulatingtheprincipalequationsandapplyingtheseinpractice.Equallyimportantis
thatasolidgraspofthefundamentalsmakesthesubjectfuture-proof,buildingthefoundationto studymorespecializedsubjects,asthedemandscontinuetoshift.
Thankstodecadesofexperienceindeeplyresearchingandteachingthesubject,worldrenownedProfessorsTimurandGülşenDoğ udoamarvelousjobatpreparingthebuddingchemicalengineerorotherinterestedreaderthroughtheessentialsteps,followingthemulti-scale approachthatmakesthistextbookstandout.Alogical,systematicapproachtakesthereaderfrom thebasicsofchemicalkineticsandthermodynamicstoreactorengineering.Here,theintroductionofthebasicreactortypesinthefirstchapterprovidesthebasisforanincreasinglymore detailedapproachtoembracetransportphenomenaandheterogeneouscatalysis,fromsimple singletomultiplereactions(selectivity!),fromidealtonon-idealreactors,andfromsingle-phase tomultiphasereactors.
Thereisalsomorethantheusualattentiontodiffusionandreactioninporouscatalysts,atopic forwhichtheauthorsaregloballyrecognized.Intoomanyreactorengineeringcourses,thistopicis barelytouchedupon,whichisashame,consideringthatmostprocessesemployaporouscatalyst, anddiffusionlimitationsplayakeyrole,includingintheworld’s(byfar)mostemployedreactor, namelytheautomotivecatalyticconverter,andprocessesfromammoniasynthesistosteamreformingandcatalyticcracking.
Afurtheruniqueaspectofthisbookistheinclusionofachapteronprocessintensification,which isasubjectofincreasinginterestworldwide,fromprocessesthatintegrateseparationsandreactions tominiaturizationfordistributedprocessing,andsafer,morecompact,andenvironment-friendly production.
Itisaprivilegeformetowritethesefewlinestoencouragethereaders,andtocommendthe authorsforsharingtheirdecadesofexperiencetoguidefuturegenerationsofchemicalengineers. AsastudentattheUniversityofGhent,underthenotablechemicalreactorengineeringProfessor GilbertFromentinthe1990s,IhadthepleasuretomeettheProfessorsDoğuwhentheyvisitedour university,andIrememberreadingtheirdefiningarticlesondiffusionandreactioninbimodal porouscatalysts,whichwerecrucialtomyownstartingresearchatthetime.Yearslater,in 2014,IhadthegreathonortopresenttheSomerLecturesatMETUinAnkaraandsharethetable withthemataspecialcelebration.Thiswillalwaysremainafondmemory.
AsIcouldbeinspiredbytheauthorsalreadyasastudent,Itrustthereaderwillenjoythejourney ProfessorsTimurandGülşenDoğutakeusontodiscoverthebeautifulworldofchemicalreactor engineeringanddemystifysomeofitsmagic!
Marc-OlivierCoppens
RamsayMemorialProfessor DepartmentofChemicalEngineering UniversityCollegeLondon(UCL),UK
Foreword
Thisisacomprehensivebookthatcanbeusedforbothundergraduateandgraduate “Chemical reactionengineeringandkinetics” coursesinchemicalengineeringcurricula.Whileincluding allthefundamentalconceptsinaclearandconcisemanner,thebookalsoencompassesmany newandtimelytopics,suchasprocessintensification,integrationofchemicalreactionandseparationprocessesintoasingleunit,andtheuseofalternativeenergysources,suchasmicrowave, solarenergy,ultrasound,inchemicalprocessing.Itsuccessfullydemonstratesthemulti-scale natureofchemicalreactorengineeringbycoveringthefundamentalsateveryscale.Itestablishes therelationshipsamongthermodynamics,transportphenomena,catalysis,andreactionengineeringinaseamlessmanner.Inadditiontoofferingacomprehensiveapproachtomeettheneedsof instructorsandstudentsalike,itwillalsobeanidealreferenceforresearchersandindustrialpractitionersofchemicalreactionengineering.
UmitS.Ozkan
CollegeofEngineeringDistinguishedProfessor Chair
WilliamG.LowrieDepartmentofChemicalandBiomolecularEngineering TheOhioStateUniversity,USA
AbouttheAuthorsandAcknowledgments
BothProfessorTimurDoğuandProfessorGülşenDoğuearnedtheirBSdegreesinchemicalengineeringfromtheMiddleEastTechnicalUniversity(METU)inAnkara,Turkey,theirMSdegrees fromStanfordUniversity,andtheirPhDdegreesinchemicalengineeringfromtheUniversityof CaliforniaDavis.TheybothstartedtheiracademiccareersintheChemicalEngineeringDepartmentofMETU.
ProfessorTimurDoğuwaspromotedtofullprofessorshipin1985.HealsoservedastheDeanof theFacultyofSciencesofAnkaraUniversity.HeisamemberoftheTurkishAcademyofSciences. ProfessorGülşenDoğuwasappointedasanassociateprofessoratMETU,followedbyafullprofessorshipatGaziUniversityin1985.Atthisuniversity,ProfessorGülşenDoğuheldthepositionsof DeanofEngineeringandUniversityAcademicVicePresident.BothTimurDoğuandGülşenDoğu contributedtotheteachingandresearchactivitiesatMcGillUniversityin1980–1981asvisiting professors.
BothauthorsofthisbookhadtheopportunitytotaketheheterogeneouscatalysisandthechemicalengineeringkineticscoursestaughtbyProfessorM.BoudartandProfessorD.M.Masonduring theirgraduatestudiesatStanfordUniversity.TheyalsohadthechancetoparticipateinthechemicalreactionengineeringandchemicalkineticscoursestaughtbyProfessorN.A.Doughartyand ProfessorJ.SwinehartduringtheirPhDworkatUCDavis.Theyhadtheprivilegeofstudyingwith thenotablechemicalreactionengineeringProfessorJ.M.Smith,whowasalsothePhDthesisadvisorofGülşenDoğu.
BothTimurDoğuandGülşenDoğucontributedtotheadvancementofdiffusionandreactionin porouscatalysts,environmentalcatalysis,multifunctionalreactors,aswellastothedesignand analysisofchemicalreactors.ContributionsofProfessorGülşenDoğuandProfessorTimurDoğu tochemicalreactionengineeringarehonoredbythetwospecialissuesofthe InternationalJournal ofChemicalReactorEngineering in2019.
Theauthorsareindebtedtotheirstudentsandcolleaguesfortheircontinuingcollaborationsin chemicalreactionengineeringandheterogeneouscatalysis.Prof.B.McCoyofUniversityofCaliforniaDavis,Prof.H.deLasaoftheUniversityofWesternOntario,Prof.N.OrbeyofUniversityof MassachusettsLowell,Prof.K.Mürtezaoğlu,Prof.N.Oktar,Prof.N.Yaşyerli,Prof.S.Yaşyerli,Prof. S.Balcı,Prof.M.Dogan,Prof.D.Varışlı ofGaziUniversity,Prof.G.Karaka ş,Prof.N.A.Sezgiof METU,Prof.T.KopaçofZonguldakBülentEcevitUniversity,andAsst.Prof.Dr.DorukDoğu ofAtılımUniversityaresomeofthesecontinuingcollaboratorswhoinfluencedtheapproachof theauthorsinwritingthisbook.
TheauthorsareindebtedtoProfessorMarc-OlivierCoppensofUniversityCollegeLondonand ProfessorUmitS.OzkanofOhioStateUniversityfortheenlighteningforewordstheywroteforthis
xx AbouttheAuthorsandAcknowledgments
book.Also,thevaluablesuggestionsofProf.RachelGetman(ClemsonUniversity)andProf.Coppens,whichmadethisbookmorepurposeful,aregratefullyacknowledged.
TimurDoğuandGülşenDoğuwouldalsoliketothanktheirfriendsatMETU,GaziUniversity, andotherinstitutionsinTurkeyandabroadfortheirsupportandfriendship.TheyalsothankDr. DorukDoğuforhisvaluablesuggestionsandtheirstudentMerveSarıyerforherhelpandcontributionsinfinalizingthemanuscriptofthisbook.
ListofSymbols
a Poreradiusm
ab Bubbleareaperunitliquidvolumeinaslurrym2/m3
ac Activityfactor
ae Externalareaofthecatalystpelletperunitvolumeinaslurrym 1
ai Theactivityofspecies i
amem Membranesurfaceareaperreactorvolumem2/m3
Ac Thecross-sectionalareaofthereactorm2
Ae Externalsurfaceareaofcatalystpelletm2
Ah Heattransferaream2
b Halfofthecellsizeinamonolithm
B ParameterdefinedbyEq.(8.39)
Bih Biotnumberforheattransfer(Eq.(10.79))
Bim Biotnumberformasstransfer(Eq.(10.42))
c SpecificheatofthemixtureJ/kgK
C Totalconcentrationmol/m3
Cd Darcycoefficient
Ci Theconcentrationofspecies i inthereactormol/m3
C ia , C ii Theconcentrationofspecies i inthemacro-andmicro-porous regions mol/m3
Cib Bubblephaseconcentrationofspecies i inafluidizedbedmol/m3
Cid Emulsion(dense)phaseconcentrationof i inafluidizedbedmol/m3
C ie Theconcentrationofspecies i atequilibrium
Cp MolarheatcapacityJ/molK
db Bubblediameterm
dp Pelletdiameterm
dt Tubediameterm
DaDamköhlernumber(Eq.(10.44))
Da, Di Effectivemacro-andmicro-porediffusivitym2/s
DAB MoleculardiffusioncoefficientofAinBm2/s
De Effectivediffusioncoefficientm2/s
DK i Knudsendiffusioncoefficientofspecies i (Eq.(12.7))m2/s
Ds Surfacediffusioncoefficientm2/s
DT Compositediffusivity(Eq.(12.21))m2/s
DT a , DT i Compositediffusivityinthemacro-andmicro-poreregionsm2/s
Dz Axialdispersioncoefficientm2/s
e EnergyfluxJ/m2 s
Ea TheactivationenergyofthereactionJ/mol
E aobs ObservedactivationenergyJ/mol
fi Fugacityofspecies i
Fi Molarflowrateofspecies i mol/s
FT Totalmolarflowratemol/s
G GibbsfreeenergyJ/mol
G Themeanvalueofthemolarflowrateofthevaporstreamina distillationcolumn mol/s
GN MolarflowrateofvaporstreamleavingstageNinadistillation column mol/s
h HeattransfercoefficientJ/m2 sK
Hi Enthalpyofspecies i J
JD J factorformasstransfer(Eq.(9.24))
Ji Diffusionfluxofspecies i mol/m2 s
k Reactionrateconstantforan nth-orderreaction(mol/m3)(1 n)/s
kc Masstransfercoefficientoncatalystsurfaceinaslurrym/s
kd Deactivationrateconstants 1
kf Forwardreactionrateconstantof(nth-orderreaction)(mol/m3)(1 n)/s
kb Backwardreactionrateconstant(nth-orderreaction)(mol/m3)(1 n)/s
kg Gas-sidemasstransfercoefficientinaslurrym/s
kl Liquidsidemasstransfercoefficientinaslurrym/s
km Masstransfercoefficientm/s
kobs Observedrateconstant(first-orderreaction)s 1
ko FrequencyfactorintheArrheniusequation
kw Reactionrateconstantbasedoncatalystmass
Ki Adsorptionequilibriumconstantofspecies i
KC Theequilibriumconstantintermsofconcentrations
Kf Theequilibriumconstantintermsoffugacities
KH Henry’sconstant
Kl Overallmasstransfercoefficientm/s
KP Theequilibriumconstantintermsofpartialpressures
Ky Theequilibriumconstantintermsofmolefractions
L Lengthofthereactorm
Ls Halfthicknessofaslab
L Meanvalueofmolarliquidflowrateinadistillationcolumnmol/s
LN Liquidflowrateleavingstage N inadistillationcolumnmol/s
mn The nthmoment(Eq.(8.57))
Mi Themolecularweightofspecies i kg/mol
n Unitnormalvector
ni Numberofmolesof i mol
ni,ads Adsorbedconcentrationofspecies i perunitmassofthecatalystmol/kg
P PressurePa,atm
Pc CriticalpressurePa,atm
Ped Pecletnumberintermsoftubediameter(8.46)
Pez AxialPecletnumber(Eq.(8.36))
q HeattransferrateJ/s
qG HeatgenerationrateJ/s
qR HeatremovalrateJ/s
Q Volumetricflowratem3/s
r Radialdirection
rc Coreradiusforunreacted-coremodelm
rcy Theradiusofthecylindricalcatalystpelletm
rg Microporousparticle/micro-grainradiusm
ri Theradialdirectioninthemicroporousparticles
ro Theradiusofthetubularreactorm
Ri Thereactionrateforspecies i basedonreactorvolumemol/m3 s
Ri, p Thereactionrateforspecies i basedonpelletvolumemol/m3 s
Ri, w Thereactionrateforspecies i basedoncatalystmassmol/kgs
R Specificrateofreactionbasedonreactorvolumemol/m3 s
R(j), p Rateofreaction j basedonpelletvolumemol/m3 s
Rp Intrinsicrateofreactionbasedonpelletvolumemol/m3 s
Rg GasconstantJ/molK
s Laplacevariable
sBA PointselectivityofBwithrespecttoA(Eq.(6.3))
SBA OverallselectivityofBwithrespecttoA(Eq.(6.4))
ScSchmidtnumber(Eq.(8.48))
Sg Surfaceareaperunitmassofacatalystm2/g
So Totalnumberofsitesperunitmassofcatalyst
t Times
t1/2
Thehalf-lifeofareactions
T TemperatureK
Ta AmbienttemperatureK
Tc CriticaltemperatureK
Tw WalltemperatureK
U OverallheattransfercoefficientJ/m2 sK
Uo Superficialvelocitym/s
vx, vy, vz Velocitycomponentsinthex,y,andzdirections,respectivelym/s
vmax Themaximumvelocityinatubularreactorm/s
V Reactorvolumem3
Vpore Porevolumeperunitmassm3/g
w Catalystmassinthereactorkg
xi Fractionalconversionofreactant i
xi, N Liquidphasemolefractionofspecies i leavingthe Nthstage
yi, N Vaporphasemolefractionofspecies i leavingthe Nthstage
Yi Theyieldofspecies i (Eq.(6.6))
z Axialdirection
ZAB Collisionratebetweenunlikegasmoleculesperunitvolumem 3/s
GreekLetters
α ParameterdefinedbyEq.(10.93)
α ParameterdefinedbyEq.(12.18)
β Pratergroup(Eq.(10.62))
γ DimensionlessArrheniusgroup(Eq.(10.69))
γ i Fugacitycoefficientofspecies i
Γ ParameterdefinedbyEq.(8.82)
δ Thethicknessofthecatalystlayeronthesurfacesofamonolithm
δo ParameterdefinedbyEq.(12.44)
δ1 ParameterdefinedbyEq.(12.45)
ΔH HeatofreactionJ/mol
ΔH o T R StandardheatofreactionatthereferencetemperatureJ/mol
ΔH o i,f Standardheatofformationofspecies i J/mol
ΔG GibbsfreeenergyofthereactionJ/mol
ΔGo i,f Gibbsfreeenergyofformationofspecies i atstandardstateJ/mol
ΔTLM Logmeantemperaturedifference
ε, εa Porosity,macro-porosityofapellet
εb Fixedbedvoidfraction
εmf Thevoidfractionofabedatminimumfluidization
ε VolumeexpansionfactordefinedinEq.3.63
ζ Dimensionlessradialdirectioninapellet(Eq.(10.4))
ζ i Dimensionlessradialdirectioninaparticle(Eq.(10.90d))
ς Dimensionlesslength(Eq.(8.34))
η Effectivenessfactor(Eq.(9.9))
θ Thefractionofsurfacesitescoveredbytheadsorbingmolecules
Θ Dimensionlesstemperature(Eq.(10.68))
λ Meanfreepath(Eq.(12.6))m
λb ThermalconductivityinthereactorJ/smK
μ Viscositykg/ms
μ1 Firstabsolutemoment(Eq.(8.58))s
μ2 Secondcentralmoment(Eq.(8.59))s2
μi Chemicalpotentialofspecies i
νi Stoichiometriccoefficientofspecies i
ξ Reactionextent
ρ Densitykg/m3
ρs Soliddensitykg/m3
τ Space–timeinthereactor(τ = V/Qo)s
τ Tortuosityfactorofaporousmaterial
τ s Tortuosityfactorforsurfacediffusion
φn Thielemodulusforan nth-orderreaction(Eq.(10.7))
φn ShapeandordergeneralizedThielemodulus(Eq.(10.31))
φi ParticleThielemodulus(Eq.(10.92))
Φ Observablemodulus(Eq.(10.80))
Φs Observablemodulusdefinedforasphere(Eq.(10.108))
Ψ Dimensionlessconcentration(Eq.(8.34))
ListofSymbols
Subscripts
e Indexdenotingequilibrium
e Indexdenotingeffectivevalueintransportequations
f Indexdenotingexitconditionofareactor
g Indexdenotinggasphase
i Indexdenotingspecies “i”
l Indexdenotingliquidphase
o Indexdenotingtheinletconditionofareactor
p Indexdenotingcatalystpellet
r Intheradialdirection
s Atthesurfaceconditionofthecatalystpellet
z Intheaxialdirection
Superscripts
o Indexdenotingtheinitialconditionofareactor
o Indexdenotingstandardstateforthermodynamicproperties
H (Over-hat)molarvalueofproperty H
AbouttheCompanionWebsite
Thisbookisaccompaniedbyacompanionwebsite
www.wiley.com/go/dogu/chemreacengin
Thewebsiteincludes:
1.Appendices
• OnlineAppendix1:VectorNotation
• OnlineAppendix2:MicroscopicSpeciesConservationandEnergyEquationsinDifferent CoordinateSystems
• OnlineAppendix3:Pseudo-HomogeneousTransportEquations
• OnlineAppendix4:SomeDifferentialEquationsRelevanttoReactionSystems
• OnlineAppendix5:SomeNumericalTechniquesforChemicalReactorApplications
• OnlineAppendix6:CaseStudyExamples
• OnlineAppendix7:DimensionlessGroupsandParameters
2.SolutionstoProblems
RateConceptandSpeciesConservationEquationsinReactors
Chemicalprocessesdevelopedfortheproductionofvaluableproductsinvolvebothphysicaland chemicalrateprocesses.Chemicalreactorsareusuallyattheheartoftheprocess,wherechemical conversionofreactantstotheproductsoccurs.Designandanalysisofachemicalreactorinvolve informationfromchemicalkinetics,aswellasfromthethermodynamicsoftheprocessestaking placeinthereactor.Besidesthekineticsandthermodynamicsofthechemicalconversions,hydrodynamicsofthesystem,aswellastheheatandmasstransferprocessestakingplacewithinthe reactionvessel,shouldbeunderstoodforthedesignandanalysisofsuchunits.Kineticsofachemicalconversioninvolvesunderstandingtheparametersaffectingtherateofareactionandthereactionmechanism.Thermodynamicsgivesusinformation,whetherachemicalconversioncanoccur spontaneouslyornotandaboutthemaximumpossibleextentofreactiondeterminedbychemical equilibrium.However,thereactionrategivesustheanswertohowfastthechemicalconversionis goingtotakeplaceatthegivenoperatingconditionsofthereactor,suchastemperature,thecompositionofthereactionmedium,andpressure.
1.1ReactionRatesofSpeciesinChemicalConversions
Analysisoftheratesofchemicalconversionsusingthecollisiontheoryofgasesortransition-state theoryshowsthatthereactionrateisafunctionofthetemperatureofthereactionmediumand concentrationsofthespeciesinvolvedinthechemicalconversion.Experimentalevidencealso showthatthereactionrateofanymoleculeinareactionvesselcanbeexpressedasafunction ofconcentrationsofspeciesinvolvedinthereactionandthereactiontemperature.Thus,thereactionrateforanycomponent i canbeexpressedas
Ri = f temperature,concentrations
Thereactionrateisgenerallydefinedasthemolesofspecies i reacted(orproduced)perunittime perunitvolumeofthemixtureinthereactionvessel.However,insomesolid-catalyzedreactions,it mayalsobeexpressedbasedonthecatalystvolume,catalystweight,orcatalystsurfacearea,instead ofthevolumeofthereactionmedium.ForanarbitraryreactionbetweenreactantsAandB
FundamentalsofChemicalReactorEngineering:AMulti-ScaleApproach,FirstEdition.TimurDoğuandGülşenDoğu. ©2022JohnWiley&Sons,Inc.Published2022byJohnWiley&Sons, Companionwebsite:www.wiley.com/go/dogu/chemreacengin
therelationbetweenthereactionratesofreactantsandproductscanbewrittenasfollows:
RA a = RB b = RC c = RD d = R
Here, R isthespecificrateofthereactionunderconsideration.Moregenerally,therelationbetween theratesofdifferentspeciescanbeexpressedas
where νi isthestoichiometriccoefficientofspecies i inthereaction,suchthat
νi <0forreactants
νi >0forproducts
Forinstance,fortheoxidationofsulfurdioxidetosulfurtrioxide
SO2 + 1 2 O2 SO3
therelationbetweentheratesofdifferentspeciesshouldbewrittenasfollows:
Therelationsbetweenthereactionratesofdifferentspeciescanbeobtainedbywritingtheconservationequationsfortheatomicspeciesinvolvedintheprocess.Forinstance,fortheoxidationof sulfurdioxide,thesulfuratomshouldbeeitherwithinSO2 orSO3 molecules.Similarly,theoxygen atomiseitherinO2 orSO2 orSO3 molecules.Hence,therelationsfortheconservationofthesulfur andoxygenatomscanbeexpressedasfollows:
Here,wehavethreeunknowns RSO2 , RSO3 , RO2 andtwoequationsfortheseunknowns,indicating thatoneoftheratescanbearbitrarilyselectedastheindependentrate.Theothertwounknowns (rates)canbeexpressedintermsofthechosenindependentreactionrate.Theothertworatescan beexpressedfromthetwoequationswrittenabovebyselecting RSO3 astheindependentrateand followinganeliminationprocedure:
Thisanalysisshowsthatthereisonlyoneindependentrateterm,indicatingthepresenceofonly oneindependentreaction.
Inmanyoftheindustrialprocesses,morethanonereactionmaytakeplacewithinthereactors. Someofthesereactionsmaybedesiredreactions,whilesomeothersmaybeundesiredparasitic reactions.Foramultiple-reactionsystem,therelationsbetweentheratesofdifferentspecies involvedinthereactioncannotbedirectlyexpressedasinEq.(1.1),usingtheirstoichiometriccoefficients.Instead,therelationshipsbetweentheratesofdifferentspeciescanbeobtainedbywriting atomicconservationexpressions.
1.2RateofaChemicalChange 3
Letusconsiderthereactionofethylenewithoxygentoproduceethyleneoxideoverasilver-based solidcatalyst.Inthereactorexitstream,carbonmonoxide,carbondioxide,andwatermoleculesare alsoobserved,inadditiontoethylene,ethyleneoxide,andoxygen.Hence,therearesixspecies, involvedeitherasreactantsorproductsinthisreactionsystem.Toobtaintherelationsbetween theratesofthesesixspecies,namely RC2 H4 , RC2 H4 O , RO2 , RCO, RCO2 ,and RH2 O ,wecanwriteconservationrelationsforcarbon,hydrogen,andoxygenatoms.
Asillustratedabove,wehavethreerelationsfortheratesofsixdifferentspeciesinthissystem.This analysisshowedthreeindependentratesforthissystem,indicatingthepresenceofthreeindependentreactions.Ingeneral,ifthereare n numberofspeciesinvolvedinareactionsystem(n numberof ratevalues)andifwecanwrite m numberofatomicconservationrelations,weshouldexpect(n m)= p numberofindependentratevalues.Hence,weexpecttohave p numberofindependent reactions.
Returningtotheethyleneoxidationexample,wecanarbitrarilyselectthereactionratevaluesof thethreespeciesastheindependentrates.Wecanexpresstheotherratesintermsoftheseindependentrates,followinganeliminationprocedure(refertoOnlineAppendixO.5.2).Ifwearbitrarilyselect RC2 H4 O , RC2 H4 ,and RCO2 astheindependentrates,theotherthreeratescanbeexpressedas follows:
Thepresenceofthreeindependentratesindicatestheoccurrenceofthreeindependentreactionsin thissystem.Threepossibleindependentreactionsforthissystemare
Ofcourse,wecouldalsowriteotherreactionstoichiometriesforthissystem.Forinstance,further oxidationoftheproductethyleneoxideisanotherpossiblereaction.
However,thisreactionisdependentonthethreereactions(R.1.1)–(R.1.3)mentionedabove.
1.2RateofaChemicalChange
Therateofanychemicalconversioncanbeconsideredasthespeedofthatprocesstoapproachthe equilibriumcondition.Chemicalconversionprocessesmaytakeplaceeitherinahomogeneoussystem,wherethewholeprocesstakesplacewithinasinglephase,orinaheterogeneousenvironment, wheremorethanonephaseisinvolvedduringthereaction.Wemayhaveliquid-orgas-phase
Figure1.1 Schematicrepresentationofanelementaryreaction.
homogeneousreactionsinbatchorflowreactionvessels,whicharecalledchemicalreactors.Inthe caseofheterogeneoussystems,thereactionmaytakeplaceattheinterphasebetweenthephases. Forinstance,inthecaseofreactionscatalyzedbysolidcatalysts,chemicalconversionsmayproceed onthesurfaceofthecatalystinvolvingtheadsorbedreactingspecies.
Oneofthemostcommonlyacceptedtheoriesforthereactionkineticsofgas-phasereactionsis collisiontheory.DuringtheinteractionoftworeactantmoleculesAandBtogivenewchemical compounds,theymustfirstapproacheachotherveryclosely.Asaresultofthiscollisionprocess, rearrangementofchemicalbondsmayoccur,yieldingnewmolecules(products)ifthecolliding moleculeshavesufficientkineticenergy(Figure1.1).However,notallofthecollisionswould yieldproductmolecules.Onlyafractionofcollisionshavingthesumoftheenergiesofthecollidingmoleculesbeinghigherthanacriticalvaluewouldgiveproductmolecules.Thiscritical energylevelisgenerallycalledtheactivationenergyofthechemicalconversion.ThisisillustratedinFigure1.2.
Accordingtothegaskinetictheory,thenumberofcollisionsbetweentwounlikemoleculesper unittimeandunitvolumeofagascanbeexpressedasfollows[1]:
Here, dAB isthemeanmoleculardiameter,whichisdefinedas dAB = dA + dB 2 , μm isthereduced massofcollidingmolecules,whichisdefinedas μm = M A M B M A + M B , Rg isthegasconstant.N∗ A and N∗ B arethenumberdensitiesofreactantsAandB(numberofmoleculesperunitvolume)inthe vessel.Therateofachemicalreactionasaresultofthiselementaryprocessofcollisionoftwo unlikemoleculesisthenexpressedasbeingproportionaltotheproductof ZAB withtheprobability ofcollisionshavingenergiesequaltoorhigherthanthecriticalenergylevelof Ea
Activated complex
Figure1.2 Schematicrepresentationoftheactivation energiesoftheforwardandreversereactionrateconstants (exothermicreaction).
Here, p isastericfactor,dependingupontheorientationofcollision.Hence,thereactionrateofthis elementaryreactionstepcanbeexpressedasfollows:
Here, k isthereactionrateconstant,whichisgenerallydefinedasfollows:
Here, ko iscalledthefrequencyfactoroftherateconstant.ThisrelationiscalledtheArrhenius equation,anditshowsthatthedependenceofreactionrateconstantonreactiontemperatureis exponential.ExperimentaldataonreactionratesalsosupportedtheArrheniusdependenceof thereactionrateconstantofanelementaryreactionstep.
Theactivationenergyofchemicalconversion Ea andthepre-exponentialfactor(frequencyfactor)ofthereactionrateconstant ko aregenerallydeterminedexperimentallyfromtheplotofln(k) vs.1/T,asillustratedinFigure1.3.
Accordingtothecollisiontheoryofgas-phasereactions,thepre-exponentialfactor ko isproportionaltothesquarerootoftemperature.Hence,thetemperaturedependenceofthereactionrate constantcanalsobeexpressedasfollows:
However,thetemperaturedependenceofthepre-exponentialfactorisquiteweak.Hence,formany cases,itmaybeconsideredasbeingconstant.
Anothertheoryproposedforthemechanismofachemicalconversioniscalledtransition-state theory(oractivatedcomplextheory).Accordingtothistheory,thereactantmoleculesfirstforman unstableactivatedcomplex,andthenthisactivatedcomplexdecomposestoformtheproducts.
A+B AB ‡ Products
Theactivatedcomplexisassumedtobeinequilibriumwiththereactantmolecules.Activatedcomplexdecomposestogivetheproducts.Theconversionrateofthereactantstotheproductsisproportionaltotheconcentrationoftheactivatedcomplex.Thereactionrateisdeterminedbythe productoftheconcentrationofactivatedcomplexandthefrequencywithwhichitgoesoverto theproducts.Therateexpressioncanthenbeobtainedbytheuseofstatistical-thermodynamic principles.Detailsofbothcollisiontheoryandtransition-statetheorycanbefoundinphysical chemistryandreactionkineticsbooks[1–3].Bothofthesetheoriespredicttheconcentration andtemperaturedependencesofthereactionratesofelementaryreactions.
Figure1.3 Schematicdiagramofthetemperature dependenceofthereactionrateconstant. 1.2RateofaChemicalChange
Reactionorderisdefinedasthesummationofexponentsoftheconcentrationtermsinthereactionrateexpression.Anyreactiontakingplacethroughasinglephysicochemicalprocessiscalled anelementaryreaction.Fortheelementaryreactiondescribedabove,thereactionisfirstorderwith respecttotheconcentrationofreactantAandfirstorderwithrespecttotheconcentrationofreactantB.Theoverallorderofthisreactionissecondorder.Inthecaseofanelementaryreaction, reactionorderswithrespecttotheconcentrationsinvolvedinthereactionarethesameasthe molecularityofthespeciesinthereactionstep(stoichiometricconstantsintheelementaryreaction step).However,manyofthereactionsdonotproceedthroughasinglephysicochemicalprocess,but involveaseriesofelementarystepstogivethereactionproducts.Hence,forareactioninvolvinga numberofelementarysteps,thereactionordersfortheconcentrationsofthespeciesinvolvedin thischemicalconversionarenotnecessarilythesameasthestoichiometricconstantsofthespecies ofthatoverallreaction.Forthegeneralcase,therateofanirreversiblechemicalreactionmaybe writteninapower-lawformasfollows:
Here,thereactionorders n, m, p, areusuallydeterminedexperimentally. Inmanycases,chemicalconversionsarereversible.Insuchcases,therateexpressionshouldbe expressedasthedifferenceintheratesoftheforwardandthereversereactions.
Here, kf and kb aretheforwardandthebackwardrateconstants,respectively.Theybothdepend upontemperatureaccordingtotheArrheniuslaw.Foran nth-orderreaction,theunitofthereactionrateconstantisexpressedas(mol/l)(1 n) s 1.Inthecaseofafirst-orderreaction,theunitofthe rateconstantiss 1 .
1.3ChemicalReactorsandConservationofSpecies
Chemicalreactorsarethevesselsinwhichchemicalconversionstakeplace.Mostreactorsmaybe classifiedasbatchreactorsorflowreactors.Therearealsosomereactorsoperatinginsemi-batch mode.Thedesignofachemicalreactorinvolvesspeciesconservationandenergybalanceequations writtenaroundthereactionsystem.Hydrodynamicsofthefluidwithinareactorshouldalsobe consideredduringthedesignofachemicalreactor.Letusconsiderareactionvesselinwhich anarbitraryreactionA+B C+Distakingplace(Figure1.4).
Another random document with no related content on Scribd:
R S , P M
In the list of tone poets, Richard Strauss (1864), or Richard II is one of the most important. It is strange that he should have the same name as Wagner, for his father Franz Strauss, a skilled horn player, disliked Wagner and his compositions intensely. Richard’s mother was the daughter of a brewer and they all lived in Munich, where the son was born.
When he was a little boy, he wrote musical notes before he could write the alphabet, and at six, composed little pieces. By the time he was twenty he had written compositions which put him with Schubert and Mozart, in the ranks of musical prodigies.
Until his sixteenth work Aus Italien (From Italy) (1886), his first tone poem, he did not depart from the classic forms, although there were a few signs of change in style in a violin sonata which he wrote just before the tone poem. In fact, he was so much against Wagner and his innovations, that no one could have guessed that later he himself would be considered an innovator and would be accused of imitating Wagner.
During his youth, after hearing Siegfried he wrote to a friend about the music of Mime: “It would have killed a cat and the horror of musical dissonances would melt rocks into omelettes.”
When he met von Bülow, the old master thought little of his talents, but the young man gave him a surprise. For, when Richard went to Meiningen he had never led an orchestra in his life and without one rehearsal, conducted his Serenade for Strings, opus 7. Von Bülow realized his great ability, made him assistant conductor, and a year later when he left Meiningen, Strauss took his place.
It was about now that Richard met Alexander Ritter the violinist and radical thinker who, he said, changed his life by introducing to him new ideas. He became converted to Wagner. When he heard Tristan and Isolde he was thrilled by it. So, like Proteus, the god who changed his form to suit his adventure, Strauss, the musical Proteus changed his ideas to suit his opinions.
Wearied by hard work after writing many classical pieces including a sonata, an overture, the Festmarsch, a violin concerto, songs, a horn concerto and other things, he became very ill. He said to a friend that he was ready to die, and then added, “No, before I do, I should love to conduct Tristan.” This shows that the young man could change his opinion and become devoted to what he loathed years before, a fine quality which continually brought down upon his head criticism from smaller folk. Yet this Proteus-like quality was a sign of his power for growth.
Because he did not gain strength quickly from his illness, he went to Italy and then wrote his first symphonic poem Aus Italien (From Italy) in a new and modern vein.
When he returned, he led the orchestra in the Court Theatre of Munich and then went to Weimar for two years, and this former young classicist was now hailed as the leader of modern composers! He produced, here, three tone poems: Macbeth, Don Juan and Tod und Verklärung (Death and Transfiguration) (1888–1890).
Then, on account of illness (1892) he went to Greece, Egypt and Sicily. During this tour, he wrote Guntram, which he produced on his return to Weimar.
He became interested in the Bayreuth festivals and in 1894 he conducted a production of Tannhäuser, after which he married Pauline de Ana who played Elizabeth. Before this, he had made her the heroine of his first opera, Guntram (1893).
Not long after this he gave up the Weimar post and went to Munich with his bride. He became the conductor there and at the same time, led the Berlin Philharmonic concerts until the double work and commuting became too much for him. He gave up Berlin and Arthur Nikisch succeeded him,—the same Arthur Nikisch who later took the baton of the Boston Symphony Orchestra in America.
In 1899 he became the leader of the Royal Opera in Berlin in which city he decided to live and from there made trips all over the world including the United States, first in 1904 and later, after the World War. During his last tour, we heard him play the piano for his songs which are unsurpassed in beauty, and conduct some of his own orchestral works with skill and enthusiasm.
He is tall and slender, with kindly blue eyes, rather informal in manner. He has the air of a happy man even if he has received some of the harshest criticism from friends and foes that any composer has had from earliest times. His wife used to sing his songs in public. He is fond of games, especially the card game “skat” and like the true grandson of a brewer enjoys his glass of beer.
Among Strauss’ greatest works are his operas Electra, Salome and Der Rosenkavalier and his nine tone poems. Despite all the harsh things critics have said of him, Strauss has always maintained that, although he did not write in accepted forms, he felt that the form should always be suitable to the subject, for “as moods and ideas change so must forms.” This, Ernest Newman said in defence of Strauss, and it may be applied to all arts.
So Strauss is not formless but like Proteus, has many forms. Cecil Gray said, “he seems to have an irresistible itch to provoke the amazement and the horror of the multitude.” This is quite true, especially in Salome, Electra and Der Rosenkavalier in which opera he went back to Mozart form as a model. It seems incredible that a man who could write the noble songs that he has written should have chosen such unpleasant plots for his operas!
In Tod und Verklärung (Death and Transfiguration) he was distinctly a follower of Liszt. His friend Alexander Ritter is said to have written the poem after the music.
At the time that it was first played, it caused so much comment that Strauss, like Browning, laughed at people for trying to “read” more into it than he wrote. Browning was asked whether he meant a certain thing in one of his poems, and his reply was something like this: “Madam, I never thought of it, but if you think it is there, I am more than glad to know it.”
His Don Juan is delightful, too, but his Til Eulenspiegel (1895) which tells of the mischievous pranks of Til, is one of the finest examples of humor in music and probably will outlive many works of this modern period, his own as well as others. He wrote it in the form of a classical Rondo, because he could picture Til’s ever recurring deviltry and exploits in this form. Poor Strauss was reviled for this daringly written music, too, yet this tone poem is an amazing piece of work and was given gloriously as a ballet in New York City a few years ago by Diaghilev’s Russian Ballet.
In Also Sprach Zarathustra (Thus Spake Zarathustra), Strauss uses the idée fixe or leit-motif. This is based on a prose poem of
Nietzsche.
In Don Quixote he goes back to the form of the classical variation, for it is an ingenious way of showing the varying sides of the character of Don Quixote. Here he shows events and not ideas, a most definite story in tones. You can almost see the attack on the wind-mills and you can actually hear the sheep bleating, the church music of passing pilgrims, and the love tale of Dulcinea. In this piece, program music reaches its height.
In Ein Heldenleben (A Hero’s Life) (1898) Strauss frankly quotes from his musical works. He does not have to prove that he is the hero, for he admits it! When Strauss was asked what the poem meant, he said, “There is no need of a program, it is enough to know that there is a hero fighting his enemies.” In it, you can really hear the carping critics, his retorts, the triumphs and the defeats. It is very interesting and amazingly well written.
The Domestic Symphony (Sinfonia Domestica) is the story of a family for one day. There is the father motif, the mother motif and the baby motif! The final fugue represents education very aptly for you get from it the sense of flight and struggle and the never endingness of education.
One of his last works is The Alpine Symphony. His other works include an early opera Feuersnoth, and his songs which are among the greatest ever written by any composer, ranking him with Franz, Schubert, Schumann, Brahms and Hugo Wolf.
Strauss shows in all his work great pictorial power. He paints in tones if ever a man does. His humor in music is amazing. He tries to make vivid in music a thing as simple as a fork and as complex as a philosophic idea. Some one said of him, comparing him to Wagner, that he started out to write symphonic poems and really wrote music dramas, while Wagner started out to write music dramas and ended by writing Tristan and Isolde, a super-symphonic poem with voices added.
Richard Strauss is the last of the great German classic and romantic composers who have ruled the musical world for the past two centuries. Still living in Germany he has opened the way to many of the younger composers, who have learned much from his methods of orchestration and handling music in the large forms. While he
out-Wagnered Wagner in strange and new harmony, he now seems old fashioned in comparison to Schoenberg, Stravinsky and Honegger. Although Strauss seemed to us very complex and exaggerated a few years ago, it was very interesting to notice that when his works were revived in America after the War, the audiences had grown up musically to the point where they seemed no longer unintelligible or ultra-modern.
We remember when we were leaving the opera house after the first performance of Salome in this country, hearing one ill bred, untutored woman say, “Gee! Goit, but that was one big noise!” By this time she has probably reached the point where she is jazzing the Salome dance with real pleasure and understanding!
He did many unusual things with instruments, added many new ones, and as someone said, he loves to have the “trombone play like a piccolo!”
No one can say where Strauss will stand as a composer, for time alone can place him. However, we make bold to state that he will stand high in the company of the world’s composers.
C (1841–1894)
As imitation is the sincerest form of flattery, there is no proof of the success of the tone poem more telling than the fact that practically every composer in the musical world has written symphonic tone poems. In fact today, one hundred tone poems are written to one symphony! Berlioz had his followers in France, and in the group around César Franck were several who wrote tone poems. One of the most charming of these poets was Alexis Emanuel Chabrier (1841–1894) who took up music first as an amateur while studying law in Paris, and while he was Minister of the Interior. Later he became so devoted to music that he gave all his time to it.
Among his works are operas and many other forms of music, the loveliest of which is the Rhapsody on Spanish tunes called España. It is a model of its kind and in it he uses the collected material with rare skill. It shows him very clever in reproducing foreign atmosphere and feeling. He was born in Ambert, France, and died in Paris.
D
Claude Achille Debussy (1862–1918) although talked of in another chapter, must be mentioned as a composer of tone poems in this. Among his most famous works are Après-midi d’Un Faune, La Mer, Les Nuages, Fêtes, and Sirènes which are all surpassingly lovely, written in Debussy’s special harmonies with which he wove a mystical, far away atmosphere, so compelling and yet so magical that you think you are in a mysterious cloudland. He usually uses a scale of whole tones. In Pelleas and Melisande, his greatest work (opera) you seem to look into a distant land which never did and never will exist, except in the glorious reaches of his or our imaginations. So to those of us who love fairy realms, cloudland and beauty of idea and serene expression, Debussy will be a rare treat and never vanish from our mind’s ear.
R
Maurice Ravel (1875) still living in Paris, seems to love Spanish themes as did Chabrier and Bizet. One of the loveliest tone poems is his Rhapsodie Espagnole in four movements. His Mother Goose suite and La Valse are also lovely, modern, short orchestral works. He writes with rare distinction and beauty. In the chapter on 20th century music, Ravel will make another appearance.
P D (1865)
Among the most humorous and delightful tone poems is L’Apprenti-Sorcier (The Sorcerer’s Apprentice) by Paul Dukas (1865). Dukas too, will appear in another chapter.
